ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The flux density of 22004et is too low compared to the rms of the visibility amplitudes (20 mmdJy) for obtaining a good result with the test of the closure phase distribution., The flux density of 2004et is too low compared to the rms of the visibility amplitudes $\sim$ mJy) for obtaining a good result with the test of the closure phase distribution.3 The average value of the cosines of all the closure phases considered in these observations is equal to 0.005+0.002., The average value of the cosines of all the closure phases considered in these observations is equal to $0.005\pm0.002$.4 This average value is slightly higher than 0., This average value is slightly higher than 0.5 The average of the absolute values of the closure phases ts 0.0065+0.0020., The average of the absolute values of the closure phases is $0.0065\pm0.0020$.6 From Fig., From Fig.7 2. we estimate a flux density of the supernova of 0.18£0.08 times the rms of the visibility amplitudes. o. used in our computations. which. as said above. is ~20 mmJy.," \ref{RelaTeo} we estimate a flux density of the supernova of $0.18\pm0.08$ times the rms of the visibility amplitudes, $\rho$, used in our computations, which, as said above, is $\sim20$ mJy."8 Hence. the estimated flux density of the (real) source in the data ts. then. 3.8+ 1.6mmJy.," Hence, the estimated flux density of the (real) source in the data is, then, $3.8\pm1.6$ mJy."9 This value is too high. but compatible (at a 2-sigma level) with the flux density estimated from the," This value is too high, but compatible (at a 2–sigma level) with the flux density estimated from the"10test our FOR output data. Subhonenko Ciramann (2003) investigated the mass function of clusters.,"test our FOF output data, Suhhonenko Gramann (2003) investigated the mass function of clusters."11 The cluster mass function in the Virgo simulations has been studied in detail bv Jenkins et al. (, The cluster mass function in the Virgo simulations has been studied in detail by Jenkins et al. (122001).,2001).13 Suhhonenko Cramann (2003) found that the agreement between our results and. these obtained by Jenkins et al. (, Suhhonenko Gramann (2003) found that the agreement between our results and these obtained by Jenkins et al. (142001) is very good.,2001) is very good.15" The FOP cluster finder depends on one parameter b. which defines the linking length as 6A,."," The FOF cluster finder depends on one parameter $b$, which defines the linking length as $b\lambda_p$."16 The conventional choice for this parameter is 6=0.2 (see e.g. Góttz. Lluchra Drandenberger 1998: Jenkins et al.," The conventional choice for this parameter is $b=0.2$ (see e.g. Göttz, Huchra Brandenberger 1998; Jenkins et al."17 2001)., 2001).18 In this paper we also define clusters by using the value 6=0.2., In this paper we also define clusters by using the value $b=0.2$.19 We also study. velocities of the clusters defined. by the parameters b=0.15., We also study velocities of the clusters defined by the parameters $b=0.15$.20 In the limit of very large numbers of particles per object. FOR approximately selects the matter enclosed. by an Isodensity contour at. ορ.," In the limit of very large numbers of particles per object, FOF approximately selects the matter enclosed by an isodensity contour at $\rho_b/b^3$."21 We studied FOF clusters that contained at least. ten particles., We studied FOF clusters that contained at least ten particles.22 Phe three-dimensional peculiar velocity. of each cluster was defined as where Ny is the number of particles in the cluster and Fis the peculiar velocity of the particle # in the cluster.," The three-dimensional peculiar velocity of each cluster was defined as where $N_{f}$ is the number of particles in the cluster and $\vec23v_i$ is the peculiar velocity of the particle $i$ in the cluster."24 We also selected DALAN clusters using the following method. (, We also selected DMAX clusters using the following method. (251) We calculated the density contrast on a eric.,1) We calculated the density contrast on a grid.26" For each grid point. the density contrast was determined as where AN ds the number of particles in the sphere of raciius £2, around the grid. point. and is the mean number of particles in the sphere of radius ("," For each grid point, the density contrast was determined as where $N$ is the number of particles in the sphere of radius $R_s$ around the grid point, and is the mean number of particles in the sphere of radius $R_s$. ("272) We found the density maxima on the grid.,2) We found the density maxima on the grid.28 The erid point was considered. as a density. maximum. if its clensity contrast. was higher than the density contrast. in all 26 neighbouring erid points.," The grid point was considered as a density maximum, if its density contrast was higher than the density contrast in all 26 neighbouring grid points."29 The location of the eric point. where the density contrast had a maximum. value. was identified as the candidate eluster centre. (," The location of the grid point, where the density contrast had a maximum value, was identified as the candidate cluster centre. ("303) The final cluster list was obtained by deleting the candidate clusters with lower density contrast in all. pairs separated by less than the radius /?..,3) The final cluster list was obtained by deleting the candidate clusters with lower density contrast in all pairs separated by less than the radius $R_s$.31 In this wav we define the clusters as maxima of the density. field smoothecl by a top-hat window: with a radius Hus, In this way we define the clusters as maxima of the density field smoothed by a top-hat window with a radius $R_s$.32 Vhe smoothing length sets a lower limit on the size of detected structures in the simulations., The smoothing length sets a lower limit on the size of detected structures in the simulations.33" We used the smoothing radii 2,=1.5h Alpe and R=1.0h !Mpe.", We used the smoothing radii $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc.34 The mean number of particles in spheres of Ry=15h* Mpe and By=1.057 Alpe is N=17.26 and N= 5.12. respectively.," The mean number of particles in spheres of $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc is $\bar N=17.26$ and $\bar N=5.12$ , respectively."35 To select the Ry=1.55.+ Alpe clusters. we used a 256% grid (the cell size /=0.920 Alpe).," To select the $R_s=1.5h^{-1}$ Mpc clusters, we used a $256^3$ grid (the cell size $l=0.936 h^{-1}$ Mpc)."36 For ἐς=1.0ht Alpe. we used a 350° grid (/=0.68401 Alpe).," For $R_s=1.0h^{-1}$ Mpc, we used a $350^3$ grid $l=0.684 h^{-1}$ Mpc)."37" For comparison. for the 2.=1.05.1 Alpe clusters we used alsoa 256""RH &rid."," For comparison, for the $R_s=1.0h^{-1}$ Mpc clusters we used alsoa $256^3$ grid."38 We studied. the rms density contrast and. the rms peculiar velocity on the 256° eric., We studied the rms density contrast and the rms peculiar velocity on the $256^3$ grid.39 Phe rms density contrast on the grid. was 5.05 and [29 for the radii R=15h+ Alpe and A;=L.0f* Alpe. respectively.," The rms density contrast on the grid was $5.05$ and $7.29$ for the radii $R_s=1.5h^{-1}$ Mpc and $R_s=1.0h^{-1}$ Mpc, respectively."40 The ris peculiar velocity. σοι was determined for the fraction of grid points. P. where the number of particles ΑΝ1l.," The rms peculiar velocity, $\sigma_v$, was determined for the fraction of grid points, $F$, where the number of particles $N>1$."41 Uf there are no particles in the neighbourhood of a grid point. the velocity field is undetermined.," If there are no particles in the neighbourhood of a grid point, the velocity field is undetermined."42" For R,=L.5h+ Alpe. we found that f=0.96 and σι=473kms5."," For $R_s=1.5h^{-1}$ Mpc, we found that $F=0.96$ and $\sigma_v=473 \kms$."43 For Ry=LOb+ Alpe. f=0.69 and σι=481kms1 respectively.," For $R_s=1.0 h^{-1}$ Mpc, $F=0.69$ and $\sigma_v=481 \kms$, respectively."44 Here we took into account the finite size of the simulation box (sec next section)., Here we took into account the finite size of the simulation box (see next section).45 We also studied the rms density contrast ane the rms peculiu velocity on the 350% eric anc found. similar results., We also studied the rms density contrast and the rms peculiar velocity on the $350^3$ grid and found similar results.46 For each DALAN cluster. we investigated the cluster mass. AM. and the peculiar velocity. ey. at the radius. f.," For each DMAX cluster, we investigated the cluster mass, $M$, and the peculiar velocity, $v_{cl}$, at the radius $R_s$."47" The mass in the cluster was determined as Al=Nyni). where IN, is the number of particles in a sphere of radius AR. around the centre of the cluster."," The mass in the cluster was determined as $M=N_d \,m_p$, where $N_d$ is the number of particles in a sphere of radius $R_s$ around the centre of the cluster."48 The peculiar velocity of each cluster was defined as where ο is the peculiar velocity of the particle 7 in the DAIAN cluster., The peculiar velocity of each cluster was defined as where $\vec v_i$ is the peculiar velocity of the particle $i$ in the DMAX cluster.49 Suhhonenko Cramann (2003) compared the cluster peculiar velocities defined by dillerent methocls (i.e. the FOL method versus the DALAN method) for massive clusters., Suhhonenko Gramann (2003) compared the cluster peculiar velocities defined by different methods (i.e. the FOF method versus the DMAX method) for massive clusters.50 By using dillerent. methods to identify the clusters. we select almost the same objects in the simulation.," By using different methods to identify the clusters, we select almost the same objects in the simulation."51 But we assign cillerent velocities to the same clusters., But we assign different velocities to the same clusters.52 To determine the rms peculiar velocities of clusters. we used the equation where the parameter ος describes the dispersion. of cluster velocities. Όρη derived from the simulations ancl the parameter ej is the linear contribution from the velocity Iluctuations on scales greater than the size of the simulation box L.," To determine the rms peculiar velocities of clusters, we used the equation where the parameter $v_s$ describes the dispersion of cluster velocities, $v_{cli}$, derived from the simulations and the parameter $v_L$ is the linear contribution from the velocity fluctuations on scales greater than the size of the simulation box $L$ ."53 Ht is given by Ny is the number of clusters studied., It is given by $N_{cl}$ is the number of clusters studied.54 Using eq. (, Using eq. (554). the linear rms peculiar velocity of peaks can be written as The second term in this expression is not sensitive to the amplitude of large-scale[uctuations at wavenumbers &.< 2x/L.,"4), the linear rms peculiar velocity of peaks can be written as The second term in this expression is not sensitive to the amplitude of large-scalefluctuations at wavenumbers $k<2\pi/L$ ."56" Vherefore. the linear rms velocity of peaks can be expressed. approximately. as where m,CH)' is. determined. by the power spectruni at the wavenumbers &2x/L andej is given by eq. ("," Therefore, the linear rms velocity of peaks can be expressed, approximately, as where $\sigma_p^{\prime} (R)$ is determined by the power spectrum at the wavenumbers $k>2\pi/L$ and$v_L$ is given by eq. ("5711).,11).58Figure & shows the normalized average power spectra of LOS velocity of the two chromospheric aand ID)) and two of the plotospheric aud À 3969.3) lines inside the uubra of the suuspot.,Figure \ref{fig:power_spectra} shows the normalized average power spectra of LOS velocity of the two chromospheric and ) and two of the photospheric and $\lambda$ 3969.3) lines inside the umbra of the sunspot.59 We chose lis iron line because it has better signal to noise aud its ormation height is distant from the laver where iis formed., We chose this iron line because it has better signal to noise and its formation height is distant from the layer where is formed.60 In the photosphere (bottom panel). the power is concentrated between 2 and { πα]. correspouding to he 5 minute baud. with a maxinuun peak at 3.5 1uIIEz.," In the photosphere (bottom panel), the power is concentrated between 2 and 4 mHz, corresponding to the 5 minute band, with a maximum peak at 3.5 mHz."61 Both spectral lines peak at the same frequency. although he power of the lue is slightlv higher.," Both spectral lines peak at the same frequency, although the power of the line is slightly higher."62 The increase of the power at requeucies above 1.5 mllz is more important than the oue for frequencies below this value., The increase of the power at frequencies above 4.5 mHz is more important than the one for frequencies below this value.63 The velocity power spectra of both chromospheric mes (top panel) have a broad distribution of frequencies. with he largest power beiug in the baud from 5 to 10 112.," The velocity power spectra of both chromospheric lines (top panel) have a broad distribution of frequencies, with the largest power being in the band from 5 to 10 mHz."64 The chromospheric power spectra has a maxi at 6.2 inllz aud several secondary peaks around it (sceforconrparisouLites1986)., The chromospheric power spectrum has a maximum at 6.2 mHz and several secondary peaks around it \citep[see for comparison][]{Lites1986}.65. These frequency. peaks correspond to the chromospheric 3 minutes oscillatious., These frequency peaks correspond to the chromospheric 3 minutes oscillations.66 At the highest peak of the power spectra. both aan thave almost the sane power. but for those frequeucies with lower power. the power of the lis ducreased comparing to theΕΠ.," At the highest peak of the power spectra, both and have almost the same power, but for those frequencies with lower power, the power of the is increased comparing to the."67.. Note that at weights sampled by our spectral lines we do not find a continuous transition from the peak at 23.5 illz o the oue at 6.2 mllz. but rather a cdiscontinuous vchavior between the photospherie aud chromospleric oower spectra.," Note that at heights sampled by our spectral lines we do not find a continuous transition from the peak at 3.5 mHz to the one at 6.2 mHz, but rather a discontinuous behavior between the photospheric and chromospheric power spectra."68 However. the promincut secondary. peak around 5.5 iilIz in the power spectra of the line is wich more obvious than the corresponding iu the ypower spectra. which could indicate some transition owards higher frequencics in the power spectra as the waves propagate upward from the formation height of he lime to the lines.," However, the prominent secondary peak around 5.5 mHz in the power spectra of the line is much more obvious than the corresponding in the power spectra, which could indicate some transition towards higher frequencies in the power spectra as the waves propagate upward from the formation height of the line to the lines."69 A phase diagram gives the phase difference (Ao) between two signals., A phase diagram gives the phase difference $\Delta \phi$ ) between two signals.70 Di our study; we use Ao to nieasure the time delay between the oscillatory velocity signals frou. two spectral lines aud assume that the difference between them is mainly due to the difference of the formation height of the two lines.," In our study, we use $\Delta \phi$ to measure the time delay between the oscillatory velocity signals from two spectral lines and assume that the difference between them is mainly due to the difference of the formation height of the two lines."71 In the following. we will show the phase difference spectra between differeut combinations of pairs of spectral lines used in this work.," In the following, we will show the phase difference spectra between different combinations of pairs of spectral lines used in this work."72 To obtain the phase spectra. we treated cach spatial point separately and calculated the Fourier-transtorm of the temporal evolution of the respective velocities.," To obtain the phase spectra, we treated each spatial point separately and calculated the Fourier-transform of the temporal evolution of the respective velocities."73 We derived the phases. aud from them the phase difference of the two signals as a function of the frequency.," We derived the phases, and from them the phase difference of the two signals as a function of the frequency."74 There is a 2z ambiguity in the computation of the pliase value. so all phase differences have been projected in the range cz.," There is a $\pi$ ambiguity in the computation of the phase value, so all phase differences have been projected in the range $\pm \pi$."75 Then we calculated listograms of the relative occurrence of a given value of the plase differences at cach frequency takiug into account all the corresponding spatial points (seealsoKvijgeretal.2001.andreferences thereiu).., Then we calculated histograms of the relative occurrence of a given value of the phase differences at each frequency taking into account all the corresponding spatial points \citep[see also][ and references therein]{Krijger+etal2001}. .76" We obtained the data displaved in Έπος, 9- 15..", We obtained the data displayed in Figs. \ref{fig:dfase_SiHe}- \ref{fig:dfase_FeSi_quiet}.77 Iun addition. to the phase difference spectra. we calculated the coherence spectra.," In addition to the phase difference spectra, we calculated the coherence spectra."78 They provide au estimate of the statistical validity of the phase aud power spectra., They provide an estimate of the statistical validity of the phase and power spectra.79 Consideriug » pairs of signals ο) aud gilt). whose Fourier transforius are IX(uw) aud ία). respectively. the coherence is defined as where Aople)=οί) hi," Considering $n$ pairs of signals $x_k(t)$ and $y_k(t)$, whose Fourier transforms are $\bar{X}_k(\omega)$ and $\bar{Y}_k(\omega)$, respectively, the coherence is defined as where $\Delta\phi_k(\omega)=\phi_{xk}(\omega)-\phi_{yk}(\omega)$."80 our case. the sub-index Á& covers the spatial Oye(e).position.," In our case, the sub-index $k$ covers the spatial position."81" The colerence evaluates statistically for every frequency w the relation of the Ao,(e) for the » A-siguals.", The coherence evaluates statistically for every frequency $\omega$ the relation of the $\Delta\phi_k(\omega)$ for the $n$ $k$ -signals.82 It takes the value 1 when Δωρίω) is the same for all the &., It takes the value 1 when $\Delta\phi_k(\omega)$ is the same for all the $k$.83 If the phase difference of the different À is arbitrary. the coherence takes very low values.," If the phase difference of the different $k$ is arbitrary, the coherence takes very low values."84 We selected a confidence limut at 0.7. and for frequencies with coherence above this value we consider the pliase spectra to be reliable.," We selected a confidence limit at 0.7, and for frequencies with coherence above this value we consider the phase spectra to be reliable."85 We also analyzed the increase of the amplitude of the oscillations., We also analyzed the increase of the amplitude of the oscillations.86 We calculated the amplification spectra as the ratio between the power at two lavers. both of them averaged all over the mubra: Following Centeneetal.(2006).. the observations were compared with a amodel of linear vertical propagation of slow magucto-acoustic wave in an isothermal atmosphere that iuchudes radiative losses described by Newtous cooling law.," We calculated the amplification spectra as the ratio between the power at two layers, both of them averaged all over the umbra: Following \citet{Centeno+etal2006}, the observations were compared with a model of linear vertical propagation of slow magneto-acoustic wave in an isothermal atmosphere that includes radiative losses described by Newton's cooling law."87 Assuming that the iuuplitude of the vertical velocity changeswith height by, Assuming that the amplitude of the vertical velocity changeswith height by88 isetal.,s et al.89 with the allowed transitions listed in the compilation of Verner et al..," with the allowed transitions listed in the compilation of Verner et al.,"90" making a total of 48 transitions involving the ground 7 P"" levels ancl upper levels.", making a total of 48 transitions involving the ground $^2$ $^o$ levels and upper levels.91 Phe indirect excitation rate by the UV radiation field of the Galaxy could then be determined: Piz=9.310Haul, The indirect excitation rate by the UV radiation field of the Galaxy could then be determined: $\Gamma_{\frac{1}{2}\frac{3}{2}}=9.3\ 10^{-11}\ \mathrm{s}^{-1}$.92 In order to assess the relevance of the ὃς δρ configuration upper levels in the relative population of the eround “Pom4 levels. we have performed. test. caleulations comparing 2:2our LO-level model ion with the 2-Ievel ion.," In order to assess the relevance of the 2s $^2$ configuration upper levels in the relative population of the ground $^2\mathrm{P}^o_{\frac{1}{2},\frac{3}{2}}$ levels, we have performed test calculations comparing our 10-level model ion with the 2-level ion."93 At high. temperatures the 2s 2p2 configuration⋅. levels may be excited. by collisions with hot electrons in the medium., At high temperatures the 2s $^2$ configuration levels may be excited by collisions with hot electrons in the medium.94" llowever. the testeases have shown that this elfect does not contribute significantly to the excitation of the 7"" levels for temperatures 2<<30000 Ix. where the discrepancies reach about 5 percent."," However, the testcases have shown that this effect does not contribute significantly to the excitation of the $^2\mathrm{P}^o$ levels for temperatures $T\leq 30000$ K, where the discrepancies reach about 5 percent."95 Therefore. for temperatures lower than 30000 Ix. only two levels can be taken into account.," Therefore, for temperatures lower than 30000 K, only two levels can be taken into account."96 The population ratio of the excited. [ine-structure level relatively to the ground level is then expressed by:, The population ratio of the excited fine-structure level relatively to the ground level is then expressed by:97thines these are hampered by uucertainties concerning the plivsies of the mnerinost disk regiois.,things these are hampered by uncertainties concerning the physics of the innermost disk regions.98 Yot woe note that in the hydrodvuamical approach explored by Psaltis Norma1 (2000). the test particle frequencies (the same as in the RPAL plus an adclitiona freqicacy at νο|14.) are selected by the response of an annulus in the disk. whe1 this is subject to a wide-band input noise.," Yet we note that in the hydrodynamical approach explored by Psaltis Norman (2000), the test particle frequencies (the same as in the RPM plus an additional frequency at $\nu_\phi+\nu_r$ ) are selected by the response of an annulus in the disk, when this is subject to a wide-band input noise."99 If confirmed. the RPAL will provide an uuprecedeuted opportunity to micasure CR effect E he strong field regime. such as the periastrou precession in the vicidtv of the mareinally stable orbit and the racial dependence of the Lense- jodal precession frequency.," If confirmed, the RPM will provide an unprecedented opportunity to measure GR effects in the strong field regime, such as the periastron precession in the vicinity of the marginally stable orbit and the radial dependence of the Lense-Thirring nodal precession frequency."100 Iu. principle. accurately measured kHz QPO and TBO freqiencies would vield crucial information ou the compact object sucli as its lass al angular moment by solving Eqs.," In principle, accurately measured kHz QPO and HBO frequencies would yield crucial information on the compact object such as its mass and angular momentum by solving Eqs."101 1-3 for ii. afAL aud r).," 1-3 for $m$, $a/M$ and $r$ )."102" Should suitable. additional observables be found. it might become possible to obtain a scelfconsistencey check of the RPM. toseether with tests of GB iu the strong field reele,"," Should suitable, additional observables be found, it might become possible to obtain a self-consistency check of the RPM, together with tests of GR in the strong field regime."103 , 104computed the Anderson-Darling statistic. as described by ?.. for each group.,"computed the Anderson-Darling statistic, as described by \citet{Hou09}, for each group."105 Only group 15 shows significant non-Gaussianity in the velocity distribution. at 795 per cent contidence.," Only group 15 shows significant non-Gaussianity in the velocity distribution, at $>95$ per cent confidence."106 Other indications of a relaxed cluster. could. be the presence of a dominant galaxy near the X-ray centre (e.g.2).. and an approximately spherical. centrally-concentrated galaxy distribution.," Other indications of a relaxed cluster could be the presence of a dominant galaxy near the X-ray centre \citep[e.g.][]{D+10}, and an approximately spherical, centrally–concentrated galaxy distribution."107 In many of the clusters. there is an obvious dominant galaxy. large and luminous. near the centre of the X-ray image.," In many of the clusters, there is an obvious dominant galaxy, large and luminous, near the centre of the X-ray image."108 To quantify this. we have selected all cluster members within 700 km/s Xf the mean redshift and 500 Κρο of the recomputed centre. and identified the most luminous (in A) as the BCG.," To quantify this, we have selected all cluster members within 700 km/s of the mean redshift and 500 kpc of the recomputed centre, and identified the most luminous (in $K$ ) as the BCG."109 Figure 14. shows the luminosity of each of these BCGs. as a function of the host cluster £Lx.," Figure \ref{fig-bcg_mag} shows the luminosity of each of these BCGs, as a function of the host cluster $L_X$."110 There is little correlation here. although we note that tree of the X-ray undetected clusters have BCGs that are among t1ο least luminous in the sample (unfortunately. all three have only shallow 2MASS imaging. and thus the total luminosities may be significantly underestimated).," There is little correlation here, although we note that three of the X-ray undetected clusters have BCGs that are among the least luminous in the sample (unfortunately, all three have only shallow 2MASS imaging, and thus the total luminosities may be significantly underestimated)."111 It is also interesting that group 15. which has a high stellar mass given its Zy. has one of the mos massive BCOs in the sample.," It is also interesting that group 15, which has a high stellar mass given its $L_X$, has one of the most massive BCGs in the sample."112 Next we calculated the luminosity ratio between the first- anc third-ranked galaxy. Lj45.," Next we calculated the luminosity ratio between the first- and third-ranked galaxy, $L_{K,13}$."113 In Figure 15 we show this as a function of AZ. which is the distance in Mpc between the brightest cluster galaxy (BCG) and the geometric centre of the cluster. recomputed as above.," In Figure \ref{fig-bcgs} we show this as a function of $\Delta R$, which is the distance in Mpc between the brightest cluster galaxy (BCG) and the geometric centre of the cluster, recomputed as above."114 Interestingly. the distribution of the X-ray undetected clusters (and also the outlier group 15) is distinet from most of the “normal” systems. in the sense that their BCG is at least 250 Κρο from the centre.," Interestingly, the distribution of the X-ray undetected clusters (and also the outlier group 15) is distinct from most of the “normal” systems, in the sense that their BCG is at least 250 kpc from the centre."115" However. we note that. of the 12 otherwise ""normal"" systems. only about half have a dominant CLis> 3). centrally located (AR«250 κο BCG,"," However, we note that, of the 12 otherwise “normal” systems, only about half have a dominant $L_{K,13}>3$ ), centrally located $\Delta R<250$ kpc) BCG."116 We now attempt to quantify the spatial distribution ofthe most luminous galaxies. i.e. those that are at most 0.6 mag fainter than Aly. so that we are equally deep in all clusters.," We now attempt to quantify the spatial distribution of the most luminous galaxies, i.e. those that are at most 0.6 mag fainter than $M_K^\ast$, so that we are equally deep in all clusters."117 The undetected cluster 18 only has three galaxies above this limit. so we omit it from the following analysis.," The undetected cluster 18 only has three galaxies above this limit, so we omit it from the following analysis."118" We calculate the concentration as he fraction of such cluster members within 0.5/2,,,.", We calculate the concentration as the fraction of such cluster members within $0.5R_{\rm rms}$.119 For the elongation. we first perform a least-squares regression analysis to tind the principle axis of each cluster on the sky: then we calculate he dispersion perpendicular to and parallel to this axis.," For the elongation, we first perform a least-squares regression analysis to find the principle axis of each cluster on the sky; then we calculate the dispersion perpendicular to and parallel to this axis."120 The elongation is the ratio of the two values. always defined as the arger divided by the smaller so the ratio is greater than unity.," The elongation is the ratio of the two values, always defined as the larger divided by the smaller so the ratio is greater than unity."121 The results are shown in Figure 16.. where the points are colour-coded as before.," The results are shown in Figure \ref{fig-shapes}, where the points are colour-coded as before."122 Error bars are computed using a jackknife resampling., Error bars are computed using a jackknife resampling.123 Interestingly. most of the X-ray underluminous systems again appear separated from the majority of the population. as either low-concentration or highly elongated clusters.," Interestingly, most of the X-ray underluminous systems again appear separated from the majority of the population, as either low-concentration or highly elongated clusters."124 Only cluster 17 lies in a region of the plane occupied by the majority of normal clusters., Only cluster 17 lies in a region of the plane occupied by the majority of normal clusters.125 Note that cluster 16 is highly elongated: from Figure 15 we see that it has a distinctly dominated galaxy. but located 350 kpe from the centre.," Note that cluster 16 is highly elongated; from Figure \ref{fig-bcgs} we see that it has a distinctly dominated galaxy, but located 350 kpc from the centre."126 This may indicate a merging or otherwise unrelaxed system., This may indicate a merging or otherwise unrelaxed system.127 Cluster 18. which is the only other X-ray undetected system with a dominant. centrally-located galaxy. has too few members to measure either quantity shown here with adequate precision.," Cluster 18, which is the only other X–ray undetected system with a dominant, centrally-located galaxy, has too few members to measure either quantity shown here with adequate precision."128 Again. however. there are examples of clusters (3 and 9) with normal X-ray properties and equally low concentrations.," Again, however, there are examples of clusters (3 and 9) with normal X-ray properties and equally low concentrations."129 This result needs to be approached with some caution. as there are multiple parameters at work here. related to the magnitude and velocity selections. the choice of centre. and the definition of concentration.," This result needs to be approached with some caution, as there are multiple parameters at work here, related to the magnitude and velocity selections, the choice of centre, and the definition of concentration."130 Nonetheless. we tentatively conclude that it seems likely dynamical age plays some role in the X-ray luminosity of a given cluster.," Nonetheless, we tentatively conclude that it seems likely dynamical age plays some role in the X-ray luminosity of a given cluster."131 All the clusters that appear relaxed in the optical — with a dominant central galaxy Qvithin 250kpe of the cluster centre. and at least three times brighter than the third-ranked galaxy). a centrally concentrated (> 0.25) galaxy population. and a spatial axis ratio of less than two — show normal X-ray," All the clusters that appear relaxed in the optical – with a dominant central galaxy (within 250kpc of the cluster centre, and at least three times brighter than the third–ranked galaxy), a centrally concentrated $>0.25$ ) galaxy population, and a spatial axis ratio of less than two – show normal X-ray"132interstellar column density.,interstellar column density.133 Several qualitative conclusions can be drawn from. the observations: First. in all cases. there is a deficit of emission expected from lower temperatures.," Several qualitative conclusions can be drawn from the observations: First, in all cases, there is a deficit of emission expected from lower temperatures."134 Second. in most cases. a continuous distribution of temperatures is nevertheless required.," Second, in most cases, a continuous distribution of temperatures is nevertheless required."135 Finally. absorption by intervening cool gas at the redshift of the cluster cannot explain the dearth of soft X-ray emission.," Finally, absorption by intervening cool gas at the redshift of the cluster cannot explain the dearth of soft X-ray emission."136 In $6 below. we perform quantitive spectral fits to further explore the departures from the cooling-flow model.," In 6 below, we perform quantitive spectral fits to further explore the departures from the cooling-flow model."137 In this section. we set quantitative limits on emission from various parts of the temperature distribution.," In this section, we set quantitative limits on emission from various parts of the temperature distribution."138 To derive these limits. we use the Monte Carlo methods presented by Jernigan&Kahn (2002).. and implicitly used by Petersonetal.