ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 We find no significaut differences iu he detection levels when the simulations are assumed ognormal or Gaussian., We find no significant differences in the detection levels when the simulations are assumed lognormal or Gaussian.3 We also investigate the performance of the wild ootstrap moethlioc for the coufidence estimation., We also investigate the performance of the wild bootstrap method for the confidence estimation.4 Table 5 shows the p-values estimated using Monte-C'arlo xocedure and wild bootstrap for the first two methods of the 3-step Saclay method.," Table \ref{tab:pvalues}5 shows the $p$ -values estimated using Monte-Carlo procedure and wild bootstrap for the first two methods of the 3-step Saclay method."6 Notice tha the bootstrap results are alnios equivalent to Monte-Carlo oiws, Notice that the bootstrap results are almost equivalent to Monte-Carlo ones.7 We fud the bootstrap method wasut always reliabe when he p-value becomes small. because the precision of the )otstrap depends on both the number of bootstrap sunuples (as auv AIClike process) and the nuuber of observed eleiieuts.," We find the bootstrap method wasn't always reliable when the $p$ -value becomes small, because the precision of the bootstrap depends on both the number of bootstrap samples (as any MC-like process) and the number of observed elements."8 This last dependence ales the ootstrap uncertain when the detection oes almost certain. hat is why we consider the bootstrapped cross-correlation as an indicator that needs refinement when the results are very significant.," This last dependence makes the bootstrap uncertain when the detection is almost certain, that is why we consider the bootstrapped cross-correlation as an indicator that needs refinement when the results are very significant."9 Iu order to investigate the different strengths of cach method. we also evaluate the rate of true positives vs. the uunuber of false positives(ic. false detections) - this information is suuumarised in Fieure 23/— which shows Receiver Operating Characteristic (ROC) curves.," In order to investigate the different strengths of each method, we also evaluate the rate of true positives vs. the number of false positives (i.e. false detections) - this information is summarised in Figure \ref{fig:roc} which shows Receiver Operating Characteristic (ROC) curves."10 The construction of the ROC curve requires the computation, The construction of the ROC curve requires the computation11nunüdnositv decreases. with lowest hnuuinositv DL Lac objects requiring a negligible amount of EC.,"luminosity decreases, with lowest luminosity BL Lac objects requiring a negligible amount of EC."12 We applied a iue SSC model to the SED of ON 231. as shown in roefüe:sed..," We applied a pure SSC model to the SED of ON 231, as shown in \\ref{fig:sed}."13 Iun particular we have tried to explain the different SED by changing the imiuunuiun nuniber of »uanmeters., In particular we have tried to explain the different SED by changing the minimum number of parameters.14 The applied models assuuie to continuously inject. iui a spherical source of radius ΠΠ embedded in a tangled uaeuetic field DB. xativistic clectrous with a power aw enerev distribution X3E between Twin mo sax:," The applied models assume to continuously inject, in a spherical source of radius $R$ embedded in a tangled magnetic field $B$, relativistic electrons with a power law energy distribution $\propto \gamma^{-s}$, between $\gamma_{\rm min}$ and $\gamma_{\rm max}$."15 The total luminosity iujected in the form of relativistic electrons is Li. calculated in the comoving frame.," The total luminosity injected in the form of relativistic electrons is $L^\prime_{\rm inj}$, calculated in the comoving frame."16 We also assumed to observe the source at the viewing anele L/T. so that the Doppler factor &=EL.," We also assumed to observe the source at the viewing angle $1/\Gamma$, so that the Doppler factor $\delta=\Gamma$."17 The steadystate particle distribution is he result of the injection and cooling processes. and we also account for possible escape of the particles. which may be relevant for ON 231.," The steady--state particle distribution is the result of the injection and cooling processes, and we also account for possible escape of the particles, which may be relevant for ON 231."18 It is assumed tha particles escape at sole velocity Cone=euo Independent of their energy.," It is assumed that particles escape at some velocity $v_{\rm esc}=c\beta_{\rm esc}$, independent of their energy."19 Further details about this meocel can be fou in Chisellini et al. (, Further details about this model can be found in Ghisellini et al. (201998).,1998).21 The input parameters for the uodoels shown in reffile:sed are given in Table 3., The input parameters for the models shown in \\ref{fig:sed} are given in Table 3.22" The size of the source aud the Doppler factor have been kept fixed: the slope s of the injected electron distribution aud 544,45 are similar.", The size of the source and the Doppler factor have been kept fixed; the slope $s$ of the injected electron distribution and $\gamma_{\rm max}$ are similar.23" The magnetic field does not chauge. while 5,,;, changes by ~ 30%. from 2300 to 3000."," The magnetic field does not change, while $\gamma_{min}$ changes by $\sim 30\%$ , from 2300 to 3000."24" The larges change COLMCCTILS the injected power. icreasing from Li;=3.3.lot cre * (1991 model). to Lh,=2.2«107 erg  (1998 model). an increase of a factor 7."," The largest change concerns the injected power, increasing from $L^\prime_{\rm inj}= 3.3\times 10^{41}$ erg $^{-1}$ (1991 model), to $L^\prime_{\rm inj}= 2.2\times 10^{42}$ erg $^{-1}$ (1998 model), an increase of a factor 7."25 Within the SSC imodclel. it is uot possible to account for the very hard 5 ray spectrin of 19911992.," Within the SSC model, it is not possible to account for the very hard $\gamma$ –ray spectrum of 1991–1992."26" The quasisnultaueous optical data requires the peak of the optical cussion to be at requenucies between the near IR aud the optical. while the iud EGRET spectra indicates that the Compton peak ina energies greater than a few GeV. This transla nna ower mut for he energy of the electron ciuitting at the deals of 2iak>OS101,"," The quasi–simultaneous optical data requires the peak of the optical emission to be at frequencies between the near IR and the optical, while the hard EGRET spectrum indicates that the Compton peak is at energies greater than a few GeV. This translates in a lower limit for the energy of the electron emitting at the peaks of $\gamma_{\rm peak}>6\times 10^4$."27 These electrons cuit at Msooeakv2<Lot! Ile if the magnetic field Bo<L1«1078! Causs.," These electrons emit at $\nu_{\rm s,peak}\sim 2\times 10^{14}$ Hz if the magnetic field $B<1.4\times 10^{-2}\delta^{-1}$ Gauss."28 This is not cousistent with the lits derived in the oevious section., This is not consistent with the limits derived in the previous section.29" Iu addition. a small magnetic fiek would nuplv a verv huge radiatiou to magnetic energy deusity ratio. C,/Up. aud hen an excessive self Compton flux. uuless the Doppler factor is exceedingly large (67LOO. see eq."," In addition, a small magnetic field would imply a very large radiation to magnetic energy density ratio, $U_{\rm r}/U_{\rm B}$, and then an excessive self Compton flux, unless the Doppler factor is exceedingly large $\delta> 100$, see eq."30 2.5 and 2.6 in Clisellini et al., 2.5 and 2.6 in Ghisellini et al.31 1996)., 1996).32 We then couclude that either the hard 19911992 + raw spectrum is duc to another source. or. if it will be confirmed to be associates with ON 231. is produced by another componcut (ec. to inverse Compton scattering with photous produce externally to the jet).," We then conclude that either the hard 1991–1992 $\gamma$ –ray spectrum is due to another source, or, if it will be confirmed to be associated with ON 231, is produced by another component (i.e. to inverse Compton scattering with photons produced externally to the jet)."33 Note that BL Lacertae showed a simular behavior (hardening of the 5 rav spectrin) durius the flare of sunuucr 1997 (Bloom et al., Note that BL Lacertae showed a similar behavior (hardening of the $\gamma$ –ray spectrum) during the flare of summer 1997 (Bloom et al.34 1997)., 1997).35 This was interpretec (Sambruna et al., This was interpreted (Sambruna et al.36 1999: Aladejski ct al., 1999; Madejski et al.37 1999: Bottcher Bloom 1999) as due to an iucreased contribution of cluission line plotous to the inverse Compton scattering process., 1999; Bottcher Bloom 1999) as due to an increased contribution of emission line photons to the inverse Compton scattering process.38 Something simular could have happened also to ON 231 (during the 19911992 EGRET observation). but the lack of spectroscopic observations preclude any further conclusious.," Something similar could have happened also to ON 231 (during the 1991–1992 EGRET observation), but the lack of spectroscopic observations preclude any further conclusions."39 What is iuterestiug. and peculiar. in ON 231 is the sharp flattening. above 2l1 keV. of the X.rav spectrin.," What is interesting, and peculiar, in ON 231 is the sharp flattening, above $2-4$ keV, of the X–ray spectrum."40" A population of clectrous which cools only radiatively cau not account or spectra as flat as observed in ON 231: the Hattest predicted spectra in the case of radiative cooling has an euergv spectral iudex a=0.5 (see e.g, Chiselni et al.", A population of electrons which cools only radiatively can not account for spectra as flat as observed in ON 231: the flattest predicted spectrum in the case of radiative cooling has an energy spectral index $\alpha=0.5$ (see e.g. Ghisellini et al.41 1998)., 1998).42 We therefore iust invoke an additional mechanisin., We therefore must invoke an additional mechanism.43 One likely possibility is escape., One likely possibility is escape.44 Iu this case high euergv clectrous would cool before escaping. while low enuergv clectrous would prefercutially escape before cooling radiativelv.," In this case high energy electrons would cool before escaping, while low energy electrons would preferentially escape before cooling radiatively."45 The corresponding steady.state particle distribution would then show a fattenme towards the low cnerey part. accounting for the very flat inverse Compton compoucut emiergme above | keV. The model we have applied to ON 231 indicates that ον0.3 0.1. correspouding to au escape time of the order of 23 lig crossing times A2/e.," The corresponding steady–state particle distribution would then show a flattening towards the low energy part, accounting for the very flat inverse Compton component emerging above 4 keV. The model we have applied to ON 231 indicates that $\beta_{\rm esc}\sim 0.3$ $0.4$, corresponding to an escape time of the order of 2–3 light crossing times $R/c$."46 The variability predicted by the model can accouut for the observed variability iu the soft Noταν baud aud for the muuch less variable hard X.rav flux. even if the bolometric huninosity does not change.," The variability predicted by the model can account for the observed variability in the soft X–ray band and for the much less variable hard X–ray flux, even if the bolometric luminosity does not change."47 This cau be achieved bx changing (even by a sinall amount) the slope s of the injected electron distribution. without changing the total injected power.," This can be achieved by changing (even by a small amount) the slope $s$ of the injected electron distribution, without changing the total injected power."48 This will change the svuchrotrou spectrin above the svuchrotron peak (characterized by a~s/2). but not the flux below. nor the self Compton fux. below the Compton peak. produced by low energy electrons scattering low frequency svuchrotrou photons.," This will change the synchrotron spectrum above the synchrotron peak (characterized by $\alpha\sim s/2$ ), but not the flux below, nor the self Compton flux below the Compton peak, produced by low energy electrons scattering low frequency synchrotron photons."49 The BeppoSANX data of ON 231 show that this source can be considered a BL Lac object intermediate between the HBL and LBL sources., The $Beppo$ SAX data of ON 231 show that this source can be considered a BL Lac object intermediate between the HBL and LBL sources.50 The concave shape of the Nvay spectruni iu the 0.110 keV band cau be used to define he class of intermediate blazars. which should beliwacterized. iu this baud. bv the presence of the steep ail of the synchrotron radiation aud the hard emerging of 1ο Compton Cluission.," The concave shape of the X–ray spectrum in the 0.1–10 keV band can be used to define the class of intermediate blazars, which should becharacterized, in this band, by the presence of the steep tail of the synchrotron radiation and the hard emerging of the Compton emission."51indicate an overabundance of BHB stars in the cluster with respect to the surrounding field (see Table 7)) at 5 c level.,indicate an overabundance of BHB stars in the cluster with respect to the surrounding field (see Table \ref{tab:hb}) ) at 5 $\sigma$ level.52 The best match with the Galactic RGB and HB ridge lines is obtained by assuming a value of reddening E(B—V)=0.12 mag and a distance modulus of (m—M)o=24.43., The best match with the Galactic RGB and HB ridge lines is obtained by assuming a value of reddening $E(B-V)=0.12$ mag and a distance modulus of $(m-M)_{0}=24.43$.53" With these assumptions, the clusters RGB fall between the ridge lines of NGC5824 and M13, indicating that the metallicity of B292 is [Fe/H]=-1.8+0.25."," With these assumptions, the cluster's RGB fall between the ridge lines of NGC5824 and M13, indicating that the metallicity of B292 is $[Fe/H]=-1.8\pm0.25$."54" This value agrees well with the spectroscopic metallicity estimates by POS and Galleti et al. (2009,,"," This value agrees well with the spectroscopic metallicity estimates by P05 and Galleti et al. \cite{G09},"55" hereafter G09), while it is just marginally more metal-poor than what was found by Barmby et al. (2000,,"," hereafter G09), while it is just marginally more metal-poor than what was found by Barmby et al. \cite{barm00},"56" hereafter BOO), and 0.45 dex more metal-rich than the value obtained by F10 from integrated photometry."," hereafter B00), and 0.45 dex more metal-rich than the value obtained by F10 from integrated photometry."57" The mismatch in color between the vertical parts of observed and template BHB may suggest a solution with a higher reddening and, consequently, a lower metallicity; this would not change the main conclusions of the present analysis significantly."," The mismatch in color between the vertical parts of observed and template BHB may suggest a solution with a higher reddening and, consequently, a lower metallicity; this would not change the main conclusions of the present analysis significantly."58" We preferred the solution presented in Fig. 7,,"," We preferred the solution presented in Fig. \ref{fig:templates},"59" which gives greater weight to the five stars at intermediate color (0.1€(B—V)o 0.6, around My~ 0.6), because, if interpreted as genuine cluster members, they provide a constraint on the vertical direction (distance) that is otherwise lacking."," which gives greater weight to the five stars at intermediate color $0.1\le (B-V)_0\le 0.6$ , around $M_V\simeq 0.6$ ), because, if interpreted as genuine cluster members, they provide a constraint on the vertical direction (distance) that is otherwise lacking."60" The best match of the color of the vertical portion of the HB can be obtained by adopting E(B-V)=0.19, and (m—M)o=24.3."," The best match of the color of the vertical portion of the HB can be obtained by adopting E(B-V)=0.19, and $(m-M)_0=24.3$."61 This solution appears unlikely because it would imply that this cluster is located several kpc above (and in front of) the M31 disk while suffering from a degree of extinction quite typical of clusters embedded in the disk (see Perina et al. 2010))., This solution appears unlikely because it would imply that this cluster is located several kpc above (and in front of) the M31 disk while suffering from a degree of extinction quite typical of clusters embedded in the disk (see Perina et al. \cite{ymc}) ).62 A small-scale Galactic cloud on this line of sight seems the only possibility to make this solution viable., A small-scale Galactic cloud on this line of sight seems the only possibility to make this solution viable.63" In any case, this solution also yields a low metallicity ([Fe/H]~ —1.9) and the old age implied by the presence of BHB."," In any case, this solution also yields a low metallicity $[Fe/H]\simeq -1.9$ ) and the old age implied by the presence of BHB."64" The CMD of B350 (Fig. 4,,"," The CMD of B350 (Fig. \ref{fig:isoc1},"65 bottom-left panel) shows a well populated blue HB clearly associated with the cluster (see Table 7 and Fig. 8))., bottom-left panel) shows a well populated blue HB clearly associated with the cluster (see Table \ref{tab:hb} and Fig. \ref{fig:low_lim}) ).66" The RGB is steep, which indicates a low metal content."," The RGB is steep, which indicates a low metal content."67" The best match of the RGB and HB features with the corresponding Galactic ridge lines is obtained by assuming a distance modulus of (m—M)o = 24.45 and maintaining the adopted starting value of E(B—V)=0.08 mag for the reddening, in good agreement with what was reported by F10 (Table 1))."," The best match of the RGB and HB features with the corresponding Galactic ridge lines is obtained by assuming a distance modulus of $(m-M)_{0}$ = 24.45 and maintaining the adopted starting value of $E(B-V)=0.08$ mag for the reddening, in good agreement with what was reported by F10 (Table \ref{tab:targets}) )."68" With these assumptions, the cluster RGB fall between the ridge lines of M13 and M5, indicating for B350 a metallicity of [Fe/H]=—1.5+0.25."," With these assumptions, the cluster RGB fall between the ridge lines of M13 and M5, indicating for B350 a metallicity of $[Fe/H]=-1.5\pm0.25$."69" This is compatible with most of the values available in literature, except for the marginal discrepancy with the estimate by F10 from integrated photometry (see Table 3))."," This is compatible with most of the values available in literature, except for the marginal discrepancy with the estimate by F10 from integrated photometry (see Table \ref{tab:met}) )."70" Owing to the high degree of crowding, the CMD of B058 is not of sufficient quality to obtain a truly reliable solution."," Owing to the high degree of crowding, the CMD of B058 is not of sufficient quality to obtain a truly reliable solution."71 The CMD previously obtained by Rich et al.( 2005)), The CMD previously obtained by Rich et al.( \cite{rich05}) )72" from WFPC2 data in the filters F555W (V) and F814W (D) with longer exposure times (5300 s and 5400 s, respectively) seems easier to interpret, because it appears to be slightly deeper and the RGB shape is straighter in the I-band."," from WFPC2 data in the filters F555W (V) and F814W (I) with longer exposure times (5300 s and 5400 s, respectively) seems easier to interpret, because it appears to be slightly deeper and the RGB shape is straighter in the I-band."73" The solution presented here must be considered as only tentative, we suggest to keep the parameters by Rich et al. (2005))"," The solution presented here must be considered as only tentative, we suggest to keep the parameters by Rich et al. \cite{rich05}) )"74 as the best set., as the best set.75 The 6.4 Gyr isochrone shown in Fig., The 6.4 Gyr isochrone shown in Fig.76" 5 seems fully compatible with the observed CMD, but an old isochrone would fit equally well."," \ref{fig:isoc2} seems fully compatible with the observed CMD, but an old isochrone would fit equally well."77 The estimate by POS had a large uncertainty (6.4+4.1 Gyr) and the CMD test is completely inconclusive., The estimate by P05 had a large uncertainty $6.4\pm4.1$ Gyr) and the CMD test is completely inconclusive.78" Ages as low as 4 Gyr or 2 Gyr, as proposed by F10 and W10, respectively, are compatible with the observed CMD as well."," Ages as low as 4 Gyr or 2 Gyr, as proposed by F10 and W10, respectively, are compatible with the observed CMD as well."79 B337 has a very clean CMD characterized by a steep RGB and a well populated red HB (see Fig. 5))., B337 has a very clean CMD characterized by a steep RGB and a well populated red HB (see Fig. \ref{fig:isoc2}) ).80 The decontamination has, The decontamination has81which would be consistent either with a nearby WD or with a distant main sequence star on an elliptical orbit and at a high velocity.,which would be consistent either with a nearby WD or with a distant main sequence star on an elliptical orbit and at a high velocity.82" We note that the w—g color of 1.01 is redder than would be expected for a WD (?),, but at the blue end of the colors of F-type main-sequence stars (?).."," We note that the $u-g$ color of 1.01 is redder than would be expected for a WD \citep{smol04}, but at the blue end of the colors of F-type main-sequence stars \citep{cove07}."83" Again, spectroscopy will be necessary to confirm the spectral type of the source and detect evidence for binarity."," Again, spectroscopy will be necessary to confirm the spectral type of the source and detect evidence for binarity."84 The median photon energy of X-ray source events provides a simple characterization of the X-ray emission properties that is particularly useful for faint sources lacking plasma temperatures derived from spectral fits., The median photon energy of X-ray source events provides a simple characterization of the X-ray emission properties that is particularly useful for faint sources lacking plasma temperatures derived from spectral fits.85" 'The distribution of median energies seen in Figure 4 is highly clustered around 1 keV and in agreement with the distribution of plasma temperatures from spectral fits, ~0.5—1.0 keV typical for stars of moderate to high activity (6-12levels MK),and for active regions and flares on the Sun (?)."," The distribution of median energies seen in Figure \ref{plasma} is highly clustered around 1 keV and in agreement with the distribution of plasma temperatures from spectral fits, $\sim 0.5 - 1.0$ keV (6–12 MK), typical for stars of moderate to high activity levels and for active regions and flares on the Sun \citep{pere00}."86" This indicates that our sample includes a large fraction of active stars, as might be expected for a luminosity-limited sample."," This indicates that our sample includes a large fraction of active stars, as might be expected for a luminosity-limited sample."87 We also observe no correlation between either the plasma temperature determined from spectral fitting or the median photon energy of a source with its spectral type., We also observe no correlation between either the plasma temperature determined from spectral fitting or the median photon energy of a source with its spectral type.88 Figure 4 shows the X-ray to bolometric luminosity ratios as a function of photon energy for all our sources., Figure \ref{plasma} shows the X-ray to bolometric luminosity ratios as a function of median photon energy for all our sources.89 For sources with medianE<1.5 keV we note a trend of increasing luminosity ratio with median photon energy., For sources with $\bar{E} \lesssim 1.5$ keV we note a trend of increasing luminosity ratio with median photon energy.90 This is similar to the relationship between the luminosity ratio and plasma temperature commonly seen in type stars and found by ?) and ?).., This is similar to the relationship between the luminosity ratio and plasma temperature commonly seen in late-type stars and found by \citet{schr84} and \citet{schm90}.91" It is thought to result from the increasing size and intensity of active regions, and the growth of flaring activity as active regions fill larger fractions of the stellar surface (e.g.?).."," It is thought to result from the increasing size and intensity of active regions, and the growth of flaring activity as active regions fill larger fractions of the stellar surface \citep[e.g.][]{drak00}."92" In order to look for the influence of flares, we compiled X-ray light curves from the ACIS event lists and tested for variability."," In order to look for the influence of flares, we compiled X-ray light curves from the ACIS event lists and tested for variability."93" We used a one-sample Kolmogorov-Smirnov test to compare the distribution of photon arrival times with that expected for a constant source null and then derived the probability of accepting(the the null hypothesis)hypothesis, Ps, as listed in Table 1.."," We used a one-sample Kolmogorov-Smirnov test to compare the distribution of photon arrival times with that expected for a constant source (the null hypothesis) and then derived the probability of accepting the null hypothesis, $P_{KS}$, as listed in Table \ref{xstars_cosmos}."94" We studied the light curves for 17 sources with Pigs«0.01 and identified six flaring events with durations of 2-5 hours, three of which are shown in Figure 5.."," We studied the light curves for 17 sources with $P_{KS} < 0.01$ and identified six flaring events with durations of 2-5 hours, three of which are shown in Figure \ref{lightcurves}. ."95 These six sources are also indicated in Figure 4 and can clearly be seen at the high Lx/Lp; end of the trend mentioned above., These six sources are also indicated in Figure \ref{plasma} and can clearly be seen at the high $L_X / L_{bol}$ end of the trend mentioned above.96" We then studied the light curves of the other sources with high Lx/Lpo1 and high E, but could find no evidence for bright flares."," We then studied the light curves of the other sources with high $L_X / L_{bol}$ and high $\bar{E}$, but could find no evidence for bright flares."97" We find no trend of median photon energy with luminosity ratio for stars with higher median energies, corresponding to plasma temperatures of ~15—45 MK."," We find no trend of median photon energy with luminosity ratio for stars with higher median energies, corresponding to plasma temperatures of $\sim 15 - 45$ MK."98 The luminosity ratios for these stars range from 10-9—10-?., The luminosity ratios for these stars range from $10^{-6} - 10^{-2}$ .99" The majority of these sources are distant with of sources with E>1.5 keV found at distances >1 kpc, compared to a fraction of for the entire sample."," The majority of these sources are distant with of sources with $\bar{E} > 1.5$ keV found at distances $> 1$ kpc, compared to a fraction of for the entire sample."100 One explanation for the spectral hardness of sources with high X-ray luminosity ratios is that these sources were observed during particularly long and bright flares., One explanation for the spectral hardness of sources with high X-ray luminosity ratios is that these sources were observed during particularly long and bright flares.101" However this cannot be the case for all the hard sources because they do not appear to be significantly more variable than the soft sources: of the hard sources have Pis<0.01, compared to for the entire sample, while all the clearly identified sources with flares are in the soft sample."," However this cannot be the case for all the hard sources because they do not appear to be significantly more variable than the soft sources: of the hard sources have $P_{KS} < 0.01$, compared to for the entire sample, while all the clearly identified sources with flares are in the soft sample."102" There will be a bias in this analysis because variability is easier to identify in sources with more counts, which are more likely to be included in the nearby soft sample, but there appear to be multiple hard X-ray stellar sources that cannot be explained by variability."," There will be a bias in this analysis because variability is easier to identify in sources with more counts, which are more likely to be included in the nearby soft sample, but there appear to be multiple hard X-ray stellar sources that cannot be explained by variability."103" It is more likely that some of these sources, particularly those with low to moderate luminosity ratios (log Lx/Loo;< —4), are members of the halo population that have extremely metal-poor coronae."," It is more likely that some of these sources, particularly those with low to moderate luminosity ratios (log $L_X / L_{bol} < -4$ ), are members of the halo population that have extremely metal-poor coronae."104" Indeed, a lack of a correlation between X-ray luminosity and plasma temperature was noted by ?) based on a survey of nearby Population close binaries."," Indeed, a lack of a correlation between X-ray luminosity and plasma temperature was noted by \citet{ottm97} based on a survey of nearby Population close binaries."105 These authors also found the Pop., These authors also found the Pop.106 stars to have harder spectra than their Pop., stars to have harder spectra than their Pop.107" counterparts, and attributed this to the lower radiative efficiency of metal-poor plasma."," counterparts, and attributed this to the lower radiative efficiency of metal-poor plasma."108" Our sample of stars appears to support this, with what must be halo stars appearing to have very hot coronae."," Our sample of stars appears to support this, with what must be halo stars appearing to have very hot coronae."109" In such coronae, it seems that the lack of plasma radiative cooling through metal lines is compensated for by much higher plasma temperatures and that radiative cooling occurs predominantly through the bremsstrahlung continuum."," In such coronae, it seems that the lack of plasma radiative cooling through metal lines is compensated for by much higher plasma temperatures and that radiative cooling occurs predominantly through the bremsstrahlung continuum."110 Finally we note that CID 546 is the only source with sufficient counts to make a reasonable two-temperature thermal plasma fit., Finally we note that CID 546 is the only source with sufficient counts to make a reasonable two-temperature thermal plasma fit.111 The difference between single and double-component thermal plasma fits is a decrease in the Cash statistic from 843 to 752 and a factor three drop in the maximum(?) fit residuals from 0.015 to 0.005., The difference between single and double-component thermal plasma fits is a decrease in the Cash statistic \citep{cash79} from 843 to 752 and a factor three drop in the maximum fit residuals from 0.015 to 0.005.112 The two-temperature thermal plasma fit consists of plasma at temperatures of 0.73 and 2.1 keV at a flux ratio of 1.3:1 (e.g.?).., The two-temperature thermal plasma fit consists of plasma at temperatures of 0.73 and 2.1 keV at a flux ratio of 1.3:1 \citep[e.g.][]{lope07}.113" Extraction of the light curve of CID 546 does not reveal any large flaring events, and the median photon energy remained relatively constant at ~1.1 keV throughout the observations."," Extraction of the light curve of CID 546 does not reveal any large flaring events, and the median photon energy remained relatively constant at $\sim$ 1.1 keV throughout the observations."114" In this paper we have studied the stellar content of the Chandra-COSMOS survey and identified a sample of 60 stellar sources for which we present X-ray properties, as well as optical and near-IR photometry."," In this paper we have studied the stellar content of the -COSMOS survey and identified a sample of 60 stellar sources for which we present X-ray properties, as well as optical and near-IR photometry."115" In additionwe have obtained spectroscopic classifications for 48 of the sources, confirming their stellar nature and allowing us to derive spectral types and distances."," In additionwe have obtained spectroscopic classifications for 48 of the sources, confirming their stellar nature and allowing us to derive spectral types and distances."116 In the Lx-distance, In the $L_X$ -distance117"high-level clouds, and a 7% overlap of both cloud layers).","high-level clouds, and a $7\%$ overlap of both cloud layers)."118 According to ? the observed average Earth’s total amount of cloud cover is 55% (68%) over land (ocean) yielding a global mean value of about 64% which is much lower than the 48% total cloud cover in the present model due to the omission of mid-level clouds., According to \citet{Warren07} the observed average Earth's total amount of cloud cover is $55\%$ $68\%$ ) over land (ocean) yielding a global mean value of about $64\%$ which is much lower than the $48\%$ total cloud cover in the present model due to the omission of mid-level clouds.119" The clear sky calculation results in a surface temperature of 293K, which is clearly too high (see Paper I for a detailed discussion of the climatic effects of clouds)."," The clear sky calculation results in a surface temperature of $293 \ \mathrm{K}$, which is clearly too high (see Paper I for a detailed discussion of the climatic effects of clouds)."120" Mid-level clouds (observed global mean cloud cover ca. 20%, ?))"," Mid-level clouds (observed global mean cloud cover ca. $20\%$, \citet{Warren07}) )"121" had been omitted in the Earth model of Paper I, as most of them have been reported to be radiatively neutral, i.e. their greenhouse and albedo effect balance each other (see and Paper I for details)."," had been omitted in the Earth model of Paper I, as most of them have been reported to be radiatively neutral, i.e. their greenhouse and albedo effect balance each other (see \citet{Poetzsch95} and Paper I for details)."122" However, the neglect of the mid-level clouds yields less back-scattered shortwave and more outgoing longwave radiation at the top of the atmosphere (TOA) compared to the global energy budget ofEarth!."," However, the neglect of the mid-level clouds yields less back-scattered shortwave and more outgoing longwave radiation at the top of the atmosphere (TOA) compared to the global energy budget of."123. A comparison with measurements of ? shows a deviation about 13Wm in the shortwave and longwave fluxes at the top of the atmosphere (see Table 1))., A comparison with measurements of \citet{Trenberth2009} shows a deviation about $13 \ \mathrm W \mathrm m^{-2}$ in the shortwave and longwave fluxes at the top of the atmosphere (see Table \ref{tab1}) ).124 Presenting the IR emission spectra corresponding to the model described in Paper I only low and high-level clouds are considered in the present study., Presenting the IR emission spectra corresponding to the model described in Paper I only low and high-level clouds are considered in the present study.125 They represent the extreme cases of the effects of clouds on the spectrum of Earth., They represent the extreme cases of the effects of clouds on the spectrum of Earth.126 Oberservations of e.g. ?? and ? showed that the effects of mid-level clouds on the spectra of Earth are between these two extremes.," Oberservations of e.g. \citet{Tinetti2006a,Tinetti2006b} and \citet{Hearty2009} showed that the effects of mid-level clouds on the spectra of Earth are between these two extremes."127" Therefore, the important range of the cloud effects on the emission spectra are covered in our study of extrasolar planetary atmospheres."," Therefore, the important range of the cloud effects on the emission spectra are covered in our study of extrasolar planetary atmospheres."128 Fig., Fig.129 3 shows the related spectra covering the spectral wavelengths range from the near UV to the IR., \ref{earth_ref_spectrum} shows the related spectra covering the spectral wavelengths range from the near UV to the IR.130 In the visible, In the visible131The observation in many pulsars. of ellipticallv volarized radiation of detectable strength. is further evidence of the existence of amplification in bo1 modes. mt now sinultaueouslv with some phase difference aux differeut gains.,"The observation in many pulsars, of elliptically polarized radiation of detectable strength, is further evidence of the existence of amplification in both modes, but now simultaneously with some phase difference and different gains."132 A major obstacle in the wmucderstanding of usar polarization until vow has been the diticulty of secing how electric fields could be generated perpendicular o the ultrastroug maenetic field lines. ouly along which he charges were constrained to move.," A major obstacle in the understanding of pulsar polarization until now has been the difficulty of seeing how electric fields could be generated perpendicular to the ultrastrong magnetic field lines, only along which the charges were constrained to move."133 The mechauisi of Luo Aielose (1995) - thanks to torsion - aOWs alle oediets radiation. perpeudieulu to the field lines. ane row reduces the explanation of any type of polarization in pulsars to a matter of detail. as oppose oa difficulty of principle.," The mechanism of Luo Melrose (1995) - thanks to torsion - allows and predicts radiation perpendicular to the field lines, and now reduces the explanation of any type of polarization in pulsars to a matter of detail, as opposed to a difficulty of principle."134 We turn now to the spectacular X-ray image provided by Chandra with two remarkably svuuuetrical arcs bisected wo the jet like feature mentioned earlier., We turn now to the spectacular X-ray image provided by Chandra with two remarkably symmetrical arcs bisected by the jet like feature mentioned earlier.135 EHeltaud et al. (, Helfand et al. (136"2001) have put forward a detailed model where hey ""assunie that the two arc-like features le along circular vines οΠοιο shocks iu which the enecrey of an outiowing cquatorial wind is clissipated to become he source of svuchnrotron cussion for the compact jiebula and attribute the icompletcucss of the rings o preferential Doppler boosting of the cuissiou im the orward direction.","2001) have put forward a detailed model where they “assume that the two arc-like features lie along circular rings highlighting shocks in which the energy of an outflowing equatorial wind is dissipated to become the source of synchrotron emission for the compact nebula"" and attribute the incompleteness of the rings to preferential Doppler boosting of the emission in the forward direction."137" They also ""assume that the two riugs straddle the equator svuuuetrically aud suppose that the deficit of emission exactly in the equatorial plane is related ο the fact that his is where the direction of a toroidally wrapped magnetic field changes sign ie. the field may vanish there”."," They also “assume that the two rings straddle the equator symmetrically and suppose that the deficit of emission exactly in the equatorial plane is related to the fact that this is where the direction of a toroidally wrapped magnetic field changes sign i.e. the field may vanish there""."138 They go ou to derive the half opening augle of the wind 0 as 237.3. aud the radius of the shock £j as a/dCost)—1«lot cm for d = 250 pe.," They go on to derive the half opening angle of the wind $\theta$ as $^o$ .3, and the radius of the shock $r_s$ as $\theta\sim 1\times10^{17}$ cm for d = 250 pc."139" We would like to propose a somewhat different model or the X-ray ares. starting from the magnetic pole model or pulsar radiation discussed at leneth earlier. aud that is invariably nuüscalled the ""rotating vector πα"," We would like to propose a somewhat different model for the X-ray arcs, starting from the magnetic pole model for pulsar radiation discussed at length earlier, and that is invariably miscalled the “rotating vector ""."140 μη hat model. the radiation (and also its amplification as just seen) are produced by highly relativistic articles streaming out along the open field lines from both naguctic poles.," In that model, the radiation (and also its amplification as just seen) are produced by highly relativistic particles streaming out along the open field lines from both magnetic poles."141 We now examine he N-rav data for the )ossibilitv that the wo ares reflect the traces ofthese two yarticle beams as they encouuter the “walls” surrounding he central cavity created by the pulsar.," We now examine the X-ray data for the possibility that the two arcs reflect the traces of these two particle beams as they encounter the “walls"" surrounding the central cavity created by the pulsar."142 Such a cavity was elaborated in the classic paper by Rees Camu (1971) or the Crab. and has since formed a part of most. if not all. subsequent diseussious aud models of pulsar created jebulae.," Such a cavity was elaborated in the classic paper by Rees Gunn (1974) for the Crab, and has since formed a part of most, if not all, subsequent discussions and models of pulsar created nebulae."143 We asstune that the particles leave the weakening field ines at some point well before sweep-back effects set in close to the Πο cylinder. and proceed “ballistically” outwards.," We assume that the particles leave the weakening field lines at some point well before sweep-back effects set in close to the light cylinder, and proceed “ballistically"" outwards."144 If this picture is valid. one of the two arcs should ows close to our sight Lue to the pulsu. as imdeed it does.," If this picture is valid, one of the two arcs should pass close to our sight line to the pulsar, as indeed it does."145 To assess this further. we have modelled the arcs as the near-side portions of two Times (seen im projection) raced by sweeps