ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 WASP-30b has the secoud simallest commpanion-to-star size ratio (AF=nz32 0.0050) of all sub-stellar yodics so far discovered by erouud-based trausit survevs., WASP-30b has the second smallest companion-to-star size ratio $\Delta F = R_{\rm p}^2/R_*^2 = 0.0050$ ) of all sub-stellar bodies so far discovered by ground-based transit surveys.3 The star in the system with the Μπα: size ratio. ILAT-P-ll (V29.6AF=0.0033:Bakosetal.2010)... is ὃ times brighter than WASP-30.," The star in the system with the smaller size ratio, HAT-P-11 \citep[$V$ = 9.6; $\Delta F = 0.0033$;][]{2010ApJ...710.1724B}, is 8 times brighter than WASP-30."4 As it is fay easier to find such an object around a smaller. cooler star. the discovery of WASP-30b sugeests that hieh-niass. sub-stellar objects in short orbits around cooler stars are rare.," As it is far easier to find such an object around a smaller, cooler star, the discovery of WASP-30b suggests that high-mass, sub-stellar objects in short orbits around cooler stars are rare."5 WASP-South is hosted dy the South Africau Astronomical Observatory and SuperWASP-N is hosted by the Issac Newton Group ou La Palma., WASP-South is hosted by the South African Astronomical Observatory and SuperWASP-N is hosted by the Issac Newton Group on La Palma.6 We are grateful for their ongoing support and assistance., We are grateful for their ongoing support and assistance.7 Funding for WASP comes froin consortimu universities and from the Ul& Science and Technology. Facilities Council., Funding for WASP comes from consortium universities and from the UK's Science and Technology Facilities Council.8 M. Gillon acknowledecss support from the Beleian SciencePolicy Office in the form of a Return Craut., M. Gillon acknowledges support from the Belgian SciencePolicy Office in the form of a Return Grant.9 WASP.," WASP,"10simultaneously fitted a svnthetic ΤΟΠ ΟΠΗ spectra. using the 18 PCIE;O0IT transitions in the observed frequency range. using (hie same constraints as lor the απο fit.,"simultaneously fitted a synthetic $^{13}$ $_3$ OH spectra, using the 18 $^{13}$ $_3$ OH transitions in the observed frequency range, using the same constraints as for the $^+$ line fit."11 The fit reproduces most of the observed features and shows that the emission from ΤΟΠ ΟΠΗ may explain (he observed non Gaussian — proliles., The fit reproduces most of the observed features and shows that the emission from $^{13}$ $_3$ OH may explain the observed non Gaussian $^+$ profiles.12 Onlv the parameters derived [or the three most intense components in (he group are given in Table 1.., Only the parameters derived for the three most intense components in the group are given in Table \ref{tab:gaussfit}.13 This is (he first (nme that the EC isotopologue of methanol is detected towards an extragalactic source., This is the first time that the $^{13}$ C isotopologue of methanol is detected towards an extragalactic source.14 Regarding the accuracy of the fitted parameters presented in Table 1.. the integrated line intensities derived for and ΟΠ ΟΠ are likely underestimated by —20% due to the baseline determination.," Regarding the accuracy of the fitted parameters presented in Table \ref{tab:gaussfit}, the integrated line intensities derived for $^+$ and $^{13}$ $_3$ OH are likely underestimated by $\sim20\%$ due to the baseline determination."15 In the next Section. we diseuss the detection of ΟΠ ΟΠ in the context of the derived abundances with respect to those of the main methanol isotopologue.," In the next Section, we discuss the detection of $^{13}$ $_3$ OH in the context of the derived abundances with respect to those of the main methanol isotopologue."16 We have estimated the fractional abundances of the newly observed species in 2253 assumine oplically thin emission. LTE conditions. aud similar spatial distribution Lor all species.," We have estimated the fractional abundances of the newly observed species in 253 assuming optically thin emission, LTE conditions, and similar spatial distribution for all species."17" Under these assumptions. we have caleulated the column densities of 000 . IICO. and for an excitation temperature ἕως=1545 NIN and an estimated source extent for each velocity component of 10""."," Under these assumptions, we have calculated the column densities of $^{13}$ $^+$ , $^+$ , HCO, and $^+$ for an excitation temperature $T_{\rm ex}=15\pm5$ K and an estimated source extent for each velocity component of $10''$."18 The Ti.=15zx 5IXIN is assumed based on the average rotational temperatures derived [rom most of the species detected towards 2253 (Martinetal.2006b)., The $T_{\rm ex}=15\pm5$ K is assumed based on the average rotational temperatures derived from most of the species detected towards 253 \citep{Martin06b}.19. Indeed (he non detection of 3—2 implies low excitation temperatures of Ti. LOW. Both the excitation temperature and (he emission extent have an important impact in the absolute derived column densities by up (o a factor of 2. however. the fractional abundances ancl abundance ratios are mostly independent of these assumptions.," Indeed the non detection of $^+\,3-2$ implies low excitation temperatures of $T_{\rm ex}\sim10$ K. Both the excitation temperature and the emission extent have an important impact in the absolute derived column densities by up to a factor of 2, however, the fractional abundances and abundance ratios are mostly independent of these assumptions."20 We asstune that the emission extent is similar for all observed species., We assume that the emission extent is similar for all observed species.21 Table 2. presents the column densiües and fractional abundance ratios wilh respect to II» for all the species., Table \ref{tab:abunRatios} presents the column densities and fractional abundance ratios with respect to $_2$ for all the species.22 The total IL;columndensity has been derived [rom the CO colunn, The total $_2$columndensity has been derived from the $^{18}$ O column23has not yet been addressed.,has not yet been addressed.24the luminosity function of LMXBs (Gilfanov.2004).,the luminosity function of LMXBs \citep{gilfanov}.25". In the luminosity range of 2-1076—2.10°""eres7!. the X-ray to K- luminosity ratio is =I4-1075ergs7!Li. in the 2—10 keV band."," In the luminosity range of $ 2 \cdot 10^{36} - 2 \cdot 10^{37} \ \mathrm{erg \ s^{-1}} $, the X-ray to K-band luminosity ratio is $ \approx 1.4 \cdot 10^{28} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $ in the $2-10$ keV band."26" To convert this value to the 0.3—0.7 keV energy range we used the average spectrum of LMXBS. described by a power-law model with a slope ofΓ=1.56 (Irwinetal..2003) and assumed a column density of Nj,=4-102em7."," To convert this value to the $ 0.3-0.7 $ keV energy range we used the average spectrum of LMXBS, described by a power-law model with a slope of $ \Gamma = 1.56 $ \citep{irwin2} and assumed a column density of $ N_{H} = 4 \cdot 10^{20} \ \mathrm{cm^{-2}} $."27 The result is Lx/Lgs(1.720.1)-1077eigs!Li.. Which 15 in reasonable agreement with the value obtained from the first method.," The result is $L_{\mathrm{X}}/L_{\mathrm{K}} \approx (1.7\pm0.1) \cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $, which is in reasonable agreement with the value obtained from the first method."28 Both methods are based on the assumption that the X/K ratio for LMXBs ts the same for all galaxies in the sample., Both methods are based on the assumption that the X/K ratio for LMXBs is the same for all galaxies in the sample.29 This assumption may be contradicted by the fact that in NGC 3377 and NGC 3585 the predicted luminosity of unresolved LMXBs exceeds the observed luminosity of unresolved emission (Table 3))., This assumption may be contradicted by the fact that in NGC 3377 and NGC 3585 the predicted luminosity of unresolved LMXBs exceeds the observed luminosity of unresolved emission (Table \ref{tab:fit}) ).30 Incidentally or not. these are the two youngest galaxies in our sample.," Incidentally or not, these are the two youngest galaxies in our sample."31 The possible age dependence of the LMXB X/K ratio cannot be excluded but still needs to be established., The possible age dependence of the LMXB X/K ratio cannot be excluded but still needs to be established.32 On the other hand. the correction due to unresolved LMXBs ts less than €40% of the observed value of Ly/Ly (Table 4)).," On the other hand, the correction due to unresolved LMXBs is less than $\la 40\%$ of the observed value of $L_X/L_K$ (Table \ref{tab:xtok}) )."33 This accuracy is sufficient for the present study. whose purpose is to constrain the luminosity of nuclear-burning white dwarfs.," This accuracy is sufficient for the present study, whose purpose is to constrain the luminosity of nuclear-burning white dwarfs."34 Therefore we defer further investigation of the possible effect of inconstant LMXB X/K ratio for a follow-up study., Therefore we defer further investigation of the possible effect of inconstant LMXB X/K ratio for a follow-up study.35 The X-ray to K-band luminosity ratios transformed to the same point source detection sensitivity are listed in Table 4.., The X-ray to K-band luminosity ratios transformed to the same point source detection sensitivity are listed in Table \ref{tab:xtok}.36 These numbers are fairly uniform Lx/Lg=(2.440.45-1077ergs!Ly! where. as before. the cited error refers to the rms of the measured values.," These numbers are fairly uniform $ L_{\mathrm{X}}/L_{\mathrm{K}} = (2.4 \pm 0.4) \cdot 10^{27} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $ , where, as before, the cited error refers to the rms of the measured values."37 The excellent source detection sensitivity. achieved in the bulge of M31. and the large number of compact X-ray sources in this galaxy allows us to estimate the contribution of unresolved LMXBs having the luminosities below the adopted threshold of 2-10°°ergs| to the Ly/Ly ratio.," The excellent source detection sensitivity, achieved in the bulge of M31, and the large number of compact X-ray sources in this galaxy allows us to estimate the contribution of unresolved LMXBs having the luminosities below the adopted threshold of $2\cdot 10^{36} \ \mathrm{erg \ s^{-1}}$ to the $L_X/L_K$ ratio."38 We consider the inner 6’ of the bulge where the source detection is complete down to 2-10?ergs7! (Voss&Gilfanov.2007).., We consider the inner $ 6 \arcmin $ of the bulge where the source detection is complete down to $ 2 \cdot 10^{35} \ \mathrm{erg \ s^{-1}} $ \citep{voss}.39 In this region we collected all compact sources with the luminosity in the range 2-10?—2.1079eres7!. excluding those classified as supersoft sources.," In this region we collected all compact sources with the luminosity in the range $2 \cdot 10^{35} - 2\cdot 10^{36} \ \mathrm{erg \ s^{-1}}$, excluding those classified as supersoft sources."40 The combined X-ray luminosity of these sources is divided by the near-infrared luminosity of the same region. to produce Ly/Ly=(3.6€0.3)-1075ergs!Ly...," The combined X-ray luminosity of these sources is divided by the near-infrared luminosity of the same region, to produce $L_X/L_K= (3.6 \pm 0.3) \cdot 10^{26} \ \mathrm{erg \ s^{-1} \ L_{K,\odot}^{-1}} $."41 This number represents the Lx/Ly ratio in the soft band of low-mass X-ray binaries with luminosities in the 2-10?—10°°ergs7! range., This number represents the $L_X/L_K$ ratio in the soft band of low-mass X-ray binaries with luminosities in the $2 \cdot 10^{35} - 2\cdot 10^{36} \ \mathrm{erg \ s^{-1}}$ range.42 We conclude that LMXBs contribute ~15 per cent to the Lx/Ly ratio derived above., We conclude that LMXBs contribute $ \sim 15 $ per cent to the $L_X/L_K$ ratio derived above.43 The possible effect of the interstellar absorption on the observed X-ray luminosities. depends on the energy spectra of the main X-ray emitting components — active binaries and supersoft sources.," The possible effect of the interstellar absorption on the observed X-ray luminosities, depends on the energy spectra of the main X-ray emitting components – active binaries and supersoft sources."44 ABs have significantly harder spectra than supersoft sources. which is illustrated in Fig. 3..," ABs have significantly harder spectra than supersoft sources, which is illustrated in Fig. \ref{fig:softsrc}."45 The class of ABs ts represented by V711 Tau. it was observed by for 3.2 ks in Obs-ID 0116340601. while RX JO439.8- is an example of steady hydrogen-burning sources. based on a exposure with 8.1 ks in Obs-ID 83.," The class of ABs is represented by V711 Tau, it was observed by for $ 3.2 $ ks in Obs-ID 0116340601, while RX J0439.8-6809 is an example of steady hydrogen-burning sources, based on a exposure with $ 8.1 $ ks in Obs-ID 83."46 As a consequence of the harder spectra. ABs are less affected by the interstellar absorption.," As a consequence of the harder spectra, ABs are less affected by the interstellar absorption."47 In Fig., In Fig.48" + we plot the corrected X/K ratio ((Ly/L4), in Table 3) against the Galactic column density.", \ref{fig:xtokplot} we plot the corrected X/K ratio $\left(L_X/L_K\right)_{corr}$ in Table 3) against the Galactic column density.49 A weak anti- between these two quantities appears to exist., A weak anti-correlation between these two quantities appears to exist.50 This dependence or. rather. absence of a stronger one. can be used. in principle. to further constrain the contribution of sources," This dependence or, rather, absence of a stronger one, can be used, in principle, to further constrain the contribution of sources"51WOS5S mask. shown in figure laa. bv those of simulation B shown in figure 2bb. After this replacement the smoothing of LO” is applied.,"KQ85 mask, shown in figure \ref{Fig:KQ85_masks_nside_512_and_nside_16}a a, by those of simulation B shown in figure \ref{Fig:CutSky_Info_Input_maps}b b. After this replacement the smoothing of $10^\circ$ is applied."52 Phe last step transfers now the “wrong” information to the pixels outside the mask., The last step transfers now the “wrong” information to the pixels outside the mask.53 This smootheed map is shown in figure 2cc. Downgrading this map to Naas=16 provides the data outside the mask which are used for the reconstruction., This smoothed map is shown in figure \ref{Fig:CutSky_Info_Input_maps}c c. Downgrading this map to $N_{\hbox{\scriptsize side}} =16$ provides the data outside the mask which are used for the reconstruction.54 Lf the reconstruction would not use the information within the mask. the reconstructed map of figure 3aa should reappear.," If the reconstruction would not use the information within the mask, the reconstructed map of figure \ref{Fig:CutSky_Info_Extraction_lmax_10}a a should reappear."55 However. as revealed in figure Sec. the reconstruction algorithm generates within the mask the main structures of simulation D. which is. displayed in ligure 2bb. This clearly demonstrates the information transfer. so that one has to be careful in testing the reconstruction algorithm.," However, as revealed in figure \ref{Fig:CutSky_Info_Extraction_lmax_10}c c, the reconstruction algorithm generates within the mask the main structures of simulation B, which is displayed in figure \ref{Fig:CutSky_Info_Input_maps}b b. This clearly demonstrates the information transfer, so that one has to be careful in testing the reconstruction algorithm."56 This leads to the question whether the reconstruction can be carried out using only unsmootheel maps where no information about pixels within the mask is, This leads to the question whether the reconstruction can be carried out using only unsmoothed maps where no information about pixels within the mask is57across a fare.,across a flare.58 The light curves in Fie., The light curves in Fig.59 6 clearly reveal (hie. presence of rapid flares (hat last [ον less (han an hour., 6 clearly reveal the presence of rapid flares that last for less than an hour.60 Panel {shows a beautiful example of such a flare., Panel f shows a beautiful example of such a flare.61 In fact. (here are significant sub-structures associated with the event. suggesting the presence of two overlapping Lares of even shorter cdurations.," In fact, there are significant sub-structures associated with the event, suggesting the presence of two overlapping flares of even shorter durations."62 Interestingly. (he X-ray spectrum of the source varies little across (his flare (see Panel [in Fig.," Interestingly, the X-ray spectrum of the source varies little across this flare (see Panel f in Fig."63 7)., 7).64 The effort to precisely determine the duration of each flare was. in general. complicated bx (he presence of data gaps. as well as (he co-existence of fIares on a wide range of timescales.," The effort to precisely determine the duration of each flare was, in general, complicated by the presence of data gaps, as well as the co-existence of flares on a wide range of timescales."65 Sometimes. only a portion of a flare is seen.," Sometimes, only a portion of a flare is seen."66 The shortest rise or decay lime seen is about. 1000 s. although it can be argued that it might be even shorter in some cases (see. e.g.. Panel e of Fig.," The shortest rise or decay time seen is about 1000 s, although it can be argued that it might be even shorter in some cases (see, e.g., Panel e of Fig."67 6)., 6).68 The observed. variability may extend to shorter timescales. on which individual X-ray flares become unresolvable.," The observed variability may extend to shorter timescales, on which individual X-ray flares become unresolvable."69 The collective effects of such variability can be investigated by adopting a more sophisticated time-domain or Fourier-domain based technique., The collective effects of such variability can be investigated by adopting a more sophisticated time-domain or Fourier-domain based technique.70 We chose to follow the latter approach to obtain a representative power-clensily spectrum (PDS) οἱ Alrk 421 in the low or flaring state., We chose to follow the latter approach to obtain a representative power-density spectrum (PDS) of Mrk 421 in the low or flaring state.71 We selected a subset of the 1997 observations Chat are relatively long for the low state ancl. similarly. a subset of the 2001 observations for the flaring state.," We selected a subset of the 1997 observations that are relatively long for the low state and, similarly, a subset of the 2001 observations for the flaring state."72 The total exposure (ime is comparable lor the two data sets., The total exposure time is comparable for the two data sets.73 For each observation. we made a lisht curve from the data that has a tme resolution of 1/8 s (but no energv resolution).," For each observation, we made a light curve from the data that has a time resolution of 1/8 s (but no energy resolution)."74 We then broke the light curve into segments. each of which is 4096 s long (which requires the padding of data gaps or shorter segments wilh the average count rate).," We then broke the light curve into segments, each of which is 4096 s long (which requires the padding of data gaps or shorter segments with the average count rate)."75 We performed Fast-Fourier transformation on each segment to obtain a PDS., We performed Fast-Fourier transformation on each segment to obtain a PDS.76 The PDS was normalized according to a scheme proposed by Leahy et al. (, The PDS was normalized according to a scheme proposed by Leahy et al. (771983).,1983).78 The individual PDSs of the segments were (hen weighted (bv the total number of photons) aud averaged to obtain the PDS for the observation., The individual PDSs of the segments were then weighted (by the total number of photons) and averaged to obtain the PDS for the observation.79 To further improve statistics. we weighted and averaged the PDSs of the selected observations in a similar manner.," To further improve statistics, we weighted and averaged the PDSs of the selected observations in a similar manner."80 From the resulted PDS. we subtracted olf noise power due to Poisson counting statistics to obtain the PDS of the source.," From the resulted PDS, we subtracted off noise power due to Poisson counting statistics to obtain the PDS of the source."81 Fie., Fig.82 9 shows the final PDS for each state., 9 shows the final PDS for each state.83" The observed PDS can be fitted bv a simple power law. 1//"". where a=1.9-Ε0.2 for the low state and 2.26£0.06 for the flaring state. although statistics is quite limited for the low state."," The observed PDS can be fitted by a simple power law, $1/f^{\alpha}$, where $\alpha=1.9\pm 0.2$ for the low state and $2.26\pm 0.06$ for the flaring state, although statistics is quite limited for the low state."84 The latter value is in general agreement with the published results for the [Iaring state (Ixataoka et al., The latter value is in general agreement with the published results for the flaring state (Kataoka et al.85 2001: Brinkmann et al., 2001; Brinkmann et al.86 2003)., 2003).87 The PDS appears to fall more steeply in (he flaring state. although the difference is only of marginal statistical significance.," The PDS appears to fall more steeply in the flaring state, although the difference is only of marginal statistical significance."88 The power-law type of PDS is twpical of AGN., The power-law type of PDS is typical of AGN.89 What is remarkable here is (hat the variability, What is remarkable here is that the variability90)unded by. Aj=1.,bounded by $\Delta_b = 1$.91 Each segmoeut is composed of teus o hmndreds of exid cells; cach with width z Lian |.," Each segment is composed of tens to hundreds of grid cells, each with width $\approx 1~$ km $^{-1}$."92 For each overdeuse segment. our scheme attenuates the ionizing backeround (half of which is assumed to cuter roni each side) based ou the amount aud distribution of11.," For each overdense segment, our scheme attenuates the ionizing background (half of which is assumed to enter from each side) based on the amount and distribution of."93".. The scheme starts the assumption that ⋅ ≓↽⊀ ∪↥∎⋜↧∐↸⋡↸∖∐↴∖↴⋜↧↸⋡↥∎∪↴∖↴↴∖↴↑↕↓↸∖↴∖↴↸∖∶↰⋎↕⊔↸∖∐↑∙↖↖↽∐↸∖↥⋅↸∖∣↕⋜∏⋝↸∖↕↴∖↴↑∐↸∖↸⊳↸∖∐TyDQyvolwithue""⋅⇁ ⊔∐⊔↴⋝↸∖↥⋅∙⋜⋯≺∟∖∐↖⋅⊔⋜⋯≺↧⋅∫∣⊽≼∑⋟⋜⋯∖↥⋅↸∖↴∖↴↻↸∖↸⋡↑↕↖⊽↸∖↕⋅↖⊽↾↕⊔∖∐↸∖∐ ↸⋡⋯↕⋯⊔∐≺∐∖∐↴∖↴↕↑⋅↖⊽⋜⋯≺↧↕∐∏≺∐∖∐↑↕↕↑↸∖∐↴∖↴↕↑⋅↖⊽↑∪≼⋡↸∖∐∣↕↥⋅∩⋯ ∕∙"," The scheme starts with the assumption that $x_{{\rm HeII}, {\it i}} = 1$ and $J_{i}(E) = J(E)^{\rm void} \,\exp[-\sigma_{\rm HeII}(E) \, N_{{\rm HeII}, {\it i}}]$ for all cells across the segment, where $i$ labels the cell number, and $N_{{\rm HeII}, {\rm i}}$ and $J_{i}(E)$ are respectively the column density and incident intensity to cell $i$ from $< i$."94≋↕⋯∐⋜∐⋅↕⋅↖⇁∙↑∐∖↥⋅↸∖↕↴∖↴⋜↧↸⊳∪∐↑↥⋅∏∏↕↑↕∪∐↑∪⋅∫∣⇁⋖⊏⋝↕⋟↥⋅∪⋯ >7.," Similarly, there is a contribution to $J_{i}(E)$ from $>\,i$."95 Next. the scheme iterates to converge to Dur; and οι. assume photoionization equilibrium.," Next, the scheme iterates to converge to $\Gamma_{{\rm HeII}, {\it i}}$ and $x_{{\rm HeII}, {\it i}}$, assuming photoionization equilibrium."96 For our calculations. J(Ey? is set to have a spectral iudex of 1.5. as expected for quasars.," For our calculations, $J(E)^{\rm void}$ is set to have a spectral index of $-1.5$, as expected for quasars."97 LLve forest sigltlines show that Typ fluctuates wildly ⊲ ∙∖↽↕⊰↸∖↕⋯↸∖↥⋅↴∖↴⊇∩∩⊤⋟⋈↖↖⊽↸∖≺↧∪∐∪↑⋜↧↑↑↸∖∐∏≻↑↑∪↕⊔∪≼∐∖↕↑∐↸," $\alpha$ forest sightlines show that $\Gamma_{\rm HeII}$ fluctuates wildly on scales of $\gtrsim10~$ cMpc \citep{zheng04, fechner07}."98∖↴∖↴↸∖∪↕↴∖↴↸⊳⋜↧↕↸∖↴∖↴∪↕≼↓∩↸⊳⋀∖↕↻↸⊳⋖∑↕∐∖∐∶↴⋁↸∖↑⋜↧↕∙−≻∩∩↓∶⊟∖↸⊳∐∐↸∖↥⋅ ∏⋯⊳↑∏⋜↧↑↕∪∐↴∖↴∐↸∖↥⋅↸∖∙↴⋝∏↑↖↖↽↕∐↸⊳∪∐∐⊔↸∖∐↑∪∐∐∪↖↖↽↑," We do not attempt to model these fluctuations here, but will comment on how they could affect our conclusions."99∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧, These fluctuations will spatially modulate the number of dense self-shielding regions100∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑, These fluctuations will spatially modulate the number of dense self-shielding regions101∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸, These fluctuations will spatially modulate the number of dense self-shielding regions102∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions103∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑, These fluctuations will spatially modulate the number of dense self-shielding regions104∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐, These fluctuations will spatially modulate the number of dense self-shielding regions105∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸, These fluctuations will spatially modulate the number of dense self-shielding regions106∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions107∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐, These fluctuations will spatially modulate the number of dense self-shielding regions108∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯, These fluctuations will spatially modulate the number of dense self-shielding regions109∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔, These fluctuations will spatially modulate the number of dense self-shielding regions110∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴, These fluctuations will spatially modulate the number of dense self-shielding regions111∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈, These fluctuations will spatially modulate the number of dense self-shielding regions112∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖, These fluctuations will spatially modulate the number of dense self-shielding regions113∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥, These fluctuations will spatially modulate the number of dense self-shielding regions114∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅, These fluctuations will spatially modulate the number of dense self-shielding regions115∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪, These fluctuations will spatially modulate the number of dense self-shielding regions116∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕, These fluctuations will spatially modulate the number of dense self-shielding regions117∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡, These fluctuations will spatially modulate the number of dense self-shielding regions118∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺, These fluctuations will spatially modulate the number of dense self-shielding regions119∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐, These fluctuations will spatially modulate the number of dense self-shielding regions120∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖, These fluctuations will spatially modulate the number of dense self-shielding regions121∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐, These fluctuations will spatially modulate the number of dense self-shielding regions122∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴, These fluctuations will spatially modulate the number of dense self-shielding regions123∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions124∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions125∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸, These fluctuations will spatially modulate the number of dense self-shielding regions126∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions127∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions128∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions129∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions130∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸, These fluctuations will spatially modulate the number of dense self-shielding regions131∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions132∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐, These fluctuations will spatially modulate the number of dense self-shielding regions133∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟, These fluctuations will spatially modulate the number of dense self-shielding regions134∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴, These fluctuations will spatially modulate the number of dense self-shielding regions135∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions136∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions137∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕, These fluctuations will spatially modulate the number of dense self-shielding regions138∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐, These fluctuations will spatially modulate the number of dense self-shielding regions139∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸, These fluctuations will spatially modulate the number of dense self-shielding regions140∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions141∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕, These fluctuations will spatially modulate the number of dense self-shielding regions142∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼, These fluctuations will spatially modulate the number of dense self-shielding regions143∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐, These fluctuations will spatially modulate the number of dense self-shielding regions144∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐, These fluctuations will spatially modulate the number of dense self-shielding regions145∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶, These fluctuations will spatially modulate the number of dense self-shielding regions146∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴, These fluctuations will spatially modulate the number of dense self-shielding regions147∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁, These fluctuations will spatially modulate the number of dense self-shielding regions148∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥, These fluctuations will spatially modulate the number of dense self-shielding regions149∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅, These fluctuations will spatially modulate the number of dense self-shielding regions150∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸, These fluctuations will spatially modulate the number of dense self-shielding regions151∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖, These fluctuations will spatially modulate the number of dense self-shielding regions152∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶, These fluctuations will spatially modulate the number of dense self-shielding regions153∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴, These fluctuations will spatially modulate the number of dense self-shielding regions154∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙, These fluctuations will spatially modulate the number of dense self-shielding regions155∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾, These fluctuations will spatially modulate the number of dense self-shielding regions156∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕, These fluctuations will spatially modulate the number of dense self-shielding regions157∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪, These fluctuations will spatially modulate the number of dense self-shielding regions158∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐, These fluctuations will spatially modulate the number of dense self-shielding regions159∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐↴, These fluctuations will spatially modulate the number of dense self-shielding regions160∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐↴∖, These fluctuations will spatially modulate the number of dense self-shielding regions161∐∖⋅↖↽↸⊳∪∏↕≼↧ ⋜↕↽∱↸∖↸⊳↑≺∏∐⋅↸⊳∪↕⊔⊳↕∏↴∖↴↕∪∐↴∖↴∙↽∕∏∐∖↴∖↴↸∖∏⋯⊳↑∏⋜↕⊓∪∐↴∖↴↖↖↽↕∐↴∖↴↻⋜↧↑↕⋜↧∐⋅↖↽ ⋯∪≼⊔∏⋜↧↑↸∖↑∐↸∖∐⋯⊔↴⋈∖↥⋅∪↕⋡≺∐∖∐↴∖↴↸∖↴∖↴↸∖∐∟↴∖↴↕∐↸∖↕≼∐∐∶↴⋁↥⋅↸∖∶↴∙⊾↕∪∐↴∖↴, These fluctuations will spatially modulate the number of dense self-shielding regions162ways.,ways.163" For example. nonlinear interactions among Alfvénn waves occur only between waves propagating in opposite directions in the plasma frame (Iroshnikov 1963. Kraichnan 1965). and so if the energy in waves propagating towards the Sun is very small. then the energy cascade rate and turbulent heating rate also become small (Dobrowolny et al 1980. Hossain et al 1995, Chandran et al 2009)."," For example, nonlinear interactions among Alfvénn waves occur only between waves propagating in opposite directions in the plasma frame (Iroshnikov 1963, Kraichnan 1965), and so if the energy in waves propagating towards the Sun is very small, then the energy cascade rate and turbulent heating rate also become small (Dobrowolny et al 1980, Hossain et al 1995, Chandran et al 2009)."164 Finite cross helicity may also modify the wavenumber scalings of the inertial-range power spectra of the density. magnetic field. and velocity.," Finite cross helicity may also modify the wavenumber scalings of the inertial-range power spectra of the density, magnetic field, and velocity."165" Because the “minority” Sunward Alfvénn waves and the passive scalar fluctuations are both cascaded by the ""dominant anti-Sunward Alfvénn waves. the passive scalar spectrum Is expected to have the same inertial-range scaling as the Sunward waves (Lithwick Goldreich 2003; Chandran 2008b)."," Because the “minority” Sunward Alfvénn waves and the passive scalar fluctuations are both cascaded by the “dominant” anti-Sunward Alfvénn waves, the passive scalar spectrum is expected to have the same inertial-range scaling as the Sunward waves (Lithwick Goldreich 2003; Chandran 2008b)."166 In some studies of Alfvennic turbulence with cross helicity (e.g.. Grappin et al. 1983: Chandran 2008a: Beresnyak Lazarian 2009) the minority Alfvénn waves have a shallower power spectrum than the dominant Alfvénn waves. suggesting that the passive scalar spectrum is shallower than the magnetic spectrum in highly imbalanced turbulence.," In some studies of Alfvénnic turbulence with cross helicity (e.g., Grappin et al 1983; Chandran 2008a; Beresnyak Lazarian 2009) the minority Alfvénn waves have a shallower power spectrum than the dominant Alfvénn waves, suggesting that the passive scalar spectrum is shallower than the magnetic spectrum in highly imbalanced turbulence."167 This finding may be related to the shallow density spectra seen in radio observations of the corona. in which the turbulence is expected to be highly “imbalanced™ (Cranmer van Ballegooijen 2005. Verdini Velli However. a number of other studies find that the inertial-range spectra of the minority waves and dominant waves scale with wavenumber in the same way (Lithwick. Goldreich. Sridhar 2007: Perez Boldyrev 2009: Podesta Bhattacharjee 2009).," This finding may be related to the shallow density spectra seen in radio observations of the corona, in which the turbulence is expected to be highly “imbalanced” (Cranmer van Ballegooijen 2005, Verdini Velli However, a number of other studies find that the inertial-range spectra of the minority waves and dominant waves scale with wavenumber in the same way (Lithwick, Goldreich, Sridhar 2007; Perez Boldyrev 2009; Podesta Bhattacharjee 2009)."168 Moreover. the different studies cited above disagree over Whether the spectra of the minority and dominant waves are equal at the dissipation scale (“pinning”).," Moreover, the different studies cited above disagree over whether the spectra of the minority and dominant waves are equal at the dissipation scale (“pinning”)."169 Because imbalanced Alfvénnic turbulence is still not fully understood. and is likely the norm in the solar wind. we are only able to derive upper limits on the turbulent heating rates from the density observations. às discussed further below.," Because imbalanced Alfvénnic turbulence is still not fully understood, and is likely the norm in the solar wind, we are only able to derive upper limits on the turbulent heating rates from the density observations, as discussed further below."170 In addition. this uncertainly implies that the precise power-law scalings for in Figures 1 and 2. should not be taken too literally. althoughIP we believe that our conclusions about the relative contribution of the active and passive density fluctuations are robust.," In addition, this uncertainly implies that the precise power-law scalings for $\Phi_{\rm ne}^{\rm 1D}$ in Figures \ref{fig:dn_sw} and \ref{fig:dn_cor} should not be taken too literally, although we believe that our conclusions about the relative contribution of the active and passive density fluctuations are robust."171 In this section. we discuss observational constraints on density fluctuations in the solar corona and solar wind. and their implications for low-frequency Alfvénnic turbulence models.," In this section, we discuss observational constraints on density fluctuations in the solar corona and solar wind, and their implications for low-frequency Alfvénnic turbulence models."172" Coles Harmon (1989) analyzed the spectral broadening of Arecibo radar observations of Venus near superior conjunction to determine the. three-dimensional power spectrum of electron density fluctuations «b,(7:K). (treated as an isotropic function. of wave vector k) at a range of heliocentric distances r in the slow solar wind."," Coles Harmon (1989) analyzed the spectral broadening of Arecibo radar observations of Venus near superior conjunction to determine the three-dimensional power spectrum of electron density fluctuations $\Phi_{ne}(r,k)$ (treated as an isotropic function of wave vector ${\bf k}$ ) at a range of heliocentric distances $r$ in the slow solar wind."173" They were able to fit ,,(&) at r25R. with one power law at em7! sa slightly shallower power law atkj. and an exponential or Gaussian at &>Kj. where is the ""inner-scale"" wave number at r=5R.."," They were able to fit $\Phi_{ne}(r,k)$ at $r=5 R_{\sun}$ with one power law at $k < 10^{-7} \mbox{ cm}^{-1}$ , a slightly shallower power law at, and an exponential or Gaussian at $k> k_i$, where is the “inner-scale” wave number at $r=5 R_{\sun}$."174 They found that atk =k; and r=5R.. δι~9.0<10°em?km? (see their Fig.," They found that at $k= k_i$ and $r= 5 R_{\sun}$, $\Phi_{ne} \simeq 9.0 \times 10^3175\mbox{ cm}^{-6} \mbox{ km}^3$ (see their Fig."176 4)., 4).177 We focus on the inner scale for reasons that will become clearer below., We focus on the inner scale for reasons that will become clearer below.178" Coles et al (1991) found that ϱ,, is a factor of 215 smaller in coronal holesthan in the slow wind. and thus we set The rms electron density fluctuation δη, is given by ont~Atk?b,(K;). which implies ón,~87em? at r25R.."," Coles et al (1991) found that $\Phi_{ne}$ is a factor of $\simeq 15$ smaller in coronal holesthan in the slow wind, and thus we set The rms electron density fluctuation $\delta n_{k_i}$ is given by $\delta n_{k_i}^2 \simeq 4\pi k_i^3 \Phi_{ne}(k_i)$ , which implies $\delta n_{k_i} \simeq 87 \mbox{ cm}^{-3}$ at $r=5 R_{\sun}$."179 We estimate the coronal-hole electron density from Eqn. (, We estimate the coronal-hole electron density from Eqn. (180"4) of Feldman et al (1997). which gives n,=5.9«10°em? at rF—SR. this is very close to the value inferred by Fisher Guhathakurta (1995) from observations taken with the Spartan 201-01 coronagraph.","4) of Feldman et al (1997), which gives $n_e = 5.9 \times 10^3 \mbox{ cm}^{-3}$ at $r= 5R_{\sun}$; this is very close to the value inferred by Fisher Guhathakurta (1995) from observations taken with the Spartan 201-01 coronagraph."181 This value forthe background density then gives atr —5R.., This value forthe background density then gives at $r=5 R_{\sun}$.182" An upper limit on the rms amplitude of the Alfvénnic velocity fluctuation at perpendicular scale kel, denoted ὄνς,. can be obtained by assuming that the density fluctuations at scale ko! arise entirely from KAWs."," An upper limit on the rms amplitude of the Alfvénnic velocity fluctuation at perpendicular scale $k_i^{-1}$, denoted $\delta183v_{k_i}$, can be obtained by assuming that the density fluctuations at scale $k_i^{-1}$ arise entirely from KAWs."184" Using the linear eigenfunctions of KAWs. we can write If the compressibility of the KAWs noticeably affects the density spectrum from 1077em!