(2001) and Xuetal.(2002).," To derive these limits, we use the Monte Carlo methods presented by \cite{peterson3}, and implicitly used by \cite{peterson1} and \cite{xu}."139. The basic procedure is based on an astrophysical model for the spatial and spectral dependence of the emission., The basic procedure is based on an astrophysical model for the spatial and spectral dependence of the emission.140 The Monte Carlo approach ts required because a different spectrum at each projected spatial position is required to test the cooling-flow model in detail., The Monte Carlo approach is required because a different spectrum at each projected spatial position is required to test the cooling-flow model in detail.141 We randomly generate photons with an associated dispersion angle. cross-dispersion angle. and CCD pulseheight value.," We randomly generate photons with an associated dispersion angle, cross-dispersion angle, and CCD pulseheight value."142 The resulting count distributions are then compared with the raw data. after the various data selection cuts and transformations.," The resulting count distributions are then compared with the raw data, after the various data selection cuts and transformations."143 In fitting for global parameters. such as the background normalization. we find the best fitting solution by using multivariate methods. as described in Peterson.Jernigan&Kahn(2002).," In fitting for global parameters, such as the background normalization, we find the best fitting solution by using multivariate methods, as described in \cite{peterson3}."144. For the abundances and temperatures. we use a X statistic of the combined extracted first and second order spectra for both instruments and we iteratively adjust the surface brightness distribution to match the cross-dispersion profile.," For the abundances and temperatures, we use a $\chi^2$ statistic of the combined extracted first and second order spectra for both instruments and we iteratively adjust the surface brightness distribution to match the cross-dispersion profile."145 Por the cluster emission we adopt a relatively simple model. so as to reduce sensitivity to fitting biases.," For the cluster emission we adopt a relatively simple model, so as to reduce sensitivity to fitting biases."146 For the surface brightness. we use a spherical } profile where the core radius is left free and the ./ parameter is fixed to the value determined from EPIC spectral fits (Kaastraetal. 2002)).," For the surface brightness, we use a spherical $\beta$ profile where the core radius is left free and the $\beta$ parameter is fixed to the value determined from EPIC spectral fits \citealt{kaastra2}) )."147" Additionally. we allow the normalization of the emission inside of a three-dimensional radius. 7,4. to be larger than the normalization outside of the radius."," Additionally, we allow the normalization of the emission inside of a three-dimensional radius, $r_{cool}$, to be larger than the normalization outside of the radius."148 In this way. the spatial profile can be much more peaked than the standard / profile.," In this way, the spatial profile can be much more peaked than the standard $\beta$ profile."149 This three dimensional distribution is then projected on the sky., This three dimensional distribution is then projected on the sky.150 The precise shape of the spatial distribution is not eritically important for determining the cooling luminosity limits as long as it reproduces the rough behavior of the emission profile., The precise shape of the spatial distribution is not critically important for determining the cooling luminosity limits as long as it reproduces the rough behavior of the emission profile.151 Outside of 7544. the emission is set to an isothermal temperature.," Outside of $r_{cool}$, the emission is set to an isothermal temperature."152 Inside that radius. we fit for the normalization of the differential emissionmeasure distribution below the upper temperature. 75.," Inside that radius, we fit for the normalization of the differential emissionmeasure distribution below the upper temperature, $T_0$ ."153 The emission measure is divided into several temperature bins between 175 and Tp. JT; and io. io and and isTo and T," The emission measure is divided into several temperature bins between $\case{1}{2} T_0$ and $T_0$, $\case{1}{4} T_0$ and $\case{1}{2} T_0$, $\case{1}{8} T_0$ and $\case{1}{4} T_0$, and $\case{1}{16} T_0$ and $\case{1}{8} T_0$."154his choice is arbitrary. but it providesiT. robust fitting i.solutions since the fractional ionization curves are roughly equally spaced in the logarithm of the temperature.," This choice is arbitrary, but it provides robust fitting solutions since the fractional ionization curves are roughly equally spaced in the logarithm of the temperature."155 Preliminary fits indicate that only negligible hot ambient plasma coexists mside the cooling radius. so additional isothermal emission inside this radius ts ignored.," Preliminary fits indicate that only negligible hot ambient plasma coexists inside the cooling radius, so additional isothermal emission inside this radius is ignored."156 Within each temperature bin. we use the isobaric radiative cooling-flow model to predict the shape of the emission measure distribution. but this is not critically important since we do not have the spectral sensitivity to sample the emission measure distribution m very fine intervals.," Within each temperature bin, we use the isobaric radiative cooling-flow model to predict the shape of the emission measure distribution, but this is not critically important since we do not have the spectral sensitivity to sample the emission measure distribution in very fine intervals."157 This approach clearly forces the coolest emission to conform to a specified spatial distribution., This approach clearly forces the coolest emission to conform to a specified spatial distribution.158 Further detailed analyses are required to pinpoint its exact spatial location., Further detailed analyses are required to pinpoint its exact spatial location.159 Our spatial model. however. seems to be compatible qualitatively with the relatively small differences in the observed emission lines spatial profiles of M$7 (Sakelliouetal.2002)).," Our spatial model, however, seems to be compatible qualitatively with the relatively small differences in the observed emission lines spatial profiles of M87 \citealt{sakelliou}) )."160 We assume uniform spatial abundances throughout the cluster. emission., We assume uniform spatial abundances throughout the cluster emission.161 This considerably simplifies. the. fitting procedure. and makes the limits on the coolest emission conservative.," This considerably simplifies the fitting procedure, and makes the limits on the coolest emission conservative."162 It is known that abundance gradients exist in clusters. but they are generally flat within the cooling-flow region and weaken whenever more freedom is given to the temperature distribution (Molendi&Pizzolato2001).," It is known that abundance gradients exist in clusters, but they are generally flat within the cooling-flow region and weaken whenever more freedom is given to the temperature distribution \citep{molendi}."163.. The iron. neon. oxygen. magnesium. and silicon abundances are left as free parameters.," The iron, neon, oxygen, magnesium, and silicon abundances are left as free parameters."164 All other elements are tied to tron since they contribute few counts., All other elements are tied to iron since they contribute few counts.165 In Abell 1835 and Abell 665. the magnesium. neon. and silicon abundances are tied to iron since the emission is from very high temperatures.," In Abell 1835 and Abell 665, the magnesium, neon, and silicon abundances are tied to iron since the emission is from very high temperatures."166 The absorption column density is left as a free parameter to account for variations along the line of sight to the cluster., The absorption column density is left as a free parameter to account for variations along the line of sight to the cluster.167 In NGC 533 the absorption is set to the galactic value since it has little low energy continuum emission., In NGC 533 the absorption is set to the galactic value since it has little low energy continuum emission.168 We also ignore the effects of resonant scattering (cf. Xuetal.2002)).," We also ignore the effects of resonant scattering (cf. \citealt{xu}) ),"169 which redistribes emission line photons within our aperture. but otherwise results in the same detected emission line flux.," which redistribes emission line photons within our aperture, but otherwise results in the same detected emission line flux."170 For the background. we use a semi-empirical model calibrated on blank sky Lockman Hole observations (XMM Revolutions 0070/0073).," For the background, we use a semi-empirical model calibrated on blank sky Lockman Hole observations (XMM Revolutions 0070/0073)."171 The model includes a spatial model for soft protons. low energy detector readout noise. and characterizations of the in-flight Al K and F K calibration sources.," The model includes a spatial model for soft protons, low energy detector readout noise, and characterizations of the in-flight Al K and F K calibration sources."172 All parameters are frozen in this model except the relative normalization of the particle component. and the overall normalization which can vary by factors of 10 from observation to observation.," All parameters are frozen in this model except the relative normalization of the particle component, and the overall normalization which can vary by factors of 10 from observation to observation."173 The background is relatively flat in wavelength., The background is relatively flat in wavelength.174 The model has the following free parameters: local column density. normalization of each part of the cooling flow emission measure distribution. abundances of magnesium. neon. silicon. oxygen. and iron. background temperature (75). particle background normalization. position of the source in the cross-dispersion direction. core radius. cooling radius. and overall normalization.," The model has the following free parameters: local column density, normalization of each part of the cooling flow emission measure distribution, abundances of magnesium, neon, silicon, oxygen, and iron, background temperature $T_0$ ), particle background normalization, position of the source in the cross-dispersion direction, core radius, cooling radius, and overall normalization."175 For each spectrum. we apply selection cuts discussed in $44.," For each spectrum, we apply selection cuts discussed in 4."176 However. the background model parameters and position of the source are determined before applying any data selection cuts.," However, the background model parameters and position of the source are determined before applying any data selection cuts."177 In addition to the model described above. we also set limits on a model wherein an intrinsic absorber embedded in the cooling-flow volume ts invoked to suppress the expected soft emission.," In addition to the model described above, we also set limits on a model wherein an intrinsic absorber embedded in the cooling-flow volume is invoked to suppress the expected soft emission."178 If the absorber is evenly embedded. the transmission function is given by. (1—e7'£)/z(E). where 7(E) is the photoelectric optical depth as a function of energy. as opposed to the usual exponential form.," If the absorber is evenly embedded, the transmission function is given by, $\left( 1 - e^{-\tau(E)} \right) /\tau(E)$, where $\tau(E)$ is the photoelectric optical depth as a function of energy, as opposed to the usual exponential form."179 For this case. we otherwise take the isobaric cooling-flow emission measure distribution. without allowing any variation from one temperature bin to the next.," For this case, we otherwise take the isobaric cooling-flow emission measure distribution, without allowing any variation from one temperature bin to the next."180 The errors are quoted at the 90% statistical confidence level for setting limits on the parameters., The errors are quoted at the $\%$ statistical confidence level for setting limits on the parameters.181 The uncertainty in the wavelength scale of 8 mA and the characteristic line spread function uncertainty of 5 mA make negligible contributions to these errors for extended sources like clusters., The uncertainty in the wavelength scale of 8 ${\mbox{m\AA}}$ and the characteristic line spread function uncertainty of 5 ${\mbox{m\AA}}$ make negligible contributions to these errors for extended sources like clusters.182 The effective area uncertainty is of order 10%., The effective area uncertainty is of order $\%$ .183 Additionally. there is known to benon-statistical noise at the 5% level of the source flux in the RGS spectra. caused by systematic dark current variations which can sometimes produce false," Additionally, there is known to benon-statistical noise at the $\%$ level of the source flux in the RGS spectra, caused by systematic dark current variations which can sometimes produce false"184distribution of z>0.5 quasars in AGES ,distribution of $z>0.5$ quasars in AGES ).185"These quasars are primarily mid-IR and X-ray 2011)).selected, like much of the present sample, but with a much deeper optical spectroscopic limit."," These quasars are primarily mid-IR and X-ray selected, like much of the present sample, but with a much deeper optical spectroscopic limit."186" We have adjusted the AGES magnitudes for the AE(B—V)~0.14 mag extinction difference between AGES and a typical LMC site line although this may underestimate the (Udalskicorrection 1999)),necessary for a true background population."," We have adjusted the AGES magnitudes for the $\Delta E(B-V)\simeq 0.14$ mag extinction difference between AGES and a typical LMC site line ), although this may underestimate the correction necessary for a true background population."187 The completeness of our present sample relative to AGES is roughly (30%)) at 18.6 mag (19.3 mag)., The completeness of our present sample relative to AGES is roughly ) at 18.6 mag (19.3 mag).188 Figure 8 also shows the cumulative distribution of the SDSS quasars with 0.3«z2.2 from(2006)., Figure \ref{fig:cumul} also shows the cumulative distribution of the SDSS quasars with $0.3 < z < 2.2$ from.189". Given the change in bandpass (i—I)~0.5 mag color term varies significantly (thewith redshift, see Figure 9)) and the additional line width and luminosity selection criteria in it is harder to make a direct comparison, but (2006)after matching as best possible, we obtain similar completeness estimates."," Given the change in bandpass (the $(i-I) \simeq 0.5$ mag color term varies significantly with redshift, see Figure \ref{fig:AGNcolor}) ) and the additional line width and luminosity selection criteria in it is harder to make a direct comparison, but after matching as best possible, we obtain similar completeness estimates."190" As expected from filling the fibers with targets, most targets are peculiar stars of various types, particularly at the brighter magnitudes."," As expected from filling the fibers with targets, most targets are peculiar stars of various types, particularly at the brighter magnitudes."191" Unclassifiable spectra dominate at the fainter magnitudes, and with the weather-limited integration times, there was an effective magnitude limit of roughly 19.5-20 mag."," Unclassifiable spectra dominate at the fainter magnitudes, and with the weather-limited integration times, there was an effective magnitude limit of roughly $19.5$ $20$ mag."192are difficulties with formation of the planet Fom b because the time-scales for core accretion are so long: recall that the self-stirring time-scale gives the time required to form Plito--sized objeetssitu.. while the mass of Fom b may be as high as that of Jupiter.,"are difficulties with formation of the planet Fom b because the time-scales for core accretion are so long: recall that the self-stirring time-scale gives the time required to form -sized objects, while the mass of Fom b may be as high as that of Jupiter."193" The time to form a Pluto-sized body at Fomalhaut b's orbit is aroundMMyr for ry,=1.", The time to form a Pluto-sized body at Fomalhaut b's orbit is aroundMyr for $x_{\mathrm{m}}=1$.194 The planet most likely formed closer to the star and later moved to its current location. for example by outwards migration (e.g..2) or being scattered by another planet (e.g.. 2»).," The planet most likely formed closer to the star and later moved to its current location, for example by outwards migration \citep[e.g.,][]{2007MNRAS.378.1589M} or being scattered by another planet (e.g., \citealt*{2009arXiv0902.2779V}) )."195 Both of these processes would however likely disturb the dise as well., Both of these processes would however likely disturb the disc as well.196 Secondly. we note that. although c;z0.1. the material in the Fomalhaut dise appears to have very low proper eccentricities (22). as evidenced by the sharp inner edge to the disc.," Secondly, we note that, although $e_{\mathrm{f}}\approx 0.1$, the material in the Fomalhaut disc appears to have very low proper eccentricities \citep{2006MNRAS.372L..14Q,2009ApJ...693..734C}, as evidenced by the sharp inner edge to the disc."197 If the proper eccentricity of Fomalhaut's dise is only 10 per cent of the forced eccentricity then this increases the time-scale for orbit crossing to MMyr (see Equation 1-2). still much less than the system's age.," If the proper eccentricity of Fomalhaut's disc is only 10 per cent of the forced eccentricity then this increases the time-scale for orbit crossing to Myr (see Equation \ref{eq:tcross}) ), still much less than the system's age."198 Reducing proper eccentricities also reduces the relative velocities amongst planetesimals in direct proportion. although given the large value of e this will not prevent Fom b from causing erosive collisions.," Reducing proper eccentricities also reduces the relative velocities amongst planetesimals in direct proportion, although given the large value of $a^*$ this will not prevent Fom b from causing erosive collisions."199 For the Solar System's Neptune we find αἲ= 130AAU. making the Kuiper Belt able to be stirred by Neptune.," For the Solar System's Neptune we find $a^*=730$ AU, making the Kuiper Belt able to be stirred by Neptune."200 However. when we compare with self-stirring we find that planet-stirring acts more quickly only out to «b.=33 AAU. so Neptune's secular perturbations would not have stirred the belt before Pluto formed. assuming that the planets formed at their current semi-major.," However, when we compare with self-stirring we find that planet-stirring acts more quickly only out to $\Phi = 33$ AU, so Neptune's secular perturbations would not have stirred the belt before Pluto formed, assuming that the planets formed at their current semi-major."201. So this simple model is consistent with the outer Solar System. although we note that the dynamical evolution of the early Kuiper Belt and outer planets may have been more complicated than formation of Neptune followed by growth of Kuiper Belt Objects (?)..," So this simple model is consistent with the outer Solar System, although we note that the dynamical evolution of the early Kuiper Belt and outer planets may have been more complicated than formation of Neptune followed by growth of Kuiper Belt Objects \citep{2005Natur.435..459T}."202 We also note that highly excited eccentricities and inclinations of KBOs may have been required to explain the details of the capture of Neptune's Trojans (2).. and capture of KBOs into high order mean motion resonances (e.g.. 2)).," We also note that highly excited eccentricities and inclinations of KBOs may have been required to explain the details of the capture of Neptune's Trojans \citep{2009AJ....137.5003N}, and capture of KBOs into high order mean motion resonances (e.g., \citealt{2003AJ....126..430C}) )."203 Such high inclinations might be achievable through self-stirring but not planet-stirring., Such high inclinations might be achievable through self-stirring but not planet-stirring.204 When dealing with multiple planets previously we treated the disc as being stirred by the planet with the lowest {ώμος assuming that the other planets had no effect on the dise.," When dealing with multiple planets previously we treated the disc as being stirred by the planet with the lowest $t_{\mathrm{cross}}$, assuming that the other planets had no effect on the disc."205 Such an approach is unrealistic because it neglects not only the effects of other planets on the disc. but also the mutual interactions of the planets amongst themselves.," Such an approach is unrealistic because it neglects not only the effects of other planets on the disc, but also the mutual interactions of the planets amongst themselves."206 We plot the precession rate 1 for planetesimals orbiting in the Sun-Jupiter-Saturn system in Figure (123)., We plot the precession rate $A$ for planetesimals orbiting in the Sun-Jupiter-Saturn system in Figure \ref{fig:A-jupsat}) ).207 This also shows the location of secular resonances. where the planetesimal's precession rate equals one of the system's eigenfrequencies and the forced eccentricity is formally infinite.," This also shows the location of secular resonances, where the planetesimal's precession rate equals one of the system's eigenfrequencies and the forced eccentricity is formally infinite."208 Figure (123) also shows the effect of reducing Saturn's mass to that of Earth: the precession rate approaches that in the planet case of Jupiter alone. and the width of the region strongly affected by the outer planets perturbations decreases.," Figure \ref{fig:A-jupsat}) ) also shows the effect of reducing Saturn's mass to that of Earth: the precession rate approaches that in the single-planet case of Jupiter alone, and the width of the region strongly affected by the outer planet's perturbations decreases."209 So as far as the precession rate is concerned. the behaviour is similar to the single-planet case.," So as far as the precession rate is concerned, the behaviour is similar to the single-planet case."210 Performing a similar analysis to that in refs:timescale.. we find that. for planetesimals on initially circular orbits. the time-scale for orbit crossing in the multi-planet case is given by," Performing a similar analysis to that in \\ref{s:timescale}, , we find that, for planetesimals on initially circular orbits, the time-scale for orbit crossing in the multi-planet case is given by"211sodium fills the volume between the cylinders and the end walls.,sodium fills the volume between the cylinders and the end walls.212" Solid plates attached to and co-rotating with the outer cylinder with an angular velocity, Q5 define the end walls. ("," Solid plates attached to and co-rotating with the outer cylinder with an angular velocity, $\Omega_2$ define the end walls. ("213"In addition, for the dynamo experiment, an external source of helicity is supplied, driven plumes, but this is not part of the MRI experiment.)","In addition, for the dynamo experiment, an external source of helicity is supplied, driven plumes, but this is not part of the MRI experiment.)"214" The schematic of the flow field, (Fig. 1)),"," The schematic of the flow field, (Fig. \ref{fig1}) ),"215" places particular emphasis on the primary diagnostic of multiple, 3-axis, magnetic field Hall effect detectors (sensitivity: 0.1 to 10kG) located in aerodynamically shaped probes within the rotating conducting fluid."," places particular emphasis on the primary diagnostic of multiple, 3-axis, magnetic field Hall effect detectors (sensitivity: $0.1$ to $10\,\mbox{kG}$ ) located in aerodynamically shaped probes within the rotating conducting fluid."216" We expect that the radial perturbations from the MRI and their azimuthally sheared result will produce a fluctuating B, and Bg field from an original imposed static B, field through MRI growth.", We expect that the radial perturbations from the MRI and their azimuthally sheared result will produce a fluctuating $B_r$ and $B_{\theta}$ field from an original imposed static $B_z$ field through MRI growth.217" These fluctuating fields are the result of the linear and non-linear growth of the various MRI modes transformed by the difference of the sheared Couette flow at a given radius and the probe angular velocity, £25, of the outer cylinder."," These fluctuating fields are the result of the linear and non-linear growth of the various MRI modes transformed by the difference of the sheared Couette flow at a given radius and the probe angular velocity, $\Omega_2$, of the outer cylinder."218" A significant difficulty will be the observation of the linear growth of any particular MRI mode because the time constant for establishing the initial axial field within the conducting liquid sodiumwill be long, ~30/Q2, compared to the expected growth rate, ~Qe, of the instabilities as derived in this paper."," A significant difficulty will be the observation of the linear growth of any particular MRI mode because the time constant for establishing the initial axial field within the conducting liquid sodiumwill be long, $\sim 30/\Omega_2$, compared to the expected growth rate, $\sim219\Omega_2$, of the instabilities as derived in this paper."220" We therefore expect to observe primarily the near steady state of the non-linear limit of various modes, but the sequential linear phases may be observed during the comparatively slow rise of the field."," We therefore expect to observe primarily the near steady state of the non-linear limit of various modes, but the sequential linear phases may be observed during the comparatively slow rise of the field."221" If the applied field or flux is amplified by the MRI such as a dynamo, then we expect to see fluctuating fields significantly greater than the applied field."," If the applied field or flux is amplified by the MRI such as a dynamo, then we expect to see fluctuating fields significantly greater than the applied field."222" In addition since the inner and outer cylinders are driven separately, the relative torque as a function of the applied magnetic field becomes an integral diagnostic of the non-linear limits of the instability growth."," In addition since the inner and outer cylinders are driven separately, the relative torque as a function of the applied magnetic field becomes an integral diagnostic of the non-linear limits of the instability growth."223 By driving the inner cylinder and applying a variable brake with a corresponding torque measurement to the outer cylinder one can explore the full range of Couette velocity profiles including the marginal Couette flow hydrodynamic stability condition discussed next., By driving the inner cylinder and applying a variable brake with a corresponding torque measurement to the outer cylinder one can explore the full range of Couette velocity profiles including the marginal Couette flow hydrodynamic stability condition discussed next.224 This condition of maximum or marginal stable Couette profile can be established in the experiment precisely by gear ratios and so the degree of turbulence measured by the torque can be explored at the stability boundary., This condition of maximum or marginal stable Couette profile can be established in the experiment precisely by gear ratios and so the degree of turbulence measured by the torque can be explored at the stability boundary.225 In addition the pressure will be measured at five radii and compared to the pressure distributions expected of the various Couette profiles., In addition the pressure will be measured at five radii and compared to the pressure distributions expected of the various Couette profiles.226 A finite torque measurement can be interpreted in terms of turbulence existing between the two cylinders., A finite torque measurement can be interpreted in terms of turbulence existing between the two cylinders.227" No turbulence or perfectly laminar flow will exert a torque of the order 1/R., R. the fluid Reynolds number where Re~107, compared to a turbulent torque, 1/Re'/?, if the Ekman layer circulation leads to the weak turbulence that we discuss later."," No turbulence or perfectly laminar flow will exert a torque of the order $1/R_e$, $R_e$ the fluid Reynolds number where $Re \simeq 10^7$, compared to a turbulent torque, $\sim 1/Re^{1/2}$, if the Ekman layer circulation leads to the weak turbulence that we discuss later."228" This same possible weak turbulence can also be measured by introducing a very weak field, Bmin1G, small enough so as not to cause the growth of MRI in resistive liquid but large enough so that an unstable flow or weakly turbulent flow can be measured as fluctuations in B, and Bg with the Hall effect probes."," This same possible weak turbulence can also be measured by introducing a very weak field, $B_{min} \simeq 1\,\mbox{G}$, small enough so as not to cause the growth of MRI in resistive liquid but large enough so that an unstable flow or weakly turbulent flow can be measured as fluctuations in $B_r$ and $B_{\theta}$ with the Hall effect probes."229 Therefore the fluid flow conditions can be fully explored before the application of magnetic fields designed to create the MRI., Therefore the fluid flow conditions can be fully explored before the application of magnetic fields designed to create the MRI.230" When the MRI does take place, then the instability can be recognized as a departure from the previously measured initial fluid state."," When the MRI does take place, then the instability can be recognized as a departure from the previously measured initial fluid state."231 It is critical to have large shear rates in order to observe the maximum growth rates of the MRI., It is critical to have large shear rates in order to observe the maximum growth rates of the MRI.232" However, excessive shear will hydrodynamically destabilize the flow by the Kelvin-Helmholtz instability."," However, excessive shear will hydrodynamically destabilize the flow by the Kelvin-Helmholtz instability."233 Let us consider a Couette flow profile in cylindrical coordinates., Let us consider a Couette flow profile in cylindrical coordinates.234" Take r,0,z as the radial, azimuthal and axial directions respectively."," Take $r, \theta, z$ as the radial, azimuthal and axial directions respectively."235" The radial distribution of angular velocity of the flow, Q(r), is given by (Landau&Lifshitz1959) where Γή(10) and Ω](Ως) are the inner(outer) radii and angular velocities."," The radial distribution of angular velocity of the flow, $\Omega ( r )$ , is given by \citep{lan59}236 where $R_1(R_2)$ and $\Omega_1(237\Omega_2)$ are the inner(outer) radii and angular velocities."238system).,system).239 They also noted that a wide variety of planetary paratjeters can produce the twin-lobed structure seen in Vega., They also noted that a wide variety of planetary parameters can produce the twin-lobed structure seen in Vega.240" Whilst our code was able to reproduce the results of Wilreretal.