of the (magnetic) polar coney.," To assess this further, we have modelled the arcs as the near-side portions of two rings (seen in projection) traced by sweeps of the (magnetic) polar cones."146 The rotating maenctic-axis vector is as described in Deshpande et al. (, The rotating magnetic-axis vector is as described in Deshpande et al. (1471999).,1999).148 The model parameters are the pair of radial distances (rq ro as measured from the star location and expressed in areseconds) associated with the two rug traces. the inclination (a) of the magnetic axis of the star to its rotation axis. the angle of closes approach (the inpact anele 9) of the magnetic axis to our sight-liuc. aud the position angle (PAo) of the rotation axis projection ou the skv-plane.," The model parameters are the pair of radial distances $r_1$ $r_2$ as measured from the star location and expressed in arcseconds) associated with the two ring traces, the inclination $\alpha$ ) of the magnetic axis of the star to its rotation axis, the angle of closest approach (the impact angle $\beta$ ) of the magnetic axis to our sight-line, and the position angle (PAo) of the rotation axis projection on the sky-plane."149 The angle (6) between he rotation axis alu our siglit-line is simply (6|jj., The angle $\zeta$ ) between the rotation axis and our sight-line is simply $(\alpha + \beta)$.150 Doesired. cousistcacy with radio polarization observations would allow ouly certain combinations of the wviewius ecometry: that is sinafsind should be equal to the steepest sweep rate (dx fdo} of the polarization position angle with respect to the rotational longitude., Desired consistency with radio polarization observations would allow only certain combinations of the viewing geometry; that is $sin\alpha/sin\beta$ should be equal to the steepest sweep rate $d\chi/d\phi$ ) of the polarization position angle with respect to the rotational longitude.151" When we constrain the a&.j combinations using (dXfdas, of -9 degree/degree (as listed by Lyne Alauchester 1988). the best fit PAy is fouud to be 129 degrees (1neasured from) North through East). the radial distances rp ro» are unequal (about 22 29 arcsec for the"," When we constrain the $\alpha \& \beta$ combinations using $(d\chi/d\phi)_{max}$ of -9 degree/degree (as listed by Lyne Manchester 1988), the best fit $_0$ is found to be 129 degrees (measured from North through East), the radial distances $r_1$ $r_2$ are unequal (about 22 29 arcsec for the"152galaxies are biased towards more distaut ealaxics. we checked that the low luminosity tail in the late types is not caused by the distance effect by examining the distribution excluding ealaxies with clistances 4212 Mpc.,"galaxies are biased towards more distant galaxies, we checked that the low luminosity tail in the late types is not caused by the distance effect by examining the distribution excluding galaxies with distances $d \ge 12\,$ Mpc."153 Again we find no tendency for the late type (L> 5) galaxies to slow more hunimous brightest regions than their carly type counterparts., Again we find no tendency for the late type $T > 5$ ) galaxies to show more luminous brightest regions than their early type counterparts.154 This result is iu clear contrast with the behavior of disk regions., This result is in clear contrast with the behavior of disk regions.155 Ieunicutt (19588) found that the brightest regions in iregular galaxies are approximately 6 times brighter than those in She-Se galaxies of the same absolute blue magnitude. aud approximately 50 times brighter than their counterparts in Sab.Sh galaxies.," Kennicutt (1988) found that the brightest regions in irregular galaxies are approximately 6 times brighter than those in Sbc-Sc galaxies of the same absolute blue magnitude, and approximately 50 times brighter than their counterparts in Sab–Sb galaxies."156 This result is always referred to disk regions., This result is always referred to disk regions.157 Moreover. three of the six ealaxies in our sannple with Iubble morphological types SU/a to Sab show ζημία} near or above the limit eiven iu Caldwell et al. (," Moreover, three of the six galaxies in our sample with Hubble morphological types S0/a to Sab show $L_{\rm br}({\rm H}\alpha)$ near or above the limit given in Caldwell et al. ("1581991). whereas two only show faint ceutral cussion.,"1991), whereas two only show faint central emission."159 Although the nuubers are small. it is evideut that some carly-type galaxies can harbor very hDmuuinuous ceutral regions.," Although the numbers are small, it is evident that some early-type galaxies can harbor very luminous central regions."160 Possible explanations for these discrepant results are resolution effects. reduced extinction in our Pan data. but more likely a different behavior of eireuunuclear regions versus disk reeious.," Possible explanations for these discrepant results are resolution effects, reduced extinction in our $\alpha$ data, but more likely a different behavior of circumnuclear regions versus disk regions."161 The bar potential in a disk galaxw. which bw its non-axisviunietric nature cau funnel gaseous material frou the disk inwards toward the ceutral regions. is usually iuvoked as a trigecring of the SF iu the ceuters of galaxies (c.g. Shlosiman. Beechuan Frank 1990).," The bar potential in a disk galaxy, which by its non-axisymmetric nature can funnel gaseous material from the disk inwards toward the central regions, is usually invoked as a triggering of the SF in the centers of galaxies (e.g., Shlosman, Begelman Frank 1990)."162 There. the gas can accumulate. possibly near one or more inner Lindblad resonances. become eravitationally wustable. aud this can lead to chhanced massive star formation.," There, the gas can accumulate, possibly near one or more inner Lindblad resonances, become gravitationally unstable, and this can lead to enhanced massive star formation."163 We cau now check this scenario by comparing the huninosity of the brightest region with the bar class (right panel of Figure 2)., We can now check this scenario by comparing the luminosity of the brightest region with the bar class (right panel of Figure 2).164 There is a clear tendency for barred ealaxics to show amore huumous brightest regions than their uubarred counterparts. as can be seen from the increasing value of the median of the brightest region distribution from uubmrred (A) to stronelv xured (B) galaxies.," There is a clear tendency for barred galaxies to show more luminous brightest regions than their unbarred counterparts, as can be seen from the increasing value of the median of the brightest region distribution from unbarred (A) to strongly barred (B) galaxies."165 Althoneh the median distance of the strouglv barred galaxies is higher than that of mubarrec ealaxies. the distance effect alone is not enough to account or the differiue medians of the distributions of the xiehtest regions.," Although the median distance of the strongly barred galaxies is higher than that of unbarred galaxies, the distance effect alone is not enough to account for the differing medians of the distributions of the brightest regions."166 If galaxies in the Vireo cluster. which populate of the stronely barred galaxy bin aud of the weakly barred galaxy biu. are excluded. we fn that the median of the distribution of the brightest regions iu barred galaxies (AB|D) is slightly higher han in uubarred galaxies. but on average the brightest regions in barred galaxies are a factor of five brighter than hose in uubarred systems.," If galaxies in the Virgo cluster, which populate of the strongly barred galaxy bin and of the weakly barred galaxy bin, are excluded, we find that the median of the distribution of the brightest regions in barred galaxies (AB+B) is slightly higher than in unbarred galaxies, but on average the brightest regions in barred galaxies are a factor of five brighter than those in unbarred systems."167 A I-S test shows that there is ouly a probability of Py4=0.11 that both distributious are drawn from the same population. for galaxies with d 12Mpe.," A K-S test shows that there is only a probability of $P_{\rm K-S}=0.11$ that both distributions are drawn from the same population, for galaxies with $d<12\,$ Mpc."168 The scenario described above is proven here ina statistical aud qualitative way. a conclusion that fits in well with the long kuown preference for ceutral starburst ealaxies to be barred (e.2.. Heckiian 1980: Balzano 1983: Devereux 1987). aud with the occurrence of circumnnuuclear vine-like regious of much eulianced SF in barred galaxies (Iknapen 1999).," The scenario described above is proven here in a statistical and qualitative way, a conclusion that fits in well with the long known preference for central starburst galaxies to be barred (e.g., Heckman 1980; Balzano 1983; Devereux 1987), and with the occurrence of circumnuclear ring-like regions of much enhanced SF in barred galaxies (Knapen 1999)."169 The size of an region is not as easy to case as its 1unuinositv. because the former quantity is obscrvationally nostly influenced by pixels at the ραποτ of the region. thus maximizing the scusitivity to blending aud vackeround noise. Whereas the huninosity is determined nostly by the bright pixels near the centers of regions.," The size of an region is not as easy to measure as its luminosity, because the former quantity is observationally mostly influenced by pixels at the perimeter of the region, thus maximizing the sensitivity to blending and background noise, whereas the luminosity is determined mostly by the bright pixels near the centers of regions."170 Nevertheless. Hodge (1986) found that late-type galaxies (Sc and hr) tend to have larger regions than carly-ype galaxies.," Nevertheless, Hodge (1986) found that late-type galaxies (Sc and Irr) tend to have larger regions than early-type galaxies."171 Ieunicutt (1988) measured the sizes of the first ranked regious in a sauple of spiral aud imegular ealaxies. and reached a simular conclusion. although the rend was nof as siguif&cant as for the huninosity of the xiehtest PC@IOUS.," Kennicutt (1988) measured the sizes of the first ranked regions in a sample of spiral and irregular galaxies, and reached a similar conclusion, although the trend was not as significant as for the luminosity of the brightest regions."172 Iu Figure 3 (see also Table 2) we compare the size of the, In Figure 3 (see also Table 2) we compare the size of the1732006).,.174. Given that of our sample have ages less than 56) Myr and have ages less than 1.6 Gyr (see Table |). it is likely that most of our clusters are not in the last of their lifetimes. but we can not rule out the possibility that some might be near the end of their lifetimes.," Given that of our sample have ages less than 80 Myr and have ages less than 1.6 Gyr (see Table 1), it is likely that most of our clusters are not in the last of their lifetimes, but we can not rule out the possibility that some might be near the end of their lifetimes."175 Thus the effect of dissolution on their colours is likely small. typically smaller than our assumed uncertainties of 0.14 magnitudes.," Thus the effect of dissolution on their colours is likely small, typically smaller than our assumed uncertainties of 0.14 magnitudes."176 Using the stellar data available on WEBDA for a sample of our OCs covering a representative range of distances. we found that δρ contained stars <0.5 M...," Using the stellar data available on WEBDA for a sample of our OCs covering a representative range of distances, we found that $\sim85\%$ contained stars $\la$ 0.5 $_{\odot}$."177 To determine the effects that low mass stars have on the model integrated colours we compared Kroupa models with lower mass cutoff of 0.1 M. with those with 0.5 M.., To determine the effects that low mass stars have on the model integrated colours we compared Kroupa models with lower mass cutoff of 0.1 $_{\odot}$ with those with 0.5 $_{\odot}$.178 We found no significant differences in the(U B. V). Ri ος Deolours.," We found no significant differences in the $-$ B), $-$ V), $-$ R), or $-$ I) colours."179 We present an empirical assessment of the use of broadbanc colours as age indicators for unresolved extragalactic clusters anc investigate stochastic sampling effects on integrated colours., We present an empirical assessment of the use of broadband colours as age indicators for unresolved extragalactic clusters and investigate stochastic sampling effects on integrated colours.180 The population synthesis codeStarburs/99 (Leithereretal.1999). anc four optical colours were used to estimate how well we can recover the ages of 62 well-studied Galactic open clusters with published ages., The population synthesis code \citep{lei99} and four optical colours were used to estimate how well we can recover the ages of 62 well-studied Galactic open clusters with published ages.181 We conclude the following: 1) Galactic open clusters can be used for testing the integrated properties from population synthesis and serve as. reasonable benchmarks for future assessments of age-dating methods., We conclude the following: 1) Galactic open clusters can be used for testing the integrated properties from population synthesis and serve as reasonable benchmarks for future assessments of age-dating methods.182 2)The(U Bi colouris critical., 2) The $-$ B) colour is critical.183 Only colour combinations tha included —. B) resulted in good age and extinction predictions. consistent with previous results.," Only colour combinations that included $-$ B) resulted in good age and extinction predictions, consistent with previous results."184 3) Only with (UB) included were the predicted age uncertainties reasonably constrained., 3) Only with $-$ B) included were the predicted age uncertainties reasonably constrained.185 4) Changes of a factor of ~2 in assumed metal abundance do not result in significantly different predictions of cluster age., 4) Changes of a factor of $\sim$ 2 in assumed metal abundance do not result in significantly different predictions of cluster age.186 This indicates that the uncertainties in predicting the age of a cluster resulting from the age-reddening degeneracy dominate over the other sources of degeneracy in these optical bands. over our age range and metallicity range.," This indicates that the uncertainties in predicting the age of a cluster resulting from the age-reddening degeneracy dominate over the other sources of degeneracy in these optical bands, over our age range and metallicity range."187 Another possibility is that uncertainties in the measured colours (and hence the predicted ages) dwarf the metallicity-age degeneracy., Another possibility is that uncertainties in the measured colours (and hence the predicted ages) dwarf the metallicity-age degeneracy.188 5) A A7 minimization and a 47 detined to give confidence levels provide reliable age estimates. and more importantly. reliable age uncertainties.," 5) A $\chi^2$ minimization and a $\Delta\chi^2$ defined to give confidence levels provide reliable age estimates, and more importantly, reliable age uncertainties."189 The difference in the photometric ages and the ages derived from the HR-diagrams of our selected cluster sample with both the (UB) and V) colours are smaller than 0.5 dex for of the clusters. with a maximum difference of 1.5 dex.," The difference in the photometric ages and the ages derived from the HR-diagrams of our selected cluster sample with both the $-$ B) and $-$ V) colours are smaller than 0.5 dex for of the clusters, with a maximum difference of 1.5 dex."190 6) Tt is likely that the uncertainties in the measured colours and/or ages are large enough (0.14 mag and ~20% respectively) that the effects of stochastic sampling are washed out., 6) It is likely that the uncertainties in the measured colours and/or ages are large enough (0.14 mag and $\sim20\%$ respectively) that the effects of stochastic sampling are washed out.191 A more detailed analysis of the stellar content of these resolved OCs will be required to further investigate the extent to which stochastic sampling of the IMF affects the integrated broadband colours., A more detailed analysis of the stellar content of these resolved OCs will be required to further investigate the extent to which stochastic sampling of the IMF affects the integrated broadband colours.192 7) If stochastic sampling effects are observationally characterized in this sample of OCs. they will provide a good bench mark for testing future population synthesis models.," 7) If stochastic sampling effects are observationally characterized in this sample of OCs, they will provide a good bench mark for testing future population synthesis models."193 We thank the anonymous referee for his/her helpful comments and suggestions., We thank the anonymous referee for his/her helpful comments and suggestions.194 This research has made use of the WEBDA database. operated at the Institute for Astronomy of the University of Vienna.," This research has made use of the WEBDA database, operated at the Institute for Astronomy of the University of Vienna."195 The authors would like to thank Ernst Paunzen for providing ASCII tables of the WEBDA data., The authors would like to thank Ernst Paunzen for providing ASCII tables of the WEBDA data.196 The authors also thank Alessandra Stone for help with the data acquisition., The authors also thank Alessandra Stone for help with the data acquisition.197" This work has been supported by the NASA LTSA grant NAGS-13079,", This work has been supported by the NASA LTSA grant NAG5-13079.198Figure 2 panels).,Figure 2 ).199" The X values vary between 1.2 and 3.0, a range that is lower than the upper limit compression of 4 given by X=(y+1)/(y—1) for a mono-atomic gas (y= 5/3)."," The $X$ values vary between 1.2 and 3.0, a range that is lower than the upper limit compression of 4 given by $X = (\gamma+1)/ (\gamma-1)$ for a mono-atomic gas $\gamma = 5/3$ )."200" An interesting new result is given by the latitudinal dependence: at both times X maximizes at the center of the shock surface, progressively decreasing towards the flanks of the shock."," An interesting new result is given by the latitudinal dependence: at both times $X$ maximizes at the center of the shock surface, progressively decreasing towards the flanks of the shock."201" Notice that values plotted in this Figure may also depend on unknown latitudinal changes in the L values, which have been assumed constant at all latitudes."," Notice that values plotted in this Figure may also depend on unknown latitudinal changes in the $L$ values, which have been assumed constant at all latitudes."202" A second new result is the time evolution: as the shock expands, the latitudinal dependence is preserved, but the X values decrease all along the shock surface."," A second new result is the time evolution: as the shock expands, the latitudinal dependence is preserved, but the $X$ values decrease all along the shock surface."203" This means that the shock is losing its energy with propagation and that, at least for this event, it is stronger at the center of the front, as one would expect because this is the shock part moving faster in the corona, hence with larger M4."," This means that the shock is losing its energy with propagation and that, at least for this event, it is stronger at the center of the front, as one would expect because this is the shock part moving faster in the corona, hence with larger $M_A$."204 The latter conclusion is demonstrated in the next section., The latter conclusion is demonstrated in the next section.205" The relationship between the compression ratio X and the Alfvénnic Mach number Ma depends on the plasma-to-magnetic pressure ratio 6 and the angle 6g, between the shock normal and the upstream magnetic field.", The relationship between the compression ratio $X$ and the Alfvénnic Mach number $M_{\rm A}$ depends on the plasma-to-magnetic pressure ratio $\beta$ and the angle $\theta_{Bn}$ between the shock normal and the upstream magnetic field.206" In the solar corona, the plasma is mainly controlled by the magnetic field (8« 1)."," In the solar corona, the plasma is mainly controlled by the magnetic field $\beta\ll 1$ )."207 In, In208 particles. rather o. uw and g are considered as coarseerained fields.," particles, rather $\varrho$ , ${\bf u}$ and ${\bf g}$ are considered as coarse–grained fields."209 This coarseeraiing is the origin of the two new terms on the righthandside of Euler's equation (3))., This coarse–graining is the origin of the two new terms on the right–hand–side of Euler's equation \ref{cosmohydrob}) ).210 One of these new teris is the pressure force Vp. which accounts for the isotropic part of the inultistream force. and therefore models velocity dispersion (that is. the fact that iu auv infinitesimal cell there are particles with different velocities).," One of these new terms is the pressure force $\nabla p$, which accounts for the isotropic part of the multi--stream force, and therefore models velocity dispersion (that is, the fact that in any infinitesimal cell there are particles with different velocities)."211 Because of this. the iuteeral curves of u represeut trajectories of the (possibly iiultistreamusec) flow after averaging over velocity space.," Because of this, the integral curves of ${\bf u}$ represent trajectories of the (possibly multi–streamed) flow after averaging over velocity space."212 This pressure termi isnotrelated to thermal pressure. which cau be indeed neglected on the scales we are interested in.," This pressure term is related to thermal pressure, which can be indeed neglected on the scales we are interested in."213" It is à mode of the velocity clispersion eenerated by eravitational instability (see Buchert nguez 1998 and. for a recen eeneralizatiou to general relativity, Miuuteus et al."," It is a model of the velocity dispersion generated by gravitational instability (see Buchert nguez 1998 and, for a recent generalization to general relativity, Maartens et al."214 1999)., 1999).215 The other new term is the stochastic force represented we the noise s: if accounts for processes hidden b he coarseerained description of the fluid and whose ypical time and leusthscales are much shorter than hose explicitly considered for LSS formation., The other new term is the stochastic force represented by the noise ${\bf s}$; it accounts for processes hidden by the coarse–grained description of the fluid and whose typical time– and length–scales are much shorter than those explicitly considered for LSS formation.216 We have resorted to imodelling these processes as a stochastic οποιο aud include: (a) the effects of sinallscale deerecs of freedom whose plivsics ds also governed by noneravitational processes. (b) deviations from mean field ychavior. manifested as random forces acting on the yarticles of the eravitational eas as a consequence of independent iupulses of random size and amplitude arising from “sline-like” processes in encounters (Ixaudriup L980). (ο) deviations ofthe density aud velocity fields from the values prescribed by the deterministic version of Eqs. (2--1))," We have resorted to modelling these processes as a stochastic forcing and include: (a) the effects of small–scale degrees of freedom whose physics is also governed by non--gravitational processes, (b) deviations from mean field behavior, manifested as random forces acting on the particles of the gravitational gas as a consequence of independent impulses of random size and amplitude arising from “sling-like” processes in encounters (Kandrup 1980), (c) deviations of the density and velocity fields from the values prescribed by the deterministic version of Eqs. \ref{cosmohydroa}- \ref{cosmohydroc}) )"217 due to the eraininess of the underline plyvsical system of particles (Lifshitz Pitaevskii 1980)., due to the graininess of the underlying physical system of particles (Lifshitz Pitaevskii 1980).218 To close the system of Eqs. (2—1)), To close the system of Eqs. \ref{cosmohydroa}- \ref{cosmohydroc}) )219 a relation is reededL between he dynamical pressure p and the two independentfields o and τα. as well as a specification of the statistical properties of the stochastic force s.," a relation is needed between the dynamical pressure $p$ and the two independentfields $\varrho$ and ${\bf u}$, as well as a specification of the statistical properties of the stochastic force ${\bf s}$."220 As for the Orner. we asstune the local relatiouship p=plo).," As for the former, we assume the local relationship $p=p(\varrho)$."221 There does not seem to be anypriori reason for this “slaving” of oressure to deusitv (one cannot resort to the hypothesis of local equilibrium as is cone for the thermocdvuamical oessure in fuids). so the success of this assunption must be judged according to the conclusions ollowiug from it.," There does not seem to be any reason for this “slaving” of pressure to density (one cannot resort to the hypothesis of local equilibrium as is done for the thermodynamical pressure in fluids), so the success of this assumption must be judged according to the conclusions following from it."222 In fact. a detailed study. of the origin of pressure forces in Eq. (3))," In fact, a detailed study of the origin of pressure forces in Eq. \ref{cosmohydrob}) )"223 provides px0%? under the assumption of suiall velocity dispersion (Buchert ngueze 1998) and therefore p=plo) is the most straightforward plicnomenological ecucralization., provides $p \propto \varrho^{5/3}$ under the assumption of small velocity dispersion (Buchert nguez 1998) and therefore $p=p(\varrho)$ is the most straightforward phenomenological generalization.224 We also require p/(o)>0. that is. pressure opposes eravitational collapse.," We also require $p'({\varrho})>0$, that is, pressure opposes gravitational collapse."225 As for the noise. we make the assuuiption of Gaussian distributed noise.," As for the noise, we make the assumption of Gaussian distributed noise."226 Since noise is due to the shortscale degrees of freedom. this assumption could be justified by the ceutral nuit theorem.," Since noise is due to the short–scale degrees of freedom, this assumption could be justified by the central limit theorem."227 As is well known. Caussiau nolse can be characterized by just two moments: its mean. which we require to vanish. (s;=0 (since any systematic forcing should be made explicit iu Eq. (3))).," As is well known, Gaussian noise can be characterized by just two moments: its mean, which we require to vanish, $\langle {\bf s} \rangle = {\bf 0}$ (since any systematic forcing should be made explicit in Eq. \ref{cosmohydrob}) )),"228 aud its twopoiut correlations where Di(xxf.f) is the covariance imatrx with nüxed discrete aud continuous indices (Carcdiner 1991: Vau Iampenu 1992).," and its two–point correlations where $D_{ij} ({\bf x}, {\bf x}', t, t')$ is the covariance matrix with mixed discrete and continuous indices (Gardiner 1994; Van Kampen 1992)."229 We ignore the possibility that Dj; depends ou 9 or u (quenched noise). since this reuders the analvsis of Eqs. (2-- 10))," We ignore the possibility that $D_{ij}$ depends on $\varrho$ or ${\bf u}$ (quenched noise), since this renders the analysis of Eqs. \ref{cosmohydroa}- \ref{cosmohydroc}) )"230 too difficult., too difficult.231 As with pressure. this must be seen as aphenomenological assuuptiou. whose merit will be judeed from the final results.," As with pressure, this must be seen as a assumption, whose merit will be judged from the final results."232 Notice however that we consider the possibility ofcolored Ciussiau noise. ic. the noise s is correlated over space and fine. as expressed by the Gn general) nontrivial dependence of D on position aud time iu Eq. (5)).," Notice however that we consider the possibility of Gaussian noise, i.e., the noise $s$ is correlated over space and time, as expressed by the (in general) non–trivial dependence of $D$ on position and time in Eq. \ref{scorrelation}) )."233 Colored noise represents a richer texture of physical effects thau white noise aud the particular case of powerlaw correlated nolse is still amenable to analytical study by means of the Renormalization Croup uguez et al., Colored noise represents a richer texture of physical effects than white noise and the particular case of power–law correlated noise is still amenable to analytical study by means of the Renormalization Group nguez et al.234 1999)., 1999).235 We later restrict the ecnerality further bv choosing a curlfree noise aud characterize it statistically by a single function D iustead of D;;., We later restrict the generality further by choosing a curl–free noise and characterize it statistically by a single function $D$ instead of $D_{ij}$.236 The analytical study of the svstem of Eqs. (2--1)), The analytical study of the system of Eqs. \ref{cosmohydroa}- \ref{cosmohydroc}) )237 is very difficult in eeuceral., is very difficult in general.238 Iuspired by the deteriiuistie dust case (LC. po—0. 5= 0). we smnplifv the problem aud out forward the asstuption of parallelism: we impose the condition that the peculiar.velocity is a potential field aud roimnadus parallel to the eravitational peculiaracceleration Beld: where F(t)>0 is a proportionality coefficient which ollows from the deterministic linear theory for dust (see Sect.," Inspired by the deterministic dust case (i.e., $p=0$, ${\bf s}={\bf239 0}$ ), we simplify the problem and put forward the assumption of parallelism: we impose the condition that the peculiar–velocity is a potential field and remains parallel to the gravitational peculiar–acceleration field: where $F(t)>0$ is a proportionality coefficient which follows from the deterministic linear theory for dust (see Sect."240 ο and in particular the discussion after Eqs. (65-- 66))," \ref{linear_regime}241 and in particular the discussion after Eqs. \ref{Fexpansiona}- \ref{Fexpansionb}) )"242 in Appendix D)., in Appendix B).243 This assuuption implicitly requires iat both pressure and the intensity ofthe noise are stall when compared with the dominant selferavityv in Eq. (3)).," This assumption implicitly requires that both pressure and the intensity of the noise are small when compared with the dominant self–gravity in Eq. \ref{cosmohydrob}) ),"244 which restricts our considerations to spatial scale regimes close to the validity lait of the dust model: noise and pressure will typically dominate on scales 12all compared to this limit., which restricts our considerations to spatial scale regimes close to the validity limit of the dust model; noise and pressure will typically dominate on scales small compared to this limit.245" The assuuptiou of parallelisia uuderlies the wellknown ""Zebdovich approximation” Golovicli 1970). and is welljustified for deteriuüuistie dust models in the linear as well as iu the weakly noulinear regimes (seo Bildhauer Buchert 1991: Ioftman 1991: Buchert 1992: Πα Bertschinger 1996: Susperveei Buchert 1997)."," The assumption of parallelism underlies the well–known “Zel'dovich approximation” (Zel'dovich 1970), and is well–justified for deterministic dust models in the linear as well as in the weakly nonlinear regimes (see Bildhauer Buchert 1991; Kofman 1991; Buchert 1992; Hui Bertschinger 1996; Susperregi Buchert 1997)."246 This Guclece oversimplifving assuniption) will be very useful to analytically access the problem. aud to define 7οσα approxiniations.," This (indeed oversimplifying assumption) will be very useful to analytically access the problem, and to define “local” approximations."247"4. Also. we study that assumption first because popular models like the ""adhesionapproximation (Cawhbatoy et al."," Also, we study that assumption first because popular models like the “adhesionapproximation” (Gurbatov et al."248 1989) can be derived ou the basis of this assunption., 1989) can be on the basis of this assumption.249 As we shall sec. this assumption is consistent with the picture that. comune from large scales. the mean motion isruled by the dust model. but incorporation of the effects," As we shall see, this assumption is consistent with the picture that, coming from large scales, the mean motion is ruled by the dust model, but incorporation of the effects"250approximates the ZAMS.,approximates the ZAMS.251 In contrast. the more massive blue stragelers evolve much. faster. aud they are also formed far from the ZAMS in the first. place. since their precursors have already uudergone considerable nuclear processing.," In contrast, the more massive blue stragglers evolve much faster, and they are also formed far from the ZAMS in the first place, since their precursors have already undergone considerable nuclear processing."252 Thus a burst of recent blue strageler formation will create a blue strageler distribution like that in Figure LE. with a narrow sequence at the low L enc. auc a relatively large number of stars with a range of temperatures at the bright eu.," Thus a burst of recent blue straggler formation will create a blue straggler distribution like that in Figure 1E, with a narrow sequence at the low L end, and a relatively large number of stars with a range of temperatures at the bright end."253 Figure 2 sllows a sequence of blue strageler distributions in. which blue stragelerMOD formatio[un began at the start of the cluster lifetime. but ermiuated at some point in the past.," Figure 2 shows a sequence of blue straggler distributions in which blue straggler formation began at the start of the cluster lifetime, but terminated at some point in the past."254 The limiting case When the termination point is the present is the same as Figure LÀ aud bas thus been omitted., The limiting case when the termination point is the present is the same as Figure 1A and has thus been omitted.255 Figure 2 shows progressively older blue strageler sequences., Figure 2 shows progressively older blue straggler sequences.256 Ouce again. the dramatic changes in distribution are easy to understand.," Once again, the dramatic changes in distribution are easy to understand."257 The more massive aud Iuminous blue stragelers evolve first. aud move away from the ZAMS. and then ou of the blue strageler region altogether when they become giants.," The more massive and luminous blue stragglers evolve first, and move away from the ZAMS, and then out of the blue straggler region altogether when they become giants."258 A population of blue stragelers like theshown in Figure 2d. in which all of the blue stragelers have ages > SCvis. will therefore contal ouly relatively faint blue stragelers aud will be skewed toward the red away from the ZAMS.," A population of blue stragglers like that shown in Figure 2d, in which all of the blue stragglers have ages $\ge 8$ Gyrs, will therefore contain only relatively faint blue stragglers and will be skewed toward the red away from the ZAMS."259 Te dramatic difference between Figure LE aud Figure 2D. which were created. using identical ASSLiptious about binary fraction. mass function. auc other ΕΠ parameters. illustrates the Luportance of includiug changes in formation rate iu studies of blue strageler clistributious.," The dramatic difference between Figure 1E and Figure 2D, which were created using identical assumptions about binary fraction, mass function, and other dynamical parameters, illustrates the importance of including changes in formation rate in studies of blue straggler distributions."260 It is cdi[fic to produce such drastic changes in the shape oL the blue strageler distribution by varying the lass funetions aud binary fraction. although these parameters do have a strong iuflueuce on the total 1uber of blue stragelers (Sills&Bailyu1999).," It is difficult to produce such drastic changes in the shape of the blue straggler distribution by varying the mass functions and binary fraction, although these parameters do have a strong influence on the total number of blue stragglers \citep{SB99}."261 Fig 3 shows distributions of blue stragelers in which the formation rate turned oin at soie point alter the cluster was born. aud then turned off aganos jonor to the present.," Fig 3 shows distributions of blue stragglers in which the formation rate turned on at some point after the cluster was born, and then turned off again prior to the present."262 As mieht be expected. these distributions show characteristics similar ο 1ose in both Figs 1 and 2. since both elfects described above apply in these cases.," As might be expected, these distributions show characteristics similar to those in both Figs 1 and 2, since both effects described above apply in these cases."263 We have also wed the binary destruction rate from Figure 3 of Hut.MeMilan&Romani(1992) as au approxiuation for blue strageler creation. siuce botli elfects result [rom the same close stellar encounters.," We have also used the binary destruction rate from Figure 3 of \cite{hmr92} as an approximation for blue straggler creation, since both effects result from the same close stellar encounters."264 The resulting distribution is dominated by old. low luminosity blue stragelers. but also coutains a siall. but potentially observable population of vounger blue stragelersMOD (Figure 1).," The resulting distribution is dominated by old, low luminosity blue stragglers, but also contains a small, but potentially observable population of younger blue stragglers (Figure 4)."265 Observatiois of I7 Tucanae were obtainec between July 1996 aud January 1997., Observations of 47 Tucanae were obtained between July 1996 and January 1997.266 Data were taken nearly every night for 6 weeks. with solue acditional coverage over six months with the CTIO 0.9 m teescope aud ον CCD.," Data were taken nearly every night for 6 weeks, with some additional coverage over six months with the CTIO 0.9 m telescope and 2K CCD."267" Repeater ""I images were obtained for a 13° x 13° field centered on RADEC (2000) = 00:22:06.75 -72:32.1. with the closest edge 138.57 west of cluster center."," Repeated UBVI images were obtained for a 13' $\times$ 13' field centered on RA,DEC (2000) = 00:22:06.75 -72:04:22.1, with the closest edge 138.5” west of cluster center."268 The priuary purpose was to study va‘iabiliv on the elant branch. aud the time series results will be oreseuted. elsewhere.," The primary purpose was to study variability on the giant branch, and the time series results will be presented elsewhere."269 Iu this payer. W'' present color-maguituce diagrams created from sunmunecd clata.," In this paper, we present color-magnitude diagrams created from summed data."270 The exposure times were clOsell ο avoid saturation of giant brauch stars. aud are therefore deepest iu bluer baudpasses. which mases this data set ideal for stuclying hot stars. such as blue stragelers.," The exposure times were chosen to avoid saturation of giant branch stars, and are therefore deepest in bluer bandpasses, which makes this data set ideal for studying hot stars, such as blue stragglers."271 The summed images were aialvzed with DAOPHOT and calibrated with, The summed images were analyzed with DAOPHOT and calibrated with272he shape of the variations. ancl is fairly computationally intensive.,"the shape of the variations, and is fairly computationally intensive."273 However. when trving to detect planetary transits. most of the information is concentrated in a very small »ortion of the light curve.," However, when trying to detect planetary transits, most of the information is concentrated in a very small portion of the light curve."274" In a previous paper (?.hereafter""aper D.. we adapted the Ciregory-Loredo method to the jxanetary transit case by having one long out-ol-transit.bin (bin 0) and » short in-transit bins (see Fig. 2.."," In a previous paper \citep[][hereafter Paper~I]{af02}, we adapted the Gregory-Loredo method to the planetary transit case by having one long out-of-transitbin (bin $0$ ) and $n$ short in-transit bins (see Fig. \ref{fig:newmod},"275 top panel)., top panel).276 The value of η used. was typically 4., The value of $n$ used was typically $4$.277 For a given à. the »»wameters defining cach candidate model are then p. €. and the transit duration d.," For a given $n$, the parameters defining each candidate model are then $p$, $e$, and the transit duration $d$."278 The likelihood computation was carried out as described in 6:99., The likelihood computation was carried out as described in G99.279 This algorithm performed well when. tested on simulateddata.. but the likelihood calculation. was still computationally intensive.," This algorithm performed well when tested on simulated, but the likelihood calculation was still computationally intensive."280 The odds ratio method was not used to identify light curves showing significant evidence of transits. due to considerations detailed in Paper L. Instead. bootstrap simulations containing hundreds of light. curves with cillerent realisations of the same noise distribution. with and without transits. were used to celine optimised detection thresholds in terms of posterior probability niaxinma.," The odds ratio method was not used to identify light curves showing significant evidence of transits, due to considerations detailed in Paper I. Instead, bootstrap simulations containing hundreds of light curves with different realisations of the same noise distribution, with and without transits, were used to define optimised detection thresholds in terms of posterior probability maxima."281 A number of improvements have been made since the publication of Paper 1: The algorithm. used in the present paper evolved. from hat of Paper L. taking into consideration the points listed in Sect. 2.L.," A