«k107 em-!, as conjectured above and as is suggested by Figure 2.. then Óv,, may beclose to the upper limit given in equation (7)): this is because the fraction of ®,,. that arises from KAWs increases at larger κ (Fig. 2))."," Using the linear eigenfunctions of KAWs, we can write If the compressibility of the KAWs noticeably affects the density spectrum from $10^{-7} \mbox{ cm}^{-1} < k < 10^{-5} \mbox{ cm}^{-1}$ , as conjectured above and as is suggested by Figure \ref{fig:dn_cor}, then $\delta v_{k_i}$ may beclose to the upper limit given in equation \ref{eq:deltan}) ); this is because the fraction of $\Phi_{ne}$ that arises from KAWs increases at larger $k$ (Fig. \ref{fig:dn_cor}) )."185 To evaluate the right-hand side of equation (7)) we assume y;=| and 7;=2.0«10° K and adopt the coronal-hole magnetic field model of Cranmer van Ballegooijen (2005) (their eq.," To evaluate the right-hand side of equation \ref{eq:deltan}) ) we assume $\gamma_i = 1$ and $T_i =1862.0\times 10^6$ K and adopt the coronal-hole magnetic field model of Cranmer van Ballegooijen (2005) (their eq."187 2). which gives By=5.8ν107 G at r25...," 2), which gives $B_0 =1885.8 \times 10^{-2}$ G at $r=5 R_{\sun}$."189" These parameters give p;=2.3101em. di2341054em. v4=1.6«107m/s. and or. equivalently. Atk—Kj.the density spectrum at r=5R. is still close to the value obtained by extrapolating a power-law fit to ®,,, for values of k between 1077em7! and 1075em7!."," These parameters give $\rho_i = 2.3 \times 10^{4} \mbox{ cm}$, $d_i = 3 \times 10^{5} \mbox{190 cm}$, $v_{\rm A} = 1.6 \times 10^8 \mbox{ cm/s}$, and or, equivalently, At $k = k_i$,the density spectrum at $r=5 R_{\sun}$ is still close to the value obtained by extrapolating a power-law fit to $\Phi_{ne}$ for values of $k$ between $10^{-7} \mbox{ cm}^{-1}$ and $10^{-6} \mbox{191 cm}^{-1}$."192" We can thus assume that most of the cascade power is still present atk,κι and that most of the dissipation occurs at k4.7 ky.", We can thus assume that most of the cascade power is still present at $k_\perp=k_i$ and that most of the dissipation occurs at $k_\perp >k_i$ .193" Moreover. because k;p;—0.2. the kinetic energy and magnetic energy of Alfvénnie fluctuations at 4,=κι are comparable. as in incompressible MHD. but not like the short-wavelength regime kp;>> |. in which the magneticenergy dominates."," Moreover, because $k_i \rho_i \simeq 0.2$, the kinetic energy and magnetic energy of Alfvénnic fluctuations at $k_\perp = k_i$ are comparable, as in incompressible MHD, but not like the short-wavelength regime $k_\perp \rho_i \gg 1$ , in which the magneticenergy dominates."194 The energy density of Alfvénnic fluctuations at scale ko! Is thus ~ pov; ," The energy density of Alfvénnic fluctuations at scale $k_i^{-1}$ is thus $\simeq \rho \delta195v_{k_i}^2$ ."196The time required for the fluctuationenergy at ky=Κι to cascade to ky> 2A. denoted {.. ct satisfies the inequality," The time required for the fluctuationenergy at $k_\perp197= k_i$ to cascade to $k_\perp \geq 2 k_i$ , denoted $t_c$ , satisfies the inequality"198in Figure 7..,in Figure \ref{figrv}.199 The fleure has suggested that there is a correlation between A: aud log(P)., The figure has suggested that there is a correlation between $R_V$ and $\log(P)$.200 However. if we adopt such a period dependency of Ry and apply this to our OGLE data (with the OGLE extinction map). we still obtain a significant detection of noulinearity of the P-L relation with F=6.71.," However, if we adopt such a period dependency of $R_V$ and apply this to our OGLE data (with the OGLE extinction map), we still obtain a significant detection of nonlinearity of the P-L relation with $F=6.74$."201 Therefore a period dependency of Ay still caunot explain the observed nonlinear LMC P-L relation., Therefore a period dependency of $R_V$ still cannot explain the observed nonlinear LMC P-L relation.202 Another piece of evidence against extinction errors causing the observed ποποσα P-L relation is the P-C relation at παπα elt., Another piece of evidence against extinction errors causing the observed nonlinear P-L relation is the P-C relation at maximum light.203 The observed P-C relation for the Galactic aud LAIC long period Cepheids is shown to be flat at the maxima light (Code1917:Ikaubur&Necow2001).," The observed P-C relation for the Galactic and LMC long period Cepheids is shown to be flat at the maximum light \citep{cod47,kan04}."204. There is a souncl plivsical reason behind the flatuess of the P-C relation at the masximaun liebt (Simonetal.1993:IkauburNecow2006):: the interaction of hydrogen ionization front (IF) aud plotosphere at the maximal ieht.," There is a sound physical reason behind the flatness of the P-C relation at the maximum light \citep{sim93,kan04a,kan06}: the interaction of hydrogen ionization front (HIF) and photosphere at the maximum light."205 As period increases. Cepheids can only ect cooler or stay roughly in the same temperature range (i.c. he P-C relation is flat) at maxima light.," As period increases, Cepheids can only get cooler or stay roughly in the same temperature range (i.e. the P-C relation is flat) at maximum light."206 If an additional amount of extinction 1s needed to make the P-C relation linear at the mean lieht. the the same amount of extinction would force the Cepheids to become totter as period increases at miaxinmun light.," If an additional amount of extinction is needed to make the P-C relation linear at the mean light, the the same amount of extinction would force the Cepheids to become hotter as period increases at maximum light."207 This is iu serious contradiction with the pulsation theories and observations., This is in serious contradiction with the pulsation theories and observations.208 Iu fact. some researcliers have used the flatuess of the P-C relation at the παπα light O crive the extinction values (Sinonctal.1993:Feruie1991).," In fact, some researchers have used the flatness of the P-C relation at the maximum light to derive the extinction values \citep{sim93,fer94}."209. Furthermore. the multi-phase study of he LMC P-L and P-C relatious implies that the LAIC P-L aud P-C relations are nonlinear at most ofthe phases over the pulsation evcle. especially at pliases near 0.8 (Necow&Ixaubur 2006b)..," Furthermore, the multi-phase study of the LMC P-L and P-C relations implies that the LMC P-L and P-C relations are nonlinear at most ofthe phases over the pulsation cycle, especially at phases near $0.8$ \citep{nge06}. ."210 Based on the above aretunents and the aremmeuts preseuted in Waubur&Necow(200L).. Saudageetal.(2001)... (2005) aud Ἱναια&Necow(2006).. we believe that frou the current available extinction studies.," Based on the above arguments and the arguments presented in \citet{kan04}, \citet{san04}, \citet{nge05} and \citet{kan06}, we believe that from the current available extinction studies."211 The P-L relation aud the period-color (P-C) relation for Cepheid variables are not independent of eac[um other., The P-L relation and the period-color (P-C) relation for Cepheid variables are not independent of each other.212 Madore&Freecanan(1991). have eiven a thorough review for the physics behind the Cephlieid P-L and P-C relations., \citet{mad91} have given a thorough review for the physics behind the Cepheid P-L and P-C relations.213 At mean light in the optical bands. a nonlinear P-L relation will imply that the P-C relation is also nonlinear and vice versa.," At mean light in the optical bands, a nonlinear P-L relation will imply that the P-C relation is also nonlinear and vice versa."214 The maxima belt P-C relation shows a slightly different behavior. see Necow&Ixaubur(2006b).," The maximum light P-C relation shows a slightly different behavior, see \citet{nge06}."215. Compared to the P-L relation. the nonlinearity of the P-C relation is compelling and easier to visualize (seetheP-CplotsinTamunanu&Reindl2002:ἹναονNecow2001:Sandageetal.2001:Necowetal.2005:IKaubur& 2006).," Compared to the P-L relation, the nonlinearity of the P-C relation is compelling and easier to visualize \citep[see the P-C plots in][]{tam02,kan04,san04,nge05,kan06}."216. Towever the evidence for the uoulinear LMC P-C relation is larecly ignored when the detection of nonlinear P-L relation is criticized., However the evidence for the nonlinear LMC P-C relation is largely ignored when the detection of nonlinear P-L relation is criticized.217 The large scatter at eiven period in the P-C relation is Ooeven as an example of possible errors iu extinction., The large scatter at given period in the P-C relation is given as an example of possible errors in extinction.218 However. we state againOo that if the extinction errors are ercat. they should also affect the PC relation at 1naxiumua belt but the P-C relation at mmaxinuun light is flat as predicted by theory.," However, we state again that if the extinction errors are great, they should also affect the PC relation at maximum light but the P-C relation at maximum light is flat as predicted by theory."219 The F-test applied to the P-C relation has already been discussed ii Ianbur&Necow(2001.2006) and Necowetal.(2005). and will not be repeated here.," The $F$ -test applied to the P-C relation has already been discussed in \citet{kan04,kan06} and \citet{nge05} and will not be repeated here."220 The results again strouely support the nonlinear P-C relation., The results again strongly support the nonlinear P-C relation.221 Unless new evidence aud/or new theory emerges to show that the Cepheid P-L aud P-C relations should be totally independent. r," Unless new evidence and/or new theory emerges to show that the Cepheid P-L and P-C relations should be totally independent, ."222"elation, There is a nis-conception that if the P-Lrelation is nonlinear in the optical (BV RI) bauds. then the"," There is a mis-conception that if the P-Lrelation is nonlinear in the optical $BVRI$ ) bands, then the"223spectra were then normalized. via Legendre polvnomial fits to the continuum regions.,spectra were then normalized via Legendre polynomial fits to the continuum regions.224 The empirical S/N ratios in the normalized spectra range from about 35r to LOO per half resolution clement for the ECII-D cata and from about SO to 150 for the lower resolution GIGOAL cata., The empirical S/N ratios in the normalized spectra range from about 35 to 100 per half resolution element for the ECH-B data and from about 80 to 150 for the lower resolution G160M data.225 More detailed discussions of the GIRS data and our adopted: reduction and analysis procedures may be found. in. Welty ο al. (, More detailed discussions of the GHRS data and our adopted reduction and analysis procedures may be found in Welty et al. (2261999b).,1999b).227 The normalized. line profiles for and toward LD 72127. and LD 72127D are shown in Fig. 1.., The normalized line profiles for and toward HD 72127A and HD 72127B are shown in Fig. \ref{fig:naca}.228 In cach case. the stronger member of the doublet. (if present). is shown at à continuum level of 1.0. and the weaker member of the doublet. GÉ present) is olfsetbv. | 0.2.," In each case, the stronger member of the doublet (if present) is shown at a continuum level of 1.0, and the weaker member of the doublet (if present) is offsetby $+$ 0.2."229 Velocities with respect to the local standard of rest (LSR) may be obtained w subtracting13.4 km + from the heliocentrie velocities shown in theLigure’., Velocities with respect to the local standard of rest (LSR) may be obtained by subtracting13.4 km $^{-1}$ from the heliocentric velocities shown in the.230.. Several previously observed. proliles or LD 72127 and from 1988 (EWIIM ~ 2527 km +: Hobbs et al., Several previously observed profiles for HD 72127A – and from 1988 (FWHM $\sim$ 2.5–2.7 km $^{-1}$; Hobbs et al.231 1991) and from. 1994 (FNLIN ~ 0.3 kmsI: Welty et al., 1991) and from 1994 (FWHM $\sim$ 0.3 km $^{-1}$; Welty et al.232 1996) are included or comparison., 1996) – are included for comparison.233 Spectra of some of the weaker optical lines are shown in Fig. 2..," Spectra of some of the weaker optical lines are shown in Fig. \ref{fig:weak},"234 where the profile for WD 72127. is ollset above the one for LID 72127D in cach case (ancl note he expanded vertical scale for all the lines)., where the profile for HD 72127A is offset above the one for HD 72127B in each case (and note the expanded vertical scale for all the lines).235 Profiles of some of the UV absorption lines toward HD 72127X are shown in Lig.e 3..," Profiles of some of the UV absorption lines toward HD 72127A are shown in Fig. \ref{fig:uv},"236 where (again)o the vertical scale has been expauded or the weaker lines., where (again) the vertical scale has been expanded for the weaker lines.237 Equivalent widths for the various lines measured from the normalized optical and UV. spectra are isted in Table 1:: for comparison. values reported for LL. Sin. and by Wallerstein et al. (," Equivalent widths for the various lines measured from the normalized optical and UV spectra are listed in Table \ref{tab:ewids}; for comparison, values reported for , , and by Wallerstein et al. ("2381995b). (from. GLIRS,1995b) (from GHRS239whereαρ is the incidence angle for a source on-axis.,where$\alpha_0$ is the incidence angle for a source on-axis.240 However. we lack a with a given reflective coating. as a function of the off-axis angle of the X-ray source.," However, we lack a with a given reflective coating, as a function of the off-axis angle of the X-ray source."241 In this paper. we present a solution to that problem.," In this paper, we present a solution to that problem."242 We develop an analytical approach that can be applied to double cone grazing-incidence X-ray mirrors and. with reasonable accuracy. to Wolter-I. mirrors (unless the f-number is small).," We develop an analytical approach that can be applied to double cone grazing-incidence X-ray mirrors and, with reasonable accuracy, to Wolter-I mirrors (unless the f-number is small)."243 The limits of this approximation are discussed in Sect. 2.., The limits of this approximation are discussed in Sect. \ref{DC_WI}.244 In Sect. 3..," In Sect. \ref{EffArea},"245 we derive general integral formulae (such as Eq. (25))), we derive general integral formulae (such as Eq. \ref{eq:Aeff_fin_offaxis}) ))246 to compute the off-axis effective area for a double-reflection X-ray mirror with shallow incident angles. for reflective coating.," to compute the off-axis effective area for a double-reflection X-ray mirror with shallow incident angles, for reflective coating."247 As a particular case. in Sect.," As a particular case, in Sect."248 4 we obtain some algebraic expressions for the geometric area and verify that the well-known Eq. (1)), \ref{Geometric} we obtain some algebraic expressions for the geometric area and verify that the well-known Eq. \ref{eq:SC_formula}) )249 can be derived as a particular case., can be derived as a particular case.250 In Sect. 5..," In Sect. \ref{Comp},"251 the predictions of the analytical approach are validated. for some particular cases. by means of a compariso with the outputs of a ray-tracing routine.," the predictions of the analytical approach are validated, for some particular cases, by means of a comparison with the outputs of a ray-tracing routine."252 The results are briefly discussed in Sect. 6.., The results are briefly discussed in Sect. \ref{Final}.253 We note that we assume that the off-axis mutual obstructio of mirrors in densely nested mirror assemblies has a negligible effect., We note that we assume that the off-axis mutual obstruction of mirrors in densely nested mirror assemblies has a negligible effect.254 Therefore. the results are valid. for either isolated double cone or Wolter-I mirrors. or for mirror modules know to be neghgibly obstructed. such that their effective area simply equals the sum of the contributions of the individual mirrors.," Therefore, the results are valid for either isolated double cone or Wolter-I mirrors, or for mirror modules known to be negligibly obstructed, such that their effective area simply equals the sum of the contributions of the individual mirrors."255 The quantification of the off-axis obstruction m mirror assemblies will be considered in future., The quantification of the off-axis obstruction in mirror assemblies will be considered in future.256We consider. in a preliminary way. a grazing-1incidence | mirror. and an on-axis photon source (Fig. 1)).,"We consider, in a preliminary way, a grazing-incidence Wolter-I mirror, and an on-axis photon source (Fig. \ref{fig:mirror_section}))."257 The optical axis is aligned with the z axis., The optical axis is aligned with the $z$ axis.258" We define Ry, to be the radius at the parabolic end (1.e.. the maximum radius). Ro the radius at =0 (the plane). Δι the radius at the hyperbolic end (ie. the minimum radius). F the focal point. and f the distance of F from the intersection plane (1.e.. the focal distance)."," We define $R_{\mathrm M}$ to be the radius at the parabolic end (i.e., the maximum radius), $R_0$ the radius at $z=0$ (the ), $R_m$ the radius at the hyperbolic end (i.e., the minimum radius), $F$ the focal point, and $f$ the distance of $F$ from the intersection plane (i.e., the focal distance)."259" In general. we refer to ""primary"" and ""secondary"" segments. instead of “parabola” and “hyperbola”."," In general, we refer to “primary” and “secondary"" segments, instead of “parabola"" and “hyperbola""."260" We denote with Z, the primary segment length along the z axis. and {5 that of the secondary."," We denote with $L_1$ the primary segment length along the $z$ axis, and $L_2$ that of the secondary."261 The polar coordinate ts ᾧ., The polar coordinate is $\varphi$.262 Because of the surface curvature. the incidence angles on the two surfaces vary in general with the z coordinate.," Because of the surface curvature, the incidence angles on the two surfaces vary in general with the $z$ coordinate."263 We define a(z) to be this angle on the primary (0<z Li mirror segment. and on the secondary (-L2<z« 0) mirror for a source on the optical axis. at infinite distance.," We define $\alpha(z)$ to be this angle on the primary $0<z<L_1$ ) mirror segment, and on the secondary $-L_2<z<0$ ) mirror for a source on the optical axis, at infinite distance."264 In general (Van Speybroeck and Chase 1972)). the incidence angle of rays close to z = 0. ag. 1s the same for both surfaces.," In general (Van Speybroeck and Chase \cite{VanSpeybroeck}) ), the incidence angle of rays close to $z$ = 0, $\alpha_0$, is the same for both surfaces."265 Therefore. we have the well-known relation Since oo is shallow. we hereafter assume that the (απ) function can be approximated by dj itself.," Therefore, we have the well-known relation Since $\alpha_0$ is shallow, we hereafter assume that the $\tan(4\alpha_0)$ function can be approximated by $4\alpha_0$ itself."266 To obtain an analytical expression for the effective area of a Wolter-I mirror when a source is off-axis by an angle &. we have to find algebraic expressions for: To compute the effective area for a source off-axis. we begin with the prototypical case of a mirror with a source but at a finite. although very large. distance D. which ts the usual configuration for on-ground calibration facilities.," To obtain an analytical expression for the effective area of a Wolter-I mirror when a source is off-axis by an angle $\theta$, we have to find algebraic expressions for: To compute the effective area for a source off-axis, we begin with the prototypical case of a mirror with a source on-axis, but at a finite, although very large, distance $D$ , which is the usual configuration for on-ground calibration facilities."267 All rays impinge the primary segment within a meridional plane. and in the double cone approximation they are all incident at the same grazing angle. independently of z and y.," All rays impinge the primary segment within a meridional plane, and in the double cone approximation they are all incident at the same grazing angle, independently of $z$ and $\varphi$."268 The finite distance of the source causes the beam to have a divergence at the primary segment. which can be assumed to be constant as long as Lj. with an half-aperture angle of ὁ=ΑαD.," The finite distance of the source causes the beam to have a divergence at the primary segment, which can be assumed to be constant as long as $D \gg L_1$ , with an half-aperture angle of $\delta \simeq R_0/D$."269 In this simplified case. every point of the mirror sees the source by an angle 6. regardless of y.," In this simplified case, every point of the mirror sees the source by an angle $\delta$, regardless of $\varphi$."270 We demonstrate hereafter that the solution to these problems is simpler to express analytically if the profile of the mirror can be approximated with à double cone. if we are interested only in the effective area.," We demonstrate hereafter that the solution to these problems is simpler to express analytically if the profile of the mirror can be approximated with a double cone, if we are interested only in the effective area."271 In contrast. the curvature of mirrors along the axis is essential for their angular resolution. but we do not consider this aspect here.," In contrast, the curvature of mirrors along the axis is essential for their angular resolution, but we do not consider this aspect here."272 In the remainder of this section. we quantify the errors caused by the substitution of a Wolter-I profile with a double cone. by keeping Ro. ao. Ly. and L» constant.," In the remainder of this section, we quantify the errors caused by the substitution of a Wolter-I profile with a double cone, by keeping $R_0$, $\alpha_0$ , $L_1$ , and $L_2$ constant."273 The problems to be faced are related to the system geometry. rather than to the absolute size of themirrors.," The problems to be faced are related to the system geometry, rather than to the absolute size of themirrors."274 Hence. it is convenient to report the results of this section in terms of both the f- f#= f/(RQ). instead of f itself. and L!= ΚΑ).," Hence, it is convenient to report the results of this section in terms of both the f-number, $f\# = f/(2R_0)$ , instead of $f$ itself, and $L_1' = L_1/(2R_0)$ ,"275ffrom llines. we consider at first our data inferred only from these lines.,"from lines, we consider at first our data inferred only from these lines."276" In particular. when considering all stars of the first group and the stars of the second group with 7.0 llinesgivcV, bbetween ϐ and 5 aand a mean value -— 25lu note that these stars have effective temperatures (325500 A andsurfacegqeavciticslog : 3.9."," In particular, when considering all stars of the first group and the stars of the second group with $<$ 0.7, lines give between 0 and 5 and a mean value = 2.5; note that these stars have effective temperatures $<$ 25500 K and surface gravities $\geqslant$ 3.9."277" For the unevolved stars of the third group A (21000endlog GI O)weefoundfromO llines.asfromlles Hines. substantiallyggrealerV, vvalues. 5.8 oon average."," For the unevolved stars of the third group $>$ 27000 K and $>$ 4.0) we found from lines, as from lines, substantially greater values, 5.8 on average."278 In accordance with this finding. we selected from the lists of Daflon et al. (," In accordance with this finding, we selected from the lists of Daflon et al. ("2792003. 2004a.b) two groups of stars. namely the stars with i:25500 A andthestarsmwith (2Y000A: inbotheaseslos (4.0.,"2003, 2004a,b) two groups of stars, namely the stars with $<$ 25500 K and the stars with $>$ 27000 K; in both cases $>$ 4.0."280" E hecorrespondingmeanW, vvalues are compared with our data in Table 3.", The corresponding mean values are compared with our data in Table 3.281" One may see from Table 3 that there is a significant difference inl, ffor both groups between our and Daflon et al", One may see from Table 3 that there is a significant difference in for both groups between our and Daflon et al.282s (2003) results. while the difference with Daflon et al. (,"'s (2003) results, while the difference with Daflon et al. ("2832004a.b) is markedly smaller.,"2004a,b) is markedly smaller."284 It is necessary to remember that we have used the vvalues averaged on aand lines. so our real mean vvalues are somewhat smaller than in Table 3.," It is necessary to remember that we have used the values averaged on and lines, so our real mean values are somewhat smaller than in Table 3."285 It is important to note once again that we determined independently from lines of three chemical elements. namelyI.. aandΠ.," It is important to note once again that we determined independently from lines of three chemical elements, namely, and."286. Moreover. the Vt determination from aand llines was implemented by the standard method. but that from lines was effected by a quite different method (Paper TT).," Moreover, the Vt determination from and lines was implemented by the standard method, but that from lines was effected by a quite different method (Paper III)."287 Nevertheless. all three sets of aare in rather good agreement.," Nevertheless, all three sets of are in rather good agreement."288" In particular. for the B stars with i:25500 A we foundlhal(i)individualV, vvalues range. as a rule. between and 5Iz Gi) mean vvalues are 1.0. 0.5 and 2.5 fforHe. παπάOL. respectively. ("," In particular, for the B stars with $<$ 25500 K we found that (i) individual values range, as a rule, between 0 and 5; (ii) mean values are 1.0, 0.5 and 2.5 for, and, respectively. ("289"Note that we have not found reasons to prefer ID) over 1,(@O1D). so we used an averaged value 102).","Note that we have not found reasons to prefer ) over ), so we used an averaged value ))."290 Thus. our results fromr. aand llines confirm that our lower sscule is preferable to the higher sscule of Daflon et al. (," Thus, our results from, and lines confirm that our lower scale is preferable to the higher scale of Daflon et al. ("2912003. 2004a.b).,"2003, 2004a,b)."292" It is important to remember as well that our mean Mg abundance 7.59 obtained with the 1D) values from the AAS| line is precisely contirmed from an analysis of the weak TISTI line that is insensitive to1,.", It is important to remember as well that our mean Mg abundance 7.59 obtained with the ) values from the 4481 line is precisely confirmed from an analysis of the weak 7877 line that is insensitive to.293. We implemented trial determinations of logz(Mg) with various for some stars from first and second groups.," We implemented trial determinations of $\log \varepsilon({\rm294Mg})$ with various for some stars from first and second groups."295" The changes in ogz(Mg) depend substantially on the effective temperature7,41 nevertheless. the final conclusion is clear: the differences in the vvalues explain completely the above-mentioned discrepancies between our and Daflon et al"," The changes in $\log \varepsilon({\rm Mg})$ depend substantially on the effective temperature; nevertheless, the final conclusion is clear: the differences in the values explain completely the above-mentioned discrepancies between our and Daflon et al."296’s (2003) mean magnesium abundance.,'s (2003) mean magnesium abundance.297 It is interesting to note that. according to Daflon (2004). the ower vvalues can be a result of the cooler effective temperatures7;r.," It is interesting to note that, according to Daflon (2004), the lower values can be a result of the cooler effective temperatures."298. The difference between our and Daflon et al, The difference between our and Daflon et al.299/s sscales cannot be sufficient to cause a marked change in thermal velocities and. hence. a change in;.,"'s scales cannot be sufficient to cause a marked change in thermal velocities and, hence, a change in."300". We believe that the difference inl; ddiscussed above may be connected with a rough correlation between the observed equivalent widths 11 and excitation potentials x: lines with higher x, tend to show lower IV on average.", We believe that the difference in discussed above may be connected with a rough correlation between the observed equivalent widths $W$ and excitation potentials $\chi_e$: lines with higher $\chi_e$ tend to show lower $W$ on average.301 These lines are more sensitive to tthan weaker lines. so their calculated ΤΕ values change more significantly when increases.," These lines are more sensitive to than weaker lines, so their calculated $W$ values change more significantly when increases."302 In this case one should increase tto eliminate a discrepancy in the derived abundances between relatively weak and strong lines., In this case one should increase to eliminate a discrepancy in the derived abundances between relatively weak and strong lines.303 For more than ten years the C. N. and O abundances have been considered as indicators of the metallicity of early B stars in reference to the Sun.," For more than ten years the C, N, and O abundances have been considered as indicators of the metallicity of early B stars in reference to the Sun."304 However. it is gradually becoming clear that this choice is not the best one.," However, it is gradually becoming clear that this choice is not the best one."305 On the one hand. there are empirical data that mixing exists in the early B-type MS stars between their interiors and surface layers. so the observed abundances of the CNO-cycle elements may be affected by evolutionary alterations.," On the one hand, there are empirical data that mixing exists in the early B-type MS stars between their interiors and surface layers, so the observed abundances of the CNO-cycle elements may be affected by evolutionary alterations."306 On the other hand. the solar C. N and O abundances were continuously revised and tended to decrease during this period.," On the other hand, the solar C, N and O abundances were continuously revised and tended to decrease during this period."307 Unfortunately. it was impossible in these cases to use the accurate meteoritic abundances. because C. N and O are incompletely condensed in meteorites. so their meteoritic abundances are signiticantly lower than the solar ones.," Unfortunately, it was impossible in these cases to use the accurate meteoritic abundances, because C, N and O are incompletely condensed in meteorites, so their meteoritic abundances are significantly lower than the solar ones."308 Magnesium. unlike C. N and O. does not have such demerits.," Magnesium, unlike C, N and O, does not have such demerits."309 First. this chemical element should not alter markedly its abundance in B stars during the MS phase.," First, this chemical element should not alter markedly its abundance in B stars during the MS phase."310 Second. its solar abundance is known now very precisely from spectroscopic and meteoritic data.," Second, its solar abundance is known now very precisely from spectroscopic and meteoritic data."311 Displaying the rather strong LHH8I.2À line in spectra of early and medium B stars. this element is appropriate as a reliable indicator of their metallicity.," Displaying the rather strong 4481.2 line in spectra of early and medium B stars, this element is appropriate as a reliable indicator of their metallicity."312 Using the high-resolution spectra of 52 B stars we effected a non-LTE analysis of the A4481.2 lline and determined the magnesium abundance., Using the high-resolution spectra of 52 B stars we effected a non-LTE analysis of the 4481.2 line and determined the magnesium abundance.313 We studied the role of the neighbouring, We studied the role of the neighbouring314curve to the right).,curve to the right).315 This is not unexpected and is discussed in Section 3.3. below., This is not unexpected and is discussed in Section \ref{ssechighm} below.316 “Phere is no evidence of a departure [rom the PS curve at amass of 64. corresponding to the size of smoothing blocks of side 4 (this is in contrast to the ηΞ case. discussed below).," There is no evidence of a departure from the PS curve at a mass of 64, corresponding to the size of smoothing blocks of side 4 (this is in contrast to the $n=-2$ case, discussed below)."317 The maximum mass of collapsed halos is quite small. less than 125 even for the largest box. L=256.," The maximum mass of collapsed halos is quite small, less than 125 even for the largest box, $L=256$."318 Given that the smallest halos to collapse in our nmoclel (apart from isolated cells) have mass 8. then this gives avery small cvnamic range.," Given that the smallest halos to collapse in our model (apart from isolated cells) have mass 8, then this gives a very small dynamic range."319 We could. force larger objects to form by allowing a larger fraction of the box to collapse (this would be legitimate if. for example. one were to regard the whole box as a single collapsed halo) however one would not then expect the evolution to be self-similar.," We could force larger objects to form by allowing a larger fraction of the box to collapse (this would be legitimate if, for example, one were to regard the whole box as a single collapsed halo) however one would not then expect the evolution to be self-similar."320 The curves for the steeper spectrum. m=2. extend to much higher masses because the spectrum has much more power on large scales than for n=Q0.," The curves for the steeper spectrum, $n=-2$, extend to much higher masses because the spectrum has much more power on large scales than for $n=0$."321 Lere we cdo see evidence of kinks at the blocking masses of 64. 512 and 4096. especially at the final output time when half the box has collapsed: there is an excess of halos of slightly higher mass and a deficit of slightlv lower mass than these.," Here we do see evidence of kinks at the blocking masses of 64, 512 and 4096, especially at the final output time when half the box has collapsed: there is an excess of halos of slightly higher mass and a deficit of slightly lower mass than these."322 Overall the spectrum is a reasonable Gt to the PS prediction at masses above 100. but shows and excess between masses of SN and 100.," Overall the spectrum is a reasonable fit to the PS prediction at masses above 100, but shows and excess between masses of 8 and 100."323 6 shows a projection of the largest halos in one L=128 box of cach spectral type at a time when half the mass has collapsed into halos., \ref{fig:proj} shows a projection of the largest halos in one $L=128$ box of each spectral type at a time when half the mass has collapsed into halos.324 Many of the irregular shapes which are visible are due to projection ellects., Many of the irregular shapes which are visible are due to projection effects.325 Our halos tend to exhibit more variety of axial ratios than in theAloclel., Our halos tend to exhibit more variety of axial ratios than in the.326. Phere the relative length of the major- and minor-axes is fixed all times at approximately 1:11.59. whereas ours start with more typically 1:1 (for collapse of isolated. blocks as in 2bb) or 1:1.5 (for the collapse of overlapping blocks as in 2ec). developping rapidlv to more complex structures with a great. variety of shapes.," There the relative length of the major- and minor-axes is fixed all times at approximately 1:1.59, whereas ours start with more typically 1:1 (for collapse of isolated blocks as in \ref{fig:halo}b b) or 1:1.5 (for the collapse of overlapping blocks as in \ref{fig:halo}c c), developping rapidly to more complex structures with a great variety of shapes."327 S shows the distribution of axial ratios for all halos of mass greater than or equal to 8 for η=0 and greater than, \ref{fig:axes} shows the distribution of axial ratios for all halos of mass greater than or equal to 8 for $n=0$ and greater than328the initial separation and the initial orbital energy such that models which start with a larger separation require a smaller initial eccentricity.,the initial separation and the initial orbital energy such that models which start with a larger separation require a smaller initial eccentricity.329 In all cases. the apparent orbit of the two galaxies becomes (or was to beein with) nearly parabolic at the present (ime. consistent with recent estimates. of the Milky WayAndromeda orbit. (see.e$...2)..," In all cases, the apparent orbit of the two galaxies becomes (or was to begin with) nearly parabolic at the present time, consistent with recent estimates of the Milky Way–Andromeda orbit \citep[see, e.g.,][] {vdM07}."330 While the rest of this paper will primarily present. the results of one particular model. we will also show that all models. vield similar estimates for the eventual merger between the Milky Way and Andromeda.," While the rest of this paper will primarily present the results of one particular model, we will also show that all models yield similar estimates for the eventual merger between the Milky Way and Andromeda."331 We will argue in refssee:time that this convergence results naturally from our assumed intragroup medium., We will argue in \\ref{ssec:time} that this convergence results naturally from our assumed intragroup medium.332 The model we choose to focus upon begins with an initial separation of 1.3 Alpe. and initializes the Milky Way and Xndromeda on an eccentric orbit «€=0.494. with a distance at. perigalacticon of 450 κρο," The model we choose to focus upon begins with an initial separation of 1.3 Mpc, and initializes the Milky Way and Andromeda on an eccentric orbit $\epsilon=0.494$, with a distance at perigalacticon of 450 kpc."333 With this orbit the initial angular velocity is 65 which could likely. originate from tical torques (??)..," With this orbit the initial angular velocity is 65, which could likely originate from tidal torques \citep{GT78,RLB89}."334 This particular moce begins with the largest separation of all our moclels ai therefore may be the best representation of the evolution of the Local Group since its decoupling from the universa expansion., This particular model begins with the largest separation of all our models and therefore may be the best representation of the evolution of the Local Group since its decoupling from the universal expansion.335 Since this model tracks the Local Group the farthest into the past. the intragroup medium. also has a significant amount of time to react to the two galaxies anc therefore is likely to be the most insensitive to its initia configuration.," Since this model tracks the Local Group the farthest into the past, the intragroup medium also has a significant amount of time to react to the two galaxies and therefore is likely to be the most insensitive to its initial configuration."336 Jo simulate the evolution of our. Local Group and in particular the interaction between the Ην Was ando Ancromeda use the publically available N-bodyfhverodvnamic coce (?).., To simulate the evolution of our Local Group and in particular the interaction between the Milky Way and Andromeda use the publically available N-body/hydrodynamic code \citep{SpGad2}.337 This. version of the code employs the “conservativeentropy formulation of Smoothee Particle Lvdrodyvnamics (SPLH.7) that conserves both energv and entropy (unlikeearlier.versionsofSPL:seec.g. 7).. while improving shock-capturing.," This version of the code employs the “conservative–entropy” formulation of Smoothed Particle Hydrodynamics \citep[SPH,][]{SHEnt} that conserves both energy and entropy \citep[unlike earlier versions of SPH; see338e.g.,][]{H93sph}, while improving shock-capturing."339 We assume that the eas is of primordial composition. and include the ellects of radiative cooling.," We assume that the gas is of primordial composition, and include the effects of radiative cooling."340 Star formation and its associated feedback: are. both included in a manner very similar to that clescribed in 2.., Star formation and its associated feedback are both included in a manner very similar to that described in \citet{Cox06}.341 As is commonly assumed. stars are stochastically formed at a rate determined by the SPII eas density (sec.c.g.2???) with an ellicieney set to match. the observed: correlation oetween star formation and gas density (?)