(2002).. their syuthetic observatious (al ilje. resolution of the Hollaudetal.(1998) Vega obse""valions show nearly svlninetrical emissio. whereas the Hollaudetal.(1998) Observatllous show a significa1| asyininetry. ("," Whilst our code was able to reproduce the results of \citet{whk02}, their synthetic observations (at the resolution of the \citet{holland98} Vega observations) show nearly symmetrical emission, whereas the \citet{holland98} observations show a significant asymmetry. ("241It should be noted. however. that here are uucertaluties in the Hollandeta.(1995 observations.,"It should be noted, however, that there are uncertainties in the \citet{holland98} observations."242 In the moclel we are about to present. we are assuming that he observed. asyiuijetry is real.)," In the model we are about to present, we are assuming that the observed asymmetry is real.)"243 Based on results [rom our syuthetic catalogue. we have modelled Vega. usiu: an eutirely different plauetary configuration in au atteupt to better match these observations.," Based on results from our synthetic catalogue, we have modelled Vega using an entirely different planetary configuration in an attempt to better match these observations."244 αι Our jodel. a more distant. (app=73.7 AU). less eccentric (ej= 0.1) 3 Jupier inass plauet rep'oduces the observed disk structure. with no constraints on the iniial test. particle perilielia (since we a'e modelliug a lower eccenricity planet).," In our model, a more distant $a_{pl} = 73.7$ AU), less eccentric $e_{pl} = 0.1$ ) 3 Jupiter mass planet reproduces the observed disk structure, with no constraints on the initial test particle perihelia (since we are modelling a lower eccentricity planet)."245" We use 5000 test pa‘icles released from parent bocdies With initial orbital elements in the range 90<dy,«120. 0.0<C€pbSs0.3. and Q<ipycs."," We use 5000 test particles released from parent bodies with initial orbital elements in the range $90<a_{pb}<120$, $0.0<e_{pb}<0.3$, and $0\degree<i_{pb}<8\degree$."246 Denteal.(20OO) state that to fit the o»erved spectral energy. distribitou. the dust gralus which make up the Vega disk must have ciameters in the raree 60—100 jn. corresponding to 9 = 0.02 — 0.11 or Vegas estimated lass ax Luminosity.," \citet{dent00} state that to fit the observed spectral energy distribution, the dust grains which make up the Vega disk must have diameters in the range 60–400 $\mu$ m, corresponding to $\beta$ = 0.02 – 0.11 for Vega's estimated mass and luminosity."247 Wie have simulated this system with οὐ values [9] 0.02. 0.05 and 0.1. and found negligibe differences between he syutheic observations. (," We have simulated this system with $\beta$ values of 0.02, 0.05 and 0.1, and found negligible differences between the synthetic observations. ("248Note that Wilneretal.(2002) used 3=0.01 wit lsu— 0.),Note that \citet{whk02} used $\beta=0.01$ with $sw = 0$ .)249 Figure 7 s1ows thie cust distribution. simulatecl [9]servation and resonance occupancy plots obtained. using our Vega model with ο=0.05.," Figure \ref{fig:vega} shows the dust distribution, simulated observation and resonance occupancy plots obtained using our Vega model with $\beta=0.05$."250 We rote that ¢jur model for Vega o»oduces a dust distriition which is essentially stationary ist the planets [raije. of reference., We note that our model for Vega produces a dust distribution which is essentially stationary in the planet's frame of reference.251 Such a distribution ineaus that as the planet orbits the star. [9]servations [rom Eart1 will show positional changes in tje emission peass Over ali orbital timescale.," Such a distribution means that as the planet orbits the star, observations from Earth will show positional changes in the emission peaks over an orbital timescale."252 Dust cdistributions rom the four orbital phases recorde are show iin Figure &.., Dust distributions from the four orbital phases recorded are shown in Figure \ref{fig:vegaphase}.253 The model accurately reproduces tlie twin lobes see nin the Wilneretal.(2002) observations. as well as the exteided emission seen iu the lower resoutiou Hollandeal.(1998) observatious.," The model accurately reproduces the twin lobes seen in the \citet{whk02}254 observations, as well as the extended emission seen in the lower resolution \citet{holland98} observations."255 Figure Taa shows asyunetry in the two emission featsres. whicl are |ot collirear with the star jor the same cistaice from the sta “as seen intle Wijeretal.(2002) observations.," Figure \ref{fig:vega}a a shows asymmetry in the two emission features, which are not collinear with the star nor the same distance from the star, as seen inthe \citet{whk02} observations."256" This me«el also provides reasolable constraiuts ou the orbital pararιδίου» of the pro»osed pauet: for example. he same model wi he,=0.2 results ina markedly cdierent sl""ucture. as does a significantly less nassive (Mj<AL pup) planet."," This model also provides reasonable constraints on the orbital parameters of the proposed planet; for example, the same model with $e_{pl}=0.2$ results in a markedly different structure, as does a significantly less massive $M_{pl} < M_{Jup}$ ) planet."257 The primary concern wih this inodel is he reqirement that such a massive planet biewe formecl or migrated to such a la‘ee distance [rom tlie cenral star. although he [act that Vega is estimated to be 2.5 times as massive as dle sun thay iuitigate this problem.," The primary concern with this model is the requirement that such a massive planet have formed or migrated to such a large distance from the central star, although the fact that Vega is estimated to be 2.5 times as massive as the sun may mitigate this problem."258 Future detailed observatious are required to test our pluietary. tmoclel., Future detailed observations are required to test our planetary model.259 First identified as a Vega-type star in 1984 (Atmanu 1935).. hhas been the subject of ongoing planetary speculation since disk images taken at 850," First identified as a Vega-type star in 1984 \citep{aumann85}, , has been the subject of ongoing planetary speculation since disk images taken at 850"260strength ancl slope of the correlation seen in racio-selected samples is alfected by selection elfects. there is a real gap of objects with bright Lets. and low Lyjan. which shows that for a given jet power there is a minimum accretion rate.,"strength and slope of the correlation seen in radio-selected samples is affected by selection effects, there is a real gap of objects with bright $L_{\nu261 \rm 151MHz}$ and low $\nu L_{\nu \rm 12\mu m}$, which shows that for a given jet power there is a minimum accretion rate."262 This implies that there is à maximum ellicieney with which accreted energy can be converted. into jet power. and that this ellicleney is of order unity.," This implies that there is a maximum efficiency with which accreted energy can be converted into jet power, and that this efficiency is of order unity."263 We thank the anonymous. referee. for. comments and suggestions that have greatly improved this paper., We thank the anonymous referee for comments and suggestions that have greatly improved this paper.264 CACHE is supported by the Foundation for Science and Technology (FCT-Portugal) through erant ΕΙDD/30486/2006., CACF is supported by the Foundation for Science and Technology (FCT-Portugal) through grant SFRH/BD/30486/2006.265 ALL) ds supported. by an RCUWK fellowship., MJJ is supported by an RCUK fellowship.266 .AMS is supported. by an SPEC post-doctoral fellowship., AMS is supported by an STFC post-doctoral fellowship.267" “Phis work is based (in part) on observations mace with the Spitzer Space ""Telescope. which is operated bv. the Jet Propulsion Laboratory. California Institute of Technology under a contract with NASA."," This work is based (in part) on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA."268 This research. has made use of the NASA/IPAC Extragalactic Database (NED) which 15 operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration."269where j is the bin index. Pia(Pain) is the largest (inallest) period iu the period rauge of mterest (1.0. 1 and 3 davs. corresponding to ILJs with 1«P3 days). aud Prin the period upou which the histogram biu is centered.,"where $j$ is the bin index, $P_{max}\left(P_{min}\right)$ is the largest (smallest) period in the period range of interest (i.e. 1 and 3 days, corresponding to HJs with $1<P<3$ days), and $P_{bin,j}$ the period upon which the histogram bin is centered."270 The net effect of this correction is to merease the detection probability of short-period plaucts relative to that of longer period planets., The net effect of this correction is to increase the detection probability of short-period planets relative to that of longer period planets.271 Each period-frequeney histogram biu is au over all planetary raci and iuclinatious., Each period-frequency histogram bin is an over all planetary radii and inclinations.272 If wie wish to calculate the probalility of detection for a articular radius. we must multiXv the bius by vet anotlier scaling factor that quantifies whether a transit of a articular planetary radius is detected more or less efficicutly thu average.," If we wish to calculate the probability of detection for a particular radius, we must multiply the bins by yet another scaling factor that quantifies whether a transit of a particular planetary radius is detected more or less efficiently than average."273 For this adjustinent we use the radius-frequeucy histograms in Fie., For this adjustment we use the radius-frequency histograms in Fig.274 5 MOS. Fie.," 5 M08, Fig."275 8 in MO6. aud Fig.," 8 in M06, and Fig."276 7 M05. which plot the average probability of detecting a planet of a particular radius. where the probabilitics represcut an average over all cousidered periods aud mcliuations.," 7 M05, which plot the average probability of detecting a planet of a particular radius, where the probabilities represent an average over all considered periods and inclinations."277" The scaling factor is given by where is the probability. road from the radius-frequency Py,histogram. of detecting a plauct of radius Πρ. and CP is the average detection probability over all radi."," The scaling factor is given by where $\mathcal{P}_{R_p}$ is the probability, read from the radius-frequency histogram, of detecting a planet of radius $R_p$, and $\langle{\mathcal{P}\rangle}$ is the average detection probability over all radii."278 With these scaling factors we can then calculate the detection cficiency for anv desired period range aud planet radius. 7. froii Equ. 5..," With these scaling factors we can then calculate the detection efficiency for any desired period range and planet radius, $\mathcal{P}_{\epsilon}$ from Eqn. \ref{eqn:pepsilon},"279" described as where P; is the probability of detection in cach period bin in the frequency-period listoeram. N5;,; ds the ΠΠΟΙ of bius contained in the period rauge Pin«P< Pray Al AP is the period width of cach individual biu."," described as where $\mathcal{P}_{j}$ is the probability of detection in each period bin in the frequency-period histogram, $N_{bins}$ is the number of bins contained in the period range $P_{min}<P<P_{max}$ , and $\Delta{P}$ is the period width of each individual bin."280" This technique is applied to all three of the clusters NGC 1δο, NGC 2158 and NCC 6791."," This technique is applied to all three of the clusters NGC 188, NGC 2158 and NGC 6791."281 As noted earlier. it is critical that we have estimates of the actual uuniber of cluster stars observed.," As noted earlier, it is critical that we have estimates of the actual number of cluster stars observed."282 The ALO5 paper provides estimates the nuuber of cluster aud field stars in the sample used for the transit analysis., The M05 paper provides estimates the number of cluster and field stars in the sample used for the transit analysis.283 Candidate cluster members are selected as those stars vat lie within 0.06 mae of the V.Rove cluster 1lain sequence., Candidate cluster members are selected as those stars that lie within 0.06 mag of the $V-R$ $R$ cluster main sequence.284 While this significantly reduces the field y.ar contauinatiou. there is still a nou-uceligible uuuber )f field stars among these candidate cluster muoenibers iat happe- O have the same colors as he cluster lain sequence.," While this significantly reduces the field star contamination, there is still a non-negligible number of field stars among these candidate cluster members that happen to have the same colors as the cluster main sequence."285 To quautifv this contamination we use 16 Besancguu stellar population svuthesis galaxy model Robinοal.2003) to estimate the number of field stars at shotid present in the region of the cluster CMD 1sed to deteruuue membership., To quantify this contamination we use the Besanco̧nn stellar population synthesis galaxy model \citep{robin2003} to estimate the number of field stars that should be present in the region of the cluster CMD used to determine membership.286 Secondly. O confirm 1ο ECSU.t 6 he first method. we then estimate the vpical fiek star density on the CMD aud check that je resulting uembership is consistent with the estimates derived frou. the galaxy model.," Secondly, to confirm the result of the first method, we then estimate the typical field star density on the CMD and check that the resulting membership is consistent with the estimates derived from the galaxy model."287 We first 1tilized the Desancouu galaxy uodel to estimate the munhber of field stars expected iu the M05 field of NGC GT91., We first utilized the Besanco̧nn galaxy model to estimate the number of field stars expected in the M05 field of NGC 6791.288 The models were run for a field of vjew of QO.11 deg? with 25 dust clouds evenly spaced every 2pe fimu the observer. each with an extinction Of 0.019 for a total Ay=0.177. from Schleeclctal. (1998).," The models were run for a field of view of 0.144 $^{2}$ with 25 dust clouds evenly spaced every 2pc from the observer, each with an extinction of 0.019 for a total $A_{V}=0.477$ from \citet{schlegel1998}."289. We ound that this vielded more realistic star counts than using a uniform difhse extinction over the entire distance to the cluster., We found that this yielded more realistic star counts than using a uniform diffuse extinction over the entire distance to the cluster.290 We restrict the sample iu the same manner as M5 to stars with Π2 maguitudes 17R.19.5. which correspoids to all stars below the main sequence turnoff aud au rus uncertainty im the R inaguitude iu tje MOS. survey of less than 0.05 mae.," We restrict the sample in the same manner as M05 to stars with $R$ magnitudes $17<R<19.8$, which corresponds to all stars below the main sequence turnoff and an rms uncertainty in the $R$ magnitude in the M05 survey of less than 0.05 mag."291 Allstars from the Besaucouu simlation within 0.06 mag Of the cluster mai1 sequence were then selected as field star contaminants., All stars from the Besanco̧nn simulation within 0.06 mag of the cluster main sequence were then selected as field star contaminants.292 1523 of the 5225 field stars predicted lyv the model were within this region., 1523 of the 5225 field stars predicted by the model were within this region.293 The MO5 member selection method twrefore would have found 1523 cluster aud 3702 fields stars in this model data., The M05 member selection method therefore would have found 1523 cluster and 3702 fields stars in this model data.294 It is important τς» note that we do not trust the absolute star comnts produced by the model. but expect the fractional umber οf stars that have colors siuilay to the cluster main sequence to be more accurate.," It is important to note that we do not trust the absolute star counts produced by the model, but expect the fractional number of stars that have colors similar to the cluster main sequence to be more accurate."295 The ratio of stars detected ο ffo he main sequence m M05 and the simulation is 2στι3702zz0.78. and thus AL05 sees ~22% fewer stars that are more than 0.06 mae from the AIS than the Slulations of the same field.," The ratio of stars detected off of the main sequence in M05 and the simulation is $2871/3702 \approx 0.78$, and thus M05 sees $\sim22\%$ fewer stars that are more than 0.06 mag from the MS than the simulations of the same field."296 We scale the nuniber of stars preseut in the model near the MS to the ratio of the 11ulXv of stars detected in the field portions of both the slnuaed and actual cluster CMD., We scale the number of stars present in the model near the MS to the ratio of the number of stars detected in the field portions of both the simulated and actual cluster CMD.297 We would therefore expect that 1523«0.78=1181 stars selected as cluster 1110111XYs dn MOD are actually ποια star coutsininaunts., We would therefore expect that $1523 \times 0.78 = 1181$ stars selected as cluster members in M05 are actually field star contaminants.298 Tjs duplies that only 1997 of 3175 candidate cluster, This implies that only 1997 of 3178 candidate cluster299fact. there is another arm. ΣΣ... sspiral arm (unfortunately sometimes called the | kpc anu) that is also expaudius from the GC at a ealactocentric radius of [| kpc (Menon ποτ 1970: Creaves Williams 199D).,"fact, there is another arm, the $-$ 30 spiral arm (unfortunately sometimes called the 4 kpc arm), that is also expanding from the GC at a galactocentric radius of 4 kpc (Menon Ciotti 1970; Greaves Williams 1994)."300 Is expausion velocity nieasured at a Galactic longitude of s 30s ((Moenuou Ciotti 1970: Liszt et al., Its expansion velocity measured at a Galactic longitude of is $-$ 30 (Menon Ciotti 1970; Liszt et al.301 |9rr: Linke. Stark. Frevking 1981: Careaves Willis 199I: Saudqvist et al.," 1977; Linke, Stark, Frerking 1981; Greaves Williams 1994; Sandqvist et al."302 2003)., 2003).303 This feature was originally deected in 1967 (err Vallak 1967). but we would like to poiut that no molecular counterpart has been associated wit vit.," This feature was originally detected in 1967 (Kerr Vallak 1967), but we would like to point that no molecular counterpart has been associated with it."304 Iudeed. uulike the 3 kpe expanding arm. the 30 sspira avin can not be traced on tie velocity CO map (Fig.," Indeed, unlike the 3 kpc expanding arm, the $-$ 30 spiral arm can not be traced on the $-$ velocity CO map (Fig."305 6). possibly «ue to its proximity with the molecular ring (Dame ct al.," 6), possibly due to its proximity with the molecular ring (Dame et al."306 2001)., 2001).307 The extrapolation of its radial velocity profile in Figure 1 of Menon Ciotti (1970) to a longitude of lis consistent with the velocity of MC13D. We therefore conclude that 0.3 and MC13D are located on the 30 sspira arm., The extrapolation of its radial velocity profile in Figure 1 of Menon Ciotti (1970) to a longitude of is consistent with the velocity of MC13B. We therefore conclude that $-$ 0.3 and MC13B are located on the $-$ 30 spiral arm.308 In tha case. there is uo problem with the fact that absorpion lines against the radio continua of 0.3 are detected up to 13 Looas they would originate in AICLL.," In that case, there is no problem with the fact that absorption lines against the radio continuum of $-$ 0.3 are detected up to 43, as they would originate in MC44."309 We note that the 30 sspiral armi has to be closer to the Sun than the 3-kpe expanding arm with a separation of ~ 1.5 προ (Menon Cot1 1970)., We note that the $-$ 30 spiral arm has to be closer to the Sun than the 3-kpc expanding arm with a separation of $\sim$ 0.5 kpc (Menon Ciotti 1970).310 Iu any case. he distance to the 30 sspiral arm ds set bw the nani velocity of the absorption lines. i.e. 15 + 0.6 kpe. wuch is completely consistent with the spectrophotometric distance of 3.1 4 0.6 kpe for 0.3 (Bhun et al.," In any case, the distance to the $-$ 30 spiral arm is set by the maximum velocity of the absorption lines, i.e. 4.5 $\pm$ 0.6 kpc, which is completely consistent with the spectrophotometric distance of 3.4 $\pm$ 0.6 kpc for $-$ 0.3 (Blum et al."311 2001)., 2001).312 We note that at a Galactic longitude of07.. the 3. K2 expanding arn aud the 30 sspiral arma have a velocity separation of ~ 23i. which is alinost the difference in velocity between 11010 aud AICI3B. This therefore strengthens our association of the 3-kpe expanding arm with MC-16 andthe 30)aus sspiral arin with AICI3B. We also note that these two artus could be related to the presence of a bar at the GC (e.g. Blitz Spergel 1991).," We note that at a Galactic longitude of, the 3 kpc expanding arm and the $-$ 30 spiral arm have a velocity separation of $\sim$ 23, which is almost the difference in velocity between MC-16 and MC13B. This therefore strengthens our association of the 3-kpc expanding arm with MC-16 and the $-$ 30 spiral arm with MC13B. We also note that these two arms could be related to the presence of a bar at the GC (e.g. Blitz Spergel 1991)."313 So if 0.3 is af a closer distance. ave the other uajor components of W31 at the same distance?," So if $-$ 0.3 is at a closer distance, are the other major components of W31 at the same distance?"314 In their detailed study of W231. Riu Koo (2002) performed a unmnpofGl0.2 0.3 and 0.1 (see their Figures. {. Ὁ and 9).," In their detailed study of W31, Kim Koo (2002) performed a map of $-$ 0.3 and $-$ 0.1 (see their Figures 4, 5 and 9)."315 Their peak CO maps over the velocity range 0.22 sshows two main compoucuts (one centered ou each rreelon) that could be interpreted as πο separate nolecular clouds (see also Fie., Their peak CO maps over the velocity range 0–22 shows two main components (one centered on each region) that could be interpreted as two separate molecular clouds (see also Fig.316 Sa with the integrated imap), 5a with the integrated map).317 But based ou our new CO results it might be possible that the southern part is associated with MCT13D as 0.3. and the northern part with MCT2À iux 0.1 (Fig.," But based on our new CO results, it might be possible that the southern part is associated with MC13B as $-$ 0.3, and the northern part with MC13A and $-$ 0.1 (Fig."318 5a)., 5a).319 Tf this is the case. it would imply that W31 could be decomposed iuto several components. with 0.1 located at the kincmatic distance associate with MCI3A. ie. 13 kpe.," If this is the case, it would imply that W31 could be decomposed into several components, with $-$ 0.1 located at the kinematic distance associated with MC13A, i.e. $^{+1.8}_{-1.3}$ kpc."320 Fig., Fig.321 7 shows the !?CO spectrum aloug the line of sight to these two rreeions., 7 shows the $^{12}$ CO spectrum along the line of sight to these two regions.322" These profiles are very different. especially at. velocities above ~ LOτν, aud the profile of 0.1 is verv simular to the one of (the additional CO emission above LO day also be related to the variation in galactic latitude of these sources)."," These profiles are very different, especially at velocities above $\sim$ 40, and the profile of $-$ 0.1 is very similar to the one of (the additional CO emission above 40 may also be related to the variation in galactic latitude of these sources)."323 So it is not unlikely that this ivegion. Which has a recombination line at 7.7 + 0.51. could be associated with MCI3A. As noted above (section 2.1). the nap of this part of W31 bv Nam Ίου (2002) couk x0 interpreted as being due to the preseuce of two separate molecular clouds.," So it is not unlikely that this region, which has a recombination line at 7.7 $\pm$ 0.5, could be associated with MC13A. As noted above (section 2.1), the map of this part of W31 by Kim Koo (2002) could be interpreted as being due to the presence of two separate molecular clouds."324" Iu hat case. one should wonder ""hy no absorption line is detected. as in the case of20. at — 7L ffor 0.1 (Ixalberla et al."," In that case, one should wonder why no absorption line is detected, as in the case of, at $\sim$ 71 for $-$ 0.1 (Kalberla et al."325 1982)?, 1982)?326 In Fig., In Fig.327 5b. we use the oof Iun Ixoo (2002) to illustrate the spatial extent of AIC?3.," 5b, we used the of Kim Koo (2002) to illustrate the spatial extent of MC73."328" We found almost no ecinission in the velocity range 61 to SOον, which is consistent with the non detection of absorption line above 50 ((IXalborla et al."," We found almost no emission in the velocity range 61 to 80, which is consistent with the non detection of absorption line above 50 (Kalberla et al."329 1982) toward 0.1. even if it were associated with MCI2AÀ. However. our sspectrum towards 0.1 (Fig.," 1982) toward $-$ 0.1, even if it were associated with MC13A. However, our spectrum towards $-$ 0.1 (Fig."330 7) indicates a weak contribution of MC72 along this lie sight aud sugeest that the line of sight of 0.1 might be close to the edge, 7) indicates a weak contribution of MC73 along this line sight and suggest that the line of sight of $-$ 0.1 might be close to the edge331collisions (?)..,collisions \citep{Guillet09}.332 Second. if oue assuines that SiO is ormned iu gas phase. there is a threshold shock velocity of ~25 ün order to eject Si frou the eraiu cores bv sputtering (?)..," Second, if one assumes that SiO is formed in gas phase, there is a threshold shock velocity of $\sim 25$ in order to eject Si from the grain cores by sputtering \citep{Gusdorf08a}."333 Iu coutrast. other molecules as he orgauies are in the evain nuantles and there is not such a high velocity threshold &x them to be ejected to gas johase.," In contrast, other molecules as the organics are in the grain mantles and there is not such a high velocity threshold for them to be ejected to gas phase."334 The IINCO abundance in the molecular clouds in the center of the MBlkv. Wav and in the nuclei of stirburs ealaxies is similar or a bit hieicr (at inost bv a factor of 2) than in Galactic hot cores (Table D)., The HNCO abundance in the molecular clouds in the center of the Milky Way and in the nuclei of starburst galaxies is similar or a bit higher (at most by a factor of 2) than in Galactic hot cores (Table \ref{tab:comp}) ).335 TINCO becomes another piece in the well know1 puzzle of the chemistry of the Galactic center molecular clouds., HNCO becomes another piece in the well known puzzle of the chemistry of the Galactic center molecular clouds.336 This puzzle cau be stununarized as follows: the abundance of SiO and complex organic molecules in the Galacic center is as high as iu lo cores C???)..," This puzzle can be summarized as follows: the abundance of SiO and complex organic molecules in the Galacic center is as high as in hot cores \citep{Martin-Pintado97, Rodriguez06, Requena06}."337 Th contrast. (2) the emission in the Galactic center is exteuded over the central 300 pe and it does not resemble a collection of discrete sources with the size of a hot core (~ 0.1 pc). (v7) the gas density (10°10! )) as much lower than in hot cores (74) and the dust temperatures (<30 IN) are also much lower thau in hot cores.," In contrast, ) the emission in the Galactic center is extended over the central 300 pc and it does not resemble a collection of discrete sources with the size of a hot core $\sim$ 0.1 pc), ) the gas density $10^3-10^4$ ) is much lower than in hot cores ) and the dust temperatures $<30$ K) are also much lower than in hot cores."338 The Calactic ceuter clotds preseut a “hot core chemistry without hot cores” (?)..," The Galactic center clouds present a “hot core chemistry without hot cores"" \citep{Requena06}."339 The origin of this chemistry is not known although it is thought to be due to sole type of mechanical processes as shock waves (277)..," The origin of this chemistry is not known although it is thought to be due to some type of mechanical processes as shock waves \citep{Martin-Pintado97, Martin-Pintado01, Rodriguez04}."340 The origin of the shocks can be related to the complex dynamics in the Inner reeious of the Galaxy (277)..," The origin of the shocks can be related to the complex dynamics in the inner regions of the Galaxy \citep{Huttemeister98, Rodriguez06, Rodriguez08}."341 Based ou the spatial distribution of the IENC'O aud the conparison wit1 other species. as ΠΟΠ. ? have also sugeested that the TINC'O emission iu IC312 is tracing shocks.," Based on the spatial distribution of the HNCO and the comparison with other species, as $_3$ OH, \cite{Meier05} have also suggested that the HNCO emission in IC342 is tracing shocks."342 Receutly. 