number of improvements have been made since the publication of Paper I: The algorithm used in the present paper evolved from that of Paper I, taking into consideration the points listed in Sect. \ref{sec:af}."282 The model therefore. consists of one out-o[-transit bin and. a single level in-transit bin. (, The model therefore consists of one out-of-transit bin and a single level in-transit bin. (283Although his simplification may seem cisingenuous. by suitably pre-oocessing. or adaptively filtering. the signal to. remove intrinsic stellar variability. this is a valid approximation to ransit detection in practice.),"Although this simplification may seem disingenuous, by suitably pre-processing, or adaptively filtering, the signal to remove intrinsic stellar variability, this is a valid approximation to transit detection in practice.)"284 All the data. points falling into the out-of-transit bin form the ensemble O. while those alling into the in-transit bin form the ensemble {.," All the data points falling into the out-of-transit bin form the ensemble $O$, while those falling into the in-transit bin form the ensemble $I$."285 No Davesian priors are used., No Bayesian priors are used.286 Adapting Eq. (13)), Adapting Eq. \ref{eq:chi2tot}) )287 to this mocel elves: Provided the transits are shallow and of short duration (he most common case). the ensemble QO contains the vast majority of the cata points. so that do=d (where d is the weighted mean of the entire light curve).," to this model gives: Provided the transits are shallow and of short duration the most common case), the ensemble $O$ contains the vast majority of the data points, so that $\ov{d\os} \approx \ov{d}$ (where $\ov{d}$ is the weighted mean of the entire light curve)."288 Substituting this approximation into Iq. (14)):, Substituting this approximation into Eq. \ref{eq:chi2n}) ):289 The first two terms in Eq. (15)), The first two terms in Eq. \ref{eq:chi2sp}) )290 are constant., are constant.291" The minimisation of x7 is therefore achieved by maximising the detection statistic (Q. given by: which can also be expanded as: Ifthe light curve is robustly ""mean-corrected prior to running the algorithm. such that d; is replaced by Ad;. dy becomes Ad;. the depth of the model transit."," The minimisation of $\chi^2$ is therefore achieved by maximising the detection statistic $Q$ , given by: which can also be expanded as: If the light curve is robustly “mean-corrected” prior to running the algorithm, such that $d_i$ is replaced by $\Delta d_i$, $\ov{d\is}$ becomes $\ov{\Delta d\is}$ , the depth of the model transit."292 This results in a further simplification where the only free.parameters are now the phase. period. and duration of the transit. since the," This results in a further simplification where the only freeparameters are now the phase, period, and duration of the transit, since the"293the standard electromagnetism.,the standard electromagnetism.294 For the specific case that the magnetic field lines touch the disk at a single radius. the calculations are carried out by Li(2000€).," For the specific case that the magnetic field lines touch the disk at a single radius, the calculations are carried out by \citet{li00b}."295".. In Chis case. the sign ol Ey+£p (and thus the direction of the transler of energy and angular momentum) is determined by the sien of Qy,—O5. where Oy is the angular velocity of the black hole which is constant over the black hole horizon. Qy is the angular velocity of the disk at the radius where the magnetic field touches the disk."," In this case, the sign of ${\cal E}_H + {\cal E}_D$ (and thus the direction of the transfer of energy and angular momentum) is determined by the sign of $\Omega_H-\Omega_D$, where $\Omega_H$ is the angular velocity of the black hole which is constant over the black hole horizon, $\Omega_D$ is the angular velocity of the disk at the radius where the magnetic field touches the disk."296 If ο>Op. ie. if the black hole rotates faster than the disk. enerev and angular momentum are transfered [rom the black hole to the disk.," If $\Omega_H > \Omega_D$, i.e. if the black hole rotates faster than the disk, energy and angular momentum are transfered from the black hole to the disk."297 If O5<p. ie. if the black hole rotates slower than the disk. energy. and angular momentum are translered [rom the clisk to the black hole.," If $\Omega_H <\Omega_D$, i.e. if the black hole rotates slower than the disk, energy and angular momentum are transfered from the disk to the black hole."298" I£ ,;=Op. there is no transfer ol energv and angular momentum between the black hole and the disk."," If $\Omega_H 299=\Omega_D$, there is no transfer of energy and angular momentum between the black hole and the disk."300 For fixed values of ihe magnetic flix. the mass and (he angular momentum of the black hole. and the resistance of the black hole. (he power peaks at £5=O5/2 (Li2000c).," For fixed values of the magnetic flux, the mass and the angular momentum of the black hole, and the resistance of the black hole, the power peaks at $\Omega_D = \Omega_H/2$ \citep{li00b}."301. If the magnetic field is distributed over a clifferentially rotating disk. the formulae given in Li(2000¢) [or the EMF of the disk. the power. and the torque on the disk should be replaced with integrations over the radius of the disk.," If the magnetic field is distributed over a differentially rotating disk, the formulae given in \citet{li00b} for the EMF of the disk, the power, and the torque on the disk should be replaced with integrations over the radius of the disk."302 Assume (he magnetic lield is stationary and axisvmmetrice. ancl touches the disk al radii ranging from r4 to rs. then. the total EAIF induced on the disk is where Vj=WVyrp(r) is the magnetic [hix through a surface whose boundary is a circle with a constant r in the disk.," Assume the magnetic field is stationary and axisymmetric, and touches the disk at radii ranging from $r_1$ to $r_2$, then, the total EMF induced on the disk is where $\Psi_{HD} = \Psi_{HD}(r)$ is the magnetic flux through a surface whose boundary is a circle with a constant $r$ in the disk."303 In such a case. an infinite number of adjacent. infinitesimal poloidal electric current loops [low between the black hole and the disk along the magnetic lield lines connecting them.," In such a case, an infinite number of adjacent infinitesimal poloidal electric current loops flow between the black hole and the disk along the magnetic field lines connecting them."304 Each infinitesimal current loop produces an infinitesimal power and au infinitesimal torque on (he disk. whose summation eives the the total power and the total torque on the disk.," Each infinitesimal current loop produces an infinitesimal power and an infinitesimal torque on the disk, whose summation gives the the total power and the total torque on the disk."305 Thus. assuming the disk is perfectly conducting. the total power produced by the black hole on the disk is where we have treated the black hole's resistance Ζμ as a Tinetion of the disks radius. which is defined by a map from (he black hole horizon to the disk surface given by the mmagnelic field lines.," Thus, assuming the disk is perfectly conducting, the total power produced by the black hole on the disk is where we have treated the black hole's resistance $Z_H$ as a function of the disk's radius, which is defined by a map from the black hole horizon to the disk surface given by the magnetic field lines."306 Similarly. the total torque produced by the black hole on the disk is," Similarly, the total torque produced by the black hole on the disk is"307SER history are sensitive to the parameters describing SER aud feedback. but these were chosen as in [5]. to fit observations of prescut-day galaxies. without any knowledge of the observational data iu Figure 3.,"SFR history are sensitive to the parameters describing SFR and feedback, but these were chosen as in \cite{C94} to fit observations of present-day galaxies, without any knowledge of the observational data in Figure 3."308 Our model results are therefore real predictions. and the observational comparison represents a real success of the model.," Our model results are therefore real predictions, and the observational comparison represents a real success of the model."309The EIS spectrum at each location in (he raster contains 17 spectral lines.,The EIS spectrum at each location in the raster contains 17 spectral lines.310 We select 11 lines among them spanning a temperature range of 0.0510 δν., We select 11 lines among them spanning a temperature range of 0.05–16 MK.311 Details of the lines are shown in Table 1.., Details of the lines are shown in Table \ref{line_data}.312 The majority of these lines are well resolved with no blends or only trivial blends that can be safely ignored in the active region (Youngetal.2007b)., The majority of these lines are well resolved with no blends or only trivial blends that can be safely ignored in the active region \citep{youn07b}.313. We find that most of the observed line profiles have symmetric Gaussian shapes that can be fitted using a single Gaussian function., We find that most of the observed line profiles have symmetric Gaussian shapes that can be fitted using a single Gaussian function.314 ILowever. in some areas. (he line profiles are asvnuuetric and can be well fitted by double Gaussian components.," However, in some areas, the line profiles are asymmetric and can be well fitted by double Gaussian components."315 We reduce the data using the standard EIS software cata reduction package., We reduce the data using the standard EIS software data reduction package.316 This includes the correction of detector bias and dark current. as well as hot pixels and cosmic ray hits. resulting in absolute intensities in eres 7s Fus EAT ," This includes the correction of detector bias and dark current, as well as hot pixels and cosmic ray hits, resulting in absolute intensities in ergs $^{-2}$ $^{-1}$ $^{-1}$ $^{-1}$."317We also make a correction for a slight tilt of the slit on the CCDs., We also make a correction for a slight tilt of the slit on the CCDs.318 An additional effect that is corrected for is a variation of line positions over the [inode orbit due to temperature variations in (he spectrometer., An additional effect that is corrected for is a variation of line positions over the Hinode orbit due to temperature variations in the spectrometer.319 Such an orbital variation is obtained by averaging the centroid positions over a length of slit for which the wniderlving solar region is mostly a quiet region., Such an orbital variation is obtained by averaging the centroid positions over a length of slit for which the underlying solar region is mostly a quiet region.320 We choose the bottom 50 rows in the EIS Fe XII raster (see (he red box in Figure 1)) as a quiet region., We choose the bottom 50 rows in the EIS Fe XII raster (see the red box in Figure \ref{EISandMDI}) ) as a quiet region.321 The result is then subtracted Irom the line center positions measured in all wavelength windows., The result is then subtracted from the line center positions measured in all wavelength windows.322 EIS does not have an absolute wavelength calibration., EIS does not have an absolute wavelength calibration.323 We adopt the observed line centers averaged over the quiet reeion (the red box in Figure 1)) as (he rest wavelengths., We adopt the observed line centers averaged over the quiet region (the red box in Figure \ref{EISandMDI}) ) as the rest wavelengths.324 Decause ol the EIS effective area that only peaks at about 195 and 275 ii (he short wavelength (SW) and long wavelength (LW) bands. respectively. ancl (he weak enussion in (he «quiet region. we cannot obtain (he accurate line centers [or some lines. especially the high temperature lines.," Because of the EIS effective area that only peaks at about 195 and 275 in the short wavelength (SW) and long wavelength (LW) bands, respectively, and the weak emission in the quiet region, we cannot obtain the accurate line centers for some lines, especially the high temperature lines."325 Therelore. we use the method by Brownetal.(2007) and the CHILANTI package (Dereetal.1997.2009) to determine the reference wavelengths for those lines.," Therefore, we use the method by \cite{brow07} and the CHIANTI package \citep{dere97, dere09} to determine the reference wavelengths for those lines."326 To check the reliability of the methods. we use four strong lines. e.g.. Fe XII. Fe XIII. Fe XIV. and Fe XV. for test.," To check the reliability of the methods, we use four strong lines, e.g., Fe XII, Fe XIII, Fe XIV, and Fe XV, for test."327 We find that the wavelengths of the line centers determined using the above methods are nearly the same with a deviation being within 30.005À.. which induces a velocity uncertainty of no larger (han 5 km 1," We find that the wavelengths of the line centers determined using the above methods are nearly the same with a deviation being within $\pm$ 0.003, which induces a velocity uncertainty of no larger than 5 km $^{-1}$."328 We co-align the SOT/FG and EIS images by adopting the method described bv (2009)., We co-align the SOT/FG and EIS images by adopting the method described by \cite{guoy09}.329. Taking into account the instrumental offset between the images taken in the two EIS CCDs. we also shilt the LW images by 2” in the solar X direction and 17” in the solar Y direction (Youngetal. 2007a)..," Taking into account the instrumental offset between the images taken in the two EIS CCDs, we also shift the LW images by $\arcsec$ in the solar X direction and $\arcsec$ in the solar Y direction \citep{youn07a}. ."330"We are grateful to G. Cassam-Chenai and ο, Gabici lor reading an intermediate version of the present manuscript.",We are grateful to G. Cassam-Chenai and S. Gabici for reading an intermediate version of the present manuscript.331 We are also grateful to the anonvimous releree for his/her precious comments., We are also grateful to the anonymous referee for his/her precious comments.332 This work was partially supported by PRIN-2006. by ASI through contract 1/088/06/0 and (for PB) by the US DOE and by NASA grant NÀAG5-10842.," This work was partially supported by PRIN-2006, by ASI through contract ASI-INAF I/088/06/0 and (for PB) by the US DOE and by NASA grant NAG5-10842."333 Fermilab is operated by Fermi Research Alliance. LLC under Contract No.," Fermilab is operated by Fermi Research Alliance, LLC under Contract No."334 DE-ACO2-07C1111359 with the United States DOE., DE-AC02-07CH11359 with the United States DOE.335being ~70 Le in only a few cases (e.g.. Evansetal.2009)).,"being $\sim70$ $_{\sun}$ in only a few cases (e.g., \cite{evans2009}) )."336 IRAS 13037-6112 and IRAS 13039-6108 have similar SED parameters (see Fig., IRAS 13037-6112 and IRAS 13039-6108 have similar SED parameters (see Fig.337 5. and Table 5)) suggesting that they probably represent the same evolutionary. stage.," \ref{figure:sed} and Table \ref{table:sed}) ), suggesting that they probably represent the same evolutionary stage."338 Based on its IRAS [25—12] and [60—12] colours (0.61 and 1.55. respectively). IRAS 13037-6112 belongs to the so-called sources. and could potentially be associated with ultra-compact (UC) region (e.g.. Wood&Churchwell1989:: Pallaetal. 1991:: Molinarietal. 1996).," Based on its IRAS $[25-12]$ and $[60-12]$ colours (0.61 and 1.55, respectively), IRAS 13037-6112 belongs to the so-called sources, and could potentially be associated with ultra-compact (UC) region (e.g., \cite{wood1989}; \cite{palla1991}; \cite{molinari1996}) )."339 However. the M/L ratio of IRAS 13037-6112 (0.04) is more typical of sources younger than UC regions (Sridharanetal. 2002).," However, the $M/L$ ratio of IRAS 13037-6112 (0.04) is more typical of sources younger than UC regions \cite{sridharan2002}) )."340 IRAS 13039-6108 has a [25-12] colour index of 0.27. settling it to the so-called sources.," IRAS 13039-6108 has a $[25-12]$ colour index of 0.27, settling it to the so-called sources."341 Moreover. Fontani et al. (," Moreover, Fontani et al. ("3422005) found that the CO and CS linewidths in IRAS 13039-6108 are significantly smaller than. those typically observed in massive clumps associated with UC regions (e.g.. Cesaronietal.1991:: Hofneretal. 2000)).,"2005) found that the $^{17}$ O and CS linewidths in IRAS 13039-6108 are significantly smaller than those typically observed in massive clumps associated with UC regions (e.g., \cite{cesaroni1991}; \cite{hofner2000}) )."343 This further supports the idea that both IRAS 13037-6112 and IRAS 13039-6108 represent the same evolutionary stage (earlier than UC HID., This further supports the idea that both IRAS 13037-6112 and IRAS 13039-6108 represent the same evolutionary stage (earlier than UC ).344" Using the assumption of an isothermal sphere with Ti=22 K and a density profile of the form n(7)«r7 5, which is typical of high-mass star-forming clumps (e.g.. Beutheretal. 2002a)). the C'/O(2-1) linewidth of 0.93 km s7! observed by Fontani et al. ("," Using the assumption of an isothermal sphere with $T_{\rm kin}=22$ K and a density profile of the form $n(r)\propto r^{-1.6}$ , which is typical of high-mass star-forming clumps (e.g., \cite{beuther2002a}) ), the $^{17}$ $(2-1)$ linewidth of 0.93 km $^{-1}$ observed by Fontani et al. ("3452005) implies a virial mass of ~99 Mo for IRAS 13039-6108 (Miήν=0.8. Maip/My= 0.9. Le. the virial parameter defined by Bertoldi McKee (1992) is ov=Maj/M1.1- 1.3) (see. e.g.. Eqs. (,"2005) implies a virial mass of $\sim99$ $_{\sun}$ for IRAS 13039-6108 $M_{\rm cont}/M_{\rm vir}\simeq0.8$, $M_{\rm SED}/M_{\rm vir}\simeq0.9$ , i.e., the virial parameter defined by Bertoldi McKee (1992) is $\alpha_{\rm vir}=M_{\rm vir}/M\simeq1.1-1.3$ ) (see, e.g., Eqs. ("3461) and (2) of Chenetal. 2008)).,1) and (2) of \cite{chen2008}) ).347 Thus the clump ts near virtal equilibrium., Thus the clump is near virial equilibrium.348 IRAS 13042-6105 in the northern part of the cloud is probably in an earlier stage of evolution than the other two IRAS sources because it is not as bright at FIR wavelengths (see Table 3))., IRAS 13042-6105 in the northern part of the cloud is probably in an earlier stage of evolution than the other two IRAS sources because it is not as bright at FIR wavelengths (see Table \ref{table:IRAS}) ).349 The mass distribution of clumps/cores is important parameter concerning the cloud fragmentation mechanism., The mass distribution of clumps/cores is important parameter concerning the cloud fragmentation mechanism.350 Our sample of clumps is. however. so small (12 in total. 8 MIR dark) that it is not reasonable to study their mass distribution directly.," Our sample of clumps is, however, so small (12 in total, 8 MIR dark) that it is not reasonable to study their mass distribution directly."351 Therefore. we only compared it with the mass distributions derived for other. larger IRDC clump samples. using the results of Sridharan et al. (," Therefore, we only compared it with the mass distributions derived for other, larger IRDC clump samples, using the results of Sridharan et al. ("3522005). RJSO6. Vasyunina et al. (,"2005), RJS06, Vasyunina et al. ("3532009). and RBGO09.,"2009), and RBG09."354 Figure 7 presents the observed cumulative mass functions. which include clumps of mass less than M. i.e. N(M)=Non« ΜΟΝ. for G304.74 and for a sample of cold clumps from RJSO6 and RBGOY.," Figure \ref{figure:CMF} presents the observed cumulative mass functions, which include clumps of mass less than $M$, i.e., $\mathcal{N}(M)=N(m<M)/N_{\rm tot}$ , for G304.74 and for a sample of cold clumps from RJS06 and RBG09."355 We note that the IRDC clump mass functions in RJSO6 and in our work are constructed by removing the MIR bright clumps from the samples (in the case of G304.74. this means the three IRAS sources and SMM 6).," We note that the IRDC clump mass functions in RJS06 and in our work are constructed by removing the MIR bright clumps from the samples (in the case of G304.74, this means the three IRAS sources and SMM 6)."356 From the sample of Sridharan et al. (, From the sample of Sridharan et al. (3572005). we excluded the high temperature clump No.,"2005), we excluded the high temperature clump No."358 9. because its temperature (32.7 K) was much higher than the rest of the sample.," 9, because its temperature (32.7 K) was much higher than the rest of the sample."359 From the the sample of RBGO9. we removed the clumps associated with YSOs. and the clumps possibly contaminated by foreground (or background) stars.," From the the sample of RBG09, we removed the clumps associated with YSOs, and the clumps possibly contaminated by foreground (or background) stars."360 Thus. the mass functions include only those clumps that initially have all their mass available for star formation.," Thus, the mass functions include only those clumps that initially have all their mass available for star formation."361 The previous studies taken into this comparison. used slightly different assumptions about the dust temperature and opacity., The previous studies taken into this comparison used slightly different assumptions about the dust temperature and opacity.362" We scaled all the clump masses included in the cumulative mass functions to correspond to a uniform dust temperature of Ty=15 K. and an opacity that is consistent with our «xz;=0.17 m Καὶ,"," We scaled all the clump masses included in the cumulative mass functions to correspond to a uniform dust temperature of $T_{\rm d}=15$ K, and an opacity that is consistent with our $\kappa_{870}=0.17$ $^2$ $^{-1}$."363 RBGO9 derived clump masses from the total hydrogen column densities. Ny. as estimated from the 8 um optical thicknesses. ts.," RBG09 derived clump masses from the total hydrogen column densities, $N_{\rm H}$, as estimated from the 8 $\mu$ m optical thicknesses, $\tau_8$."364 For the dust extinction cross-section per H nucleus at 8 jum. oy. they used the value 2.3x10-2 cnr. basec on the Weingartner Draine (2001) dust model.," For the dust extinction cross-section per H nucleus at 8 $\mu$ m, $\sigma_8$, they used the value $2.3\times10^{-23}$ $^2$, based on the Weingartner Draine (2001) dust model."365 According to the model we have used (Ossenkopf&Henning 1994)). the corresponding number is 3.5x1072 em? per H nucleus (see Sect.," According to the model we have used \cite{ossenkopf1994}) ), the corresponding number is $3.5\times10^{-23}$ $^2$ per H nucleus (see Sect."366 5.3)., 5.3).367 In their mass formula. RBGO9 used a factor of 1.16 às the ratio of the total gas mass (including. He) and the hydrogen mass.," In their mass formula, RBG09 used a factor of 1.16 as the ratio of the total gas mass (including He) and the hydrogen mass."368 In our calculations this ratio has been 1.4 (Sect., In our calculations this ratio has been 1.4 (Sect.369 5.3)., 5.3).370 These differences have been accounted for by scaling the masses from RBGO9 by 0.8 in the comparison with our results., These differences have been accounted for by scaling the masses from RBG09 by 0.8 in the comparison with our results.371 To determine whether our clump masses and those from other studies are derived from the same clump mass distribution. we carried out the two-sample Kolmogorov-Smirnov (K-S) test.," To determine whether our clump masses and those from other studies are derived from the same clump mass distribution, we carried out the two-sample Kolmogorov-Smirnov (K-S) test."372 For this test. the mass scales were matched. Le.. the comparison was done within the range of commo=) mass interval.," For this test, the mass scales were matched, i.e., the comparison was done within the range of common mass interval."373 The K-S test results are shown in Table 8.., The K-S test results are shown in Table \ref{table:KS}.374 The columns of this table are: (1) the survey used in the comparison: (2) number of clumps included; (3) the maximum vertical difference between the cumulative mass distributions (Dinas)! (4) the probability for the null hypothesis that the two functions are drawn form the sameparent distribution (the significance level of the K-S statistic)., The columns of this table are: (1) the survey used in the comparison; (2) number of clumps included; (3) the maximum vertical difference between the cumulative mass distributions $D_{\max}$ ); (4) the probability for the null hypothesis that the two functions are drawn form the sameparent distribution (the significance level of the K-S statistic).375"travel time differences relative to the quiet Sun are approximately 0.3 minutes in Figure 5aa and 1.0 minute in Figure 5bb, and these numbers are significantly different from the result in (2005a),, which is approximately 180° in phase shift, i.e., 1.7 minutes.","travel time differences relative to the quiet Sun are approximately 0.3 minutes in Figure \ref{fg5}a a and 1.0 minute in Figure \ref{fg5}b b, and these numbers are significantly different from the result in \citet{lin05a}, , which is approximately $180\degr$ in phase shift, i.e., 1.7 minutes."376" Once again, these differences may be caused by the different frequency bands, filtering technique and very different sizes of annulus (or pupil)."," Once again, these differences may be caused by the different frequency bands, filtering technique and very different sizes of annulus (or pupil)."377 It is very important to note that the magnitude and sign of the travel time variations are different for different travel distances., It is very important to note that the magnitude and sign of the travel time variations are different for different travel distances.378" If travel time variations are caused by the surface magnetism, then one may expect that these variations do not significantly change with travel distances."," If travel time variations are caused by the surface magnetism, then one may expect that these variations do not significantly change with travel distances."379" Therefore, the very different behaviors of the acoustic travel times for different measurement annuli indicate that a large fraction of the observed travel time deviations from the mean travel time in the quiet Sun is due to the interior structures and dynamics of active regions."," Therefore, the very different behaviors of the acoustic travel times for different measurement annuli indicate that a large fraction of the observed travel time deviations from the mean travel time in the quiet Sun is due to the interior structures and dynamics of active regions."380" The observed deviations of the travel times in sunspots compared to the travel times in the quiet regions are explained as changes in the sound-speed structures of sunspots with depths, and the asymmetry in the outgoing and ingoing travel times is explained as the advection effect due to subphotospheric flows."," The observed deviations of the travel times in sunspots compared to the travel times in the quiet regions are explained as changes in the sound-speed structures of sunspots with depths, and the asymmetry in the outgoing and ingoing travel times is explained as the advection effect due to subphotospheric flows."381" The arguments that all travel time deviations from 0 are caused by the showerglass effect, and that all such deviations be removed from acoustic signals are not justified."," The arguments that all travel time deviations from 0 are caused by the showerglass effect, and that all such deviations be removed from acoustic signals are not justified."382 Such corrections will substantially underestimate sound-speed variations and flow velocities in the sunspot interior., Such corrections will substantially underestimate sound-speed variations and flow velocities in the sunspot interior.383" How and how much the surface magnetism affects the acoustic travel times are definitely worth more studies, and that will likelyrely on numerical modelings."," How and how much the surface magnetism affects the acoustic travel times are definitely worth more studies, and that will likelyrely on numerical modelings."384"F, is calculated at the cell interfaces.",$\vec{F}_*$ is calculated at the cell interfaces.385" To calculate the mean radiative force inside this cell it is necessary to integrate the radiative force over the cell volume (e.g. a simple ansatz of averaging only the stored fluxes at the interfaces towards the cell center would lead to unphysically high radiative forces for T>>1, i.e. for the case that most of the flux is absorbed on a length scale much smaller than the grid size)."," To calculate the mean radiative force inside this cell it is necessary to integrate the radiative force over the cell volume (e.g. a simple ansatz of averaging only the stored fluxes at the interfaces towards the cell center would lead to unphysically high radiative forces for $\tau >> 1$, i.e. for the case that most of the flux is absorbed on a length scale much smaller than the grid size)."386 Integrating the above formula Eq., Integrating the above formula Eq.387 over space (for simplicity here: an one-dimensional cartesian grid with an uniform grid spacing of Ax) leads to: The flux at position x inside the grid cell is given by the flux Fi entering the cell at the interface i and the absorption of this flux along the length x: with the optical depth t=«px., over space (for simplicity here: an one-dimensional cartesian grid with an uniform grid spacing of $\Delta x$ ) leads to: The flux at position $x$ inside the grid cell is given by the flux $\vec{F}_*^i$ entering the cell at the interface $i$ and the absorption of this flux along the length $x$: with the optical depth $\tau = \kappa ~ \rho ~ x$.388" The remaining integral yields: Finally, the oemean radiative force is therefore given by the difference of the left and the right flux into and/or out of the cell respectively which equals in continuous space the derivative of the radiative flux Combining Eqs."," The remaining integral yields: Finally, the mean radiative force is therefore given by the difference of the left and the right flux into and/or out of the cell respectively which equals in continuous space the derivative of the radiative flux Combining Eqs."389 and reflects the fact that without emission the radiative flux is given by the differential equation, and reflects the fact that without emission the radiative flux is given by the differential equation390The 5gradual transfer of energy.g to the 1plasma implies1 that the product η)Gp) will not remain constant. as ina simple expansion. but will slowly increase.,"The gradual transfer of energy to the plasma implies that the product $R(\eta) T(\eta)$ will not remain constant, as in a simple expansion, but will slowly increase."391 In this respect σ simulates inflation. but on a much longer time scale.," In this respect $\sigma$ simulates inflation, but on a much longer time scale."392 The equations involved here are analogous to those used previously. but are considerably. more complicated. so we just give the main results.," The equations involved here are analogous to those used previously, but are considerably more complicated, so we just give the main results."393 The wave number. A&. the permittivity. ¢(77). and the conductivity. m. satisfy the dispersion relation By analogy with Maxwell's equations in flat space. the equations (17)). C18)) and (19)) for our dipole fields become: From these we obtain an equation for fs alone: Writing Av for ace this equation takes a familiar form: fs can be derived. from the cmipty-space formula: simply bv writing & for n everywhere. except. of course. for the normalization function. which we denote now by ησ]: C'a(n.o) is most easily determined in fat space: this is sullicient since we only have to consider small distances.," The wave number, $k$ , the permittivity, $\epsilon (n)$ , and the conductivity, $\sigma$, satisfy the dispersion relation By analogy with Maxwell's equations in flat space, the equations \ref{eq:dip1}) ), \ref{eq:dip2}) ) and \ref{eq:dip3}) ) for our dipole fields become: From these we obtain an equation for $f_3$ alone: Writing $k^2$ for $n^2 \epsilon$ this equation takes a familiar form; $f_3$ can be derived from the empty-space formula simply by writing $k$ for $n$ everywhere, except, of course, for the normalization function, which we denote now by $C_3 (n,\sigma)$: $C_3 (n,\sigma)$ is most easily determined in flat space; this is sufficient since we only have to consider small distances."394 The calculation is done in appendix A.., The calculation is done in appendix \ref{app:normalize}.395 We find: The Fourier transform of the magnetic field becomes We can integrate around the pole at à=0 in the same wav as before. except that we have to respect the branch points of Ao at η20and η=4tiia.," We find: The Fourier transform of the magnetic field becomes We can integrate around the pole at $n=0$ in the same way as before, except that we have to respect the branch points of $k$, at $n=0$and $n=-4\pi {\mathrm i} \sigma$."396 We have also to take account of the pole at ài= Szim/3., We have also to take account of the pole at $n = -8 \pi {\mathrm i} \sigma / 3$ .397 A suitable contour is shown in ligure 6.., A suitable contour is shown in figure \ref{fig:CONTOUR2EPS}.398 The integrals5 are straightforward.5 and. the resulting5 propagation of F4» is shown in figure 7..," The integrals are straightforward, and the resulting propagation of $F_{12}$ is shown in figure \ref{fig:HP2EPS}. ."399 Lere we follow the prescription of Landau and Lilshitz (?):: use the same equations relating potentials ancl fields as in empty space. ie. (400). (41)) and. (42)). but. modify the Lorenz condition by including the permittivity in the fo tern: From these equations. as before. we can derive an equation [or fo alone: This is the sameequationas we obtained for empty space. except that. just as for the magnetic field. in place of n we must write A— nc. (47))," Here we follow the prescription of Landau and Lifshitz \citep{landau2}: use the same equations relating potentials and fields as in empty space, i.e. \ref{eq:heq1}) ), \ref{eq:heq2}) ) and \ref{eq:heq3}) ), but modify the Lorenz condition by including the permittivity in the $h_0$ term: From these equations, as before, we can derive an equation for $h_0$ alone: This is the sameequationas we obtained for empty space, except that, just as for the magnetic field, in place of $n^2$ we must write $k^2 \equiv n^2 \epsilon$ . \ref{eq:h0out1}))"400 appliesas before. provided," appliesas before, provided"401 appliesas before. provided.," appliesas before, provided"402orbital plane is then equally plausible.,orbital plane is then equally plausible.403 Using the notations of Figure 1.. an elementary. solid. angle around the orbital planes normal is given by dS=sinididQO.," Using the notations of Figure \ref{orbitps}, an elementary solid angle around the orbital plane's normal is given by $dS = \sin i \,di \,d\Omega$."404 Since the direction 5 is uniformly. clistributed one obtains as the distribution of the inclination., Since the direction $S$ is uniformly distributed one obtains as the distribution of the inclination.405 In. Soederhjelm (1999).. the orbital parameters and. masses of about 200 nearby visual binaries are given.," In Soederhjelm \cite{soe}, the orbital parameters and masses of about 200 nearby visual binaries are given."406 Phe data are obtained [rom Llippareos and erounc-basecl telescopes., The data are obtained from Hipparcos and ground-based telescopes.407 Figure 3. shows the clistribution of the inclination. extracted from this catalog. and clearly demonstrates the validity of (19)).," Figure \ref{soei} shows the distribution of the inclination, extracted from this catalog, and clearly demonstrates the validity of \ref{disi}) )."408 The distribution of the semi-major axis cannot readily be extracted from a catalog., The distribution of the semi-major axis cannot readily be extracted from a catalog.409 Catalogs of visual. binarics usually only contain the semi-major axis expressecl in areseconds since their distances are not known., Catalogs of visual binaries usually only contain the semi-major axis expressed in arcseconds since their distances are not known.410 Catalogs of spectroscopic binaries do give the semi-major axis expressec in e.g. AU but they tend to be strongly. biased: towards very tight binaries since these will have the highest orbita velocities and hence the largest and the easiest. measurable Doppler-shifts., Catalogs of spectroscopic binaries do give the semi-major axis expressed in e.g. AU but they tend to be strongly biased towards very tight binaries since these will have the highest orbital velocities and hence the largest and the easiest measurable Doppler-shifts.411 Llowever. it is natural to assume that more tightly bound. binaries are less casily disrupted by externa influences.," However, it is natural to assume that more tightly bound binaries are less easily disrupted by external influences."412 Hence. one would expect to observe less binarics with lower binding energies.," Hence, one would expect to observe less binaries with lower binding energies."413 We therefore adopt as the distribution of α (the orbital radius with respect to the secondary).Here. £ is the binarv's binding energy and 5 is a real number.," We therefore adopt as the distribution of $a$ (the orbital radius with respect to the secondary).Here, $E$ is the binary's binding energy and $\gamma$ is a real number."414 The closest gravitational [ew-bocdv system at hand. our planetary system. obevs (20)) quite well with 5zI.," The closest gravitational few-body system at hand, our planetary system, obeys \ref{disa}) ) quite well with $\gamma \approx4151$."416 The upper and lower bounds for αν ruin and rus respectively. can be estimated: as follows.," The upper and lower bounds for $a$, $r_{\rm min}$ and $r_{\rm max}$ respectively, can be estimated as follows."417 For a binary to be stable. the mutual gravitational attraction between its members should. overcome the tical forces exerted by the host galaxy.," For a binary to be stable, the mutual gravitational attraction between its members should overcome the tidal forces exerted by the host galaxy."418 In other words. if we denote the average mass ofa star by nr with + the distance of the binary to the galaxy's center and A(7) the total mass inside a sphere with radius r.," In other words, if we denote the average mass of a star by $\overline{m}$: with $r$ the distance of the binary to the galaxy's center and $M(r)$ the total mass inside a sphere with radius $r$."419 This leads to the following expression for the maximum orbital radius : with 7 the average number density of the stars inside the radius r., This leads to the following expression for the maximum orbital radius : with $\overline{n}$ the average number density of the stars inside the radius $r$.420 For reasonable values of v. ryax is very large.," For reasonable values of $\overline{n}$, $r_{\rm max}$ is very large."421 lor instance. n=1pc? [eads to ως&107AU.," For instance, $\overline{n}=1~{\rm pc}^{-3}$ leads to $r_{\rm max} \approx 10^5~{\rm AU}$."422 Binaries can also be disrupted by an encounter with a third star., Binaries can also be disrupted by an encounter with a third star.423 For typical number densities. stars approach each other to about 1500 AU once in a Hubble time as they orbit in a galaxys eravitational potential well.," For typical number densities, stars approach each other to about 1500 AU once in a Hubble time as they orbit in a galaxy's gravitational potential well."424 Of. course. not every. such an encounter necessarily breaks up a binary pair.," Of course, not every such an encounter necessarily breaks up a binary pair."425 Hence. rax is at least a couple of thousand AU and can be as large as 100.000 AU.," Hence, $r_{\rm426max}$ is at least a couple of thousand AU and can be as large as 100,000 AU."427 Our results turn about to be rather insensitive to the value of rus., Our results turn about to be rather insensitive to the value of $r_{\rm max}$.428 If the members of a binary are very close together. one of them can be in the others Roche lobe and he disrupted. by tidal and centrifugal forces.," If the members of a binary are very close together, one of them can be in the other's Roche lobe and be disrupted by tidal and centrifugal forces."429 Back-ol-the-envelope calculations based. on typical masses ancl raclii of Wegiants (with a mass around 1.AL. ane a radius. of approximately 10 It.)which one is most likely to observe since they are so luminous — give Mun7&151t. as a fair mean value.," Back-of-the-envelope calculations based on typical masses and radii of K-giants (with a mass around $1~{\rm M}_\odot$ and a radius of approximately $10~{\rm R}_\odot$ )–which one is most likely to observe since they are so luminous – give $r_{\rm min} \approx43015~{\rm R}_\odot$ as a fair mean value."431" Due to (2)). the distribution of a, is with ey,η(η|M)ryi aid analogously for ex."," Due to \ref{defa}) ), the distribution of $a_p$ is with $a_{\rm m} = m/(m+M) r_{\rm min}$ and analogously for $a_{\rm432 M}$."433 For the distribution of the secondary mass. we take the Salpeter initial mass function with oe=2.35.," For the distribution of the secondary mass, we take the Salpeter initial mass function with $x=2.35$."434 The lower bound for the mass clistribution is taken to be mi=0.08M... the mass of the most light-weight stars capable of nuclear fusion.," The lower bound for the mass distribution is taken to be $m_1=0.08~{\rm M}_\odot$, the mass of the most light-weight stars capable of nuclear fusion."435 Ehe upper bound mo is treated as a free parameter of the binary orbital distribution., The upper bound $m_2$ is treated as a free parameter of the binary orbital distribution.436 Realistic values for mo are around. 