..," As is commonly assumed, stars are stochastically formed at a rate determined by the SPH gas density \citep[see, e.g.][]{Kz92,SH03,SdMH05,342Cox06} with an efficiency set to match the observed correlation between star formation and gas density \citep{Kenn98}."343 Feedback from stellar winds and supernovae is treated in à very simplistic manner. namely the SPL particles that inve sullicient density to form stars are fixed to have an elective temperature of 107 Ix. This methodology is sinilar in principle to most of the currently. favored: models. for eedback (see.e.g..2222). and is easy to implement.," Feedback from stellar winds and supernovae is treated in a very simplistic manner, namely the SPH particles that have sufficient density to form stars are fixed to have an effective temperature of $10^5$ K. This methodology is similar in principle to most of the currently favored models for feedback \citep[see, e.g.,][]{Sp00,SH03, Stin06,Cox06}, and is easy to implement."344 Since he focus of this work is the large.scale evolution of the Local Group and the generic dynamics of the collision between he Alilky Way and. Ancromeda. the detailed treatment of he interstellar medium does not influence our primary conclusions.," Since the focus of this work is the large–scale evolution of the Local Group and the generic dynamics of the collision between the Milky Way and Andromeda, the detailed treatment of the inter–stellar medium does not influence our primary conclusions."345 Numerical resolution is a significant consideration or any computational problem., Numerical resolution is a significant consideration for any computational problem.346 For our purposes here. we require sullicient resolution to reliably follow the interaction and merger of the Milky Way and Andromeda. while maintaining the ability to perform a number of simulations with the available computational resources.," For our purposes here, we require sufficient resolution to reliably follow the interaction and merger of the Milky Way and Andromeda, while maintaining the ability to perform a number of simulations with the available computational resources."347 ‘These considerations motivated the particle number choices outlined in refsec:model.., These considerations motivated the particle number choices outlined in \\ref{sec:model}.348 Given the large. number of components. in ese simulations (stellar disks. dark halos. and intragroup =jiedium) and the desire to reduce twobody. cllects. we required all particles to have an identical mass of 210 and we emploved a universal gravitational softening eneth of 150 pe.," Given the large number of components in these simulations (stellar disks, dark halos, and intragroup medium) and the desire to reduce two–body effects, we required all particles to have an identical mass of $2\times 10^{7}$ and we employed a universal gravitational softening length of 150 pc."349 To test the sensitivity of the results to dese) parameter choices. we also ran a higher resolution Persion of one model with 30 times the barvonic disk mass resolution (and therefore number of particles) and 2 times 10 resolution of the dark matter and intragroup medium.," To test the sensitivity of the results to these parameter choices, we also ran a higher resolution version of one model with 30 times the baryonic disk mass resolution (and therefore number of particles) and 2 times the resolution of the dark matter and intragroup medium."350 In lis case we also decreased the gravitational softening length X the barvons by a factor of 3. and increased that of the ark matter by a factor of 3.," In this case we also decreased the gravitational softening length of the baryons by a factor of 3, and increased that of the dark matter by a factor of 3."351 While this test. vielded much »tter resolution of the stellar disks and in particular the idal material. the general merger dynamics were identical o the low resolution version.," While this test yielded much better resolution of the stellar disks and in particular the tidal material, the general merger dynamics were identical to the low resolution version."352 In Figures 2. through 6 we present the basic propertics of he dynamical evolution of our Local Group. from 5 Car in he past and until 10 Gar into the future. bevond the merger ime between the Milky Way aid Andromeda.," In Figures \ref{fig:starimages}~ through \ref{fig:crelvel} we present the basic properties of the dynamical evolution of our Local Group, from 5 Gyr in the past and until 10 Gyr into the future, beyond the merger time between the Milky Way and Andromeda."353 Most. of the eatures present in these figures are generic to binary galaxy interactions. and have been described in great detail by prior studies (see.e.g.27227).," Most of the features present in these figures are generic to binary galaxy interactions, and have been described in great detail by prior studies \citep[see, e.g.,][]{TT72,BH91,354BH92rev,MH96,Cox06}."355 However. we will review some of he details that are particularly relevant to the Local Group. ancl subsequently highlight the unique status of our own Sun which will be a participant in this galaxy. interaction.," However, we will review some of the details that are particularly relevant to the Local Group, and subsequently highlight the unique status of our own Sun which will be a participant in this galaxy interaction."356 The uture evolution of structures bevond the local group was simulated elsewhere (2??7)..," The future evolution of structures beyond the local group was simulated elsewhere \citep{NL03,NL04,Bus03,Bus05}."357 ‘To begin. Figures 2. and 3. present the entire evolution of the Local Group from the point of view of a. distant observer.," To begin, Figures \ref{fig:starimages}~ and \ref{fig:gasimages} present the entire evolution of the Local Group from the point of view of a distant observer."358" These images begin at the start of our simulation. when the Milky Way anc Andromeda: are separated: by 1.3 Alpe. and include the present state of the Local Croup (labeled. ""Today) and the eventual merger of the Milly Way and Andromeda."," These images begin at the start of our simulation, when the Milky Way and Andromeda are separated by 1.3 Mpc, and include the present state of the Local Group (labeled “Today”) and the eventual merger of the Milky Way and Andromeda."359 As a guide to the eve. each. panel includes the trajectory of both the Milkv Way and Andromeda.," As a guide to the eye, each panel includes the trajectory of both the Milky Way and Andromeda."360 Shown in Ligure 2. is the evolution. of the stellar component. which in our simulation only has contributions from the Milkv Way anc Andromeda. as we ignore any structure smaller than the two largest galaxies in the Local Croup.," Shown in Figure \ref{fig:starimages} is the evolution of the stellar component, which in our simulation only has contributions from the Milky Way and Andromeda as we ignore any structure smaller than the two largest galaxies in the Local Group."361 Figure 3. presents the projected gas distribution during the interaction. with panels shown at the same times as in Figure 2..," Figure \ref{fig:gasimages} presents the projected gas distribution during the interaction, with panels shown at the same times as in Figure \ref{fig:starimages}."362 Here. the colorscale has been stretched to emphasize the abundant quantity of lowdensity gas that is spread. throughout the local group., Here the color–scale has been stretched to emphasize the abundant quantity of low–density gas that is spread throughout the local group.363 The initial condition of our Local Group model assumes a uniform cistribution of warm eas. however the gas quickly responds to. the nonuniform potential.," The initial condition of our Local Group model assumes a uniform distribution of warm gas, however the gas quickly responds to the non–uniform potential."364 In. particular gas is accreted and shocked to form a hvelrostatic halo of warm gas around the Alilky Wavy and Andromeda galaxies., In particular gas is accreted and shocked to form a hydrostatic halo of warm gas around the Milky Way and Andromeda galaxies.365 The gas cistribution is also clearly allected by the interaction itself. as shocks," The gas distribution is also clearly affected by the interaction itself, as shocks"366drastically changed by a gas stream and depend strongly on the mass and its internal structure of the cloud. i.e. mainly on its binding energy.,"drastically changed by a gas stream and depend strongly on the mass and its internal structure of the cloud, i.e. mainly on its binding energy."367 In general. the relative motion of a subsonically hot plasma stream stabilizes the clouds.," In general, the relative motion of a subsonically hot plasma stream stabilizes the clouds."368 Without heat conduction. clouds with their initial states close to or inside the KH-unstable regime suffer from huge mass loss in the form of stripped-off cloudlets.," Without heat conduction, clouds with their initial states close to or inside the KH-unstable regime suffer from huge mass loss in the form of stripped-off cloudlets."369" While a small homogeneous cloud (nodel K) is stable for about 5 7,, and then strongly exposec to disruption into small gas packets. small dense clouds (model E) can avoid the transition into the KH-unstable state ard resist the violent hot plasma so that mass loss or even any strong deformation of the cloud does not occur."," While a small homogeneous cloud (model K) is stable for about 5 $\tau_{\mbox{\tiny dyn}}$ and then strongly exposed to disruption into small gas packets, small dense clouds (model E) can avoid the transition into the KH-unstable state and resist the violent hot plasma so that mass loss or even any strong deformation of the cloud does not occur."370 Large massive clouds (model U) lose about of their mass within 5 nud may dissolve on larger timescales., Large massive clouds (model U) lose about of their mass within 5 $\tau_{\mbox{\tiny dyn}}$ and may dissolve on larger timescales.371detailed analysis of figure 2. where the core temperaturenumostv (1;L) relationship obtained iu this work solid. liue and in IHausen (1999) dotted line are shown in the upper paucl. whereas in the lower paucl hei relative differeuce is shown as a function of the core cluperature.,"detailed analysis of figure 2, where the core temperature--luminosity $T_{\rm c}-L$ ) relationship obtained in this work — solid line — and in Hansen (1999) — dotted line — are shown in the upper panel, whereas in the lower panel their relative difference is shown as a function of the core temperature."372 As it can be seen there. for a given T; the uminositv is about lavecr dowutolos(L/L.)2 L5 and. thus. the model envelopes of Hansen (1999) are systematically more transparent than our envelopes for he same Z.. resulting iu a more efficient cooliug of the white dwarf interior.," As it can be seen there, for a given $T_{\rm c}$ the luminosity is about larger down to $\log(L/L_{\sun})\simeq -4.5$ and, thus, the model envelopes of Hansen (1999) are systematically more transparent than our envelopes for the same $T_{\rm c}$, resulting in a more efficient cooling of the white dwarf interior."373 To be precise. let us quantify how this affects the cooling sequences.," To be precise, let us quantify how this affects the cooling sequences."374 For Iuniuosities smaller thui Ly=10?L:; the contribution of thermal neutrinos aud unclear reactions are negligible aud. thus. oue cau sately asstune that the sole contribution to the cooling process is the release of binding energy.," For luminosities smaller than $L_0=10^{-2}L_{\sun}$ the contribution of thermal neutrinos and nuclear reactions are negligible and, thus, one can safely assume that the sole contribution to the cooling process is the release of binding energy."375 Therefore we cau write: Accordingly. the difference in the cooling times between both cooling sequences can be easily estimated: where τν1ο) stands for the TZ.E relationship derived in this paper aud Zpgt(T.) is the oue derived by IHauseu 1999).," Therefore we can write: Accordingly, the difference in the cooling times between both cooling sequences can be easily estimated: where $L_{\rm TW}(T_{\rm c})$ stands for the $T_{\rm c}-L$ relationship derived in this paper and $L_{\rm BH}(T_{\rm c})$ is the one derived by Hansen (1999)."376 We have independently computed a set of binding snereies with the same equation of state described iu 1ο previous section and used equation (2) to obtain an tinte of the difference introduced by the differences i je transparency of the cuvelope., We have independently computed a set of binding energies with the same equation of state described in the previous section and used equation (2) to obtain an estimate of the difference introduced by the differences in the transparency of the envelope.377 At log(L/L.)=L5 we eot Afz2.1 Cyr. which is in good agreecinent with the value derived from the evolutionary code (1.8 Cr).," At $\log(L/L_{\sun})=-4.5$ we got $\Delta t\simeq 2.1$ Gyr, which is in good agreement with the value derived from the evolutionary code (1.8 Gyr)."378 Thus. us difference can be mainly ascribed to the differences iu 1ο frauspareuceyv of the adopted model envelopes.," Thus, this difference can be mainly ascribed to the differences in the transparency of the adopted model envelopes."379 Now the question is. why is there a difference in the nodel envelopes?," Now the question is, why is there a difference in the model envelopes?"380 This question cannot be answered , This question cannot be answered categorically.381Iu fact. we are using the same thicknesses for the IT aud lle lavers. the same euvelope EOS aud the same OPAL (Z= 0) opacities for T>6000 IX. but not the same model atmospheres for the boundary conditions.," In fact, we are using the same thicknesses for the H and He layers, the same envelope EOS and the same OPAL $Z=0$ ) opacities for $T\geq6000$ K, but not the same model atmospheres for the boundary conditions."382 However we do have indirect wavs of checking the consistency. of our results., However we do have indirect ways of checking the consistency of our results.383 We recoimputed the cooling sequence of our 0.606 AL: white dwarf using a erev T(r) relation for deriving the boundary conditions., We recomputed the cooling sequence of our 0.606 $M_{\sun}$ white dwarf using a grey $T(\tau)$ relation for deriving the boundary conditions.384 We found that the {ο£L relationship derived in this way was coincident. as loug as Tig=GOOQ Tk. with the one obtained using the model atiuosplieres boundary conditions. mn agreement with the fudines bv Tausen (1999).," We found that the $T_{\rm c}-L$ relationship derived in this way was coincident, as long as $T_{\rm eff}\geq 6000$ K, with the one obtained using the model atmospheres boundary conditions, in agreement with the findings by Hansen (1999)."385 This allows us to directly compare our 7;L rolatioushipa (for τω=6000 IK) with the iudepenudoeut results of Althaus Beuvenuto (1998) for their 0.600 AL; white dwarf cooling track., This allows us to directly compare our $T_{\rm c}-L$ relationship (for $T_{\rm eff}\geq 6000$ K) with the independent results of Althaus Benvenuto (1998) for their 0.600 $M_{\sun}$ white dwarf cooling track.386 This calculation adopts our sale imetallicitv aud thickness for the We and II lavers., This calculation adopts our same metallicity and thickness for the He and H layers.387 Moreover. Althaus Benvenuto (1998) also used the same EOS in the envelope and the same OPAL opacities for T26000 Ik. The oulv differences of this calculation with respect to our calculation aud that of Hansen (1999) are threefold.," Moreover, Althaus Benvenuto (1998) also used the same EOS in the envelope and the same OPAL opacities for $T\geq 6000$ K. The only differences of this calculation with respect to our calculation and that of Hansen (1999) are threefold."388 First. Althaus Deuvenuto (1998) used a exev P(r) relation for deriving the boundary conditious.," First, Althaus Benvenuto (1998) used a grey $T(\tau)$ relation for deriving the boundary conditions."389 As we Lave shown. this procedure is well justified as long as Digg=6000 IX. Second. Althaus Benvenuto (1998) adopted a slightly differeut C/O profile for the core.," As we have shown, this procedure is well justified as long as $T_{\rm eff}\geq 6000$ K. Second, Althaus Benvenuto (1998) adopted a slightly different C/O profile for the core."390" Since the adopted internal C/O stratification docs not affect at all the derived 1.1, relationship. the slightly differcut C/O profile adopted by Althaus Benvenuto (1998) does not iuflueuce the result of the comparison."," Since the adopted internal C/O stratification does not affect at all the derived $T_{\rm c}-L$ relationship, the slightly different C/O profile adopted by Althaus Benvenuto (1998) does not influence the result of the comparison."391 Third. they ciploved the full.spectra. turbulence theory of convection by Canuto. Goldiiau Mazztoelli (1996) instead of the mixing leugth theory. for the computation of the convective superadiabatie eracdicut the cuvelope.," Third, they employed the full–spectrum turbulence theory of convection by Canuto, Goldman Mazzitelli (1996) instead of the mixing length theory, for the computation of the convective superadiabatic gradient in the envelope."392 However. the treatiieut of supcradiabatic categorically!convection does not affect the Το relationship.," However, the treatment of superadiabatic convection does not affect the $T_{\rm c}-L$ relationship."393 Tn the upper panel of figure 2 we also show the core temperatureluninosity relationship derived by Althaus Benvenuto (1998) as a dasheddotted. line. whereas in the lower panel of this Segure the relative difference with respect to the present calculation is shown.," In the upper panel of figure 2 we also show the core temperature–luminosity relationship derived by Althaus Benvenuto (1998) as a dashed–dotted line, whereas in the lower panel of this figure the relative difference with respect to the present calculation is shown."394 Our result closely follows that of Althaus Deuveuuto (1998) in the core temperature range when {μι=6000 EK. and therefore it is quite apparent from this feure that for some reason the model euvelopes of Hansen (1999) appear to be. at least in this temperature range. far more transparent than ours.," Our result closely follows that of Althaus Benvenuto (1998) in the core temperature range when $T_{\rm eff}\geq 6000$ K, and therefore it is quite apparent from this figure that for some reason the model envelopes of Hansen (1999) appear to be, at least in this temperature range, far more transparent than ours."395 It is however remarkable that the calculation reported iu the present work and that of Hansen (1999) are parallel for almost the full rauge of Iuniunosities studied here., It is however remarkable that the calculation reported in the present work and that of Hansen (1999) are parallel for almost the full range of luminosities studied here.396 Finally both our calculation and that of Tausen (1999) differ considerably at low 7; from the calculation of Althaus Benvenuto (1998). as is expected because of the improved atinospheric treatiueut at very low luminosities.," Finally both our calculation and that of Hansen (1999) differ considerably at low $T_{\rm c}$ from the calculation of Althaus Benvenuto (1998), as is expected because of the improved atmospheric treatment at very low luminosities."397 For the sake of completcucss we also show the relationship obtained by Wood (1995) as a long dashed line (he also used a ervey T(r) relationship to derive the boundary conditions). although we refrain from doiug a detailed comparison with our results because this cooling sequence was computed using a differcut EOS for the white dwarf envelope.," For the sake of completeness we also show the relationship obtained by Wood (1995) as a long dashed line (he also used a grey $T(\tau)$ relationship to derive the boundary conditions), although we refrain from doing a detailed comparison with our results because this cooling sequence was computed using a different EOS for the white dwarf envelope."398 Note. however. that at high," Note, however, that at high"399of disk is important to investigate the disk evolution. and fragmentation⋅ mlor /zz101 vvears.,of disk is important to investigate the disk evolution and fragmentation for $t\gtrsim 10^4$ years.400 In this study. no model shows the formation of a star-λαοί system during the main aceretion phase because the secondary object continues to increase its mass and. finally exceeds the hyvdrogen-burning limit (AZ0.08 MM).," In this study, no model shows the formation of a star-planet system during the main accretion phase because the secondary object continues to increase its mass and finally exceeds the hydrogen-burning limit $M\gtrsim0.08$ $_\odot$ )."401 On he other hand. Vorobvov&Basu(2010a) and. Machidaοἱal.(2010). showed the formation of a star-planct svsten during the main aceretion phase.," On the other hand, \citet{vorobyov_basu10a} and \citet{machidaetal10} showed the formation of a star-planet system during the main accretion phase."402 The dilference is thought o be caused by treatment of the protostar and sink., The difference is thought to be caused by treatment of the protostar and sink.403 In Vorobvov&Basu(2010a) and Machida (2010).. the protostar (or sink cell) is fixed at the center of the computational domain.," In \citet{vorobyov_basu10a} and \citet{machidaetal10}, the protostar (or sink cell) is fixed at the center of the computational domain."404 Lt is expected. that. such reatment promotes fragmentation., It is expected that such treatment promotes fragmentation.405 In reality. the density luctuation arising around the protostar can cancel out by movement of the protostar.," In reality, the density fluctuation arising around the protostar can cancel out by movement of the protostar."406 Thus. fragmentation tends to occur when the protostar is fixed.," Thus, fragmentation tends to occur when the protostar is fixed."407 In αστον. Vorobxov&Basu(2010a) ancl Machidaοἱal.(2010) did not impose the sink on fragments formed in the circumstellar disk.," In addition, \citet{vorobyov_basu10a} and \citet{machidaetal10} did not impose the sink on fragments formed in the circumstellar disk."408 Instead. they suppressed. further collapse of fragments with adiabatie equation of state.," Instead, they suppressed further collapse of fragments with adiabatic equation of state."409 Such treatment decreases the mass accretion onto fragments in some degree., Such treatment decreases the mass accretion onto fragments in some degree.410 On the other hand. our sink treatment may overestimate the mass accretion onto fragments or protostar.," On the other hand, our sink treatment may overestimate the mass accretion onto fragments or protostar."411 So far. few authors have investigated the evolution of circumstellar disk. from molecular cloud core.," So far, few authors have investigated the evolution of circumstellar disk from molecular cloud core."412 With an isothermal equation of state. WKratterefaf(2010). showed that fragmentation occurs in the circumstellar disk with a wide parameter space during the carly stage in the main accretion phase and claimed that fragmentation Lrecqucnthy occurs when the disk-to-stellar mass ratio is greater than unity.," With an isothermal equation of state, \citet{ketal10} showed that fragmentation occurs in the circumstellar disk with a wide parameter space during the early stage in the main accretion phase and claimed that fragmentation frequently occurs when the disk-to-stellar mass ratio is greater than unity."413" However. their assumption of isothermality seenis not to be valid. for the disk evolution of the carly main accretion phase. because the gas becomes opaque and behaves adiabatically when the gas density exceeds. the critical density of p,=102$qpii&cm ο. 2010))."," However, their assumption of isothermality seems not to be valid for the disk evolution of the early main accretion phase, because the gas becomes opaque and behaves adiabatically when the gas density exceeds the critical density of $\rho_c \simeq 10^{-13}-10^{- 14} {\rm g~cm^{-3}}$ (e.g., )."414 In. addition. the radiative cooling can allect the disk evolution ~10! vears after the protostar formation as described in refsec:cooling..," In addition, the radiative cooling can affect the disk evolution $\sim 10^4$ years after the protostar formation as described in \\ref{sec:cooling}."415 Since the adiabatic equation. of. state stabilizes the circumstellar clisk. fragmentation barely occurs in our calculation even when the disk-to-stellar mass ratio exceeds unity.," Since the adiabatic equation of state stabilizes the circumstellar disk, fragmentation barely occurs in our calculation even when the disk-to-stellar mass ratio exceeds unity."416 Thus. Ixrattere£a£.(2010) may overestimate the fragmentation condition. while our calculation may unclerestimate it because of lack of radiative cooling.," Thus, \citet{ketal10} may overestimate the fragmentation condition, while our calculation may underestimate it because of lack of radiative cooling."417 Walchefa£.(2009) also stucied the circumstellar clisk formation with the aciabatic equation ofstate and radiative cooling., \citet{wetal09} also studied the circumstellar disk formation with the adiabatic equation of state and radiative cooling.418 Vhey showed no fragmentation in the circumstellar disk. because the disk becomes very hot. during the early stage of main accretion. phase.," They showed no fragmentation in the circumstellar disk, because the disk becomes very hot during the early stage of main accretion phase."419 Vheir spatial resolution is. iowever. somewhat coarse: the minimum smoothing length of their study is Z4=2 AU.," Their spatial resolution is, however, somewhat coarse; the minimum smoothing length of their study is $h_{\rm min}= 2$ AU."420 On the other hand. P~3 AU in our simulations.," On the other hand, $h_{\rm min}\sim0.3$ AU in our simulations."421 Lo addition. they restricted their initial conditions to rapidlv rotating cases 67>107) to investigate cisk evolution before the central density becomes ugh.," In addition, they restricted their initial conditions to rapidly rotating cases $\beta > 10^{-2}$ ) to investigate disk evolution before the central density becomes high."422 The observation suggested that molecular cloud cores iie the rotational energy of 10.3<3«0.07 with a typical value of 3270.02 (Caselliefa£2002)., The observation suggested that molecular cloud cores have the rotational energy of $10^{-4}<\beta< 0.07$ with a typical value of $\beta \simeq 0.02$ \citep{cetal02}.423. Thus. they studied he cloud evolution in the limited parameter range.," Thus, they studied the cloud evolution in the limited parameter range."424 We have carried out. hvdro-dvnamical. simulation to investigate the evolution of the circumstellar disk with two non-dimensional parameters representing the thermal anc rotational energy of the initial cloud., We have carried out hydro-dynamical simulation to investigate the evolution of the circumstellar disk with two non-dimensional parameters representing the thermal and rotational energy of the initial cloud.425 Phe thermal energy a is related to the mass accretion rate onto the circumstellar disk as Mask=aUT+ (seo. Machidaefaf 2011).," The thermal energy $\alpha$ is related to the mass accretion rate onto the circumstellar disk as $\dot{M}_{\rm disk }= \alpha^{-3/2} c_s^3 G^{-1}$ (see, \citealt{machidaetal11}) )."426 Thus. smaller a provides a high aceretion rate onto the circumstellar disk. ancl vice versa.," Thus, smaller $\alpha$ provides a high accretion rate onto the circumstellar disk and vice versa."427 On the other hand. the initial rotational energy that is represented. by parameter dis related to the disk radius.," On the other hand, the initial rotational energy that is represented by parameter $\beta$ is related to the disk radius."428 The centrifugal radius of theinitial cloud is related to 3 as regc=3402. where Ry is the initial cloud radius.," The centrifugal radius of theinitial cloud is related to $\beta$ as $r_{\rm cent} = 3 R_0 \beta$, where $R_0$ is the initial cloud radius."429 Thus. with larger 2. the cloud forms a larger disk in the main accretion phase.," Thus, with larger $\beta$, the cloud forms a larger disk in the main accretion phase."430 La other words. with larger 2. a large fraction of the in-falling matter accretes onto the disk. rather than directly onto the primary protostar.," In other words, with larger $\beta$, a large fraction of the in-falling matter accretes onto the disk, rather than directly onto the primary protostar."431 As a result. smaller a and larger 3 increase disk surface density and makes a gravitationally unstable clisk.," As a result, smaller $\alpha$ and larger $\beta$ increase disk surface density and makes a gravitationally unstable disk."432 On the other hand. the non-axisvmimetric structure arose in such unstable disk can stabilize the disk. because it can redistribute the angular momentum ancl promote mass accretion onto the protostar.," On the other hand, the non-axisymmetric structure arose in such unstable disk can stabilize the disk, because it can redistribute the angular momentum and promote mass accretion onto the protostar."433 Thus. no fragmentation occurs when a strong non-axisvmuametricitv grows and transfers sullicient angular. momentum outward.," Thus, no fragmentation occurs when a strong non-axisymmetricity grows and transfers sufficient angular momentum outward."434 By contrast. the disk. becomes highly eravitationally unstable ancl shows fragmentation when non-axisvmmetric structure does not erow sullicienth or when the growth timescale of the non-axisvmmetricitv is much longer than the disk growth timescale.," By contrast, the disk becomes highly gravitationally unstable and shows fragmentation when non-axisymmetric structure does not grow sufficiently or when the growth timescale of the non-axisymmetricity is much longer than the disk growth timescale."435 “Phus. fragmentation condition depends also on the growth. of the non-axisvmmetriciv. which is closely related to parameters o. anc 3 because they determine the evolution of the mass and angular momentum of the disk.," Thus, fragmentation condition depends also on the growth of the non-axisymmetriciy, which is closely related to parameters $\alpha$ and $\beta$ because they determine the evolution of the mass and angular momentum of the disk."436 With parameters a and. 2. we found that the disk evolution is qualitatively classified: into four naiocles: protostar dominant. massive disk. carly fragmentation and late fragmentation modes.," With parameters $\alpha$ and $\beta$ , we found that the disk evolution is qualitatively classified into four modes: protostar dominant, massive disk, early fragmentation and late fragmentation modes."437 The schematic classification of, The schematic classification of438unique dependence. with the hope that observations of starbursts can be used to assess ECS kick velocities and progenitor mass ranges.,"unique dependence, with the hope that observations of starbursts can be used to assess ECS kick velocities and progenitor mass ranges."439 We note that. iu the Simall Maegellenic Cloud (SAIC). dominated by 2£0 MMy-old stellar populations. a systematic overabundance of Be XRDs las been observed (?7) potentially making the SMC a unique laboratory for ECS NS formation.," We note that, in the Small Magellenic Cloud (SMC), dominated by $\simeq 40$ Myr-old stellar populations, a systematic overabundance of Be XRBs has been observed \citep{2000A&A...359..573H, 2004ApJ...609..133M} potentially making the SMC a unique laboratory for ECS NS formation."440 For our modeling of IINKD. formation aud. evolution iu starbursts we onploy a sophisticated. population svuthesis code. StarTrack. described in extensive detail in 7.. which assumes that stellar dvuamical interactions are not significant compared to the effects of binary evolution for the star formation coucitious under consideration.," For our modeling of HMXB formation and evolution in starbursts we employ a sophisticated population synthesis code, $StarTrack$, described in extensive detail in \citet{2008ApJS..174..223B}, which assumes that stellar dynamical interactions are not significant compared to the effects of binary evolution for the star formation conditions under consideration."441 We note that the paraimcter space of Alonte Carlo population svuthesis is very large. and thus a full exploration is not possible.," We note that the parameter space of Monte Carlo population synthesis is very large, and thus a full exploration is not possible."442 Instead. we consider a default model (described in detail iu ?)) and we vary sole binary evolution aud EC'S-rclated parameters with the purpose of hiehliehtiug their effects ou the proposed ECS probe.," Instead, we consider a default model (described in detail in \citet{2008ApJS..174..223B}) ) and we vary some binary evolution and ECS-related parameters with the purpose of highlighting their effects on the proposed ECS probe."443 Uere we briefly sununarize the lain assunrptious and paraueters relevant to tlis studs., Here we briefly summarize the main assumptions and parameters relevant to this study.444 We enplov a delta function star formation episode at solu iictallicity adopting: (1) a Salpeter 7°) initial mass function with primary masses above { M. and secondary masses above 0.15 ADL: (2) a flat mass ratio distribution: (3) a distribution of initial binary separations that is flat in the logarithm with an upper ΠΠ of 10° Ro. and a lower Init such that the primary star initially fills at most half of its Roche Lobe (?).. and (1) a thermal distribution for initial eccentricities (?2)..," We employ a delta function star formation episode at solar metallicity adopting: (1) a Salpeter $^{-2.35}$ ) initial mass function with primary masses above 4 $_\odot$ and secondary masses above 0.15 $_\odot$; (2) a flat mass ratio distribution; (3) a distribution of initial binary separations that is flat in the logarithm with an upper limit of $^5$ $_\odot$ and a lower limit such that the primary star initially fills at most half of its Roche Lobe \citep{1983ARA&A..21..343A}, and (4) a thermal distribution for initial eccentricities \citep{1975MNRAS.173..729H}."445" We set the πακ NS mass at 2.5 M, and craw natal kicks for “standard” ICC-SN events from a single Maxwellian kick distribution with mean265 lans ? (?)..", We set the maximum NS mass at 2.5 $_\odot$ and draw natal kicks for “standard” ICC-SN events from a single Maxwellian kick distribution with mean265 km $^{-1}$ \citep{2005MNRAS.360..974H}.446 Ilicks are potentially associated with BIT formation as well (see? for the strongest evidence at present for a DII kick)., Kicks are potentially associated with BH formation as well (see \citet{2009ApJ...697.1057F} for the strongest evidence at present for a BH kick).447 For BUs formed through SNe explosions aud subsequent fallback of material we multiply the normal Maxwellian kick by the fraction of the SN ejecta which is ultimately lost from the system., For BHs formed through SNe explosions and subsequent fallback of material we multiply the normal Maxwellian kick by the fraction of the SN ejecta which is ultimately lost from the system.448 Usually DIT formation at higher masses through direct collapse is assumed to be orfectle svaunetrie: here we adopt a simall kick of he NS kick). for reasons discussed in detail in Section L..," Usually BH formation at higher masses through direct collapse is assumed to be perfectly symmetric; here we adopt a small kick of the NS kick), for reasons discussed in detail in Section \ref{disc}."449 To obtain statistically significant results. we sample at east LO® initial binaries for cach set of input parameters and we evolve the systems for MM.," To obtain statistically significant results, we sample at least $^6$ initial binaries for each set of input parameters and we evolve the systems for Myr."450 However. we stress that the models and ΧΙΟ nmuubers preseuted rere are not normalized to match anv specific observed system. since we are purely interested duo examine herelatives ΑΟ nuubers as a function of starburst age.," However, we stress that the models and XRB numbers presented here are not normalized to match any specific observed system, since we are purely interested in examining the XRB numbers as a function of starburst age."451 — Iu order to compare our results with observations. we must determine the X-rav luuainosity. Ly. based on the calculated mass-trauster rate for both wind-fed and Roche-lobe-overflow systems.," 	 In order to compare our results with observations, we must determine the X-ray luminosity, $L_X$, based on the calculated mass-transfer rate for both wind-fed and Roche-lobe-overflow systems."452 We apply iji estimated correction for the energy. baud as described aud justified in ? (Section 9.1)., We apply an estimated correction for the energy band as described and justified in \citet{ 2008ApJS..174..223B} (Section 9.1).453 We ijidvze the IINEND. population with Ly in excess of 10° core il. appropriate for obsorvatious of nearby star-forming galaxies.," We analyze the HMXB population with $L_X$ in excess of $10^{32}$ erg $^{-1}$, appropriate for observations of nearby star-forming galaxies."454 Au muportant problem in the population svuthesis of binary stars is the treatinent of conmnon envelope (CE) phases., 	 An important problem in the population synthesis of binary stars is the treatment of common envelope (CE) phases.455 Tu our smiulations. CE eveuts are treated using the usual energy. formatlisin described by ?orbits... for stars which have established a clear corc-cnvelope boundary.," In our simulations, CE events are treated using the usual energy formalism described by \citet{1984ApJ...277..355W}, for stars which have established a clear core-envelope boundary."456 In this paper. we adopt a value for the CE efficiency of ac = IL.," In this paper, we adopt a value for the CE efficiency of $\alpha_{CE}$ = 1."457 However. in our default models. we assume that a CE phase involving a donor star on the main sequence (MS) or hertzspruug eap (IG) leads to a binary merger (27?)..," However, in our default models, we assume that a CE phase involving a donor star on the main sequence (MS) or hertzsprung gap (HG) leads to a binary merger \citep{2008ApJS..174..223B, 2000ARA&A..38..113T}."458" Following ?.. massive stars are assumed to explode in ECS eveuts if the Πο core mass at the beginning of the asvinptotic giant brauch (ACB) is between 1.83-2.25 M, (see also ?))