9) have also proposed that shocks could be the exdlanation of the hieh INCO abundauces measured iu galactic nuclei.," Recently, \cite{Martin08, Martin09} have also proposed that shocks could be the explanation of the high HNCO abundances measured in galactic nuclei."343 Discussing the precise origin of shocks in Calactic uucleiis out of the scope of this paper., Discussing the precise origin of shocks in Galactic nuclei is out of the scope of this paper.344 Nevertheless. our observatious support the scenario of TINCO tracing shocks in galactic nuclei since our L1157 results probe a imecdimm of moderate Ho deusitv where the IINCO abmudace is indeed high due to the erain processing aud eas heating by shock waves.," Nevertheless, our observations support the scenario of HNCO tracing shocks in galactic nuclei since our L1157 results probe a medium of moderate $_2$ density where the HNCO abundace is indeed high due to the grain processing and gas heating by shock waves."345 We have observed three dires of INCO. towards the protostar L1157 audi s associated molecular ouflow., We have observed three lines of HNCO towards the protostar L1157 and its associated molecular outflow.346 Our aim is to characterize the IENCO properties i1 shocked eas., Our aim is to characterize the HNCO properties in shocked gas.347 HNCO is well deected in the shocked gas. where the abuudance increases by a factor of 6-3[ with respect to the abundauce in the protostar LILS7-nun.," HNCO is well detected in the shocked gas, where the abundance increases by a factor of 6-34 with respect to the abundance in the protostar L1157-mm."348 The abundance in Bl and B2 is 0.1 and 0.3-1 ον respectively.," The abundance in B1 and B2 is 0.4-1.8 $^{-8}$ and 0.3-1 $^{-7}$, respectively."349 The abundance in D2 is the highest ever measured. considerably hieher taan those in hot cores (a ew 10?) and galactic nuclei (10918).," The abundance in B2 is the highest ever measured, considerably higher than those in hot cores (a few $10^{-9}$ ) and galactic nuclei $10^{-9}-10^{-8}$ )."350 Our results probe tliat he IINCO abundances measured i ealactic nuclei can easilv be attained i srocked eas. providing a solid basis to xevious sugecstions that the exteuced NCO in galactic miclei could trace large scale shocks (??)..," Our results probe that the HNCO abundances measured in galactic nuclei can easily be attained in shocked gas, providing a solid basis to previous suggestions that the extended HNCO in galactic nuclei could trace large scale shocks \citep{Meier05,Minh06}."351 The dominant formation pathwav of Ηνο in hot cores Is erain inautle evaporation of complex molecules ormed from TINCO auc subsequent dissociation to give again INCO., The dominant formation pathway of HNCO in hot cores is grain mantle evaporation of complex molecules formed from HNCO and subsequent dissociation to give again HNCO.352 In addition. there is coutribution from gas ghase reactions. but it is ninor due to the high activation xuriers of sole reactious (7).. (?)..," In addition, there is contribution from gas phase reactions, but it is minor due to the high activation barriers of some reactions \citep{Tideswell10}. \citep[][]{Gusdorf08a}."353could be the deviation of the azimuthally averaged mass distribution from an NEW profile as recently shown by ?..,could be the deviation of the azimuthally averaged mass distribution from an NFW profile as recently shown by \citet{Oguri_Hamana_2011}.354 Looking at the masses. a somewhat different picture emerges: The values reconstructed from the spherical fit (blue lines) are considerably more tightly constrained. with a tvpical scatter of only ~δαri and a bias at a level of only z2%...," Looking at the masses, a somewhat different picture emerges: The values reconstructed from the spherical fit (blue lines) are considerably more tightly constrained with a typical scatter of only $\sim 5\%$ and a bias at a level of only $\approx -2$."355 This becomes even more remarkable when compared to the spread. in the masses obtained. from 3D fitting. ic. Aap/AMsii..," This becomes even more remarkable when compared to the spread in the masses obtained from 3D fitting, ie. $M_\text{3D} / M_\text{Mill}$,"356 whieh we show by green lines in Figs., which we show by green lines in Figs.357 4. and 5., \ref{medians} and \ref{fig:scatter}.358 The very close agreement between these indicates that the spherical WL mass reconstruction is as accurate as could. be hoped for., The very close agreement between these indicates that the spherical WL mass reconstruction is as accurate as could be hoped for.359" The negative bias in the ""perfect and ""default, simulations is thus due to the mass distribution outside roo.", The negative bias in the `perfect' and `default' simulations is thus due to the mass distribution outside $r_{200}$.360 As in the case of concentration. a likely explanation for this bias is the deviation of the mass distribution outside reoo from an NEW profile (see. e.g.. 11 o£ ?2)).," As in the case of concentration, a likely explanation for this bias is the deviation of the mass distribution outside $\sim r_{200}$ from an NFW profile (see, e.g., 1 of \citealt{Hayashi_White_2008}) )."361 This leads to less mass along the line of sight than expected from an NEW profile extending to infinity. which explains the negative mass bias (see also ?)).," This leads to less mass along the line of sight than expected from an NFW profile extending to infinity, which explains the negative mass bias (see also \citealt{Oguri_Hamana_2011}) )."362 We demonstrated above that most of the scatter and. bias in reconstructed concentrations is due to deviations from a spherically svmimetrie NEW profile within racy., We demonstrated above that most of the scatter and bias in reconstructed concentrations is due to deviations from a spherically symmetric NFW profile within $r_{200}$.363 Phe obvious culprits responsible for these deviations are asphericity (e.g... riaxial haloes) and substructure.," The obvious culprits responsible for these deviations are asphericity (e.g., triaxial haloes) and substructure."364 We now investigate the role plaved. by cach of these sources of error., We now investigate the role played by each of these sources of error.365 To begin with. an overall sense of the validity. of the (spherically averaged) NEW approximation is given by the Algo/Adsqiy distributions shown in Fig.," To begin with, an overall sense of the validity of the (spherically averaged) NFW approximation is given by the $M_\text{3D} / M_\text{Mill}$ distributions shown in Fig."366 4 and 5. (green ines)., \ref{medians} and \ref{fig:scatter} (green lines).367 With Any being a mocel-independent. quantity. it oovides a reference value for Algo which can be used as an indication of how well the NEW profile describes a cluster.," With $\mmill$ being a model-independent quantity, it provides a reference value for $\mdd$ which can be used as an indication of how well the NFW profile describes a cluster."368 The (logarithmic) scatter. and bias are both small at a evel of &54 and =2% respectively., The (logarithmic) scatter and bias are both small at a level of $\approx 5\%$ and $\approx -2\%$ respectively.369 This confirms that. despite the obvious presence of substructure and the overall riaxiality of the simulated. clusters (sec. e.g. Fig. 1)).," This confirms that, despite the obvious presence of substructure and the overall triaxiality of the simulated clusters (see, e.g., Fig. \ref{projections}) ),"370 the density is: still well-cleseribecl by the SEW profile., the density is still well-described by the NFW profile.371 iut while the 3D. mass structure of the haloes mav »e relatively well described by an NEW. profile for many clusters. the lensing deflection depends. on (the gradient of) the density.," But while the 3D mass structure of the haloes may be relatively well described by an NFW profile for many clusters, the lensing deflection depends on (the gradient of) the density."372 For. realistic. non-spherically-symmetric cluster haloes. deviations from svmmetry can be expected to alfect 3D and 2D reconstructions differently. so it is cntively plausible that the shear signal for a cluster. even one that is well represented by an NEW profile in 3D. may not be well described by a 2D profile derived. from it.," For realistic, non-spherically-symmetric cluster haloes, deviations from symmetry can be expected to affect 3D and 2D reconstructions differently, so it is entirely plausible that the shear signal for a cluster, even one that is well represented by an NFW profile in 3D, may not be well described by a 2D profile derived from it."373 We first look at the cllect of halo triaxialitv., We first look at the effect of halo triaxiality.374 ? sugeest a triaxial generalisation of the spherical NEN profile by replacing the radius i in bv roar where where Y. Y ancl Z are the distances along the major. intermediate ancl minor axes respectively: the numbers a and b are the ratio of the major ancl minor axis to the intermediate axis. respectively.," \citet{Jing_Suto_2002} suggest a triaxial generalisation of the spherical NFW profile by replacing the radius $r$ in by $\reff$ where where $X$, $Y$ and $Z$ are the distances along the major, intermediate and minor axes respectively; the numbers $a$ and $b$ are the ratio of the major and minor axis to the intermediate axis, respectively."375 In a similar wav to our standard 3D fitting procedure deseribed above. we now also fit this triaxial NEW. profile to our lensing haloes.," In a similar way to our standard 3D fitting procedure described above, we now also fit this triaxial NFW profile to our lensing haloes."376 Each halo is first subcdivided into five concentric shells covering a racial range from -1.5 to 0 in σιους)., Each halo is first subdivided into five concentric shells covering a radial range from -1.5 to 0 in $\log_{10} (r/r_{200})$.377 Each shell is further divided into 247 sectors of equal volume., Each shell is further divided into $24^2$ sectors of equal volume.378 Overall. this procedure divides the cluster into 2880 cells. for cach of which we compute the average density p;.," Overall, this procedure divides the cluster into 2880 cells, for each of which we compute the average density $\rho_i$ ."379" The triaxial NEW profile is then fit hy least- regression"".", The triaxial NFW profile is then fit by least-squares .380 Applying this to the question of the influence of halo triaxiality on lensing reconstructions. we show. in the first panel of Fig. 6..," Applying this to the question of the influence of halo triaxiality on lensing reconstructions, we show, in the first panel of Fig. \ref{fig:mcrelative},"381 how the angle 9. between the line of sight and the major halo axis correlates with over- and underpredietion. of the lensing clusters. mass ancl concentration., how the angle $\delta$ between the line of sight and the major halo axis correlates with over- and underprediction of the lensing cluster's mass and concentration.382 Each point corresponds to a mock WL reconstruction. of a simulated cluster: we include. all simulated clusters with 5 projections each., Each point corresponds to a mock WL reconstruction of a simulated cluster; we include all simulated clusters with 5 projections each.383" It is immecdiately obvious that projections with small 9 lead to overpredictions in both mass and concentration. the opposite being true [or cases with 6~90""."," It is immediately obvious that projections with small $\delta$ lead to overpredictions in both mass and concentration, the opposite being true for cases with $\delta \sim 90^o$."384 The role of orientation. becomes even more obvious when we move to the spherical WL fit described. above and only analyse the region inside roug. as shown in the second. panel in Fig. 6..," The role of orientation becomes even more obvious when we move to the spherical WL fit described above and only analyse the region inside $r_{200}$, as shown in the second panel in Fig. \ref{fig:mcrelative}. ."385 Ες reduces the scatter along the (1.-1) direction considerably. identifving the influence of background. galaxies on low-mass clusters as its main cause.," This reduces the scatter along the (1,-1) direction considerably, identifying the influence of background galaxies on low-mass clusters as its main cause."386 The finding that decreasing 9 increases ey and Adwy simultaneously confirms previous work on the clleet of cluster triaxiality by 2.. who analysed a sample of four massive haloes and found a strong correlation between concentration and halo orientation. ancl ? who derived a similar result using analytic cluster halocs.," The finding that decreasing $\delta$ increases $\cwl$ and $\mwl$ simultaneously confirms previous work on the effect of cluster triaxiality by \citet{Clowe_et_al_2004}, who analysed a sample of four massive haloes and found a strong correlation between concentration and halo orientation, and \citet{Corless_King_2007} who derived a similar result using analytic cluster haloes."387 The latter authors concluded. that triaxiality could: cause overpredicetions in concentration by a factor of 2. in. good agreement with the second. panel of Fig. 6..," The latter authors concluded that triaxiality could cause overpredictions in concentration by a factor of 2, in good agreement with the second panel of Fig. \ref{fig:mcrelative}."388 The scatter in niasses eviations up to a factor of 1.5 reported by these authors. on the other hand. is considerably larger than ours ( 1.1).," The scatter in masses — deviations up to a factor of 1.5 — reported by these authors, on the other hand, is considerably larger than ours $\sim 1.1$ )."389 This may be due to the best-fit NEW mass being inlluenced most severely by matter in the cluster outskirts as. discussed. above., This may be due to the best-fit NFW mass being influenced most severely by matter in the cluster outskirts as discussed above.390 The analvtic model of ? inclucles this matter bevond (so) whereas our spherical WL analysis does not., The analytic model of \citet{Corless_King_2007} includes this matter beyond $r_{200}$ whereas our spherical WL analysis does not.391 Note that in the first two panels of Fig., Note that in the first two panels of Fig.392 6 the of the ratio between major and minor axis was not taken into account at all., \ref{fig:mcrelative} the of the ratio between major and minor axis was not taken into account at all.393 We explore its inlluence in the third. panel of Fig., We explore its influence in the third panel of Fig.394 6 and find a much weaker correlation than with halo orientation., \ref{fig:mcrelative} and find a much weaker correlation than with halo orientation.395 Haloes with extremely high axis ratios have a tendeney to lead to more over- or uncderprecdieted masses and concentrations. as should be expected. but the influence is clearly much smaller than that of orientation.," Haloes with extremely high axis ratios have a tendency to lead to more over- or underpredicted masses and concentrations, as should be expected, but the influence is clearly much smaller than that of orientation."396 We notedabove that the concentration scatter slightly upon inclusion ofmatter outside rou., We notedabove that the concentration scatter slightly upon inclusion ofmatter outside $r_{200}$ .397 One possible, One possible398pathological case that all (he reference stars are members of a moving group. will a shared proper motion and identical parallaxes. then the method of dillerential astrometry would [ail as the shared motions would be interpreted as detector offsets.,"pathological case that all the reference stars are members of a moving group, with a shared proper motion and identical parallaxes, then the method of differential astrometry would fail as the shared motions would be interpreted as detector offsets."399 There is no evidence that (his is the case., There is no evidence that this is the case.400 Note that a bulk motion will only affect the derived proper motions., Note that a bulk motion will only affect the derived proper motions.401 We show later (hat (he reference stars in this field are at distances 710 kpc. so (he correction from relative to absolute parallaxes must be small.," We show later that the reference stars in this field are at distances $>$ 10 kpc, so the correction from relative to absolute parallaxes must be small."402 Because the parallax is small — a fraction of a pixel in size — we need to (take great care with the reductions., Because the parallax is small – a fraction of a pixel in size – we need to take great care with the reductions.403 Therefore. we decided that each of the investigators would analvze the data independently. using different fitting techniques.," Therefore, we decided that each of the investigators would analyze the data independently, using different fitting techniques."404 We started [rom a common set of processed images., We started from a common set of processed images.405 The initial data processing consists of cleaning the images of cosmic rays. and correcting the pixel positions for distortions in (he detector.," The initial data processing consists of cleaning the images of cosmic rays, and correcting the pixel positions for distortions in the detector."406 Cosmic rays are a problem with all CCD detectors., Cosmic rays are a problem with all CCD detectors.407" While largely cosmetic. occasionally a cosmic rav does hit within the point spread Ποιος of a source. and will affect both the astrometrv and the photometry,"," While largely cosmetic, occasionally a cosmic ray does hit within the point spread function of a source, and will affect both the astrometry and the photometry."408 We begin with the flat-fiekled ΠΠ images., We begin with the flat-fielded flt.fits images.409 We reject all pixels with a data quality Πας set to 2048 or greater (those identified as saturated pixels and cosmic ravs) by setting the data value equal to the median of the surrounding 8 pixels., We reject all pixels with a data quality flag set to 2048 or greater (those identified as saturated pixels and cosmic rays) by setting the data value equal to the median of the surrounding 8 pixels.410 About of the pixels in each image are so-alfected., About of the pixels in each image are so-affected.411 This is mostly done to simplify the data reduction code. where large data values can craw olf a mean or median.," This is mostly done to simplify the data reduction code, where large data values can draw off a mean or median."412 But in the end (his is of little consequence., But in the end this is of little consequence.413 We save (his cosmeticallv-corrected image as a fits file., We save this cosmetically-corrected image as a fits file.414 The ACS is aracial bay instrument on the LIST. hence there is significant and asvimimetric distortion in the images (Anderson&Ning2004).," The ACS is a radial bay instrument on the HST, hence there is significant and asymmetric distortion in the images \citep{AK04}."415. We use Anderson's #ng2rym_Fortran code to find the stars in the cosmetically-corrected images and to correct for the instrumental distortion., We use Anderson's Fortran code to find the stars in the cosmetically-corrected images and to correct for the instrumental distortion.416 This code determines positions bv doing a P5E-fit using the liller-specilic point spread function., This code determines positions by doing a PSF-fit using the filter-specific point spread function.417 According to Anderson&Wing(2004).. the distortion correction corrects to better Chan 0.01 pixel in each coordinate lor sufficiently. bright stars.," According to \citet{AK04}, the distortion correction corrects to better than 0.01 pixel in each coordinate for sufficiently bright stars."418 The output of this code is a list of raw and corrected X and Y positions in the instrumental frame. along with an instrumental magnitude.," The output of this code is a list of raw and corrected X and Y positions in the instrumental frame, along with an instrumental magnitude."419 The code does not return any estimate of the uncertainty in the »osition., The code does not return any estimate of the uncertainty in the position.420 We adopt the mean pixel scale of 0.02827 arcsecf/pin., We adopt the mean pixel scale of 0.02827 arcsec/pix.421 Using the thresholds we selected (IIMUIN=5. FAHN=150). we iclentily 21 stars in the field that are common to at least five of the visits. in additional to the neutron star.," Using the thresholds we selected (HMIN=5, FMIN=150), we identify 21 stars in the field that are common to at least five of the visits, in additional to the neutron star."422 Thirteen of these stars are recovered in all visits. and five are seen in seven of the visits.," Thirteen of these stars are recovered in all visits, and five are seen in seven of the visits."423 The others lie, The others lie424"The maximum change in Y, is therefore = A similar limit pertains at lower densities.",The maximum change in $Y_e$ is therefore = A similar limit pertains at lower densities.425 One way to exceed this limit in the high density case is if additional reaction chains occur (see 32.2)., One way to exceed this limit in the high density case is if additional reaction chains occur (see 2.2).426" We show AY,4, as a dashed line in Figure 4. in comparison to the AY,’s that result from X(C7Ne)20.007 and 0.02 lines)."," We show $\Delta Y_{e,\rm max}$ as a dot-dashed line in Figure 4, in comparison to the $\Delta Y_e$ 's that result from $X(^{22}$ $)=0.007$ and $0.02$ )."427" By coincidence. the maximum effect of neutronization during simmering is comparable to that associated with a solar metallicity,"," By coincidence, the maximum effect of neutronization during simmering is comparable to that associated with a solar metallicity."428 The other possible limiter of neutronization is the onset of the explosion., The other possible limiter of neutronization is the onset of the explosion.429" The reactions in Table 1 show that Q~16 MeV is released as thermal energy when six carbon nuclei are If we let E, be the total thermal content that is within the convective core with respect to the initial isothermal WD. this implies a change AY,=—jE,/QM. in a convective core of mass M... AY, = δις For this to compete with the --Ne contribution. a total energy E. = or 71015ergsg! must be released prior to the explosion."," The reactions in Table 1 show that $Q\approx 16$ MeV is released as thermal energy when six carbon nuclei are If we let $E_c$ be the total thermal content that is within the convective core with respect to the initial isothermal WD, this implies a change $\Delta Y_e=-\eta E_cm_p/QM_c$ in a convective core of mass $M_{c}$, Y_e = -6.5 For this to compete with the $^{22}$ Ne contribution, a total energy 	E_c = or $7\times10^{15}\ {\rm ergs \ g^{-1}}$, must be released prior to the explosion."430 Simmering ends when dynamical burning is triggered. requiring 7.~8«105K (Woosleyetal.2004).," Simmering ends when dynamical burning is triggered, requiring $T_c\approx8\times 10^8\ {\rm K}$ \citep{woo04}."431. If the burning occurred within a single zone with the specific heat of 32. then reaching this 7. would require z1.31010ergsel. in excess of that implied by equation (10)).," If the burning occurred within a single zone with the specific heat of 2, then reaching this $T_c$ would require $\approx1.3\times10^{16}\ {\rm ergs \ g^{-1}}$, in excess of that implied by equation \ref{eq:ec}) )."432 Of course. in reality the convective zone extends outward. so that little mass is at 7..," Of course, in reality the convective zone extends outward, so that little mass is at $T_c$."433 To accurately determine the resulting neutronization. we construct hydrostatic WD models consisting of fully convective cores as described at the beginning of $2..," To accurately determine the resulting neutronization, we construct hydrostatic WD models consisting of fully convective cores as described at the beginning of \ref{sec:rates}."434 We consider isothermal temperatures of either 10°K or 2«105K., We consider isothermal temperatures of either $10^8\ {\rm K}$ or $2\times 10^8\ {\rm K}$.435 At any given moment there is a well defined M. (Lesaffreetal.2006:Piro 2007).. and we evaluate the current thermal content by integrating the specific heat relative to the initially isothermal WD. where 7; is the isothermal WD temperature.," At any given moment there is a well defined $M_c$ \citep{les06,pir07}, and we evaluate the current thermal content by integrating the specific heat relative to the initially isothermal WD, where $T_i$ is the isothermal WD temperature."436" In this way we use our time independent models to find the fraction of carbon that must have burned. f. and the associated AY, as T, and M. increase with time."," In this way we use our time independent models to find the fraction of carbon that must have burned, $f$, and the associated $\Delta Y_e$ as $T_c$ and $M_c$ increase with time."437 We assume no neutrino losses and thus all ee16MeV of thermal energy contributes to heating., We assume no neutrino losses and thus all $\approx16\ {\rm MeV}$ of thermal energy contributes to heating.438 In Figure 4. we summarize the results of these calculations., In Figure \ref{fig:ye} we summarize the results of these calculations.439" —1 each case. the slope of AY, shows a break at the transition from 42 (fg>fo o3) to. =1."," In each case, the slope of $\Delta Y_e$ shows a break at the transition from $\eta=2$ $t_h>t_{\rm ec,23}$ ) to $\eta=1$."440 This break occurs later for more massive WDs (Fig. 1) ," This break occurs later for more massive WDs (Fig. \ref{fig:simmering}) ),"441thus these have more neutronization during simmering., thus these have more neutronization during simmering.442" Increasing the isothermal temperature decreases M,. so that it takes less burning to reach a given 7..."," Increasing the isothermal temperature decreases $M_c$, so that it takes less burning to reach a given $T_c$."443 These fully integrated models make it clear that substantial neutronization occurs prior to the explosion., These fully integrated models make it clear that substantial neutronization occurs prior to the explosion.444" In comparison to the AY, from Ne. simmering effects dominate if X Ne)«0.013 orZ/Z ..X2/3."," In comparison to the $\Delta Y_e$ from $^{22}$ Ne, simmering effects dominate if $X(^{22}$ $)<0.013$ or $Z/Z_\odot\lesssim2/3$."445" This thwarts the occurrence of high Y, SNe la in low metallicity progenitors.", This thwarts the occurrence of high $Y_e$ SNe Ia in low metallicity progenitors.446 We have found that significant neutronization of the WD core occurs throughout the simmering stage of carbon burning until the onset of the explosion., We have found that significant neutronization of the WD core occurs throughout the simmering stage of carbon burning until the onset of the explosion.447 If substantial energy is lost to the convective Urea process (Lesaffreetal.2005.andrefer-ences therein). then the neutronization is truncated by proton captures onto freshly synthesized heavy elements (resulting in eq. [6].," If substantial energy is lost to the convective Urca process \citep[][and references therein]{les05}, then the neutronization is truncated by proton captures onto freshly synthesized heavy elements (resulting in eq. \ref{eq:yemax}] ])."448" The main consequence is a uniform ""floor"" to the amount of neutronization that dominates over the metallicity dependent contribution for all progenitors with Z/Z..=2/3.", The main consequence is a uniform “floor” to the amount of neutronization that dominates over the metallicity dependent contribution for all progenitors with $Z/Z_\odot\lesssim2/3$.449 Given the likely significance this has for SNe Ia. more work needs to be done.," Given the likely significance this has for SNe Ia, more work needs to be done."450 In particular. at high ignition densities. heavy element electron captures and a full reaction network are needed to follow the resulting diverse collection of elements (see the discussion in $2.2).," In particular, at high ignition densities, heavy element electron captures and a full reaction network are needed to follow the resulting diverse collection of elements (see the discussion in 2.2)."451 The convective Urea process is another complication we have not addressed., The convective Urca process is another complication we have not addressed.452 In principle. if more energy is lost to neutrinos then more burning (and thus more neutronization) is required to make the burning dynamical.," In principle, if more energy is lost to neutrinos then more burning (and thus more neutronization) is required to make the burning dynamical."453 Assessing this will necessitate coupling a full nuclear network (Chamulaketal.2007b) to convective calculations.," Assessing this will necessitate coupling a full nuclear network \citep{cha07b}454 to convective calculations."455 Such models would accurately determine jj rather than simply setting it to | or 2., Such models would accurately determine $\eta$ rather than simply setting it to 1 or 2.456 In closing. we highlight some important features exhibited by recent observations of SNe Ia. It is clear that the amount of ?