1.25 M., Realistic values for $m_2$ are around 1.25 $_\odot$ .437 This corresponds to stars with a total life-time of 5-6 Car. comparable to the ages of the stellar populations in Local Group dwarf galaxies (e.g. Smecker-lLlane (1994))).," This corresponds to stars with a total life-time of 5-6 Gyr, comparable to the ages of the stellar populations in Local Group dwarf galaxies (e.g. Smecker-Hane \cite{smh}) )."438 These distributions can be compared to those. found. by Duquennov Alavor (1901). for a sample of 164. solar- stars in the solar neighborhood., These distributions can be compared to those found by DuquennoyMayor \cite{dm} for a sample of 164 solar-type stars in the solar neighborhood.439 For their sample. they find the following distribution ofthe binary. periods :," For their sample, they find the following distribution ofthe binary periods :"440not deep enough to retain the gas which is clearly observed in outflows.,not deep enough to retain the gas which is clearly observed in outflows.441 Luminous DBCCGs have recently experienced. a mereer event or accreted a considerable amount of gas (seeOstlinetal.2001:Adamo2010a.201 a.b)...," Luminous BCGs have recently experienced a merger event or accreted a considerable amount of gas \citep[see][]{2001A&A...374..800O, A2010, A2010c, A2011a}."442 This may have favoured the formation of hundreds of massive clusters., This may have favoured the formation of hundreds of massive clusters.443 Moreover. these svstems are likely one or two orders of magnitude more massive than the ones in the Billett et al.," Moreover, these systems are likely one or two orders of magnitude more massive than the ones in the Billett et al."444 sample. allowing them to retain the gas more ellicicntly.," sample, allowing them to retain the gas more efficiently."445 The ALE LSER relation. presented in the previous section. suggests that BCCGs are. in the local universe. among the systems which form very massive (bright) clusters.," The $_V^{\textnormal{brightest}}$ -SFR relation, presented in the previous section, suggests that BCGs are, in the local universe, among the systems which form very massive (bright) clusters."446 Although they follow the trend it is also clear that they ave slightly olfset from the prediction made hy DOS of a constant cluster formation clliciency., Although they follow the trend it is also clear that they are slightly offset from the prediction made by B08 of a constant cluster formation efficiency.447 Phe svstematic scatter observed in the position of the BCGs in the AL SER. relation suggests that a higher CFE is operating in these svstems. which are not cynamically relaxed. e.g.. in a mereine/interaction phase.," The systematic scatter observed in the position of the BCGs in the $_V^{\textnormal{brightest}}$ -SFR relation suggests that a higher CFE is operating in these systems, which are not dynamically relaxed, e.g., in a merging/interaction phase."448 The trends. observed. in the other two relations. Ιου) anc Tí;(U)-Mapn. even if uncertain. support this scenario.," The trends observed in the other two relations, $\Gamma$ $\log(\Sigma_\mathrm{SFR})$ and $_L$ $\Sigma_\mathrm{SFR}$, even if uncertain, support this scenario."449 A close look at the Goddard et al., A close look at the Goddard et al.450 relation reveals an interesting point., relation reveals an interesting point.451 In the diagram in Figure 7.. two dillerent groups can be delineated bv the distributions of the data points.," In the diagram in Figure \ref{sfr-cfr}, two different groups can be delineated by the distributions of the data points."452 Using the values listed in Table 4 of €10. we estimate that the mean ChE of the group with lower values (the Silva-Villa Larsen sample has been cxeluclecd) of Xapp is D—8.7$4.3%.. close to the value found by BOs.," Using the values listed in Table 4 of G10, we estimate that the mean CFE of the group with lower values (the Silva-Villa Larsen sample has been excluded) of $\Sigma_\mathrm{SFR}$ is $\Gamma=8.7 \pm 4.3$, close to the value found by B08."453 Phe more eLlicient sample includes 2 targets from GIO (the starburst nucleus of the spiral MS3 and the Ελλ NCC 3256) and the BCCs., The more efficient sample includes 2 targets from G10 (the starburst nucleus of the spiral M83 and the LIRG NCG 3256) and the BCGs.454 Their mean CEE is b=35.64E10%.. roughly a factor of 4 higher.," Their mean CFE is $\Gamma = 35.6 \pm 10$, roughly a factor of 4 higher."455 The two subsamples suggest that cluster formation cllicicney is not constant at all scales of SER., The two subsamples suggest that cluster formation efficiency is not constant at all scales of SFR.456 We see that in star-orming svstems where star formation has proceeded. more or less constantly. without any significant burst. the CET las à mean value of ~8X.," We see that in star-forming systems where star formation has proceeded more or less constantly without any significant burst, the CFE has a mean value of $\sim 8$."457 Starburst svstems. on the other iand. are very active in producing star clusters.," Starburst systems, on the other hand, are very active in producing star clusters."458 Possibly. he cüllerence in CEEs reflects a dilference in the conditions of the interstellar medium in the hosts (Elmegreen2008)..," Possibly, the difference in CFEs reflects a difference in the conditions of the interstellar medium in the hosts \citep{2008ApJ...672.1006E}."459 The universal cluster formation ellicicney discussed by BOS could be valid in the local universe assuming that the interstellar mecium censity is lower than in hieh redshift ealaxies., The universal cluster formation efficiency discussed by B08 could be valid in the local universe assuming that the interstellar medium density is lower than in high redshift galaxies.460 However. it is dillicult to extend. its valiclity to ealaxics with an extreme environment. (merging svstems).," However, it is difficult to extend its validity to galaxies with an extreme environment (merging systems)."461 Numerical simulations have shown that GCs may have formed in strongly shocked. media and high pressure fields. which have enhanced the gas compression and favoured the formation of more tightlv bound structures (Elmegreen&Efremoy 1997... Journaudοἱal. 2008)).," Numerical simulations have shown that GCs may have formed in strongly shocked media and high pressure fields, which have enhanced the gas compression and favoured the formation of more tightly bound structures \citealp{1997ApJ...480..235E}, \citealp{2008MNRAS.389L...8B}) )."462 Such conditions are usually reached in galaxy mergers. where the very massive voung star clusters are observed. (Antennae svstem. Mengeletal. 2005: Arp 220. Wilsonetal.2006: the Bird galaxy. Vülsünenetal. 2008)).," Such conditions are usually reached in galaxy mergers, where the very massive young star clusters are observed (Antennae system, \citealp{2005A&A...443...41M}; Arp 220, \citealp{2006ApJ...641..763W}; the Bird galaxy, \citealp{2008MNRAS.384..886V}) )."463 Xn increase of the CEE as function of redshift has also been found in simulations by Muratov&CGnedin (2010).., An increase of the CFE as function of redshift has also been found in simulations by \citet{2010ApJ...718.1266M}.464 They. observed that the cluster formation cllicieney (e.g. the mass in cluster. versus the total mass of the host) at redshift ~3 was much higher (about 20 )) than then in the local universe., They observed that the cluster formation efficiency (e.g. the mass in cluster versus the total mass of the host) at redshift $\sim 3$ was much higher (about 20 ) than then in the local universe.465 For this reason it is possible that the formation anc survival of voung and massive clusters formed. in extreme environments such as BCGs or LIRGs could help to trace the formation of the old GCs. if they have formed. under similar conclitions.," For this reason it is possible that the formation and survival of young and massive clusters formed in extreme environments such as BCGs or LIRGs could help to trace the formation of the old GCs, if they have formed under similar conditions."466 llowever. only better cata in terms of number statistics ancl quality. (high. resolution is required. in| order to distinguish. clusters from associations) are needed to reach more stringent conclusions.," However, only better data in terms of number statistics and quality (high resolution is required in order to distinguish clusters from associations) are needed to reach more stringent conclusions."467 To understand the role of BCCGs in the galaxy. formation scenario. we have tried to constrain how the star and cluster ormation is operating in these systems.," To understand the role of BCGs in the galaxy formation scenario, we have tried to constrain how the star and cluster formation is operating in these systems."468 We have looked into the ellicieney of the formation of massive star clusters., We have looked into the efficiency of the formation of massive star clusters.469 Lt is known that some properties of he cluster population and the mean star formation in the dost system are correlated. suggesting that the formation of a cluster is not a local event but intrinsically connected to he mean properties of the galaxy.," It is known that some properties of the cluster population and the mean star formation in the host system are correlated, suggesting that the formation of a cluster is not a local event but intrinsically connected to the mean properties of the galaxy."470 In general. we find that DOCS follow fairly well these relations. even if their SET and. cluster properties are more extremo.," In general, we find that BCGs follow fairly well these relations, even if their SFRs and cluster properties are more extreme."471 We discuss possible uncertainties allecting our results., We discuss possible uncertainties affecting our results.472 The relation. which is least. allectec is the MERE one. which suggests that the cluster formation cllicicney is higher in BCGs than in quiescent) spiral ancl dwarf starburst galaxies.," The relation which is least affected is the $_V^{\textnormal{brightest}}$ -SFR one, which suggests that the cluster formation efficiency is higher in BCGs than in quiescent spiral and dwarf starburst galaxies."473 The same evidence is also suggested by the other two relations. E-log(Xzpp) ane “Py (U)-Xapn.)- which appear to be consistent with the general picture despite the uncertainties of the data.," The same evidence is also suggested by the other two relations, $\Gamma$ $\log(\Sigma_\mathrm{SFR})$ and $_L$ $\Sigma_\mathrm{SFR}$, which appear to be consistent with the general picture despite the uncertainties of the data."474 In particular. we observe that the inclusion of the BCG sample separates the Ιου) plane into two regions.," In particular, we observe that the inclusion of the BCG sample separates the $\Gamma$ $\log(\Sigma_\mathrm{SFR})$ plane into two regions."475 Local spiral galaxies and chvarl starbursts as the Magellanic Clouds occupy. the area around. a mean CEE of S+!5 in agreement with the prediction made by Bos., Local spiral galaxies and dwarf starbursts as the Magellanic Clouds occupy the area around a mean CFE of $8 \pm 5$ in agreement with the prediction made by B08.476 The BCGs. together with a LIRG and a nuclear starburst region (included in the CLO sample). are in a region with a mean CFE of 35.6+10%.," The BCGs, together with a LIRG and a nuclear starburst region (included in the G10 sample), are in a region with a mean CFE of $35.6 \pm 10$."477. This indicates that the merger even has enhanced the cluster formation in these svstenis., This indicates that the merger event has enhanced the cluster formation in these systems.478 We observe that the fraction of light. produced. by star clusters in DCCGs increases at shorter wavelengths anc contribute significantly to the UV and U luminosities., We observe that the fraction of light produced by star clusters in BCGs increases at shorter wavelengths and contribute significantly to the UV and U luminosities.479 This sugeests that clustered: regions contribute a substantia fraction to the rest-frame UV light of z—1-3 galaxies with metallicities similar to the BCCs., This suggests that clustered regions contribute a substantial fraction to the rest-frame UV light of $\sim$ 1-3 galaxies with metallicities similar to the BCGs.480 In studies of Lyman break ealaxy analogs at redshift between 0.1 and 0.2. Overziereal.(2008). observed super starburst compact regions which dominate the UV light of these targets.," In studies of Lyman break galaxy analogs at redshift between $\sim$ 0.1 and 0.2, \citet{2008ApJ...677...37O} observed super starburst compact regions which dominate the UV light of these targets."481 In our analysis. we find some evidence that those bright elumps are. probably unresolved star cluster knots. similarly to the ones observed in BCGs.," In our analysis, we find some evidence that those bright clumps are probably unresolved star cluster knots, similarly to the ones observed in BCGs."482 ALA. thanks Ana Chies-Santos. for reading the manuscript and interesting discussions on globular cluster formation scenarios. and Esteban Silva-Villa lor useful inputs on the interpretation of the current host-cluster relations.," A.A. thanks Ana Chies-Santos, for reading the manuscript and interesting discussions on globular cluster formation scenarios, and Esteban Silva-Villa for useful inputs on the interpretation of the current host-cluster relations."483 The referee. Nate Bastian is thanked. for the numerous sugeestions ancl valuable comments which have improved this work.," The referee, Nate Bastian is thanked for the numerous suggestions and valuable comments which have improved this work."484" οΟι, is a Roval Swedish Academy. of Sciences research fellow. supported. from a grant from. the |xnut and Alice Wallenberg foundation."," G.Ö.. is a Royal Swedish Academy of Sciences research fellow, supported from a grant from the Knut and Alice Wallenberg foundation."485 A.A. GO. and EZ. also acknowledge support from. the Swedish Research council ancl the Swedish. National Space Board.," A.A, G.Ö.. and E.Z. also acknowledge support from the Swedish Research council and the Swedish National Space Board."486 This. research, This research487aand that is affected by selfabsorption.,and that is affected by self-absorption.488 As the maps show. he blue cussion in the northeru region forms a wellcollimated lobe with 1220231 near oue eud aud exteuds iortheast. while the red cussion shows two peaks. one at 1220231 aud the other lO” to the west.," As the maps show, the blue emission in the northern region forms a well-collimated lobe with 20231 near one end and extends northeast, while the red emission shows two peaks, one at 20231 and the other $''$ to the west."489 There are two chuups emiereiug in the 18 to channel map (right bottom paucl in ref20231-all-clunap)). with a more compact oue located about 2 wes of 1220231 aud another one centered around the southern dust coutiuuun peak SMM2.," There are two clumps emerging in the 18 to channel map (right bottom panel in \\ref{20231-all-chmap}) ), with a more compact one located about $'$ west of 20231 and another one centered around the southern dust continuum peak SMM2."490 They are most likely cloudlets along the light-ofsight towards 85870. but the slncimatic distances could not be csxtimated since their characteristic velocities fall into a forbidden zono.," They are most likely cloudlets along the light-of-sight towards 870, but the kinematic distances could not be estimated since their characteristic velocities fall into a forbidden zone."491 As shown in Fie.7.. the strongc» selfabsorption at ambicut velocities in the northern core appears between two bright Cluission peaks at about 3 audlaus.," As shown in \ref{20231-co32-pv}, the strong self-absorption at ambient velocities in the northern core appears between two bright emission peaks at about 3 and."492 The mean optical depth in the line wines. calculated Yoni to line ratios. is ~3.0 for bluc- (12 to σας). aud ~2.0 for redshifted (9 to kkius) wing clinission.," The mean optical depth in the line wings, calculated from to line ratios, is $\sim$ 3.0 for blue- (–12 to ) and $\sim$ 2.0 for redshifted (9 to kms) wing emission."493 From the ratio of CO 7 =32 and 21 brightuess cluperatures (tle 32 spectra were sanoothled to the aneular resolution of the 21 profiles). we estunate the LTE excitation temperature Z4 of the outflowing gas to ο INK to 10191 for an extended source and LOW to LLNS for a point source.," From the ratio of CO $J$ = 3–2 and 2–1 brightness temperatures (the 3–2 spectra were smoothed to the angular resolution of the 2–1 profiles), we estimate the LTE excitation temperature $T_{\rm ex}$ of the outflowing gas to be K to K for an extended source and K to K for a point source."494" We therefore take 7,220 IKE or our outflow parameter calculations described below.", We therefore take $T_{\rm ex}$ K for our outflow parameter calculations described below.495 Asstuning that the CO emission is near LTE aud that he, Assuming that the CO emission is near LTE and that the496lareer than inmost Sevfert 1s.,larger than in most Seyfert 1s.497 On the other haud. in order to explain this ratio bv having Calactic-type dust scattering in the UV. the UV scattered hight needs to have been suppressed somehow considerably.," On the other hand, in order to explain this ratio by having Galactic-type dust scattering in the UV, the UV scattered light needs to have been suppressed somehow considerably."498 This is because the UV. scattering cross section of the Galactic dust erains per II atom is much larecr than στ (roughlv ~ 500 στ in our UV range. though of course it depends on the sieht lines). wlile ΙΟ the scattering cross section 1s esseutiallv op.," This is because the UV scattering cross section of the Galactic dust grains per H atom is much larger than $\sigma_T$ (roughly $\sim$ 500 $\sigma_T$ in our UV range, though of course it depends on the sight lines), while in X-ray, the scattering cross section is essentially $\sigma_T$."499 The suppression could come from the possible opaqueness of the scattering region., The suppression could come from the possible opaqueness of the scattering region.500 The X-ray observation suggests a rather high col density for the scattering region., The X-ray observation suggests a rather high column density for the scattering region.501 In Mk 3. the direct light from the nucleus dominates in the hard X-rav. Which eives us the iutrinsic nuclear N-rav lunimositv.," In Mrk 3, the direct light from the nucleus dominates in the hard X-ray, which gives us the intrinsic nuclear X-ray luminosity."502 Comparing this direct flux (Εν~:2.101 erg 9 s1 at :1 keV.τ absorption: corrected) with the scattered N-ray luuinosity quoted above. Sako ct al.," Comparing this direct flux $\nu503F_{\nu} \sim 2 \times 10^{-11}$ erg $^{-2}$ $^{-1}$ at 1 keV, absorption corrected) with the scattered X-ray luminosity quoted above, Sako et al."504 estimate the scattering optical depth iu XN-ravs to be ~0.01 Cassimine conical scattering region of half openiueg angle507: this corresponds to the average coluun density of 1.5«107? cm7? using στι note the typo in Sako et al., estimate the scattering optical depth in X-rays to be $\sim 0.01$ (assuming conical scattering region of half opening angle; this corresponds to the average column density of $1.5\times10^{22}$ $^{-2}$ using $\sigma_T$: note the typo in Sako et al.505 2000)., 2000).506 This would mean that the average UV extinction optical thickness is ~ 10 for Calactic-tvpoe dust of the normal dust-to-gas ratio (scattering optical thickness of —5 with albedo  0.5)., This would mean that the average UV extinction optical thickness is $\sim$ 10 for Galactic-type dust of the normal dust-to-gas ratio (scattering optical thickness of $\sim 5$ with albedo $\sim 0.5$ ).507 Iu the IIST nuages. the scattering region is not filled unifoxiily. but instead it is οπαν aud re covering factor could be small. so the column leusitv through cach cloud would be even larger iui this average column deusity.," In the HST images, the scattering region is not filled uniformly, but instead it is clumpy and the covering factor could be small, so the column density through each cloud would be even larger than this average column density."508 Ouce the clouds become opaque at the UV. ie ammount of the UV scattered light will not sscitially depend on the columnu density of ch cloud. but will approximately saturate at ie amount for the extinction optical thickucss around unity.," Once the clouds become opaque at the UV, the amount of the UV scattered light will not essentially depend on the column density of each cloud, but will approximately saturate at the amount for the extinction optical thickness around unity."509 Then the scattered light amount will essentially be proportional to the coveriug factor., Then the scattered light amount will essentially be proportional to the covering factor.510 Therefore. given the same average columu denusity. if we cousider a case of 22ller covering factor (e.g. the case that the resolved clouds cousist of smaller unresolved clouds) with cach cloud having larger cohuun density. the scattered Lelt will be reduced in the UV. but not in the X-ray. as long as the clouds do not get also opaque in the X-ray.," Therefore, given the same average column density, if we consider a case of smaller covering factor (e.g. the case that the resolved clouds consist of smaller unresolved clouds) with each cloud having larger column density, the scattered light will be reduced in the UV, but not in the X-ray, as long as the clouds do not get also opaque in the X-ray."511 Thus. scattering by cluupy UV-opaque clouds. as well as electron scattering. would be consisteut with the observed. UVδαν scattered fiux ratio.," Thus, scattering by clumpy UV-opaque clouds, as well as electron scattering, would be consistent with the observed UV/X-ray scattered flux ratio."512 However. the extreme case of a very siunall covering actor. with the clouds being X-rav opaque. i.c. Conmptou-thick (covering factor of makes the col density already of order LO?! 7). seenis o be ruled out. since in this case the N-rav scattered: continuum from such clumps would be Hatter (photon index P—0 or bluer at ~110 seV. for matter that is not too lighly ionized: e.g. Aller. Ctoodrich. Mathews 1991: Ross Fabian 1993) than observed (EP for the extended scattered conrponeut is larger than 1.2: M. Sako. private conumaimuication 2001: the CCD spectrum from the zeroth order N-rav nuage is also consistent with this).," However, the extreme case of a very small covering factor, with the clouds being X-ray opaque, i.e. Compton-thick (covering factor of makes the column density already of order $10^{24}$ $^{-2}$ ), seems to be ruled out, since in this case the X-ray scattered continuum from such clumps would be flatter (photon index $\Gamma \sim 0$ or bluer at $\sim 1-10$ keV for matter that is not too highly ionized; e.g. Miller, Goodrich, Mathews 1991; Ross Fabian 1993) than observed $\Gamma$ for the extended scattered component is larger than 1.2; M. Sako, private communication 2001; the CCD spectrum from the zeroth order X-ray image is also consistent with this)."513 On the other liaud. electrou scattering might eive a siuple explanation for the UV to X-ray scattered flux ratio and the serav color iu the bright knots.," On the other hand, electron scattering might give a simple explanation for the UV to X-ray scattered flux ratio and the gray color in the bright knots."514 If this is the case. the gas in these regions should have lost its dust content almost conipletelv.," If this is the case, the gas in these regions should have lost its dust content almost completely."515 This could nÓuplv that this electron scatteringo eas cane as a wind from the nucleus. where the dust equilibrium temperature is above the sublimation temperature. though it might be odd that the eas from a wind apparently resides in knottv regions.," This could imply that this electron scattering gas came as a wind from the nucleus, where the dust equilibrium temperature is above the sublimation temperature, though it might be odd that the gas from a wind apparently resides in knotty regions."516 A rather simple alternative explanation is that the low UV scattering efficiency and grav scattering described above could be the iutrinsic properties of the dust erain population iu the ciretunmuclear region of active ealactic nuclei (AGNs)., A rather simple alternative explanation is that the low UV scattering efficiency and gray scattering described above could be the intrinsic properties of the dust grain population in the circumnuclear region of active galactic nuclei (AGNs).517 Anomalous properties of dust erains iu the AGN vicinity have been reported by several authors. aud these properties have been sunnarized recently by Molino et al. (," Anomalous properties of dust grains in the AGN vicinity have been reported by several authors, and these properties have been summarized recently by Maiolino et al. ("5182001a).,2001a).519 They have shown that the dust erams iu the cireumauclear region of 16 ACGNs have a lower reddening £py than the standard Galactic dust has for the column density δι obtained from the N-rav plotoclectric absorption., They have shown that the dust grains in the circumnuclear region of 16 AGNs have a lower reddening $E_{B-V}$ than the standard Galactic dust has for the column density $N_{\rm H}$ obtained from the X-ray photoelectric absorption.520 They also poiute out that in many cases the optical absorption zd is also lower than expected from Nyy. compare with the Galactic case.," They also pointed out that in many cases the optical absorption $A_V$ is also lower than expected from $N_{\rm521H}$, compared with the Galactic case."522 The lower Ep.yfNyy leads o relatively grav scattering. and lower νι cads to lower UV/optical scattering efficiency.," The lower $E_{B-V} / N_{\rm H}$ leads to relatively gray scattering, and lower $A_V / N_{\rm H}$ leads to lower UV/optical scattering efficiency."523 These low ely/Ny aud Epy-/Nyp cau be explained by a dust size distribution donuünuatec wolaree eraius (Laor Draine 1993: Mbüolino et al., These low $A_V / N_{\rm H}$ and $E_{B-V} / N_{\rm H}$ can be explained by a dust size distribution dominated by large grains (Laor Draine 1993; Maiolino et al.524 2001)., 2001b).525 This anomalous cistribution could ve caused bv the formation of luge grains, This anomalous distribution could be caused by the formation of large grains526our work nav wish to skip 877. and §?? aud proceed directly to. 877... where we sunuuarize our fudiugs and discuss how future polarization nieasuremients nia constrain the geometrical and rotational properties of PATIs.,"our work may wish to skip \ref{sec:model} and \ref{sec:results} and proceed directly to \ref{sec:concl}, where we summarize our findings and discuss how future polarization measurements may constrain the geometrical and rotational properties of PAHs."527 As discussed by ?.. planar PAID inolecules may enüt partially polarized light as a result of anisotropic illumination by a source of UV photons.," As discussed by \citet{leger_88}, planar PAH molecules may emit partially polarized light as a result of anisotropic illumination by a source of UV photons."528 UV absorption is favored if the molecular plane is perpendicular to the ihunination direction., UV absorption is favored if the molecular plane is perpendicular to the illumination direction.529 Following UV absorption. m-plane and out-of-plane vibrational modes are excited. producing the observed IR cussion features.," Following UV absorption, in-plane and out-of-plane vibrational modes are excited, producing the observed IR emission features."530" The erain augular momentum J stavs approximately constant during the whole process of UV absorption and IR cussion (7): first. the augulu momentum contributed by the absorbed UW photon or removed via vibrational IR cutission or rotational radio enüssion is stnall compared to the mean augular momentum of iuterstelhu PAITIs: secoudhy. collisions of the enittiug erain with interstellar atoms or ions hardly occur during the few seconds of IR cussion: finally, Larmor precession of J around the interstellar maguetic field takes much longer than the IR cussion burst (2)."," The grain angular momentum $\bJ$ stays approximately constant during the whole process of UV absorption and IR emission \citep{leger_88}: first, the angular momentum contributed by the absorbed UV photon or removed via vibrational IR emission or rotational radio emission is small compared to the mean angular momentum of interstellar PAHs; secondly, collisions of the emitting grain with interstellar atoms or ions hardly occur during the few seconds of IR emission; finally, Larmor precession of $\bJ$ around the interstellar magnetic field takes much longer than the IR emission burst \citep{rouan_92}."531. With J conserved. sole memory of the source direction is retained aud the IR enmüssiou bands will be partially polarized.," With $\bJ$ conserved, some memory of the source direction is retained and the IR emission bands will be partially polarized."532 We adopt the system of coordinates used bv ? to specity the illumination ecometry aud the oricutation of the emitting molecule 1))., We adopt the system of coordinates used by \citet{leger_88} to specify the illumination geometry and the orientation of the emitting molecule ).533 The fixed coordinate system (x.y.Z) is centered on the enüttius grain: the volar axis z is along the illumination direction and x is in the plane defined by z aud the direction n from the uolecule to the observer xu," The fixed coordinate system $(\hat{\b{x}},\hat{\b{y}},\hat{\b{z}})$ is centered on the emitting grain; the polar axis $\hat{\b{z}}$ is along the illumination direction and $\hat{\b{x}}$ is in the plane defined by $\hat{\b{z}}$ and the direction $\hat{\b{n}}$ from the molecule to the observer )."534aj) Iu this frame. the erain augular momentiun J is spherical angles 0 and y xub)).," In this frame, the grain angular momentum $\bJ$ has spherical angles $\theta$ and $\varphi$ )."535 In order to describe the position of the molecule with respect to J. we define a frame (x'.y/.z/) ceutered on the erain with 2’ aloug J aud x’ perpeudicular to the lane (z.z/). as shown in xub.," In order to describe the position of the molecule with respect to $\bJ$, we define a frame $(\hat{\b{x}}',\hat{\b{y}}',\hat{\b{z}}')$ centered on the grain with $\hat{\b{z}}'$ along $\bJ$ and $\hat{\b{x}}'$ perpendicular to the plane $(\hat{\b{z}},\hat{\b{z}}')$, as shown in ."536. We choose the erain axes of inertia (ay.a2.a;) so hat ay is the axis of largest moment of inertia (i.c.. the xincipal axis): for a disk molecule. ay is perpendicular o the plane of the molecule. whereas a» aud a5 are in the lane.," We choose the grain axes of inertia $(\hat{\b{a}}_1,\hat{\b{a}}_2,\hat{\b{a}}_3)$ so that $\ba$ is the axis of largest moment of inertia (i.e., the principal axis); for a disk molecule, $\ba$ is perpendicular to the plane of the molecule, whereas $\hat{\b{a}}_2$ and $\hat{\b{a}}_3$ are in the plane."537 Their position in the frame (x.y.z/) is described with Euler's aneles uc). untation auele. between z/ (or J) aud aq: (6 xecessiou angle. between x aud the line of nodes. i6. he intersection of the plaue (x. y/) with the molecular aue (αυ. a3): o. angle of proper rotation. between the ine of nodes and ay.," Their position in the frame $(\hat{\b{x}}',\hat{\b{y}}',\hat{\b{z}}')$ is described with Euler's angles ): $\beta$, nutation angle, between $\hat{\b{z}}'$ (or $\bJ$ ) and $\ba$; $\psi$, precession angle, between $\hat{\b{x}}'$ and the line of nodes, i.e., the intersection of the plane $(\hat{\b{x}}',\hat{\b{y}}'$ ) with the molecular plane $\hat{\b{a}}_2,\hat{\b{a}}_3$ ); $\phi$, angle of proper rotation, between the line of nodes and $\hat{\b{a}}_2$."538 The classical motion of a rigid axisviunietrie eral is a combined rotation aroundits sviuunietry axis aq aud a precession of this axis around he angular momentum J with constant Jt To describe he polarization of the enütted radiation. we define o. he angle between the illuuinatiou direction z aud the observer direction n. and the polarization directions u and v. respectively parallel and perpendicular to y iu the plane of the sky pala)}.," The classical motion of a rigid axisymmetric grain is a combined rotation aroundits symmetry axis $\ba$ and a precession of this axis around the angular momentum $\bJ$ with constant $\beta.$ To describe the polarization of the emitted radiation, we define $\alpha$, the angle between the illumination direction $\hat{\b{z}}$ and the observer direction $\hat{\b{n}}$ , and the polarization directions $\hat{\b{u}}$ and $\hat{\b{v}}$, respectively parallel and perpendicular to $\hat{\b{y}}$ in the plane of the sky )."539 The absorption cross section for incident light with electric field E is proportional to (?) where the suniniatiou is over molecular states |/j aud [/j and d is the electric dipole moment operator.," The absorption cross section for incident light with electric field $\b{E}$ is proportional to \citep{leger_88}540 where the summation is over molecular states $|i\rangle$ and $|j\rangle$ and $\b{d}$ is the electric dipole moment operator."541 The x& electronic transitions responsible for UW absorption in PAIIs have (j|d]/) ouly in the molecularplane., The $\pi-\pi^\ast$ electronic transitions responsible for UV absorption in PAHs have $\langle j|\b{d}|i\rangle$ only in the molecularplane.542 For a disk molecule. rapid spiuniug around its principal axis a4 results iu averaging over the auele of proper rotation o.," For a disk molecule, rapid spinning around its principal axis $\ba$ results in averaging over the angle of proper rotation $\phi$."543" ""Thus. the erain absorption cross section may be written. for incident mupolarized light. where Ο is the angle between the normal to the erain plane (.0.. the principal axis a4. for a disk molecule) aud the direction of propagation k of the absorbed photon."," Thus, the grain absorption cross section may be written, for incident unpolarized light, where $\Theta$ is the angle between the normal to the grain plane (i.e., the principal axis $\ba$, for a disk molecule) and the direction of propagation $\hb{k}$ of the absorbed photon."544 Iu other words. when a planar PAT faces an unpolarized source. its UV absorption cross section is twice that when it is edge-eon. because both components of the iluninatimg electric field cau be absorbed in the first case aud oulv one in the second.," In other words, when a planar PAH faces an unpolarized source, its UV absorption cross section is twice that when it is edge-on, because both components of the illuminating electric field can be absorbed in the first case and only one in the second."545 The angle O depends on the instantancous oricutation of the erain with respect to the illumination direction., The angle $\Theta$ depends on the instantaneous orientation of the grain with respect to the illumination direction.546 Ilowever. since the precession period of ay around J is ιο. shorter than the time between absorption aud cluission. we can average over the precession motion (and the precession angle c) for the absorption aud the emission process imndepenudeutlv.," However, since the precession period of $\ba$ around $\bJ$ is much shorter than the time between absorption and emission, we can average over the precession motion (and the precession angle $\psi$ ) for the absorption and the emission process independently."547 For a poiut-like ilunünatiug source. all inconuug ravs have k=z (see pana}).," For a point-like illuminating source, all incoming rays have $\hb{k}=\hb{z}$ (see )."548 The corresponding c-averaged absorption cross section. for fixed J aud a fixed angle 3 between ay aud J. is If the ilhuninating source is an exteuded disk galaxy. the augle O also depends ou the spherical aueles 0 aud £ of the rav direction k in the fixed (x.y.z) frame.," The corresponding $\psi$ -averaged absorption cross section, for fixed $\bJ$ and a fixed angle $\beta$ between $\ba$ and $\bJ$, is If the illuminating source is an extended disk galaxy, the angle $\Theta$ also depends on the spherical angles $\theta'$ and $\varphi'$ of the ray direction $\hb{k}$ in the fixed $(\hat{\b{x}},\hat{\b{y}},\hat{\b{z}})$ frame."549 We asstune that the cmutting molecules are above the ealactic center: z is then the direction from the ceuter of the galactic disk to the erains., We assume that the emitting molecules are above the galactic center; $\hat{\b z}$ is then the direction from the center of the galactic disk to the grains.550 For au axisviunetric surtace-brightnessprofile. the absorption coefficient for incomine ravs with polar angle 0 can be averaged over the azimmthal ilhuuination augle y’: where we have also averaged over the precession augle c.," For an axisymmetric surface-brightnessprofile, the absorption coefficient for incoming rays with polar angle $\theta'$ can be averaged over the azimuthal illumination angle $\varphi'$ : where we have also averaged over the precession angle $\psi$ ."551 In the previous expression. C(0..3) is the same as in eq. (3))," In the previous expression, $C(\theta,\beta)$ is the same as in eq. \ref{eq:absstar}) )"552 and we define For the sake of simplicity. in the following we assune a uniforni-briehtness disk galaxv: for ageneric," and we define For the sake of simplicity, in the following we assume a uniform-brightness disk galaxy; for ageneric"553noise seems much less severe in simulations Da3 anc Bat in which the clise is non linearly. perturbed. in agreement with the global run C5.,"noise seems much less severe in simulations Ba3 and Ba4 in which the disc is non linearly perturbed, in agreement with the global run G5."554 In these cases turbulent [uetuations seem to be less able to modulate the torque estimates and non zero net torques arising from features added to bias the box are more reacily measurable., In these cases turbulent fluctuations seem to be less able to modulate the torque estimates and non zero net torques arising from features added to bias the box are more readily measurable.555 To illustrate the reduced: effects. of noise on. the simulations with stronely perturbing protoplancts. we compare running time averages of the torques acting on the protoplanet in simulation Bat with those obtained from the corresponding laminar disc simulation in figure 24..," To illustrate the reduced effects of noise on the simulations with strongly perturbing protoplanets, we compare running time averages of the torques acting on the protoplanet in simulation Ba4 with those obtained from the corresponding laminar disc simulation in figure \ref{figbox3}."556 The averages commence from when the protoplanet was introduced., The averages commence from when the protoplanet was introduced.557 Corresponding plots from the two simulations are very similar., Corresponding plots from the two simulations are very similar.558 Note that the torques tend. to relatively weaken at later times in the laminar case., Note that the torques tend to relatively weaken at later times in the laminar case.559" This is because this simulation with (ALR?(Al,df?)=2 produces a wider and deeper gap than the turbulent case (see paper LLL).", This is because this simulation with $(M_p R^3/(M_* H^3) =2 $ produces a wider and deeper gap than the turbulent case (see paper III).560" ""Ehis in turn results in less matter for the protoplanet to interact with locally on average and hence weaker average torques at later times.", This in turn results in less matter for the protoplanet to interact with locally on average and hence weaker average torques at later times.561 Finally we comment on the magnitudes of the time averaged: one sided. torques., Finally we comment on the magnitudes of the time averaged one sided torques.562 As for the elobal runs these are similar for turbulent and. corresponding laminar disc simulations., As for the global runs these are similar for turbulent and corresponding laminar disc simulations.563 For the shearing box simulations. the fiducial value expected. for the one sided. linear torques in the 2D laminar case with no potential softening is = where the surface density X—(pd. with £p being the volume ancl time averaged. density in the box (see Ward 1907).," For the shearing box simulations, the fiducial value expected for the one sided linear torques in the 2D laminar case with no potential softening is = _p^2 ) where the surface density $\Sigma = \langle \rho \rangle H ,$ with $\langle \rho \rangle$ being the volume and time averaged density in the box (see Ward 1997)."564" For simulation Bal. 5,=1015 in our computational units making the tvpical averaged: torques about fifty. percent. of the fiducial value."," For simulation Ba1, $ F_{y0} = 10^{-13}$ in our computational units making the typical averaged torques about fifty percent of the fiducial value."565 Such a reduction may occur as a result of softening the gravitational potential due to the protoplanet (see section. 