."," Following \citet{2000MNRAS.315..543H}, , massive stars are assumed to explode in ECS events if the He core mass at the beginning of the asymptotic giant branch (AGB) is between 1.83-2.25 $_\odot$ (see also \citet{2007arXiv0706.4096I}) )."459 This choice. in effect. selects specific initial lnass ranges which depend on the binary evolution of the progenitors.," This choice, in effect, selects specific initial mass ranges which depend on the binary evolution of the progenitors."460 Towever. given the uncertaiufies involved in selecting this mass range. we examine a nunber of Ile core mass ranges in what follows.," However, given the uncertainties involved in selecting this mass range, we examine a number of He core mass ranges in what follows."461 We assume that ECS natal kicks follow a \laxwellian distribution with a sunaller mean than ICC-SN kicks. thus we linearly. scale down the “standard”.. ICC-SN AMaswellian distribution by varving factors.," We assume that ECS natal kicks follow a Maxwellian distribution with a smaller mean than ICC-SN kicks, thus we linearly scale down the “standard” ICC-SN Maxwellian distribution by varying factors."462 The mass of ECS-formed NS is assumed equal to AMAL. (2??).. although we note that 7.. ? and ? find slishtlv higher cud masses for single star ECS events (1.358 - 1.1 M...," The mass of ECS-formed NS is assumed equal to $_\odot$ \citep{1987ApJ...322..206N, 2004ApJ...612.1044P, 2007arXiv0706.4096I}, although we note that \citet{2006ApJ...644.1063D}, \citet{2006A&A...450..345K} and \citet{2008ApJ...675..614P} find slightly higher end masses for single star ECS events (1.338 - 1.4 $_\odot$ )."463 Exanuuuation of our simulation results in terms of the iuuber of IINEXNDs as a function of starburst age reveals an intriguing role of EC'S NS formation: ECS events cau dominate IINEND. formation between 20 and Αλία yost-starburst. creating a clearly ideutified “bump” iu he time evolution of TAENB nuiibers (sec Figure 1)).," Examination of our simulation results in terms of the number of HMXBs as a function of starburst age reveals an intriguing role of ECS NS formation: ECS events can dominate HMXB formation between 20 and Myr post-starburst, creating a clearly identified “bump” in the time evolution of HMXB numbers (see Figure \ref{ecsplot}) )."464 At any eivennctallicity. the width aud relative height of this is primarily dependent on two parameters: the vpical ECS natal kick magnitude aud the massrauge of ECSprogeuitors.," At any given metallicity, the width and relative height of this is primarily dependent on two parameters: the typical ECS natal kick magnitude and the massrange of ECSprogenitors."465 We first exinume the effect of ECS kicks (Figure 1.. top ucl).," We first examine the effect of ECS kicks (Figure \ref{ecsplot}, , top panel)."466 We typically find two significant bursts of IINI, We typically find two significant bursts of HMXB467 We typically find two significant bursts of IININ, We typically find two significant bursts of HMXB468 We typically find two significant bursts of IININD, We typically find two significant bursts of HMXB4696.,.470" Therefore, we estimate this fraction as the ratio of the azimuthal angular frequency of the orbiting satellite to the angular frequency of the satellite’s mass shell."," Therefore, we estimate this fraction as the ratio of the azimuthal angular frequency of the orbiting satellite to the angular frequency of the satellite's mass shell."471" Consequently, the torque on the satellite mass shell becomes: 'This torque leads to expansion and the expansion rate can be estimated as This expansion reduces the satellite’s density as Ap "," Consequently, the torque on the satellite mass shell becomes: This torque leads to expansion and the expansion rate can be estimated as This expansion reduces the satellite's density as $\Delta \rho \propto472-\frac{\Delta r}{r^{4}}$ ."473We also use this relationship to compute the mass loss in At.Step (iv) of the algorithm above., We also use this relationship to compute the mass loss in Step (iv) of the algorithm above.474" 'The mass loss histories for the circular orbit simulation, the eccentric orbit simulation, and the inner orbit simulation are compared with the results of our mass-loss algorithm in Figs."," The mass loss histories for the circular orbit simulation, the eccentric orbit simulation, and the inner orbit simulation are compared with the results of our mass-loss algorithm in Figs."475" 22 — 24,, respectively."," \ref{fig:massloss.XC1} – \ref{fig:massloss.XK2}, respectively."476" For the circular orbit case, there are no gravitational shocks."," For the circular orbit case, there are no gravitational shocks."477 Fig., Fig.478 22 shows two analytic estimates: andTorque.., \ref{fig:massloss.XC1} shows two analytic estimates: and.479 The estimate only includes tidal truncation and predicts negligible mass loss., The estimate only includes tidal truncation and predicts negligible mass loss.480 The estimate includes both the resonant torque approximation and tidal truncation., The estimate includes both the resonant torque approximation and tidal truncation.481 Its mass loss history is much more similar to the simulation: more than of the original mass is lost., Its mass loss history is much more similar to the simulation: more than of the original mass is lost.482 This suggests that mass loss for a satellite on a circular orbit mainly results from resonant torques and our algorithm for resonant torque provides a dramatically improved description., This suggests that mass loss for a satellite on a circular orbit mainly results from resonant torques and our algorithm for resonant torque provides a dramatically improved description.483" For the eccentric orbit and inner orbit simulation cases, the gravitational shock plays an important role in driving mass loss."," For the eccentric orbit and inner orbit simulation cases, the gravitational shock plays an important role in driving mass loss."484 Figs., Figs.485 23 and 24 compares our mass loss algorithm to the simulations., \ref{fig:massloss.XE1} and \ref{fig:massloss.XK2} compares our mass loss algorithm to the simulations.486" Here, we include the model, the impulse approximation with the Spitzer correction [Shock(S)], the impulse approximation with the Weinberg correction [Shock(W)]], and the impulse approximation with Weinberg correction together with our resonant torque approximation Torque]]."," Here, we include the model, the impulse approximation with the Spitzer correction ], the impulse approximation with the Weinberg correction ], and the impulse approximation with Weinberg correction together with our resonant torque approximation ]."487 All the estimates include tidal truncation., All the estimates include tidal truncation.488 The model best represents the mass loss seen in the simulation while the with no resonant torque predicts less mass loss than that seen., The model best represents the mass loss seen in the simulation while the with no resonant torque predicts less mass loss than that seen.489 The importance of the resonant torque is most obvious for the inner orbit simulation., The importance of the resonant torque is most obvious for the inner orbit simulation.490" Compared to the simulation, the estimate including the shock and the resonant torque [Shock(W)--Torque]] does significantly better estimating the mass loss in the simulation than that of the shock alone, which significantly underpredicts the mass loss."," Compared to the simulation, the estimate including the shock and the resonant torque ] does significantly better estimating the mass loss in the simulation than that of the shock alone, which significantly underpredicts the mass loss."491 Tidal truncation alone Shock]| shows the worst agreement., Tidal truncation alone ] shows the worst agreement.492could not be well constrained by the PCA: we thus fixed the energy of the line to lie between ~ 6 keV and 7.5 keV. An additional line at 2 keV (due to calibration problems) was sometimes needed in XRT.,could not be well constrained by the PCA: we thus fixed the energy of the line to lie between $\sim$ 6 keV and 7.5 keV. An additional line at 2 keV (due to calibration problems) was sometimes needed in XRT.493 Absorption was a combination of a fixed interstellar component (abundances fixed to ?)) plus a variable local component., Absorption was a combination of a fixed interstellar component (abundances fixed to \citealt{wilms00}) ) plus a variable local component.494" XRT found the total absorption to vary between 4.9-6.3 x 107! em"". taking into account the statistical uncertainties (0.07). and the dependence on the position of the source in the HID."," XRT found the total absorption to vary between 4.9–6.3 $\times$ $^{21}$ $^{-2}$, taking into account the statistical uncertainties $\pm$ 0.07), and the dependence on the position of the source in the HID."495 The lower end (4.9 x 107! em?) is compatible. within the errors. with the average Galactic column density in the source direction estimated from ?u it is possible that. up to about L4 x 107! em- is intrinsic and variable (see ? for a detailed discussion of the variations of the absorption in this source: XRT data were not always available to do that in this work).," The lower end (4.9 $\times$ $^{21}$ $^{-2}$ ) is compatible, within the errors, with the average Galactic column density in the source direction estimated from \citet{kalberla05}; it is possible that, up to about 1.4 $\times$ $^{21}$ $^{-2}$ is intrinsic and variable (see \citet{cabanac} for a detailed discussion of the variations of the absorption in this source; XRT data were not always available to do that in this work)."496 For the dise component. the model in (?) was used.," For the disc component, the model in \citep{Mitsuda:1984} was used."497 We then replaced the phenomenological models. that first allowed us to easily compare the spectral parameters over the outburst. with à more physical one. the thermal Comptonisation model of ?..," We then replaced the phenomenological models, that first allowed us to easily compare the spectral parameters over the outburst, with a more physical one, the thermal Comptonisation model of \citet{Titarchuk:1994}."498 We tested the best modelling by adding additional contributions and we carefully checked any improvement in the goodness of the fit., We tested the best modelling by adding additional contributions and we carefully checked any improvement in the goodness of the fit.499 When a cut-off was needed. this provided a good fit to almost all our data (see Table 2 and 3. for details: otherwise. we used a simple power law model). although the temperature of the seed photons (tied to the disc temperature) was not always well constrained.," When a cut-off was needed, this provided a good fit to almost all our data (see Table \ref{tab:para} and \ref{tab:cutoffPL} for details; otherwise, we used a simple power law model), although the temperature of the seed photons (tied to the disc temperature) was not always well constrained."500 The best-fit parameters are reported in Table 2:: Table 3 shows the phenomenological cut-off power law parameters., The best-fit parameters are reported in Table \ref{tab:para}; Table \ref{tab:cutoffPL} shows the phenomenological cut-off power law parameters.501 In addition to providing a more physical interpretation to the data. this model also permits us to avoid the divergence of the power law flux towards low energy since Comptonisation," In addition to providing a more physical interpretation to the data, this model also permits us to avoid the divergence of the power law flux towards low energy since Comptonisation"502be discussed in the following sections that the estimation of CMB bispectra is similar and related to the case of lensing reconstruction of the CMB sky (Smith.Zahn&Dore2007).,be discussed in the following sections that the estimation of CMB bispectra is similar and related to the case of lensing reconstruction of the CMB sky \citep{SmZaDo00}.503. The problem of estimation of the skew spectrum is very similar to that of the primary CMB bispectrum., The problem of estimation of the skew spectrum is very similar to that of the primary CMB bispectrum.504 There has been a recent surge in activity in this area. driven by the claim of detection of non-gaussianity in the WMAP data release (see Yadav&Wandelt (2007))).," There has been a recent surge in activity in this area, driven by the claim of detection of non-gaussianity in the WMAP data release (see \citet{YaWa08,Yadav08,YKW}) )."505 Different techniques were developed which introduce various weighting schemes in the harmonie domain to make the method optimal (i.e. saturates the Cramer-Rao bound)., Different techniques were developed which introduce various weighting schemes in the harmonic domain to make the method optimal (i.e. saturates the Cramer-Rao bound).506 Maps are constructed by weighting the observed CMB sky with /-dependent weights obtained from inflationary theoretical models., Maps are constructed by weighting the observed CMB sky with $l$ -dependent weights obtained from inflationary theoretical models.507 These weighted maps are then used to compute one-point quantities which are generalisation of skewness and can be termed mixed skewness., These weighted maps are then used to compute one-point quantities which are generalisation of skewness and can be termed mixed skewness.508 These mixed skewness measures are useful estimators of fv; parameters., These mixed skewness measures are useful estimators of $f_{NL}$ parameters.509 A more general treatment was provided in Smith(2009) who took into account mode-mode coupling in an exact way with the use of proper inverse-covariance weighting of harmonie modes.," A more general treatment was provided in \cite{SmZa06,SmZaDo00,SmSeZa09} who took into account mode-mode coupling in an exact way with the use of proper inverse-covariance weighting of harmonic modes."510 Recent work by Munshi&Heavens(2009). has improved the situation by focussing directly on the skew spectrum., Recent work by \cite{MuHe09} has improved the situation by focussing directly on the skew spectrum.511 Their technique does not compress all the available information in the bispectrum into a single number but provides a power-spectrum which depends on the harmonic wavenumber /., Their technique does not compress all the available information in the bispectrum into a single number but provides a power-spectrum which depends on the harmonic wavenumber $l$.512 This method has the advantage of being able to separate various contributions as they will have different dependence on /s. thus allowing an assessment of whether any non-gaussianity is primordial or not.," This method has the advantage of being able to separate various contributions as they will have different dependence on $l$ s, thus allowing an assessment of whether any non-gaussianity is primordial or not."513 In this section we compute the contaminating secondary bispectrum contributions from lensing-secondary coupling., In this section we compute the contaminating secondary bispectrum contributions from lensing-secondary coupling.514 The study of the bispectrum related to secondary anisotropy (see Cooray&Seth(2000) for more details and analytical modelling based on halo model which we use here) is arguably as important as that generated by the primary anisotropy.," The study of the bispectrum related to secondary anisotropy (see \cite{sethcoo}515 for more details and analytical modelling based on halo model which we use here) is arguably as important as that generated by the primary anisotropy."516 Primary non-Gaussianity in simpler inflationary models is vanishingly small (Salopek&Bond1990.1991:Falketal.1993:Gangui1994:Acquaviva2003:Maldacena2003): see &Riotto(2006) and references therein for more details.," Primary non-Gaussianity in simpler inflationary models is vanishingly small \citep{Salopek90,Salopek91,Falk93,Gangui94,Acq03,Mal03}; see \citet{Bartolo06}517 and references therein for more details."518 However. variants of simple inflationary models such as multiple scalar fields 2003).. features in the inflationary potential. non-adiabatie fluctuations. non-standard kinetic terms. warm inflation (Gupta.Berera&Heavens2002:MossXiong2007).. or deviations from Bunch-Davies vacuum can all lead to a much higher level of non-Gaussianity.," However, variants of simple inflationary models such as multiple scalar fields \citep{lindemukha,Lyth03}, features in the inflationary potential, non-adiabatic fluctuations, non-standard kinetic terms, warm inflation \citep{GuBeHea02,Moss}, or deviations from Bunch-Davies vacuum can all lead to a much higher level of non-Gaussianity."519 Early observational work on the bispectrum from COBE (Komatsuetal.2002) and MAXIMA (Santosetal.2003) was followed by much more accurate analysis with WMAP (Komatsuetal.2003:Creminelli2007:Spergel2007).," Early observational work on the bispectrum from COBE \citep{Komatsu02} and MAXIMA \citep{Santos} was followed by much more accurate analysis with WMAP \citep{Komatsu03,Crem07a,Spergel07}."520. The primary bispectrum encodes information about inflationary dynamics and hence can constrain various inflationary scenarios. where as the secondary bispectrum will provide valuable information regarding the low-redshift universe and constrain structure formation scenarios.," The primary bispectrum encodes information about inflationary dynamics and hence can constrain various inflationary scenarios, where as the secondary bispectrum will provide valuable information regarding the low-redshift universe and constrain structure formation scenarios."521 These bispectra are generated because of the cross-correlation effect of lensing due to various intervening materials and the secondary anisotropy such as the Sunyaev-Zeldovich effect due to inverse Compton scattering of CMB photons from hot gas in intervening clusters., These bispectra are generated because of the cross-correlation effect of lensing due to various intervening materials and the secondary anisotropy such as the Sunyaev-Zeldovich effect due to inverse Compton scattering of CMB photons from hot gas in intervening clusters.522 The power spectrum C7 is the unlensed power spectrum of the CMB anisotropy., The power spectrum $\myC^S_l$ is the unlensed power spectrum of the CMB anisotropy.523" We have introduced the subscript 9 to distinguish it from the Cs that appear in the denominator which take contribution from the instrumental noise from signal to noise computation point of view (C;=€|IN/b(I)"". where JN is the instrumental noise and 6(/) is the beam function in multipole space)."," We have introduced the subscript $S$ to distinguish it from the $C_l$ s that appear in the denominator which take contribution from the instrumental noise from signal to noise computation point of view $C_l=C_l+N/b(l)^2$, where $N$ is the instrumental noise and $b(l)$ is the beam function in multipole space)."524 We detine the different fields which are constructed from underlying harmonies and corresponding Cys. These will be useful for constructing an unbiased near optimal estimator., We define the different fields which are constructed from underlying harmonics and corresponding ${\cal C}_l$ s. These will be useful for constructing an unbiased near optimal estimator.525" The corresponding fields that we construct are 41(0)=22sYn, and in an analogous manner D and C."," The corresponding fields that we construct are $A^{(i)}(\hat \Omega) \equiv \sum_{lm}Y_{lm}(\hat\Omega)A^{(i)}_{lm}$, and in an analogous manner $B^{(i)}$ and $C^{(i)}$."526 The optimised skew spectrum in the presence of all-sky coverage and homogeneous noise can now be (QA.written as: The cyclic terms that are considered here will have to constructed likewise from the corresponding terms in the expression for the reduced bispectrum discussed above 35.., The optimised skew spectrum in the presence of all-sky coverage and homogeneous noise can now be written as: The cyclic terms that are considered here will have to constructed likewise from the corresponding terms in the expression for the reduced bispectrum discussed above \ref{eq:bi_komatsu}.527 The linear-order correction terms which needs to be included in the absence of spherical symmetry due to presence of cuts to avoid the galactic foreground and the inhomogeneous noise can be written as:, The linear-order correction terms which needs to be included in the absence of spherical symmetry due to presence of cuts to avoid the galactic foreground and the inhomogeneous noise can be written as:528"numerical simulations (??),, and given by p(r)= where r is the distance from the Galactic center and pp = 0.385 GeV cm? (??)..","numerical simulations \citep{1996ApJ...462..563N, 2008Natur.454..735D}, and given by $\rho(r) = \rho_0 \, (r/8.5 \, {\rm kpc})^{-1.25}$, where $r$ is the distance from the Galactic center and $\rho_0$ = 0.385 GeV $^{-3}$ \citep{2010JCAP...08..004C, 2011arXiv1105.4166L}."529" We also adopt a dark matter annihilation cross section of (συ)=3x10776 cm? s-!, which is the value predicted for a simple thermal relic."," We also adopt a dark matter annihilation cross section of $\langle\sigma v\rangle=3\times~10^{-26}$ $^3$ $^{-1}$, which is the value predicted for a simple thermal relic."530" Assuming approximate cylindrical symmetry for the filament geometry, the annihilation rate within a filament of length | and diameter w is given by: where r is the distance of the filament from the Galactic center."," Assuming approximate cylindrical symmetry for the filament geometry, the annihilation rate within a filament of length $l$ and diameter $w$ is given by: where $r$ is the distance of the filament from the Galactic center."531" We note that in many NRFs, the distance from the Galactic center changes considerably across the length of the filaments - we will discuss the effect of this when modeling specific filaments."," We note that in many NRFs, the distance from the Galactic center changes considerably across the length of the filaments - we will discuss the effect of this when modeling specific filaments."532 The types and spectra of particles produced in dark matter annihilations depend on the details of the particle physics model., The types and spectra of particles produced in dark matter annihilations depend on the details of the particle physics model.533" In order to generate a bright flux of synchrotron emission with a spectrum peaking at 10 GHz, we will focus on dark matter which annihilates dominantly to charged leptons."," In order to generate a bright flux of synchrotron emission with a spectrum peaking at $\sim$ 10 GHz, we will focus on dark matter which annihilates dominantly to charged leptons."534" In particular, we will consider a democratic model which annihilates equally to e, u~, and 7- final states."," In particular, we will consider a democratic model which annihilates equally to $e^\pm$, $\mu^\pm$, and $\tau^\pm$ final states."535" The nearly instantaneous decays of the taus and muons produce lower energy electrons/positrons, as well as a prompt flux of 4-rays (as opposed to y-rays from the inverse-Compton scattering of energetic "," The nearly instantaneous decays of the taus and muons produce lower energy electrons/positrons, as well as a prompt flux of $\gamma$-rays (as opposed to $\gamma$ -rays from the inverse-Compton scattering of energetic electrons)."536It is this prompt flux of y-rays which ? find to be electrons).consistent with the excess observed in the Galactic center by Fermi-LAT., It is this prompt flux of $\gamma$ -rays which \citet{2011PhLB..697..412H} find to be consistent with the excess observed in the Galactic center by Fermi-LAT.537 The spectrum of electrons and positrons produced through dark matter annihilations within a given NRF is calculated using the Pythia package (??). ," The spectrum of electrons and positrons produced through dark matter annihilations within a given NRF is calculated using the Pythia package \citep{2001CoPhC.135..238S, 2004JCAP...07..008G}."538"In the left frame of Fig. 2,,"," In the left frame of Fig. \ref{fig:leptonflux},"539" we show the injected electron spectrum per dark matter annihilation for our canonical case of a dark matter particle with a mass of 8 GeV, annihilating equally into e*e, uty and r*r-."," we show the injected electron spectrum per dark matter annihilation for our canonical case of a dark matter particle with a mass of 8 GeV, annihilating equally into $e^+ e^-$, $\mu^+ \mu^-$ and $\tau^+ \tau^-$."540" We note that the electron/positron spectrum is very hard, following a spectrum between 9? and E? between 100 MeV and 8 GeV, although we caution that this spectrum is not a continuous power law."," We note that the electron/positron spectrum is very hard, following a spectrum between $^{-0.5}$ and $^{0}$ between 100 MeV and 8 GeV, although we caution that this spectrum is not a continuous power law."541 The majority (~2/3) of the electron energy is deposited in a delta function at 8 GeV following the dark matter annihilations directly into electrons., The majority $\sim$ 2/3) of the electron energy is deposited in a delta function at 8 GeV following the dark matter annihilations directly into electrons.542" These 8 GeV electrons will dominate the synchrotron spectrum from NRFs, in part due to their shorter synchrotron energy loss time."," These 8 GeV electrons will dominate the synchrotron spectrum from NRFs, in part due to their shorter synchrotron energy loss time."543 We note that the positron spectrum is identical and lends another factor of two to the overall synchrotron flux., We note that the positron spectrum is identical and lends another factor of two to the overall synchrotron flux.544" In order to determine the synchrotron spectrum expected from dark matter annihilations, we must also model the diffusion of electrons throughout the NRFs."," In order to determine the synchrotron spectrum expected from dark matter annihilations, we must also model the diffusion of electrons throughout the NRFs."545 Models of the filaments typically require an electron diffusion timescale similar to the energy loss time of the electron population in the NRF's magnetic field ," Models of the filaments typically require an electron diffusion timescale similar to the energy loss time of the electron population in the NRF's magnetic field \citep{1995ApJ...448..164G, 1999ApJ...526..727L}."546This has the effect of smearing out the electron (??)..energy distribution and softening the overall synchrotron spectrum., This has the effect of smearing out the electron energy distribution and softening the overall synchrotron spectrum.547" Through considerations of the electron gyroradius similar to those discussed in refsec:filamentaryarcs,, electrons created within the NRFs are constrained from effective diffusion perpendicular to the ordered magnetic field."," Through considerations of the electron gyroradius similar to those discussed in \\ref{sec:filamentaryarcs}, electrons created within the NRFs are constrained from effective diffusion perpendicular to the ordered magnetic field."548" In the case of an entirely ordered magnetic field, charged leptons would spiral freely along the magnetic field lines until exiting the filament."," In the case of an entirely ordered magnetic field, charged leptons would spiral freely along the magnetic field lines until exiting the filament."549" However, in the observed regime containing significant ordered and unordered fields, diffusion is expected to be significantly more complicated."," However, in the observed regime containing significant ordered and unordered fields, diffusion is expected to be significantly more complicated."550" In the case of very low turbulence levels, much work has been done within the perturbative framework of quasi-linear theory which seeks to calculate the parallel and perpendicular diffusion components as a function of the power in turbulent modes of the magnetic field with a wavenumber resonant with the inverse of the particles momentum (??).. "," In the case of very low turbulence levels, much work has been done within the perturbative framework of quasi-linear theory which seeks to calculate the parallel and perpendicular diffusion components as a function of the power in turbulent modes of the magnetic field with a wavenumber resonant with the inverse of the particles momentum \citep{1966ApJ...146..480J, 1971RvGSP...9...27J}."551"The amplitude of these modes, however, is poorly constrained in galactic simulations."," The amplitude of these modes, however, is poorly constrained in galactic simulations."552" More recently, numerical simulations have been used to analyze the parallel and perpendicular diffusion constants in regimes in which the ordered and unordered field are co-dominant."," More recently, numerical simulations have been used to analyze the parallel and perpendicular diffusion constants in regimes in which the ordered and unordered field are co-dominant."553" Notably, ? found that in the case of a magnetic field which is approximately ordered, the parallel diffusion constant exceeds the perpendicular diffusion constant by a factor of ~125."," Notably, \citet{2002PhRvD..65b3002C} found that in the case of a magnetic field which is approximately ordered, the parallel diffusion constant exceeds the perpendicular diffusion constant by a factor of $\sim$ 125."554 Very similar results were later obtained for the case of more energetic cosmic rays (?).. , Very similar results were later obtained for the case of more energetic cosmic rays \citep{2007JCAP...06..027D}. .555"Since the length travelled by diffusive particles can be written as £ = V2Dt, where D is the assumed diffusion constant."," Since the length travelled by diffusive particles can be written as $\ell$ = $\sqrt{2Dt}$ , where D is the assumed diffusion constant."556 This implies that perpendicular and parallel diffusion will remove particles from the filaments on equivalent, This implies that perpendicular and parallel diffusion will remove particles from the filaments on equivalent557which there is a great deal of evidence Arnett 1988. Pinto Woosley 1988. Shigevama. Nomoto Hashimoto 1988. Woosley 1988. Laas et al.,"which there is a great deal of evidence Arnett 1988, Pinto Woosley 1988, Shigeyama, Nomoto Hashimoto 1988, Woosley 1988, Haas et al."558 1990. Spvronulio. Meikle Allen 1990. Fassia Aleikle 1999).," 1990, Spyromilio, Meikle Allen 1990, Fassia Meikle 1999)."559 Light elements (Hl. He) are mixed down to low velocities. and iron group elements are mixed. up to high velocities.," Light elements (H, He) are mixed down to low velocities, and iron group elements are mixed up to high velocities."560 COT. dlxXLMOS. and. IxF98a.b. introduce. this mixing in dillerent wavs.," C97, dKLM98 and KF98a,b introduce this mixing in different ways."561" However. they. all invoke a macroscopically mixed “core” lving within ~2000 km/s. (ULMOS refer to the inwardly mixed. 11Πο zones as the ""inner envelope”.)"," However, they all invoke a macroscopically mixed “core” lying within $\sim$ 2000 km/s. (dKLM98 refer to the inwardly mixed H/He zones as the “inner envelope”.)"562 The core thus contains zones that are L-rich. Le-rich. intermediate-element-rich.. ancl iron-group-rich. with the nebula being bathed in the radioactive decay energy.," The core thus contains zones that are H-rich, He-rich, intermediate-element-rich, and iron-group-rich, with the nebula being bathed in the radioactive decay energy."563 The core is generally of mass 4:6 M..., The core is generally of mass 4–6 $_\odot$.564 In addition. €C97 and IxE98a.b. include an outer. H-envelope. of mass 10. M. extending out to a velocity of 6000.7000 km/s. 1n general. the [raction. of the radioactive decay energy that does not. directly. escape from the nebula is injected into the nebular material via Coulomb interaction with the positrons ancl Compton-scattored electrons.," In addition, C97 and KF98a,b include an outer H-envelope of mass 10 $_\odot$ extending out to a velocity of 6000–7000 km/s. In general, the fraction of the radioactive decay energy that does not directly escape from the nebula is injected into the nebular material via Coulomb interaction with the positrons and Compton-scattered electrons."565 The energy. of the resulting non-thermal high energy electrons then goes towards excitation. ionisation and heating of the nebula (IxE9582).," The energy of the resulting non-thermal high energy electrons then goes towards excitation, ionisation and heating of the nebula (KF98a)."566 Three ellects play important roles in the evolution of the temperature ancl ionisation at the very late times considered here., Three effects play important roles in the evolution of the temperature and ionisation at the very late times considered here.567" These are the ionisation/thermal ""freeze-out” elfect. acliabatic cooling. and the ""Hi-catastrophe."," These are the ionisation/thermal ``freeze-out'' effect, adiabatic cooling, and the “IR-catastrophe”."568 The first two are important in the HL/Le envelope. while the third plàvs an important role in the metal-rich core.," The first two are important in the H/He envelope, while the third plays an important role in the metal-rich core."569 The ionisation [reeze-out effect. was suggested: originally. w Clavton. ct al. (, The ionisation freeze-out effect was suggested originally by Clayton et al. (5701992) and bv Fransson Kozma (1993).,1992) and by Fransson Kozma (1993).571 “These authors pointed out that as the SN evolves. here will eventually come a time when the recombination imescale exceeds the radioactive or expansion. timescale. so that the rate of change in the level of ionisation slows significantly.," These authors pointed out that as the SN evolves, there will eventually come a time when the recombination timescale exceeds the radioactive or expansion timescale, so that the rate of change in the level of ionisation slows significantly."572 Once this phase is reached. the bolometric uninositv exceeds that of the instantaneous raclioactive decay deposition. since some of the luminosity results from recombination following ionisation at a significantly earlier epoch.," Once this phase is reached, the bolometric luminosity exceeds that of the instantaneous radioactive decay deposition, since some of the luminosity results from recombination following ionisation at a significantly earlier epoch."573 In the model of KEOSa.b the ionisation [reeze-out phase begins at SOQ900 cays in most zones. but has a more pronounced effect on the luminosity in the L/Lle envelope.," In the model of KF98a,b the ionisation freeze-out phase begins at 800–900 days in most zones, but has a more pronounced effect on the luminosity in the H/He envelope."574" However. in their. ""inner-envelope"" model. ΟΗΕMOS finc that the freeze-out clocs not occur until much later than this."," However, in their “inner-envelope” model, dKLM98 find that the freeze-out does not occur until much later than this."575" Instead. they identify a ""thermal. [reeze-out” where the radiative cooling timescale exceeds that of the expansion timescale."," Instead, they identify a “thermal freeze-out'' where the radiative cooling timescale exceeds that of the expansion timescale."576 In their model. this occurs before," In their model, this occurs before"577"The excess in the rms spectrum of NGC 3783 is similar in strength to the broad iron line in the time-averaged spectrum, so in the accretion disk model, the line and continuum vary together.","The excess in the rms spectrum of NGC 3783 is similar in strength to the broad iron line in the time-averaged spectrum, so in the accretion disk model, the line and continuum vary together."578 ΝΟ7 found an ionized H-like line at 6.97 keV that is not seen to be variable in the rms spectrum., N07 found an ionized H-like line at 6.97 keV that is not seen to be variable in the rms spectrum.579" This offers support for the speculation of NO7 that this originates from hot gas filling the torus, which is not expected to be variable."," This offers support for the speculation of N07 that this originates from hot gas filling the torus, which is not expected to be variable."580" Turning to MCG-6-30-15, NO7 found a strong requirement for a blurred accretion disk component in the time averaged spectrum (as in several previous studies, e.g. Tanaka et al."," Turning to MCG-6-30-15, N07 found a strong requirement for a blurred accretion disk component in the time averaged spectrum (as in several previous studies, e.g. Tanaka et al."581 1995; Fabian et al., 1995; Fabian et al.582 2002)., 2002).583" The variability line profile matches well with the time-averaged line profile in the first of our observations, MCG-6-30-15(1), which follows the simple disk interpretation."," The variability line profile matches well with the time-averaged line profile in the first of our observations, MCG-6-30-15(1), which follows the simple disk interpretation."584" However, there is a large change between this and the variability profile for the second observation (see Section 3.5)."," However, there is a large change between this and the variability profile for the second observation (see Section 3.5)."585" NGC 3783 and MCG-6-30-15(1) are the only observations in our sample which both show clear evidence for broad line variations, and an amplitude consistent with the continuum, although there are others where the signal-to-noise ratio prevents definitive conclusions."," NGC 3783 and MCG-6-30-15(1) are the only observations in our sample which both show clear evidence for broad line variations, and an amplitude consistent with the continuum, although there are others where the signal-to-noise ratio prevents definitive conclusions."586 There are four observations which show variability of the iron line redward of the core that exceeds that of the time averaged spectrum., There are four observations which show variability of the iron line redward of the core that exceeds that of the time averaged spectrum.587" NGC 3516(2) and NGC 5548(2) are the clearest cases, along with NGC 4151(2) and MCG-5-23-16(2) showing narrower or more marginal excesses."," NGC 3516(2) and NGC 5548(2) are the clearest cases, along with NGC 4151(2) and MCG-5-23-16(2) showing narrower or more marginal excesses."588" If the red wing is indeed more strongly variable than the continuum, it is a compelling indicator that relativistic effects are in play (Ponti et al."," If the red wing is indeed more strongly variable than the continuum, it is a compelling indicator that relativistic effects are in play (Ponti et al."589 2004; Miniutti Fabian 2004)., 2004; Miniutti Fabian 2004).590" Curiously, however, NO7 did not find evidence in either NGC 5548(2) or NGC 4151(2) for strong gravitational effects in the time averaged spectra."," Curiously, however, N07 did not find evidence in either NGC 5548(2) or NGC 4151(2) for strong gravitational effects in the time averaged spectra."591" NGC 5548(2) is the most puzzling case, with a non-relativistic iron line but a strong, broad variable excess that extends down to 5.0 keV, a much lower energy than the time- profile."," NGC 5548(2) is the most puzzling case, with a non-relativistic iron line but a strong, broad variable excess that extends down to 5.0 keV, a much lower energy than the time-averaged profile."592" MCG-5-23-16(2) and NGC 3516(2) are different in that they possess relativistically broad iron lines, as well as having strong variability excesses across the red wing."," MCG-5-23-16(2) and NGC 3516(2) are different in that they possess relativistically broad iron lines, as well as having strong variability excesses across the red wing."593 This means that the iron line is more variable than the continuum and is likely to be explained by relativistic effects such as beaming or emission from iron moving with a large bulk velocity., This means that the iron line is more variable than the continuum and is likely to be explained by relativistic effects such as beaming or emission from iron moving with a large bulk velocity.594" While most of the excess variability is always seen in the red wings, in MCG-5-23-16(2) and NGC 5548(2) the variability also extends up to 7.0 keV. The second class of observations exhibit the majority of their variability blueward of the line core, and include Mrk 766(3), MCG-6-30-15(2), NGC 5506(1) and the more marginal cases of NGC 4051 and Ark 564."," While most of the excess variability is always seen in the red wings, in MCG-5-23-16(2) and NGC 5548(2) the variability also extends up to 7.0 keV. The second class of observations exhibit the majority of their variability blueward of the line core, and include Mrk 766(3), MCG-6-30-15(2), NGC 5506(1) and the more marginal cases of NGC 4051 and Ark 564."595" In Mrk 766(3), the variability excess in the 6.6-7.0 keV bin"," In Mrk 766(3), the variability excess in the 6.6-7.0 keV bin"596and In Eq.,and In Eq.597 35 and Eq., \ref{eq:delta_r_deq_ac} and Eq.598 36 the V is D is from ?.. and in Eq.," \ref{eq:delta_r_deq_bc} the $\nabla$ is $D$ is from \citet{1970SAOSR.309.....K}, , and in Eq."599 36. the Ho(v) is the radiative flux., \ref{eq:delta_r_deq_bc} the $H_0(\nu)$ is the radiative flux.600 Solving Eq., Solving Eq.601 34. for om. using the coefficients in Eq. 35..," \ref{eq:delta_r_deq_sol} for $\delta m$, using the coefficients in Eq. \ref{eq:delta_r_deq_ac},"602 Eq., Eq.603 36 and Eq. 37..," \ref{eq:delta_r_deq_bc} and Eq. \ref{eq:delta_r_deq_cc},"604 the corresponding temperature change based on conserving the flux is uses two additional temperature corrections near the surface. where the flux error loses sensitivity.," the corresponding temperature change based on conserving the flux is uses two additional temperature corrections near the surface, where the flux error loses sensitivity."605 One correction is based on the flux derivative., One correction is based on the flux derivative.606 Because this correction applies high in the atmosphere where the gas Is quite transparent. radiation will carry almost all the energy. and it is a good approximation to ignore convective energy transport.," Because this correction applies high in the atmosphere where the gas is quite transparent, radiation will carry almost all the energy, and it is a good approximation to ignore convective energy transport."607 The zeroth angular moment of the spherical radiative transfer equation (Eq. 10)), The zeroth angular moment of the spherical radiative transfer equation (Eq. \ref{eq:sph_rad_tran_m}) )608 is Replacing J(v) by A[Sέν). expanding the Planck function in S(v) in terms of T. integrating over frequency and retaining just the diagonal terms of the A operator. the resulting temperature correction becomes The term Agia IS approximated by the plane-parallel expression given in. 2.. assuming it has minimal dependence on the geometry.," is Replacing $J(\nu)$ by $\Lambda[S(\nu)]$, expanding the Planck function in $S(\nu)$ in terms of $T$, integrating over frequency and retaining just the diagonal terms of the $\Lambda$ operator, the resulting temperature correction becomes The term $\Lambda_{\mathrm{dia}}$ is approximated by the plane-parallel expression given in \citet{1970SAOSR.309.....K}, assuming it has minimal dependence on the geometry."609" A third temperature correction is used in the original. code to smooth the region of overlap between the first two corrections,", A third temperature correction is used in the original code to smooth the region of overlap between the first two corrections.610 This is and this is retained here., This is and this is retained here.611 The total temperature correction is therefore. One test of the validity of the spherical code is to compute a spherical solar atmosphere. which should be nearly identical to the plane-parallel model.," The total temperature correction is therefore, One test of the validity of the spherical code is to compute a spherical solar atmosphere, which should be nearly identical to the plane-parallel model."612" For both models we used the Kuruez file for the starting model and the file for the opacity distribution function,", For both models we used the Kurucz file for the starting model and the file for the opacity distribution function.613" To eliminate other possible sources of differences. we used the Bulirsch-Stoer solution to solve for the pressure structures and the Rybicki method for the radiative transfer in. the plane-parallel model as well as for the spherical calculations,"," To eliminate other possible sources of differences, we used the Bulirsch-Stoer solution to solve for the pressure structures and the Rybicki method for the radiative transfer in the plane-parallel model as well as for the spherical calculations."614" The spherical model used the atmospheric parameters 3.8458x10? ergs/s. Ma=1.9891x10? g. and Ro=6.95508x10"" em."," The spherical model used the atmospheric parameters $L_{\sun} = 3.8458 \times 10^{33}$ ergs/s, $M_{\sun} = 1.9891 \times 10^{33}$ g, and $R_{\sun} = 6.95508 \times 10^{10}$ cm."615 These correspond to T;[u=5779.5 K and logg=4.43845. which are slightlydifferent from the canonical values used by Kuruez.," These correspond to $T_{\mathrm{eff}} = 5779.5$ K and $\log g = 4.43845$, which are slightlydifferent from the canonical values used by Kurucz."616 Therefore. we computed the plane-parallel model with the consistent values of Tj and logg.," Therefore, we computed the plane-parallel model with the consistent values of $T_{\mathrm{eff}}$ and $\log g$."617 The comparison is shown in Fig. 6.., The comparison is shown in Fig. \ref{fig:spsol_ppsol}.618" The |AT| is <0.25% until logy,Po<2. where the temperature of the spherical model begins to trend lower than the plane-parallel] model."," The $| \Delta T |$ is $\leq 0.25\%$ until $\log_{10} P_{\mathrm{gas}} < 2$, where the temperature of the spherical model begins to trend lower than the plane-parallel model."619 The dip in the temperature difference down to —2.4% 1s due to the kink in the temperature structure of the model., The dip in the temperature difference down to $- 2.4\%$ is due to the kink in the temperature structure of the model.620 This feature was discussed earlier in connection with Fig. 5.., This feature was discussed earlier in connection with Fig. \ref{fig:tp_ryb_josh}.621 However. in this case the ? method is used to compute the radiative transfer in models. using the surface boundary condition in both codes.," However, in this case the \citet{1971JQSRT..11..589R} method is used to compute the radiative transfer in models, using the surface boundary condition in both codes."622 Therefore. this difference cannot be due to a