*Ni produced in SNe la has a dynamic range (0.1-1M.) larger than can be explained by metallicity or simmering neutronization.," In closing, we highlight some important features exhibited by recent observations of SNe Ia. It is clear that the amount of $^{56}$ Ni produced in SNe Ia has a dynamic range $0.1-1M_\odot$ ) larger than can be explained by metallicity or simmering neutronization."457 However. since an intriguing trend is the," However, since an intriguing trend is the"458Figure Rellectivily spectrum of comet 9P/Tempel 1 after the impact. near the time of maximum brightness in à 2.4 aperture.,"Figure Reflectivity spectrum of comet 9P/Tempel 1 after the impact, near the time of maximum brightness in a $\arcsec$ aperture."459 The spectrum is the ratio of the comet spectrum and (hat of solar analog star DO41C and is displaved here in arbitrary linear [Iux units., The spectrum is the ratio of the comet spectrum and that of solar analog star P041C and is displayed here in arbitrary linear flux units.460 The blue ancl red channel of the instrument were individually photometrically calibrated. and the data match very well without further adjustment., The blue and red channel of the instrument were individually photometrically calibrated and the data match very well without further adjustment.461 The emission lines of CN and ΟΕ are Clearly visible. and the C band is faintly indicated.," The emission lines of CN and [OI] are clearly visible, and the $_3$ band is faintly indicated."462 The feature at 763 nm is an artifact from thestrong telluric Os absorption., The feature at 763 nm is an artifact from thestrong telluric $_2$ absorption.463 Filled circles represent the data that are considered reliable., Filled circles represent the data that are considered reliable.464 We also show the data at the ends of the spectral ranges of the blue spectrograph arm (small open circles) and of the red spectrograph arm (small plus signs) to illustrate that at the ends of each spectrum. the calibration was not reliable and why these data have not been included in the analvsis.," We also show the data at the ends of the spectral ranges of the blue spectrograph arm (small open circles) and of the red spectrograph arm (small plus signs) to illustrate that at the ends of each spectrum, the calibration was not reliable and why these data have not been included in the analysis."465 The boundary between where the blue vs. red data were used is at 520 nm and this boundary is indicated in the Figure., The boundary between where the blue vs. red data were used is at 520 nm and this boundary is indicated in the Figure.466 This boundary does not coincide with the change in slope of the spectrum., This boundary does not coincide with the change in slope of the spectrum.467 Below 580 nm. (he normalized slope between 350 nm and 580 nm is22.65... between 580 nm and 940 nm. the normalized slope," Below 580 nm, the normalized slope between 350 nm and 580 nm is, between 580 nm and 940 nm, the normalized slope is ."468surrounding clusters.,surrounding clusters.469 It is superimposed. on a probable bow-shock -—33' to the southwest of 1127. and Wltll53ab., It is superimposed on a probable bow-shock $\sim$ $'$ to the southwest of 127 and 153ab.470 Llowever. this bow-shock seems to have been generated in 22.," However, this bow-shock seems to have been generated in 2."471 We may be witnessing sequential elfects of star formation., We may be witnessing sequential effects of star formation.472 The presence of the trapezium system in the center of 1127 will certainlv have an important9900. role in the cluster evolution., The presence of the trapezium system 900 in the center of 127 will certainly have an important role in the cluster evolution.473 Trapezium systems evolve into hierarchical svstems (with a much larger separation among its components) or even disperse in a few million. vears producing runaway stars., Trapezium systems evolve into hierarchical systems (with a much larger separation among its components) or even disperse in a few million years producing runaway stars.474 The oldest one identified so far has ~ 550Myr (Abt&Corbally 20003)., The oldest one identified so far has $\sim$ Myr \citealt{abtcor00}) ).475 1127. is close to WlIC1I53ab that djs a spectroscopic binary with a primary WNG6o and an OGL (Smith.Shara&Alotlat 1996))., 127 is close to 153ab that is a spectroscopic binary with a primary WN6o and an O6I \citealt*{ssm96}) ).476 Evolution of this WR. to spectral type WC and its subsequent explosion as supernova will certainly have an impact on the dynamical evolution of neighbouring clusters 1127. SBDB11 and 22). by means of gas removal.," Evolution of this WR to spectral type WC and its subsequent explosion as supernova will certainly have an impact on the dynamical evolution of neighbouring clusters 127, 1 and 2), by means of gas removal."477 SBBIL is the vounges cluster in the sample and remains embedded., 1 is the youngest cluster in the sample and remains embedded.478 Ehe residual gas expulsion aud. stellar evolution may cause an increase of core radius., The residual gas expulsion and stellar evolution may cause an increase of core radius.479 Since 22 expulsed its residual gas. star formation must have stopped and its survival as à bound OC depends on the dvnamies and evolution of neighbouring clusters and specially of the WIUIIS3ab star.," Since 2 expulsed its residual gas, star formation must have stopped and its survival as a bound OC depends on the dynamics and evolution of neighbouring clusters and specially of the 153ab star."480 SBB33 hosts the 1152 star of type WN3(h)-w. a mass of MM. and mass loss rate log MM. ==--5.5 (Hamann.Grafener&Liermann 2006)).," 3 hosts the 152 star of type WN3(h)-w, a mass of $_{\odot}$ and mass loss rate $\log \dot{M}$ $_{\odot}$ -5.5 \citealt*{hgl06}) )."481 Since 1152 has a relatively low mass for a WR. star (the minimum initial mass for a star to become a WR. at Solar-metallicity is MM.) it can explode as supernova without evolving through the WC type. expulsing σας and dissolving the star cluster very carly.," Since 152 has a relatively low mass for a WR star (the minimum initial mass for a star to become a WR at Solar-metallicity is $_{\odot}$ ) it can explode as supernova without evolving through the WC type, expulsing gas and dissolving the star cluster very early."482 Two possible destinations are sugeested for the central clusters of 5h2-132:, Two possible destinations are suggested for the central clusters of Sh2-132:483 7? azz120 (72)...," \citet{kalas08} $a \approx 120$ $a = \{24,38,68\}$ \citep{marois08}."484 >>1.5 =3 20120 uieht at fixst seem unlikely. given that A stars uake up less than the stellar population iu he Solar neighborhood aud because the stir-plauet contrast ratios are unfavorable compared to svsteiis witli autor. less massive central stars.," $> 1.5$ $\lesssim 3$ $20-120$ might at first seem unlikely, given that A stars make up less than of the stellar population in the Solar neighborhood and because the star-planet contrast ratios are unfavorable compared to systems with fainter, less massive central stars."485 However. in light of recent discoveries οι Doppler-based planet searches of nassive stars it is becomine appareut that A cavarfs be ideal target stars for direct imacing survers (7777777)..," However, in light of recent discoveries from Doppler-based planet searches of massive stars it is becoming apparent that A dwarfs may in fact be ideal target stars for direct imaging surveys \citep{hatzes03, setiawan05, reffert06, sato07,486 nied07, liu08, dollinger09}."487" Measurements of the frequency of eiut plancts around the vretired” counterparts of A-ype cawarts (subgiauts aud giauts) have found that the occurence of Jovian plancts scales with stellar mass: A-ype stars CM,z1.5 MJ) are at least 5 times ore ikely than Mo dwarfs to harbor a giant planet (22?).."," Measurements of the frequency of giant planets around the “retired” counterparts of A-type dwarfs (subgiants and giants) have found that the occurrence of Jovian planets scales with stellar mass: A-type stars $M_\star \gtrsim 1.5$ ) are at least 5 times more likely than M dwarfs to harbor a giant planet \citep{johnson07b,bowler10,johnson10a}."488 Aud just like the current sample of imaged planets. Doppler-detected plauets around retired A stars are ore massive (7) ancl orbit farther from their stars than do planets ound around Sun-like. F. € and Is (FCI) dwarfs (?7?)..," And just like the current sample of imaged planets, Doppler-detected planets around retired A stars are more massive \citep[][]{lovis07} and orbit farther from their stars than do planets found around Sun-like, F, G and K (FGK) dwarfs \citep{johnson07, sato08b}."489 Tudeed. there is stroug evidence that the orbita characteristics of planets around A stars are drawn from a statistical parcut population that is distinct from those of planets around FOS dwarts.," Indeed, there is strong evidence that the orbital characteristics of planets around A stars are drawn from a statistical parent population that is distinct from those of planets around FGK dwarfs."490" ? performicc a statistical analysis of planets detected im the Lick Subeiauts Survey, which comprises 31 massive stars (QU.z1.5 Αι} monitored for the past 5 vem"," \citet{bowler10} performed a statistical analysis of planets detected in the Lick Subgiants Survey, which comprises 31 massive stars $M_\star491\gtrsim 1.5$ ) monitored for the past 5 years."492 The imass-period distribution of exoplauets arouik FCS chwarts ids typically described by a double-power-law relationship. with the frequeney of planets rising toward lower masses and remaining flat i losarithiuic seiiniajor-axis bins from ~0.05 AU to ~5 AU (????)..," The mass-period distribution of exoplanets around FGK dwarfs is typically described by a double-power-law relationship, with the frequency of planets rising toward lower masses and remaining flat in logarithmic semimajor-axis bins from $\sim 0.05$ AU to $\sim5$ AU \citep{tab02,lineweaver03,493 cumming08, johnson09rev}."494 Based ou the 7 planet detections from the Lick survey. Bowler et al.," Based on the 7 planet detections from the Lick survey, Bowler et al."495 concluded that the power-law indices of the distribution of planets around A stars and Sun-like stis differ at the Lo level: the planets in their sample all have >1.5 , concluded that the power-law indices of the distribution of planets around A stars and Sun-like stars differ at the $\sigma$ level; the planets in their sample all have $ > 1.5$ 496o (Shakura Suuvaev 1973). this timescale can be written approximately as.1.(2-1) where {1 is the local diskκοΠοιους aud O the local aneular velocity.,"$\alpha$ (Shakura Sunyaev 1973), this timescale can be written approximately as, where $H$ is the local disksemi-thickness and $\Omega$ the local angular velocity."497 It was originally assumed (Barcdecn Petterson 1975: Rees 1978) that the component of the disk aneular momentum ling in the pluie of the disk (that is. the warp) is transterred racially on a similar timescale.," It was originally assumed (Bardeen Petterson 1975; Rees 1978) that the component of the disk angular momentum lying in the plane of the disk (that is, the warp) is transferred radially on a similar timescale."498 However. if was discovered by Papaloizou Pringle (1983) hat consideration of the propagation of disk warp mist recessarily take uto account the internal lvdrodvuauiucs of the disk itself.," However, it was discovered by Papaloizou Pringle (1983) that consideration of the propagation of disk warp must necessarily take into account the internal hydrodynamics of the disk itself."499 In the regime in which Z//R«6<<1. and in which the disk is close to beime Keplerian. thev ound (see also Kamar Pringle 1985) that the disk schaviowr is somewhat complicated. but that to a first approximation the component of angular monmentuun ia he disk plane is transferred within the disk on a timescale of order A/15. where νο=1/207 (assunüng that a<< 1)," In the regime in which ${H/R}\,<\,{\alpha}500\,<<1$, and in which the disk is close to being Keplerian, they found (see also Kumar Pringle 1985) that the disk behaviour is somewhat complicated, but that to a first approximation the component of angular momentum in the disk plane is transferred within the disk on a timescale of order $R^2/\nu_2$, where $\nu_2/\nu_1 = 1/2 \alpha^2$ (assuming that $\alpha\,<<\,1$ )."501 Thus. the relevant timescale for commmication of the disk warp is. Hg The original calculations by Papaloizou Pringle (1983) were carried out using Enlerian linear perturbation theory about an initially flat disk. and so were formally oulv valid for disk warp augles. 2. uch less than the disk opening auele ΠΠ.," Thus, the relevant timescale for communication of the disk warp is, t_R. The original calculations by Papaloizou Pringle (1983) were carried out using Eulerian linear perturbation theory about an initially flat disk, and so were formally only valid for disk warp angles, $\beta$ , much less than the disk opening angle $H/R$."502 For ACN disks for which ΠΠ~103? (see below). this is somewla Iunitiug.," For AGN disks for which $H/R\,\sim\, 10^{-2} --50310^{-3}$ (see below), this is somewhat limiting."504 Recent work by Ogilvie (1998w.b) however. has shown that simular conchisious remain valid for warps of significant auplitude.," Recent work by Ogilvie (1998a,b) however, has shown that similar conclusions remain valid for warps of significant amplitude."505 These results have a considerable effect on the so-called Bardecu-Petterson radius. Rpp. the radius out to which the disk is aligned with the spin of the hole. as well as ou the hole/disk aligniueut timescale.," These results have a considerable effect on the so-called Bardeen-Petterson radius, $R_{\rm BP}$, the radius out to which the disk is aligned with the spin of the hole, as well as on the hole/disk alignment timescale."506 Since the disk turus out to be far more cficicnt at transferre warp in the radial direction than the initial estimates. which had ignored the iuterual disk liavcdvodvuaimics. it follows that both Rpp (παν Pringle 1985) aud the aliguimeut timescale are wach smaller than was originally thought.," Since the disk turns out to be far more efficient at transferring warp in the radial direction than the initial estimates, which had ignored the internal disk hydrodynamics, it follows that both $R_{\rm BP}$ (Kumar Pringle 1985) and the alignment timescale are much smaller than was originally thought."507 The timescale ou which a nmüsaligned. black hole aligus with its disk and the radius out to which the aliguimicut occurs have been calculated by Scheucr Feiler (1996)., The timescale on which a misaligned black hole aligns with its disk and the radius out to which the alignment occurs have been calculated by Scheuer Feiler (1996).508 Writing the Lense-Thirringe precession rate iu the disk as Opp=uyD. thev find that the radius out to which the disk is aligned with the spin of the hole is eiven simply as the radius at which the timescale for radial diffusion of the warp. Ap. is ofthe order of the local Leuse-Thirring precession. timescale Oil.," Writing the Lense-Thirring precession rate in the disk as $\Omega_{\rm LT}\,=\,\omega_p/R^3$, they find that the radius out to which the disk is aligned with the spin of the hole is given simply as the radius at which the timescale for radial diffusion of the warp, $t_{\rm warp}$, is ofthe order of the local Lense-Thirring precession timescale $\Omega_{\rm LT}^{-1}$."509 Equating these we obtain.fo.," Equating these we obtain,."510 where wy=2607ο. the angular momentiun of the hole. J. is given bv J=aeAl(GAL/e7). AL is the mass of the hole. aud α (0<e 1) the dimensionless spin paralcter.," where $\omega_p = 2 G J / c^2$, the angular momentum of the hole, J, is given by $J\,=\,a\,c\,M\,(G\,M/c^2)$, $M$ is the mass of the hole, and $a$ $0\,<\,a\,<\,1$ ) the dimensionless spin parameter."511" Using these expressions. together with the fact that τονι=1/207. and writing 7)=aH7?Q. we find that Roya, aay be written as. (Roao: where RS=206Mfc? is the Seisiuzschild. radius."," Using these expressions, together with the fact that $\nu_2/\nu_1\,=\,1/{2\,\alpha^2}$, and writing $\nu_1\,=\,\alpha\,H^2\,\Omega$, we find that $R_{\rm warp}$ may be written as, ), where $R_s\,=\,2\,G\,M/c^2$ is the Schwarzschild radius."512" Taking account of the fact that far from the hole.SY, we find that."," Taking account of the fact that far from the hole, we find that,."513πο To proceed further we need a model for the ACN disk at the relevant radii., To proceed further we need a model for the AGN disk at the relevant radii.514 We make use of the AGN disk models computed by Collin-Souttrin Duiuout (1990) from which in the relevant range of radii we fiud that. Uere e is the cfficicney of the aceretion process defined ax €=L/Ale?. and Lg is the Eddington hunuinosity. Lg=LL10MAM erg to where Ma is the black hole lass in units of LOSAL...," We make use of the AGN disk models computed by Collin-Souffrin Dumont (1990) from which in the relevant range of radii we find that, Here $\epsilon$ is the efficiency of the accretion process defined as, $\epsilon\,=\,{L/{\dot M c^2}}$, and $L_{\rm E}$ is the Eddington luminosity, $L_{\rm E}\,=\,1.4 \times 10^{46}\,M_8$ erg $^{-1}$, where $M_8$ is the black hole mass in units of $10^8\,M_\odot$."515 Throughout this letter we shall take a=0.03 and £=0.1επ to represent the typically expected standard values.," Throughout this letter we shall take $\alpha\,=\,0.03$ and $L\,=\,0.1\,L_E$ to represent the typically expected standard values."516 Using this we fiud that.," Using this we find that,."517 This expression is valid provided that, This expression is valid provided that.518 We note that although Scheuer and Feiler (1995) used a simplified set of evolution equations (Pringle 1992) which take iuto account the difference between r4 aud ro. but do not take the full effects of internal disk νοτονταος iuto account. their estimates of the alizuneut radius are in substantial agreement with the full calculations of Iuuuar Pringle (1985) for values of aZi0.3.," We note that although Scheuer and Feiler (1995) used a simplified set of evolution equations (Pringle 1992) which take into account the difference between $\nu_1$ and $\nu_2$, but do not take the full effects of internal disk hydrodynamics into account, their estimates of the alignment radius are in substantial agreement with the full calculations of Kumar Pringle (1985) for values of $\alpha\,\simle\,0.3$."519 Scheuer Feiler (1996) find that the effect of the disk ou the black hole is to force the spin axis of the hole to precess and to align with the disk., Scheuer Feiler (1996) find that the effect of the disk on the black hole is to force the spin axis of the hole to precess and to align with the disk.520 Both precession aud alieumieut taxe place ou the same timescale which is eiveu by.. where J ds the angular iioiieutui of the disk within the warp radius Aag and Opr is the Lense-Thirring augularvelocity also evaluated at Pj.," Both precession and alignment take place on the same timescale which is given by, where $J_d$ is the angular momentum of the disk within the warp radius $R_{\rm warp}$ , and $\Omega_{\rm LT}$ is the Lense-Thirring angularvelocity also evaluated at $R_{\rm warp}$ ."521 It should be noted that the trausfer of angular momentum between the hole aud the disk does not depend i any wav on the disk being, It should be noted that the transfer of angular momentum between the hole and the disk does not depend in any way on the disk being522"TLUSTY/SYNSPEC synthetic spectra our observations are consistent with Τε=25000 K and logg=3.5 (cgs), in agreement with the work of?.","TLUSTY/SYNSPEC synthetic spectra our observations are consistent with $T_{\rm eff}=25000$ K and $\log g=3.5$ (cgs), in agreement with the work of."523. The spectral lines appear distorted and show rapid variations very likely due to f Cep-type pulsations., The spectral lines appear distorted and show rapid variations very likely due to $\beta$ Cep-type pulsations.524" No obvious abundance peculiarity, nor manifestation of circumstellar matter is observed within the spectra."," No obvious abundance peculiarity, nor manifestation of circumstellar matter is observed within the spectra."525 In Fig., In Fig.526" 1. (middle), we superimposed the LSD 7, V, and N profiles of our observations."," \ref{fig:lsd} ), we superimposed the LSD $I$, $V$, and $N$ profiles of our observations."527" According to the ephemeris of?,, the 3 observations are roughly at the same orbital phase (~0.5), and both components have radial velocities (~14 and 4 for the primary and secondary respectively), which explains why it is difficult to distinguish both components in the profiles."," According to the ephemeris of, the 3 observations are roughly at the same orbital phase $\sim$ 0.5), and both components have radial velocities $\sim$ 14 and $\sim$ 4 for the primary and secondary respectively), which explains why it is difficult to distinguish both components in the profiles."528" The shape of the LSD profile shows variations during the run that can be understood7 in terms of radial pulsations in the primary, which would occasionally broaden the profile."," The shape of the LSD $I$ profile shows variations during the run that can be understood in terms of radial pulsations in the primary, which would occasionally broaden the profile."529" As a result, both components can be clearly distinguished in the profile of May 27 (full black line in Fig."," As a result, both components can be clearly distinguished in the profile of May 27 (full black line in Fig."530" 1 middle), while it is less obvious in the other observations."," \ref{fig:lsd} ), while it is less obvious in the other observations."531" Zeeman signatures are detected in many individual spectral lines, the LSD V profiles."," Zeeman signatures are detected in many individual spectral lines, the LSD $V$ profiles."532" The signatures are as broad as the secondary profile, meaning that the magnetic field is detected only in the secondary component of the system."," The signatures are as broad as the secondary profile, meaning that the magnetic field is detected only in the secondary component of the system."533" However, considering the faint Zeeman signatures in the secondary, and the broad line shape of the primary, a magnetic field of the same strength as the secondary's could exist in the primary, without being detected in our observations."," However, considering the faint Zeeman signatures in the secondary, and the broad line shape of the primary, a magnetic field of the same strength as the secondary's could exist in the primary, without being detected in our observations."534" this aim, we have first fitted the I profile of the binary with the method described above for the individual spectral lines."," this aim, we have first fitted the $I$ profile of the binary with the method described above for the individual spectral lines."535 Then we have subtracted from the observed J profile the fit of the primary., Then we have subtracted from the observed $I$ profile the fit of the primary.536 Finally we have measured By using the corrected J and the original V profiles., Finally we have measured $B_{\ell}$ using the corrected $I$ and the original $V$ profiles.537 The values are reported in Table 1., The values are reported in Table 1.538 HD 105382 (= HR 4618) is member of the Sco-Cen association(?)., HD 105382 (= HR 4618) is member of the Sco-Cen association.539". classified it as He-weak with He patches enhanced where Si is depleted, and derived a Τεῃ of 17400+800 K, a logg=4.18+0.20 (cgs), a rotation period of 1.295+0.001 d and an inclination anglesight i=50+10°."," classified it as He-weak with He patches enhanced where Si is depleted, and derived a $T_{\rm eff}$ of $17400\pm800$ K, a $\log g=4.18\pm0.20$ (cgs), a rotation period of $1.295 \pm 0.001$ d and an inclination angle $i=50\pm10$."540". In ourthree spectra, we observe strong variations in the spectral lines, mainly in He1, Si and Feπι, that are due to abundance spots on the stellar surface described by?."," In our spectra, we observe strong variations in the spectral lines, mainly in He, Si and Fe, that are due to abundance spots on the stellar surface described by."541". Clear Zeeman signatures are detected in the metallic and Balmer lines, as well as in the LSD V profiles (Fig."," Clear Zeeman signatures are detected in the metallic and Balmer lines, as well as in the LSD $V$ profiles (Fig."542 1 right)., \ref{fig:lsd} ).543" The rotation phases of our observations, calculated with a rotation period of 1.295 d, are very different (0.35, 0.14, and 0.63), and yet the V profiles are all similarly negative (Table 1)."," The rotation phases of our observations, calculated with a rotation period of 1.295 d, are very different (0.35, 0.14, and 0.63), and yet the $V$ profiles are all similarly negative (Table 1)."544" According to the OR model, this implies that the magnetic obliquity angle (with respect to the rotation axis) cannot be very high (|6|<40° if i=50°), otherwise the positive magnetic pole would sometimes appear on the visible stellar hemisphere, creating a positive profile at least once during the run."," According to the OR model, this implies that the magnetic obliquity angle (with respect to the rotation axis) cannot be very high $|\beta| < 40^{\circ}$ if $i = 50^{\circ}$ ), otherwise the positive magnetic pole would sometimes appear on the visible stellar hemisphere, creating a positive profile at least once during the run."545 HD 105382 was independently discovered as magnetic by and?., HD 105382 was independently discovered as magnetic by and.546". derived the longitudinal field from FORS 1 observations and found values ranging from —923 G to 840 G. Among their four values, the May 2004 (840+58 G) is clearly inconsistent with our data as positive values are not expected."," derived the longitudinal field from FORS 1 observations and found values ranging from $-923$ G to $840$ G. Among their four values, the May 2004 $840\pm58$ G) is clearly inconsistent with our data as positive values are not expected."547" very carefully re-reduced the same FORS 1 data and except for that observation B,=-29+69 G).", very carefully re-reduced the same FORS 1 data and except for that observation $B_{\ell}=-29\pm69$ G).548 We performed a least-square sinusoidal fit to our B; values simultaneously with the Briquet et al. (, We performed a least-square sinusoidal fit to our $B_{\ell}$ values simultaneously with the Briquet et al. (5492007) data and could find a solution only by removing the May 2004 datapoint.,2007) data and could find a solution only by removing the May 2004 datapoint.550 We also performed an independent fit using the re-reduced data of and found a similar result., We also performed an independent fit using the re-reduced data of and found a similar result.551" In both cases, the derived period is consistent with that of Briquet et al. ("," In both cases, the derived period is consistent with that of Briquet et al. ("5522004).,2004).553" The fitted B; values are very similar in both cases, from —670 G to —20 G, implying a magnetic obliquity of ~38° and a polar field strength of ~2.3 kG, assuming a dipole field(?)."," The fitted $B_{\ell}$ values are very similar in both cases, from $-670$ G to $-20$ G, implying a magnetic obliquity of $\sim38$ and a polar field strength of $\sim2.3$ kG, assuming a dipole field."554". We report direct detections of magnetic fields in three hot B-type stars (18000 K - 25000 K), among a sample of 55 stars in which we were searching for magnetic fields with HARPSpol."," We report direct detections of magnetic fields in three hot B-type stars (18000 K - 25000 K), among a sample of 55 stars in which we were searching for magnetic fields with HARPSpol."555 Two of them (HD 122451 and HD 130807) are completely new detections., Two of them (HD 122451 and HD 130807) are completely new detections.556 For the other one - HD 105382 is the first direct detection of a Zeeman signature., For the other one - HD 105382 is the first direct detection of a Zeeman signature.557 One of the main MiMeS results is the systematic detection of chemical peculiarities at the surface of magnetic hot stars?)., One of the main MiMeS results is the systematic detection of chemical peculiarities at the surface of magnetic hot stars.558. Among the three stars discussed in this paper two are unambiguously He-weak., Among the three stars discussed in this paper two are unambiguously He-weak.559" The third one (HD 122451) belongs to a binary system with a8 Cep primary, that makes the interpretation of the spectrum and the detection of peculiarities inside spectral lines very difficult."," The third one (HD 122451) belongs to a binary system with a $\beta$ Cep primary, that makes the interpretation of the spectrum and the detection of peculiarities inside spectral lines very difficult."560 More observations well sampled over the orbital period of the system are required, More observations well sampled over the orbital period of the system are required561that 1.6A4.ve1 of hydrogen is aceveted [rom the corona.,that $1.6\moyr$ of hydrogen is accreted from the corona.562 Including the Hle content. this value rises to 2.3Al.vr.4.," Including the He content, this value rises to $2.3\moyr$."563 ‘This accretion rate is in excellent agreement with estimates of the accretion rate required to sustain the Galaxy's current rate of star formation without depleting its rather meagre stock of interstellar gas., This accretion rate is in excellent agreement with estimates of the accretion rate required to sustain the Galaxy's current rate of star formation without depleting its rather meagre stock of interstellar gas.564 Unfortunately. two problems prevent us from. tightly constraining the value of a.," Unfortunately, two problems prevent us from tightly constraining the value of $\alpha$."565 The first is that it is inferred from some quite subtle features in the deatacube., The first is that it is inferred from some quite subtle features in the datacube.566 The second is that the optimum. value of à depends on the value adopted. for. ee. the equilibrium dillerence in the rotation velocities of the hhalo and the corona.," The second is that the optimum value of $\alpha$ depends on the value adopted for $v_{\rm lag}$, the equilibrium difference in the rotation velocities of the halo and the corona."567" When ry, is raisecl to 100kms the optimum value of. a decreases to .OCvr which corresponds to an accretion rate of L0A4.ve| (1.1AM.vr! including the Le content)."," When $v_{\rm lag}$ is raised to $100\kms$ the optimum value of $\alpha$ decreases to $4.0\Gyr^{-1}$, which corresponds to an accretion rate of $1.0\moyr$ $1.4\moyr$ including the He content)."568 Fig., Fig.569 10. illustrates how successfully the mocel simulates cenussion at. Intermediate. Velocities the simulation is probably as perfect as it can be without reproducing individual superbubbles., \ref{channels} illustrates how successfully the model simulates emission at Intermediate Velocities – the simulation is probably as perfect as it can be without reproducing individual superbubbles.570 By contrast. the model does. not reproduce emission at High. Velocities. presumably. because IIVC'S are extragalactic in origin.," By contrast, the model does not reproduce emission at High Velocities, presumably because HVCs are extragalactic in origin."571 We find. remarkable agreement between the optimum values of the models. parameters. and the values. fou in earlier work., We find remarkable agreement between the optimum values of the model's parameters and the values found in earlier work.572 In particular.our value of fy 2?," In particular,our value of $h_{\rm v}$ \cite{Marinacci+11} \\ref{thickness})"573 B <=0.692 $82. 