3.1. and paper LLL)., Such a reduction may occur as a result of softening the gravitational potential due to the protoplanet (see section \ref{calibration} and paper III).566 This would indicate that the magnitude of the torques is essentially given. by the laminar disc theory., This would indicate that the magnitude of the torques is essentially given by the laminar disc theory.567 However. the urbulence adds a significant noise component. when the sotoplanct mass is small enough to place the response in he linear regime.," However, the turbulence adds a significant noise component when the protoplanet mass is small enough to place the response in the linear regime."568 We comment that the averaged. torque magnitudes in Bal and Ba2 are consistent with a scaling xAIP appropriate to the linear response regime but. that he torque is weaker than suggested. by such a scaling in Da3 and Bat., We comment that the averaged torque magnitudes in Ba1 and Ba2 are consistent with a scaling $\propto M_p^2$ appropriate to the linear response regime but that the torque is weaker than suggested by such a scaling in Ba3 and Ba4.569 This is consistent with the response being non linear in those cases., This is consistent with the response being non linear in those cases.570 In this paper we have performed. both global and. local simulations of embedded: protoplanets interacting with a turbulent disc and. studied. the behaviour of the torques exerted. between the dise and. protoplancts and. the consequences for orbital migration., In this paper we have performed both global and local simulations of embedded protoplanets interacting with a turbulent disc and studied the behaviour of the torques exerted between the disc and protoplanets and the consequences for orbital migration.571" The global simulations were for a disc with ///r=0.07 that. exhibited MIID turbulence with zero net magnetic [ux withmean a~0.007. The protoplanet masses considered. were AL,=3.10 and 30 Earth masses. and 3 Jupiter masses."," The global simulations were for a disc with $H/r =0.07$ that exhibited MHD turbulence with zero net magnetic flux with mean $\alpha \sim 0.007.$ The protoplanet masses considered were $M_p= 3, 10$ and $30$ Earth masses, and 3 Jupiter masses."572" The local shearing box simulations can be characterized by values of the dimensionless parameter. AZ,/(AL2°). Phe simulations adopted: 0.1.0.3.1.0. and 2.0. respectively."," The local shearing box simulations can be characterized by values of the dimensionless parameter $M_p R^3/(M_* H^3).$ The simulations adopted $0.1, 0.3, 1.0, $ and $2.0$ respectively."573" The first two of these are directly comparable to the global simulations with Ad,=10M,. and M,=30A/, respectively."," The first two of these are directly comparable to the global simulations with $M_p= 10M_{\oplus},$ and $M_p = 30M_{\oplus}$ respectively."574 The latter two have gap forming protoplanets. but whose masses correspond. to less massive planets than the 3 Jupiter mass planet. considered. in the global run G5. and. enable the behaviour of the torques in the non linear gap forming regime to be studied.," The latter two have gap forming protoplanets, but whose masses correspond to less massive planets than the 3 Jupiter mass planet considered in the global run G5, and enable the behaviour of the torques in the non linear gap forming regime to be studied."575 For a first. study. the protoplanets considered here were held in fixed circular orbit.," For a first study, the protoplanets considered here were held in fixed circular orbit."576 ]t was abways found that the instantaneous torque experienced by a protoplanet was a highly variable quantity on account of the protoplanet interacting with the turbulent density wakes that shear past it., It was always found that the instantaneous torque experienced by a protoplanet was a highly variable quantity on account of the protoplanet interacting with the turbulent density wakes that shear past it.577 For low mass protoplanets that are not able to begin to form a gap. the torque is dominated by these Duüctuations. such that at any particular time. the usual distinction. between inner (positive) and outer (negative) dise torques is blurred.," For low mass protoplanets that are not able to begin to form a gap, the torque is dominated by these fluctuations, such that at any particular time, the usual distinction between inner (positive) and outer (negative) disc torques is blurred."578 The net. torque experienced. by embedded: protoplancts oscillates between negative and positive values. such that. the protoplanet migration is likely to occur as a random walk.," The net torque experienced by embedded protoplanets oscillates between negative and positive values, such that the protoplanet migration is likely to occur as a random walk."579 This is in, This is in580The origin of fermion masses and mixines alongwith the related problem of CP violation constitute a formidable challenge for elementary particle physics.,The origin of fermion masses and mixings alongwith the related problem of CP violation constitute a formidable challenge for elementary particle physics.581 Leaving apart extremely small neutrino masses. even the charged fermion mass hierarchy ranges over al least five orders of magnitudes.," Leaving apart extremely small neutrino masses, even the charged fermion mass hierarchy ranges over at least five orders of magnitudes."582 Since the fermion masses and (he mixing angles are derived. [vom the Yukawa couplings. which are free parameters within the Standard Model (SM). these Yukawa couplings must span several orders of magnitude to accommodate the strongly hierarchical pattern of fermion masses and mixings.," Since the fermion masses and the mixing angles are derived from the Yukawa couplings, which are free parameters within the Standard Model (SM), these Yukawa couplings must span several orders of magnitude to accommodate the strongly hierarchical pattern of fermion masses and mixings."583 However. (he currently available data on fermion masses and mixing are insullicient for an unambiguous reconstruction of lermion mass matrices.," However, the currently available data on fermion masses and mixing are insufficient for an unambiguous reconstruction of fermion mass matrices."584 To make matters worse. radiative corrections can obscure the underlving structure.," To make matters worse, radiative corrections can obscure the underlying structure."585 Thus. the existing data cannot. without some additional assumptions. determine all the elements of (he Yukawa coupling matrices for quarks and leptons.," Thus, the existing data cannot, without some additional assumptions, determine all the elements of the Yukawa coupling matrices for quarks and leptons."586 Some of these asstuuplious. invoked (o restrict (he form. of fermion mass matrices include the presence of texture zeros |L].. requirement of zero determinant 2) and zero trace condition [3]. to name just a lew.," Some of these assumptions, invoked to restrict the form of fermion mass matrices include the presence of texture zeros \cite{FGM paper}, requirement of zero determinant \cite{zero determinant} and zero trace condition \cite{zero trace} to name just a few."587 The main motivation lor invoking different mass matrix ansatze is to relate fermion masses and mixing angles in a testable manner which reduces the number of tree parameters in (he Yukawa sector of SAL, The main motivation for invoking different mass matrix ansatze is to relate fermion masses and mixing angles in a testable manner which reduces the number of free parameters in the Yukawa sector of SM.588 The recent evidence for non-zero neutrino Inasses and mixings leads (to a further proliferation of [ree parameters in (he Yukawa. sector., The recent evidence for non-zero neutrino masses and mixings leads to a further proliferation of free parameters in the Yukawa sector.589 In the absence of a significant breakthrough in the theoretical understanding of fermion flavors. (he phenomenological approaches are bound to play a crucial role in interpreting new experimental data on quark and lepton mixing.," In the absence of a significant breakthrough in the theoretical understanding of fermion flavors, the phenomenological approaches are bound to play a crucial role in interpreting new experimental data on quark and lepton mixing."590 These approaches are expected (ο provide, These approaches are expected to provide591"sources in a portion of sky all the time, monitoring all of these sources is a possibility only limited by the available computing power.","sources in a portion of sky all the time, monitoring all of these sources is a possibility only limited by the available computing power."592" Because the current slew of radio telescopes are not sensitive enough to detect typical sources for microlensing in the Galactic bulge and the Magellanic clouds, observations of local analogues must provide an estimate of the expected radio spectra of these objects."," Because the current slew of radio telescopes are not sensitive enough to detect typical sources for microlensing in the Galactic bulge and the Magellanic clouds, observations of local analogues must provide an estimate of the expected radio spectra of these objects."593" 'To survey the types of common radio sources in the bulge, it is natural to focus on local low-mass stars that also happen to be radio sources."," To survey the types of common radio sources in the bulge, it is natural to focus on local low-mass stars that also happen to be radio sources."594 Typically isolated low-mass stars do not exhibit strong continuous radio emission., Typically isolated low-mass stars do not exhibit strong continuous radio emission.595" Even at the modest distance of one parsec, the radio emission from the quiet sun is only about one pJy (?)."," Even at the modest distance of one parsec, the radio emission from the quiet sun is only about one $\mu$ Jy \citep{GalacticRadioAstronomy}."596" At one kiloparsec this is down to one pJy, well below the detection threshold of even the SKA."," At one kiloparsec this is down to one pJy, well below the detection threshold of even the SKA."597" Fortunately, evolved low-mass stars exhibit much greater quiescent radio emission than the sun; these objects will be the focus."," Fortunately, evolved low-mass stars exhibit much greater quiescent radio emission than the sun; these objects will be the focus."598 Arcturus (oa Bóootis) at 11.25 pc is one of the closest giant stars to Earth (?).., Arcturus $\alpha$ Böootis) at 11.25 pc is one of the closest giant stars to Earth \citep{1997A&A...323L..49P}.599 ? presented observations of this star at 2 cm and 6 cm with flux densities of 0.68 mJy and 0.28 mJy respectively., \citet{1986AJ.....91..602D} presented observations of this star at 2 cm and 6 cm with flux densities of 0.68 mJy and 0.28 mJy respectively.600 At both wavelengths the emission is well characterised by a brightness temperature of about 1.3x10* K — the source is larger at longer wavelengths.," At both wavelengths the emission is well characterised by a brightness temperature of about $1.3\times60110^4$ K — the source is larger at longer wavelengths."602 At a distance of 1 kpc the flux density would be using the spectral index found by ?.., At a distance of 1 kpc the flux density would be using the spectral index found by \citet{1986AJ.....91..602D}.603 This yields an expected amplitude variation of at 10 GHz., This yields an expected amplitude variation of at 10 GHz.604 The nearby variable M7-giant star Mira (o Ceti) provides an exemplar for the rarer asymptotic giant stars observed by OGLE in the bulge of our galaxy., The nearby variable M7-giant star Mira (o Ceti) provides an exemplar for the rarer asymptotic giant stars observed by OGLE in the bulge of our galaxy.605" ? find that the radio emission of Mira is well fit by a blackbody emission with S,7:θνόμ,μγ, and Hipparcos found its distance to be about 110 pc (?),, yielding a diameter of about 8 AU."," \citet{1997ApJ...476..327R} find that the radio emission of Mira is well fit by a blackbody emission with $S_\nu \approx6066\nu_\mathrm{GHz}^2 \mu\mathrm{Jy} $, and Hipparcos found its distance to be about 110 pc \citep{1997A&A...323L..49P}, yielding a diameter of about 8 AU."607" The signal of a diffractive lensing event on a Mira-like star (Ty—1500 K) at 10 GHz is given by Although an AGB star is typically more luminous that a giant both in the optical and the radio, flux only plays a subordinate role in the expected diffractive microlensing variation, the significantly lower brightness temperature of the AGB stars in the radio reduces the expected signal."," The signal of a diffractive lensing event on a Mira-like star $T_b=1500$ K) at 10 GHz is given by Although an AGB star is typically more luminous that a giant both in the optical and the radio, flux only plays a subordinate role in the expected diffractive microlensing variation, the significantly lower brightness temperature of the AGB stars in the radio reduces the expected signal."608" The M2-supergiant Betelgeuse (a Orionis) provides an exemplar for the red supergiant stars observed by OGLE in the Magellanic clouds, assuming a distance of 48 kpc to the Large Magellanic Cloud."," The M2-supergiant Betelgeuse $\alpha$ Orionis) provides an exemplar for the red supergiant stars observed by OGLE in the Magellanic clouds, assuming a distance of 48 kpc to the Large Magellanic Cloud."609" ? find that the spectrum of Betelgeuse is well characterised by S,©240viiluJy, and ? give a distance of 197 pc to this object."," \citet{1982ApJ...263L..85N} find that the spectrum of Betelgeuse is well characterised by $S_\nu \approx 240 \nu_\mathrm{GHz}^{1.32}610\mu\mathrm{Jy} $, and \citet{2008AJ....135.1430H} give a distance of 197 pc to this object."611 ? found that the photosphere at a wavelength of 7 mm subtends an ellipse about 95 mas by 80 mas., \citet{1998Natur.392..575L} found that the photosphere at a wavelength of 7 mm subtends an ellipse about 95 mas by 80 mas.612 The signal of a diffractive lensing event on a Betelgeuse-like star (T5=2500 K) at 10 GHz is given by The increased luminosity of the supergiant Betelgeuse is offset by its larger size and flatter spectrum., The signal of a diffractive lensing event on a Betelgeuse-like star $T_b=2500$ K) at 10 GHz is given by The increased luminosity of the supergiant Betelgeuse is offset by its larger size and flatter spectrum.613 ? found that the B8-supergiant Rigel (8 Orionis) has a, \citet{1989AJ.....98.1831D} found that the B8-supergiant Rigel $\beta$ Orionis) has a614luminous BSss.,luminous BSSs.615 According to above discussions. the stellar population of a cluster is assumed to be composed of (wo components in our work.," According to above discussions, the stellar population of a cluster is assumed to be composed of two components in our work."616 The first one is a package of all the menmber stars [itted. by an isochrone in the CMD. plus the low-mass stars (hat have been peeled olf by tidal effects.," The first one is a package of all the member stars fitted by an isochrone in the CMD, plus the low-mass stars that have been peeled off by tidal effects."617 This is obviously nothing but the conventional SSP model ancl named as (he SSP component for use in the following text., This is obviously nothing but the conventional SSP model and named as the SSP component for use in the following text.618 The second one includes all the other members strageling away from the isochrone., The second one includes all the other members straggling away from the isochrone.619 In the light of above discussions. only BSSs are considered into this component.," In the light of above discussions, only BSSs are considered into this component."620 We label it as the BSS component., We label it as the BSS component.621 Assuming that the cluster. CMD can be well fitted by a theoretical model. the SSP component of a cluster can be substituted with a theoretical isochrone that best. fits the age and metallicity of (he cluster.," Assuming that the cluster CMD can be well fitted by a theoretical model, the SSP component of a cluster can be substituted with a theoretical isochrone that best fits the age and metallicity of the cluster."622 While. (he BSS component is specified in the CMD with photometric data of AL95.," While, the BSS component is specified in the CMD with photometric data of AL95."623 Figure 3 shows the composite CMD of NGC 6791 as an example. where the solid line is the isochrone. the dotted line is (he zero age main sequence (ZANIS). and the dots are (he BSSs delined by photometry.," Figure 3 shows the composite CMD of NGC 6791 as an example, where the solid line is the isochrone, the dotted line is the zero age main sequence (ZAMS), and the dots are the BSSs defined by photometry."624 We notice that (here is a number of objects located below the ZAMS loci., We notice that there is a number of objects located below the ZAMS loci.625 This is partly due to observational uncertainties., This is partly due to observational uncertainties.626 It is a growing consensus (that the major mechanisms of BSS production are and merger events in close binary svstems. or stellar collisions in dense environment (Schounherner Napiwotzki 1994).," It is a growing consensus that the major mechanisms of BSS production are mass-transfer and merger events in close binary systems, or stellar collisions in dense environment (Schönnberner Napiwotzki 1994)."627 The physically interactive processes in binary svstenis will transfer fresh hydrogen fuel from hydrogen-rich envelop to hydrogen-depleted or exhausted core and re-ignite it. which makes the remnants behave like MS stars (Benz Hills L987.1992). as such. σος are treated as lvclrogen-burning MS stars in our work.," The physically interactive processes in binary systems will transfer fresh hydrogen fuel from hydrogen-rich envelop to hydrogen-depleted or exhausted core and re-ignite it, which makes the remnants behave like MS stars (Benz Hills 1987,1992), as such, BSSs are treated as hydrogen-burning MS stars in our work."628 Their masses. Iuminosities and effective temperatures can be determined by fitting their positions in the CMD with evolutionary tracks of higher masses than the turnolf.," Their masses, luminosities and effective temperatures can be determined by fitting their positions in the CMD with evolutionary tracks of higher masses than the turnoff."629 Given the effective temperature (7:5) and surface gravity (log g). a theoretical spectrum from the library (Lejeune et al.," Given the effective temperature $\it{T_{eff}}$ ) and surface gravity $\it{log}$ $\it{g}$ ), a theoretical spectrum from the library (Lejeune et al."630 1997.1993) can be assigned to the BSSs.," 1997,1998) can be assigned to the BSSs."631 This process is performed for all (he BSSs in our sample clusters., This process is performed for all the BSSs in our sample clusters.632 As shown in Figure 3. there are some BSSs located below the ZAMS.," As shown in Figure 3, there are some BSSs located below the ZAMS."633 Except for possible photometric errors. (heir missing-positions are most likely due to the helium-enrichment in the atmosphere alter merger events (Benz Ilills 1987.1992).," Except for possible photometric errors, their missing-positions are most likely due to the helium-enrichment in the atmosphere after merger events (Benz Hills 1987,1992)."634 The intrinsic properties of these stars need more carefully observational studies., The intrinsic properties of these stars need more carefully observational studies.635 In. our work. these low-Iuminositv BsSs are not considered in computing the ISEDs of the clusters. since (heir contributions to ihe integratede lightex are even much lower than the stars in the turnolf region.," In our work, these low-luminosity BSSs are not considered in computing the ISEDs of the clusters, since their contributions to the integrated light are even much lower than the stars in the turnoff region."636 In. our work. these low-Iuminositv BsSs are not considered in computing the ISEDs of the clusters. since (heir contributions to ihe integratede lightex are even much lower than the stars in the turnolf region.e," In our work, these low-luminosity BSSs are not considered in computing the ISEDs of the clusters, since their contributions to the integrated light are even much lower than the stars in the turnoff region."637than expected. however.,"than expected, however."638 The implied density fluctuations have a standard deviation of around 4 per cent., The implied density fluctuations have a standard deviation of around 4 per cent.639 In the pressure-squared-sensitive 3.5 to 7.5 keV band. the 3D pressure fluctuations appear to be 4 per cent or less.," In the pressure-squared-sensitive 3.5 to 7.5 keV band, the 3D pressure fluctuations appear to be 4 per cent or less."640 We find that there is a large difference between the signal in the A-variance spectra between the north and south of the cluster., We find that there is a large difference between the signal in the $\Delta$ -variance spectra between the north and south of the cluster.641 On the longest scales there is roughly a factor of two less A- signal in the north relative to the south., On the longest scales there is roughly a factor of two less $\Delta$ -variance signal in the north relative to the south.642 The authors thank E. Churazov for giving a talk making them aware of the A-variance method., The authors thank E. Churazov for giving a talk making them aware of the $\Delta$ -variance method.643 ACF acknowledges the support of the Royal Society., ACF acknowledges the support of the Royal Society.644'unction. i.e. the real-space boundary has a correlation function that depends on ry.,"function, i.e. the real-space boundary has a correlation function that depends on ${\bf r_p}$."645 The inclusion or exclusion of galaxies is balanced in terms of the 3D correlation function within the boundary: while we lose voids. we gain clusters and these give the same clustering signal.," The inclusion or exclusion of galaxies is balanced in terms of the 3D correlation function within the boundary; while we lose voids, we gain clusters and these give the same clustering signal."646 However. we assume that the projected field has a constant projection length. and this implies that the underdensity of the void will become larger (since we include less of the galaxies) and the overdensity of the cluster becomes larger (since we will include more of its galaxies).," However, we assume that the projected field has a constant projection length, and this implies that the underdensity of the void will become larger (since we include less of the galaxies) and the overdensity of the cluster becomes larger (since we will include more of its galaxies)."647 Thus the overall clustering signal becomes stronger., Thus the overall clustering signal becomes stronger.648 The apparent shift in galaxy positions caused by moving from real to redshift space (s..—r.) can be treated by Taylor expanding the selection function (Fisheretal.1993)... which gives to first order We consider this to be an Eulerian picture as it is based on apparent galaxy motions.," The apparent shift in galaxy positions caused by moving from real to redshift space $(s_z-r_z)$ can be treated by Taylor expanding the selection function \citep{fisher93}, which gives to first order We consider this to be an Eulerian picture as it is based on apparent galaxy motions."649 We can write to first order in 0(v)., We can write to first order in $\delta({\bf r})$ .650 Following linear theory. (5.7.) can be written as a function of the overdensity field. where 97=fb. with f being the logarithmic derivative of the linear growth rate with respect to the logarithm of the scale factor. and b the galaxy bias.," Following linear theory, $(s_z-r_z)$ can be written as a function of the overdensity field, where $\beta\equiv f/b$, with $f$ being the logarithmic derivative of the linear growth rate with respect to the logarithm of the scale factor, and $b$ the galaxy bias."651 We therefore have that If we think of ó(s.) as setting up boundaries in 5.. then substituting Eq. (8) ," We therefore have that If we think of $\phi(s_z)$ as setting up boundaries in $s_z$, then substituting Eq. \ref{eq:delp_proj_delta}) )"652into Eq. (3)), into Eq. \ref{eq:xi_proj_red1}) )653 shows that we can expect coherent apparent galaxy motion across these boundaries., shows that we can expect coherent apparent galaxy motion across these boundaries.654 Correlations between galaxies moved into the sample by the redshift-space distortions. and those already within the sample. give rise to cross erms from the two terms in Eq. (89).," Correlations between galaxies moved into the sample by the redshift-space distortions, and those already within the sample, give rise to cross terms from the two terms in Eq. \ref{eq:delp_proj_delta}) )."655 The second term in Eq. (59), The second term in Eq. \ref{eq:delp_proj_delta}) )656 also adds a component to the projected correlation function from ye coherence of the velocities at different points on the boundary., also adds a component to the projected correlation function from the coherence of the velocities at different points on the boundary.657 We see that. even with constant ó(s.) within a fixed interval. edshift-space distortions can still affect the correlation function of ye volume within the sample due to the motion of galaxies across ye boundary.," We see that, even with constant $\phi(s_z)$ within a fixed interval, redshift-space distortions can still affect the correlation function of the volume within the sample due to the motion of galaxies across the boundary."658 Modelling the effect of redshift-space distortions based on predicting galaxy motions (e.g. Regos&Szalay1995)) is difficult because we need to correlate multiple points on the boundary and internal locations within the bin., Modelling the effect of redshift-space distortions based on predicting galaxy motions (e.g. \citealt{regos95}) ) is difficult because we need to correlate multiple points on the boundary and internal locations within the bin.659 In addition to the Eulerian picture given by Eq. (89).," In addition to the Eulerian picture given by Eq. \ref{eq:delp_proj_delta}) ),"660 we can also consider a Lagrangian picture based on the redshift-space overdensity field that we wish to project., we can also consider a Lagrangian picture based on the redshift-space overdensity field that we wish to project.661 Following this equivalent picture. we can work directly with redshift-space overdensities using Eq. (3)).," Following this equivalent picture, we can work directly with redshift-space overdensities using Eq. \ref{eq:xi_proj_red1}) ),"662 In the plane-parallel approximation. we can use the redshift- correlation function of equation 5 of Hamilton(1992). as input into the projection equation.," In the plane-parallel approximation, we can use the redshift-space correlation function of equation 5 of \citet{hamilton92} as input into the projection equation."663 where I are the standard Legendre polynomials. and b is the large-scale bias of the galaxy population. being considered. f is the standard. dimensionless linear growth rate. £ is the 3-dimensional real-space correlation function. and sr is the cosine of the angle between the separation along the line of sight and the transverse separation. j/=|s.κ.α.," where $P_i$ are the standard Legendre polynomials, and $b$ is the large-scale bias of the galaxy population being considered, $f$ is the standard dimensionless linear growth rate, $\xi$ is the 3-dimensional real-space correlation function, and $\mu$ is the cosine of the angle between the separation along the line of sight and the transverse separation, $\mu\equiv|s_z-s_z^{\prime}|/d$."664 One strong advantage of the Lagrangian framework is that it is straightforward to determine the projected correlation function. even. when the galaxy selection function is discontinuous.," One strong advantage of the Lagrangian framework is that it is straightforward to determine the projected correlation function, even when the galaxy selection function is discontinuous."665 This allowssimple comparison between the results one expects to obtain with and without redshift-space distortions., This allowssimple comparison between the results one expects to obtain with and without redshift-space distortions.666 For pairs of galaxies. we can detine the mean m.τν|ri)2 ," For pairs of galaxies, we can define the mean $m_z\equiv(r_z+r_z^{\prime})/2$ "667The SCUBA LAI Degree. Extragalactic Survey (SLIADES: Alortieretal. 2005: Coppinetal.2006)) mapped 2O25dee> of sky with an RAIS of 2mnmJy. at S50um with the Submillimetre. Common-User. Bolometer Array (SCUBA: Llollandetal. 1999)).,"The SCUBA HAlf Degree Extragalactic Survey (SHADES; \citealt{Mortier}; ; \citealt{Coppin06}) ) mapped $\simeq0.25\,\mathrm{deg^{2}}$ of sky with an RMS of mJy at $850\,\mathrm{\mu m}$ with the Submillimetre Common-User Bolometer Array (SCUBA; \citealt{Holland}) )."668 The area was split approximately evenly between the Lockman Hole. (LI) and the Deep Field (SXDE)., The area was split approximately evenly between the Lockman Hole (LH) and the Deep Field (SXDF).669 Using uniform selection criteria. the survey uncovered 120 SMGs with a median ceboosted flux density of 5mJy. (Coppinetal. 2006).," Using uniform selection criteria, the survey uncovered 120 SMGs with a median deboosted flux density of $\sim\!5\,\mathrm{mJy}$ \citep{Coppin06}."670. Phe SLADES programme was designed to study the nature and evolution of high star-formation rate (SER) submillimetre galaxies (SMS) via à svstematic study of a well-characterisecl ancl statistically meaningful. sample., The SHADES programme was designed to study the nature and evolution of high star-formation rate (SFR) submillimetre galaxies (SMGs) via a systematic study of a well-characterised and statistically meaningful sample.671 The programme includes an effort to identify members of the source list at. other wavelengths using. deep follow-up cata from the radio (visonetal.2007) to X-ray. in order to characterise the SLLADES population ancl to probe the variation in the star-formation and clustering with redshift.," The programme includes an effort to identify members of the source list at other wavelengths using deep follow-up data from the radio \citep{paper3} to X-ray, in order to characterise the SHADES population and to probe the variation in the star-formation and clustering with redshift."672 Phe relatively precise positions available from the radio data greatlv aid in identifving secure counterparts at other wavelengths. which can then be used. to. provide spectroscopic or photometric redshifts (Arctxaga and to categorise the sources.," The relatively precise positions available from the radio data greatly aid in identifying secure counterparts at other wavelengths, which can then be used to provide spectroscopic or photometric redshifts \citep{paper4} and to categorise the sources."673 Even combined with knowledge of source redshift. SCUBA 8505m and millimetre wavelength. [luxes do not constrain the total dust mass of a galaxy because there is an ambiguity between column density and source temperature.," Even combined with knowledge of source redshift, SCUBA $850\,\mathrm{\mu m}$ and millimetre wavelength fluxes do not constrain the total dust mass of a galaxy because there is an ambiguity between column density and source temperature."674 The submillimetre. (submm) spectral energy. distribution (SED) of à luminous clusty galaxy arises [rom the re- at. far-infrared (PLR) wavelengths. of absorbed optical/UV. radiation [rom regions of intense star-formation (see e.g. Sanders&Mirabel19060 and references therein), The submillimetre (submm) spectral energy distribution (SED) of a luminous dusty galaxy arises from the re-emission at far-infrared (FIR) wavelengths of absorbed optical/UV radiation from regions of intense star-formation (see e.g. \citealt{SandMir} and references therein).675 Typically the dust temperature is within a factor of 2 of T4740k (Blainctal.2002).. so the restframe SED peaks in the range 120//m and the SED is almost a simple power law at the SCUBA wavelengths and longer.," Typically the dust temperature is within a factor of 2 of $T_\mathrm{d}\sim40\,\mathrm{K}$ \citep{Blain}, so the restframe SED peaks in the range $120\,\mathrm{\mu m}$ and the SED is almost a simple power law at the SCUBA wavelengths and longer."676" Ata redshift, of (2)~2 or 3. typical of SMS (Chapmanetal.2005).. the peak of the SED is. shifted o be near 350yam. and the Submillimetre High. Angular vesolution. Camera (SILABRC-IHE: Dowelletal. 2003)). αἱ he Caltech Submillimetre Observatory (CSO) is very well Lgituated to provide the photometry needed to constrain the emperatures. and therefore the luminosities and masses. of he SILXADES sources."," At a redshift of $\left\langle z\right\rangle\,{\sim}\,2$ or 3, typical of SMGs \citep{Chapman2005}, the peak of the SED is shifted to be near $350\,\mathrm{\mu m}$, and the Submillimetre High Angular Resolution Camera (SHARC-II; \citealt{Dowell}) ) at the Caltech Submillimetre Observatory (CSO) is very well situated to provide the photometry needed to constrain the temperatures, and therefore the luminosities and masses, of the SHADES sources."677 We have therefore mapped: a subset of the SILVDIZS catalogue with SILABC-IH., We have therefore mapped a subset of the SHADES catalogue with SHARC-II.678 In this paper we constrain the FIR SEDs of our sample by fitting modified. blackbocdvy curves to the FIERO photometry of 31 SUADES SAIGs including SLUARC-LL cata at 350j/m.," In this paper we constrain the FIR SEDs of our sample by fitting modified blackbody curves to the FIR photometry of 31 SHADES SMGs including SHARC-II data at $350\,\mathrm{\mu m}$."679 Sections ?? and. ?? describe the observations and data reduction., Sections \ref{obs} and \ref{dr} describe the observations and data reduction.680 Section ?? presents the 350jn flux densities of the SLLADIES galaxies and the PIR SEDs.," Section \ref{results} presents the $350\,\mathrm{\mu m}$ flux densities of the SHADES galaxies and the FIR SEDs."681 Section 77. provides a discussion of the results., Section \ref{discussion} provides a discussion of the results.682 Conclusions and. future prospects are discussed. in section ??.., Conclusions and future prospects are discussed in Section \ref{fp}.683" We adopt the Cosmological parameters from the fits in Spergeletal.(2003): O4= 0.73. Oy,= 0.27. and y=Tlkkm  7."," We adopt the Cosmological parameters from the fits in \citet{Spergel}: $\Omega_\Lambda=0.73$ , $\Omega_\mathrm{m}=0.27$ , and $H_\mathrm{0}=71$ $^{-1}$ $^{-1}$."684 SUARC-LE is a background-limited 0580 anc 450jum comnmon-user continuum camera with a 3aremin1.5arcmün Geld of view (FOV) at the 10.4-1mitre. CSO in Hawai (Dowellctal.2003).," SHARC-II is a background-limited 350 and $450\,\mathrm{\mu m}$ common-user continuum camera with a $3\,\mathrm{arcmin}\times1.5\,\mathrm{arcmin}$ field of view (FOV) at the 10.4-metre CSO in Hawaii \citep{Dowell}."685. The dish has ai very low surface error. (10.3jm. RATS at 350μαι) due to the active Dish Surface. Optimization System (Leong2005) which corrects the primary for surface. imperfections and gravitational deformations as a function of elevation angle during Observations to improve the telescope efficiency. ancl pointing.," The dish has a very low surface error $10.4\,\mathrm{\mu m}$ RMS at $350\,\mathrm{\mu m}$ ) due to the active Dish Surface Optimization System \citep{Leong} which corrects the primary for surface imperfections and gravitational deformations as a function of elevation angle during observations to improve the telescope efficiency and pointing."686 Phe result is that the CSO is probably the best telescope in the world at shorter subnim wavelengths., The result is that the CSO is probably the best telescope in the world at shorter submm wavelengths.687 The resulting beam size. (with good. focus and pointing) is Üaarcsec ENIIM at 350jim.," The resulting beam size (with good focus and pointing) is arcsec FWHM at $350\,\mathrm{\mu m}$."688 120 submunm sources have been identified in the SILADES fieles (Coppinetal.2006)., 120 submm sources have been identified in the SHADES fields \citep{Coppin06}.689. Obtaining useful photometry for the full set would require several hundred hours of excellent weather. so we have chosen to observe a carefully. chosen subset of the SILXADIZS catalogue.," Obtaining useful photometry for the full set would require several hundred hours of excellent weather, so we have chosen to observe a carefully chosen subset of the SHADES catalogue."690 Many. sources lie. close enough together that multiple targets can be selected. within a single SLLIARC-LE FOV., Many sources lie close enough together that multiple targets can be selected within a single SHARC-II FOV.691 We chose eight of our 12 fields to contain a large fraction of the SLLADIES close angular pairs., We chose eight of our 14 fields to contain a large fraction of the SHADES close angular pairs.692 This is mostly just for efficiency. but there is also a small chance that the observations would help measure clustering in the SILADES catalogue.," This is mostly just for efficiency, but there is also a small chance that the observations would help measure clustering in the SHADES catalogue."693 We chose a deliberate mixture of sources with compact. extended. or no radio counterparts (Ivisonetal.2007): 11 sources with one robust. compact radio LD: three sources with two robust compact radio counterparts: three sources with one extended-lIooking racio counterpart: ancl seven sources with no reliable radio LD.," We chose a deliberate mixture of sources with compact, extended, or no radio counterparts \citep{paper3}: 11 sources with one robust compact radio ID; three sources with two robust compact radio counterparts; three sources with one extended-looking radio counterpart; and seven sources with no reliable radio ID."694 Choosing targets with this mixture of radio characteristics could help refine the SELADIES redshift. distribution. and test if there is a sub-population with a high-redshift. tail (c.g. Dunlop2001.. [visonetal. 2006)).," Choosing targets with this mixture of radio characteristics could help refine the SHADES redshift distribution and test if there is a sub-population with a high-redshift tail (e.g. \citealt{Dunlop01}, \citealt{Ivison07}) )."695 Two of our fields were also observed by Ixovacsοἱal.(2006) or Laurentetal.(2006) (sources LOCIXS50.3. LOCIX850.1. and. LOCIXS50.41). which allows for cross-calibration. and checks of svstematies in observation and analysis.," Two of our fields were also observed by \citet{Kovacs} or \citet{Laurent06} (sources LOCK850.3, LOCK850.1, and LOCK850.41), which allows for cross-calibration and checks of systematics in observation and analysis."696 One field (LOCI44/45) covered two 850jin source candidates from a preliminary SLLADIES catalogue which were later eliminated. [rom the ollicial SILADES catalogue since they were deemed Likely to be spurious sources (Coppinotal. 200G6).," One field (LOCK44/45) covered two $850\,\mathrm{\mu m}$ source candidates from a preliminary SHADES catalogue which were later eliminated from the official SHADES catalogue since they were deemed likely to be spurious sources \citep{Coppin06}."697. This field is not used in the ensuing analysis., This field is not used in the ensuing analysis.698" ‘Ten SILADES Lockman Hole (LIED) fields were mapped over the course of four superb stable weather nights in. March 2005 and February 2006 (0.035<TmescH, 0.06)."," Ten SHADES Lockman Hole (LH) fields were mapped over the course of four superb stable weather nights in March 2005 and February 2006 $0.035\!<\!\tau_{\mathrm{225\,GHz}}\!<\!0.06$ )."699 Four additional fieldswereobserved in more marginal observing conditions., Four additional fieldswereobserved in more marginal observing conditions.700 For each fielddata were collected in LO minute scans using a non-connecting Lissajous scan pattern with small amplituces of typically aaresec in both altitude and azimuth and a ‘period’ of 1520 seconds., For each fielddata were collected in 10 minute scans using a non-connecting Lissajous scan pattern with small amplitudes of typically arcsec in both altitude and azimuth and a `period' of 15–20 seconds.701 Integration times.," Integration times,"702The optical and infrared magnitudes of the radiogalaxies immediately imply that they He at significant redshift.,The optical and infrared magnitudes of the radiogalaxies immediately imply that they lie at significant redshift.703 In particular. given the A-band Hubble diagram for faint radiosources (such as the 7C sample of Willott. Rawlings and Blundell. 2001). the A=15 magnitudes of the TOC 70233.343021 radiogalaxies suggest that they are L galaxies at redshifts of ze 1.0.," In particular, given the $K$ -band Hubble diagram for faint radiosources (such as the 7C sample of Willott, Rawlings and Blundell, 2001), the $K \approx 18$ magnitudes of the TOC J0233.3+3021 radiogalaxies suggest that they are $L^*$ galaxies at redshifts of $z\approx 1.0$ ."704 We next consider the /7JA. colours of the radiogalaxies., We next consider the $RJK$ colours of the radiogalaxies.705 It is now well-established that faint radiogalaxies at 21 are hosted by Extremely Red Objects (EROs) with colours as red as 2fyz6. (," It is now well-established that faint radiogalaxies at $z \sim 1$ are hosted by Extremely Red Objects (EROs) with colours as red as $R-K706\approx 6$. ("707e.g. Dunlop et al.,e.g. Dunlop et al.708 1996: Willott. Rawlings and Blundell. 