coding difference between the two routines.," Therefore, this difference cannot be due to a coding difference between the two routines."623 This feature might be due to the number of rays used in the calculation of the radiative transfer., This feature might be due to the number of rays used in the calculation of the radiative transfer.624 The Rybicki solution for the plane-parallel code uses three rays for each depth. whereas the same method in the spherical code uses =80 rays for the layers approaching the surface.," The Rybicki solution for the plane-parallel code uses three rays for each depth, whereas the same method in the spherical code uses $\approx 80$ rays for the layers approaching the surface."625 Perhaps this finer griding produces a smoother temperature profile in these layers., Perhaps this finer griding produces a smoother temperature profile in these layers.626 There is. however. no physical significance to the temperature differences nearthe surface because these layers are located in the solar chromosphere (?).. well above the temperature minimum. where other physics is completely dominant.," There is, however, no physical significance to the temperature differences nearthe surface because these layers are located in the solar chromosphere \citep{2006ApJ...639..441F}, , well above the temperature minimum, where other physics is completely dominant."627 A test where larger differences are expected is. for the coolest model (Fay=3500 K. logg= 0.0)," A test where larger differences are expected is for the coolest model $T_{\mathrm{eff}} = 3500$ K, $\log g = 0.0$ )"628Alb these five sources are present in the £LRST catalogue (and in the FAST map as clearly. showed in Figure 21)).,All these five sources are present in the $FIRST$ catalogue (and in the $FIRST$ map as clearly showed in Figure \ref{vla_no_nvss}) ).629 Their absence in the ΑΕSS catalogue is an indication of the incompleteness of the NVS survey near the Dux limit., Their absence in the $NVSS$ catalogue is an indication of the incompleteness of the $NVSS$ survey near the flux limit.630 Using the restriction of an oll-axis value lower than 34 arcmin and a peak Lux density Sp ‘1.0 (the limit of the FIRST catalogue). we have 215 compact sources in common with the LYIST survey.," Using the restriction of an off-axis value lower than 34 arcmin and a peak flux density $_P>$ 1.0 (the limit of the $FIRST$ catalogue), we have 215 compact sources in common with the $FIRST$ survey."631 In Figure 22 we show a comparison between our VLA and £LEST total Lux densities., In Figure \ref{ff_FIRST} we show a comparison between our VLA and $FIRST$ total flux densities.632 Besicles these 215 common sources. there ΕΛ... sources that we did not detected in our survey and 29 sources present in our survey but not in the £LRST catalogue.," Besides these 215 common sources, there are 14 $FIRST$ sources that we did not detected in our survey and 29 sources present in our survey but not in the $FIRST$ catalogue."633 A flux distribution and à contour maps of these last 20 sources are shown in Figure 23. and 24. while a contour maps of the 14. £LRST sources that we did. not. detect are shown in Figure 24.., A flux distribution and a contour maps of these last 29 sources are shown in Figure \ref{vla_no_first_histo} and \ref{vla_no_first} while a contour maps of the 14 $FIRST$ sources that we did not detect are shown in Figure \ref{first_no_vla}.634 As shown in Figure 23. all the radio sources missing in the £LRST catalogue have a peak [ux density lower than 2 my., As shown in Figure \ref{vla_no_first_histo} all the radio sources missing in the $FIRST$ catalogue have a peak flux density lower than 2 mJy.635 However. as shown in Fieure 24.. many of them appear on the ££LARST maps.," However, as shown in Figure \ref{vla_no_first}, many of them appear on the $FIRST$ maps."636 This result. confirms the incompleteness of the FIRST survey below ~2 mJx. as already indicated by the cülferential source counts reported in Figure 5..," This result confirms the incompleteness of the $FIRST$ survey below $\sim$ 2 mJy, as already indicated by the differential source counts reported in Figure \ref{counts_tab}."637 On the other hand. Figure 24. shows that many of the 14 £LARST sources missing in our survey probably are not real.," On the other hand, Figure \ref{first_no_vla} shows that many of the 14 $FIRST$ sources missing in our survey probably are not real."638 Some of them may be uneleaned residual around strong sources (sec. for example. FELISTI61318|541607. ELISST163646|405442. FIRSTIG3S15|405840) or simply spurious sources in à not well cleaned. map (see. for example. the PIAST maps of ELItST161351|543258. ELIT163634|4213013 and ΓΗΤοτο|405125).," Some of them may be uncleaned residual around strong sources (see, for example, FIRST161318+541607, FIRST163646+405442, FIRST163815+405840) or simply spurious sources in a not well cleaned map (see, for example, the $FIRST$ maps of FIRST161351+543258, FIRST163634+413013 and FIRST163706+405125)."639 As shown in Figure 19 and 22 the ux densities of our survey are in good agreement with the LLRST and VVSS Hux densities over two order of magnitude., As shown in Figure \ref{ff_NVSS} and \ref{ff_FIRST} the flux densities of our survey are in good agreement with the $FIRST$ and $NVSS$ flux densities over two order of magnitude.640 Llowever. as xpected. the high resolution surveys tend to estimate lower flux than the lower resolution survey.," However, as expected, the high resolution surveys tend to estimate lower flux than the lower resolution survey."641 This effect is evident in the lower panels of Figure 19. ancl 22: our VLA [lux densities are. in mean. lower than the INYSS [lux densities out higher than the £IST Dux densities.," This effect is evident in the lower panels of Figure \ref{ff_NVSS} and \ref{ff_FIRST} : our VLA flux densities are, in mean, lower than the $NVSS$ flux densities but higher than the $FIRST$ flux densities."642 High resolution Lgurvevs. with their smaller svnthesized beam size. lose {lux ue to the resolution surface brightness elfect.," High resolution surveys, with their smaller synthesized beam size, lose flux due to the resolution surface brightness effect."643 Llowever some consideration cam be made from Figure 19. ancl 22.., However some consideration cam be made from Figure \ref{ff_NVSS} and \ref{ff_FIRST}.644" In spite a factor of 3 in angular resolution between our VLA and ANMSS survev (157 vs. 45"" EWLIALD) the Lux ratio of the two survevs is always lower than 0.5 while the Lux ratio between our VLA and £2RST surveys reaches values of ~ 4. although the two surveys have still a factor of 3 in angular resolution differences (57 vs. 157 ENIM)."," In spite a factor of 3 in angular resolution between our VLA and $NVSS$ survey $^{\prime\prime}$ vs. $^{\prime\prime}$ FWHM) the flux ratio of the two surveys is always lower than 0.5 while the flux ratio between our VLA and $FIRST$ surveys reaches values of $\sim$ 4, although the two surveys have still a factor of 3 in angular resolution differences $^{\prime\prime}$ vs. $^{\prime\prime}$ FWHM)."645 The missing Dux between the £442ST (VLA - D configuration) and our survey (VLA - € configuration) is greater than the missing [ux between our survey and the [NYSS survey (VLA - D configuration)., The missing flux between the $FIRST$ (VLA - B configuration) and our survey (VLA - C configuration) is greater than the missing flux between our survey and the $NVSS$ survey (VLA - D configuration).646" Therefore the € configuration of our survey with a svnthesized. beam: size of 15"". seems to be the better compromise between high (B configuration) and low (D configuration) resolution racio surveys.", Therefore the C configuration of our survey with a synthesized beam size of $^{\prime\prime}$ seems to be the better compromise between high (B configuration) and low (D configuration) resolution radio surveys.647 Lt is less prone to surface brightness ellects than the B configuration without an excessive loss of Lux in comparison with the D configuration., It is less prone to surface brightness effects than the B configuration without an excessive loss of flux in comparison with the D configuration.648 Using the Very. Large. Array (VLA) radio telescope. we observed at L4 Giz a total area of 4.222 deg? in the ISO/ELAIS regions NI N2 and N3.," Using the Very Large Array (VLA) radio telescope, we observed at 1.4 GHz a total area of 4.222 $^2$ in the ISO/ELAIS regions N1 N2 and N3."649 The lower Ilux density limit reached by our observation is 0.135 mv. (at 5 0 level) on an area of 0.118 deg. while the bulk. of the observed regions are mapped with a flux density limit of 0.250 mJ. (5 7).," The lower flux density limit reached by our observation is 0.135 mJy (at 5 $\sigma$ level) on an area of 0.118 $^2$, while the bulk of the observed regions are mapped with a flux density limit of 0.250 mJy (5 $\sigma$ )."650 The data were analyzed using the NILAO reduction package., The data were analyzed using the NRAO reduction package.651 The source extraction has been carried out with the taskSAD., The source extraction has been carried out with the task.652 The reliability ofSAD has been tested using the maps of the radio surveys LLRST and NVSS., The reliability of has been tested using the maps of the radio surveys $FIRST$ and $NVSS$.653 Considering all the available observations. we detected a total of S67 sources at 5 c level. 44 of which have multiple components.," Considering all the available observations, we detected a total of 867 sources at 5 $\sigma$ level, 44 of which have multiple components."654 These sources were used to calculate. the normalized dillerential source counts., These sources were used to calculate the normalized differential source counts.655 They. provide a check on catalogue completeness ancl reliability. plus information about source evolution., They provide a check on catalogue completeness and reliability plus information about source evolution.656 A comparison with other surveys shows a very good agreement. confirming the presence of the well-know flattening of the counts below 1 mv. the completeness of our catalogue ancl the reliability. of our procedure for the source extraction.," A comparison with other surveys shows a very good agreement, confirming the presence of the well-know flattening of the counts below 1 mJy, the completeness of our catalogue and the reliability of our procedure for the source extraction."657 A comparison with the PAST and NVSS radio surveys has confirmed. the incompleteness of these two surveys near their [lux limits. while a flux comparison between the three surveys has shown that. our. survey with the VLA array in € configuration is the best compromise between high and low resolution radio surveys.," A comparison with the $FIRST$ and $NVSS$ radio surveys has confirmed the incompleteness of these two surveys near their flux limits, while a flux comparison between the three surveys has shown that our survey with the VLA array in C configuration is the best compromise between high and low resolution radio surveys."658 The positional errors of the radio sources are ~ 2 aresec for the fainter sources (70.13 mJv) and ~ 0.6 aresec for the brighter sources (2 10 mv)., The positional errors of the radio sources are $\sim$ 2 arcsec for the fainter sources $\sim$ 0.13 mJy) and $\sim$ 0.6 arcsec for the brighter sources $>$ 10 mJy).659 This small value will enable us to obtain an accurate and Fast optical/infrared identification of the racio sources., This small value will enable us to obtain an accurate and fast optical/infrared identification of the radio sources.660" This work was supported. by. the EC. PALR Network programme (EMIUN-C""E96-0068).", This work was supported by the EC TMR Network programme (FMRX-CT96-0068).661. GM. thanks the Roval Society for support., RGM thanks the Royal Society for support.662 We thank Rick White for discussions on the optimal pointing grid and both Bob Becker and Jim Condon for discussion on the optimal observing strategy aud Bob Becker for the provision of a FIRST observe file., We thank Rick White for discussions on the optimal pointing grid and both Bob Becker and Jim Condon for discussion on the optimal observing strategy and Bob Becker for the provision of a FIRST observe file.663The svuibiotic nova RR Telis an extraordinary laboratory for spectroscopic studies of low-density astrophysical plasinas on account of the richness of its enission line spectrum that COVCTS a wide range du ionization and excitation stages.,The symbiotic nova RR Tel is an extraordinary laboratory for spectroscopic studies of low-density astrophysical plasmas on account of the richness of its emission line spectrum that covers a wide range in ionization and excitation stages.664 Since the fundamental study by Thackeray (1977). new optical observations with higher spectral resolution and S/N ratio have have gradually luprovec the quality of the data aud have allowed the identification of weaker and blended spectral features (sce Me Kenna et al 1997. aud Crawford ct al.," Since the fundamental study by Thackeray (1977), new optical observations with higher spectral resolution and S/N ratio have have gradually improved the quality of the data and have allowed the identification of weaker and blended spectral features (see Mc Kenna et al 1997, and Crawford et al."665 1999)., 1999).666 Also. the presence of a strict correlation between the FWIIM aud the ionization level of the enuüssion lines. as pointed out bv Thackerav (1977) ane confirmed by Peuston et al. (," Also, the presence of a strict correlation between the FWHM and the ionization level of the emission lines, as pointed out by Thackeray (1977) and confirmed by Penston et al. ("6671983). has provided a simple but powerful tool for the identification of spectral lines that las uot vet been fully exploited.,"1983), has provided a simple but powerful tool for the identification of spectral lines that has not yet been fully exploited."668" With this in mind. we have taken advantage of| very recent ligh resolution VETUVES observations of RR Tel to revisit the spectral features of the j0va and to perform, anénmitio ideutification of its chussion features."," With this in mind, we have taken advantage of very recent high resolution VLT–UVES observations of RR Tel to revisit the spectral features of the nova and to perform an identification of its emission features."669 We present here some highlielts of these recen observations. deferring to a next paper a detailed. description of the spectral identifications aud nueasurenments.," We present here some highlights of these recent observations, deferring to a next paper a detailed description of the spectral identifications and measurements."670 Details on the UVES spectrograph iux its performances may be found in D'Odorico et al (2000) as well as iu the UVES User Manual (D'Odorico Kaper. 2000).," Details on the UVES spectrograph and its performances may be found in D'Odorico et al (2000) as well as in the UVES User Manual (D'Odorico Kaper, 2000)."671 The data we used consists of a spectrin obtained ou October l6th 1999 with the dichroic 1 and the standard setting centered at 3160 in the blue aria aud 5800 in the red anu. the exposure time was of 1200 s for both arms.," The data we used consists of a spectrum obtained on October 16th 1999 with the dichroic 1 and the standard setting centered at 3460 in the blue arm and 5800 in the red arm, the exposure time was of 1200 s for both arms."672 The detector in the blue arm is an EEV CCD. while in the red it is a mosaic of one EEV Gdeutical to that used in the blue arm) aud oue MIT CCD.," The detector in the blue arm is an EEV CCD, while in the red it is a mosaic of one EEV (identical to that used in the blue arm) and one MIT CCD."673 All CCDs are composed of £006015 square pixels of 15 jan side., All CCDs are composed of $4096\times 2048$ square pixels of 15 $\rm\mu m $ side.674 The shit width was in the blue aud in the red., The slit width was in the blue and in the red.675 The data was reduced using the coutext of aud. each CCD was treated iudepeudoeutlv: reduction meluded background subtraction. cosmic rav filteriue. flat ficldiug. extraction. waveleusth calibration and order imereine.," The data was reduced using the context of and each CCD was treated independently; reduction included background subtraction, cosmic ray filtering, flat fielding, extraction, wavelength calibration and order merging."676 Since no arc spectra for waveleneth calibration with this setting are available for the date of observation. we used Cibration spectra acquired. ou different davs.," Since no arc spectra for wavelength calibration with this setting are available for the date of observation, we used calibration spectra acquired on different days."677 From. our previous experience with UVES (Donifacio et al 2000). we expect the wavelength scale to be reproducible to within a shift of a few tenths of a κο]: suce we are nof interested in accurate radial velocities such a shift is of no consequence for our analysis.," From our previous experience with UVES (Bonifacio et al 2000), we expect the wavelength scale to be reproducible to within a shift of a few tenths of a pixel; since we are not interested in accurate radial velocities such a shift is of no consequence for our analysis."678 The resolution. as ucasured from the Th lines of the calibration lup is z64000 for," The resolution, as measured from the Th lines of the calibration lamp is $\approx 65000$ for"679llalos are populated with a central galaxy wilh probabilitw ολ).,Halos are populated with a central galaxy with probability $N_{cen}(M)$.680 Central galaxies are placed at the center of their host halos ancl assigned the peculiar velocity of their halos., Central galaxies are placed at the center of their host halos and assigned the peculiar velocity of their halos.681" llalos with a central galaxy are populated with Ny, galaxies. where Να,ANCM)) is drawn from a Poisson distribution."," Halos with a central galaxy are populated with $N_{sat}$ galaxies, where $P(N_{sat}|N(M))$ is drawn from a Poisson distribution."682 Our parameter constraints are derived using SO halo catalogs., Our parameter constraints are derived using SO halo catalogs.683 For those. (he position and velocity of the satellite galaxies are taken to be that of a randomly selected dark matter particle halo member.," For those, the position and velocity of the satellite galaxies are taken to be that of a randomly selected dark matter particle halo member."684 For mock catalogs based on the FoF halos. the satellite galaxies ave independently distributed following an NEW prolile with concentration of the dark matter halo determined by Eqn. 6..," For mock catalogs based on the FoF halos, the satellite galaxies are independently distributed following an NFW profile with concentration of the dark matter halo determined by Eqn. \ref{conceqn}."685 The peculiar velocity of a satellite galaxy is (he sum of the halo peculiar. velocity and a random velocity drawn [rom a Gaussian distribution determined by the virial velocity of the halo (?):: We assign comoving redshift space position s to an object in our mock catalogs using the conversion at τω=0.2: where typos is (he comoving distance along the line of sight in real The hypothesis underlying the Counts-In-Cdinders technique to constrain the LRG HOD is that 1-halo and 2-halo LRG pairs are separable based on their relative angular and redshift space positions., The peculiar velocity of a satellite galaxy is the sum of the halo peculiar velocity and a random velocity drawn from a Gaussian distribution determined by the virial velocity of the halo \citep{lokas/mamon:2001}: We assign comoving redshift space position $s$ to an object in our mock catalogs using the conversion at $z_{box} = 0.2$: where $x_{LOS}$ is the comoving distance along the line of sight in real The hypothesis underlying the Counts-In-Cylinders technique to constrain the LRG HOD is that 1-halo and 2-halo LRG pairs are separable based on their relative angular and redshift space positions.686 In the regime of small separations where (he 1-halo term dominates. a cvlinder should be a good approximation to the density contours surrounding central ealaxies. as long as the satellite velocity is uncorrelated. with its distance from the halo center. and (he relative velocity dominates the separation of central ancl satellite objects in (he redshift direction.," In the regime of small separations where the 1-halo term dominates, a cylinder should be a good approximation to the density contours surrounding central galaxies, as long as the satellite velocity is uncorrelated with its distance from the halo center, and the relative velocity dominates the separation of central and satellite objects in the redshift direction."687" Based on our initial analvsis of completeness ancl contamination ol mock catalogs derived from. FoF halos. we set Arως=0.8 Mpe/h and Ate,=20 Mpe/h [or our z=0.2 catalogs."," Based on our initial analysis of completeness and contamination of mock catalogs derived from FoF halos, we set $\Delta r_{\perp,max} = 0.8$ $h$ and $\Delta z_{max} = 20$ $h$ for our $z=0.2$ catalogs."688" Arie, is set bv the typical comoving size of halos hosting salellite galaxies. and «σαν is set bv the amplitude of the velocity dispersion in halos massive enough to host satellite galaxies."," $\Delta r_{\perp,max}$ is set by the typical comoving size of halos hosting satellite galaxies, and $\Delta z_{max}$ is set by the amplitude of the velocity dispersion in halos massive enough to host satellite galaxies."689 In later work we plan to improve the fidelity of our (ας eroup identification., In later work we plan to improve the fidelity of our CiC group identification.690 ILowever. the choice made here is sullicient since we calibrate the," However, the choice made here is sufficient since we calibrate the"691 , 692the space of the gas ring toward the center.,the space of the gas ring toward the center.693 As an alternative. they may be a surposition of the gas circulating inside the bar in elliptic streamings with that of the disc in circular motion.," As an alternative, they may be a surposition of the gas circulating inside the bar in elliptic streamings with that of the disc in circular motion."694 But the map of the tontsed gas distribution appears quite irregular. so we preferred do not search solutions with warped dises. to avoid increasing the number of variables present in the model.," But the map of the ionised gas distribution appears quite irregular, so we preferred do not search solutions with warped discs, to avoid increasing the number of variables present in the model."695 Taking into account the clear symmetry of the HI ring around NGC 4262. it is unlikely it comes from a primordial cloud of neutral hydrogen such that discussed in detail by Thilker et al. (," Taking into account the clear symmetry of the HI ring around NGC 4262, it is unlikely it comes from a primordial cloud of neutral hydrogen such that discussed in detail by Thilker et al. ("6962009).,2009).697 On the contrary. Bekki et al. (," On the contrary, Bekki et al. ("6982005) do model the stripping of rings and ares of cold gas as due to interaction with other galaxies.,2005) do model the stripping of rings and arcs of cold gas as due to interaction with other galaxies.699 In this context. a stream of gas pulled out of the disk of the galaxy (or contributed by a perturber) forms stars when it is compressed.," In this context, a stream of gas pulled out of the disk of the galaxy (or contributed by a perturber) forms stars when it is compressed."700 Such an interaction scenario is supported also by a further hint. namely the observed inner decoupling of gas and stars velocity fields in NGC 4262 (Sarzi et al.," Such an interaction scenario is supported also by a further hint, namely the observed inner decoupling of gas and stars velocity fields in NGC 4262 (Sarzi et al."701 2006)., 2006).702 In the specific case of GC 4262 the existence of a mutual interaction with the other Virgo galaxy NGC [254 has been proposed by Chyzy et al. (, In the specific case of NGC 4262 the existence of a mutual interaction with the other Virgo galaxy NGC 4254 has been proposed by Chyzy et al. (7032007). while another example of such merger-induced. ringed lenticular galaxies could be NGC 404 (Thilker et al.,"2007), while another example of such merger-induced, ringed lenticular galaxies could be NGC 404 (Thilker et al."704 2010)., 2010).705 As far as the UV- disk’s star formation is concerned. is likely occurring ndependently of the above possible (ring-forming) interaction event.," As far as the UV-detected, disk's star formation is concerned, is likely occurring independently of the above possible (ring-forming) interaction event."706 Thanks to the UV-sensitive GALEX satellite we were able to detect an extended. UV-bright ring surrounding the otherwise normal SBO galaxy NGC 4262.," Thanks to the UV-sensitive GALEX satellite we were able to detect an extended, UV-bright ring surrounding the otherwise normal SB0 galaxy NGC 4262."707 Such a feature (not recognizable in the optical) appears to host several knots. likely consisting of hot star clusters.," Such a feature (not recognizable in the optical) appears to host several knots, likely consisting of hot star clusters."708 In this respect. NGC 4262—having clustered UV-bright sources 1n its outer parts—could be classified as a Type | extended ultraviolet disk (XUV).," In this respect, NGC 4262---having clustered UV-bright sources in its outer parts—could be classified as a Type 1 extended ultraviolet disk (XUV)."709 About the origin of such a structure. one should be aware that theoretical models (e.g. Bekki 2005: Higdon Higdon 2010) ascribe the onset of rings and ares of cold gas as well as the formation of young star rings to the past interaction with other galaxies.," About the origin of such a structure, one should be aware that theoretical models (e.g. Bekki 2005; Higdon Higdon 2010) ascribe the onset of rings and arcs of cold gas as well as the formation of young star rings to the past interaction with other galaxies."710 As a consequence. taking account also of the observed inner decoupling of gas and stars velocity fields (Sarzi et al.," As a consequence, taking account also of the observed inner decoupling of gas and stars velocity fields (Sarzi et al."711 2006). we are pretty confident that à past major interaction episode underwent by NGC 4262 is responsible of the onset of the UV-bright ring we see today.," 2006), we are pretty confident that a past major interaction episode underwent by NGC 4262 is responsible of the onset of the UV-bright ring we see today."712"‘Phe ""radio loudness' of an active galactic nucleus (AGN) is usually defined. as the ratio of its radio and optical Ilux densities or luminosities at two specific frequencies.",The `radio loudness' of an active galactic nucleus (AGN) is usually defined as the ratio of its radio and optical flux densities or luminosities at two specific frequencies.713" A possible bimodality in the radio loudness distribution. of the AGw population. the so-called: ""racio-Ioud/racdio-cquiet clichotomy. is an often-debated. somewhat contenious. and ongoing topic of study (c.g.Strittmatteretal.1980:SramekSingalοἱal. 2011)."," A possible bimodality in the radio loudness distribution of the AGN population, the so-called `radio-loud/radio-quiet dichotomy', is an often-debated, somewhat contentious, and ongoing topic of study \citep*[e.g.][]{strittmatter80,sramek80,condon81,kellermann89,miller90,miller93,xu99,white00,ivezic02,cirasuolo03a,cirasuolo03b,gopal08,zamfir08,singal11}."714. The resolution of this issue is crucial if fundamental questions relating to the physics of rlack ole (BIL) aceretion. jet formation and feedback are to be fully ackelressect.," The resolution of this issue is crucial if fundamental questions relating to the physics of black hole (BH) accretion, jet formation and feedback are to be fully addressed."715" One standard definition of radio loudness that has been used. particularly. in quasar studies is the ratio Sp./ S. where S,, and 5,, are the monochromatic 5 Cllz radio and nuclear 4400 ((D-band) Uux densities. respectively (Ixellermann.etal. 1989)."," One standard definition of radio loudness that has been used particularly in quasar studies is the ratio $S_{\nu_{5}}/S_{\nu_{B}}$ , where $S_{\nu_{5}}$ and $S_{\nu_{B}}$ are the monochromatic 5 GHz radio and nuclear 4400 $B$ -band) flux densities, respectively \citep[][]{kellermann89}."716". Raclio-loucl quasars were at. first. considered. to be hose with 5,4δρ210. while for most racdio-quiet quasars Klo<SpfSe,lo (egPeterson.1997)."," Radio-loud quasars were at first considered to be those with $S_{\nu_{5}}/S_{\nu_{B}} \gtrsim 10$, while for most radio-quiet quasars $0.1 < S_{\nu_{5}}/S_{\nu_{B}} < 1$ \citep[e.g.][]{peterson97}."717. llowever. in more recent times. DII mass have allowed a more sophisticated approach to be adopted when studying he radio Lloudnesses of AGN: the dependence. of racio oudness on the Extington ratio. A (>πμσα. where Lua is the nuclear radiative bolometric luminosity and Lpgaa is the Ecclington lIuminositv).," However, in more recent times, BH mass have allowed a more sophisticated approach to be adopted when studying the radio loudnesses of AGN: the dependence of radio loudness on the Eddington ratio, $\lambda$ $\equiv L_{\rm bol}/L_{\rm Edd}$, where $L_{\rm bol}$ is the nuclear radiative bolometric luminosity and $L_{\rm Edd}$ is the Eddington luminosity)."718 For example. Sikora.Stawarz&Lasota (2007).. henceforth referred to as SSLOT. investigated. the radioloudnesses of a total of 199 sources spread across five dilferent populations: broad-line racio," For example, \citet*[][]{sikora07}, henceforth referred to as SSL07, investigated the radioloudnesses of a total of 199 sources spread across five different populations: broad-line radio"719Correspondingly. we can express the angular momentum of the external gas as the following dimensionless ratio When .#>>|. we expect the flow to be viscously driven and to resemble an ADAF solution. whereas when. Z«|. the flow should be practically identical to the Bondi solution.,"Correspondingly, we can express the angular momentum of the external gas as the following dimensionless ratio When ${\cal L}\gg1$, we expect the flow to be viscously driven and to resemble an ADAF solution, whereas when ${\cal L}\ll1$, the flow should be practically identical to the Bondi solution."720 These expectations are borne out by the numerical solutions described in refresults.., These expectations are borne out by the numerical solutions described in \\ref{results}.721 For our choice of coup=10SOF =| corresponds to #—0.0037.," For our choice of $c_{\rm out} = 10^{-3}c$, ${\cal722 L}=1$ corresponds to ${\cal R} = 0.0037$."723 Since the viscous accretion equations tend to be very stiff. we use a relaxation method (Press et al.," Since the viscous accretion equations tend to be very stiff, we use a relaxation method (Press et al."724 1992) to solve Figure | shows sample solutions correspondingto @=0.1. y=5/3. Cou=105 and Pow=1 (the value of pau is arbitrary since we can rescale the density profile to any external density as needed. retbes)).," 1992) to solve Figure 1 shows sample solutions correspondingto $\alpha=0.1$, $\gamma=5/3$, $c_{\rm out} = 10^{-3}$ and $\rho_{\rm725 out}=1$ (the value of $\rho_{\rm out}$ is arbitrary since we can rescale the density profile to any external density as needed, \\ref{bcs}) )."726 Four solutions are shown. corresponding to Z7=85. 12. 1.8. O.LI. respectively (compare with Fig.," Four solutions are shown, corresponding to ${\cal L} = 85$, 12, 1.8, 0.11, respectively (compare with Fig."727 | in Park 2009)., 1 in Park 2009).728 Note that the rotation parameter .z is small for all the solutions. so these truly represent slowly-rotating flows.," Note that the rotation parameter ${\cal R}$ is small for all the solutions, so these truly represent slowly-rotating flows."729 Even the most rapidly rotating solution 647— 0.31) has a centrifugal support of only of Keplerian at r—rp., Even the most rapidly rotating solution ${\cal R}=0.31$ ) has a centrifugal support of only of Keplerian at $r=r_{\rm B}$.730 The solution with .Z=0.11 — the lowest curve in the panel of Fig., The solution with ${\cal L}=0.11$ – the lowest curve in the top-left panel of Fig.731 | — is clearly in the Bondi regime since the gas has negligible outer specific angular momentum relative to hy., 1 – is clearly in the Bondi regime since the gas has negligible outer specific angular momentum relative to $l_{\rm ms}$.732" The sonic radius ry. shown by the black dot. is located at 317r,. which is almost exactly where a pure non-rotating Bondi flow has its sonic radius for our choice of P(r). Cou and y."," The sonic radius $r_s$, shown by the black dot, is located at $417r_g$, which is almost exactly where a pure non-rotating Bondi flow has its sonic radius for our choice of $\Phi(r)$, $c_{\rm out}$ and $\gamma$."733 The two solutions with .Z=85 and 12 (the highest two curves) are definitely rotation-dominated., The two solutions with ${\cal L}= 85$ and 12 (the highest two curves) are definitely rotation-dominated.734 The gas in these solutions has too much angular momentum to permit steady accretion in the absence of viscosity. so the accretion flow settles down to a viscously-driven ADAF solution.," The gas in these solutions has too much angular momentum to permit steady accretion in the absence of viscosity, so the accretion flow settles down to a viscously-driven ADAF solution."735" Correspondingly. the sonic radius is close to the marginally stable orbit. rj,=3r,."," Correspondingly, the sonic radius is close to the marginally stable orbit, $r_{\rm ms}=3r_g$."736 The solution with .Zz=1.8 represents a transition state between the Bondi and ADAF regimes., The solution with ${\cal L}=1.8$ represents a transition state between the Bondi and ADAF regimes.737 Its sonic radius is at an intermediate location. ry=|42re.," Its sonic radius is at an intermediate location, $r_s=142r_g$."738 In Figure 2. the top-left panel shows how the sonic radius moves as we change .ZZ.," In Figure 2, the top-left panel shows how the sonic radius moves as we change ${\cal L}$."739" For all values of κI. ry is located at the position one would calculate for the non-rotating Bondi problem (upper dotted line). while for .Z greater than a few. ry is close to Tii, Cower dotted line)."," For all values of ${\cal L}<1$, $r_s$ is located at the position one would calculate for the non-rotating Bondi problem (upper dotted line), while for ${\cal L}$ greater than a few, $r_s$ is close to $r_{\rm ms}$ (lower dotted line)."740 The transition between these two regimes is quite sudden. with most of the change happening over the range L5«Vx3.," The transition between these two regimes is quite sudden, with most of the change happening over the range $1.5 < {\cal L} < 2$."741 The bottom two panels in Fig., The bottom two panels in Fig.742 | show the profiles of density p and pressure p—pc; for the same four solutions as in the top left panel., 1 show the profiles of density $\rho$ and pressure $p=\rho c_s^2$ for the same four solutions as in the top left panel.743 Even though the rotation profiles of these solutions are very different. and their sonic radii move around considerably. the profiles of p and p are nearly identical.," Even though the rotation profiles of these solutions are very different, and their sonic radii move around considerably, the profiles of $\rho$ and $p$ are nearly identical."744 The insensitivity to the location of Ες is at least in part because we selected y=5/3. which is known to be a critical value of the adiabatic index both for the Bondi problem and for ADAFs.," The insensitivity to the location of $r_s$ is at least in part because we selected $\gamma=5/3$, which is known to be a critical value of the adiabatic index both for the Bondi problem and for ADAFs."745 Nevertheless. it is clear that in many respects. an ADAF is very similar to a Bondi flow.," Nevertheless, it is clear that in many respects, an ADAF is very similar to a Bondi flow."746 The top-right panel in Fig., The top-right panel in Fig.747 | shows the radial velocity profiles of the four solutions., 1 shows the radial velocity profiles of the four solutions.748 We see that the radial velocity is smaller for a rotating ADAF ¢the solutions with .#= 85. 12) compared to a slowly-rotating Bondi-like flow (27= 0.113.," We see that the radial velocity is smaller for a rotating ADAF (the solutions with ${\cal L}=85$ , 12) compared to a slowly-rotating Bondi-like flow ${\cal L}=0.11$ )."749 Since the density profiles of both Kinds of solution are nearly the same. this means that the mass accretion rates are different.," Since the density profiles of both kinds of solution are nearly the same, this means that the mass accretion rates are different."750 This is illustrated in the, This is illustrated in the751"and fy=bf"".",and $R_0=bl^p$.752 Xs expected. we see that increasing / while ioleüng all other parameters fixed decreases the zero-signal racius.," As expected, we see that increasing $l$ while holding all other parameters fixed decreases the zero-signal radius."753 Table 3. shows the best fit parameters for this power aw for the data shown in Figure 5.., Table \ref{tab:nfw_l} shows the best fit parameters for this power law for the data shown in Figure \ref{fg:nfw_l}.754" Finally. we consider the behaviour of the peak FAM, signal and the zero-signal radius for an NEW. profile. of ixed mass. with fixed aperture parameters A and /. as a ""unction of concentration parameter e."," Finally, we consider the behaviour of the peak $\fmap$ signal and the zero-signal radius for an NFW profile of fixed mass, with fixed aperture parameters $R$ and $l$ , as a function of concentration parameter $c$."755 Phe data have a strong dependence on halo mass. therefore Figure 6. shows he behaviour of the peak signal and. zero-signal contours for various combinations of/ ane 2 for both a halo of mass OthM. and 1075.TAL...," The data have a strong dependence on halo mass, therefore Figure \ref{fg:nfw_c} shows the behaviour of the peak signal and zero-signal contours for various combinations of $l$ and $R$ for both a halo of mass $10^{11}h^{-1}\,M_\odot$ and $10^{15}h^{-1}\,M_\odot$."756" Llere. again. the behaviour of cach appears to be a power law of the form men,=ae” and fy=be""."," Here, again, the behaviour of each appears to be a power law of the form $m_{peak}=ac^n$ and $R_0=bc^p$."757 “Table 40 shows the best fit parameters for these power laws for the data shown in Figure 6.., Table \ref{tab:nfw_c} shows the best fit parameters for these power laws for the data shown in Figure \ref{fg:nfw_c}.758" The behaviour of the peak PAZ, signal from the NEW. profile dillers ereathy from. that of the SES model as the aperture radius and filter polynomial order are changed.", The behaviour of the peak $\fmap$ signal from the NFW profile differs greatly from that of the SIS model as the aperture radius and filter polynomial order are changed.759 Moreover. the behaviour changes with halo mass and concentration parameter in a non-trivial way.," Moreover, the behaviour changes with halo mass and concentration parameter in a non-trivial way."760 A similar trend. is seen when considering the behaviour of the zero-signal radius. where the slope of the power law behaviour changes based on aperture size. filter shape. virial mass and concentration parameter.," A similar trend is seen when considering the behaviour of the zero-signal radius, where the slope of the power law behaviour changes based on aperture size, filter shape, virial mass and concentration parameter."761 Again. it is not. possible to model this behaviour simply and arrive at à general analytic expression for the zero-signal radius that simultaneously describes its behaviour as a function of all the parameters one might vary.," Again, it is not possible to model this behaviour simply and arrive at a general analytic expression for the zero-signal radius that simultaneously describes its behaviour as a function of all the parameters one might vary."762 This vastly dilfering behaviour implies that if one were to consider several llexion aperture mass reconstructions of a lens field using dilferent aperture radii and filter polynomial order. one might be able to distinguish not only between an SIS model anc an NEW. model. but. between NEW models with dillerent masses and concentration parameters.," This vastly differing behaviour implies that if one were to consider several flexion aperture mass reconstructions of a lens field using different aperture radii and filter polynomial order, one might be able to distinguish not only between an SIS model and an NFW model, but between NFW models with different masses and concentration parameters."763 Moreover. considering the behaviour exhibited in. Figures 4 and 5. it appears that a change in aperture radius shows a greater change inthe overall peak signal than a change in polynomial order. and thus might provide a better," Moreover, considering the behaviour exhibited in Figures \ref{fg:nfw_r} and \ref{fg:nfw_l}, it appears that a change in aperture radius shows a greater change inthe overall peak signal than a change in polynomial order, and thus might provide a better"764AT V streneth aud A3 V wines... example of two normal parent spectra producing a peculiar composite”.,"A7 V strength and A3 V wings... example of two normal parent spectra producing a peculiar composite""."765 The effect of voiliug in the spectrum of a binary with components nof very dissimilar from one another (M—2 and 1.4 solar masses) has been investigated iu detail by Lyubiniukoy (1992)., The effect of veiling in the spectrum of a binary with components not very dissimilar from one another (M=2 and 1.4 solar masses) has been investigated in detail by Lyubimkov (1992).766 Most of lis analysis. devoted to Am stars. refers to courposi| spectra (computed for Lb sclected evolutionary phases) obtained by combining two spectra for which solar abundances are adopted ouly for clemeuts lighter than Ti.," Most of his analysis, devoted to Am stars, refers to composite spectra (computed for 4 selected evolutionary phases) obtained by combining two spectra for which solar abundances are adopted only for elements lighter than Ti."767 A ecneral apparcut uuderabunudauce of these elements is derived by his computatious when the original duplicity is ucelected. in agreement with the weak metal lines obtained by our example plotted im Fig.," A general apparent underabundance of these elements is derived by his computations when the original duplicity is neglected, in agreement with the weak metal lines obtained by our example plotted in Fig."768" {,", 4.769 AccordingC» to the data collected in the previous sectionis. 