83. S4.. z20., $B$ $z$ \ref{obs2} \ref{obs3} \ref{proper}.574692 between properties of the linearly polarized and unpolarized absorption spectra provides new information about the spatial structure of this gas on scales of ~ 100 pe., $z$ between properties of the linearly polarized and unpolarized absorption spectra provides new information about the spatial structure of this gas on scales of $\sim$ 100 pc.575 We use the new data to determine both the kinetic temperature and hyperfine spin temperature of the gas. which in turn tells us about its thermal state.," We use the new data to determine both the kinetic temperature and hyperfine spin temperature of the gas, which in turn tells us about its thermal state."576 We use these results to evaluate the standard assumption of a large-scale. uniform. cloud.," We use these results to evaluate the standard assumption of a large-scale, uniform cloud."577 We start by constructing models to describe the re-analyzed spectra in. terms of multiple clouds distributed across the spatially extended structure of 3C 286., We start by constructing models to describe the re-analyzed spectra in terms of multiple clouds distributed across the spatially extended structure of 3C 286.578 In $5., In \ref{cloudstructure}.579.1 we use VLBI maps to exhibit the core-jet structure of 3C 286 near the 21 em absorption frequency., .1 we use VLBI maps to exhibit the core-jet structure of 3C 286 near the 21 cm absorption frequency.580 In 85., In \ref{cloudstructure}.5812 we describe a two-cloud configuration to model the absorption feature., .2 we describe a two-cloud configuration to model the absorption feature.582 We use a chi square minimization technique to fit the model to the Stokes / spectrum and the fractional polarization spectrum and show that the model does not work., We use a chi square minimization technique to fit the model to the Stokes $I$ spectrum and the fractional polarization spectrum and show that the model does not work.583 In $45., In \ref{cloudstructure}.584.3 we show how an adjustment in covering factors and the presence of velocity gradients in the cloud toward the polarized jet source results in a three-component model that provides an adequate fit to the Stokes /. fractional polarization. and polarization position-angle spectra.," .3 we show how an adjustment in covering factors and the presence of velocity gradients in the cloud toward the polarized jet source results in a three-component model that provides an adequate fit to the Stokes $I$, fractional polarization, and polarization position-angle spectra."585 The implications of the results are discussed in 86.., The implications of the results are discussed in \ref{discussion}.586 All the results are then summarized in §7.., All the results are then summarized in \ref{summary}.587" Throughout this paper we use a WMAP cosmology in which (/7.Q,,.Q4) =(0.7. 0.3. 0.7)."," Throughout this paper we use a WMAP cosmology in which $h, {\Omega_{\rm m}}, {\Omega_{\Lambda}}$ ) =(0.7, 0.3, 0.7)."588 We used the Green Bank Telescope in 2007 to observe the z20.692 2] em absorption spectrum against 3C 286., We used the Green Bank Telescope in 2007 to observe the $z=0.692$ 21 cm absorption spectrum against 3C 286.589" We observed all four Stokes parameters simultaneously using the digital FX Spectral Processor. which provides all the necessary self- and eross-products; here ""FX"" means that first it Fourier transforms the input signal and then multiplies the voltage spectra with appropriate phase shifts."," We observed all four Stokes parameters simultaneously using the digital FX Spectral Processor, which provides all the necessary self- and cross-products; here “FX” means that first it Fourier transforms the input signal and then multiplies the voltage spectra with appropriate phase shifts."590 This technique is described indetailby Heiles et (2001) and Heiles (2001)., This technique is described indetailby Heiles et (2001) and Heiles (2001).591 Our original paper reported a very statistically significant, Our original paper reported a very statistically significant592orbital light curve we decided to perform a folding of these data using the known binary orbital period of tie source. after vorifviug that this folding docs not affect tie results reported here i any case.,"orbital light curve we decided to perform a folding of these data using the known binary orbital period of the source, after verifying that this folding does not affect the results reported here in any case."593 Fokine the data is not an imiportant issue for the two Chandra observaIOUS axd the NMM observation. where just oue or two consecutive eclipses are observed.," Folding the data is not an important issue for the two Chandra observations and the XMM observation, where just one or two consecutive eclipses are observed."594 But it is imporaut for the RNTE observations. because hese are short and sparse. axd also because the RNTE observaIOUS are coniunouslv interrupted by the Eart1r occultatiou a every RXTE orbit (lasting approximately 1.5 h).," But it is important for the RXTE observations, because these are short and sparse, and also because the RXTE observations are continuously interrupted by the Earth occultation at every RXTE orbit (lasting approximately 1.5 h)."595 In his case the olding is required to sample a couplete orbial light curve from the source. because this is inix»rtant for a meanineful fitting of the eclipse.," In this case the folding is required to sample a complete orbital light curve from the source, because this is important for a meaningful fitting of the eclipse."596 For cach «ft these observations we hence folded the data using the local orütal period as derived from the epliemeris publis red1 v., For each of these observations we hence folded the data using the local orbital period as derived from the ephemeris published by \citet{Parmar_00}.597 The 2002-2003 RATE dataset (DT0036 aud P70037) was lois enough aud we decided to divide it iuto tl1e followii femr periods: 1) 2002 June 7-10. ii) 2002 Augus 2-18. i) 202 September 2-30. and iv) 2003 Aueust 31 - September 3.," The 2002-2003 RXTE dataset (P70036 and P70037) was long enough and we decided to divide it into the following four periods: i) 2002 June 7-10, ii) 2002 August 2-18, iii) 2002 September 2-30, and iv) 2003 August 31 - September 3."598 Iu this wav we obtained a total of LO orbital liebt. «uwves m which the eclipses were clearly visible (see Tale L for details on the used observations)., In this way we obtained a total of 10 orbital light curves in which the eclipses were clearly visible (see Table \ref{tabobs} for details on the used observations).599 We then fitted these orbital ight curves to derive eclipse arrival times with the proc(ure described below., We then fitted these orbital light curves to derive eclipse arrival times with the procedure described below.600 Because the eclipses are asvaiunievical and partial. f10 exact eclipse centroid times crucialy depend on the iioccl aopted to describe their sha2ο as well as the variable COntinuuni they are superimposeL on.," Because the eclipses are asymmetrical and partial, the exact eclipse centroid times crucially depend on the model adopted to describe their shape as well as the variable continuum they are superimposed on."601 Tn order to COnservative in our estimates. we he ecided to fit foded light curves using 10 «ifferen models.," In order to be conservative in our estimates, we then decided to fit the folded light curves using 10 different models."602 The firs model is that used bv ? COsisting a Cassia a constant fitted ou a plae interval o 01 around ipse., The first model is that used by \citet{Parmar_00} consisting of a Gaussian and a constant fitted on a phase interval of 0.1 around the eclipse.603 The second aud third aodels consist again Gaussian aud a coust:uit uus a linear term (seco model) aud a near anc quavilratic erm (third moc fited on a plase interva of 13 around the eclipse., The second and third models consist again of a Gaussian and a constant plus a linear term (second model) and a linear and quadratic term (third model) fitted on a phase interval of 0.3 around the eclipse.604 T foruth model is as the hire model plus a cubic ter fited on a plase interva of 1 around the eclipse., The fourth model is as the third model plus a cubic term fitted on a phase interval of 0.4 around the eclipse.605 T th imodel cosists of a απουσία aud a constait plus sinusoid of peio fixed to the orbital period Ἡted on he whole 0-1 oiase interval., The fifth model consists of a Gaussian and a constant plus a sinusoid of period fixed to the orbital period fitted on the whole 0-1 phase interval.606" The uodels frou the sixth one to the teuth ore are as the fitth model.ph s from 2 to 6 sinusoids wihn periods fixe to 1/2 up to 1/6 of he orlvital period. respectively,"," The models from the sixth one to the tenth one are as the fifth model, plus from 2 to 6 sinusoids with periods fixed to 1/2 up to 1/6 of the orbital period, respectively."607 Tje acdition of lüeher ιαχο] COMPOLCeifs Was required to better «escribe he overall orbital ight curve shape. wich «litters from a pure sinusoid.," The addition of higher harmonic components was required to better describe the overall orbital light curve shape, which differs from a pure sinusoid."608 We restricted οιY fitius to the first six harmonics because the additioi of higher harmonic colponcuts was not statisticalv sienificantOo based on an F-test., We restricted our fitting to the first six harmonics because the addition of higher harmonic components was not statistically significant based on an F-test.609 Thus we obtained 10 ecIpsec arrival times (each COLTCSvonding to one of the modes described. above) for each orbita helt curve., Thus we obtained 10 eclipse arrival times (each corresponding to one of the models described above) for each orbital light curve.610 The final eclipse arrival time for each orbita helt curve was chose1i to be the average hese |0 values. aud the associaed uucertaiutv was chos o be iadf o the maxi ra1ος TNsined by these vali (lo error include).," The final eclipse arrival time for each orbital light curve was chosen to be the average of these 10 values, and the associated uncertainty was chosen to be half of the maximum range spanned by these values $1\; \sigma$ error included)."611 The uncertaiity derived ii this way ullv tales into ac‘count sienificaut liserepancics auo he cdiffereu eclipse arrival tiues fouid with a particule nodel to describe the eclipse aud he orbital modulatio, The uncertainty derived in this way fully takes into account significant discrepancies among the different eclipse arrival times found with a particular model to describe the eclipse and the orbital modulation.612 The otained values of the eclipse epochs for cach of the LO orbital light. curves aud the reative uncertainties are reportc «lin Table J, The obtained values of the eclipse epochs for each of the 10 orbital light curves and the relative uncertainties are reported in Table \ref{tabobs}.613 We then computed the ecipse time delis by subtracting from our measures the eclipse arrival tines predicted by a constant orbital iod model adopting the orlvital period. Payy. and t1ο reference time. Tj. even bv ?..," We then computed the eclipse time delays by subtracting from our measures the eclipse arrival times predicted by a constant orbital period model adopting the orbital period, $P_{\rm orb \; 0}$, and the reference time, $T^e_0$, given by \citet{Parmar_00}."614 These time delavs were plotted versus he orbital evele πο NV., These time delays were plotted versus the orbital cycle number $N$.615 The integer IN is the exact nuuer of orbital eveles elapsed. since 75: Le. NV is the closest integer to (TXTIj)P.uo under the asstuuption trat HS(TyΕΕ<<Pano that we have verifiedposteriori.," The integer $N$ is the exact number of orbital cycles elapsed since $T^e_0$ ; i.e., $N$ is the closest integer to $(T^e_N - T^e_0)/ P_{\rm orb \;0}$ under the assumption that $| T^e_N - (T^e_0 + N P_{\rm orb \; 0}) | << P_{\rm orb \; 0}$ that we have verified."616 These results aye shown in Fig., These results are shown in Fig.6171l. togetos with all delavs computed from previously available ecliIBC ties. namely thosegiven by ? aud bv ?.. respectively.,"\ref{fig:timedelays} together with all delays computed from previously available eclipse times, namely thosegiven by \citet{Hellier_90} and by \citet{Parmar_00}, , respectively."618"Metallicities of individual stars in groups 1, 3, 5 (Table 1)) are compared in Fig. 5,,","Metallicities of individual stars in groups 1, 3, 5 (Table \ref{GGCsample}) ) are compared in Fig. \ref{FoHdiffs},"619 which shows the difference between [Fe/H] estimates obtained by KI03 and those derived by other authors., which shows the difference between $\FeoH$ estimates obtained by KI03 and those derived by other authors.620" Whenever available, we used metallicities derived from the Fe II lines, to avoid possible bias due to inadequate treatment of Fe I lines with LTE model atmospheres of late-type giants (cf."," Whenever available, we used metallicities derived from the Fe II lines, to avoid possible bias due to inadequate treatment of Fe I lines with LTE model atmospheres of late-type giants (cf."621 Thevenin Idiart 1999; see also KI03 for a discussion)., Thevenin Idiart 1999; see also KI03 for a discussion).622" There is a clear indication that Fe abundances derived by CG97 are systematically higher than those obtained by KI03, by ~0.16 ddex on average (with an RMS scatter of +0.12 ddex)."," There is a clear indication that Fe abundances derived by CG97 are systematically higher than those obtained by KI03, by $\simeq0.16$ dex on average (with an RMS scatter of $\pm0.12$ dex)."623" Similarly, [Fe/H] values of CG97 are higher than those derived by MPG96 by ~0.11 ddex."," Similarly, $\FeoH$ values of CG97 are higher than those derived by MPG96 by $\simeq0.11$ dex."624" On the other hand, the data from MPG96 and R01 are in good agreement with the [Fe/H] estimates of KI03."," On the other hand, the data from MPG96 and R01 are in good agreement with the $\FeoH$ estimates of KI03."625" Since the abundances in KI03 seem to agree well with the [Fe/H] scales of Zinn&West(1984),, and Rutledgeetal.(1997),, it is most likely that these differences simply reflect a well known discrepancy between the metallicity scales of Zinn&West(1984) and CG97."," Since the abundances in KI03 seem to agree well with the $\FeoH$ scales of \citet{ZW84}, and \citet{R97}, it is most likely that these differences simply reflect a well known discrepancy between the metallicity scales of \citet{ZW84} and CG97."626" We, therefore, derive two average [Fe/H] values for each cluster group: one estimate based on CG97 metallicities, the other on KI03, combined with data from other sources (MPG96, S00, R01)."," We, therefore, derive two average $\FeoH$ values for each cluster group: one estimate based on CG97 metallicities, the other on KI03, combined with data from other sources (MPG96, S00, R01)."627 Only in groups 1 and 2 is there a good agreement between the two scales; differences within the other groups are marginally significant (at the 1—2σ level)., Only in groups 1 and 2 is there a good agreement between the two scales; differences within the other groups are marginally significant (at the $1-2\sigma$ level).628" It should be mentioned though, that in all cases the spread in metallicities within a particular cluster group is small; typically, ~95% of stars are within a +0.2 ddex margin from the mean values given in Table 1.."," It should be mentioned though, that in all cases the spread in metallicities within a particular cluster group is small; typically, $\sim95\%$ of stars are within a $\pm 0.2$ dex margin from the mean values given in Table \ref{GGCsample}."629 Ages of the individual clusters (taken from Salaris Weiss 2002) are provided in Table 1 (age estimate for NGC 7006 is from Santos Piatti 2004)., Ages of the individual clusters (taken from Salaris Weiss 2002) are provided in Table \ref{GGCsample} (age estimate for NGC 7006 is from Santos Piatti 2004).630" The cluster ages of Salaris&Weiss(2002) were derived from the difference in luminosity of the horizontal branch and the main sequence turn-off point in the cluster magnitude diagram, using both CG97 and metallicity scales."," The cluster ages of \citet{SW02} were derived from the difference in luminosity of the horizontal branch and the main sequence turn-off point in the cluster color-magnitude diagram, using both CG97 and metallicity scales."631" The differences between ages corresponding to the two metallicity scales are small: for all clusters in Table 1 they are well within ~0.5 GGyr (Salaris&Weiss2002),, thus averaged values are given in Table 1.."," The differences between ages corresponding to the two metallicity scales are small: for all clusters in Table \ref{GGCsample} they are well within $\sim0.5$ Gyr \citep{SW02}, thus averaged values are given in Table \ref{GGCsample}."632" All clusters in our sample are old, with individual ages between ~10—13 GGyr (Table 1))."," All clusters in our sample are old, with individual ages between $\sim10-13$ Gyr (Table \ref{GGCsample}) )."633" The shift between the RGB isochrones corresponding to these limiting ages is ΔΤος«100 KK at [Fe/H]=—0.7, and decreases with lower [Fe/H] (Yi et al."," The shift between the RGB isochrones corresponding to these limiting ages is $\Delta634T_{\rm eff}<100$ K at $\FeoH=-0.7$, and decreases with lower $\FeoH$ (Yi et al."635 2001)., 2001).636" While the age differences may indeed introduce additional scatter in the T.g-log g plane, no clear indication for such spread is seen in the observed sequences of different cluster groups (Fig. 6,,"," While the age differences may indeed introduce additional scatter in the $T_{\rm eff}$ $\log g$ plane, no clear indication for such spread is seen in the observed sequences of different cluster groups (Fig. \ref{figTGscales},"637" Sect. 4.2)),"," Sect. \ref{TGrelations}) ),"638 most likely because these differences are smeared out by the larger errors in spectroscopically or photometrically derived effective temperatures and/or gravities., most likely because these differences are smeared out by the larger errors in spectroscopically or photometrically derived effective temperatures and/or gravities.639 'The gravities of individual stars in all five cluster groups (Table 1)) are plotted versus the effective temperature in Fig. 6.., The gravities of individual stars in all five cluster groups (Table \ref{GGCsample}) ) are plotted versus the effective temperature in Fig. \ref{figTGscales}.640" Generally, there is good consistency in Tog and logg of individual giants within a particular cluster group (even though these stars belong to different clusters), especially in groups 2, 4, and 5."," Generally, there is good consistency in $T_{\rm eff}$ and $\log g$ of individual giants within a particular cluster group (even though these stars belong to different clusters), especially in groups 2, 4, and 5."641" Several stars at Tog~ 4500KK in M15 (group 5, Fig."," Several stars at $T_{\rm eff} \sim 4500$ K in M15 (group 5, Fig."642" 6aa) are somewhat off the main trend, as their spectroscopic gravities are considerably lower than those of other stars in this effective temperature range; similarly deviating is one star in M92 at Teg~ 4200KK. It should be reminded that spectroscopic logg of these stars are about 0.4 ddex lower than their evolutionary gravities (see Fig. 4))."," \ref{figTGscales}a a) are somewhat off the main trend, as their spectroscopic gravities are considerably lower than those of other stars in this effective temperature range; similarly deviating is one star in M92 at $T_{\rm eff} \sim 4200$ K. It should be reminded that spectroscopic $\log g$ of these stars are about $0.4$ dex lower than their evolutionary gravities (see Fig. \ref{figGGCloggs}) )."643" Note however, that the resulting 7T,g-logg scale for this cluster group remains essentially unaffected if these stars are not employed in its derivation."," Note however, that the resulting $T_{\rm644eff}$ $\log g$ scale for this cluster group remains essentially unaffected if these stars are not employed in its derivation."645" Slightly larger scatter is seen in group 3, though data from different sources seem to agree well with no noticeable differences or trends between them."," Slightly larger scatter is seen in group 3, though data from different sources seem to agree well, with no noticeable differences or trends between them."646" With the exception of the CG97 data for NGC 104, there is also a good consistency in the effective temperatures and gravities of individual stars in group 1."," With the exception of the CG97 data for NGC 104, there is also a good consistency in the effective temperatures and gravities of individual stars in group 1."647 There is a faint hint that the sequence of CG97 stars in M92 is slightly shifted towards lower effective temperatures with respect to the best fitting sequence containing all stars in group 5., There is a faint hint that the sequence of CG97 stars in M92 is slightly shifted towards lower effective temperatures with respect to the best fitting sequence containing all stars in group 5.648" A similar offset is more clearly seen for the CG97 data in NGC 104 (group 1), where effective temperatures of CG97 are lower by about ~150 KK. Fortunately, in both cases these offsets have minor impact on the resulting T.g-logg scales (which are not altered significantly if these stars are excluded), and we therefore retain them in the further analysis."," A similar offset is more clearly seen for the CG97 data in NGC 104 (group 1), where effective temperatures of CG97 are lower by about $\sim 150$ K. Fortunately, in both cases these offsets have minor impact on the resulting $T_{\rm eff}$ $\log g$ scales (which are not altered significantly if these stars are excluded), and we therefore retain them in the further analysis."649 The new empirical T.g—logg relations obtained as best fits to the observed giant sequences in the five cluster groups (Table 1)) are shown in Fig., The new empirical $T_{\rm eff}$ $\log g$ relations obtained as best fits to the observed giant sequences in the five cluster groups (Table \ref{GGCsample}) ) are shown in Fig.650 6 and are provided in numerical form in Tables 2 and 3 (Table 3 lists coefficients of polynomial fits representing the new," \ref{figTGscales}651 and are provided in numerical form in Tables \ref{empGGCscales}652 and \ref{TGscalefits} (Table \ref{TGscalefits} lists coefficients of polynomial fits representing the new"653aud the corresponding plysical fine-structure coustaut becomes From the coordinate transformation Eq.(6)). it is easy to derive the coordinate velocity transformation between two inertial Beltrami [rames.,"and the corresponding physical fine-structure constant becomes From the coordinate transformation \ref{x-trans}) ), it is easy to derive the coordinate velocity transformation between two inertial Beltrami frames."654" For the velocity of light in the or1 direction through the origin of the original Grame. in the transformed one. it reads Examining the QSO frame aid the earth frame. we have a0—al, therefore. ]t means that the speed of light euitted from QSO to tje earth is the saije as that observed today on tlie earth."," For the velocity of light in the $x^1$ direction through the origin of the original frame, in the transformed one, it reads Examining the QSO frame and the earth frame, we have $a^0=a^1$, therefore, It means that the speed of light emitted from QSO to the earth is the same as that observed today on the earth."655 Iu the meanwhile. the QSO observaions show that fine-strLCUre colisant has a nonzero change Nafay=(past—00)/007»—1Q07. which can only. ceye from the variaion of the part ezJg/fi.," In the meanwhile, the QSO observations show that fine-structure constant has a nonzero change $\Delta\alpha/\alpha_0\equiv(\alpha_{\rm656past}-\alpha_0)/\alpha_0\sim-10^{-5}$, which can only come from the variation of the part $e^2/\hbar$."657 The large uunbers hypothesis is raised by Dirac [11].. whicl argued he fact that some large dimensiouless uumbers have the sale order leads oue to believe soiue fundamental constants vary with the epoch.," The large numbers hypothesis is raised by Dirac \cite{dirac}, which argued the fact that some large dimensionless numbers have the same order leads one to believe some fundamental constants vary with the epoch."658 Based οι this hypothesis. we assuue ecDy/f i.s only the [uuction ol time /. so tlie variations of a in the QSO observations are the 'esults cdie to the variations of e?/fi. that is thus Iu the Letter. the quantities with subscript 0 staud for those iueasured ou the earth now.," Based on this hypothesis, we assume $e^2/\hbar$ is only the function of time $t$, so the variations of $\alpha$ in the QSO observations are the results due to the variations of $e^2/\hbar$, that is thus In the Letter, the quantities with subscript $0$ stand for those measured on the earth now."659 Iu the Oklo case. the inertial Beltrami coordinate transformation is between tle present earth aud tle frame whose origin is the spacetime point when aid where the Oklo phenomenon took place. so a10. and Eq. (10))," In the Oklo case, the inertial Beltrami coordinate transformation is between the present earth and the frame whose origin is the spacetime point when and where the Oklo phenomenon took place, so $a^1=0$, and Eq. \ref{u-trans}) )"660 bas the form Since the Oklo phenomenon occurred before about 2xLO? vears. we can cursorilv take," has the form Since the Oklo phenomenon occurred before about $2\times10^9$ years, we can cursorily take"661The brightest Galactic X-ray point sources are X- binaries. in which either a neutron star or a black ⋅ ↓↕∪↓∢⊾⋯∼≼∼↓⋅∢⊾∩⊾⊳∖⊔↓⋜↧⊳∖⊳∖⇂↓⋅∪⊔↓⋜↧≼∼∪⊔↓,"The brightest Galactic X-ray point sources are X-ray binaries, in which either a neutron star or a black hole accretes mass from a companion star."662↓≻⋜⋯↓∪⊔⊳∖⋯↓⋅⊳∖∖↓↕⋖⋅⊔⇂↓∐⊾⊀ ⇁ ⋯⇍≼∼↓⋅∢⊾↿⊲↓∪⊔∐∪∖∖⊽⊲↓⊳∖≼⇍∪⊔↿⊀↓⊔⊔∪⊔⊳∖⋜⋯∠⇂↿⇂⊔⊾⇀∖−↓⋅⋜↧∙∖⇁⇂⊔⊔↓⊲↓⊔∪⊳∖⊲∐∙∖⇁ remains constant within a [actor of a few. a system is classified. as persistent.," When the accretion flow is continuous and the X-ray luminosity remains constant within a factor of a few, a system is classified as persistent."663 “Transient X-ray binaries. on the," Transient X-ray binaries, on the"664power law to which a Gaussian Lue is added.,power law to which a Gaussian line is added.665 We left all the paraicters free. which viclded (7 /721.19 for v=611 degrees of freedom.," We left all the parameters free, which yielded $\chi^2/\nu$ =1.19 for $\nu=611$ degrees of freedom."666 The results of spectral fitting are shown iu Table 1.., The results of spectral fitting are shown in Table \ref{table2}.667 Uncertainties are given at a 90% confidence level., Uncertainties are given at a $90\%$ confidence level.668" There. Nyy is the equivalent cobi density of neutral hydrogen. D the photon index. Er the enerev of the line. a, its width. and Ny and Np t1ο normalization of he Gaussian line aud the power-law colmponcnt. respectively."," There, $N_H$ is the equivalent column density of neutral hydrogen, $\Gamma$ the photon index, $E_L$ the energy of the line, $\sigma_L$ its width, and $N_L$ and $N_{\Gamma}$ the normalization of the Gaussian line and the power-law component, respectively."669 The corresponding 0.210 keV fiux is shown in fje last column., The corresponding $0.2-10$ keV flux is shown in the last column.670 Both the localon axd widh of tus line 6.59 keV and 0.23 keV) are indications that we are dealing with a blending of multiple lives that. uufortunatelv. cannot be reslved.," Both the location and width of this line $6.59$ keV and $0.23$ keV) are indications that we are dealing with a blending of multiple lines that, unfortunately, cannot be resolved."671" The source LRNS JI18013]1-273932 has been observed in the past bv the ROSAT satelite with an exposure time of 255 s. The main observatioial characteristics are thus available in the ROSAT ALSkv Survey CatalogueOo where he source shows an .V-rayv c""OTut nuuber of 6.1Lx1ο7 counts +.", The source 1RXS J180431.1-273932 has been observed in the past by the ROSAT satellite with an exposure time of $255$ s. The main observational characteristics are thus available in the ROSAT All-Sky Survey Catalogue where the source shows an $X$ -ray count number of $6.14\times 10^{-2}$ counts $^{-1}$.672 By using PIMAIS. Ora power-law model with photon iudex P=1 aud coUWun desity Vycm1075 7. one ects a flux of 5.618«1012 eres 278 1 (im the 0.2-10 τον band) corresponding t« Hani unabsorbed of flux6.159«.101?» ere »ον 1+. consiste.it wit 1what waserived by he XNMM observation.," By using PIMMS, for a power-law model with photon index $\Gamma=1$ and column density $N_H \simeq 10^{21}$ $^{-2}$, one gets a flux of $5.618\times 10^{-12}$ erg $^{-2}$ $^{-1}$ (in the 0.2-10 keV band) corresponding to an unabsorbed flux of $6.159\times 10^{-12}$ erg $^{-2}$ $^{-1}$, consistent with what was derived by the XMM observation."673 We analyzed the light curve of IRNS J15ο.το» and searched for a period sigral betweeu 5 sec aid 10 ah. The loug-teri light curve is flat (but see nex secion). aud we found a periodic signal at ss using a Lomb-Scarele periodoeram (Lou1976:Scarele 1982)).," We analyzed the light curve of 1RXS J180431.1-273932 and searched for a period signal between 5 sec and 10 h. The long-term light curve is flat (but see next section), and we found a periodic signal at s using a Lomb-Scargle periodogram \citealt{Lomb1976,Scargle1982}) )."674 By ineaus of Aloute Carlo simulations. we evaluated t1ο confideuce level by assunius a null hythesis o* white iodjse. and the results are plotted in Fie. δν with t1οOS," By means of Monte Carlo simulations, we evaluated the confidence level by assuming a null hypothesis of white noise, and the results are plotted in Fig. \ref{fig:period},"675%.... ad confidence levels.," with the, and confidence levels."676 We fouud that he ss period Is Significant at à confideuce evel 299%., We found that the s period is significant at a confidence level $>99\%$.677 To esnuate the error. we fitted he light curve witLa sine function usi18o he IDL taskcurvefit.. ke«ping the trial periods fixed.," To estimate the error, we fitted the light curve with a sine function using the IDL task, keeping the trial periods fixed."678 The method has been described in more detail i1 Carpanoctal. (2007)., The method has been described in more detail in \cite{Carpano2007}.679. The 36 error «X the 1.158 pulse period iρα 25s. The NMM light curve folde« at shown iu Fig. 3.., The $\sigma$ error of the s pulse period is s. The XMM light curve folded at s is shown in Fig. \ref{fig:fold}.680 To get more information aout TRANS JI80131.1-273932 and to address some hypotheses on its nature. we searched for possible optical couuterp:uts (within a few arcsecouds frou the nominal positio l0 the N-rayv source) m available catalogues.," To get more information about 1RXS J180431.1-273932 and to address some hypotheses on its nature, we searched for possible optical counterparts (within a few arcseconds from the nominal position of the X-ray source) in available catalogues."681 Amoug over 200000 Galactic bulee variable stars contained in the o»iblie domain OGLE catalogue (Wrayetal. 