2001).," 1996; Willott, Rawlings and Blundell, 2001)."709 This is consistent with a picure in which faint radiosources at these redshifts are hosted by old elliptical galaxies., This is consistent with a picure in which faint radiosources at these redshifts are hosted by old elliptical galaxies.710 Comparing the the radiogalaxies with galaxies in the +=1.27 cluster CIG JO8484+4453 found by Stanford et al. (, Comparing the the radiogalaxies with galaxies in the $z = 1.27$ cluster ClG J0848+4453 found by Stanford et al. (7111997). we find a close similarity in /7/ἐν magnitude diagrams (Fig. 69).,"1997), we find a close similarity in $RJK$ colour-magnitude diagrams (Fig. \ref{fig:rjk_colmag_plot}) )."712 If we plot the /7./A colours of the radiogalaxies against the track of a redshifted EO galaxy. we find that they cluster about the 27| region on colour-colour space (Fig. 7»).," If we plot the $RJK$ colours of the radiogalaxies against the track of a redshifted E0 galaxy, we find that they cluster about the $z \approx 1$ region on colour-colour space (Fig. \ref{fig:rjk_colcol_plot}) )."713 Lastly. the faint red continuum detected in the optical spectra of the radiogalaxies is also consistent with their lying at za1.," Lastly, the faint red continuum detected in the optical spectra of the radiogalaxies is also consistent with their lying at $z \approx 1$."714 These optical and infrared data do not alone demonstrate unequivocally that this overdensity of radiogalaxies is a real cluster., These optical and infrared data do not alone demonstrate unequivocally that this overdensity of radiogalaxies is a real cluster.715 However. the coincidence between the overdensity of sources and the CMB decrement leads us to conclude that we are seeing the SZ effect of a massive cluster. and that most. if not all. the radiogalaxies are eluster members.," However, the coincidence between the overdensity of sources and the CMB decrement leads us to conclude that we are seeing the SZ effect of a massive cluster, and that most, if not all, the radiogalaxies are cluster members."716 From the SZ flux on the shortest spacing. we can now estimate the gas mass of the cluster.," From the SZ flux on the shortest spacing, we can now estimate the gas mass of the cluster."717 We used (Grainge et al., We used (Grainge et al.718 2001b) to model the cluster as a spherical King-protile gas distribution. with a σας temperature of 7keV. :;-parameter 0.65. and find the best tit value of the central electron density (20) to the data for varying core radius θε.," 2001b) to model the cluster as a spherical King-profile gas distribution, with a gas temperature of 7keV, $\beta$ -parameter 0.65, and find the best fit value of the central electron density $n_0$ ) to the data for varying core radius $\theta_C$."719 While the temperature and .? parameter are unknown in the absence of deep X-ray imaging. the values we assume are typical of those which have been been measured in X-ray selected 2>0.5 clusters (see. e.g.. Grego et al.," While the temperature and $\beta$ parameter are unknown in the absence of deep X-ray imaging, the values we assume are typical of those which have been been measured in X-ray selected $720z > 0.5$ clusters (see, e.g., Grego et al."721 2001 for a summary)., 2001 for a summary).722" For an Oy,=0.3. O4=0.7 cosmology. with {ο=65kms ‘Mpc 1 we find that the gas mass within a radius of 1 Mpe is proportiona to ar7,"," For an $\Omega_M = 0.3$, $\Omega_{\Lambda} = 0.7$ cosmology, with $H_0 =72365$ $^{-1}$ $^{-1}$, we find that the gas mass within a radius of 1 Mpc is proportional to $\theta_C^{1/2}$."724" We place the constraint θε>20"" from our measuremen that the flux on the second shortest RT baseline is less than 200 rly.", We place the constraint $\theta_C>20^{\prime\prime}$ from our measurement that the flux on the second shortest RT baseline is less than 200 $\mu$ Jy.725 This core radius corresponds to a physical distance of 178 Kpe and the appropriate best fit model has ny=10mi*5 and a centra decrement of 900 ;;K. We therefore estimate that the minimum gas mass of the cluster is 5«107744..., This core radius corresponds to a physical distance of 178 kpc and the appropriate best fit model has $n_0 = 10^4~\rm m^{-3}$ and a central decrement of $900~\mu$ K. We therefore estimate that the minimum gas mass of the cluster is $5 \times 10^{13} M_{\odot}$.726 Assuming that the total mass of the cluster is ten times greater than this. TOC J0233.34-3021 is clearly a massive cluster similar to those identified at 2>0.5 in X-ray surveys such as EMSS.," Assuming that the total mass of the cluster is ten times greater than this, TOC J0233.3+3021 is clearly a massive cluster similar to those identified at $z > 0.5$ in X-ray surveys such as EMSS."727 The accurate measurement of the properties of this population of high-z massive clusters is a significant goal in observationa cosmology., The accurate measurement of the properties of this population of $z$ massive clusters is a significant goal in observational cosmology.728 In this Letter. we have demonstrated that current SZ observations are effective in confirming high-z cluster candidates which have been selected by other means: SZ investigations of other TOCcandidates are continuing.," In this Letter, we have demonstrated that current SZ observations are effective in confirming $z$ cluster candidates which have been selected by other means; SZ investigations of other TOCcandidates are continuing."729 The new generation of SZ survey telescopes will not be restricted to the use of “signposts” to high-z clusters. and promise to detect the majority of the distan οuster population.," The new generation of SZ survey telescopes will not be restricted to the use of `signposts' to $z$ clusters, and promise to detect the majority of the distant cluster population."730through the large uncertaiuties for the retrieved masses.,through the large uncertainties for the retrieved masses.731 The fact that the stars in he Andersen sample are all nearby. and therefore are roughly of solar metallicitv is very useful to demonstrate this feature.," The fact that the stars in the Andersen sample are all nearby, and therefore are roughly of solar metallicity is very useful to demonstrate this feature."732 Fie. 3..," Fig. \ref{Fig2solar},"733 represeuts a coniparison of the same magnitudes as in Fie. 2..," represents a comparison of the same magnitudes as in Fig. \ref{Fig2},"734 but now the masses. radii ik Tags have been estimated assundue roughly solar metallicitv. 0.7« |Fe/T] « POLL). ane then further restricting he set of isochrones.," but now the masses, radii, and $T_{\rm eff}$ s, have been estimated assuming roughly solar metallicity $-0.7 <$ [Fe/H] $< +0.4$ ), and then further restricting the set of isochrones."735 The aerecmuent between observed and predicted radii nuproves very lile. as reflects the standard deviation of aud 1ο significant improvement is achieved iu the effective temperature. but the tendency to underestimate sole of the masses no louger exists: the standard deviation of the relative differences between predicted aud observed lnasses is now reduced toS%.," The agreement between observed and predicted radii improves very little, as reflects the standard deviation of, and no significant improvement is achieved in the effective temperature, but the tendency to underestimate some of the masses no longer exists: the standard deviation of the relative differences between predicted and observed masses is now reduced to."736. These results indicate that the combination of these masses and radii will cad to eravitics estimates with a standard deviation iu logg of 0.06 dex., These results indicate that the combination of these masses and radii will lead to gravities estimates with a standard deviation in $\log g$ of 0.06 dex.737 For low-eravity stars of solar mictallicity. a sanaller mass will be derived by asstunineg the star to be inetal-poor. aud then the average of all metallicitics underestimate the true value. as shown in Fig. 2..," For low-gravity stars of solar metallicity, a smaller mass will be derived by assuming the star to be metal-poor, and then the average of all metallicities underestimate the true value, as shown in Fig. \ref{Fig2}."738 Ouly one of the stars in Andersen's sample (TZ For A) has a eravity lower than logy=3 and hence the sample is restricted to objects on. or close to the nin sequence.," Only one of the stars in Andersen's sample (TZ For A) has a gravity lower than $\log g = 3$ and hence the sample is restricted to objects on, or close to the main sequence."739 To avoid this restriction we have extended the suuple including a few of other svstcus with somewhat poorer deteriunations., To avoid this restriction we have extended the sample including a few of other systems with somewhat poorer determinations.740 We lave included the 5 resolved spectroscopic binaries compiled by Popper (1980): TID1I6739. IID16861. Ó Equ. Capella. aud Spica: and 2 detached subgiaut eclipsing svsteiis: TY Pyx aud Z IIo. also iucluded in the compilation bx Popper.," We have included the 5 resolved spectroscopic binaries compiled by Popper (1980): HD16739, HD168614, $\delta$ Equ, Capella, and Spica; and 2 detached subgiant eclipsing systems: TY Pyx and Z Her, also included in the compilation by Popper."741 The sunuple was completed with the studies of ¢ Ai by Bennett et al. (, The sample was completed with the studies of $\zeta$ Aur by Bennett et al. (7421996) and + Per bx Popper McAlister (1957).,1996) and $\gamma$ Per by Popper McAlister (1987).743 The D.V for the two compoucuts of 5 Per have been estimated from their spectral type aud the tables of Aller et al. (, The B–V for the two components of $\gamma$ Per have been estimated from their spectral type and the tables of Aller et al. (7441982).,1982).745 dogs are xovided for the stars in these systems. the resolved spectroscopic binaries with open circles. aud the two components of + Per aud ¢ Aur with asterisks.," $T_{\rm eff}$ s are provided for the stars in these systems, the resolved spectroscopic binaries with open circles, and the two components of $\gamma$ Per and $\zeta$ Aur with asterisks."746 Fie., Fig.747 1 , \ref{Fig3} 748 (?): P.x VF.,\citep{1972ApJ...171..565S}: : $P \propto \sqrt{t}$ .749 In ? we demonstrated that this braking law is not applicable in the pre-main sequence evolution of VLM objects. because it predicts periods 2 4ddays at  LOOMAIvr. while the upper WLAL period. limit at. this age. reliably determined from the available period and esinὁ data. is only ~2 clays.," In \citet{2004A&A...421..259S} we demonstrated that this braking law is not applicable in the pre-main sequence evolution of VLM objects, because it predicts periods $>4$ days at $\sim 100$ Myr, while the upper VLM period limit at this age, reliably determined from the available period and $v\sin i$ data, is only $\sim 2$ days."750 Thus. à more moderate braking law has to be used. as it is expected for objects with saturated dvnamo (22). or for objects with a strong concentration of magnetic [ux near the pole (2)..," Thus, a more moderate braking law has to be used, as it is expected for objects with saturated dynamo \citep{2000AJ....119.1303T,2003ApJ...586..464B} or for objects with a strong concentration of magnetic flux near the pole \citep{1997A&A...324..943S}."751 We use here an exponential form for the braking law Pxexp(/). as it is expected for à saturated dyvnamo.," We use here an exponential form for the braking law $P \propto \exp{(t)}$, as it is expected for a saturated dynamo."752 Civen the lack of understanding for the uncerlving physies for this tvpe of rotational braking. this should be treated as an ad-hoc solution to provide moderate braking. rather than an accurate physical mocel.," Given the lack of understanding for the underlying physics for this type of rotational braking, this should be treated as an ad-hoc solution to provide moderate braking, rather than an accurate physical model."753 ‘Taken together. the rotational evolution can he expressed as: (42): initial raclius. £y: final radius. £: initial period) with a=1 for zero wind braking and a=exp(//7) for exponential braking. where 7 is the braking (or spin-down) timescale.," Taken together, the rotational evolution can be expressed as: $R_i$: initial radius, $R_f$ : final radius, $P_i$ : initial period) with $\alpha = 1$ for zero wind braking and $\alpha = \exp{(t/\tau)}$ for exponential braking, where $\tau$ is the braking (or spin-down) timescale."754 In Fig., In Fig.755 3. we plot both cases. no braking with dotted. lines. exponential braking with dashed. lines.," \ref{f3} we plot both cases, no braking with dotted lines, exponential braking with dashed lines."756 The rotational evolution is shown for M... starting at D;—40 hh (upper limit in the Pleiades) and AL. . starting P; -—3hh (lower limit in the Pleiades).," The rotational evolution is shown for $\,M_{\odot}$, starting at $P_i=40$ h (upper limit in the Pleiades) and $\,M_{\odot}$ , starting $P_i=3$ h (lower limit in the Pleiades)."757 Phe different values for 2 were chosen to relleet the P-M relationship discussed in Sect. 4.1.., The different values for $P_i$ were chosen to reflect the P-M relationship discussed in Sect. \ref{rotmass}.758 As can be seen from the tracks. changing the mass does not significantly allect model tracks.," As can be seen from the tracks, changing the mass does not significantly affect model tracks."759 In the discussion of this plot. it is important not to be misguided by the small number of periods.," In the discussion of this plot, it is important not to be misguided by the small number of periods."760 In particular. it is essential to keep in mind that the Praesepe period range is probably incomplete (in contrast to the younger clusters).," In particular, it is essential to keep in mind that the Praesepe period range is probably incomplete (in contrast to the younger clusters)."761 Thus. rather than reproducing upper and lower period limits. the rotational evolutionary tracks should simply be able to explain the of the periods. measured. in Pracsepe.," Thus, rather than reproducing upper and lower period limits, the rotational evolutionary tracks should simply be able to explain the of the periods measured in Praesepe."762 As can be seen in Fig 3..," As can be seen in Fig. \ref{f3},"763 tracks without any braking on the main sequence (dotted lines) have problems reproducing the longest. periods measured. so far in NGC2516. M4. ancl Praesepe.," tracks without any braking on the main sequence (dotted lines) have problems reproducing the longest periods measured so far in NGC2516, M34, and Praesepe."764 Thus. some rotational braking on the main-sequence is likely occuring among WLAL objects. in agreement with our findines in ?..," Thus, some rotational braking on the main-sequence is likely occuring among VLM objects, in agreement with our findings in \citet{2004A&A...421..259S}."765 From the tracks for exponential braking. we can rule out that the braking imescale 7 is shorter than MMSyr: Such low values for T would imply that an object with 3hh rotation period at MMyr (lower limit in the Pleiades) has à period longer han 100hh at the age of Praesepe thus not allowing for any of our five measured. periods.," From the tracks for exponential braking, we can rule out that the braking timescale $\tau$ is shorter than Myr: Such low values for $\tau$ would imply that an object with h rotation period at Myr (lower limit in the Pleiades) has a period longer than h at the age of Praesepe – thus not allowing for any of our five measured periods."766 The plausible range for he braking timescales is between MMyr ancl Gyr (in Fig., The plausible range for the braking timescales is between Myr and Gyr (in Fig.767 3. we show the tracks for 7=600MMwyr)., \ref{f3} we show the tracks for $\tau = 600$ Myr).768 ‘These results are mostly consistent with earlier findings or the spin-down timescale in theVLM regime., These results are mostly consistent with earlier findings for the spin-down timescale in theVLM regime.769 In ? we conclude that the rotational braking in the VLM regime occurs on timescales of a few hundred Alves’., In \citet{2004A&A...421..259S} we conclude that the rotational braking in the VLM regime occurs on timescales of a 'few hundred Myrs'.770 Consistentlv. 7 [ind a value of τς246£55 MMyvr from a comparison of esin? in Pleiades and Hades.," Consistently, \citet{2000AJ....119.1303T} find a value of $\tau = 246 \pm 55$ Myr from a comparison of $v\sin i$ in Pleiades and Hyades."771 Several studies point to spin-clown timescales in the range of or larger than Gyr (??7)..," Several studies point to spin-down timescales in the range of or larger than Gyr \citep{1998A&A...331..581D,2000ApJ...534..335S,2003ApJ...586..464B}."772 ALL these estimates are in order-ol-maenituce agreement with our new constraint., All these estimates are in order-of-magnitude agreement with our new constraint.773 Taken together. the available rotational data for VLAL objects. favours. the occurence of weak rotational braking on the main-sequence. with exponential spin-down timescales larger than MMyr. maybe as long as à few Ces.," Taken together, the available rotational data for VLM objects favours the occurence of weak rotational braking on the main-sequence, with exponential spin-down timescales larger than Myr, maybe as long as a few Gyrs."774 According to 7.. the spin-down timescales for [ast rotating Ci-stars in voung open clusters are ~30 MMyr.," According to \citet{2003ApJ...586..464B}, the spin-down timescales for fast rotating G-stars in young open clusters are $\sim 30$ Myr."775 Thus. among VLM objects. the spin-down happens at a much slower rate than lor solar-mass stars: the braking timescales are 10-100. times longer.," Thus, among VLM objects, the spin-down happens at a much slower rate than for solar-mass stars: the braking timescales are 10-100 times longer."776 This results in fast rotating main-scquence objects. as already evidenced: by the rotation vs. mass plot in Sect. 4.1..," This results in fast rotating main-sequence objects, as already evidenced by the rotation vs. mass plot in Sect. \ref{rotmass}."777 Both finclines. the steep drop in rotation. periods and the similarly. steep increase in the spin-down timescales. are. complementary observational manifestation of a fundamental change in the angular momentum regulation in the VLM regime.," Both findings, the steep drop in rotation periods and the similarly steep increase in the spin-down timescales, are complementary observational manifestation of a fundamental change in the angular momentum regulation in the VLM regime."778 Rotation periods havebeen measured. from photometric monitoring for five stars in theopencluster. Praesepe (age «το MMyr). all with masses <0.5 M..," Rotation periods havebeen measured from photometric monitoring for five stars in theopencluster Praesepe (age $\sim$ Myr), all with masses $<0.5\,M_{\odot}$ ."779 Our work demonstrates that itis possible to obtain reliableperiods for faint objects at the bottom of the main-sequence using, Our work demonstrates that itis possible to obtain reliableperiods for faint objects at the bottom of the main-sequence using780Once a displacement aud orientation of the vortex line are given al. for example. z = 0. we can solve equations (16)) aud (17)) and derive (he equilibrium configurations of vortex lines.,"Once a displacement and orientation of the vortex line are given at, for example, z = 0, we can solve equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) and derive the equilibrium configurations of vortex lines."781 llerealter. for numerical calculations we use the physical parameters such as the pinning energy. the coherence length and the lattice constant at densities of pe3.4x10P&em where a large fraction of crust supertIuids resides and (he pinning energv peaks.," Hereafter, for numerical calculations we use the physical parameters such as the pinning energy, the coherence length and the lattice constant at densities of $\rho782\sim 3.4 \times 10^{13}\mbox{ g cm}^{-3}$, where a large fraction of crust superfluids resides and the pinning energy peaks."783 We adopt eo101ems+ for the superfhüd velocity unless otherwise stated.," We adopt $v_s \sim 10^4 \mbox{784cm s}^{-1}$ for the superfluid velocity unless otherwise stated."785 The first. second ancl third terms in equations (16)) and (17)) correspond to the pinning force. (he Magnus force and the vortex tension. respectivelv.," The first, second and third terms in equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) correspond to the pinning force, the Magnus force and the vortex tension, respectively."786" The pinning force per site is E,~9.6x10"" dvne and the vortex tension is T~8.1xLO"" dyne. while the Magnus fororce acting{ing on tlthe vortexri sectiontion of a length:length corresponding to the latilattice constantnstant eα iis prea~3.9x107 dvne."," The pinning force per site is $F_p \sim 9.6 \times 10^5$ dyne and the vortex tension is $T \sim 8.1 \times 10^7 $ dyne, while the Magnus force acting on the vortex section of a length corresponding to the lattice constant $a$ is $\rho \kappa v_s a \sim 3.9 \times 10^3$ dyne."787 We note that the Magnus term is much smaller than the pinning and tension terms., We note that the Magnus term is much smaller than the pinning and tension terms.788 We should note that equations (16)) and (17)) are analogous to the energy conservation equation for the particle motion n a potential well., We should note that equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) are analogous to the energy conservation equation for the particle motion in a potential well.789 The first and second terms and. third term on the left hand side of equations (16)) and (17)) may correspond to the potential ancl kinetic energies in the particle motion. respectively. while the integration constant on the right hand side to the total energy.," The first and second terms and third term on the left hand side of equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) may correspond to the potential and kinetic energies in the particle motion, respectively, while the integration constant on the right hand side to the total energy."790 The gradient of the vortex line against the z-axis may be looked as the velocity of a particle., The gradient of the vortex line against the z-axis may be looked as the velocity of a particle.791" The dillerence between the “total aud potential energies"" vields the gradient of the vortex line."," The difference between the ""total and potential energies"" yields the gradient of the vortex line."792 The pinning term in equation (16)) (equation (11))) has peaks al o=2nz (6= 2nz) with n being integer. while (he Magnus term increases (decreases) linearly with ὁ (0).," The pinning term in equation \ref{eq:stst-int1}) ) (equation \ref{eq:stst-int2}) )) has peaks at $\phi =2n\pi$ $\psi =2n\pi$ ) with $n$ being integer, while the Magnus term increases (decreases) linearly with $\phi$ $\psi$ )."793 As easily inferred [rom this analogy. solutions to equations (16)) and (17)) can be elassifiecl into the three characteristic cases in terms of the magnitude ol the integration constant ( the total οποιον) relative to the peak values of the potential enerev due to the pinning and Magnus forces.," As easily inferred from this analogy, solutions to equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) can be classified into the three characteristic cases in terms of the magnitude of the integration constant ( the ""total energy"") relative to the peak values of the potential energy due to the pinning and Magnus forces."794" Let us consider the case where the integration5 constant (the total οποιονSS) in equations (16)) and (17)) is just equal to a peak value of the sum of pinning and Magnus terms (the ""potential energv)."," Let us consider the case where the integration constant (the ""total energy"") in equations \ref{eq:stst-int1}) ) and \ref{eq:stst-int2}) ) is just equal to a peak value of the sum of pinning and Magnus terms (the ""potential energy"")."795 The derivative of © and c will respect to z should be zero over an entire vortex line., The derivative of $\phi$ and $\psi$ with respect to z should be zero over an entire vortex line.796 Hence. the equilibrium solution for the vortex configuration is a straight line which is in parallel with the z-axis or the major axis of a single crystal lattice (Fig. 1)).," Hence, the equilibrium solution for the vortex configuration is a straight line which is in parallel with the z-axis or the major axis of a single crystal lattice (Fig. \ref{straight}) )."797 Note that the average orientation of a vortex line expresses (he direction of the rotation axis., Note that the average orientation of a vortex line expresses the direction of the rotation axis.798 Thus. (he rotation axis of the star is also parallel to the z-axis.," Thus, the rotation axis of the star is also parallel to the z-axis."799 When the Magnus, When the Magnus800"de Vaucouleurs. G.. de Vaucouleurs. A.. Corwin. IL.G.. Buta. B.J.. Paturel. G.. Fouque. P. 1991 ""Third Beference Catalaogue of Bright Galaxies”. 5Springer-Verlag: New York Freedman. W. L. 1983.ApJ.. 326. 691 Gieren W.. et al.","de Vaucouleurs, G., de Vaucouleurs, A., Corwin, H.G., Buta, R.J., Paturel, G., Fouque, P. 1991 “Third Reference Catalaogue of Bright Galaxies”, Springer-Verlag: New York Freedman, W. L. 1988, 326, 691 Gieren W., et al."801 2006.ÀpJ.. G17. 1056 Grieve. G.R Madore. D.F.. Welch. D.L. 1935.Αρ... 294. 513 Jackson. D.C... Skillman. E.D.. Gehrz. R.D.. Polomski. E.. Woodward. CLE.. 2007a," 2006, 647, 1056 Grieve, G.R Madore, B.F., Welch, D.L. 1985, 294, 513 Jackson, D.C., Skillman, E.D., Gehrz, R.D., Polomski, E., Woodward, C.E., 2007a"802medlev of populations.,medley of populations.803 Paper IV. describes the Ser field as a composite of seven populations (see (heir Fieuree 2). the most prominent of which are shown in Figuree 4:," Paper IV describes the Sgr field as a composite of seven populations (see their Figure 2), the most prominent of which are shown in Figure\ref{f:sgrbgdem}: :"804channels.,channels.805 These channels were combined iuto one sinele channel of 10.625 MITz bandwidth aud centered at 15.653 Cz. covering most of the expected CO L0 emission line.," These channels were combined into one single channel of 40.625 MHz bandwidth and centered at 45.653 GHz, covering most of the expected CO $1-0$ emission line."806 We also performed contimmun obscrvatious of this source by placing two 50 MITIz chanuels at cach side of the expected CO L0 line., We also performed continuum observations of this source by placing two 50 MHz channels at each side of the expected CO $1-0$ line.807 These channels were centered at 15.585 CGIIz and 15.685 GIIz. respectively.," These channels were centered at 45.585 GHz and 45.685 GHz, respectively."808 The higher frequency channel overlaps the central 10.625 Mz baudwidth region bv 18 MIIZ., The higher frequency channel overlaps the central 40.625 MHz bandwidth region by 18 MHz.809 Iu all cases. we used fast-switching calibration uk observed the VLA calibrators | 57Ls and 30286 1305) for fux calibration.," In all cases, we used fast-switching calibration and observed the VLA calibrators $+$ 5748 and 3C286 $+$ 305) for flux calibration."810 The AIPS software was used for data editing aud calibration., The AIPS software was used for data editing and calibration.811 Most of the data showed good phase stability: however. some time ranges were removed due to antennae with bac amplitudes.," Most of the data showed good phase stability; however, some time ranges were removed due to antennae with bad amplitudes."812 Finally. we used the AIPS task IMACR. which ciuplovs the CLEAN algoritlin. aud uatura weighting to deconvolve the images down to residuals of ~lo in a box ceutered on our targets.," Finally, we used the AIPS task IMAGR, which employs the CLEAN algorithm, and natural weighting to deconvolve the images down to residuals of $\sim1\sigma$ in a box centered on our targets."813 Table 1 sunmnarzes the relevant observational parameters., Table \ref{table:1} summarizes the relevant observational parameters.814" We also perforned observations of two of our Dzl ealaxics with the/ Robert C. Byrd Cacen Bank elescope (GBT) during 2009 April aud 2009 October to November, wader very good weather conditions."," We also performed observations of two of our BzK galaxies with the Robert C. Byrd Green Bank telescope (GBT) during 2009 April and 2009 October to November, under very good weather conditions."815 Typical computed opacities at 15 CGIIz are 7Ot0.2 and uicasured wind velocities were <2 m 1., Typical computed opacities at 45 GHz are $\tau\sim0.1-0.2$ and measured wind velocities were $\lesssim2$ m $^{-1}$.816" At these yequencies the GBT beam is ~16"".", At these frequencies the GBT beam is $\sim16\arcsec$.817 We observed in sub-reflector nodding mode. with a halfevele time of 6 s. At the begiuniug of cach run. we observed the following flux density calibrators for 10 mun cach: 3€286. 3CLIT or 30205.," We observed in sub-reflector nodding mode, with a half-cycle time of 6 s. At the beginning of each run, we observed the following flux density calibrators for 10 min each: 3C286, 3C147 or 3C295."818 We estimate our measured fiuxes densities to rc accurate within 410%., We estimate our measured fluxes densities to be accurate within $\pm10\%$.819 We used the source | 511 as the pointing aud focus calibrator., We used the source $+$ 514 as the pointing and focus calibrator.820 Potting aud focus were checked every 30 miu to 1 h depending on the stability aud accuracy of t1e obained corrections 1n cach run., Pointing and focus were checked every 30 min to 1 h depending on the stability and accuracy of the obtained corrections in each run.821 Pointing was stable within 5” in all uus, Pointing was stable within $5\arcsec$ in all runs.822 Typical system temperatures at 15.7 Clg aud 16.7 GIIz were in the range 85-110 Kh. We emploved two IFs of s00 AIIz bandwidth cach aud two polarizations each. with a spectral resolution of 390.625 kITz per chauucl. or ~2.6 ]au | per channel.," Typical system temperatures at 45.7 GHz and 46.7 GHz were in the range 85-110 K. We employed two IFs of 800 MHz bandwidth each and two polarizations each, with a spectral resolution of 390.625 kHz per channel, or $\sim$ 2.6 km $^{-1}$ per channel."823 We placed the couter of both IPs 200 ΑΠ from cach other and about 100 MITz from the line frequency each., We placed the center of both IFs 200 MHz from each other and about 100 MHz from the line frequency each.824 In this way. the overlap region covered a baud of ~600 MIIz.," In this way, the overlap region covered a band of $\sim$ 600 MHz."825 The data were reduced using the GBTIDL software. removing a few scaus that presented bad chamnels or strongly distorted baselines.," The data were reduced using the GBTIDL software, removing a few scans that presented bad channels or strongly distorted baselines."826 For cach source. we averaged all scans aud both TFs.," For each source, we averaged all scans and both IFs."827 The combination of both IFs produce a gain of about 5LO% in the obtained signal-to-noise ratio due to digitization noise., The combination of both IFs produce a gain of about $5-10\%$ in the obtained signal-to-noise ratio due to digitization noise.828 We fitted polvuouials of order 3) and subtracted them from the averaged spectra., We fitted polynomials of order 3 and subtracted them from the averaged spectra.829 This eblimiuates baseline structure on scales ~2 times larger than the expected dinewidtht of the CO lines., This eliminates baseline structure on scales $\sim2$ times larger than the expected linewidth of the CO lines.830 Finally. we downeraded their spectral," Finally, we downgraded their spectral"831pointing also covered by the Stripe 82 scans in the Sloan Digital Sky Survey (SDSS); the SDSS photometry of sources identified as point-like was used to derive the zero point in the SUBARU image.,pointing also covered by the Stripe 82 scans in the Sloan Digital Sky Survey (SDSS); the SDSS photometry of sources identified as point-like was used to derive the zero point in the SUBARU image.832" In the case of the MEGACAM-CFHT u* band images, reduced images and photometric zero points are already available from the CADC public archive, hence only astrometric calibration and stacking were required."," In the case of the MEGACAM-CFHT $u^*$ band images, reduced images and photometric zero points are already available from the CADC public archive, hence only astrometric calibration and stacking were required."833 Table 2 summarizes the photometric properties of the final coadded images (average FWHMs and limiting magnitudes for point-like sources) for each band., Table \ref{MagSeeing} summarizes the photometric properties of the final coadded images (average FWHMs and limiting magnitudes for point-like sources) for each band.834 All magnitudes were converted to the AB system; magnitudes of sources classified as galaxies were corrected for Galactic extinction using the Schlegel maps (?).., All magnitudes were converted to the AB system; magnitudes of sources classified as galaxies were corrected for Galactic extinction using the Schlegel maps \citep{schlegel}.835 The weak lensing analysis was done on the R—band image., The weak lensing analysis was done on the $R-$ band image.836" The masking of reflection haloes and diffraction spikes near bright stars are performed byExAM,, a code developed for this purpose."," The masking of reflection haloes and diffraction spikes near bright stars are performed by, a code developed for this purpose."837" In short, takes the catalog as input, locates the stellar locus in the size-magnitude diagram (see Sect. 4.1)),"," In short, takes the catalog as input, locates the stellar locus in the size-magnitude diagram (see Sect. \ref{sec:sgclass}) ),"838" picks out stars with spike-like features from the isophotal shape analysis, and outputs mask region file that may be visualized in the software, and finally creates a mask image in FITS format."," picks out stars with spike-like features from the isophotal shape analysis, and outputs mask region file that may be visualized in the software, and finally creates a mask image in FITS format."839" The reflection haloes are masked by estimating the background contrast near the bright stars, whose positions are obtained from the USNO-B1."," The reflection haloes are masked by estimating the background contrast near the bright stars, whose positions are obtained from the USNO–B1."840 The effective area available after removal of regions masked in such way was 801 arcmin?., The effective area available after removal of regions masked in such way was 801 $^2$.841" Catalogs for the other bands were extracted using in dual-mode, where the R—band image was used as the detection image."," Catalogs for the other bands were extracted using in dual–mode, where the $R-$ band image was used as the detection image."842" Photometric redshifts were computed from uBVRIz photometry, using the code (?).."," Photometric redshifts were computed from $uBVRIz$ photometry, using the code \citep{Feldmann06}."843" This software allows to define 6 basic templates (elliptical, Sbc, Sbd, irregular and two starburst SEDs), and to compute log-interpolations between each pair of adjacent templates."," This software allows to define 6 basic templates (elliptical, Sbc, Sbd, irregular and two starburst SEDs), and to compute log-interpolations between each pair of adjacent templates."844" We first applied to the BVz magnitudes the offset derived within the COSMOS survey by ?,, that is +0.19 (B), +0.04 (V), -0.04 (z)."," We first applied to the $BVz$ magnitudes the offset derived within the COSMOS survey by \cite{capak07}, that is +0.19 $B$ ), +0.04 $V$ ), -0.04 $z$ )."845" We then convolved the stellar spectra from the Pickles’ library (?) with the transmission curves used for each filter, and derivedthe offsets for the other filters, that is: 0.0 (u), 0.0 (R), +0.05 (D)."," We then convolved the stellar spectra from the Pickles' library \citep{Pickles} with the transmission curves used for each filter, and derivedthe offsets for the other filters, that is: 0.0 $u$ ), 0.0 $R$ ), +0.05 $I$ )."846 Fig., Fig.847" 3 shows the comparison of the model colors with those derived for the stars in our catalogs, after the above offsets were applied."," \ref{fig:stars} shows the comparison of the model colors with those derived for the stars in our catalogs, after the above offsets were applied."848" We also verified that the offsets derived in this way are consistent with those obtained by running in the so-called photometry-check mode, that allows to compute magnitude offsets minimizing the average residuals of observed versus template magnitudes."," We also verified that the offsets derived in this way are consistent with those obtained by running in the so-called photometry-check mode, that allows to compute magnitude offsets minimizing the average residuals of observed versus template magnitudes."849" We then removed from the catalog those galaxies with a photometric redshift zp,>3 and σα+z)>0., where c; was derived from the 68%--level errors computed inZEBRA."," We then removed from the catalog those galaxies with a photometric redshift $z_{\rm ph} >3$ and $\sigma_z/(1+z) > 0.1$, where $\sigma_z$ was derived from the –level errors computed in."850 The distribution of the so-obtained photometric redshifts is displayed in Fig. 4.., The distribution of the so-obtained photometric redshifts is displayed in Fig. \ref{fig:zhisto}.851" The accuracy of the so obtained photometric redshifts was derived from the comparison with the SDSS photometric redshifts of galaxies in the SDSS (DR7), whose rms error is ~0.025 for r’«20 mag."," The accuracy of the so obtained photometric redshifts was derived from the comparison with the SDSS photometric redshifts of galaxies in the SDSS (DR7), whose rms error is $\sim 0.025$ for $r' < 20$ mag."852 We derived (Fig. 1)), We derived (Fig. \ref{fig:sdss}) )853 a systematic offset Az/(1+z)=0.003 and an rms error oAz/(1+z)= 0.07., a systematic offset $\Delta z / (1+z) = 0.003$ and an rms error $\sigma \Delta z / (1+z) = 0.07$ .854" As a further check, we extracted"," As a further check, we extracted"855aand pprovide equally good eestimates to within a factor of —2.,and provide equally good estimates to within a factor of $\sim 2$.856 All the slopes are roughly unity. but those of aare systematically larger than that ofMpy-Moiu.," All the slopes are roughly unity, but those of are systematically larger than that of."857. This is expected if ccorrelates with bbecause of its dependence on through the stellar M/L ratio., This is expected if correlates with because of its dependence on through the stellar $M/L$ ratio.858 From our rrelation. we find that logY4=0.18logLg—2.1: the weak dependence of Y on L fully accounts for the different slopes of aandMgy—Mpu.. and the same applies to the J and H bands.," From our relation, we find that $\log\mlr_K\,=\,0.18\log\LKsph-2.1$; the weak dependence of $\mlr$ on $L$ fully accounts for the different slopes of and, and the same applies to the J and H bands."859 All correlations are. thus. consistent with a direct proportionality between aand bulge mass., All correlations are thus consistent with a direct proportionality between and bulge mass.860 This contrasts with previous claims of a linearity of the rrelation (Laor2001) but is 1n agreement with lop (2002)...," This contrasts with previous claims of a non-linearity of the relation \citep{laor01}861 but is in agreement with \cite{mclure02}. ."862" A partial correlation analysis of ((variable νι). ((v2). and logR, (v3) shows that lis significantly correlated both with aand R,."," A partial correlation analysis of (variable $x_1$ ), $x_2$ ), and $R_e$ $x_3$ ) shows that is significantly correlated both with and $R_e$."863" The Pearson partial correlation coefficients. in which the known dependence of aand A, is eliminated. are 7j»=0.83. ιν=0.65. with a significance of >99.9%."," The Pearson partial correlation coefficients, in which the known dependence of and $R_e$ is eliminated, are $r_{12}=0.83$, $r_{13}=0.65$, with a significance of $>99.9\%$."864" This is shown graphically in reffig:corree. where the residuals of the Τ02 ccorrelation are plotted against R,: there is a weak. but significant. correlation of these residuals with Α.."," This is shown graphically in \\ref{fig:corr}c c, where the residuals of the T02 correlation are plotted against $R_e$; there is a weak, but significant, correlation of these residuals with $R_e$."865" Consequently. when galaxy structural parameters are measured carefully from 2D image analysis. the additional. weaker. dependence of oon AR, is uncovered."," Consequently, when galaxy structural parameters are measured carefully from 2D image analysis, the additional, weaker, dependence of on $R_e$ is uncovered."866" Thus. a combination of both aand R, is necessary to drive the correlations between παπά other bulge properties."," Thus, a combination of both and $R_e$ is necessary to drive the correlations between and other bulge properties."867 Thisplane of black holes will be further investigated elsewhere., This of black holes will be further investigated elsewhere.868 The average logMgyu/My can be estimated assuming a log-normal distribution with normally distributed observational errors., The average $\log \MBH/\Msph$ can be estimated assuming a log-normal distribution with normally distributed observational errors.869 With maximum likelihood we find (logMpy/Mbuw)=—2.63 with an