1l stars of our origiualOo sample are doubles with an angular separation smaller than 1.2 arcsec. 3 stars are SD2 iux | are probably non-imgle. according to the Iipparcos data.," According to the data collected in the previous sections, 11 stars of our original sample are doubles with an angular separation smaller than 1.2 arcsec, 3 stars are SB2 and 4 are probably non-single, according to the Hipparcos data."770 In couchision. for 18/89 20 '4 of our siuuple stars duplicitv mmus be exaimiued in further detail before determuning atmospheric abunuidanuces.," In conclusion, for 18/89= 20 $ \%$ of our sample stars duplicity must be examined in further detail before determining atmospheric abundances."771 Cremer et al. (, Grenier et al. (7721999) in them radial velocity study of a sample of D to F stars. included in the Tipparcos catalogue. obtained spectra for 16 stars of our sample.,"1999) in their radial velocity study of a sample of B to F stars, included in the Hipparcos catalogue, obtained spectra for 16 stars of our sample."773 Of these 12 are suspected. probable or established binarics. ouly lofthese are amoug the 18 known binaries previously meutioned.," Of these 12 are suspected, probable or established binaries, only 4 of these are among the 18 known binaries previously mentioned."774 If all of them will be confined to be binaries the percentage will raise to., If all of them will be confirmed to be binaries the percentage will raise to.775 We note also that 11 of these stars are in conunou with the € list aud 8 are classified as POL by hun., We note also that 11 of these stars are in common with the G list and 8 are classified as PHL by him.776 If we apply the preseut knowledge to the 15 stars analyzed by St93. we see that 2 of them are SB2 (IID 9δ19. ane the atinospherie parameters. derived frou the combined photometric iudices. require the hypothesis that the two stars are strictly the same so that the same 2nd ee can be adopted.," If we apply the present knowledge to the 15 stars analyzed by St93, we see that 2 of them are SB2 (HD 38545 and HD 111786), for HD 198160 and HD 198161 the atmospheric parameters, derived from the combined photometric indices, require the hypothesis that the two stars are strictly the same so that the same and g can be adopted."777 The duplicity of these stars requires to be further examined in order to determine accurate suele clemeuts abuudances., The duplicity of these stars requires to be further examined in order to determine accurate single elements abundances.778 Furthermore. the variability of the 5 variable stars niust be examined to assess that its amplitude docs not affect the photometrically derived atimospheric parameters.," Furthermore, the variability of the 5 variable stars must be examined to assess that its amplitude does not affect the photometrically derived atmospheric parameters."779 Ileh S/N spectroscopic data of spectral resions iu which not severely blended features are present are necessary ο discriminate between velius (spectral ines when they retain the breadth of their temperature ype. but are shallower than normal (Corbally 1987}) which indicates a composite spectrum and normal xofiles with weak intensities. which are sign of real uetal uuderabuudauces.," High S/N spectroscopic data of spectral regions in which not severely blended features are present are necessary to discriminate between ""veiling"" (spectral lines when they retain the breadth of their temperature type, but are shallower than normal (Corbally 1987)) which indicates a composite spectrum and normal profiles with weak intensities, which are sign of real metal underabundances."780 Such discrimination. however. )ocomies extremely difficult when the observed. spectrum is characterized by broad aud weak metal lines as in most candidates.," Such discrimination, however, becomes extremely difficult when the observed spectrum is characterized by broad and weak metal lines as in most candidates."781 What we can expect in a composite spectrum of two similar A-type stars ive Balmer lines broader than those of the sinele commponcuts by an amount which depends on the relative RV of the commponcuts. so simulating a star with a higher eecee value when compared to computed spectra or intrinsically very hieh for an carly A-type star as it iav be the case of ΠΟ 291255 (the parameters derived bx AID programs are Z;4g42110370 Is oooge=50).," What we can expect in a composite spectrum of two similar A-type stars are Balmer lines broader than those of the single components by an amount which depends on the relative RV of the components, so simulating a star with a higher g value when compared to computed spectra or intrinsically very high for an early A-type star as it may be the case of HD 294253 (the parameters derived by MD programs are 10370 K g=4.50)."782 Moreover. the composite Balmer line profile will present a flat iuner core which depends on the differeuce of the two radial velocities as well as a global profile which uav be different from what is expected from the douinatiug broadenings: Doppler core aud linear Stark wines.," Moreover, the composite Balmer line profile will present a flat inner core which depends on the difference of the two radial velocities as well as a global profile which may be different from what is expected from the dominating broadenings: Doppler core and linear Stark wings."783 For the stars recognized to be double by speckle observations. and not observed by the Iipparcos satellite. the extraction of luminosity ratios from speckle data will be frndamental ο better define the character of the two componcuts.," For the stars recognized to be double by speckle observations, and not observed by the Hipparcos satellite, the extraction of luminosity ratios from speckle data will be fundamental to better define the character of the two components."784 Algorithms to extract luminosity ratios from 4.oeckle data have been developed. but these tecliuiques are still limited (Sowell Wilson 1993).," Algorithms to extract luminosity ratios from speckle data have been developed, but these techniques are still limited (Sowell Wilson 1993)."785 If the luminosity of the companion is large enoueh (of the order of of the total huninosity). the veiling may not be neglected: iu fact the metallic lines will appear weaker. thus leading to zu underestimate of the metallicity.," If the luminosity of the companion is large enough (of the order of of the total luminosity), the veiling may not be neglected; in fact the metallic lines will appear weaker, thus leading to an underestimate of the metallicity."786 The IR colows could also prove to be powerful diagnostic tool for the presence of cooler companious., The IR colours could also prove to be powerful diagnostic tool for the presence of cooler companions.787 A cool companion of ΠΟ 111786 was predicted Dy its photometry in the JAD and Io bands by Cerbaldi (1990) ou the basis of the discrepancy with the (B-V) value aud was ascribed to a probable cool companion.," A cool companion of HD 111786 was predicted by its photometry in the J,H and K bands by Gerbaldi (1990) on the basis of the discrepancy with the (B-V) value and was ascribed to a probable cool companion."788 The foregone discussion leads us tfo formulate he hypothesis hat a considerable fraction of candidates are du fact ynarics., The foregoing discussion leads us to formulate the hypothesis that a considerable fraction of candidates are in fact binaries.789 This is supported by he large fraction of binaries recently discovered along stars ether through the speckle techuique or w the Tipparcos experiment., This is supported by the large fraction of binaries recently discovered among stars either through the speckle technique or by the Hipparcos experiment.790 Also the lieh nuuboer of stars with a υπο colour excess supports that our μπατν hvpothesis is at the origin of distorted energy distributions aud of not colerent uvby.? indices of several candidates.," Also the high number of stars with a ""blue"" colour excess supports that our binarity hypothesis is at the origin of distorted energy distributions and of not coherent $\beta$ indices of several candidates."791 The PHL phenomenon cannot be easilv explained if the stars are single. however its explanation becomes trivial if the stars are binary as has Όσσα demonstrated in the case of the stars IID 38515 aud ID 111756. classified PIIL by Cray (1988. 1998). which iade turned out to be binaries.," The PHL phenomenon cannot be easily explained if the stars are single, however its explanation becomes trivial if the stars are binary, as has been demonstrated in the case of the stars HD 38545 and HD 111786, classified PHL by Gray (1988, 1998), which indeed turned out to be binaries."792 The appareutlv erratic abundance patterus pose serious problems to the accretion hypothesis. but again it nav be casily reconciled iu the case of binary stars.," The apparently erratic abundance patterns pose serious problems to the accretion hypothesis, but again it may be easily reconciled in the case of binary stars."793 The fact that some of the stars are binaries does uot exclude the possibility that chemical peculiarities are actually present in their atmospheres., The fact that some of the stars are binaries does not exclude the possibility that chemical peculiarities are actually present in their atmospheres.794 However their quantification requires that the binaritv is properly accounted for., However their quantification requires that the binarity is properly accounted for.795 We have shown that each author has his own definition and list of A Doo caudidates and these lists only partly overlap., We have shown that each author has his own definition and list of $\lambda$ Boo candidates and these lists only partly overlap.796 Until all the classification schemes converge into, Until all the classification schemes converge into797"(and gen; /n)), the integral in equation (20)) becomes: The column density through a smoothing volume (for any impact parameter and any distance into the sphere) can now be calculated; multiplying by an opacity then provides an optical depth.","(and _f = ), the integral in equation \ref{eq:sigma}) ) becomes: The column density through a smoothing volume (for any impact parameter and any distance into the sphere) can now be calculated; multiplying by an opacity then provides an optical depth."798" Typically, )isconstructedusingcubicsplines(?).."," Typically, is constructed using cubic splines \citep{Monaghan_92}."799" T hekernelusedinthisworkis This provides compact support (i.e. it reduces to zero outside the smoothing volume), and is simple to integrate."," The kernel used in this work is This provides compact support (i.e. it reduces to zero outside the smoothing volume), and is simple to integrate."800" With a prescription for calculating optical depth for a single sphere in place, a scheme for calculating ray/sphere intersections must be constructed."," With a prescription for calculating optical depth for a single sphere in place, a scheme for calculating ray/sphere intersections must be constructed."801" To this end, the code creates a data object called araylist,, which stores (in order of intersection) all particles that the ray (given its origin and direction vector) will intersect."," To this end, the code creates a data object called a, which stores (in order of intersection) all particles that the ray (given its origin and direction vector) will intersect."802" Once the list is created, the optical depth can be calculated quickly using equation (18))."," Once the list is created, the optical depth can be calculated quickly using equation \ref{eq:scatter}) )."803 The construction of the raylist must be computationally efficient for the code to be effective., The construction of the raylist must be computationally efficient for the code to be effective.804 The procedure is similar to that implemented by ? inSPHRAY; the code constructs an octree to spatially index the particles efficiently (as there may be density changes over several orders of magnitude)., The procedure is similar to that implemented by \citet{SPHRAY} in; the code constructs an octree to spatially index the particles efficiently (as there may be density changes over several orders of magnitude).805" The cells either contain child cells, or particles (the cells))."," The cells either contain child cells, or particles (the )."806 The tree is constrained to have a maximum number of particles in each leaf., The tree is constrained to have a maximum number of particles in each leaf.807" All cells have an associated Axis Aligned Bounding Box (AABB), which is the minimum box size, aligned to the three cartesian axes, to contain all the smoothing volumes of the particles in the cell (see Figure 4))."," All cells have an associated Axis Aligned Bounding Box (AABB), which is the minimum box size, aligned to the three cartesian axes, to contain all the smoothing volumes of the particles in the cell (see Figure \ref{fig:aabb}) )."808" These AABBs are necessary as tree nodes may contain a particle, but not its entire smoothing volume This allows the determination of intersections between the ray and the cells (or more correctly, their AABBs)."," These AABBs are necessary as tree nodes may contain a particle, but not its entire smoothing volume 	 This allows the determination of intersections between the ray and the cells (or more correctly, their AABBs)."809" Starting with the root cell, each child cell is tested for intersection, constituting a walk through the tree."," Starting with the root cell, each child cell is tested for intersection, constituting a walk through the tree."810" If a leaf cell is intersected by the ray, then the particles in the leaf are tested for intersection (by calculating their impact parameters)."," If a leaf cell is intersected by the ray, then the particles in the leaf are tested for intersection (by calculating their impact parameters)."811 This ensures that only a minimum fraction of the particles in the system need testing for intersection., This ensures that only a minimum fraction of the particles in the system need testing for intersection.812" This illustrates the necessity of AABBs; tree nodes may contain a particle, but not its entire smoothing volume."," This illustrates the necessity of AABBs; tree nodes may contain a particle, but not its entire smoothing volume."813" Thus, calculating intersections between a ray and tree nodes may miss contributions to the density field from smoothing volumes that cross node intersections."," Thus, calculating intersections between a ray and tree nodes may miss contributions to the density field from smoothing volumes that cross node intersections."814" Tests for intersections between rays and AABBs are carried out using the ray slopes algorithm (?),, which has been shown to be faster than other commonly used methods, such as using Plüccker coordinates (?).."," Tests for intersections between rays and AABBs are carried out using the ray slopes algorithm \citep{rayslope}, which has been shown to be faster than other commonly used methods, such as using Plüccker coordinates \citep{plucker}."815 An important facet of an MCRT code is the determination of the scattering location of the photon., An important facet of an MCRT code is the determination of the scattering location of the photon.816" In general, the scattering location will occur inside a smoothing volume, and possibly at a location where the density depends on the contributions from several particles."," In general, the scattering location will occur inside a smoothing volume, and possibly at a location where the density depends on the contributions from several particles."817" Therefore, when attempting to determine the scattering location, it is important to define four classes of particle: The classes are illustrated in Figure 5.."," Therefore, when attempting to determine the scattering location, it is important to define four classes of particle: The classes are illustrated in Figure \ref{fig:classes}."818 Particles of class (i) obviously do not affect the calculation - particles of class (ii) are accounted for simply., Particles of class (i) obviously do not affect the calculation - particles of class (ii) are accounted for simply.819" Particles of classes (iii) and (iv) will have differing effects on the optical depth calculation, and will require separate treatments."," Particles of classes (iii) and (iv) will have differing effects on the optical depth calculation, and will require separate treatments."820" The scattering location is determined by iteration: firstly, the optical depth is calculated particle by particle using the raylist until the optical depth exceeds the randomly selected optical depth at particlekk."," The scattering location is determined by iteration: firstly, the optical depth is calculated particle by particle using the raylist until the optical depth exceeds the randomly selected optical depth at particle."821". Then, the optical depth is calculated from the beginning of the sphere for particle (ensuring that all potential contributors before and after this location are accounted for), iterating over distance until the answer converges ontaU."," Then, the optical depth is calculated from the beginning of the sphere for particle (ensuring that all potential contributors before and after this location are accounted for), iterating over distance until the answer converges on."822",catter-- AS the optical depth always increases with distance, convergence can be achieved with simple algorithms and relatively litle computation."," As the optical depth always increases with distance, convergence can be achieved with simple algorithms and relatively little computation."823 This code uses a recursive bisector algorithm to perform the iteration., This code uses a recursive bisector algorithm to perform the iteration.824" Starting from the path length between the beginning of sphere (k—1) to the end of sphere k, this value is halved recursively until the correct optical depth is obtained (to within some tolerance) or until the path length reaches a minimum value (defined as a fraction of the smallest smoothing length in the simulation)."," Starting from the path length between the beginning of sphere $(k-1)$ to the end of sphere $k$, this value is halved recursively until the correct optical depth is obtained (to within some tolerance) or until the path length reaches a minimum value (defined as a fraction of the smallest smoothing length in the simulation)."825are much more sparsely populated.,are much more sparsely populated.826" We obtained reliable photometry for only 168 aud 692 stars for S2 and $3. respectively,"," We obtained reliable photometry for only 468 and 692 stars for S2 and S3, respectively."827 The fal CMDs for the fields ave shown iu Figures 2 and 3.., The final CMDs for the fields are shown in Figures \ref{cmds} and \ref{outer_cmds}.828 We measured the star formation rate and metallicity as a function of stellar age using the software package AMIATCTID2002)., We measured the star formation rate and metallicity as a function of stellar age using the software package MATCH.829.. We £ft the observed CMDs @vith magnitude cuts set to limits provided in Table 1)) by populating the stellar evolution models of with a initial mass function (IME) for a erid of asstuned distance and foreground extinction values o allow for systematic differences iu stellar evolution uodels and/or systematic plotometiic crror., We fit the observed CMDs (with magnitude cuts set to limits provided in Table \ref{table}) ) by populating the stellar evolution models of with a initial mass function (IMF) for a grid of assumed distance and foreground extinction values to allow for systematic differences in stellar evolution models and/or systematic photometric errors.830 The choices of software and models used for the ANGST xoject are discussed in detail in and stummarizecd i(2009)., The choices of software and models used for the ANGST project are discussed in detail in and summarized in.831. The best fits provide the combination of ages and uctallicities that are contained in the observed field., The best fits provide the combination of ages and metallicities that are contained in the observed field.832 We attempted to fit the data with a spread in the model photometry alone the reddeuiug line to account for the effects of differential reddening., We attempted to fit the data with a spread in the model photometry along the reddening line to account for the effects of differential reddening.833" Ποπονα, applying a spread in reddening of A:=0.5 to the models degraded he quality of the CAID fits. showing that differcutial reddening docs not significantly affect our iieasurements in NGC 101."," However, applying a spread in reddening of $A_V=0.5$ to the models degraded the quality of the CMD fits, showing that differential reddening does not significantly affect our measurements in NGC 404."834 The data from the deep field were best fit wa sinele foreground reddening y-=0.140.06 aud i5 1840.09 (see Fieure 1)., The data from the deep field were best fit by a single foreground reddening $A_V$ $\pm$ 0.06 and $m-M_0$ $\pm$ 0.09 (see Figure \ref{residuals}) ).835 This distance modulus is Afyp=27.consistent with. but larger than. the value measured wo the ANGST suvev2009).," This distance modulus is consistent with, but larger than, the value measured by the ANGST survey."836. The best fit values compensate for auv svsteiuatic differences between the data aud overall nodel isochrones. whereas the survey value i50lated the well-detemmined location of the tip of the red elaut xanch iu order to measure the best distance.," The best fit values compensate for any systematic differences between the data and overall model isochrones, whereas the survey value isolated the well-determined location of the tip of the red giant branch in order to measure the best distance."837 Since hese distance and extinction values provided the best overall fit of the models to the data. we performed our fits to the data of every region asstming these values.," Since these distance and extinction values provided the best overall fit of the models to the data, we performed our fits to the data of every region assuming these values."838 Our uncertaintics in star formation rate account for changes in the SEIT measured if the assumed value. for i6 distance modulus was £0.15 mag away from the chosen value aud if the extinction value was +0.1 mae away from the chosen value., Our uncertainties in star formation rate account for changes in the SFH measured if the assumed value for the distance modulus was $\pm$ 0.15 mag away from the chosen value and if the extinction value was $\pm$ 0.1 mag away from the chosen value.839 We note that in Figure 3 1ο apparent maguitude of the tip of the RGB appears zdnter than iu our more populous CMDs., We note that in Figure \ref{outer_cmds} the apparent magnitude of the tip of the RGB appears fainter than in our more populous CMDs.840 Our fits to rese CAIDs (Figure 5)) were not significantly improved w allowing a erecater distance modulus. indicating that jo ΜΗ uunubers of stars iu these fields cause the tip of ιο RGB to be under-populated.," Our fits to these CMDs (Figure \ref{s3_fit}) ) were not significantly improved by allowing a greater distance modulus, indicating that the small numbers of stars in these fields cause the tip of the RGB to be under-populated."841" Ou the other απ, the SEIIs of these fields could be significantly different than 1ο iuner fields."," On the other hand, the SFHs of these fields could be significantly different than the inner fields."842 The shallow depth aud low uwmubers of stars du these fields limits our ability to constrain the ec, The shallow depth and low numbers of stars in these fields limits our ability to constrain the age.843", Our fits show only that of the stars are older ian 1.6 Cr.", Our fits show only that of the stars are older than 1.6 Gyr.844 Thus. it is possible that most of these stars are onlv a few Gyr old. which could produce a ziuter TRGB.," Thus, it is possible that most of these stars are only a few Gyr old, which could produce a fainter TRGB."845 Uufortunately. there is not chough data to constrain whether the cause is undersampling or age.," Unfortunately, there is not enough data to constrain whether the cause is undersampling or age."846 The CMD can be fitted equivalently well by either possibility., The CMD can be fitted equivalently well by either possibility.847 Systematic errors are determiued bv the MATCII package by comparing the results of SEIIs frou fits to the data with different values for the distance aud foreeround reddening to the feld., Systematic errors are determined by the MATCH package by comparing the results of SFHs from fits to the data with different values for the distance and foreground reddening to the field.848 These errors are then added in quadrature to the random errors governed bv our siuupling of the CAID., These errors are then added in quadrature to the random errors governed by our sampling of the CMD.849 The random errors are determined by randomly drawing from the observed CMD to produce Tess diagrams that vary due to the Poisson statistics of our photometric sample., The random errors are determined by randomly drawing from the observed CMD to produce Hess diagrams that vary due to the Poisson statistics of our photometric sample.850 By producing and fitting 100 of these Monte Carlo CAIDs. we are able to determine he xu of the residuals between SFIs from these fits and those from the fits to the original data.," By producing and fitting 100 of these Monte Carlo CMDs, we are able to determine the rms of the residuals between SFHs from these fits and those from the fits to the original data."851" The conibined le error measurements therefore account for he uncertainties in the distauce to the galaxy. the orcerouud reddening. anv systematic shifts between he model colors aud magnitudes and our measured photometry, as well as the uuuber of stars aud features xeseut in our CMD."," The combined $\sigma$ error measurements therefore account for the uncertainties in the distance to the galaxy, the foreground reddening, any systematic shifts between the model colors and magnitudes and our measured photometry, as well as the number of stars and features present in our CMD."852 Our Monte Carlo tests are also used to determine our ine sensitivitvtechnique)., Our Monte Carlo tests are also used to determine our time sensitivity.853. Briefly. we calculate he standard deviation of the 1iaxiumun likelihood value Toni our LOO runs.," Briefly, we calculate the standard deviation of the maximum likelihood value from our 100 runs."854 We asstune that anv fit to the data more than one standard deviation away frou the vest fit is unacceptable., We assume that any fit to the data more than one standard deviation away from the best fit is unacceptable.855 We then rerun our fits while suppressing star formation iu various time bius., We then rerun our fits while suppressing star formation in various time bins.856 If the fit quality does uot change significantly (by more than one standard deviation). we continue to expaud the lenetl of these removed tine bins until the software can no longer find an acceptable fit.," If the fit quality does not change significantly (by more than one standard deviation), we continue to expand the length of these removed time bins until the software can no longer find an acceptable fit."857 At this time resolution. we can be coufident that our data provide meaningful constraints ou the SFU.," At this time resolution, we can be confident that our data provide meaningful constraints on the SFH."858 The final time bius are all sensitive enough that their removal from the SEIT results in an unacceptable CMD fit., The final time bins are all sensitive enough that their removal from the SFH results in an unacceptable CMD fit.859 Photometric depth determines the precision with which we can recover the SEIT of a region., Photometric depth determines the precision with which we can recover the SFH of a region.860 The effects of age aud ietallicity are more difficult to distinguish with shallow photometry than with deep photometry., The effects of age and metallicity are more difficult to distinguish with shallow photometry than with deep photometry.861 Qur deepest photometry comes from our deep feld aud reaches the red chump iu the least crowded region., Our deepest photometry comes from our deep field and reaches the red clump in the least crowded region.862 This photometry therefore provides the most leverage for breaking the degeneracy between the age aud metallicity of the old populations., This photometry therefore provides the most leverage for breaking the degeneracy between the age and metallicity of the old populations.863 In coutrast. the data from our 2 shallow fields provide the least of this leverage.," In contrast, the data from our 2 shallow fields provide the least of this leverage."864 However. since the stellar populations should be well mixed at ages m1 Cyr. we used the metallicity distribution for the old stars (2 Cr) as determunmed from the fit to our full deep field to limit the range of allowed metallicities at cach age in the fits to the shallower data.," However, since the stellar populations should be well mixed at ages $\gg$ 1 Gyr, we used the metallicity distribution for the old stars $>$ 2 Gyr) as determined from the fit to our full deep field to limit the range of allowed metallicities at each age in the fits to the shallower data."865 When the free xuanmeters used to fit the shallower data were limited. we found the resulting age distribution of the ancicut xopulatious of the shallower fields to be cousisteut with hose of the deep data. aud the quality of the fit remained. in the acceptable range (within 1 standard deviation of he value obtained when the full exid of free parameters was allowed).," When the free parameters used to fit the shallower data were limited, we found the resulting age distribution of the ancient populations of the shallower fields to be consistent with those of the deep data, and the quality of the fit remained in the acceptable range (within 1 standard deviation of the value obtained when the full grid of free parameters was allowed)."866 In what follows. the full-field SFIIs for he shallower fields are the best fits possible with the restriction that the ancient population (72 (αντ) contain oulv the metallicities at cach age that contributed to the vest fit of the deep full-field data.," In what follows, the full-field SFHs for the shallower fields are the best fits possible with the restriction that the ancient population $>$ 2 Gyr) contain only the metallicities at each age that contributed to the best fit of the deep full-field data."867where pj is the DII mass. M and 22 the mass and radius of the companion star. respectively.,"where $\mbh$ is the BH mass, $M$ and $R$ the mass and radius of the companion star, respectively."868 The above equation implies that the stellar radius is roughly. half of its radius. ie.. the orbital periods of the incipient binaries are around 2—4 davs.," The above equation implies that the stellar radius is roughly half of its Roche-lobe radius, i.e., the orbital periods of the incipient binaries are around $2-4$ days."869 We have followed the evolution of the binary svstems containing an IMDBILI and a massive donor star for the initial parameters given in last section. using an updated version of the evolution code developed by Egeleton(1971).," We have followed the evolution of the binary systems containing an IMBH and a massive donor star for the initial parameters given in last section, using an updated version of the evolution code developed by \citet{e71}."870. The opacities in (he code are from Rogers& (1992).. and [rom Alexander&Ferguson(1994) [or temperatures below 1055 Ix. For the donor star we assumed a solar chemical composition (.X=0.7. Y=0.28. Z=0.02) and a mixing length parameter a=2.," The opacities in the code are from \citet{ri92}, and from \citet{af94} for temperatures below $10^{3.8}$ K. For the donor star we assumed a solar chemical composition $X=0.7$, $Y=0.28$, $Z=0.02$ ) and a mixing length parameter $\alpha=2$."871 To follow the details of mass (ransler process. we included losses of orbital angular momentum due (to mass loss and gravitational wave radiation.," To follow the details of mass transfer process, we included losses of orbital angular momentum due to mass loss and gravitational wave radiation."872 We limited ihe mass aceretion rate of the black hole to its Exdington limit rate. and let the excess mass be lost from the svstem will (he specific orbital angular momentum of the black hole.," We limited the mass accretion rate of the black hole to its Eddington limit rate, and let the excess mass be lost from the system with the specific orbital angular momentum of the black hole."873 We also assumed that the companion stars are on zero-age main-sequence when they have been captured aud settled in a circular orbit., We also assumed that the companion stars are on zero-age main-sequence when they have been captured and settled in a circular orbit.874 This means that the time lorcircular IMDII binary formation is much less than the stellar main-sequence lifetime., This means that the time for IMBH binary formation is much less than the stellar main-sequence lifetime.875 This may nol be (rue lor (he companion stus more massive (han e15M.. since the Formation history of IMBIL binaries could be as long as 10* vrs (PortegiesZwartetal.2004).," This may not be true for the companion stars more massive than $\sim 15\,\ms$, since the formation history of IMBH binaries could be as long as $\sim 10^7$ yrs \citep{pz04}."876. So our results for stars of A215AL. should be regarded as the most optimistic cases.," So our results for stars of $M\gsim 15\,\ms$ should be regarded as the most optimistic cases."877 Fieurel shows (wo examples of mass (transfer sequences for a binary containing a 1000M. DII with a 5 and 15 M. donor star. respectively [changing the BIL masses (sav. to 100 A.) does not alter the results considerably].," Figure1 shows two examples of mass transfer sequences for a binary containing a $1000\,\ms$ BH with a 5 and 15 $\ms$ donor star, respectively [changing the BH masses (say, to $100\,\ms$ ) does not alter the results considerably]."878 In the figure the mass transfer rates have been converted into X-ray. Iuminosities to be compared wilh observations., In the figure the mass transfer rates have been converted into X-ray luminosities to be compared with observations.879 The X-ray luminosities were calculated according to the slim disk model by Ohsugaetal.(2002).. in which photon trapping effect. wasincluded!.," The X-ray luminosities were calculated according to the slim disk model by \citet{o02}, in which photon trapping effect was."880. The solid and dashed curves correspond respectively (o stable and unstable mass transfer in the accretion disk. according to the criterion given in Dubusetal.(1999).," The solid and dashed curves correspond respectively to stable and unstable mass transfer in the accretion disk, according to the criterion given in \citet{d99}."881. since the initial binary orbit is (oo wide for the companion star to fill its Roche lobe. ihe mass (ransler through. Roche-lobe overflow begins until the star evolves and expands alter a time labelled below the time-axis in the figure.," Since the initial binary orbit is too wide for the companion star to fill its Roche lobe, the mass transfer through Roche-lobe overflow begins until the star evolves and expands after a time labelled below the time-axis in the figure."882 The N-rav. luminosities are generally around LOeres1 |. comparable with those of the most luminous ULXs.," The X-ray luminosities are generally around $10^{40}\,\ergs$ , comparable with those of the most luminous ULXs."883 However. the stable," However, the stable"884"In the special case of circular orbits (the majority of short-period exoplanets, for good reason), there are many useful analytic approximations that we can make to simplify the problem.","In the special case of circular orbits (the majority of short-period exoplanets, for good reason), there are many useful analytic approximations that we can make to simplify the problem."885" Furthermore, the simpler circular case offers intuition into the behavior of our model."," Furthermore, the simpler circular case offers intuition into the behavior of our model."886" In the circular limit, Equation 6 can be rewritten as: where €=TradWady is a dimensionless constant quantifying the planet’s energy recirculation efficiency?,, and ®=wat."," In the circular limit, Equation \ref{dimensionless} can be rewritten as: where $\epsilon = \tau_{\rm rad}\omega_{\rm adv}$ is a dimensionless constant quantifying the planet's energy recirculation , and $\Phi = \omega_{\rm adv} t$."887 A day in the life of a parcel of gas proceeds as shown in Figure 1.., A day in the life of a parcel of gas proceeds as shown in Figure \ref{heating}.888" Note that we have included the sin’/4@ factor in the y-axis, so that we may plot on the same figure the heating curves for parcels at different latitudes."," Note that we have included the $\sin^{1/4}\theta$ factor in the y-axis, so that we may plot on the same figure the heating curves for parcels at different latitudes."889" The two effects of a high ε are 1) a delay in the time of maximum temperature, and 2) higher night-time temperature."," The two effects of a high $\epsilon$ are 1) a delay in the time of maximum temperature, and 2) higher night-time temperature."890" Although the observed light curve depends on both the radiative and advective timescales, the heating pattern of a parcel of gas depends only on their ratio, ε."," Although the observed light curve depends on both the radiative and advective timescales, the heating pattern of a parcel of gas depends only on their ratio, $\epsilon$ ."891" The night-time temperature islargely independent of latitude, 0, but depends sensitively on ε."," The night-time temperature islargely independent of latitude, $\theta$, but depends sensitively on $\epsilon$."892" The maximum temperature reached by a parcel, on the other hand, depends sensitively on its latitude but only weakly on ε."," The maximum temperature reached by a parcel, on the other hand, depends sensitively on its latitude but only weakly on $\epsilon$."893" Because of the equivalency of latitude and albedo, the the dashed lines in Figure 1 can be thought of as the heating curves for equatorial parcels of gas, but with A=30%:: albedo has a more important impact on the day-side heating pattern than on the night-side cooling."," Because of the equivalency of latitude and albedo, the the dashed lines in Figure \ref{heating} can be thought of as the heating curves for equatorial parcels of gas, but with $A \approx 30$: albedo has a more important impact on the day-side heating pattern than on the night-side cooling."894" Finally, the delay between a parcel passing through the sub-stellar longitude and reaching its maximum temperature, ®max, depends more sensitively on e than does the maximum temperature reached, Tinax-"," Finally, the delay between a parcel passing through the sub-stellar longitude and reaching its maximum temperature, $\Phi_{\rm max}$ , depends more sensitively on $\epsilon$ than does the maximum temperature reached, $\tilde{T}_{\rm max}$."895" In the €>oo limit, T'sin!/=(1/z)!