2001)). we ‘Ouid that a source exists within =[8 areseconds of IRNS J180131.1-273932 aud has been identified as a variable red giant aud labeled as OGLE II," Among over 200,000 Galactic bulge variable stars contained in the public domain OGLE catalogue \citealt{wep03}) ), we found that a source exists within $\simeq 4.8$ arcseconds of 1RXS J180431.1-273932 and has been identified as a variable red giant and labeled as OGLE II"682which is valid when Zy « Z..,which is valid when $_{0}$ $\ll$ $_{c}$.683 Note that for computing purposes the right hand side of (4) is one half of the complementary error function ie. f(>/ogZ)=0.5xerfe(UogZ logZ.)) ," Note that for computing purposes the right hand side of (4) is one half of the complementary error function i.e. $f~(> log Z)=0.5\times erfc~\left(\frac{(log Z-log Z_{c})}{\sqrt{2}\sigma}684\right)$ ."685"By replacing M; with M,x EF. equations (1) and (2) can be written as Note (that equations (1) (2) remain the same. ("," By replacing $_{t}$ with $_{t}\times$ f, equations (1) and (2) can be written as Note that equations (1) (3) remain the same. ("686Equation (1) remains the same because the nelallicily of the gas lost by collisions is the same as (hat in the clamps at the time of the collision).,Equation (1) remains the same because the metallicity of the gas lost by collisions is the same as that in the clumps at the time of the collision).687" Because we now have an additional mass loss component. we define a new variable AL,;. Which represents the gas lost when the clumps collide."," Because we now have an additional mass loss component, we define a new variable $_{ml}$, which represents the gas lost when the clumps collide."688 Whereas Εμ is considered here to be lost to the warm hot intergalactic medium. the new Αμ component. having lost enerev in the collision. is assumed to fall to the center of the proto-galaxyv to be recycle.," Whereas $_{WHIM}$ is considered here to be lost to the `warm hot intergalactic medium', the new $_{ml}$ component, having lost energy in the collision, is assumed to fall to the center of the proto-galaxy to be recycled."689 Figurativelv. an individual classical chemical evolution ‘box’ is totally purged by having gas drop oul of the bottom on collision as well as having been blown continuously out of the lop as a result of previous ongoing star lormation!," Figuratively, an individual classical chemical evolution `box' is totally purged by having gas drop out of the bottom on collision as well as having been blown continuously out of the top as a result of previous ongoing star formation!"690 The equations governing (he evolution of these (wo mass loss components are and We limit the imumber of parameters by letting Z. define the effective vield. i.e. Equation (5) represents (he MDE of all stars formed (including those in globular clusters}.," The equations governing the evolution of these two mass loss components are and We limit the number of parameters by letting $_{c}$ define the effective yield, i.e. Equation (5) represents the MDF of all stars formed (including those in globular clusters)."691 We have not attempted to model globular cluster formation., We have not attempted to model globular cluster formation.692 It is assumed (hat the clusters are formed in bursts during collisions between clumps., It is assumed that the clusters are formed in bursts during collisions between clumps.693 We do attempt to make the chemical evolution consistent by ensuring that stars are formed. which. if assembled into a cluster svstem. would have the requisite mass aud (bv design) the appropriate Gaussian abundance distribution.," We do attempt to make the chemical evolution consistent by ensuring that stars are formed which, if assembled into a cluster system, would have the requisite mass and (by design) the appropriate Gaussian abundance distribution."694 To this end we express the amplitude of the cluster MDE as the product of the folal barvonic mass (Mj) (e.g. McLaughlin. 1999)and an efficiency. factor 7 πο that," To this end we express the amplitude of the cluster MDF as the product of the $total$ baryonic mass $_{t}$ ) (e.g. McLaughlin, 1999)and an efficiency factor $\eta$ so that"695allow us to obtain high cadence mouitoring observations i N-rav aud {Yptical/UV wavelengths quickly after initial detection. allowing the study of the earliest stages of BOB outbursts with new clarity.,"allow us to obtain high cadence monitoring observations in X-ray and Optical/UV wavelengths quickly after initial detection, allowing the study of the earliest stages of BHB outbursts with new clarity."696 MAXI 152 was first reported after detection by the DBurst Alert Telescope (BAT: Barthehuyetal.20053) at 08:05 UT. 2010 September 25 (ALTD 5561.337. all times from this poit are quoted using MJD onuat iu UTC).," MAXI $-$ 152 was first reported after detection by the Burst Alert Telescope (BAT; \citealt{Barthelmy05}) ) at 08:05 UT, 2010 September 25 (MJD 55464.337, all times from this point are quoted using MJD format in UTC)."697 Follow up observations performed by the ANaav Telescope (XRT: Burrowsotal. 2005a)) aud UV/Optical Telescope (UVOT: Romiicetal. 20053) 3l imunutes later localized the transicut (Mauganoctal. 2010).. although it was initially uusidentified as a Canuna-Rav Burst aud named CRB 10925A. Based ou its detection by the NNova Alert System (Negoro2009) at MJD 5516L101 (02:530lLT. ~SA hhours before the BAT trigecr). ALANI 152 was determined to be a previously: uukuown Galactic X-ray transicut (Negoroctal.2010).," Follow up observations performed by the X-ray Telescope (XRT; \citealt{Burrows05}) ) and UV/Optical Telescope (UVOT; \citealt{Roming05}) ) 31 minutes later localized the transient \citep{Mangano10}, although it was initially misidentified as a Gamma-Ray Burst and named GRB 100925A. Based on its detection by the Nova Alert System \citep{Negoro09} at MJD 55464.104 (02:30UT, $\sim5.5$ hours before the BAT trigger), MAXI $-$ 152 was determined to be a previously unknown Galactic X-ray transient \citep{Negoro10}."698. IR spectroscopy was obtained which coufirmed that the optical counterpartshowed emission ues consistent with that of an N-rav Binary (deUgartePostigo 2010)., IR spectroscopy was obtained which confirmed that the optical counterpartshowed emission lines consistent with that of an X-ray Binary \citep{deUP10}.699. The transient was also detected in radio (vanHorstetal. 2010).. by citepvovkl0.. citepluulkerslü0a αμα RATE. which detected a 1.6 Iz tvpe-C ΟΡΟ iu the powerspectrum. iudicatiug that ATANI 152 is a BUB (salaiikaretal.," The transient was also detected in radio \citep{vdH10}, by \\citep{vovk10}, , \\citep{Kuulkers10a} and , which detected a 1.6 Hz type-C QPO in the power-spectrum, indicating that MAXI $-$ 152 is a BHB \citep{Kalamkar11}."7002011).. Ikuulkersetal.(2010b) reported evidence for periodicity in the hour rauge from ddata. sugecsting that2.5 this is the shortest period DIID vet known.," \cite{Kuulkers10b} reported evidence for periodicity in the hour range from data, suggesting that this is the shortest period BHB yet known."701 Bellonietal.(2010) reported a refined the perio measurement from ddata of 2.1112 hhowrs., \cite{Belloni10} reported a refined the period measurement from data of $2.4142$ hours.702 The light-curve revealed irregular structure dips lasting ο10 iniu. aux sugeest that dips analogous to those often seen in Low Alass X-ray Binaries (LAINBs) are the source of the —2. hour period. rather than eclipses frou the companion star (I&uulkersetal.2010b).," The light-curve revealed irregular structure dips lasting $5-40$ min, and suggest that dips analogous to those often seen in Low Mass X-ray Binaries (LMXBs) are the source of the $\sim2.4$ hour period, rather than eclipses from the companion star \citep{Kuulkers10b}."703. We report here on broadband. observations of ALANI 152 utilizing/ all three instruments ou dauiug the first ddays of the outbirst after its initia detection., We report here on broadband observations of MAXI $-$ 152 utilizing all three instruments on during the first days of the outburst after its initial detection.704 We preseut spectral aud temporal analysis. iucluding the broadband UV/optical. X-ray aud had X-rav light-curves. analysis of QPOs. time resolved spectra evolution utilizing broadband spectral fits across the NRT aud BAT cucrev ranges. aud search for periodicities in the A-ray data.," We present spectral and temporal analysis, including the broadband UV/optical, X-ray and hard X-ray light-curves, analysis of QPOs, time resolved spectral evolution utilizing broadband spectral fits across the XRT and BAT energy ranges, and search for periodicities in the X-ray data."705 Observations with bheean after the rius lard XN-rav brightuess οἳ ALANI 152 trigecred the BAT. at MJD. 5516L337., Observations with began after the rising hard X-ray brightness of MAXI $-$ 152 triggered the BAT at MJD 55464.337.706 This prompted the standard CRB follow-up mode (e.g. Gehrelsetal. 2001)) 1n which the trausient was observed as an “Automated Tarect™ (AT) every z96 nuuiuute orbit with exposures of kks per orbit., This prompted the standard GRB follow-up mode (e.g. \citealt{Gehrels04}) ) in which the transient was observed as an “Automated Target” (AT) every $\approx96$ minute orbit with exposures of ks per orbit.707 From MJD 54168 onwards the observation cadence was lowered two 2kks observations a day. approximately spaced bv 12hhours," From MJD 55468 onwards the observation cadence was lowered two ks observations a day, approximately spaced by hours."708 Observations of the source continued with this cadence uutil the final observation ended at ΑΠΟ 55191.259. —27 ddavs after the initial BAT detection. after which MAXI J1659 152 became too close to the Sun for tto. observe.," Observations of the source continued with this cadence until the final observation ended at MJD 55491.259, $\sim27$ days after the initial BAT detection, after which MAXI $-$ 152 became too close to the Sun for to observe."709 Between MJD. 55180. and MJD 55182 ALANI 152 was not observable by NRT or |UVOT due to the proximity of the Moon., Between MJD 55480 and MJD 55482 MAXI $-$ 152 was not observable by XRT or UVOT due to the proximity of the Moon.710 XRT observed in Windowed Timing (WT) mode for all observations except for à Ls observation taken ou MJD 55106 in Photon Counting (PC) node. which was performed to obtain an accurate localization.," XRT observed in Windowed Timing (WT) mode for all observations except for a ks observation taken on MJD 55466 in Photon Counting (PC) mode, which was performed to obtain an accurate localization."711 UVOT data were typically collected utilizing all 6 UVOT filters. apart from a period between NJD 55168 aud NOD 55179 when observatious were taken utiliziug a dailv rotation of the 3 UV filters aud 4.," UVOT data were typically collected utilizing all 6 UVOT filters, apart from a period between MJD 55468 and MJD 55479 when observations were taken utilizing a daily rotation of the 3 UV filters and $u$."712 NANI 152 was observed by ffor Lkks on MJD 55508. 107 davs after the initial mouitoring observations euded. with NRT data collected iu PC mode. aud UVOT utilizine all 6 filters.," MAXI $-$ 152 was observed by for ks on MJD 55598, 107 days after the initial monitoring observations ended, with XRT data collected in PC mode, and UVOT utilizing all 6 filters."713 BAT data from the observations durime which wwas pointed at NANI 1995 were processed using the IIEASOFT script to produce cight-channel Που curves which were then converted to spectra covering the euergv range 14b.195 kkeV. BAT lieht-curves were produced automatically by the BAT Transicut Monitor web page (ταιetal.2006)., BAT data from the observations during which was pointed at MAXI $-$ 152 were processed using the HEASOFT script to produce eight-channel light curves which were then converted to spectra covering the energy range $14-195$ keV. BAT light-curves were produced automatically by the BAT Transient Monitor web page \citep{Krimm06}.714. NRT light-curves aud spectra were extracted utilizing the methods deseribed by Evansetal.(2009).. with full corrections for pile-up and hot coluunus applied to the data based ona PSF fitted position of MAXI 152 obtained frou PC mode observations.," XRT light-curves and spectra were extracted utilizing the methods described by \cite{Evans09}, with full corrections for pile-up and hot columns applied to the data based on a PSF fitted position of MAXI $-$ 152 obtained from PC mode observations."715 NRT spectra were extracted over time mtervals strictly simultaneous with the BAT survey spectra. and binned to a minima of 20 counts per cuerey bin.," XRT spectra were extracted over time intervals strictly simultaneous with the BAT survey spectra, and binned to a minimum of 20 counts per energy bin."716 UVOT photometry was derived from) images viauvotmaghist. using an extraction region of radius," UVOT photometry was derived from images via, using an extraction region of radius."717"Magnuitudes are based on the UVOT photometric svsteni (Pooleetal.2008) ind were uncorrectedfor the Galactic extinction in the direction of MANI 152 of Epy,=0.606 (Schlegeletal.1998)..","Magnitudes are based on the UVOT photometric system \citep{poole2008:MNRAS383} and were uncorrectedfor the Galactic extinction in the direction of MAXI $-$ 152 of $E_{(B-V)} =7180.606$ \citep{schlegel1998:ApJ500}."719" Taking this value as an upper limit to the extinction of the counterpart and using the effective wavelengths of the filters (Pooleetal.2005) aud the parameterization of Pei(1992).. the extinctions iu the bbauds are: el.x Lah. ely,<2.36. 4,<2.96. usuX LIO. AyeXLas. «ο<Sl."," Taking this value as an upper limit to the extinction of the counterpart and using the effective wavelengths of the filters \citep{poole2008:MNRAS383} and the parameterization of \cite{Pei92}, the extinctions in the bands are: $A_{v} \leq 1.85$ , $A_{b} \leq 2.36$, $A_{u} \leq7202.96$, $A_{uvw1} \leq 4.10$ , $A_{uvw2} \leq 4.88$, $A_{uvm2} \leq 5.84$."721 Maenitudes of the UVOT photometric system are indicated by lowercase letters of the filter used (c.g. 0). aud catalog magnitudes by upper-case letters of the filter (e.g. V).," Magnitudes of the UVOT photometric system are indicated by lower-case letters of the filter used (e.g. $v$ ), and catalog magnitudes by upper-case letters of the filter (e.g. $V$ )."722 However within UVOT measurement errors. we can assiuine that UVOT a. b and ce magnitudes are equivaleut to C. B aud V.," However within UVOT measurement errors, we can assume that UVOT $u$, $b$ and $v$ magnitudes are equivalent to $U$, $B$ and $V$."723 All quoted uncertainties are given at 90% confidence level for one interesting parameter unless otherwise stated., All quoted uncertainties are given at $90\%$ confidence level for one interesting parameter unless otherwise stated.724" Utilizing a short NRTobservation iun PC inodo taken ou MJD 55598. we derived a position of RÀ. Dec = 1659""01*.71. 15715/28"".5 (T2000. eerror radius)."," Utilizing a short XRTobservation in PC mode taken on MJD 55598, we derived a position of RA, Dec = $16^h59^m01^s.71$ , $-15^\circ15'28''.5$ (J2000, error radius)."725 This position was corrected for svstemiaticerrors dn astrometry utilizing UVOT data taken simultaneously with theNRT data. utilizing the methods described by Coadetal. (2007).," This position was corrected for systematicerrors in astrometry utilizing UVOT data taken simultaneously with theXRT data, utilizing the methods described by \cite{Goad07}."726 This position is nuproved over the previously reported NRT position (I&euneaetal. 2010)... which was based ou PC inodo data," This position is improved over the previously reported XRT position \citep{Kennea10}, , which was based on PC mode data"727"The magnitude of the two mass ratioSIs glveni as while (he CP- violating Majorana phases a and 9 are given by Since.H ins> and Aims,> are known experimentallv. the values of mass ratios (p.c) from Eq. (","The magnitude of the two mass ratios is given as while the CP- violating Majorana phases $\alpha$ and $\beta$ are given by Since, $\Delta m_{12}^{2}$ and $\Delta m_{23}^{2}$ are known experimentally, the values of mass ratios $(\rho,\sigma)$ from Eq. ("72818) and (19) can be used to calculate 2.,18) and (19) can be used to calculate $m_1$.729 This can be done by inverting Eqs. (, This can be done by inverting Eqs. (73014) ancl (15) to obtain (hie two values of nmi. viz.,"14) and (15) to obtain the two values of $m_1$, viz."731 and We vary the oscilation parameters within their known experimental ranges., and We vary the oscillation parameters within their known experimental ranges.732 However. the Dirac type CP- violating phase 9 is varied within its full range and 844 is varied 11 ils 30 range given bv the CIIOOZ |sound.," However, the Dirac type CP- violating phase $\delta$ is varied within its full range and $\theta_{13}$ is varied in its $\sigma$ range given by the CHOOZ bound."733 The two values of mq obtained from the nass ralios p alc Lo. respectively mus{ be equal to within the errors of the oscillation parameters for the simultaneous existence of a texture zero and a vanishing minor.," The two values of $m_1$ obtained from the mass ratios $\rho$ and $\sigma$, respectively must be equal to within the errors of the oscillation parameters for the simultaneous existence of a texture zero and a vanishing minor."734 There are in total thirty six possible slructures of neutrino mass matrix [Table 1.), There are in total thirty six possible structures of neutrino mass matrix [Table 1.]735 with a single texture zero and a vanishing minor., with a single texture zero and a vanishing minor.736 As can be seen from Table 1..," As can be seen from Table 1.,"737". (wenly one structures Corrosponds to two texture zero cases which have. already. been studied extensively,"," twenty one structures corrosponds to two texture zero cases which have, already, been studied extensively."738 We examine the phenomenological viability of all (he remaining texture structures ancl also present «letailed phenomenological implications for the viable structures., We examine the phenomenological viability of all the remaining texture structures and also present detailed phenomenological implications for the viable structures.739current is J4(0)zmJon which matches the constant current. 74i(0)=joy.,"current is $j_\parallel(0)\approx-\beta_{-0}n_-$, which matches the constant current $j_\parallel(0)=j_{0\parallel}$."740 Phe electrons momentum is derived as As for (50)). for electrons to be accelerated: outward one must have dyz-0.," The electron's momentum is derived as As for \ref{eq:E1}) ), for electrons to be accelerated outward one must have $\delta\eta>0$."741 That the same condition (37)20) is required. in. both cases is hardly surprising., That the same condition $\delta\eta>0$ ) is required in both cases is hardly surprising.742 In. (50)). one has d£~educ0 and xO. while in (50))r one has d&~ditz-0 but x«," In \ref{eq:E1}) ), one has $d\xi\sim -\beta_V du<0$ and $\chi>0$, while in \ref{eq:E1}) ) one has $d\xi\sim du>0$ but $\chi<0$."743" OM Ly~O0. the electron's momentum increases with Z quackatically, οτνδη/2."," If $\tilde{E}_0\sim0$, the electron's momentum increases with $\tilde{z}$ quadratically, $u_-\sim \delta\eta\tilde{z}^2/2$."744" In the conventional SCLE models CXrons&Scharle-mann1979:Harding&Muslimov L998)... £24«0 is obtained with dy«0. bv imposing an upper boundary. usually located at the. PEE. where £(=0. and à conducting surface of the side wall of the open field line region: in these models jo, is then determined. locally by these boundary conditions."," In the conventional SCLF models \citep{as79,hm98}, , $E_\parallel<0$ is obtained with $\delta\eta<0$, by imposing an upper boundary, usually located at the PFF, where $E_\parallel=0$, and a conducting surface of the side wall of the open field line region; in these models $j_{0\parallel}$ is then determined locally by these boundary conditions."745 The basic assumption in the SCLE models is the nonconstaney of 07g along How., The basic assumption in the SCLF models is the nonconstancy of $\delta\eta$ along flow.746 This means that if one sets oj=O initially. a nonzero δησὲ0 develops along the How inducing a parallel electric field.," This means that if one sets $\delta\eta=0$ initially, a nonzero $\delta\eta\neq0$ develops along the flow inducing a parallel electric field."747 Pwo cllects that Lead to on«0 have been considered in the literature. including field line curvature. corresponding to the field lines curving toward the rotation axis. and frame dragging. (Muslimov&Tsvgan 1902).," Two effects that lead to $\delta\eta<0$ have been considered in the literature, including field line curvature, corresponding to the field lines curving toward the rotation axis, and frame dragging \citep{mt92}."748". The latter dominates near the star: the elfective angular velocity. so is the €] density. is reduced by aactor (1.Aj(7ry?)« Las compared to that observed in a [at space at infinity. where A,=26(COT)υπο ο«οR=10'm. and 444=£/(1077kem) is the moment of inertia of the star (Alustimoyv&Psvean1992)."," The latter dominates near the star; the effective angular velocity, so is the GJ density, is reduced by a factor $(1-k_g(R/r)^3)<1$ as compared to that observed in a flat space at infinity, where $k_g=2GI/(c^2R^3)\approx0.15I_{38}$, $z<R=10^4\,\rm m$, and $I_{38}=I/(10^{38}\,{\rm kg}\,{\rm m}^2)$ is the moment of inertia of the star \citep{mt92}."749 Η one assumes Oy=QO initially at the surface. one has BhanuefRc0 Dor ges«0.," If one assumes $\delta\eta=0$ initially at the surface, one has $\delta\eta=3k_g\eta_{GJ}z/R<0$ for $\eta_{GJ}<0$."750 Eq (53)) ancl (54)) are similar to the result. derived. by Shibata(1997) based on a generic SCLE model in which no specific local boundary. condition is imposed., Eq \ref{eq:E2}) ) and \ref{eq:u2}) ) are similar to the result derived by \citet{s97} based on a generic SCLF model in which no specific local boundary condition is imposed.751 When jo| is treated as a free parameter. for initially δη= 0. δηo>0 is required to produce £)«0.," When $j_{0\parallel}$ is treated as a free parameter, for initially $\delta\eta=0$ , $\delta\eta>0$ is required to produce $E_\parallel<0$."752 This can occur only on the curvingeawavy (from the rotation axis) field lines along which [Q-B| decreases (Shibata1997:Mestel.1999).," This can occur only on the curving-away (from the rotation axis) field lines along which $|\bOmega\cdot\bB|$ decreases \citep{s97,m99}."753.. A. major problem with this scenario in the context of the state limit is that the growth in [£4 is unstoppable (Shibata1997:Moestel 1999).," A major problem with this scenario in the context of the steady-state limit is that the growth in $|E_\parallel|$ is unstoppable \citep{s97,m99}."754.. Llowever. such run-away growth does nol occur in our oscillatory model becausepair. creation ultimately leacs the system to switch to an oscillatory phase. as discussed in Sec.," However, such run-away growth does not occur in our oscillatory model becausepair creation ultimately leads the system to switch to an oscillatory phase, as discussed in Sec."755 3., 3.756 For 95«0. Eq (54)) implies an oscillatory (in space) solution similar to that. found previously (Alestel&Shibata1994:1997).," For $\delta\eta<0$, Eq \ref{eq:u2}) ) implies an oscillatory (in space) solution similar to that found previously \citep{ms94,s97}."757". When the acceleration. region extends to ROR""PEE ""the ellect of the conducting side wall. at which £=0. becomes important."," When the acceleration region extends to $>R(R/R_{LC})^{1/2}$, the effect of the conducting side wall, at which $E_\parallel=0$, becomes important."758 When such cllect is included: acceleration of outllowing electrons is possible at BGBue)? even when oy«0 (provided that an electric field arising from such elect. dominates over that. from δή« 0) (Shibata 1991)., When such effect is included acceleration of outflowing electrons is possible at $>R(R/R_{LC})^{1/2}$ even when $\delta\eta<0$ (provided that an electric field arising from such effect dominates over that from $\delta\eta<0$ ) \citep{s97}.759. We present an oscillatory polar gap model. in which the system initially undergoes a low-clensity phase. involving rapid acceleration of particles to ultra high energy. initiating a pair cascade.," We present an oscillatory polar gap model, in which the system initially undergoes a low-density phase, involving rapid acceleration of particles to ultra high energy, initiating a pair cascade."760 The system evolves to απ oscillatory phase., The system evolves to an oscillatory phase.761 The oscillations are treated as a superluminal. large amplitude clectrostatic wave that propagates along the magnetic field.," The oscillations are treated as a superluminal, large amplitude electrostatic wave that propagates along the magnetic field."762 The charge continuity equation implies a current-charge invariant (Jj=const) ) that ds independent of pair creation., The charge continuity equation implies a current-charge invariant $j_\parallel-\beta_V\eta={\rm const}$ ) that is independent of pair creation.763 As a result. the phase velocity  is no longer a free parameter and can be written in terms of the initial velocity and density of the plasma.," As a result, the phase velocity $\beta_V$ is no longer a free parameter and can be written in terms of the initial velocity and density of the plasma."764 ]t is shown that only the superluminal case y291 is relevant here., It is shown that only the superluminal case $\beta_V>1$ is relevant here.765 An analytical formalism for LEAWs is derived in the hieh-density regime in which the pair density is uigher than the GJ density., An analytical formalism for LEAWs is derived in the high-density regime in which the pair density is higher than the GJ density.766 We ignore wave damping in our analvtical solution., We ignore wave damping in our analytical solution.767 Neglecting damping is justified. as the vpical damping time due to energy losses through radiation is much longer than the wave period., Neglecting damping is justified as the typical damping time due to energy losses through radiation is much longer than the wave period.768 In most. cases. the damping time is also longer than the light-crossing time over he gap.," In most cases, the damping time is also longer than the light-crossing time over the gap."769 The model predicts an outflow of relativistic pairs due o particles being dragged along in LALA., The model predicts an outflow of relativistic pairs due to particles being dragged along in LAEW.770 Such feature is needed: to avoid. overheating of the polar cap., Such feature is needed to avoid overheating of the polar cap.771 Outflowing ours would contribute to the pulsar wind., Outflowing pairs would contribute to the pulsar wind.772 Pairs oscillate with a net drift velocity directed along the magnetic field. »oducing a current that oscillates about the global constant current jo.," Pairs oscillate with a net drift velocity directed along the magnetic field, producing a current that oscillates about the global constant current $j_0$."773 Phe amplitude. of the oscillating current. is arger than the global current by a large [actor that. ds of order of magnitude the ratio of the pair censity to he C.J density., The amplitude of the oscillating current is larger than the global current by a large factor that is of order of magnitude the ratio of the pair density to the GJ density.774 The wave form of an inductive electric ield is characterized by a triangular shape. which can be unclerstoocl as the current being nearly constant except for a ie period during which it switches sign.," The wave form of an inductive electric field is characterized by a triangular shape, which can be understood as the current being nearly constant except for a brief period during which it switches sign."775 Lhe basic features of the oscillations are not sensitive to the initial conditions including the electron's or positron’s initial velocity., The basic features of the oscillations are not sensitive to the initial conditions including the electron's or positron's initial velocity.776 There are two possiblities for. particle acceleration. in the initial phase that leads to oscillations: (1) a vacuum-like initial electric field. which may. be applicable for the polar cap where charges are tightly. bound to the surface. and (2) SCLE. in which there is an ample supply of charges.," There are two possiblities for particle acceleration in the initial phase that leads to oscillations: (1) a vacuum-like initial electric field, which may be applicable for the polar cap where charges are tightly bound to the surface, and (2) SCLF, in which there is an ample supply of charges."777 Vhe first case was discussed. in Levinsonetal.(2005)., The first case was discussed in \citet{letal05}.778. Lere we consider specifically. the SCLE case where an initial electric. field: appears as a result. of an imbalance oween the charge density ancl the GJ density with the atter mimicking the positive background charges., Here we consider specifically the SCLF case where an initial electric field appears as a result of an imbalance between the charge density and the GJ density with the latter mimicking the positive background charges.779 Electrons are accelerated. monotonically in the electric field. that increases lincarly with the phase xy., Electrons are accelerated monotonically in the electric field that increases linearly with the phase $\chi$.780 Since X comprises both emporal and spatial variables. such particle acceleration arises [rom a mixture of inductive and non-inductive ellects.," Since $\chi$ comprises both temporal and spatial variables, such particle acceleration arises from a mixture of inductive and non-inductive effects."781 An interesting limit is Vsox. in which the electric field comes. purely inductive.," An interesting limit is $V\to \infty$, in which the electric field becomes purely inductive."782 Qualitativelv. the usual steady-state theory can be reproduced in the limit of a zero phase speed.," Qualitatively, the usual steady-state theory can be reproduced in the limit of a zero phase speed."783 Ln this limit. the svstem is time independent ancl the acceleration occurs at a specific spatial location.," In this limit, the system is time independent and the acceleration occurs at a specific spatial location."784 By contrast. acceleration due to an inductive field can occur everywhere in the region concerned.," By contrast, acceleration due to an inductive field can occur everywhere in the region concerned."785 An implication of the oscillatory mocel is the prediction of plasma instability arising from. counterstreaming of electrons and. positrons: in cach oscillation electrons. and positrons are accelerated in opposite direction. and.such counterstreaming provides an ideal condition for two-stream instability which may be directly. relevant for. pulsar. raclioemission (Verdon&Alelrose 2007).., An implication of the oscillatory model is the prediction of plasma instability arising from counterstreaming of electrons and positrons; in each oscillation electrons and positrons are accelerated in opposite direction andsuch counterstreaming provides an ideal condition for two-stream instability which may be directly relevant for pulsar radioemission \citep{vm07}. .786 Although various formis of streaming instability have been discussed in connection with the radio emission in conventional models. the growth rate is generally too low to be ellective. requiring sonie separate assumption to enhance it.," Although various forms of streaming instability have been discussed in connection with the radio emission in conventional models, the growth rate is generally too low to be effective, requiring some separate assumption to enhance it."787 In the oscillatory, In the oscillatory788With these points in mind. we can now explain what controls the distinctions in [lux and power spectrin between the different quadrants.,"With these points in mind, we can now explain what controls the distinctions in flux and power spectrum between the different quadrants."789 For lace-on views. thev all contribute identically to the light curve; as (he viewing angle moves off-axis. special relativisiic beaming and boosting enhances the approaching sides. while general relativistic light. bending and frame-clrageine enhance the back sides.," For face-on views, they all contribute identically to the light curve; as the viewing angle moves off-axis, special relativistic beaming and boosting enhances the approaching sides, while general relativistic light bending and frame-dragging enhance the back sides."790 The result is Chat over most of i». 