intrinsic dispersion of 0.27 dex (-2.79 and 0.49 dex for all galaxies)., With maximum likelihood we find $\langle \log\MBH/\Msph \rangle = -2.63$ with an intrinsic dispersion of 0.27 dex (-2.79 and 0.49 dex for all galaxies).870 Adopting the method of Merritt&Fer-rarese (2001).. we find (logMpy/Miu)=-2.81 and ris=0.36 (-2.86 and 0.44 for all galaxies) consistently with their result of -2.9 and 0.45 dex (see also MeLure&Dunlop 2002)).," Adopting the method of \cite{mf01}, we find $\langle \log\MBH/\Msph \rangle = -2.81$ and $rms=0.36$ (-2.86 and 0.44 for all galaxies) consistently with their result of -2.9 and 0.45 dex (see also \citealt{mclure02}) )."871 We thank CCapetti. EEmsellem. MMaciejewski. NNorman. and OOliva for useful discussions.," We thank Capetti, Emsellem, Maciejewski, Norman, and Oliva for useful discussions."872 This paper was partially supported by ASI (/R/112/0] and L/R/048/02) and MIUR (Cotin01-02-02)., This paper was partially supported by ASI (I/R/112/01 and I/R/048/02) and MIUR (Cofin01-02-02).873 This publication uses the LEDA database. the NASA/IPAC Extragalactic Database operated by JPL. CalTech. undercontract with NASA. and data products from 2MASS. a joint project of the University of Massachusetts and the IPAC/CalTech. funded by NASA and NSF.," This publication uses the LEDA database, the NASA/IPAC Extragalactic Database operated by JPL, CalTech, undercontract with NASA, and data products from 2MASS, a joint project of the University of Massachusetts and the IPAC/CalTech, funded by NASA and NSF."874elobular cluster metallicity scales obtained [rom hieh resolution spectroscopy: Carrella& and Ixraft&Ivans(2003.hereafterIXIQ3)..,"globular cluster metallicity scales obtained from high resolution spectroscopy: \citet[hereafter CG97]{cg97} and \citet[hereafter875KI03]{ki03}."876 There is a third metallicity seale obtained [rom low-resolution data: Zinn&West(1934.hereafterZW84).., There is a third metallicity scale obtained from low-resolution data: \citet[hereafter ZW84]{zw84}.877 There are svstematic differences among (hese (liree scales. but there is no reason (o preler anv particular one of them.," There are systematic differences among these three scales, but there is no reason to prefer any particular one of them."878 For this reason. here we are going to study (he behaviour of the CaL lines with metallieitv in these (three scales.," For this reason, here we are going to study the behaviour of the CaT lines with metallicity in these three scales."879 Lamentably. there is not a homogeneous metallicityv scale obtained Ivom high-resolution spectroscopy lor open clusters.," Lamentably, there is not a homogeneous metallicity scale obtained from high-resolution spectroscopy for open clusters."880 However. the metallicities of some of them have been obtained directly in the CG97 scale by some authors: NGC 6819 (Dragagliaetal.2001): NGC 2506 (Carrettaοἱal.2004): NGC στο! (Grattonetal.2006) and Berkeley 32 (Sestitoetal.2006).," However, the metallicities of some of them have been obtained directly in the CG97 scale by some authors: NGC 6819 \citep{bra01}; NGC 2506 \citep{cbgt04}; ; NGC 6791 \citep{gratton06} and Berkeley 32 \citep{sestito06}."881. These metallicities were obtained using Fe and FeΠ lines., These metallicities were obtained using Fe and Fe lines.882 For (he other 8 open clusters in our sample there are also metallicities obtained [rom high-resolution spectroscopy in RGB stars and using Fe and FeII lines in a similar wav lo CG9T., For the other 8 open clusters in our sample there are also metallicities obtained from high-resolution spectroscopy in RGB stars and using Fe and Fe lines in a similar way to CG97.883 Even though some discrepancies could exist because the procedures are not exactly the same. we are considering these metallicities also to be on the CG97 scale.," Even though some discrepancies could exist because the procedures are not exactly the same, we are considering these metallicities also to be on the CG97 scale."884 The reference values in (his scale are listed in column 2 of Table 1. and the sources for each of them are listed in column 3., The reference values in this scale are listed in column 2 of Table \ref{clustersample} and the sources for each of them are listed in column 3.885 The reference metallicities in the ZWs4 and IxI03 are listed in columns 4 and 5 respectively., The reference metallicities in the ZW84 and KI03 are listed in columns 4 and 5 respectively.886 In both cases. we have used only values obtained directly by these authors.," In both cases, we have used only values obtained directly by these authors."887" Figures LO and LL show the run of Wt and WW) with metallicity,", Figures \ref{calv} and \ref{calI} show the run of $W'_V$ and $W'_I$ with metallicity.888 ID most cases. the errors are smaller (han (he size of the points.," In most cases, the errors are smaller than the size of the points."889 The circles indicate clusters vounger (han 4 Gyr., The circles indicate clusters younger than 4 Gyr.890 The solid line shows the best fit to the data., The solid line shows the best fit to the data.891 The dashed lines represent the confidence level., The dashed lines represent the confidence level.892 Note that in both cases there is a linear correlation., Note that in both cases there is a linear correlation.893 The bottom panels show the residuals of the linear fit., The bottom panels show the residuals of the linear fit.894 We have used 22 clusters for the calibration in V. and 20 for that in J., We have used 22 clusters for the calibration in $V$ and 20 for that in $I$.895 There are (hree clusters that differ from the fit by more than 0.2 dex in both filters., There are three clusters that differ from the fit by more than 0.2 dex in both filters.896 These clusters are NGC 2420. NGC 2506 ancl Berkelev 32.," These clusters are NGC 2420, NGC 2506 and Berkeley 32."897 Thev have been excluded. [rom the analysis., They have been excluded from the analysis.898 In the case of NGC 2420. only 6 stars in V. and 4 in J are radial velocity members.," In the case of NGC 2420, only 6 stars in $V$ and 4 in $I$ are radial velocity members."899 This. together with a relatively large uncertainty in iis metallicity (Gratton2000).. contributes to its large error bar.," This, together with a relatively large uncertainty in its metallicity \citep{gratton00}, contributes to its large error bar."900 In the case of NGC! 2506 ancl Berkeley 32. there are only 3 and 4 stars respectively wilh membership confirmed by their racial velocities.," In the case of NGC 2506 and Berkeley 32, there are only 3 and 4 stars respectively with membership confirmed by their radial velocities."901" Thus. slieht differences in ihe ©C'a value of one of them could change the derived W"" significantly."," Thus, slight differences in the $\Sigma Ca$ value of one of them could change the derived $W'$ significantly."902 Two of the three very deviant clusters (NGC 2420 and NGC 2506) have ages less Chan 4 Gvyrs. but 5 other voung clusters fit (he mean relationships in Figures 10 and 11. to better than 0.2 dex.," Two of the three very deviant clusters (NGC 2420 and NGC 2506) have ages less than 4 Gyrs, but 5 other young clusters fit the mean relationships in Figures \ref{calv} and \ref{calI} to better than 0.2 dex."903 We doubt therefore that cluster age is the majorcause of the large deviations., We doubt therefore that cluster age is the majorcause of the large deviations.904ave to of PD2 and PD3 8)).,are directly comparable to those of PD2 and PD3 ).905 In particular.directly the comparablerange of thoseallowed distances. ΕΕ(Fig.46kpe. is the same and the reconstructed: orbits show comparable accuracy (Figs.," In particular, the range of allowed distances, $44-46\kpc$, is the same and the reconstructed orbits show comparable accuracy (Figs."90612 ancl 14))., \ref{pd56-dist} and \ref{pd56-vt}) ).907"number of massive stars but suppresses the fraction of intermediate mass stars, with the overall result of a higher Carbon density at any cosmic epoch.","number of massive stars but suppresses the fraction of intermediate mass stars, with the overall result of a higher Carbon density at any cosmic epoch."908" Interestingly, run kr37mdw (momentum-driven winds, blue triangles—dotted line) follows the sa37edw500 even if the latter produces much less CIV as we will show in Section (Figure12,, left panel)."," Interestingly, run kr37mdw (momentum-driven winds, blue $-$ dotted line) follows the sa37edw500 even if the latter produces much less CIV as we will show in Section (Figure, left panel)."909" Run kr37co-edw500 (coupled energy- winds, red squares—dot-dashed line) has the same trend as kr37edw500 but with a slightly higher normalization."," Run kr37co-edw500 (coupled energy-driven winds, red $-$ dot-dashed line) has the same trend as kr37edw500 but with a slightly higher normalization."910" As we stated above, this is due to the fact that the coupled winds are less efficient than the normal winds and therefore this simulation has a higher star formation that results in a higher Carbon abundance."," As we stated above, this is due to the fact that the coupled winds are less efficient than the normal winds and therefore this simulation has a higher star formation that results in a higher Carbon abundance."911" This situation is even more extreme for the kr37nf (no-feedback, green crosses— dashed line) and kr37agn (AGN-feedback, black crosses—dashed line) runs, in fact down to redshift z~3 both of these simulations do not suppress effectively the star formation and for them Qc is higher."," This situation is even more extreme for the kr37nf (no-feedback, green $-$ dashed line) and kr37agn (AGN-feedback, black $-$ dashed line) runs, in fact down to redshift $z\sim3$ both of these simulations do not suppress effectively the star formation and for them $\Omega_{\rm C}$ is higher."912 Going to lower redshift AGN feedback becomes active in quenching the star formation and lowers the amount of gas used by the stars and converts in other species (note the excess in Qc with respect to the kr37nf run at z« 2.7).," Going to lower redshift AGN feedback becomes active in quenching the star formation and lowers the amount of gas used by the stars and converts in other species (note the excess in $\Omega_{\rm913 C}$ with respect to the kr37nf run at $z<2.7$ )."914" The kr37agn+edw300 run (AGN + energy-driven winds, yellow solid line) shows the same Qc trend of kr37edw500 even if with squares—higher normalization at high redshift due to the lower strength of the winds (300 km s-! instead of 500 km s)."," The kr37agn+edw300 run (AGN + energy-driven winds, yellow $-$ solid line) shows the same $\Omega_{\rm C}$ trend of kr37edw500 even if with higher normalization at high redshift due to the lower strength of the winds (300 km $^{-1}$ instead of 500 km $^{-1}$ )."915" At low redshift AGN feedback becomes active, but, differently from the kr37agn case: i) winds have already made the haloes devoid of gas therefore reducing the efficiency of the black holes accretion and thus the power of the AGN feedback; i?) winds suppress star formation at high redshift lowering the Carbon content, so when the AGN starts to work the net result is a further decrease of Ως."," At low redshift AGN feedback becomes active, but, differently from the kr37agn case: $i)$ winds have already made the haloes devoid of gas therefore reducing the efficiency of the black holes accretion and thus the power of the AGN feedback; $ii)$ winds suppress star formation at high redshift lowering the Carbon content, so when the AGN starts to work the net result is a further decrease of $\Omega_{\rm C}$."916" Finally, at high redshift the kr37p400edw500 run (resolution test, black diamonds line), shows a higher Qc with respect to the kr37edw500 due to solidthe improved resolution of this simulation (as explained above), while at low redshift the Carbon content ofthe kr37p400edw500 approaches that of the kr37edw500 run."," Finally, at high redshift the kr37p400edw500 run (resolution test, black $-$ solid line), shows a higher $\Omega_{\rm C}$ with respect to the kr37edw500 due to the improved resolution of this simulation (as explained above), while at low redshift the Carbon content ofthe kr37p400edw500 approaches that of the kr37edw500 run."917" Comparing the Ως evolution of our simulations with the one showed in ?,Figure12,, we found that in general the normalization of our runs is higher, although a very precise comparison is not possible given the different setup of the simulations used, especially regarding the chemical evolution model."," Comparing the $\Omega_{\rm C}$ evolution of our simulations with the one showed in \citet[][Figure 12]{oppe06}, we found that in general the normalization of our runs is higher, although a very precise comparison is not possible given the different setup of the simulations used, especially regarding the chemical evolution model."918" However, for the kr37mdw run (and also for the sa37edw500 run) the agreement is much better, the latter simulation producing momentum-driven galactic winds and therefore being the yardstick for the comparison with the ? work."," However, for the kr37mdw run (and also for the sa37edw500 run) the agreement is much better, the latter simulation producing momentum-driven galactic winds and therefore being the yardstick for the comparison with the \citet{oppe06} work."919" Before focusing on the CIV evolution, we address some flux statistics related to the properties and the evolution of neutral hydrogen in the IGM."," Before focusing on the CIV evolution, we address some flux statistics related to the properties and the evolution of neutral hydrogen in the IGM."920" For all the neutral hydrogen statistics discussed in this paper, we considered HI/ines (while for the CIV we considered from time to time lines or sytems of lines)."," For all the neutral hydrogen statistics discussed in this paper, we considered HI (while for the CIV we considered from time to time lines or sytems of lines)."921 For each simulation performed we have extracted several physical quantities interpolated along lines-of-sight (LOSs) through the box., For each simulation performed we have extracted several physical quantities interpolated along lines-of-sight (LOSs) through the box.922" Given the positions, velocities, densities and temperatures of all SPH particles at a given redshift, we compute spectra along a given LOS through the box following the procedure of ?.."," Given the positions, velocities, densities and temperatures of all SPH particles at a given redshift, we compute spectra along a given LOS through the box following the procedure of \citet{theunsetal98}."923 We divide the sight line into N=1024 bins of width A in distance x along the sight line., We divide the sight line into $N=1024$ bins of width $\Delta$ in distance $x$ along the sight line.924" For a bin i at position z(i) we compute the density and the density weighted temperature and velocity from: where is the scale factor, X(i) is the abundance of species X of SPH particlea 2, assuming ionization equilibrium, and"," For a bin $i$ at position $x(i)$ we compute the density and the density weighted temperature and velocity from: where $a$ is the scale factor, $X(i)$ is the abundance of species $X$ of SPH particle $i$ , assuming ionization equilibrium, and"925If the exposure time is short cnough then the atinosphliere cau be taken to be static duriug the exposure.,If the exposure time is short enough then the atmosphere can be taken to be static during the exposure.926 The conunon term that describes this is that ‘the atmosphere has beenfreezed during the exposure’., The common term that describes this is that `the atmosphere has been during the exposure'.927 From experiments it has been found that for exposures below 20 ms the atimosphere can be cousidered as fairly static for reasonably stable nights., From experiments it has been found that for exposures below 20 ms the atmosphere can be considered as fairly static for reasonably stable nights.928 A larec iuuber of such short exposure iniages (specklegrams) of the object of interest is taken., A large number of such short exposure images (specklegrams) of the object of interest is taken.929 Also nuages of a reference star which is kuown to be a unresolved star G.c.. a point source. a two dineusioual ó function on the sky) and which les in the same isoplauatic patch as that of the program star. is taken at the same time.," Also images of a reference star which is known to be a unresolved star (i.e., a point source, a two dimensional $\delta$ function on the sky) and which lies in the same isoplanatic patch as that of the program star, is taken at the same time."930 It is assumed that the atmospheric distortion affects the reference star in the same way as it does to the program star., It is assumed that the atmospheric distortion affects the reference star in the same way as it does to the program star.931" The cuscuuble average of the power spectrum is even by The refercuce star being a sinele star. the Fourier transform of its nuage 1s unity. i6. O,-¢(a) = 1."," The ensemble average of the power spectrum is given by The reference star being a single star, the Fourier transform of its image is unity, i.e., $O_{ref}({\bf u})$ = 1."932 The power spectrmu of the program star is therefore eiven by and by Wiener-Iiuchin theorem. the autocorrelation of the object is given by where A deuotes Autocorrelationκ aud FT1 denotes the operation. of2. inverse Fourier transform.," The power spectrum of the program star is therefore given by and by Wiener-Kinchin theorem, the autocorrelation of the object is given by where $A$ denotes Autocorrelation and ${\mathcal FT}^{-1}$ denotes the operation of inverse Fourier transform."933 The program for finding the power spectrum is written in FORTRAN., The program for finding the power spectrum is written in FORTRAN.934 It uses IRAF commuands and hence the macros in ΤΠΑΕ are called and used., It uses IRAF commands and hence the macros in IRAF are called and used.935 The prograin is written in such away that a large ταιον of data files can be haudled and large umber of images can be averaged to increase the signal-to-noise ratio., The program is written in such a way that a large number of data files can be handled and large number of images can be averaged to increase the signal-to-noise ratio.936 The set of input specklegraims ofobject and the reference stars are read and their power spectrum is calculated., The set of input specklegrams of object and the reference stars are read and their power spectrum is calculated.937 The object power spectimu aud the image power spectrmm are averaged iu the Fourier space., The object power spectrum and the image power spectrum are averaged in the Fourier space.938 Finally the autocorrelated image is calculated using another programe., Finally the autocorrelated image is calculated using another programme.939 The disadvantage with a division as in equation (1). is that the zeros iu the denominator will corrupt the ratio aud spurious hieh frequency conrponeuts will be created in the reconstructed image.," The disadvantage with a division as in equation (4), is that the zeros in the denominator will corrupt the ratio and spurious high frequency components will be created in the reconstructed image."940 Moreover. a certain amount of noise is inherent im any kind of observation.," Moreover, a certain amount of noise is inherent in any kind of observation."941 Iu our preseut case noise is primarily due, In our present case noise is primarily due942This iustrmment operates from (1.892.5/0 using three independent cameras.,This instrument operates from $0.8-2.5\micron$ using three independent cameras.943 The setup allows for broad. medi and narrow band imaging. coronoeraplic Huaeging. broad-band imagine polarimetry. aud eris spectroscopy.," The setup allows for broad, medium and narrow band imaging, coronographic imaging, broad-band imaging polarimetry, and grism spectroscopy."944 NIC2. the camera focused on in this study. is a 256< TeCdTe array with a 070075 pixel scale giving a 4.19733 field of view (Thoupsonetal. 1998).," NIC2, the camera focused on in this study, is a $256\times256$ HgCdTe array with a 075 pixel scale giving a $\times$ 3 field of view \citep{thom98}."945. After installation ouZST the dewar was allowed to be brought up to operating temperature., After installation on the dewar was allowed to be brought up to operating temperature.946 Unfortunately. this temperature was not tested on the eround and the subsequent ice expansion provided enough dewar deformation to allow contact between oue of the optical baffles aud the vapor cooled shield.," Unfortunately, this temperature was not tested on the ground and the subsequent ice expansion provided enough dewar deformation to allow contact between one of the optical baffles and the vapor cooled shield."947 The resultiug heat sink not only altered the foci of the three cameras. but also depleted the crvogen bx the beegimnius of 1999 (two and a half νους ahead of schedule).," The resulting heat sink not only altered the foci of the three cameras, but also depleted the cryogen by the beginning of 1999 (two and a half years ahead of schedule)."948 ILowever. a iuechanical cervocooler. the NICAIOS Cooling System (NCS). which was successfully installed in March 2002. has since brought NICAIOS back to life and restored the infrared capabilitics of/79T.," However, a mechanical cryocooler, the NICMOS Cooling System (NCS), which was successfully installed in March 2002, has since brought NICMOS back to life and restored the infrared capabilities of."949 While the iustimment performance is comparable pre- and post-NCS (Ilines2002).. it must be noted that NICMLOS now displays a different set of characteristics.," While the instrument performance is comparable pre- and post-NCS \citep{hines02}, it must be noted that NICMOS now displays a different set of characteristics."950 The reasou for these changes are at present muclear. however. for individual observations. these effects can be incorporated as changes in the transmission efficiencies of polarizing clemeuts.," The reason for these changes are at present unclear, however, for individual observations, these effects can be incorporated as changes in the transmission efficiencies of polarizing elements."951 One must also be aware that different quadrauts of the array may exhibit differeut bias levels introduced by resetting the array. plus additional bias offsets that are related to operating temperature aud main bus voltage (Berecron2005).," One must also be aware that different quadrants of the array may exhibit different bias levels introduced by resetting the array, plus additional bias offsets that are related to operating temperature and main bus voltage \citep{berg05}."952". While this ""pedestal effect has been reduced by modified flight software. it has not been cutirely clininated aud may lead to inconsistent polarization measurements."," While this “pedestal effect” has been reduced by modified flight software, it has not been entirely eliminated and may lead to inconsistent polarization measurements."953 More specific details can be obtained from the NICMOS Iustriuneut Παπάους (Schultzctal.2005)., More specific details can be obtained from the NICMOS Instrument Handbook \citep{sch05}.954. A conmpreheusive search of the NICMOS data archive has been performed with the aim of analyzing all observed polarimetric standard stars., A comprehensive search of the NICMOS data archive has been performed with the aim of analyzing all observed polarimetric standard stars.955 There are also a outmber of extended sources (c.g. CRL 2688 - the Eee Nebula) available for use in a calibration study., There are also a number of extended sources (e.g. CRL 2688 - the Egg Nebula) available for use in a calibration study.956 However. the eround truth for such objects is useless as the measured polarizations are depeudeut ou resolution.," However, the ground truth for such objects is useless as the measured polarizations are dependent on resolution."957 They also generalv exhibit a high degree of polarization and are often variable., They also generally exhibit a high degree of polarization and are often variable.958 Cousequeutly. such objects will not be couducive to determining the polaruuctric accuracies for the low polarization targets (mo5%) with which we are concerned.," Consequently, such objects will not be conducive to determining the polarimetric accuracies for the low polarization targets $\lesssim5\%$ ) with which we are concerned."959 A prerequisite for the standards to be included im the saluple ds indepeudent polarization measures frou well calibrated and characterized polaviuucters., A prerequisite for the standards to be included in the sample is independent polarization measures from well calibrated and characterized polarimeters.960 The ρολο standards found. anc associated details. are presentedο in Table 1.," The polarimetric standards found, and associated details, are presented in Table \ref{tab:sample}."961 In addition to the data iu Table 1 there are also pre-NCS data for two unpoluized standards. IIDIOTOQ aud ITD30652 (Leroy&LeBorene1989:Leroy 1993).," In addition to the data in Table \ref{tab:sample} there are also pre-NCS data for two unpolarized standards, HD10700 and HD30652 \citep{landb89,leroy93}."962. Uufortunately. the program for which these observation were made (477611) called for the investigation of circuustellar structures.," Unfortunately, the program for which these observation were made 7614) called for the investigation of circumstellar structures."963 The actual stars are therefore lopelessly overexposed for accurate study here., The actual stars are therefore hopelessly overexposed for accurate study here.964 The data and calibration files were retrieved and passed through the latest versions of the andος pipelines where appropriate., The data and calibration files were retrieved and passed through the latest versions of the and pipelines where appropriate.965 Each uou-destructive readout of individual observations was examined., Each non-destructive readout of individual observations was examined.966 The total counts in cach frame were inspected as a function of the total exposure time., The total counts in each frame were inspected as a function of the total exposure time.967 Deviations of this curve of growth from linear. especially at very carly times. were deemed to be evideuce for the existence of signal persistence.," Deviations of this curve of growth from linear, especially at very early times, were deemed to be evidence for the existence of signal persistence."968 In the cases where the telescope was offset between exposures. the areas of the array exposed to source pliotous iu the previous visit were also examined for persistence.," In the cases where the telescope was offset between exposures, the areas of the array exposed to source photons in the previous visit were also examined for persistence."969 The individual exposures were also checked for any remaining cosmic ravs or hot jXxel« not flageed by the reduction routine., The individual exposures were also checked for any remaining cosmic rays or hot pixels not flagged by the reduction routine.970 Theepphot package in was used iu order Oo perforin aperture photometry on each polarized standard., The package in was used in order to perform aperture photometry on each polarized standard.971 Circular apertures with radi from 0.5 to 50.5 Xxel« απ 1 pixel intervals) were ceutroiled on cach standard., Circular apertures with radii from 0.5 to 50.5 pixels (in 1 pixel intervals) were centroided on each standard.972 The observable point spread function (PSF) was conmfortablv included im the outer aperture., The observable point spread function (PSF) was comfortably included in the outer aperture.973 In cach rene the sky was sampled (aud removed frou the areet photometry) using a disk whose ier aunulus was defined by the edge of the observable PSF. and whose outer annulus was defined by the edge of the array.," In each frame the sky was sampled (and removed from the target photometry) using a disk whose inner annulus was defined by the edge of the observable PSF, and whose outer annulus was defined by the edge of the array."974 Iu, In975i.c. we include also those sources whose best-fitting redshift estimate would. put. them below the lower-limit of the top-decade in luminosity. anc consider the contribution from the high-redshift tail of their probability distributions.,"i.e. we include also those sources whose best-fitting redshift estimate would put them below the lower-limit of the top-decade in luminosity, and consider the contribution from the high-redshift tail of their probability distributions."976 The spectroscopic redshifts. when available. are also taken into consideration.," The spectroscopic redshifts, when available, are also taken into consideration."977 Phe sources with spectroscopic redshifts contribute to a single bin each. if their. luminosity lies above the lower limit of the top-cecacde (see Fable. 3)).," The sources with spectroscopic redshifts contribute to a single bin each, if their luminosity lies above the lower limit of the top-decade (see Table \ref{tab:top-decade}) )."978 GC*0TAT|5618. the source which is not detected. in. A-band and does not have a spectroscopic redshift. contributes also to à single bin (4<z« 5).," 6C**0737+5618, the source which is not detected in $K$ -band and does not have a spectroscopic redshift, contributes also to a single bin $4 < z <9795$ )."980 The resulting recdshift distribution is presented in Fig. 12.., The resulting redshift distribution is presented in Fig. \ref{fig:redshift.pdf}.981 The distribution derived. from. the data appears to be in very good agreement with the mocdel distribution., The distribution derived from the data appears to be in very good agreement with the model distribution.982 This is confirmed by the application of the chi-squarecl goodness- test. which gives12. with a probability p=0.54 ofobtaining this. or greater than this value of 47.," This is confirmed by the application of the chi-squared goodness-of-fit test, which gives, with a probability $p = 0.54$ of obtaining this, or greater than this value of $\chi^{2}$."983 We perform also the same analysis by omitting 6C**0737|5618 in the 4<zX5 bin.," We perform also the same analysis by omitting 6C**0737+5618 in the $4984\leq z \leq 5$ bin."985 This source is unidentified and it is debatable that its magnitude limit (A2:21 mag in a S-aresee aperture at the 30. level) implies. bv extrapolation of the ἐνz diagram. a very high redshift’ (c 4).," This source is unidentified and it is debatable that its magnitude limit $K \,\,\gtsim\,\, 21$ mag in a 8-arcsec aperture at the $\sigma$ level) implies, by extrapolation of the $K-z$ diagram, a very high redshift $z > 4$ )."986 Ht is also possible that this source. Like 6C77(0935|1348. is at à lower redshift (272 3) but is perhaps at à very carly stage of its formation. and/or highly obscured. or is simply. underluminous (see discussion in Section 4)).," It is also possible that this source, like 6C**0935+4348, is at a lower redshift $z987\simeq 2-3$ ) but is perhaps at a very early stage of its formation and/or highly obscured, or is simply underluminous (see discussion in Section \ref{sec:comparison}) )."988 However. a very high-redshift cannot be ruled oul.," However, a very high-redshift cannot be ruled out."989 change the results significantly., Omitting 6C**0737+5618 from our analysis does not change the results significantly.990 We find V7—2.4. with p— (0.36.," We find $\chi^{2} = 2.4$, with $p = 0.36$ ."991 Again. we conclude that the data are consistent with the constant co-moving space density model of Jarvis et al. (," Again, we conclude that the data are consistent with the constant co-moving space density model of Jarvis et al. ("9922001c).,2001c).993 Finally. we compare the data with the predictions from five declining co-moving space density models. using Jarvis et al. (," Finally, we compare the data with the predictions from five declining co-moving space density models, using Jarvis et al. ("99420010) model € with: y=—2.0 (dashed. line in 12).59g,"2001c) model C with: $\eta = -2.0$ (dashed line in Fig. \ref{fig:redshift.pdf}) ),"995= δη—38.0 (dotted line in Fig. 12)).," $\eta = -2.5$ , $\eta = -3.0$ (dotted line in Fig. \ref{fig:redshift.pdf}) ),"996 y=385 and p=4.0 (clot-dashecl line in Fig. 12))., $\eta = -3.5 $ and $\eta = -4.0$ (dot-dashed line in Fig. \ref{fig:redshift.pdf}) ).997 The results of the chi-squared goodness-of-fit test are Listed in ‘Table 4.0., The results of the chi-squared goodness-of-fit test are listed in Table \ref{tab:chi-square}.998 It can be seen that. although the data are also consistent with moderate declines by factors of 2 to 3. declines by a factor of 3.5 and 4.0 can be excluded at the ~23a level.," It can be seen that, although the data are also consistent with moderate declines by factors of 2 to 3, declines by a factor of 3.5 and 4.0 can be excluded at the $\sim 2 - 3\sigma$ level."999 have limitations when it comes to confirming a decline in co-moving space density.," As discussed by Jarvis (2000), filtered samples such as 6C** have limitations when it comes to confirming a decline in co-moving space density."1000 Ehe major problem is that the lack of sources at à given redshift may not be due to a decline in their space density but to imperfections in the filtering technique., The major problem is that the lack of sources at a given redshift may not be due to a decline in their space density but to imperfections in the filtering technique.1001 For example. with respect to the 6C* sample. Jarvis (2000) estimated that the angular size selection is filtering out an increasingly laree fraction of the sources with redshift: from ~POW to ~30% between z=0 and ~ Sand ~3050% bevond z>5.," For example, with respect to the 6C* sample, Jarvis (2000) estimated that the angular size selection is filtering out an increasingly large fraction of the sources with redshift: from $\sim 20$ to $\sim 30$ between $z = 0$ and $z \sim 5$; and $\sim 30-50$ beyond $z > 5$."1002 Jarvis (2000) concluded that samples with similar filtering criteria to that of οςὃν and in particular with [lux-density [limits similar to that of 6C. are only able to confirm roughly constant or increasing co-moving space density at high redshifts.," Jarvis (2000) concluded that samples with similar filtering criteria to that of 6C*, and in particular with flux-density limits similar to that of 6C**, are only able to confirm roughly constant or increasing co-moving space density at high redshifts."1003 The presence ofa decline would be dillieult to interpret due to the uncertainties introduced by the filtering criteria., The presence of a decline would be difficult to interpret due to the uncertainties introduced by the filtering criteria.1004 However. the filtering is helpfulin placing strong lower limits on any decline.," However, the filtering is helpfulin placing strong lower limits on any decline."1005"In Fig. 3,,","In Fig. \ref{density},"1006 we show the resulting //PSPC density profile., we show the resulting /PSPC density profile.1007 The dotted black line shows the estimate of rogo from (09., The dotted black line shows the estimate of $r_{200}$ from G09.1008" Beyond r=17’, we do not detect any significant cluster emission, and set an upper limit to the density in the 17—25' range of ni;ay.«4.2x107? em-? confidence level)."," Beyond $r=17^{\prime}$, we do not detect any significant cluster emission, and set an upper limit to the density in the $17-25^\prime$ range of $n_{17-25^{\prime}}<4.2\times10^{-5}$ $^{-3}$ confidence level)."1009" To compare the and profiles, we used a method similar to the one reported in ?.."," To compare the and profiles, we used a method similar to the one reported in \citet{bowyer}."1010" More specifically, we converted the projected profile into the MEKAL normalization (Eq. 1)),"," More specifically, we converted the projected profile into the MEKAL normalization (Eq. \ref{meknorm}) ),"1011 and folded it through the response of ROSAT//PSPC to compute the count rate that should be seen by PSPC., and folded it through the response of /PSPC to compute the count rate that should be seen by PSPC.1012" The resulting profile (black), compared to the background-subtracted PSPC profile with the same binning (red), is shown in Fig. 4.."," The resulting profile (black), compared to the background-subtracted PSPC profile with the same binning (red), is shown in Fig. \ref{projected}."1013" While in the inner 4 annuli the profiles differ by only ~11% (the difference in the innermost 2 bins being explained by the broader PSF), a clear discrepancy between the and profiles is found beyond 13.5’."," While in the inner 4 annuli the profiles differ by only $\sim11$ (the difference in the innermost 2 bins being explained by the broader PSF), a clear discrepancy between the and profiles is found beyond $13.5^{\prime}$."1014" In the 13.5-18.5 arcmin bin, the profile exceeds the data point by a factor of three, while in the 18.5-24 arcmin bin our upper limit lies a factor of 2.1 below the detection."," In the 13.5-18.5 arcmin bin, the profile exceeds the data point by a factor of three, while in the 18.5-24 arcmin bin our upper limit lies a factor of 2.1 below the detection."1015 The profiles at the largest radii are discrepant at more than 7.76., The profiles at the largest radii are discrepant at more than $7.7\sigma$.1016 This result is stable in terms of the background level., This result is stable in terms of the background level.1017 We indeed reach the same conclusion when we use the lowest allowed value for the background instead of the mean value., We indeed reach the same conclusion when we use the lowest allowed value for the background instead of the mean value.1018" As shown above, our ROSAT//PSPC density profile is statistically inconsistent with the profile from G09 at high significance."," As shown above, our /PSPC density profile is statistically inconsistent with the profile from G09 at high significance."1019 We discuss here several possibilities to reconcile the two results., We discuss here several possibilities to reconcile the two results.1020clear tilt iu the extinction.,clear tilt in the extinction.1021 This tilt follows a path line be(405<7 for |]«87. so it runs below the plane at positive longitudes aud above the pluie at negative longitudes.," This tilt follows a path line $b\approx -0.05\times l$ for $|l|<8^\circ$, so it runs below the plane at positive longitudes and above the plane at negative longitudes."1022 This is à well-kuown feature in the CO aud III maps (Liszt Burton 1980: Sanders et al., This is a well-known feature in the CO and HI maps (Liszt Burton 1980; Sanders et al.1023 1981)., 1984).1024 Observing a tilt in the extinction map clearly indicates that this extinction is due to gas and dust in the centre of the Galaxy. where the eas distribution is tilted.," Observing a tilt in the extinction map clearly indicates that this extinction is due to gas and dust in the centre of the Galaxy, where the gas distribution is tilted."1025 Because of the tilt. the asviunietry for 1.0%<|b}0.5% is not seen in Fie.," Because of the tilt, the asymmetry for $-1.0^\circ <|b|<-0.5^\circ $ is not seen in Fig."1026 8 whilst the asvunmetry at 0.57<b<1.07 is very high., \ref{Fig:plot_av} whilst the asymmetry at $0.5^\circ <b<1.0^\circ $ is very high.1027 At positive longitudes. the extinction is around 5 maguitudes less than at negative longitudes. except for a few isolated regions. such as the excess at (|—157.b=0.57). probably associated with a cloud iu the molecular ring.," At positive longitudes, the extinction is around 5 magnitudes less than at negative longitudes, except for a few isolated regions, such as the excess at $(l=15^\circ,1028b=-0.5^\circ)$, probably associated with a cloud in the molecular ring."1029 A 1uap of the star counts with iij;<9.0 is shown in Fie., A map of the star counts with $m_{K_{\rm s}}\le 9.0$ is shown in Fig.1030 LO (upper) with a binning of A?=2° and Ab=0.57., \ref{Fig:plotestat2D} (upper) with a binning of $\Delta l=2^\circ $ and $\Delta b=0.5^\circ $.1031 This biuuiug reduces hieh frequency fluctuations due to very patchy extinction., This binning reduces high frequency fluctuations due to very patchy extinction.1032 Ouly the negative loueitudes are shown because iu this region coverage in the DENIS batches is almost complete (06 deg? are available at negative longitudes.