/4, as one would expect from Equation 6.."," In the $\epsilon \to \infty$ limit, $\tilde{T} \sin^{1/4}\theta = (1/\pi)^{1/4}$, as one would expect from Equation \ref{dimensionless}."896 The diurnal heating patterns shown in Figure 1 are similar to those measured at the surface of Earth., The diurnal heating patterns shown in Figure \ref{heating} are similar to those measured at the surface of Earth.897" In both cases parcels of gas move in and out of the sunlight: on Earth this motion is entirely due to the planet's rotation (wind velocities are small compared to rotational velocity), while on a gaseous planet this motion is due to a combination of rotation and zonal winds."," In both cases parcels of gas move in and out of the sunlight: on Earth this motion is entirely due to the planet's rotation (wind velocities are small compared to rotational velocity), while on a gaseous planet this motion is due to a combination of rotation and zonal winds."898" Indeed, our model may also be relevant to a rocky planet with a thin atmosphere and rapid rotation, provided that the rotational period is shorter than the lateral heat conduction timescale."," Indeed, our model may also be relevant to a rocky planet with a thin atmosphere and rapid rotation, provided that the rotational period is shorter than the lateral heat conduction timescale."899" For a planet on a circular orbit, we can use the fact that the temperature extrema for a particle of gas occur when it reaches its equilibrium temperature."," For a planet on a circular orbit, we can use the fact that the temperature extrema for a particle of gas occur when it reaches its equilibrium temperature."900" The temperature extrema are therefore related to their location on the planet by: and where $,;, and $44, are the angles between the sub-stellar meridian and temperature minimum and maximum, respectively."," The temperature extrema are therefore related to their location on the planet by: and where $\Phi_{\rm min}$ and $\Phi_{\rm max}$ are the angles between the sub-stellar meridian and temperature minimum and maximum, respectively."901" Since Tii, is typically much less than unity, ®min&—7/2 in most situations (see Figure 2)), while Ti is close to unity so small differences in this maximum temperature correspond to significant changes in the phase offset of the maximum, as shown in Figure 3.."," Since $\tilde{T}_{\rm min}$ is typically much less than unity, $\Phi_{\rm min}\approx -\pi/2$ in most situations (see Figure \ref{phi_min}) ), while $\tilde{T}_{\rm max}$ is close to unity so small differences in this maximum temperature correspond to significant changes in the phase offset of the maximum, as shown in Figure \ref{phi_max}."902" Note that the the diurnal heating pattern has a longitudinal asymmetry: parcels of gas are heated faster than they cool, so parcels East of the hot-spot tend to be warmer than those West of the hot-spot."," Note that the the diurnal heating pattern has a longitudinal asymmetry: parcels of gas are heated faster than they cool, so parcels East of the hot-spot tend to be warmer than those West of the hot-spot."903" This asymmetry manifests itself in the disc-integrated thermal phase curve of the planet: the offset in the peak of the lightcurve tends to be larger than ,,4..", This asymmetry manifests itself in the disc-integrated thermal phase curve of the planet: the offset in the peak of the lightcurve tends to be larger than $\Phi_{\rm max}$.904" In the Appendix we develop analytic approximations in thecircular regime for Tax, Tausk and Taawn maximum temperature reachedby a parcel, its temperature(the at the dusk terminator, and at the dawn terminator)."," In the Appendix we develop analytic approximations in thecircular regime for $T_{\rm max}$, $T_{\rm dusk}$ and $T_{\rm dawn}$ (the maximum temperature reachedby a parcel, its temperature at the dusk terminator, and at the dawn terminator)."905 Those analytic approximations are, Those analytic approximations are906keV by a [actor of 1 since 1995 or by the difficulty in carrying out backgrouud subtraction [or the syectva stemming [rom the large (—1'.5) point spread [uuction.,keV by a factor of $\sim$ 4 since 1995 or by the difficulty in carrying out background subtraction for the spectra stemming from the large $\sim$ $'$ .5) point spread function.907 Indeed. the fit to the spectra suggests the presence of a harder componeut that was not statistically significant.," Indeed, the fit to the spectra suggests the presence of a harder component that was not statistically significant."908 We believe a [actor of L is tc0 large to be ascribed to difficulties with background subtraction., We believe a factor of 4 is too large to be ascribed to difficulties with background subtraction.909 We tlie explored a variety of models., We then explored a variety of models.910 We do not include a long discussion of those moclels tliat Failed. but iustead focus ou the more successful oues.," We do not include a long discussion of those models that failed, but instead focus on the more successful ones."911 Most of the moclels failed by inissiug fIux 1[un the 0.8-1.0 keV band. a regiou kuown to contain the potential for considerable liue emission.," Most of the models failed by missing flux in the 0.8-1.0 keV band, a region known to contain the potential for considerable line emission."912" Table includes"" a .listing of+ the models ranked by increasing. y-/v.Jg", Table \ref{specfit} includes a listing of the models ranked by increasing ${\chi}^2/{\nu}$.913" The ""dual brems”E aud *bretms+imulti- models yield. adequate fits but leave systematic residuals.", The `dual brems' and `brems+multi-gauss' models yield adequate fits but leave systematic residuals.914" The uou-equilibrium iouizatic[un uodel (in ""xspec' lingo. 1vel: Borkowski.Lyerly.&Revuolds2001 and. references therein). the jxlane-parallel shock model (*pshock’: Borkowski.Lyerly.&Revuolds 2001)) as well as other shock nodels also. provided adequate fits. jit didiH not achieveH the lowest 4> values."," The non-equilibrium ionization model (in `xspec' lingo, `nei'; \citealt{Bork01} and references therein), the plane-parallel shock model (`pshock'; \citealt{Bork01}) ) as well as other shock models also provided adequate fits, but did not achieve the lowest ${\chi}^2$ values."915 The iouizationH equililium collisional plasma moclel (equilib) yielded a very poor fit., The ionization equilibrium collisional plasma model (`equilib') yielded a very poor fit.916 The single component power aw. bremsstrahluug. aud Ravinoud-Siith iuodels were included for direct comparison with the ustorical resuts from ROSATaud (e.g.. 599. Petreetal.199 [)).," The single component power law, bremsstrahlung, and Raymond-Smith models were included for direct comparison with the historical results from and (e.g., S99, \citealt{Petre94}) )."917 The best-it 1nocel was an absorbed. two-temperature. optically thin thermal plasma imocel (he variable Mekal model ‘vinelxV in xspec lingo that uses the line caleulatious of Mewe.Cirouenschild. (1985)... Mewe.Lemeu.&vaudeuOord (1986).. and Ixaastra(1992). plus the Fe L enhancements of Liedahl.Osterheld.&Golds," The best-fit model was an absorbed, two-temperature, optically thin thermal plasma model (the variable Mekal model `vmekal' in xspec lingo that uses the line calculations of \cite{Mewe1}, \cite{Mewe2}, and \cite{Kaastra92} plus the Fe L enhancements of \cite{Lied95}) )."918tein (1995))). Figure 2 shows the fitted spectrum., Figure \ref{fig-dvmek} shows the fitted spectrum.919 Thebest-[it temperatures are 0.ius and ULLο keV; and are shown as the upper set of contour plots in Figure 3.) (the lower set of contours in each figure will be discussed shortly)., The best-fit temperatures are $^{+0.04}_{-0.05}$ and $^{+0.44}_{-0.42}$ keV and are shown as the set of contour plots in Figure \ref{cont_dvmek} (the lower set of contours in each figure will be discussed shortly).920 The fluxes are isted⋅ in⋅ Table i2. aud generally [all. in⋅ the range of⋅ −⋅↽x10 13 erys 1 Do.cin the 0.5-2 keV band aud —3-1x10.13| erg |1 em7 in the 2-10 keV band with the low ΠΠους COLESpounding to the absorbed flux aud the high to the unabsorbed., The model-derived fluxes are listed in Table \ref{fluxval} and generally fall in the range of $\times$ $^{-13}$ erg $^{-1}$ $^{-2}$ in the 0.5-2 keV band and $\sim$ $\times$ $^{-13}$ erg $^{-1}$ $^{-2}$ in the 2-10 keV band with the low numbers corresponding to the absorbed flux and the high to the unabsorbed.921" These fluxes correspoud to a 0.5-2 keV luminosiy of S7.5-1LL« 109 ere Land a 2-10 keV luminosity of —6-7.5x 10 erg 1 The best-fit. column. —2.3x aqu107! »? and shown in. FigureEN .)3.. lies. about a [actor. ofaos 8-10 above the measured column in: the direction: of ""NTNGC1 pepe1313. ~3.7* —-o440910°"" 27 1905).."," These fluxes correspond to a 0.5-2 keV luminosity of $\sim$ $\times$ $^{38}$ erg $^{-1}$ and a 2-10 keV luminosity of $\sim$ $\times$ $^{38}$ erg $^{-1}$ The best-fit column, $\sim$ $\times$ $^{21}$ $^{-2}$ and shown in Figure \ref{cont_dvmek}, lies about a factor of 8–10 above the measured column in the direction of NGC 1313, $\sim$ $\times$ $^{20}$ $^{-2}$ \citep{SFD98}."922" However. it does correspoud to within with the Ejy value of 0.31 measured [rom optical spectra (Ryderοἱal.1993). and using the Ny-Ep,y conversion of (1995): Ny 95.3x107* Epv."," However, it does correspond to within with the $_{\rm B-V}$ value of 0.31 measured from optical spectra \citep{Ryder93} and using the $_{\rm923H}$ $_{\rm B-V}$ conversion of \cite{PS95}: $_{\rm H}$ $\sim$ $\times$ $^{21}$ $_{\rm B-V}$."924 The vinekal model periMts varving the abundauces of astroplivsically-iportant elemeuts., The vmekal model permits varying the abundances of astrophysically-important elements.925 We varlec the abundauces of eac‘h element iu turn but forced the correspouding abundances of the soft and hard components to va‘y slinultaneously but iudepeudently., We varied the abundances of each element in turn but forced the corresponding abundances of the soft and hard components to vary simultaneously but independently.926 This approach eusured the most robus cletection of specific liue features as well as ciffereuces between the soft aud bard coupouents., This approach ensured the most robust detection of specific line features as well as differences between the soft and hard components.927 The only abundauce incousintent with solar is that of Si for the soft component., The only abundance inconsistent with solar is that of Si for the soft component.928 Figure 1. slows the ucertainty contours. [ο “the abundance of Si., Figure \ref{cont_si} shows the uncertainty contours for the abundance of Si.929 The soft component abundauce is 3.20 which Is slg€»ülicantly different [rou solar at the confidence level., The soft component abundance is 3.20 which is significantly different from solar at the confidence level.930 The Si abundance for the hard component is consistent wit1 solar., The Si abundance for the hard component is consistent with solar.931The fluxes foreach component are listed separately tu Table 2..,The fluxes foreach component are listed separately in Table \ref{fluxval}. .932 Civen the time-scales associated with stellar formation (~10 vvr for low-mass stars). very voung clusters are expected to contain a population of PAIS stars (c.g. Bonatto&Biea2010b.. and references therein).," Given the time-scales associated with stellar formation $\sim10^7$ yr for low-mass stars), very young clusters are expected to contain a population of PMS stars (e.g. \citealt{vdB92}, and references therein)."933 Thus. he assumption that the red and. faint stars belong to the PNIS is consistent with the ~5 MMyr of age of the ECS in the complex (Sect. 5)).," Thus, the assumption that the red and faint stars belong to the PMS is consistent with the $\sim5$ Myr of age of the ECs in the complex (Sect. \ref{N2175}) )."934 Internal. cillerential reddening is implied. by the colour distribution at faint. magnitudes (J2 14). which is wider than the spread. predicted. purely o» PALS models.," Internal differential reddening is implied by the colour distribution at faint magnitudes $\jj\ga14$ ), which is wider than the spread predicted purely by PMS models."935 A comparison with the reddening vector (lor Ay=0to 10) shows cdillerent. degrees of cillerential reddening. being lower for NGC22175s ancl 1136. and uigher for the remaining cases.," A comparison with the reddening vector (for $\aV=0~{\rm to}~10$ ) shows different degrees of differential reddening, being lower for 2175s and 136, and higher for the remaining cases."936 I£ most of the colour spread is due to non-uniform reddening - and not to systematic differences in the stellar content - the upper limitto the cilferential reddening would be Xy.=6 mimae., If most of the colour spread is due to non-uniform reddening - and not to systematic differences in the stellar content - the upper limitto the differential reddening would be $\Delta\aV\la6$ mag.937 As discussed, As discussed938Collisionless shocks iu space aud other astroplivsical environments are efficient accelerators of energetic chareed-particles.,Collisionless shocks in space and other astrophysical environments are efficient accelerators of energetic charged-particles.939 Diffusive shock acceleration (hereinafterDSA:Isrvinsky1977:Axfordctal.1977:Bell1978:Blauctford&Ostriker LOTS).. is the uost popular theory for chareed-particle acceleration.," Diffusive shock acceleration \citep[hereinafter940DSA;][]{Krymsky1977,Axford1977,Bell1978a,Blandford1978}, is the most popular theory for charged-particle acceleration."941 It naturally predicts a universal power-law distribution αρ with 5~LO for stroug shocks. where f is the phase-space> distribution function. close to what observed oe1 cosnic ravs in many cifferent regions of space.," It naturally predicts a universal power-law distribution $f \varpropto p^{-\gamma}$ with $\gamma \sim 4.0$ for strong shocks, where $f$ is the phase-space distribution function, close to what observed in cosmic rays in many different regions of space."942 The asic conclusions of DSA can be drawn from the Parker ransport equation (Parker1965) bv consideriug the shock to be a compressive discontinuity iu au infinite one-dimensional aud time steady svstem., The basic conclusions of DSA can be drawn from the Parker transport equation \citep{Parker1965} by considering the shock to be a compressive discontinuity in an infinite one-dimensional and time steady system.943 DSA is thought o be the mechanisin that accelerates anomalous Cosmic ravs (ACRs) in the IHeliospherie termination shock aud also ealactic cosmic raves (GCRs) with energy up to at east LOY eV in supernova blast waves., DSA is thought to be the mechanism that accelerates anomalous cosmic rays (ACRs) in the Heliospheric termination shock and also galactic cosmic rays (GCRs) with energy up to at least $10^{15}$ eV in supernova blast waves.944 However. recent observations iu the termination shock aud the Ucliosheath by 1 (Stonectal.2005). found he intensity of ACRs is not peaked at the termination shock and the cuerey spectrum is still unfolding after entering the ILleliosheath. which stronely imdicates the simple planar shock ποσο] is inadequate to interpret the acceleration of AC'Rs.," However, recent observations in the termination shock and the Heliosheath by $1$ \citep{Stone2005} found the intensity of ACRs is not peaked at the termination shock and the energy spectrum is still unfolding after entering the Heliosheath, which strongly indicates the simple planar shock model is inadequate to interpret the acceleration of ACRs."945 Nuuerical and analytical studies sugeest the possible solution cau be made by considers the temporary and/or spatial variation (Floriuski&2008:Kota&JokipiSchwadronetal. 2008)..," Numerical and analytical studies suggest the possible solution can be made by considering the temporary and/or spatial variation \citep{Florinski2006GeoRL,McComas2006,Jokipii2008AIP,Kota2008AIP,Schwadron2008ApJ}."946 Iu xurtieular. MeConmas&Sceliiwadrou(2006). discussed the imuportauce of the magnetic ecometiy of à bluut shock onu particle acceleration.," In particular, \citet{McComas2006} discussed the importance of the magnetic geometry of a blunt shock on particle acceleration."947 They argued that the missing ACRs at the nose of the IIeliospherie termination shock is due to particle enereization occuring prinuiuilv back along the flauks of the shock where magnetic feld lues have had a longer comnection tine aud higher injection effüciency., They argued that the missing ACRs at the nose of the Heliospheric termination shock is due to particle energization occuring primarily back along the flanks of the shock where magnetic field lines have had a longer connection time and higher injection efficiency.948 Ἱνόία&Jokrpi(2008) presenteda inore sophisticated simulation which gives results stuular to that described by MeCoimas&Sclavadrou (2006)., \citet{Kota2008AIP} presenteda more sophisticated simulation which gives results similar to that described by \citet{McComas2006}.949. Sclavadronetal.(2008). also developed a 3-D analytic model for particle acceleration iu a blunt shock. including perpendicular diffusion aud drift motion due to large-scale shock structure.," \citet{Schwadron2008ApJ} also developed a 3-D analytic model for particle acceleration in a blunt shock, including perpendicular diffusion and drift motion due to large-scale shock structure."950 Large-sceale dgmnagnetie field) line mneandering is ubiquitous in the heliosphere aud other astrophlivsical euvironnients (Jokipiü1966:Jokipü&Parker1969:Parker 1979).," Large-scale magnetic field line meandering is ubiquitous in the heliosphere and other astrophysical environments \citep{Jokipii1966,Jokipii1969,Parker1979}."951 The acceleration of charged-particles in colliiouless shocks has been shown to be stronely affected by inagnetic-field. turbulence at different scales (άσσος2005a.b:Caacalone&Neugebauer2008:Guo&Caacalone 2010).," The acceleration of charged-particles in collisionless shocks has been shown to be strongly affected by magnetic-field turbulence at different scales \citep{Giacalone2005a,Giacalone2005b,Giacalone2008,Guo2010}."952.. The large-scale magnetic field variation will have iuportaut effects ou the shock acceleration since the trausport of charged particles is different in the direction parallel aud. perpendicular to the iuagnetic field. as shown in carly work (Jokipii1982. 1987)..," The large-scale magnetic field variation will have important effects on the shock acceleration since the transport of charged particles is different in the direction parallel and perpendicular to the magnetic field, as shown in early work \citep{Jokipii1982ApJ,Jokipii1987ApJ}. ."953 The bluut shocks aud shocks with fluctuating frout (Li&Zank2006) which have the similar, The blunt shocks and shocks with fluctuating front \citep{Li2006AIP} which have the similar954and E-scaling is irrelevant (and where even a hefty error in a more relevant and uncertain parameter — distance — does not change matters significantly).,"and ${\dot955E}^{1/2}$ -scaling is irrelevant (and where even a hefty error in a more relevant and uncertain parameter — distance — does not change matters significantly)."956 In all these discarded cases. in addition. the efficiencies required would be ηὃν10004. making the potential associations utterly unphysical.," In all these discarded cases, in addition, the efficiencies required would be $\eta \gg 1000\%$, making the potential associations utterly unphysical."957 Finally. in evaluating possible associations. we compare the photon indices of known pulsars (Table 1) with those of the EGRET sources (see. e.g.. Merck et al.," Finally, in evaluating possible associations, we compare the photon indices of known pulsars (Table 1) with those of the EGRET sources (see, e.g., Merck et al."958 1996; Zhang Cheng 1998: Cheng Zhang 1998)., 1996; Zhang Cheng 1998; Cheng Zhang 1998).959 We have also quantified the chance probability for obtaining these associations. adapting the numerical code described by Romero et al. (," We have also quantified the chance probability for obtaining these associations, adapting the numerical code described by Romero et al. ("96019993. b): there is a probability of having 8 chance coincidences between different unidentified 3EG sources and Parkes pulsars. as in Table Camilo et al. (,"1999a, b): there is a probability of having 8 chance coincidences between different unidentified 3EG sources and Parkes pulsars, as in Table Camilo et al. ("9612001) proposed the possible physical association #11. with required efficiency of (Table 2).,"2001) proposed the possible physical association 1, with required efficiency of (Table 2)."962 This pulsar appears to be located just outside the SNR G284.3-1.8. which itself is interacting with an adjacent— molecular cloud (Ruiz May 1986).," This pulsar appears to be located just outside the SNR $-$ 1.8, which itself is interacting with an adjacent molecular cloud (Ruiz May 1986)."963" Another Parkes pulsar. PSR J1013—5934 (#22 in Table 2). is coineident with 3EG 1013-5915. but it is an old pulsar (7=12 MMyr) with low £22.5«IO"" eeresss! and cannot be a significant 7-ray contributor."," Another Parkes pulsar, PSR $-$ 5934 2 in Table 2), is coincident with 3EG $-$ 5915, but it is an old pulsar $\tau=12$ Myr) with low $\dot E = 2.5\times96410^{32}$ $^{-1}$ and cannot be a significant $\gamma$ -ray contributor."965 D'Amico et al. (, D'Amico et al. (9662001) have studied cases #66 and 14 (efficiencies: jj=2% and7%.. respectively).,"2001) have studied cases 6 and 14 (efficiencies: $\eta = 2$ and, respectively)."967 Both are plausible candidates to generate the respective EGRET source fluxes., Both are plausible candidates to generate the respective EGRET source fluxes.968 PSR 11837-0559. is also coincident with 3EG J1837-0606 (113). but its E/d is 80 times smaller than for PSR 71837-00604. and it cannot contribute significantly to the 7-ray source.," PSR $-$ 0559, is also coincident with 3EG $-$ 0606 13), but its $\dot E/d^2$ is 80 times smaller than for PSR $-$ 0604, and it cannot contribute significantly to the $\gamma$ -ray source."969 The pulsars in pairs #88 and 9 have far too low a spin-down luminosity at too large a distance (Table 2) to explain their coincident 7-ray sources., The pulsars in pairs 8 and 9 have far too low a spin-down luminosity at too large a distance (Table 2) to explain their coincident $\gamma$ -ray sources.970 They are also both old. with 7~ 4MMvyr.," They are also both old, with $\tau \sim 4$ Myr."971 Cases #110 and ΕΙ are discussed elsewhere in connection with a proposal for a SNR shock origin of the bulk of the z-rays resulting from 3EG J1714—3857 (Butt et al., Cases 10 and 11 are discussed elsewhere in connection with a proposal for a SNR shock origin of the bulk of the $\gamma$ -rays resulting from 3EG $-$ 3857 (Butt et al.972 2001): neither of these pulsars is energetic enough to contribute significant amounts of high-energy flux., 2001); neither of these pulsars is energetic enough to contribute significant amounts of high-energy flux.973 We now discuss the remaining four EGRET sources positionally superposed with five newly discovered pulsars., We now discuss the remaining four EGRET sources positionally superposed with five newly discovered pulsars.974 We provide observational data on the apparent associations in Tables 3 and 4., We provide observational data on the apparent associations in Tables 3 and 4.975 Cases #33-5. 7 and 12 all contain Vela-like pulsars. with relatively short periods. low characteristic ages. and high spin-down luminosities (E>10° ss! ).," Cases 3–5, 7 and 12 all contain Vela-like pulsars, with relatively short periods, low characteristic ages, and high spin-down luminosities $(\dot E \ga 10^{35}$ $^{-1}$ )."976 The pulsar in case #33 would require an efficiency #=5% at its nominal distance to explain the luminosity of the corresponding 3EG source. which has photon index 2.23 (see Table 4).," The pulsar in case 3 would require an efficiency $\eta = 5\%$ at its nominal distance to explain the luminosity of the corresponding 3EG source, which has photon index 2.23 (see Table 4)."977 This spectrum is softer than that of the Crab. although it is consistent with it within the uncertainties.," This spectrum is softer than that of the Crab, although it is consistent with it within the uncertainties."978 It is also consistent with the index of 3EG 2227+6122. for which PSR J2229+6114 has been proposed as the likely source (Halpern et al.," It is also consistent with the index of 3EG 2227+6122, for which PSR J2229+6114 has been proposed as the likely source (Halpern et al."979 2001)., 2001).980 The 5-ray source in case #33 is not variable (Tompkins 1999; Torres et al., The $\gamma$ -ray source in case 3 is not variable (Tompkins 1999; Torres et al.981" 20019). as expected from direct pulsar or pulsar wind nebula/SNR shock emission,"," 2001c), as expected from direct pulsar or pulsar wind nebula/SNR shock emission."982 PSR J10135-3719 has 7=39 kkyr and E28.2«I0? ss! (Table 3).," PSR $-$ 5719 has $\tau=39$ kyr and $\dot E = 8.2\times98310^{35}$ $^{-1}$ (Table 3)."984 While no cataloged SNR is superposed with the 3EG source (Torres et al., While no cataloged SNR is superposed with the 3EG source (Torres et al.985 2001b). this absence does not mean that one does not exist. and further sensitive searches may prove fruitful.," 2001b), this absence does not mean that one does not exist, and further sensitive searches may prove fruitful."986 Thus the connection between 3EG J1014—5705 and PSR J1015—5719 appears plausible and is worth additional study., Thus the connection between 3EG $-$ 5705 and PSR $-$ 5719 appears plausible and is worth additional study.987 The pulsars in pairs #44 and 5 require unreasonably high efficiencies at their nominal distances to explain the 7-ray flux from the corresponding EGRET source ()=100%.. Table 4).," The pulsars in pairs 4 and 5 require unreasonably high efficiencies at their nominal distances to explain the $\gamma$ -ray flux from the corresponding EGRET source $\eta \ga988100$, Table 4)."989 However. both pulsars are located in the direction of the Centaurus arm. and it is known that in such directions the electron density/distance model of Taylor Cordes (1993) can be unreliable. sometimes overestimating the distances by factors of up to ~4 (see discussion in Camilo et al.," However, both pulsars are located in the direction of the Centaurus arm, and it is known that in such directions the electron density/distance model of Taylor Cordes (1993) can be unreliable, sometimes overestimating the distances by factors of up to $\sim 4$ (see discussion in Camilo et al."990 2001)., 2001).991 Both pulsars are located (at least in projection) well within the boundaries of the incomplete shell SNR G312.4—0.4 (Caswell Barnes 1985). to which Yadigaroglu Romani (1997) estimate a X—D distance of 1.9kkpe.," Both pulsars are located (at least in projection) well within the boundaries of the incomplete shell SNR $-$ 0.4 (Caswell Barnes 1985), to which Yadigaroglu Romani (1997) estimate a $\Sigma-D$ distance of kpc."992 At this distance the required efficiencies for the pulsars in cases #44 and 5 would be and3%.. respectively. which would make them considerably more plausible sources of the observed high energy emission.," At this distance the required efficiencies for the pulsars in cases 4 and 5 would be and, respectively, which would make them considerably more plausible sources of the observed high energy emission."993 Furthermore. 3EG J1410—6147 has a photon index comparable to that of the Crab. and is not variable (Tables 1. 2 and 4).," Furthermore, 3EG $-$ 6147 has a photon index comparable to that of the Crab, and is not variable (Tables 1, 2 and 4)."994 Pairs #44 and 5 therefore appear intriguing., Pairs 4 and 5 therefore appear intriguing.995 However it should be noted that X—D distances are notoriously unreliable (e.g.. for this very SNR. Caswell Barnes 1985 and Case Bhattacharya 1999 infer values in substantial disagreement both with each other and with that determined by Yadigaroglu Romani 1997).," However it should be noted that $\Sigma-D$ distances are notoriously unreliable (e.g., for this very SNR, Caswell Barnes 1985 and Case Bhattacharya 1999 infer values in substantial disagreement both with each other and with that determined by Yadigaroglu Romani 1997)."996 Ideally. further observations of SNR G312.4-0.4 may indicate whether it shows signs of interaction with PSRs J1412-6145 or JI413-6141. and possibly constrain their distances.," Ideally, further observations of SNR $-$ 0.4 may indicate whether it shows signs of interaction with PSRs $-$ 6145 or $-$ 6141, and possibly constrain their distances."997 Depending on the actual distances. the >-ray emission from 3EG JI410-6147 may conceivably arise from à combination of PSRs J1412—6145. J1413-6141. and/or SNR G312.4—0.4.," Depending on the actual distances, the $\gamma$ -ray emission from 3EG $-$ 6147 may conceivably arise from a combination of PSRs $-$ 6145, $-$ 6141, and/or SNR $-$ 0.4."998 The efficiency required to explain the EGRET flux in case #77 is 4)=12%. which seems possible.," The efficiency required to explain the EGRET flux in case 7 is $\eta = 12\%$, which seems possible."999 However. the spectral index of 2.50 is larger than those of known +-ray pulsars.," However, the spectral index of 2.50 is larger than those of known $\gamma$ -ray pulsars."1000 One of the SNRs coincident with the EGRET source. G337.8-0.1. harbors a maser (Koralesky et al.," One of the SNRs coincident with the EGRET source, $-$ 0.1, harbors a maser (Koralesky et al."1001 1998). which is indicative of interaction between the SNR shock and the ambient medium.," 1998), which is indicative of interaction between the SNR shock and the ambient medium."1002 Thus. were a sufficiently massive molecular cloud located nearby. it could help produce the high energy radiation as a result of hadronie interaction (Aharonian. Drury. ΝΟΚ 1994: Aharonian Atoyan 1996).," Thus, were a sufficiently massive molecular cloud located nearby, it could help produce the high energy radiation as a result of hadronic interaction (Aharonian, Drury, Völlk 1994; Aharonian Atoyan 1996)."1003 Part of the EGRET flux could plausibly come from PSR J1637—4642 and part from pion ~-decay via SNR G337.8—0.1’s interaction with the putative cloud., Part of the EGRET flux could plausibly come from PSR $-$ 4642 and part from pion $\gamma$ -decay via SNR $-$ 0.1's interaction with the putative cloud.1004 Inthis case. the photon index would reflect a weighted average value.," Inthis case, the photon index would reflect a weighted average value."1005 Both possible mechanisms for the high energy emission would produce a non-variable source. as is the case for 3EG J1639—4702.," Both possible mechanisms for the high energy emission would produce a non-variable source, as is the case for 3EG $-$ 4702."1006 Lastly we consider case £112. for which the required efficiency 1s high at the nominal pulsar distance and upper limit flux value. ;j=55%.," Lastly we consider case 12, for which the required efficiency is high at the nominal pulsar distance and upper limit flux value, $\eta = 55$."1007. The pulsar is located. in projection. Just outside the plerionic SNR G27.8+0.6. for which the distance is ~ 2kkpe (Reich et al.," The pulsar is located, in projection, just outside the plerionic SNR G27.8+0.6, for which the distance is $\sim10082$ kpc (Reich et al."1009 1984)., 1984).1010 Although the estimated ages are comparable (7=52 kkyr for the pulsar and 45 kkyr for the SNR). it seems unlikely that both objects are physically associated. given the offset between the centrally peaked SNR component and the pulsar (see Reich et al.," Although the estimated ages are comparable $\tau = 52$ kyr for the pulsar and $\sim 45$ kyr for the SNR), it seems unlikely that both objects are physically associated, given the offset between the centrally peaked SNR component and the pulsar (see Reich et al."1011 1984)., 1984).1012 Whatever the possible relation between pulsar and SNR. the 3EG source in case #112 is variable (Table 2). arguing against a pulsar origin.," Whatever the possible relation between pulsar and SNR, the 3EG source in case 12 is variable (Table 2), arguing against a pulsar origin."1013 Examination of X-ray archives via HEASARC has revealed no compelling counterpart sources to any of the pulsars in Table 3. (, Examination of X-ray archives via HEASARC has revealed no compelling counterpart sources to any of the pulsars in Table 3. (1014A possible X-ray source at the edge of an,A possible X-ray source at the edge of an1015The aim of the present paper is to investigate the potential cosmological signatures of a very general dark enerev component. which is characterize by an equation of state. sound. speed and. anisotropic stress.,"The aim of the present paper is to investigate the potential cosmological signatures of a very general dark energy component, which is characterize by an equation of state, sound speed and anisotropic stress."1016 In section 2. we review the parameterization of a &eneralized: cosmologica fluid and comment its relation to some recent studies of anisotropies dark energy., In section \ref{para} we review the parameterization of a generalized cosmological fluid and comment its relation to some recent studies of anisotropies dark energy.1017 The parameerization will then be subjected to the most detailed and most extensive scrutiny this far., The parameterization will then be subjected to the most detailed and most extensive scrutiny this far.1018 Ehe data ancl method utilized for this are describe in section 3.., The data and method utilized for this are described in section \ref{data}.1019 In the section d. we use the most recen cosmological data to constrain the properties of dark energy., In the section \ref{cons1} we use the most recent cosmological data to constrain the properties of dark energy.1020 Section 5. is devoted to investigate how much the future data could be able to improve the constraints., Section \ref{cons2} is devoted to investigate how much the future data could be able to improve the constraints.1021 We conclude by stating the fundamental uncertainty in the properties of dark energy but also mention some cases where a positive detection could be established., We conclude by stating the fundamental uncertainty in the properties of dark energy but also mention some cases where a positive detection could be established.1022" Consider a general [uid with the energy momentum tensor |pn, | where sy is the four-velocity of the uid. and the projection tensor Pj, is delined as Pye—gueμμ."," Consider a general fluid with the energy momentum tensor }= + + where $u_\mu$ is the four-velocity of the fluid, and the projection tensor $h_{\mu\nu}$ is defined as $h_{\mu\nu} \equiv g_{\mu\nu} + u_\mu u_\nu$."1023" llere YX,, can include only spatial inhomogeneity.", Here $\Sigma_{\mu\nu}$ can include only spatial inhomogeneity.1024 At the background level. the evolution of the Iuid is determined by the continuity equation.," At the background level, the evolution of the fluid is determined by the continuity equation, + = 0."1025 The effects. to the overall expansion are. therefore determined. by the equation of state i alone., The effects to the overall expansion are therefore determined by the equation of state $w$ alone.1026" We define aperfect UWuied by the condition My,=0.", We define a fluid by the condition $\Sigma_{\mu\nu}=0$.1027 The condition for theadiabalicili of a Iuid is p=p(p). which implies that the evolution of the sound speed is determined by the equation olstate alone.," The condition for the of a fluid is $p=p(\rho)$, which implies that the evolution of the sound speed is determined by the equation of state alone."1028 Generally. however. the sound speed is defined as the ratio of pressure and. density. perturbations in the frame comoving with the dark energy ιά (7?)..pp," Generally, however, the sound speed is defined as the ratio of pressure and density perturbations in the frame comoving with the dark energy fluid \citep{Weller:2003hw},."1029 In the adiabatic situation one has €2anαρdpPolonuSHiL[i . but in general the sound. speed is an independent:p variable.," In the adiabatic situation one has $\clam = d p/d\rho = \frac{\dot{p}}{\dot{\rho}} = w - \frac{\dot{w}}{3H(1+w)}$ , but in general the sound speed is an independent variable."1030 In. the following we will consider a constant. equation of state for simplicity., In the following we will consider a constant equation of state for simplicity.1031 ‘Taking these considerations into account. the evolution equations for the dark energy.density. perturbation ὁ and velocity. potential @ in the synchronous gauge (7).. can be written as c= | .”..- Fa... where Ph ijs the trace of the synchronous metric perturbation.," Taking these considerations into account, the evolution equations for the dark energydensity perturbation $\delta$ and velocity potential $\theta$ in the synchronous gauge \citep{Ma:1995ey}, can be written as = + - , = , where $h$ is the trace of the synchronous metric perturbation."1032 Llere e is the anisotropic stress of dark energy. related to notation. of IEq.(1)) by (p1ple=(il20;JN.," Here $\sigma$ is the anisotropic stress of dark energy, related to notation of \ref{fluid}) ) by $(\rho + p)\sigma \equiv1033-(\hat{k}_i\hat{k}_j-\frac{1}{3}\delta_{ij})\Sigma^{ij}$ ."1034" From the above equations it is then clear that. while w and ¢7,,, determine respectively the background ancl perturbative pressure of the Duid that is rotationally invariant. c quantifies how much the pressure of the Iuid varies with clirection."," From the above equations it is then clear that, while $w$ and $\clam$ determine respectively the background and perturbative pressure of the fluid that is rotationally invariant, $\sigma$ quantifies how much the pressure of the fluid varies with direction."1035 To close the system of equations. we describe the evolution of the anisotropic stress with an equation adopted from Iu (?).. Bi).," To close the system of equations, we describe the evolution of the anisotropic stress with an equation adopted from Hu \citep{Hu:1998kj}, = )."1036 This parameterization leads to reasonable results arn approximates the evolution of any Πα present in the standard: cosmological mocdel. in. particular neutrinos anc photons which have a non-zero anisotropic stress (?)..," This parameterization leads to reasonable results and approximates the evolution of any fluid present in the standard cosmological model, in particular neutrinos and photons which have a non-zero anisotropic stress \citep{Hu:1998tj}. ."1037 More specifically. for those relativistic components. the correc choice Lor the viscous paramicter 1s c7vis=1/3.," More specifically, for those relativistic components, the correct choice for the viscous parameter is $\cvis=1/3$ ."1038 X perfec ια (vanishing shear viscosity) should have ο=0., A perfect fluid (vanishing shear viscosity) should have $\cvis=0$.1039 Εναοί]. one can describe the physical properties of =o by introducing5 the rescaled Iparameter oí;=οτεLs{1|ee).," Equivalently, one can describe the physical properties of $\sigma$ by introducing the rescaled parameter $\avis = \cvis/(1+w)$."1040" While ον, is somehow physically analogous to sound spec squared. the aes. is the quantity directly. multiplying the source term of the stress (see. RIS of eq. (9)))."," While $\cvis$ is somehow physically analogous to sound speed squared, the $\avis$ is the quantity directly multiplying the source term of the stress (see RHS of eq. \ref{sigmaevol}) ))."1041 In. this study we will use both the e7;;vis and ays. parameterizations., In this study we will use both the $\cvis$ and $\avis$ parameterizations.1042 Since tw is constrained near w=1. where the relation between these parameters is divergent. using one or the other might. lead to different results ancl interpretations.," Since $w$ is constrained near $w=-1$, where the relation between these parameters is divergent, using one or the other might lead to different results and interpretations."1043 The statistical details also depend on which parameter one assumes a uniform distribution. and it is useful to test how robust ones conclusions are to such assumptions.," The statistical details also depend on which parameter one assumes a uniform distribution, and it is useful to test how robust ones conclusions are to such assumptions."1044 Usually. a dark energy Εις with nonzero γι generates shear stress which tends to smoothen its. distribution.," Usually, a dark energy fluid with nonzero $\avis$ generates shear stress which tends to smoothen its distribution."1045 ]lowever. the consequences to phantom: dark energy are qualitatively different and for such a fDuid. with a<l. a shear stress drives the clustering.," However, the consequences to phantom dark energy are qualitatively different and for such a fluid, with $w<-1$, a shear stress drives the clustering."1046 With negative γιο exponential growth is typical for all kinds of dark energy.," With negative $\avis$, exponential growth is typical for all kinds of dark energy."1047" In the case of positive a... and constant i and ¢7,,,,. the elects are confined to superhorizon scales and typically small (?) —p"," In the case of positive $\avis$, and constant $w$ and $\clam$, the effects are confined to superhorizon scales and typically small \citep{koivisto:2005}."1048his is in contrast to anisotropic stress which originates from modifications of the gravity sector or quintessence couplings. since they tvpically modify. the gravitational potentials at small scales.," This is in contrast to anisotropic stress which originates from modifications of the gravity sector or quintessence couplings, since they typically modify the gravitational potentials at small scales."1049 A recent study by Amencola a£(?) considers the possibility. of using weak lensing to obtain limits on the dark energy. parameters motivatedpartially by mocified eravity (2)..., A recent study by Amendola \citep{Amendola:2007rr} considers the possibility of using weak lensing to obtain limits on the dark energy parameters motivatedpartially by modified gravity \citep{Amendola:2007rr}.1050 Our study can be considered as an exploration of complementary aspects since the elfects. we encounter. occur (except [or negative ον or Geis) at some orders of magnitude larger scales than those possible to probe with weak lensing experiments.," Our study can be considered as an exploration of complementary aspects since the effects we encounter, occur (except for negative $\clam$ or $\avis$ ) at some orders of magnitude larger scales than those possible to probe with weak lensing experiments."1051 An interesting approach is also that of Caldwell a£(2) who. parameterizing directly the deviation from the general relativistic perfect. Ελα metric. and assuming it to depend on the amount of dark energy. find that this assumption leads to relatively weak constraints on cosmological scales. whereas the bounds on the solar svstem are known tobe tight.," An interesting approach is also that of Caldwell \citep{Caldwell:2007cw} who, parameterizing directly the deviation from the general relativistic perfect fluid metric, and assuming it to depend on the amount of dark energy, find that this assumption leads to relatively weak constraints on cosmological scales, whereas the bounds on the solar system are known tobe tight."1052 ‘Toillustrate the effect of οτε on the CAIB power spectrum. we have in Figure 1 shown the CALB temperature power spectra for models with cillerent values of w and τει ," Toillustrate the effect of $\cvis$ on the CMB power spectrum, we have in Figure \ref{fig:cls_cvis} shown the CMB temperature power spectra for models with different values of $w$ and $\cvis$ ."1053ln models with w= 1.2. one sees that the deviation," In models with $w=-1.2$ , one sees that the deviation"1054"at 12.5 Gyr) predict acceptable present-day abundances (the left column of Fig. 1)),","at 12.5 Gyr) predict acceptable present-day abundances (the left column of Fig. \ref{Fig:evonowd}) ),"1055 if one adopts a low SFE (e= 0.1) and a reasonably long burst duration (d=1 Gyr)., if one adopts a low SFE $\epsilon=0.1$ ) and a reasonably long burst duration $d=1$ Gyr).1056" For a short infall timescale (r=0.5 Gyr, model 1), the abundances of different elements increase during the burst and maintain that level in the interburst phase, whereas for a long infall timescale (r=8 Gyr, model 2) the abundances decrease during the interburst phase owing to the dilution of the infalling gas, thus the present-time abundances are lower than those predicted by the fast accretion model, even if all the other parameters are the same."," For a short infall timescale $\tau=0.5$ Gyr, model 1), the abundances of different elements increase during the burst and maintain that level in the interburst phase, whereas for a long infall timescale $\tau=8$ Gyr, model 2) the abundances decrease during the interburst phase owing to the dilution of the infalling gas, thus the present-time abundances are lower than those predicted by the fast accretion model, even if all the other parameters are the same."1057" Since there is no SF in these models (models 1 and 2) between 5.5 and 12.0 Gyr and we do not predict the existence of stars with ages between 7.5 and 1 Gyr, at variance with observations, we compiled another model with 10 short bursts (d~0.1 Gyr) and a long infall timescale (r=8 Gyr, to avoid a too high metallicity at the present time)."," Since there is no SF in these models (models 1 and 2) between 5.5 and 12.0 Gyr and we do not predict the existence of stars with ages between 7.5 and 1 Gyr, at variance with observations, we compiled another model with 10 short bursts $d\sim0.1$ Gyr) and a long infall timescale $\tau=8$ Gyr, to avoid a too high metallicity at the present time)."1058 This model (model 3) also shows acceptable abundance evolutionary tracks., This model (model 3) also shows acceptable abundance evolutionary tracks.1059" However, all of these models form too few stars and a lot of gas remains, hence the predicted gas fraction (0.8— 0.9) at the present time is very high and inconsistent with the observations"," However, all of these models form too few stars and a lot of gas remains, hence the predicted gas fraction $0.8 - 0.9$ ) at the present time is very high and inconsistent with the observations"1060One of the critical open question in star formation is (he accurate determination of the stellar Initial Mass Function (IME). especially in (he low-mass regime. in order (ο understand its origin and particularlv how it is related (o the mass distribution of the dense cores where stars orm. ie. the Core Mass Function (CME).,"One of the critical open question in star formation is the accurate determination of the stellar Initial Mass Function (IMF), especially in the low-mass regime, in order to understand its origin and particularly how it is related to the mass distribution of the dense cores where stars form, i.e. the Core Mass Function (CMF)."1061 This findamental question is investigated bv the means of surveving dense condensations in molecular clouds., This fundamental question is investigated by the means of surveying dense condensations in molecular clouds.1062 One of the classical tool for detecting dense cores in star forming regions is the search [or dust condensations using continuum measurement in the millimetre range (e.g. Testi&Sargent 19983: Johnstoneelal. 2000:; Motteetal. 2001))., One of the classical tool for detecting dense cores in star forming regions is the search for dust condensations using continuum measurement in the millimetre range (e.g. \citealt{testi98}; ; \citealt{Johnstone00}; \citealt{motte01}) ).1063 Alternatively. one can use spectroscopic survevs of dense eas molecular tracers.," Alternatively, one can use spectroscopic surveys of dense gas molecular tracers."1064 Ammonia is one of the best molecules for studying the cool. dense molecular cores where stars [orm (e.g. Myers&Benson1983:: Benson&Myers 1989)).," Ammonia is one of the best molecules for studying the cool, dense molecular cores where stars form (e.g. \citealt{myers83}; \citealt{benson89}) )."1065 density condensations are also mapped in other molecular tracers such as Nell and CS., High-density condensations are also mapped in other molecular tracers such as $_2$ $^+$ and CS.1066 In parüeular. Nell is known to be a good tracer of the dense centre of the cores. while C'S is depleted [rom the gas phase in the very centre of prestellar cores ancl preferentially samples the core edge (Casellietal.2002b:: Tafallaetal. 2002)).," In particular, $_2$ $^+$ is known to be a good tracer of the dense centre of the cores, while CS is depleted from the gas phase in the very centre of prestellar cores and preferentially samples the core edge \citealt{caselli02b}; \citealt{tafalla02}) )."1067 CS is also a good tracer of extended hieh density gas aucl is useful to probe the kinematics of the gas (Testietal.2000:: 2002))., CS is also a good tracer of extended high density gas and is useful to probe the kinematics of the gas \citealt{testi00}; \citealt{olmi02}) ).1068 The poorly studied Lupus molecular cloud is an interesting target for investigating the low mass star formation process because ils star formation regime. in terms of star formation rate and stellar clustering. represents an intermediate case between (he heavily clustered sites such as Serpens and Ophiuchus aud (he more isolated and quiescent sites such as Taurus.," The poorly studied Lupus molecular cloud is an interesting target for investigating the low mass star formation process because its star formation regime, in terms of star formation rate and stellar clustering, represents an intermediate case between the heavily clustered sites such as Serpens and Ophiuchus and the more isolated and quiescent sites such as Taurus."1069 Because of its location in the Southern hemisphere (declination [rom-337to -437)). this," Because of its location in the Southern hemisphere (declination fromto ), this"1070 ü deo— 1UT ————}).? C wuaecelengine ou the left laud sides the overline denotes the time average aud for simplicity of notation this has been dropped from the right laud sides., 0 = n_1 n_2 C Here on the left hand sides the overline denotes the time average and for simplicity of notation this has been dropped from the right hand sides.1071 The resonance condition also inuplies αποdt_0ldiy Using this aud climinating 4 from the above.ua we nqobtain for the rate of increase of 54 through nueration matta T Dati1— Also (15)) gives for the eccentricity balance Re |," The resonance condition also implies ${\overline{{1\over n_2}{dn_2\over dt} }}=1072{\overline{{1\over n_1}{dn_1\over dt} }}.$ Using this and eliminating $\delta$ from the above, we obtain for the rate of increase of $n_1$ through migration (n_1 T ) Also \ref{eca}) ) gives for the eccentricity balance e_1^2 =."1073" The a)ove determunes the ecceutricity of the outer planet e asa fiction of £f. aud f,,;4. For a svstein with myfing=3. we get eyoxUTETug. For c4 iu he 0.01 range we need f.LO orbits if tig~ orbits."," The above determines the eccentricity of the outer planet $e_1$ as a function of $t_c$ and $t_{mig}.$ For a system with $m_1/m_2 =3,$ we get $e_1 \sim \sqrt{0.07t_c/t_{mig}}.$ For $e_1$ in the $0.01$ range we need $t_c \sim10 $ orbits if $t_{mig} \sim 10^4$ orbits."1074 The ecceutzicitv of the iuner planet is deteriiued by equation] 63)., The eccentricity of the inner planet is determined by \ref{last1}) ).1075 For sinall amplitucle libratious this is given bv (10))., For small amplitude librations this is given by \ref{eccp}) ).1076 That would still apply when o is circulating provided the cosines are time averaged and the mean circulation rate is sinall., That would still apply when $\phi$ is circulating provided the cosines are time averaged and the mean circulation rate is small.1077 The protoplanetary disc is numerically simulated using an Eulerian 2D lycdrodyvuaimic code., The protoplanetary disc is numerically simulated using an Eulerian 2D hydrodynamic code.1078 The code used ix a inodified version of NIRVANA. which has been described. tested and used sccesstully elsewhere on a simular problem iwolving interacting plauets (Alasset Sucllerove 2001)).," The code used is a modified version of NIRVANA, which has been described, tested and used successfully elsewhere on a similar problem involving interacting planets (Masset Snellgrove \cite{Masset1}) )."1079 lucorparated with the hyvdrodyuaniüc code is a μονά Ruuge-I&uta inteerator which is used to evolve the orbis of the two planets., Incorparated with the hydrodynamic code is a 4th-order Runge-Kutta integrator which is used to evolve the orbits of the two planets.1080 The gravitational forces calculated from the disk model are used iu the equations of motion of the planets. and he disc. itself responds to the planetirv poential.," The gravitational forces calculated from the disk model are used in the equations of motion of the planets, and the disc itself responds to the planetary potential."1081 Tene othe system evolves iu a seltf-cousisteut fashion., Hence the system evolves in a self-consistent fashion.1082 Iu order to obain the long iutegration times needed for simulatioi oftus type the FARGO algorithin (Masset 2000)) is appied., In order to obtain the long integration times needed for simulations of this type the FARGO algorithm (Masset \cite{Masset}) ) is applied.1083 However. tests have shown that the results are not affected by this.," However, tests have shown that the results are not affected by this."1084 We use a 2D cvliudrical (ry) grid wih 20) radial zones cistiibuted uuifonulv between rk=0. and ¢=3.17 iu dineusiouless uuits aud 300 azimuthal zoics.," We use a 2D cylindrical $(r,\varphi)$ grid with 200 radial zones distributed uniformly between $r=0.4$ and $r=3.47$ in dimensionless units and 300 azimuthal zones."1085 We apply outflow conditions at the iuner boundary fc) slawlate the accretion of disc material onto the ceutral sar., We apply outflow conditions at the inner boundary to simulate the accretion of disc material onto the central star.1086 We attempt to simulate the resonance locking of the system GIS7T6 via tidally iuduced migration of the planets. plausible values of the dise parueters.," We attempt to simulate the resonance locking of the system GJ876 via tidally induced migration of the planets, using plausible values of the disc parameters."1087 The disc is assumed to be thin aud isothermal. with coustaut aspect ratio fir=0.07. and a constant Shakura Suuvaev (1973)]) a-viscositv prescriptio)icwith a=2.107 is adopted.," The disc is assumed to be thin and isothermal, with constant aspect ratio $h/r = 10880.07$, and a constant Shakura Sunyaev \cite{Shakura}) ) $\alpha$ -viscosity prescription with ${\alpha} = 2 \times 108910^{-3}$ is adopted."1090 The two plancts are iutiallv in circular orbits coplanar with the disc. at radial locations r4=1.0 aud r=0.6. IIeuce the outer plaLet ds ocated outside the exact 2:l1 conmuueusurabilitv (ro=0.63).," The two planets are initially in circular orbits coplanar with the disc, at radial locations $r_{1} =1.0$ and $r_{2} =0.6.$ Hence the outer planet is located outside the exact $2:1$ commensurability $r_{2} =0.63$ )."1091" The planet masses are chosen to correspond to he nüunmuimni nis ""ratiosU- obtained. from. observationsH (Alarey et al. 2001).", The planet masses are chosen to correspond to the minimum mass ratios obtained from observations (Marcy et al. \cite{Marcy4}) ).1092» With masses normalised so that stellar mass is M.=1. this corresponds to ny=6«10.72 aud io=L8«107.," With masses normalised so that stellar mass is $M_{*} = 1$, this corresponds to $m_{1} = 6 \times 10^{-3}$ and $m_{2} 1093= 1.8 \times 10^{-3}$."1094 The plauet masses are fixed as the planets are assmued to be no longer accreting material from the disc., The planet masses are fixed as the planets are assumed to be no longer accreting material from the disc.1095 The dise is prescribed an initial surface deusity X correspouding to what would give a dise mass of 2«10? within the orbit of the outer planet., The disc is prescribed an initial surface density $\Sigma_{0}$ corresponding to what would give a disc mass of $2 \times 10^{-3}$ within the orbit of the outer planet.1096 However we asstune that both planets are located inside a tidally truncated cavity located at ro<1.3. with low surface density Xing=O.01Ny.," However we assume that both planets are located inside a tidally truncated cavity located at $r < 1.3$, with low surface density $\Sigma_{\mathrm{cavity}} = 10970.01\Sigma_{0}$."1098 This cavity is supposed to have already been cleared by the tidal action of the two planets., This cavity is supposed to have already been cleared by the tidal action of the two planets.1099 Between 1.9«r1.5 the surface density is prescribed such that InX linearly joius to X.," Between $1.3 < r < 11001.5$ the surface density is prescribed such that $\ln \Sigma$ linearly joins to $\Sigma_0.$."1101 The tidal iuteraction of the panets with the disc material causes the planets to mierate inwards (see Fieure 11)., The tidal interaction of the planets with the disc material causes the planets to migrate inwards (see Figure \ref{Fig1}) ).1102 The inner planct is deep within f16 cavivy aud only interacts with low surface densi vinaterial aud tlis nüerates slowly., The inner planet is deep within the cavity and only interacts with low surface density material and thus migrates slowly.1103 The outer plauet has its outer 2lli idblad. resonance located outside the cavity :xd in the ody of the disc., The outer planet has its outer $2:1$ lindblad resonance located outside the cavity and in the body of the disc.1104 Ileuce there is more material exciting a negative torque ou the planet. and therefore it mierates faster. despite its lareer mass.," Hence there is more material exerting a negative torque on the planet, and therefore it migrates faster, despite its larger mass."1105 The ratio of seniuajor axes ayfay of the danets decreases until the planets lock into 24 2:1 conmaensurabilitv wit 01H05c2nq at a tfiue fz[00 orbits., The ratio of semi-major axes $a_{1} / a_{2}$ of the planets decreases until the planets 'lock' into a $2:1$ commensurability with $n_{2} \approx 2n_{1}$ at a time $t \approx 400$ orbits.1106 Both planets then subsequently nuerate Πατ» a further maintaining this raio. showing the resonance to be robust.," Both planets then subsequently migrate inwards a further maintaining this ratio, showing the resonance to be robust."1107" Figure 1 also shows the calculated values of the LOSOmance angles o and ο,"," Figure \ref{Fig1}1108 also shows the calculated values of the resonance angles $\phi$ and $\psi$."1109 Once the commensurability lock. has occured. tese are both librating abott zero.," Once the commensurability lock has occured, these are both librating about zero."1110 The resonant interaction Causes a eccentricity erowth of both lanets the growh halting at around average valucs of ey=0.06 alc Cy—O3L although both eccentricities exhibit variations around these average values.," The resonant interaction causes a eccentricity growth of both planets, the growth halting at around average values of $e_{1} = 0.06$ and $e_{2} = 0.34$ although both eccentricities exhibit variations around these average values."1111 The peribelion aneles of the two planets oscillate around the aliguinent posiion. being the natural stable state.," The perihelion angles of the two planets oscillate around the alignment position, being the natural stable state."1112 The cise cavity remaius at low density. aud the cavity edge diffuses slowly iu on f1ο viscous diffusion timescale.," The disc cavity remains at low density, and the cavity edge diffuses slowly in on the viscous diffusion timescale,"1113diffusion of radioactive heat to the photosphere.,diffusion of radioactive heat to the photosphere.1114 According to the model of Mazzali et al. (, According to the model of Mazzali et al. (11152002). about of gamma-rays are leaking. most of which are produced by *Ni outside the photosphere. at the day ~IO (K. Maeda K. Nomoto 2003. a private communication).,"2002), about of gamma-rays are leaking, most of which are produced by $^{56}$ Ni outside the photosphere, at the day $\sim 10$ (K. Maeda K. Nomoto 2003, a private communication)."1116 This should be considered as an upper limit for the leaking fraction since the model assumes the maximally possible mixing. i.e.. uniform distribution of *°Ni. [," This should be considered as an upper limit for the leaking fraction since the model assumes the maximally possible mixing, i.e., uniform distribution of $^{56}$ Ni. ["1117The best-fit model of Mazzali et al. (,The best-fit model of Mazzali et al. (11182002) has less significant mixing.,2002) has less significant mixing.]1119 Therefore.| leaking gamma-rays from or around the photosphere seem less efficient than ~°Ni in the jet. if the “Ni distribution is what is expected from isotropic modeling.," Therefore, leaking gamma-rays from or around the photosphere seem less efficient than $^{56}$ Ni in the jet, if the $^{56}$ Ni distribution is what is expected from isotropic modeling."1120 However. if the explosion is very asymmetric due to the jet formation activity and considerable amount of ?*Ni is ejected outside the photosphere. it may ionize the jet.," However, if the explosion is very asymmetric due to the jet formation activity and considerable amount of $^{56}$ Ni is ejected outside the photosphere, it may ionize the jet."1121 It should also be noted that SN 1998bw produced much larger amount of ??Ni (70.7M... Iwamoto et al.," It should also be noted that SN 1998bw produced much larger amount of $^{56}$ Ni $\sim 0.7 M_\odot$, Iwamoto et al."1122 1998) than SN 2002ap., 1998) than SN 2002ap.1123 We cannot reject that a comparable ?*Ni was produced also in SN 2002ap. but most of it is well outside the photosphere where optical depth is low and radioactive decay energy mostly escapes as gamma-rays. not in optical bands.," We cannot reject that a comparable $^{56}$ Ni was produced also in SN 2002ap, but most of it is well outside the photosphere where optical depth is low and radioactive decay energy mostly escapes as gamma-rays, not in optical bands."1124 Such ??Ni could be missed in the modeling by Mazzali et al. (, Such $^{56}$ Ni could be missed in the modeling by Mazzali et al. (11252002) based on optical observations.,2002) based on optical observations.1126 Such extreme mixing and distribution of °°Ni is unlikely to oceur simply by hydrodynamical instability in C+O stars (K. Maeda K. Nomoto 2003. à private communication. see also Shigeyama et al.," Such extreme mixing and distribution of $^{56}$ Ni is unlikely to occur simply by hydrodynamical instability in C+O stars (K. Maeda K. Nomoto 2003, a private communication, see also Shigeyama et al."1127 1990)., 1990).1128 Hence. significant ejection of °°Ni from the stellar core by jet formation activity is again indicated.," Hence, significant ejection of $^{56}$ Ni from the stellar core by jet formation activity is again indicated."1129 The observed radio emission 15 considered to be produced by shocked CSM swept-up by high velocity supernova ejecta., The observed radio emission is considered to be produced by shocked CSM swept-up by high velocity supernova ejecta.1130 Then there are two possibilities: (1) the observed radio flux is generated by CSM swept up by the jet responsible for the redshifted polarization. or (11) the radio flux is from CSM swept up by isotropic supernova ejecta that is a different component from the jet. as considered by BKCO2. and the radio emission by CSM swept up by the jet was weaker than observed.," Then there are two possibilities: (i) the observed radio flux is generated by CSM swept up by the jet responsible for the redshifted polarization, or (ii) the radio flux is from CSM swept up by isotropic supernova ejecta that is a different component from the jet, as considered by BKC02, and the radio emission by CSM swept up by the jet was weaker than observed."1131 The former option predicts that the shock front of the radio emission region is not decelerating. otherwise the shock generated 1n the jet material would overproduce much the observed radio flux.," The former option predicts that the shock front of the radio emission region is not decelerating, otherwise the shock generated in the jet material would overproduce much the observed radio flux."1132 On the other hand. since the expansion velocity of Isotropic shell considered by BKCO2 is similar to that of the jet. the mass of the isotropic ejecta in the latter option must be much smaller than the jet mass. otherwise the isotropic component would spoil the redshifted polarization produced by scattering in the jet.," On the other hand, since the expansion velocity of isotropic shell considered by BKC02 is similar to that of the jet, the mass of the isotropic ejecta in the latter option must be much smaller than the jet mass, otherwise the isotropic component would spoil the redshifted polarization produced by scattering in the jet."1133 The mass of isotropic component can be as small as the swept-up CSM. that is much smaller than the jet mass as argued above. and it should be decelerated by swept-up CSM.," The mass of isotropic component can be as small as the swept-up CSM, that is much smaller than the jet mass as argued above, and it should be decelerated by swept-up CSM."1134 BKCO2 found that the radio data is not sufficient to constrain whether the shock radius is decelerating or not. and hence cannot constrain this possibility.," BKC02 found that the radio data is not sufficient to constrain whether the shock radius is decelerating or not, and hence cannot constrain this possibility."1135 Here we examine the possibility (1) by a detailed modeling of the observed radio emission with a collimated jet., Here we examine the possibility (i) by a detailed modeling of the observed radio emission with a collimated jet.1136" Given the jet opening angle and the density of CSM (determined by ©M,. and V). we can calculate the mass and energy density of shocked CSM swept up by the jet moving at a constant velocity. 0.23c."," Given the jet opening angle and the density of CSM (determined by $\dot{M}_w$ and $V_w$ ), we can calculate the mass and energy density of shocked CSM swept up by the jet moving at a constant velocity, $0.23c$."1137 We assumed the strong shock limit with a compression factor of 4. and temperature of the shocked CSM is calculated by the standard shock theory for supersonic piston.," We assumed the strong shock limit with a compression factor of 4, and temperature of the shocked CSM is calculated by the standard shock theory for supersonic piston."1138" Then we can calculate the synchrotron flux according to the standard formulae. if fractional energy densities of nonthermal electrons (e,) and magnetic field (eg). electron power index (p.dN./d,X5,7). and the minimum Lorentz factor of nonthermal electrons (ση) are specified."," Then we can calculate the synchrotron flux according to the standard formulae, if fractional energy densities of nonthermal electrons $\epsilon_e$ ) and magnetic field $\epsilon_B$ ), electron power index $p, dN_e/d\gamma_e1139\propto \gamma_e^{-p}$ ), and the minimum Lorentz factor of nonthermal electrons $\gamma_m$ ) are specified."1140 We calculated the synchrotron flux taking into account synchrotron self-absorption (SSA) by formulations given in Li Chevalier (1999). and also free-free absorption (FFA) by formulations in Weiler et al. (," We calculated the synchrotron flux taking into account synchrotron self-absorption (SSA) by formulations given in Li Chevalier (1999), and also free-free absorption (FFA) by formulations in Weiler et al. ("1141"1986). assuming pre-shocked CSM temperature Tesm=107 K.. We fix e,=0.05. and find best-fit parameters of M,. and eg to the observed radio data (ΒΚΟ02) by v analysis. as a function of the beaming factor 5.","1986), assuming pre-shocked CSM temperature $T_{\rm CSM} = 10^4$ K. We fix $\epsilon_e = 0.05$, and find best-fit parameters of $\dot{M}_w$ and $\epsilon_B$ to the observed radio data (BKC02) by $\chi^2$ analysis, as a function of the beaming factor $b$."1142 The radio flux is showing an evidence of modulation. presumably due to the interstellar scattering and scintillation (SS). and the minimum V is unacceptably large without this effect taken into account.," The radio flux is showing an evidence of modulation, presumably due to the interstellar scattering and scintillation (ISS), and the minimum $\chi^2$ is unacceptably large without this effect taken into account."1143 Here we calculate ISS modulation index with parameters given in BKCO2. and it is added to the observational flux. errors as quadratic sum.," Here we calculate ISS modulation index with parameters given in BKC02, and it is added to the observational flux errors as quadratic sum."1144" The wind velocity is fixed to V,.—10? kny's, and different values of V, simply rescale M, via the CSM density (x™M,,./V,)."," The wind velocity is fixed to $V_w = 10^3$ km/s, and different values of $V_w$ simply rescale $\dot{M}_w$ via the CSM density $\propto \dot{M}_w / V_w$ )."1145" The change of e, is also mostly canceled by sealing of M... except for the strength of the free-free absorption."," The change of $\epsilon_e$ is also mostly canceled by scaling of $\dot{M}_w$ , except for the strength of the free-free absorption."1146" We checked that changing e, by one order of magnitude does not affect conclusions derived below.", We checked that changing $\epsilon_e$ by one order of magnitude does not affect conclusions derived below.1147" The magnetic field strength can be expressed as: B20.21MISMA""(en0.01)?4G."," The magnetic field strength can be expressed as: $B = 0.21 \ \dot{M}_{w, -6}^{1/2} V_{w,11483}^{-1/2} (\epsilon_B/0.01)^{1/2} \ \rm G$."1149" The best-fit M,. and €p. as Well as the u value. are given in Fig. 2.."," The best-fit $\dot{M}_w$ and $\epsilon_B$, as well as the $\chi^2$ value, are given in Fig. \ref{fig:eps_B_Mwind}."1150" Here we used two extreme values of >,,: a low value amp—5 and ahigh value 7,,5—μωροΕν for the thick and thin lines. respectively."," Here we used two extreme values of $\gamma_m$: a low value $\gamma_{m, l} = \gamma$ and a high value $\gamma_{m,1151h} = 1 + \mu_e m_p (\gamma - 1) / m_e$ for the thick and thin lines, respectively."1152 The former corresponds to a case that the electron minimum energy simply reflects the velocity of the shock. while the latter to a case that the kinetic energy of tons ts efficiently transfered to electrons.," The former corresponds to a case that the electron minimum energy simply reflects the velocity of the shock, while the latter to a case that the kinetic energy of ions is efficiently transfered to electrons."1153 We also used three values of p=2.2.2.5. and 2.8.," We also used three values of $p = 2.2, 2.5$ and 2.8."1154" The characteristic synchrotron frequency (7) corresponding to 7,4. the SSA frequeney (4,4). and the FPA frequency (7455) at the day 7 in these results are given in Fig. 6.."," The characteristic synchrotron frequency $\nu_m$ ) corresponding to $\gamma_m$, the SSA frequency $\nu_{\rm ssa}$ ), and the FFA frequency $\nu_{\rm ffa}$ ) at the day 7 in these results are given in Fig. \ref{fig:nu},"1155 but only for the p22.2 case.," but only for the $p =11562.2$ case."1157 The 4 degree of freedom Is fy=24—321. and the minimum reduced X=ο is less than the unity. i.e.. an acceptable fit.," The $\chi^2$ degree of freedom is $n_{\rm dof} = 24 - 3 = 21$, and the minimum reduced $\tilde{\chi}^2 \equiv \chi^2/n_{\rm dof} $ is less than the unity, i.e., an acceptable fit."1158 The confidence limit projected on the parameter 5 can be estimated by à region where AA. i.e.. difference of 47 from the minimum. is smaller than a certain value; AV7«0.19 and 0.32 for 95.4 and C.L.. respectively. assuming a pure Gaussian statistics (e.g.. Press et al.," The confidence limit projected on the parameter $b$ can be estimated by a region where $\Delta \chi^2$, i.e., difference of $\chi^2$ from the minimum, is smaller than a certain value; $\Delta \tilde{\chi}^2 < 0.19$ and 0.32 for 95.4 and C.L., respectively, assuming a pure Gaussian statistics (e.g., Press et al."1159 1992)., 1992).1160 Therefore. we conclude that a mild beaming b—0.1 1s marginally allowed and stronger beaming is excluded for the possibility (1).," Therefore, we conclude that a mild beaming $b \sim 0.1$ is marginally allowed and stronger beaming is excluded for the possibility (i)."1161 The flux evolution and comparison with observed data are shown in Fig. 7..," The flux evolution and comparison with observed data are shown in Fig. \ref{fig:flux_early},"1162 for the best-fit models with 620.1 and 1., for the best-fit models with $b = 0.1$ and 1.1163 The result in the isotropic case (5= 1) is similar to that of BKCO2. as it should be.," The result in the isotropic case $b = 1$ ) is similar to that of BKC02, as it should be."1164 A general trend seen in Fig., A general trend seen in Fig.1165 2 can be understood as follows., \ref{fig:eps_B_Mwind} can be understood as follows.1166 When jet is more strongly collimated. the amount of CSM swept-up by the jet becomes smaller. and hence higher mass loss rate is required to compensate this.," When jet is more strongly collimated, the amount of CSM swept-up by the jet becomes smaller, and hence higher mass loss rate is required to compensate this."1167 However. the observed spectral feature is mostly explained by SSA. and hence magnetic field must become smaller to keep SSA frequency at the observed value.," However, the observed spectral feature is mostly explained by SSA, and hence magnetic field must become smaller to keep SSA frequency at the observed value."1168 This explains behaviors 5= 0.1-1., This explains behaviors between $b = $ 0.1--1.1169 However. FFA becomes significant when M. betweenbecomes very large at 5< 0.1.," However, FFA becomes significant when $\dot{M}_w$ becomes very large at $b \lesssim11700.1$ ."1171 The observed data are not fitted well only by spectral break by FFA. because the early rise of radio flux due to decreasing optical depth is more rapid than SSA (see Weiler et al.," The observed data are not fitted well only by spectral break by FFA, because the early rise of radio flux due to decreasing optical depth is more rapid than SSA (see Weiler et al."1172 1986 for radio supernovae showing this feature). and it does not fit the observed slow rise of radio flux at 1.43GHz.," 1986 for radio supernovae showing this feature), and it does not fit the observed slow rise of radio flux at 1.43GHz."1173" As a result. M,. cannot increase significantly with decreasing b at b= 0.1.and SSA frequency is always higher than FFA for the best fit models(see Fig. 6))."," As a result, $\dot{M}_w$ cannot increase significantly with decreasing $b$ at $b \lesssim 0.1$ ,and SSA frequency is always higher than FFA for the best fit models(see Fig. \ref{fig:nu}) )."1174 Because of this constraint.," Because of this constraint,"1175"At tree level. there are two cliagrais: oue is re. from the sinele-W,, contribution: aud the other is the two-W,, term with fi»=0 for the secoud term of (611)). At one-loop level. five diagrams are nonzero.","At tree level, there are two diagrams: one is $\Gamma^{(2)}_{\delta}$, from the $\psid$ contribution; and the other is the $\psid$ term with $t_{12}=0$ for the second term of \ref{eqn:G2_n_detail}) ), At one-loop level, five diagrams are nonzero."1176" where Tu ((15)). Ay and A. are two-W,, contributious from the first and second terms of ((10)) respectively. Ky and AC) are contributions. aud ACs is the four-W,, contribution."," where In \ref{eqn:G2_1loop_ker}) ), $\mK_1$ and $\mK_2$ are $\psid$ contributions from the first and second terms of \ref{eqn:G2_n}) ) respectively, $\mK_3$ and $\mK_4$ are $\psid$ contributions, and $\mK_5$ is the $\psid$ contribution."1177" At last. the thice-W,,nou-linear power spectra of the log-transformed field 6, can be expressed as m his section. we slow our nuuerical results."," At last, the non-linear power spectrum of the log-transformed field $\phid$ can be expressed as In this section, we show our numerical results."1178 To siniplifv t1ο calculation. we adop the approximation ((26)). which has been shown to be accurate enough in Bernardeaneta].(2008).," To simplify the calculation, we adopt the approximation \ref{eqn:gammpsi_apprx}) ), which has been shown to be accurate enough in \cite{BCS08}."1179. For the trec-kvel propagator. we only include the feistest-erowing mode. Le. the sandard perturbation kernel FY.," For the tree-level propagator, we only include the fastest-growing mode, i.e. the standard perturbation kernel $F^{(n)}$."1180 Since the non-incarη quantity: D;Und. is involved throiehout our formulac. all the calculation 1s done miuerically," Since the non-linear quantity $\Gamma^{(n)}_{\delta}$ is involved throughout our formulae, all the calculation is done numerically."1181" All results asstme the fiducial concordance ACDM cosmologv of simulation 0 of the Covote Univorse suite (Heituiumetal.2010.2009:Lawrence2010).. with (0,772. Ql? Lig. Ut Os. hi) = (0.1296. 0.0 221.0.97 2-1. 0.8. 0.72)."," All results assume the fiducial concordance $\Lambda$ CDM cosmology of simulation 0 of the Coyote Universe suite \citep{cu1,cu2,cu3}, with $\Omega_m h^2$, $\Omega_b h^2$, $n_s$, $w$, $\sigma_8$, $h$ ) = (0.1296, 0.0224, 0.97, -1, 0.8, 0.72)."1182 We use these parameters becase we conpare our perturbative md sto dmeasurements frou thi SS]uula1011., We use these parameters because we compare our perturbative results to measurements from this simulation.1183 The linear power spectruni is calculated with the public Doltzuiuum code (Lewisctal.2000).. and tl10 nnnier‘ical inteeration is poronued with the multi-dineusional iutegratiou -—10.," The linear power spectrum is calculated with the public Boltzmann code \citep{camb}, and the numerical integration is performed with the multi-dimensional integration routine."1184 Iu Fie.(7)). we show the two-polunt prooeator P(1){On) up to two-loop order.," In \ref{fig:gamma_phi}) ), we show the two-point propagator $\Gamma^{(1)}_A(k)$ up to two-loop order."1185 As expected from the analysis of SPT. the propagator of the A field apxoachles a coustaut aless than one at large scales.," As expected from the analysis of SPT, the propagator of the $A$ field approaches a constant less than one at large scales."1186" The value of this large-scale bias, which also encodes the statistical information o the density fluctuation (Eq.22 )). strongly depends ou the smoothing process adopted before the transformlon."," The value of this large-scale bias, which also encodes the statistical information of the density fluctuation \ref{eqn:SPT_bias}) ), strongly depends on the smoothing process adopted before the transformation."1187" For he ziioothiung radius R>x. effectively uo loop integration contributes to D,[1th). therefore] the bias. approaches to 1 from the tree-level result. (38))."," For the smoothing radius $R \to \infty$, effectively no loop integration contributes to $\Gamma_A^{(1)}(k)$, therefore the bias approaches to $1$ from the tree-level result, \ref{eqn:GA1_tree}) )."1188 When the sincothing radius goes malle since. Cee} that appears in the loop iutegration also decays at large fk. the effect of the smoothing becomes less and less iaportautD) until fie bias freezes at some value. where higher-loop coutributious are significant.," When the smoothing radius goes smaller, since $\Gamma_{\delta}^{(n)}(k)$ that appears in the loop integration also decays at large $k$, the effect of the smoothing becomes less and less important until the bias freezes at some value, where higher-loop contributions are significant."1189 Inthis sense. the presence of DU) heps to regulate the convergence of the perturbative series.," Inthis sense, the presence of $\Gamma_{\delta}^{(n)}(k)$ helps to regulate the convergence of the perturbative series."1190 At small scales. ri(k) is daupened both by nonlinearities anc by smoothiug. while TC) has no additional sinoothliue imposed.," At small scales, $\Gamma_A^{(1)}(k)$ is dampened both by nonlinearities and by smoothing, while $\Gamma_{\delta}^{(1)}(k)$ has no additional smoothing imposed."1191 This is why Dk) decay sat larger scales than D;(1)(k) for large smoothing scales., This is why $\Gamma_A^{(1)}(k)$ decays at larger scales than $\Gamma_{\delta}^{(1)}(k)$ for large smoothing scales.1192 The top solid line shows rU) with a smooting scale R=20hMpec.. which reduces to 0.5 around &~0.17," The top solid line shows $\Gamma^{(1)}_A(k)$ with a smoothing scale $R=20$, which reduces to 0.5 around $k\sim 0.1$."1193 As the 31u000fing radius becomes sialler. the curve approaches I;(1)(k) at buge &.," As the smoothing radius becomes smaller, the curve approaches $\Gamma_{\delta}^{(1)}(k)$ at large $k$."1194 For 25h. (the bottoni solid lino). the dauipiug of boostingrith) is. similar. to that of. (1)," For $R=5$ (the bottom solid line), the damping of $\Gamma_A^{(1)}(k)$ is similar to that of $\Gamma_\delta^{(1)}(k)$."1195 Tf the large-scale bias is divide out. he A propagators to line up Dd).for siidll &. the A propagator may slightly exceed the 6 propagator on smal scales. if the ssinootlingscale is suticicutly small.," If the large-scale bias is divided out, boosting the $A$ propagators to line up for small $k$, the $A$ propagator may slightly exceed the $\delta$ propagator on small scales, if the smoothingscale is sufficiently small."1196 We have found this to be the case in preliminary siniulation nieastrvelncuts., We have found this to be the case in preliminary simulation measurements.1197 Disappointingly. this nuplies that the logarithmic transform bv itself docs uot help appreciably to recoustinct mnode-by-uxkde initial phases aud amplitudes.," Disappointingly, this implies that the logarithmic transform by itself does not help appreciably to reconstruct mode-by-mode initial phases and amplitudes."1198 But the similarity in damping is not surprising. eiven that blilk displacements roni the initial conditions affect both fields.," But the similarity in damping is not surprising, given that bulk displacements from the initial conditions affect both fields."1199 Iu SJ). we illustrate the non-linear power spectra of both P4(k) and ο) at à=0.7 aud a=1.," In \ref{fig:pk_1}) ), we illustrate the non-linear power spectra of both $P_A(k)$ and $P_{\delta}(k)$ at $a=0.7$ and $a=1$."1200 The squares and triangles are the 0 and A power spectra measured from Covote Universe simulation 0. which µας I particles iu a cubic 1300 Mpc (~Lh Cipe3) box.," The squares and triangles are the $\delta$ and $A$ power spectra measured from Coyote Universe simulation 0, which has $^3$ particles in a cubic 1300 Mpc $\sim1$ ) box."

Showing the first 1,200 of 10411 lines. Download the file for the rest.