+ while- for+ positiveeye longitudes. onlv 17— deeP are available).," Only the negative longitudes are shown because in this region coverage in the DENIS batches is almost complete (96 $^2$ are available at negative longitudes, while for positive longitudes only 47 $^2$ are available)."1033 Furthermore. previous papers have already studied the positive longitudes (0.9. II91: Went et al.," Furthermore, previous papers have already studied the positive longitudes (e.g. H94; Kent et al."1034" 1991). whereas there is relatively little published ou the negative longitudes,"," 1991), whereas there is relatively little published on the negative longitudes."1035" Iu the star-count map there are peaks in a nuniber of regions (F—Q7, 5b=the bub-— l:l-—12. boo: -- 22.,.b-tw:l-—-BOL b= 1)"," In the star-count map there are peaks in a number of regions $l=0^\circ$, $b= \pm 1.5^\circ $; $l=-5^\circ$, $b=-1^\circ $; $l=-12^\circ$, $b=0^\circ $; $l=-22^\circ$, $b=0^\circ $; $l=-30^\circ$, $b=-1^\circ $ )."1036 Some of these peaks may be due to real features in the star distribution. but others are clearly due to regions of lower extinction than in the surrounding areas.," Some of these peaks may be due to real features in the star distribution, but others are clearly due to regions of lower extinction than in the surrounding areas."1037 Often. local," Often, local"1038where Mdies=Diagmq.mo.mal is the diagonal neutrino mass matrix.,"where $M_{\nu}^{diag}=Diag \{m_1,m_2,m_3\}$ is the diagonal neutrino mass matrix."1039 The neutrino mixingmatrix V[15]. can be written as where s;;=sin@;; and ο=cos@;;., The neutrino mixingmatrix $V$ \cite{15} can be written as where $s_{ij}=\sin\theta_{ij}$ and $c_{ij}=\cos\theta_{ij}$.1040 The matrix V. is called the neutrino mixing malrix or PAINS matrix., The matrix $V$ is called the neutrino mixing matrix or PMNS matrix.1041 The matrix Ü is the lepton analogue of the CINM. quark mixing matrix and the phase matrix J? contains the (vo Majorana phases., The matrix $U$ is the lepton analogue of the CKM quark mixing matrix and the phase matrix $P$ contains the two Majorana phases.1042 Therefore (he neutrino mass matrix can be written as The elements of (he neutrino mass matrix can be caleulated from Eq. (, Therefore the neutrino mass matrix can be written as The elements of the neutrino mass matrix can be calculated from Eq. (10433).,3).1044 In hybrid textures of neutrinos. we have one equality of matrix elements ancl one zero.i.e.," In hybrid textures of neutrinos, we have one equality of matrix elements and one zero.i.e."1045 These (wo conditions vield (wo complex equations as follows and where C has been defined in Eq. (, These two conditions yield two complex equations as follows and where $U$ has been defined in Eq. (10462).,2).1047 These two complex equations involve nine physical parameters mq. mm. ma. 845. 854. 044 and three CP-violating phases a. 2 and 9.," These two complex equations involve nine physical parameters $m_{1}$ , $m_{2}$, $m_{3}$ , $\theta _{12}$, $\theta _{23}$, $\theta _{13}$ and three CP-violating phases $\alpha $, $\beta $ and $\delta $."1048 The masses na and ma can be calculated from the mass-squared differences Nis and Ams. using the relations and Thus. we have (wo complex equations relating five unknown parameters viz. nuj. 043. o.," The masses $m_{2}$ and $m_{3}$ can be calculated from the mass-squared differences $\Delta m_{12}^{2}$ and $\Delta m_{23}^{2}$ using the relations and Thus, we have two complex equations relating five unknown parameters viz. $m_1$, $\theta_{13}$, $\alpha$,"1049 2 and 6., $\beta$ and $\delta$ .1050 Therefore. il one out of these five parameters is assumed. other four parameters canbe predicted.," Therefore, if one out of these five parameters is assumed, other four parameters canbe predicted."1051Solving Eqs. (,Solving Eqs. (10525) and (6) simultaneously. we obtain anc,"5) and (6) simultaneously, we obtain and"10535) and (6) simultaneously. we obtain ancl,"5) and (6) simultaneously, we obtain and"1054precise high time resolution observations will be useful to test further if the star pulsates with low amplitudo.,precise high time resolution observations will be useful to test further if the star pulsates with low amplitude.1055 This peculiar star shows very strong lines ofextsciii.. anclextscii.. but lines of are rather weak.," This peculiar star shows very strong lines of, and, but lines of are rather weak."1056 The magnetic [field is not very strong and only partial Zeeman splitting is present in the line as can be seen in relsv 191695.., The magnetic field is not very strong and only partial Zeeman splitting is present in the line as can be seen in \\ref{sy191695}.1057. The presence of a magnetic field is. also supported by partial doublet splitting of the line., The presence of a magnetic field is also supported by partial doublet splitting of the line.1058 Nelson&Ixreidl(1993). cid not find rapid oscillations in 1191695 above a noise level of mmmag. but this cool Ap star is still à good target to search for low amplitude oulsation with high precision. using both spectroscopic and ποιοιτίς high time resolution observations.," \citet{Nelson_Kreidl93} did not find rapid oscillations in 191695 above a noise level of mmag, but this cool Ap star is still a good target to search for low amplitude pulsation with high precision, using both spectroscopic and photometric high time resolution observations."1059 Aleasured magnetic fields. in Xp stars show significant variability with rotation period., Measured magnetic fields in Ap stars show significant variability with rotation period.1060" ""The magnetic oblique rotator model explains this variability as an aspect effect of the observed star.", The magnetic oblique rotator model explains this variability as an aspect effect of the observed star.1061 Most. stars. presented. here were observed in just one or two rotation phases and require more observations over their rotation periods to establish how strong their magnetic [fields are and to determine their geometries., Most stars presented here were observed in just one or two rotation phases and require more observations over their rotation periods to establish how strong their magnetic fields are and to determine their geometries.1062 Lt is especially interesting to observe stars with strong magnetic fields like those of 770702. and 1168767., It is especially interesting to observe stars with strong magnetic fields like those of 70702 and 168767.1063 The extreme values of the fields in these and other stars we have presented. here may be higher in the other rotational phases., The extreme values of the fields in these and other stars we have presented here may be higher in the other rotational phases.1064 Table11. shows the results. of magnetic field measurements together with other determined: parameters of the stars., 1 shows the results of magnetic field measurements together with other determined parameters of the stars.1065 The. standard. deviation for magnetic feld measurements for. well resolved Zeeman components with high signal to noise ratios in the spectra is about 100 GC. while for partially split lines. blended lines ancl for spectra with high noise itis in the range 200500 GG. The clleetive temperatures in this table are based mostly on fitting the observed. Ho. profiles with svathetic profiles.," The standard deviation for magnetic field measurements for well resolved Zeeman components with high signal to noise ratios in the spectra is about $100$ G, while for partially split lines, blended lines and for spectra with high noise itis in the range $200 - 500$ G. The effective temperatures in this table are based mostly on fitting the observed $\alpha$ profiles with synthetic profiles."1066 At best we estimate the error on Z;r to be 200300 KIX. For most of the stars studied the dilference between photometric and spectroscopic ellective temperatures is less than IxIx. although for a lew cases. especially for hotter stars. this lillerence is larger.," At best we estimate the error on $T_{\rm eff}$ to be $200 - 300$ K. For most of the stars studied the difference between photometric and spectroscopic effective temperatures is less than K, although for a few cases, especially for hotter stars, this difference is larger."1067 Our οσαὁ parameter determination has a precision of ⋜∩⋯∐↓↓⋅⋅↱≻↓⊔⊔↓⊳∖⊳∖⊳∖∖⇂⊔↓⋖," Our $v \sin i$ parameter determination has a precision of about $1 - 10681.5$ $^{-1}$."1069⋅⇂∪↓⋅⊳∖∪⊔↓⋖⋅⊳∖↿⋜⊔⋅⊳∖⋜↧∣⋎⊳∖↓⊔∣∖⇁⋜↧⇂⋯⊾ ⊥⇁⋠⋅ ⋠⊽ ∪⋅∶∫≻⊔⊊⊔↓⊳∖⊳∖⊥∖∖⊽⋜↧≱∖∪∣⋡⇂⋜↧⊲↓⊔∢⊾∠⇂⊳↓↥⊲↓⊳∖⊀↓⊳∖≯↕⊔⊳∖↿⇂↓↕∢⊾↓⋯∖⋎∢⋅↓⋅↓⊲↓⊔↓⊲⊔⇂⋅∪↓⋅ ↿↓↥∢⊾↓⊲↸∟⊲∐," While for some stars a $v \sin i$ value of $^{-1}$ was obtained, this is just the lower limit for the FEROS resolution."1070↻∺↓⋅⋖⋅⊳∖∪↓⋯⊲↓∪⊔⊳≺⊲∪⊔⊳∖⊲⊔⇂∢⋅↓⋰↓⊔⋏∙≟⇂↓⋯∣↿↓⊔⋅⊔↓⋜↧⋏∙≟⊔∢⊾∣⊀⊔⇍∐⋖⋅↓∠⇂ stabilises the stellar atmosphere. we used a value of zero for the microturbulence and macroturhbulence velocities in all calculations.," Considering that the magnetic field stabilises the stellar atmosphere, we used a value of zero for the microturbulence and macroturbulence velocities in all calculations."1071 With ASAS photometry (Pojmanski2002)Y and using the Period04 program by Lenz&Breecr(2005) we tested stars from L1 and found rotation periods for three of them., With ASAS photometry \citep{Pojmanski02} and using the Period04 program by \citet{lenzetal05} we tested stars from 1 and found rotation periods for three of them.1072 A correlation of the ellective temperatures obtained by photometry and spectroscopy is shown in τοςνο f., A correlation of the effective temperatures obtained by photometry and spectroscopy is shown in \\ref{sy_ph_teff}.1073 heagreementbelweenef fectiecete," The agreement between effective temperatures obtained with different methods is mostly acceptable, while in a few cases further analysis is needed to resolve the discrepancy."1074"mperaturesoblainedwilthdif, "," We prefer to use the effective temperature obtained with spectroscopic analysis, since the photometric calibrations are known to be problematic for extremely peculiar stars, as a consequence of line blocking."1075One of the fundamental questions of the physies Ap stars concerns the relation between magnetic field strength ancl rotational period., One of the fundamental questions of the physics Ap stars concerns the relation between magnetic field strength and rotational period.1076 Phe Ap stars rotate much more slowly than normal stars with the same celfective. temperature., The Ap stars rotate much more slowly than normal stars with the same effective temperature.1077 Typically the rotation periods of magnetic Ap stars range from several days to many vears. ancl even decades.," Typically the rotation periods of magnetic Ap stars range from several days to many years, and even decades."1078 The magnetic field is responsible for braking Ap stars., The magnetic field is responsible for braking Ap stars.1079 To examine this relationship further here. we collected more magnetic field and period values for Ap stars from the literature.," To examine this relationship further here, we collected more magnetic field and period values for Ap stars from the literature."1080 A eraph for rotational period as a function of extrema of magnetic Geld modulus for a sample of magnetic stars is presented in refbsy.., A graph for rotational period as a function of extrema of magnetic field modulus for a sample of magnetic stars is presented in \\ref{bs_p}. .1081Deatafordüstarsinthisfigureweretakenf , Data for 30 stars in this figure were taken from \citet{Mathys97}.1082romMealth," For other stars the data were obtained from \citet{Elkin10b}, \citet{Freyhammer08}, \citet{Hubrig09}, \citet{Mathys07}, \citet{Ryab06} and the current paper."1083gsctal. (1997)., This figure demonstrates that the stars with strongest magnetic fields typically have rotational periods between 5 and d. This is also supported by our observations of two stars 70702 and 168767 presented in this paper.1084.," Both stars have a very strong field and relatively high projected rotational velocities, which suggests that rotational period should not be more than several days."1085F0 (Dagn," The lack of stars with very strong fields and with periods less than d may be at least partly explained by selection effects, as the fast rotators have wider spectral lines and even for fields more than kG the Zeeman components are not resolved."1086uloctal., Spectropolarimetric techniques would be useful for searching for longitudinal fields among the fast rotators.10872004). ; 'hichshowseavergstronglongiludinal fieldandhast," A good example is the star 2244-334 \citep{Bagnulo04}, , which shows a very strong longitudinal field and has wide spectral lineswith magnetic and rotational broadening."1088, This star also should have a relatively short rotational period.1089equations (2)) and (6)) to vield the system where Ao=cos#€7QF. which can easily be solved numerically for A anc V.,"equations \ref{eq:basic2}) ) and \ref{eq:Poisson}) ) to yield the system where $K = \cos\theta \xi^2 \Omega^2$, which can easily be solved numerically for $K$ and $\Psi$."1090 However. if the radiative zone is crudely approximated by a polvtrope of index 3 then dyxl/£ and pux1£ between £=0.3 and £=1.," However, if the radiative zone is crudely approximated by a polytrope of index 3 then $T_{\rm h} \propto 1/\xi$ and $\rho_{\rm h} \propto 1/\xi^3$ between $\xi=0.3$ and $\xi = 1$."1091 This leads to These expressions can be used in the system (16)) to provide a homogeneous relation between W and. A. which can (amongst other power lawoscillatory solutions) be solved. analytically with V.o—Ac constant: this corresponds to O(£)xI/£.," This leads to These expressions can be used in the system \ref{eq:KPsi}) ) to provide a homogeneous relation between $\Psi$ and $K$ , which can (amongst other power law/oscillatory solutions) be solved analytically with $\Psi \simeq -K \simeq$ constant; this corresponds to $\Omega(\xi)1092\propto 1/\xi$."1093 The comparison of this very simple analytical prediction. with the results of the fully nonlinear numerical simulation is presented in Fig. 3..," The comparison of this very simple analytical prediction with the results of the fully nonlinear numerical simulation is presented in Fig. \ref{fig:log},"1094 in the case where the convection zone shear is null and in the case where it is of order of of the mean rotation rate., in the case where the convection zone shear is null and in the case where it is of order of of the mean rotation rate.1095 When the imposed shear is small. the analytical prediction provides a good approximation to the numerical results.," When the imposed shear is small, the analytical prediction provides a good approximation to the numerical results."1096 The numerical solutions for the angular velocity and the eravitational-Dield perturbation know little of the presence of a lower boundary: the meridional. motions and the temperature Buetuations on the other hand. seem. to be stronelv linked. with the lower boundary conditions and niw not represent what can be expected of a stellar radiative zone., The numerical solutions for the angular velocity and the gravitational-field perturbation know little of the presence of a lower boundary; the meridional motions and the temperature fluctuations on the other hand seem to be strongly linked with the lower boundary conditions and may not represent what can be expected of a stellar radiative zone.1097 In particular. the numerical simulations reveal the presence of an internal shear laver (related to the internal Stewardson laver in the Proudman spheres problem (Stewardson. 1966)). which is related to the presence. of the impermeable lower boundary (ancl therefore mostly irrelevant to stellar hyerodynamics).," In particular, the numerical simulations reveal the presence of an internal shear layer (related to the internal Stewardson layer in the Proudman spheres problem (Stewardson, 1966)), which is related to the presence of the impermeable lower boundary (and therefore mostly irrelevant to stellar hydrodynamics)."1098 This shear laver is rellected. also in the temperature distribution (see Fig. 2)), This shear layer is reflected also in the temperature distribution (see Fig. \ref{fig:lambdasmall}) ).1099 lHlowever. as the meridional [low ancl temperature distribution alfect the angular velocity profile only to the next order in A. it is possible to calculate the Low pattern boundary using the simple ansatz Ox into equation (14)).," However, as the meridional flow and temperature distribution affect the angular velocity profile only to the next order in $\lambda$, it is possible to calculate the flow pattern using the simple ansatz $\Omega \propto 1/\xi$ into equation \ref{eq:ens}) )."1100 Using the polvtropic approximation again one can derive where c ds the scaled. streani-function defined as à=(o/é sind)., Using the polytropic approximation again one can derive where $\overline{\psi}$ is the scaled stream-function defined as $\overline{\bu} = - \curl( \overline{\psi}/\xi\sin\theta)$ .1101 This result. suggests that in stars. the dimensional racial component of the meridional How. varies as uxpfrr incependenthy of the stellar rotation rate when A1.," This result suggests that in stars the dimensional radial component of the meridional flow varies as $\ur \propto1102\nu/ r $ independently of the stellar rotation rate when $\lambda \ll 1$."1103 Note that this scaling is compatible with the results of the work of Talon et al. (, Note that this scaling is compatible with the results of the work of Talon et al. (11041997).,1997).1105 As Busse (1981) claimed that rapidly rotating svstems settle down to purely zonal Hows in thedimeiscid case. Hb ds not surprising to find that the typical timescale for steady circulation in this rapid-rotation limit is the very slow viscous timescale.," As Busse (1981) claimed that rapidly rotating systems settle down to purely zonal flows in the case, it is not surprising to find that the typical timescale for steady circulation in this rapid-rotation limit is the very slow viscous timescale."1106 In this paper I analysecl the consequences of rotation on the driving of meridionalmotions in stellarradiative zones., In this paper I analysed the consequences of rotation on the driving of meridionalmotions in stellarradiative zones.1107 For a slowly rotating star. this problem has been studied," For a slowly rotating star, this problem has been studied"1108As already suggested by the timing analysis. the source is Compton-thin. as in the XMM-Newton observation (Guainazzi et al.,"As already suggested by the timing analysis, the source is Compton-thin, as in the $Newton$ observation (Guainazzi et al."1109 2002) and differently from the ASCA observation. when it was Compton-thick.," 2002) and differently from the ASCA observation, when it was Compton-thick."1110" In fact. when fitting the Suzaku spectrum with a pure CR (E fixed to 2). the fit is much worse. y7/d.0.f.=180/152: moreover. the iron line EW. about 240 eV. is far too low, see e.g. Ghisellini et al. ("," In fact, when fitting the $Suzaku$ spectrum with a pure CR $\Gamma$ fixed to 2), the fit is much worse, $\chi^2_r$ /d.o.f.=1.80/152; moreover, the iron line EW, about 240 eV, is far too low, see e.g. Ghisellini et al. ("11111994); Matt et al. (,1994); Matt et al. (11121996).,1996).1113 The 4-10 keV flux is -.3x1077. ere οη s! (XISO). corresponding to a 2-10 keV unabsorbed flux of 1.9x 107! erg cm? sc! and luminosity of 7.7x107 erg s! (Hy=70 km/s/Mpe).," The 4-10 keV flux is $\times$ $^{-12}$ erg $^{-2}$ $^{-1}$ (XIS0), corresponding to a 2-10 keV unabsorbed flux of $\times$ $^{-11}$ erg $^{-2}$ $^{-1}$ and luminosity of $\times$ $^{42}$ erg $^{-1}$ $H_0$ =70 km/s/Mpc)."1114 The index of the power law. E. and the relative normalization of the Compton reflection component. R. turned out to be highly correlated with each other: see Fig. 3..," The index of the power law, $\Gamma$, and the relative normalization of the Compton reflection component, $R$, turned out to be highly correlated with each other; see Fig. \ref{contourplot1}."1115 At the 2c level. Γ can range from about 1.65 up to about 2.1. with R ranging correspondingly from about | up to 4.," At the $\sigma$ level, $\Gamma$ can range from about 1.65 up to about 2.1, with $R$ ranging correspondingly from about 1 up to 4."1116 The value of the equivalent width of the iron line. about 200 eV. strongly favours the low F. low Α scenario.," The value of the equivalent width of the iron line, about 200 eV, strongly favours the low $\Gamma$, low $R$ scenario."1117 In fact. for cosmic abundancies such a value of the iron line EW would correspond to a value of R in between | and 1.5 (e.g. Matt et al.," In fact, for cosmic abundancies such a value of the iron line EW would correspond to a value of $R$ in between 1 and 1.5 (e.g. Matt et al."1118 1991). not forgetting that part of the line (up to 50-60 eV for large covering factors. e.g. Matt et al.," 1991), not forgetting that part of the line (up to 50-60 eV for large covering factors, e.g. Matt et al."1119 2003) may originate in the absorber itself., 2003) may originate in the absorber itself.1120 Adopting the model instead of for absorption. rather different best-fit values are found. due to the different cross sections and abundancies adopted (Morrison MeCammon 1982:Anders Ebthara 1982).," Adopting the model instead of for absorption, rather different best-fit values are found, due to the different cross sections and abundancies adopted (Morrison McCammon 1982;Anders Ebihara 1982)."1121 The column density remains about the same 03x 107 em) (as well as the quality of the fit: y7/d.o.f.=0.94/150); but Tis now 2.13019. while R becomes formally consistent within the errors with the values found 5.255.usingzPHABs. but not allowing for the low R solution required by the iron line EW.," The column density remains about the same $^{+0.28}_{-0.33}\times$ $^{23}$ $^{-2}$ ) (as well as the quality of the fit: $\chi^2_r$ /d.o.f.=0.94/150); but $\Gamma$ is now $^{+0.16}_{-0.17}$, while $R$ becomes $^{+4.8}_{-2.3}$ , formally consistent within the errors with the values found using, but not allowing for the low $R$ solution required by the iron line EW."1122 The presence of a Compton-thin absorber and a Comptorthick reflection indicates that more than one circumnuclear region does exist. as often observed in Seyfert 2s.," The presence of a Compton-thin absorber and a Compton-thick reflection indicates that more than one circumnuclear region does exist, as often observed in Seyfert 2s."1123" To check this. we also fitted the data with a model developed by one of us (HA) and his collaborators (""Ehime"" model. here-in-after: Ikeda et al."," To check this, we also fitted the data with a model developed by one of us (HA) and his collaborators (“Ehime” model, here-in-after: Ikeda et al."1124 2009)., 2009).1125 The model. based on MonteCarlo simulations. assumes that the absorption and reflection come from the same material. à torus with à half-opening angle which is one of the fitting parameters.," The model, based on MonteCarlo simulations, assumes that the absorption and reflection come from the same material, a torus with a half-opening angle which is one of the fitting parameters."1126 The fit is still acceptable. v;/d.o. f.21.13/150. but significantly worse than that with the Compton-thick reflector.," The fit is still acceptable, $\chi^2_r/d.o.f.$ =1.13/150, but significantly worse than that with the Compton-thick reflector."1127 The best-fit column density is about 377x107 em7. with an half opening angle of about 30° (but very poorly constrained to be within 10° and 50°) and E.~ 1.5.," The best-fit column density is about $\times$ $^{23}$ $^{-2}$, with an half opening angle of about $^{\circ}$ (but very poorly constrained to be within $^{\circ}$ and $^{\circ}$ ) and $\Gamma\sim$ 1.5."1128 Allowing the absorbing and reflecting material to be different. not surprisingly. a fit as good as the one in Table | 1s recovered: the column density of the torus (now responsible only for the reflection) is 4.7x107 οι”. with a better determined half opening angle of 2571 degrees. and a slightly larger inclination angle.," Allowing the absorbing and reflecting material to be different, not surprisingly, a fit as good as the one in Table \ref{fit} is recovered; the column density of the torus (now responsible only for the reflection) is $\times$ $^{24}$ $^{-2}$, with a better determined half opening angle of $^{+12}_{-4}$ degrees, and a slightly larger inclination angle."1129 As noted earlier. the source flux changes during the observation.," As noted earlier, the source flux changes during the observation."1130 In particular. it is consistently higher in the second half of the observation.," In particular, it is consistently higher in the second half of the observation."1131 To search for spectral variability. we divided the observation into two parts. the dividing time at about 50 ks (elapsed time) from the start of the observation.," To search for spectral variability, we divided the observation into two parts, the dividing time at about 50 ks (elapsed time) from the start of the observation."1132" The resulting spectra (from now on denoted as “low” and ""high) have net exposures of 24 and 35 ks (XIS). and 4-10 keV count rates CXISO) of 0.044540.0015 and 0.0638+40.0015 cts/s. respectively (to be compared with a count rate in the total spectrum of 0.057720.001D)."," The resulting spectra (from now on denoted as “low” and “high”) have net exposures of 24 and 35 ks (XIS), and 4-10 keV count rates (XIS0) of $\pm$ 0.0015 and $\pm$ 0.0015 cts/s, respectively (to be compared with a count rate in the total spectrum of $\pm$ 0.0011)."1133 The 13-50 keV count rates in the PIN are 0.0704£0.005 and 0.07740.004., The 13-50 keV count rates in the PIN are $\pm$ 0.005 and $\pm$ 0.004.1134 The fits with the baseline model (E>4 keV) are reported in Table 1.., The fits with the baseline model $>$ 4 keV) are reported in Table \ref{fit}. .1135 All spectral parameters are consistent with one another within the errors. indicating that the. variation may be entirely due to a change in thenormalization of the," All spectral parameters are consistent with one another within the errors, indicating that the variation may be entirely due to a change in thenormalization of the"1136"At a distance of 4.5 Mpe. M82. nieknamed the ""Southern Pinwheel.” is the nearest massive grand-desien spiral galaxy.","At a distance of 4.5 Mpc, M83, nicknamed the “Southern Pinwheel,” is the nearest massive grand-design spiral galaxy."1137 It is a mildly barred galaxy. with a IIubble type SÀAD(s)c.," It is a mildly barred galaxy, with a Hubble type SAB(s)c."1138 Less Lunous (han its northern counterparts M51 (8.2 AIpe) and ALLOL (7.4 Alpe). M83 has been less studied in general.," Less famous than its northern counterparts M51 (8.2 Mpc) and M101 (7.4 Mpc), M83 has been less studied in general."1139 In this work. we use observations taken with the Camera 3 (WEC3) to study this galaxy in unprecedented detail.," In this work, we use observations taken with the Wide-Field Camera 3 (WFC3) to study this galaxy in unprecedented detail."1140 The combination of hieher spatial resolution. extensive wavelength coverage. aud improved photometric accuracy. especially in the ultraviolet and near-IB. make these the best observations of a graaxd-desien spiral galaxy ever taken.," The combination of higher spatial resolution, extensive wavelength coverage, and improved photometric accuracy, especially in the ultraviolet and near-IR, make these the best observations of a grand-design spiral galaxy ever taken."1141causes the atmosphere there to heat up.,causes the atmosphere there to heat up.1142 Note that the region of heating is lower than when the wave originates higher up. as in Figure 7..," Note that the region of heating is lower than when the wave originates higher up, as in Figure \ref{fig:realsaturatedeep}."1143 The heating ts significant. peaking at ~ K rotation!.," The heating is significant, peaking at $\sim\! 3000$ K $^{-1}$."1144 The ambient temperature can be doubled in approximately half of a planetary rotation., The ambient temperature can be doubled in approximately half of a planetary rotation.1145 In à more realistic scenario. dissipation—which. we have not included in our model—will likely reduce the heating rate.," In a more realistic scenario, dissipation—which we have not included in our model—will likely reduce the heating rate."1146 So far we have been focusing on the vertical transport of momentum and energy by gravity waves., So far we have been focusing on the vertical transport of momentum and energy by gravity waves.1147 However. the waves can also transport momentum and energy (cf.. refsubsubsec:ducting)).," However, the waves can also transport momentum and energy (cf., \\ref{subsubsec:ducting}) )."1148 Substituting ο=2/k into the the index of refraction. equation (11)). and rearranging gives the dispersion relation for gravity waves.," Substituting $c = \omega / k$ into the the index of refraction, equation \ref{eq:indref}) ), and rearranging gives the dispersion relation for gravity waves."1149 Here. we consider the case where 4o=0.," Here, we consider the case where $u_0 = 0$."1150 We will examine cases where uoz0 in the sections following this one., We will examine cases where $u_0 \ne 0$ in the sections following this one.1151 When there is no background mean flow. the dispersion relation simplifies to We can then use the definitions. to obtain the group velocities.," When there is no background mean flow, the dispersion relation simplifies to We can then use the definitions, to obtain the group velocities."1152" They are: Thus. for propagating waves (re... waves for which 7: is real). 4,=0."," They are: Thus, for propagating waves (i.e., waves for which $m$ is real), $u_g \neq 0$."1153 Therefore. gravity waves always propagate obliquely andcannot strictly propagate vertically when there is no background flow.," Therefore, gravity waves always propagate obliquely andcannot strictly propagate vertically when there is no background flow."1154" From equations. (25) we see that /. the angle of propagation with respect to the horizontal. is given by Since H, is nearly constant. with avalue just under 500 km. tan)varies with [/im form>107? m'!."," From equations \ref{eq:noflowgrpvel}) ) we see that $\vartheta$ , the angle of propagation with respect to the horizontal, is given by Since $H_{\rho}$ is nearly constant, with avalue just under 500 km, $\tan \vartheta$varies with $1/m$ for $m\gtrsim10^{-6}$ $^{-1}$ ."1155 This gives rise to, This gives rise to1156Favored theories of giant planet formation center around two main paradieumis. namely the core accretio- model (Saftronov 1969: Goldreich Ward 1973: Pollac et al.,"Favored theories of giant planet formation center around two main paradigms, namely the core accretion model (Safronov 1969; Goldreich Ward 1973; Pollack et al."1157 1996) aud the gravitational iustabilitv iod (Cameroun 1978: Boss 1997)., 1996) and the gravitational instability model (Cameron 1978; Boss 1997).1158 In the frame of the core accretion model. a solid core forms from the accretion of planetesinals and becomes massive enough (~5 to 10 AM) to initiate ruuaway gravitational infall of a large eascous envelope in which egas-couplecd solids coutinue their acerction (Alibert et al.," In the frame of the core accretion model, a solid core forms from the accretion of planetesimals and becomes massive enough $\sim$ 5 to 10 ) to initiate runaway gravitational infall of a large gaseous envelope in which gas-coupled solids continue their accretion (Alibert et al."1159 20052: IHubickvj ct al., 2005a; Hubickyj et al.1160 2005: Mordasini et al., 2005; Mordasini et al.1161 2009)., 2009).1162 This model provides the large amount of heavy oclemenuts uccessary to explain the supersolar imetallicities observed iu Jupiter aud Saturn via the accretion of planetesimals in their euvelopes (Gautier et al., This model provides the large amount of heavy elements necessary to explain the supersolar metallicities observed in Jupiter and Saturn via the accretion of planetesimals in their envelopes (Gautier et al.1163 2001: Sammon Cuillot 2001: Alibert et al., 2001; Saumon Guillot 2004; Alibert et al.1164 20052: Mousis ct al., 2005a; Mousis et al.1165 2006. 2009a).," 2006, 2009a)."1166 In the value of the eravitational instability model. eas eiut protoplaucts form rapidly through a eravitational instability of the eascous portion of the disk aud then more slowly coutract to planetary deusities (Boss 1997. 2005).," In the frame of the gravitational instability model, gas giant protoplanets form rapidly through a gravitational instability of the gaseous portion of the disk and then more slowly contract to planetary densities (Boss 1997, 2005)."1167 Tn this scenario. due to the limited efficiency. of planctesimals accretion durus the planet formation. its metalicity should be slightly higrer or equal to that of the parcont star (Ielled Dodenhbeiner 2010).," In this scenario, due to the limited efficiency of planetesimals accretion during the planet formation, its metallicity should be slightly higher or equal to that of the parent star (Helled Bodenheimer 2010)."1168 A puzzliis feature of he transiting rot Jupiter ΠΟ 189733h (A I—-115zu.YL M) orbitiue a W2V stellar priuarv a the ciistauuicc| of 0.03. AU (Bouchy et. al., A puzzling feature of the transiting hot Jupiter HD 189733b (M = 1.15$\pm$ 0.04 $_J$ ) orbiting a K2V stellar primary at the distance of 0.03 AU (Bouchy et al.1169 2005) Is its metallicity. |)etween subsolar to supoersoar (seo Fig.," 2005) is its metallicity, between subsolar to supersolar (see Fig."1170 1) from deternunations of carbon aud oxveeu atiuosplieric abundances ., 1) from determinations of carbon and oxygen atmospheric abundances .1171of the light. curves. the time olfset of the initial spectrums is the dillerence between the arrival of the direct. continuum Hux and the first appearance of the iron line.,"of the light curves, the time offset of the initial spectrum is the difference between the arrival of the direct continuum flux and the first appearance of the iron line."1172 There is a clear dillerence between the results for the two considered extremal values of the spin parameter (e.g. compare Fig., There is a clear difference between the results for the two considered extremal values of the spin parameter (e.g. compare Fig.1173 4 and LFig.6)., 4 and Fig.6).1174 The iron line extends to lower frequencies in the Ixerr case which is due to the cold iron line being produced very close to the black hole., The iron line extends to lower frequencies in the Kerr case which is due to the cold iron line being produced very close to the black hole.1175 Ehe influence of the ionization of the accretion disc below the radius of marginal stabilitv ry.=123m is relatively unimportant., The influence of the ionization of the accretion disc below the radius of marginal stability $r_{ms}=1.23m$ is relatively unimportant.1176 On the contrary. in the case of the Schwarzschilel black hole the ilk of the cold iron line is produced only above ως=6m and accretion disc may be in hiehly ionized within this radius.," On the contrary, in the case of the Schwarzschild black hole the bulk of the cold iron line is produced only above $r_{ms}=6m$ and accretion disc may be in highly ionized within this radius."1177 “Phus for r«6m the line may. be either destroved w the Auger process or not. produced. because of the total ionization of the cise material., Thus for $r < 6m$ the line may be either destroyed by the Auger process or not produced because of the total ionization of the disc material.1178 The radiation [rom this region would be subject to high energy shifts which means hat the lack of the iron line flux at lower energies. (see lig., The radiation from this region would be subject to high energy shifts which means that the lack of the iron line flux at lower energies (see Fig.1179" 5 and Fig.6) is the result of the fact that some parts of the disc below 5,4;=6m cannot produce the iron line.", 5 and Fig.6) is the result of the fact that some parts of the disc below $r_{ms}=6m$ cannot produce the iron line.1180 For the [lare at the position «μι the regions on the disc, For the flare at the position $\phi_{flare}$ the regions on the disc1181days for the inner planet and. 18 hours for the outer planet. which both compare well with the numerical results given that the eccentricities are not constant.,days for the inner planet and 18 hours for the outer planet which both compare well with the numerical results given that the eccentricities are not constant.1182 The extrasolar planetary svstem 55 Cancri contains à set of planets. b and ce. near the 3:1 resonance having 15 and 45 dav periods.," The extrasolar planetary system 55 Cancri contains a set of planets, $b$ and $c$, near the $3$ $1$ resonance having 15 and 45 day periods."1183 There is some evidence for another planet. d. in an extremely long orbit. and recentlya fourth low mass planet. c. was found with a 2.8 day period (2)..," There is some evidence for another planet, $d$, in an extremely long orbit, and recentlya fourth low mass planet, $e$, was found with a 2.8 day period \citep{mca04}."1184 Phe planets e. b. and e have transit probabilities of 12. 4. and 2 per cent. respectively. or an observer at arbitrary inclination.," The planets $e$, $b$, and $c$ have transit probabilities of 12, 4, and 2 per cent, respectively, for an observer at arbitrary inclination."1185 The orbit of planet 6 is approximately circular while planet e is somewhat eccentric (?).., The orbit of planet $b$ is approximately circular while planet $c$ is somewhat eccentric \citep{mar02}.1186 Table 1 gives the amplitude of the variations for the planets., Table 1 gives the amplitude of the variations for the planets.1187 We have ignored planet e: however. it is at a large enough semi-major axis to produce a  22 second. variation due to light-travel time as the barveenter of the inner binary orbits the xwvcenter of the triple svstem were the inner planets transiting.," We have ignored planet $e$; however, it is at a large enough semi-major axis to produce a $\sim$ 22 second variation due to light-travel time as the barycenter of the inner binary orbits the barycenter of the triple system were the inner planets transiting."1188 The double planet system Upsilon Andromedae has a semi-major axis ratio of 14 which is not in à mean-motion resonance (?7)..," The double planet system Upsilon Andromedae has a semi-major axis ratio of 14 which is not in a mean-motion resonance \citep{but99,mar01}."1189 The inner planet has a short period of 4.6 days. and thus a significant probability of transiting of about 12 per cent. rut has variations which are too small to currently. be detected from the ground or space.," The inner planet has a short period of 4.6 days, and thus a significant probability of transiting of about 12 per cent, but has variations which are too small to currently be detected from the ground or space."1190 “Phe outer planet has much larger ransit timing variations due to its smaller velocity. but a much smaller probability of transiting.," The outer planet has much larger transit timing variations due to its smaller velocity, but a much smaller probability of transiting."1191 The planetary system HD 37124 has two planets with a period ratio of ~10 and a period of the inner planet of 241 days (?).., The planetary system HD 37124 has two planets with a period ratio of $\sim 10$ and a period of the inner planet of 241 days \citep{vog00}.1192 The outer planet is highly: eccentric. e».=0.69. and so its periapse passage produces a large and rapid change in the ransit timing of the inner planet.," The outer planet is highly eccentric, $e_2 =0.69$, and so its periapse passage produces a large and rapid change in the transit timing of the inner planet."1193 ΤΕ this svstem were transiting. the variations would be large enough to be detected. [rom he ground.," If this system were transiting, the variations would be large enough to be detected from the ground."1194 LID 82943 is in à 2:1 resonance giving variations of order the periods ofthe planets., HD 82943 is in a 2:1 resonance giving variations of order the periods of the planets.1195 The pulsar planets are near a 32 resonance. which would cause large transit timing variations were they seen to transit the pulsar progenitor star.," The pulsar planets are near a 3:2 resonance, which would cause large transit timing variations were they seen to transit the pulsar progenitor star."1196 Finally. alien civilizations observing transits of the Sun by Jupiter would have to have ~ 10 second accuracy to detect the elfeet of he Earth.," Finally, alien civilizations observing transits of the Sun by Jupiter would have to have $\sim$ 10 second accuracy to detect the effect of the Earth."1197 The possibility of detecting terrestrial planets using the transit timing technique clearly depends strongly on (1) the period of the transiting planet: (2) the nearness to resonance of the two planets: (3) the eccentricities of the planets., The possibility of detecting terrestrial planets using the transit timing technique clearly depends strongly on (1) the period of the transiting planet; (2) the nearness to resonance of the two planets; (3) the eccentricities of the planets.1198 The detectability of such planets also depends on the measurement error. the intrinsic noise due to stellar variability. and the number of transit timing measurements.," The detectability of such planets also depends on the measurement error, the intrinsic noise due to stellar variability, and the number of transit timing measurements."1199 One requirement for the case of an external perturbing planet is that observations should be made over a time longer than the period of the timing variations. which can be longer than the period of the perturbing planet.," One requirement for the case of an external perturbing planet is that observations should be made over a time longer than the period of the timing variations, which can be longer than the period of the perturbing planet."1200 Ienoring these complications. a rough estimate of detectability can be obtained from comparing the standard. deviation of the transit timing with the measurement error.," Ignoring these complications, a rough estimate of detectability can be obtained from comparing the standard deviation of the transit timing with the measurement error."

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