0 parameter space. quadrant ais (he brightest (both approaching and in back of the black hole). d is the faintest (both receding and in front). and b and © are similar to one another (b is receding but in back: ¢ is approaching but in front).," The result is that over most of $\dot m$ $\vartheta$ parameter space, quadrant a is the brightest (both approaching and in back of the black hole), d is the faintest (both receding and in front), and b and c are similar to one another (b is receding but in back; c is approaching but in front)."791 The maximum flix contrast between the brightest and cimunest quadrants never exceeds a [actor of 5., The maximum flux contrast between the brightest and dimmest quadrants never exceeds a factor of $\sim 5$.792" The slopes of their power spectra Iollow (he same (rend seen in flux: a,>cay on average. wilh no spectral slope falling outside (he range —2.4<ax—1L.8."," The slopes of their power spectra follow the same trend seen in flux: $\alpha_a \gtrsim \alpha_b \simeq \alpha_c > \alpha_d $ on average, with no spectral slope falling outside the range $-2.4 \le \alpha \le -1.8$."793 However. relative to quadrant e. (he quadrant b becomes brighter and its PDS flatter as Vv increases.," However, relative to quadrant c, the quadrant b becomes brighter and its PDS flatter as $\vartheta$ increases."794 In the summed light curve. the contrasting effects largely cancel one another. so that the spectral slope of the composite PDS can be described bv a simple average of the euadrants: individual power-law exponents.," In the summed light curve, the contrasting effects largely cancel one another, so that the spectral slope of the composite PDS can be described by a simple average of the quadrants' individual power-law exponents."795 In our calculation. the «uadrants are precisely coherent at all frequencies when viewed exactly [ace-on.," In our calculation, the quadrants are precisely coherent at all frequencies when viewed exactly face-on."796 As the inclination angle grows. they begin to become incoherent at the hiehest frequencies. bul even lor J=7/2. the range of incoherent Irequencies is still (quite limited.," As the inclination angle grows, they begin to become incoherent at the highest frequencies, but even for $\vartheta = \pi/2$, the range of incoherent frequencies is still quite limited."797 The reason for this behavior is that our svmmetry condition makes their emissivity precisely coherent. so such incoherence as exists is entirely due to (inme-delav. effects: as just discussed. they are small except al the highest frequencies.," The reason for this behavior is that our symmetry condition makes their emissivity precisely coherent, so such incoherence as exists is entirely due to time-delay effects; as just discussed, they are small except at the highest frequencies."798 Thus. if the absolute power spectrum from a single «quadrant (before Doppler adjustments and obscuration effects) is Vv). our total power spectrum is 16.1(7) when viewed on-axis. and when viewed off-axis has essentially identical power at low frequencies. but slightly less at high.," Thus, if the absolute power spectrum from a single quadrant (before Doppler adjustments and obscuration effects) is $A^2(\nu)$, our total power spectrum is $16A^2(\nu)$ when viewed on-axis, and when viewed off-axis has essentially identical power at low frequencies, but slightly less at high."799 By contrast. in a full 2z simulation we expect that the emissiviües of the equadrants would have verv similar power spectra to the emissivilv we calculate. but. be completely incoherent if azimuthal correlations extend only over angles 0.42.," By contrast, in a full $2\pi$ simulation we expect that the emissivities of the quadrants would have very similar power spectra to the emissivity we calculate, but be completely incoherent if azimuthal correlations extend only over angles $\simeq 0.4\pi$."800 The same repertory of relativistic elfects. both special ancl general. will sGll apply. but we expect that they. will similarly cancel in sum.," The same repertory of relativistic effects, both special and general, will still apply, but we expect that they will similarly cancel in sum."801" Thus. a total flux power spectrum c£:17(v) should result. as only the 5, term contributes."," Thus, a total flux power spectrum $\simeq 4A^2(\nu)$ should result, as only the $S_a$ term contributes."802 In other words. if (his reasoning holds. the shape of the power spectrum observed from a full 2a disk would be quite similar to what we compute. but its amplitude would be lower by about a [actor of 4.," In other words, if this reasoning holds, the shape of the power spectrum observed from a full $2\pi$ disk would be quite similar to what we compute, but its amplitude would be lower by about a factor of 4."803" In this paper. we have presented a new. more plivsical method for estimating the temporal variability of radiation rom the oplically thin (""coronal) regions of 3D GRMIID"," In this paper, we have presented a new, more physical method for estimating the temporal variability of radiation from the optically thin (“coronal"") regions of 3D GRMHD"804slowly over the last 25 years. including observational issues such as the frequency coverage of radio telecopes and widespread radio frequency interference (RFI) at the low frequencies (1 GHz) of the redshifted 21 em line.,"slowly over the last 25 years, including observational issues such as the frequency coverage of radio telecopes and widespread radio frequency interference (RFI) at the low frequencies $\lesssim 1$ GHz) of the redshifted 21 cm line."805 However. an additional important reason for the relatively-small present 21 em absorption sample is simply the dearth of known DLAs towards radio-loud QSOs suitable for 21 em absorption follow-up.," However, an additional important reason for the relatively-small present 21 cm absorption sample is simply the dearth of known DLAs towards radio-loud QSOs suitable for 21 cm absorption follow-up."806 We have hence been conducting an optical survey of low-frequency-selected radio-loud quasars. specitically designed to increase the numberof 7; estimates in the redshift range 2«z<4.," We have hence been conducting an optical survey of low-frequency-selected radio-loud quasars, specifically designed to increase the numberof $\ts$ estimates in the redshift range $2<z<4$."807 While the survey is still in progress. we report here its first results. the detection of 21 em absorption from the z~2.289 DLA towards TXS 03112-4330. the first case of a low spin temperature in a high-z DLA.," While the survey is still in progress, we report here its first results, the detection of 21 cm absorption from the $z \sim8082.289$ DLA towards TXS 0311+430, the first case of a low spin temperature in a $z$ DLA."809 Optical observations of ~ 50 QSOs selected from the Texas 365 MHz survey (2). have been conducted at various facilities in order to identify DLAs suitable for 21 em follow-up., Optical observations of $\sim$ 50 QSOs selected from the Texas 365 MHz survey \citep{douglas96} have been conducted at various facilities in order to identify DLAs suitable for 21 cm follow-up.810" As part of this campaign. we observed TXS 03112430 (B=21.5. 2,4,= 2.87) with the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-orth telescope."," As part of this campaign, we observed TXS 0311+430 (B=21.5, $z_{\rm em} = 2.87$ ) with the Gemini Multi-Object Spectrograph (GMOS) on the Gemini-North telescope."811 We obtained seven 2300-second and one |700-second long-slit spectra of TXS 0311430. with a 1.0 aresecond slit and the B600.GG5303 disperser.," We obtained seven 2300-second and one 1700-second long-slit spectra of TXS 0311+430, with a 1.0 arcsecond slit and the G5303 disperser."812" The central wavelength was set to ffor four of the exposures and to ffor the other four. so as to achieve continuous wavelength coverage ""espite the gap between CCD chips in the GMOS detector."," The central wavelength was set to for four of the exposures and to for the other four, so as to achieve continuous wavelength coverage despite the gap between CCD chips in the GMOS detector."813 The CCD was binned 2»2., The CCD was binned $2 \times 2$.814 The final spectrum has a resolution of ((full-width-at-half-maximum) and extends from ~3550 toAA: this range allows the detection of DLAs in the redshift interval 1.02xz2.87. with the upper limit set by the quasar redshift.," The final spectrum has a resolution of (full-width-at-half-maximum) and extends from $\sim 3550$ to; this range allows the detection of DLAs in the redshift interval $1.92 \leq z \leq 2.87$, with the upper limit set by the quasar redshift."815 The GMOS data were reduced using standard IRAF routines including bias subtraction. flatfield correction. extraction. using APALL. wavelength fitting [the root-mean-square (RMS) error on the wavelength fits was x:0.14. ΑΠ. and finally. vacuum. and heliocentrie velocity wavelength corrections: the full procedure for this and the other optical spectra of our survey will be described in York et al. G," The GMOS data were reduced using standard IRAF routines including bias subtraction, flatfield correction, extraction using APALL, wavelength fitting [the root-mean-square (RMS) error on the wavelength fits was $\leq 0.14$ ], and finally, vacuum and heliocentric velocity wavelength corrections; the full procedure for this and the other optical spectra of our survey will be described in York et al. ("816in preparation).,in preparation).817 The final signal-to-noise ratio (S/N) ranged from ~8 per pixel at 3600 tto ~20 per pixel at 6000A.," The final signal-to-noise ratio (S/N) ranged from $\sim8188$ per pixel at 3600 to $\sim 20$ per pixel at 6000."819. ἹThe GMOS observations resulted in the detection of a DLA at z~2.289 (see Section 3.19)., The GMOS observations resulted in the detection of a DLA at $z \sim 2.289$ (see Section \ref{sec:lya_metals}) ).820 An initial search for 21 em absorption at the DLA redshift was carried out with the PFI-450 MHz receiver of the Green Bank Telescope (GBT: program. AGBT-06B-042) on September 12. 2006.," An initial search for 21 cm absorption at the DLA redshift was carried out with the PF1-450 MHz receiver of the Green Bank Telescope (GBT; program AGBT-06B-042) on September 12, 2006."821 We used the GBT Spectral Processor as the backend. with a bandwidth of 1.25 MHz centred at 431.808 MHz. two circular polarizations. 1024 spectral channels and a spectral resolution of ~0.85 km/s (before any smoothing).," We used the GBT Spectral Processor as the backend, with a bandwidth of 1.25 MHz centred at 431.808 MHz, two circular polarizations, 1024 spectral channels and a spectral resolution of $\sim 0.85$ km/s (before any smoothing)."822 The data were taken in total power mode. with On/Off position-switehing (with a [0O-minute On/Off cycle made up of 2-second integrations) and online measurements of the system temperature using a noise diode.," The data were taken in total power mode, with On/Off position-switching (with a 10-minute On/Off cycle made up of 2-second integrations) and online measurements of the system temperature using a noise diode."823 The total on-source time was ~35 minutes.," The total on-source time was $\sim82435$ minutes."825 Weak absorption was detected at the expected redshifted 2|em frequency (~431.5 MHz) in the September run., Weak absorption was detected at the expected redshifted 21cm frequency $\sim 431.8$ MHz) in the September run.826 We hence repeated the observations on October 20. 2006. and January +. 2007. to confirm the feature.," We hence repeated the observations on October 20, 2006, and January 4, 2007, to confirm the feature."827 The same observational setup was used in these observing sessions. except for the use of linear instead of circular polarizations (as laboratory calibration information was not available for the circular polarizations: we will hence not further discuss the September data).," The same observational setup was used in these observing sessions, except for the use of linear instead of circular polarizations (as laboratory calibration information was not available for the circular polarizations; we will hence not further discuss the September data)."828 The total on-source time on TXS 03114430 was ~50 minutes and ~65 minutes in October and January. respectively.," The total on-source time on TXS 0311+430 was $\sim 50$ minutes and $\sim 65$ minutes in October and January, respectively."829 A calibrator. PRS B03164162. was also observed during the October session. with the same setup. to test for RFI at the observing frequency.," A calibrator, PKS B0316+162, was also observed during the October session, with the same setup, to test for RFI at the observing frequency."830 The calibrator was observed for a total of 25 on-source minutes. broken into two runs. alternating with two runs on TXS 0311-430.," The calibrator was observed for a total of 25 on-source minutes, broken into two runs, alternating with two runs on TXS 0311+430."831 The GBT data were analyzed in AIPS4— using the package of single-dish routines., The GBT data were analyzed in AIPS++ using the package of single-dish routines.832 After the initial data-editing. to remove scans with correlator problems and RFI. the data were calibrated (assuming a telescope gain of 2 K/Ty) and averaged together to measure the flux density of TXS 03114430.," After the initial data-editing, to remove scans with correlator problems and RFI, the data were calibrated (assuming a telescope gain of 2 K/Jy) and averaged together to measure the flux density of TXS 0311+430."833 This yielded flux densities of ~(6.240.7) Jy in October and ~(6.7c0.7) Jy in January. where the errors include those from confusing sources in the primary beam (note that ? measured (4.940.10) Ty at 408 MHz).," This yielded flux densities of $\sim834(6.2 \pm 0.7)$ Jy in October and $\sim (6.7 \pm 0.7)$ Jy in January, where the errors include those from confusing sources in the primary beam (note that \citealt{ficarra85} measured $(4.94 \pm 0.10)$ Jy at 408 MHz)."835 A second-order spectral baseline was then fit to RFI- and line-free channels for each 2-second spectrum (during calibration) and subtracted out., A second-order spectral baseline was then fit to RFI- and line-free channels for each 2-second spectrum (during calibration) and subtracted out.836 The residual 2-second spectra were then averaged together and Hanning-smoothed to obtain the final spectrum for each epoch., The residual 2-second spectra were then averaged together and Hanning-smoothed to obtain the final spectrum for each epoch.837 A similar procedure was followed to obtain the final spectrum towards PKS BO316+162. whose flux density was measured to be 9.4=0.7 Jy in the October session.," A similar procedure was followed to obtain the final spectrum towards PKS B0316+162, whose flux density was measured to be $9.4 \pm8380.7$ Jy in the October session."839 Intermittent low-level RFI was seen near the absorption frequencies in all three runs and careful data-editing was hence necessary. especially in the January data.," Intermittent low-level RFI was seen near the absorption frequencies in all three runs and careful data-editing was hence necessary, especially in the January data."840 We also obtained a 602-MHz continuum image of TXS 03114430 with the Giant Metrewave Radio Telescope (GMRT) in March 2007. to determine the spatial structure of the quasar radio emission and derive an estimate of the covering factor.," We also obtained a 602-MHz continuum image of TXS 0311+430 with the Giant Metrewave Radio Telescope (GMRT) in March 2007, to determine the spatial structure of the quasar radio emission and derive an estimate of the covering factor."841 The total on-source time was 1.5 hours. with a 16 MHz bandwidth centred at a frequency of 602 MHz and sub-divided into 128 channels.," The total on-source time was 1.5 hours, with a 16 MHz bandwidth centred at a frequency of 602 MHz and sub-divided into 128 channels."842 The standard calibrator 3C48 was used for flux density and bandpass calibration., The standard calibrator 3C48 was used for flux density and bandpass calibration.843 These data were analysed in classic AIPS. using standard procedures (e.g. 23).," These data were analysed in classic AIPS, using standard procedures (e.g. \citealt{kanekar07}) )."844 Damped Lyman-a absorption is clearly visible in the GMOS spectrum towards TXS 03114430. at 2—2.289+0.002.," Damped $\alpha$ absorption is clearly visible in the GMOS spectrum towards TXS 0311+430, at $z = 2.289 \pm 0.002$."845 The Lyman-a profile. shown in Fig. | [," The $\alpha$ profile, shown in Fig. \ref{fig:dla}[ ["846"fA]. yields an ccolumn density of =(2.04£0.5)-107""=. derived by overlaying dumped protiles using the Starlink software.","A], yields an column density of $= (2.0 \pm 0.5) \times 10^{20}$, derived by overlaying damped profiles using the Starlink software."847" We quote a conservative error of25%.. to encompass the range of reasonable ""by-eye' profiles as well as systematic errors from the continuum fit."," We quote a conservative error of, to encompass the range of reasonable `by-eye' profiles as well as systematic errors from the continuum fit."848 Next. although our spectral coverage was such that only a few metal lines associated with the DLA are outside the Lyman-a forest. we were able to detect the A1526. AISOS and Al A1670 transitions at the DLA redshift: their equivalent widths are listed in Table | and the ALSOS profile shown in Fig. I[[," Next, although our spectral coverage was such that only a few metal lines associated with the DLA are outside the $\alpha$ forest, we were able to detect the $\lambda$ 1526, $\lambda$ 1808 and Al $\lambda$ 1670 transitions at the DLA redshift; their equivalent widths are listed in Table \ref{tab:metals} and the $\lambda$ 1808 profile shown in Fig. \ref{fig:dla}[ ["849B].,B].850 Despite the low resolution of our spectrum (200 ». all three metal lines have resolved structure. indicating a large velocity," Despite the low resolution of our spectrum $\sim 200$ ), all three metal lines have resolved structure, indicating a large velocity"851model.,model.852 The region shaded with eray represents the result due to heating for tear=5«109 vears aud the region shaded with dashed lines represeuts the result due to heating for tyra=5«105 vears., The region shaded with gray represents the result due to heating for $t_{\rss heat}=5\times 10^9$ years and the region shaded with dashed lines represents the result due to heating for $t_{\rss heat}=5\times 10^8$ years.853 The spread reflects the fact that there is a range of (Lj for a given tyra that satisfies the observational eutropy data at O.Lroygy and rsyy-, The spread reflects the fact that there is a range of $\langle L\rangle$ for a given $t_{\rss heat}$ that satisfies the observational entropy data at $0.1r_{\rss 200}$ and $r_{\rss 500}$.854 The relation between the mass of the group or cluster halo aud the total injected enegv (Figure 1) can be translated to the halo-black hole mass relation., The relation between the mass of the group or cluster halo and the total injected enegy (Figure 4) can be translated to the halo-black hole mass relation.855 We follow the aremmenuts in Wvithe Loeb (2003) to derive this relation., We follow the arguments in Wyithe Loeb (2003) to derive this relation.856" Mass of a virialized halo can be expressed in terms of its circular velocity ος (Barkana Loeb 2001) We can combine the above relation with the reeulation condition (Wrvithe Loeb 2003) where Lgaa is the Eddington huuinositv of the central black hole. 4 is its Eddingtou fraction. Fi, is tho fraction of energy generated by the black hole that is deposited iu the eas, ο aud. O,, are the mass density iu barvous aud in mass relative to the critical density. respectively."," Mass of a virialized halo can be expressed in terms of its circular velocity $v_{\rm c}$ (Barkana Loeb 2001) We can combine the above relation with the self-regulation condition (Wyithe Loeb 2003) where $L_{\rm Edd}$ is the Eddington luminosity of the central black hole, $\eta$ is its Eddington fraction, $F_{q}$ is the fraction of energy generated by the black hole that is deposited in the gas, $\Omega_{b}$ and $\Omega_{m}$ are the mass density in baryons and in mass relative to the critical density, respectively."857" We asstuned that the dynamical time of the halo gas is fqq,rip fee. Where mip is the virial radius of the collapsed halo (Barkana Loch 2001)."," We assumed that the dynamical time of the halo gas is $t_{\rm dyn}\sim r_{\rm vir}/v_{c}$ , where $r_{\rm vir}$ is the virial radius of the collapsed halo (Barkana Loeb 2001)."858" Combining equations (25) and (26) we ect where AA,Mito101AZ...", Combining equations (25) and (26) we get where $M_{14} = M_{\rm halo}/10^{14}M_{\odot}$.859 Note that the above relation between the mass of the cluster aud the ceutral black hole is uoulinear., Note that the above relation between the mass of the cluster and the central black hole is nonlinear.860" It is iuterestiug that a simular scaling relation would be expected in the case of the galaxy halo mass Ma, and black hole mass relation.", It is interesting that a similar scaling relation would be expected in the case of the galaxy halo mass $M_{\rm gh}$ and black hole mass relation.861" Iu such a case. the mass of the black hole scales like Af,xef. where |Xom<5."," In such a case, the mass of the black hole scales like $M_{\rm bh}\propto v_{c}^{\alpha}$, where $4\la\alpha\la 5$."862" As oe?xMara, aud royxAlyy. we have MisMj "," As $v_{c}^{2}\propto M_{\rm gh}/r_{\rm gh}$ and $r_{\rm gh}\propto M_{gh}$, we have $M_{\rm bh}\propto M_{\rm gh}^{\alpha/3}$."863Tn fact. based of the M.σ relation aud cosimological simulatious. Ferrarese Ford (2005) derive a relation between the mass of the black hole aud the mass of the galactic halo of the form MxML.," In fact, based of the $M-\sigma$ relation and cosmological simulations, Ferrarese Ford (2005) derive a relation between the mass of the black hole and the mass of the galactic halo of the form $M_{\rm}\propto M_{\rm gh}^{1.65}$."864 The slope of this relation is very sinular to the one cousidered lere., The slope of this relation is very similar to the one considered here.865" Assuming that that a fraction € of black hole mass is converted to cherey. we can also ect the relation between the injected eucerev £4, aud the cluster mass This relation is the same as the one denoted by thick dashed line in Figure Ll."," Assuming that that a fraction $\epsilon$ of black hole mass is converted to energy, we can also get the relation between the injected energy $E_{\rm agn}$ and the cluster mass This relation is the same as the one denoted by thick dashed line in Figure 4."866 We stress that the scaling of black hole mass aud the mass of the cluster derived here is not unique., We stress that the scaling of black hole mass and the mass of the cluster derived here is not unique.867 As Figure I demonstrates. relatious that lave slightly differeut slope are also acceptable.," As Figure 4 demonstrates, relations that have slightly different slope are also acceptable."868 For example a somewhat shallower slope of 1.5 is also consistent with the eutropy constraints., For example a somewhat shallower slope of 1.5 is also consistent with the entropy constraints.869 Nevertheless. we emphasize that successful fit requires the relation to be nonlinear with index steeper than unity.," Nevertheless, we emphasize that successful fit requires the relation to be nonlinear with index steeper than unity."870 Tn this paper. we have oexanüned the cffects of effervescent heating by ACN iu clusters with thermal conduction and cooling in the coutest of the excess cutropy requirements at large radi.," In this paper, we have examined the effects of effervescent heating by AGN in clusters with thermal conduction and cooling in the context of the excess entropy requirements at large radii."871 We have also examined the consequences of this heating. cooling and couduction on SZ temperature decrement.," We have also examined the consequences of this heating, cooling and conduction on SZ temperature decrement."872" As is clear frou Figure (1)). it is possible to heat the ICM, with asingle conutral AGN to match the entropy requirements at Olrs,, and μι "," As is clear from Figure \ref{fig:E_Mcombined}) ), it is possible to heat the ICM with a central AGN to match the entropy requirements at $0.1r_{\rm \scriptscriptstyle 200}$ and $r_{\rm873\scriptscriptstyle 500}$."874However. iun order o match the eutropy at both radii. the total injected enerev £nunt for a eiven value of τμ fu. nust be ightly coustrained.," However, in order to match the entropy at both radii, the total injected energy $E_{\rm\scriptscriptstyle agn}$, for a given value of $t_{\rm \scriptscriptstyle heat}$ $\ll$ $t_{\rm \scriptscriptstyle H}$, must be tightly constrained."875" In fact. our calculations have shown iif for anv value of tio,<ty. ho. for anv heating iue (or ACN lifetime). it is abwavs possible to satisfv 16 eutropy observations at radii with asingle value of the luminosity."," In fact, our calculations have shown that for any value of $t_{\rm\scriptscriptstyle heat} < t_{\rm \scriptscriptstyle H}$, i.e., for any heating time (or AGN lifetime), it is always possible to satisfy the entropy observations at radii with a value of the luminosity."876. This is different from the cooling flow problem. where must be finely tuned. to match 16 cooling rate (Ruszkowski Degelinan. 2002). because 'ooling effects on large scales are rather mild aud. thus. je results depend mostly on the total injected energy Pi=UL)fy Thins.," This is different from the cooling flow problem, where must be finely tuned to match the cooling rate (Ruszkowski Begelman 2002), because cooling effects on large scales are rather mild and, thus, the results depend mostly on the total injected energy $E_{\rm \scriptscriptstyle agn}=\langle877L\rangle\,\times\,t_{\rss heat}$."878 if we canfit the observed eutropy values for just one pair aud trea. We can do so for a wide range of such pairs.," Thus, if we can fit the observed entropy values for just one pair and $t_{\rss heat}$, we can do so for a wide range of such pairs."879 We uote here that the inclusion of thermal conduction nines down the energy which has to be provided bv the ACN over its life-time to satisfy the cutropy observations at both radi for all heating times as compared to our nodel in RRNDOIL, We note here that the inclusion of thermal conduction brings down the energy which has to be provided by the AGN over its life-time to satisfy the entropy observations at both radii for all heating times as compared to our model in RRNB04.880 Iu addition. for shorter heating tines. he Baga Is less or comaparable to the energy piuuped iu or longer heating times.," In addition, for shorter heating times, the $E_{\rss agn}$ is less or comaparable to the energy pumped in for longer heating times."881 This is iu contradiction to our &udiues in RRNBOL., This is in contradiction to our findings in RRNB04.882 This happens here because thermal conduction acts as a heating source after the ACN is switched off (for ty; treat) aud raises the eutropy at aree radii (at r= συ].," This happens here because thermal conduction acts as a heating source after the AGN is switched off (for $t_{\rss H}\,-\,t_{\rss heat}$ ) and raises the entropy at large radii (at $r=r_{\rss 500}$ )."883 The results are mostly scusitive o thefotal energy input from the black hole. rather than to aud tyeat separately.," The results are mostly sensitive to the energy input from the black hole, rather than to and $t_{\rss heat}$ separately."884 As a consequence. satisfactory fits can be obtained as long as the total injected energy falls within a relatively narrow rauge of values. which depends ou the cluster mass (Figure (3)).," As a consequence, satisfactory fits can be obtained as long as the total injected energy falls within a relatively narrow range of values, which depends on the cluster mass (Figure (3))."885" Finally, we note that cooling aud thermal conduction play important roles in controlling the heating mechanisin so that the entropy profiles broadly match the observed eutropyv profiles iu clusters (Pomman 2003)."," Finally, we note that cooling and thermal conduction play important roles in controlling the heating mechanism so that the entropy profiles broadly match the observed entropy profiles in clusters (Ponman 2003)."886" Notably. in the later stages of evolution of the eas, after the heating source is switched off. conduction removes negative entropy. eradieuts in the ceutral regious of the cluster."," Notably, in the later stages of evolution of the gas, after the heating source is switched off, conduction removes negative entropy gradients in the central regions of the cluster."887 Moreover. there is no entropy core seen iu the final stages of the evolution of the ICAL," Moreover, there is no entropy core seen in the final stages of the evolution of the ICM."888 Instead we see positive cutropy eradieuts as observed in the eutropy profiles of ealaxy groups (Mushotzky 2003. Pouman et al.," Instead we see positive entropy gradients as observed in the entropy profiles of galaxy groups (Mushotzky 2003, Ponman et al."889 2003)., 2003).890 Unlike previously proposed models our model predicts that isentropic cores are not au inevitable consequeuce of preheating.," Unlike previously proposed models, our model predicts that isentropic cores are not an inevitable consequence of preheating."891 However. the clusters that show iseutropic core have also been observed. (Pouman et al.," However, the clusters that show isentropic core have also been observed (Ponman et al."892 2003)., 2003).893 We note that our entropy profiles show a core while the source of heatiug is active., We note that our entropy profiles show a core while the source of heating is active.894 It is conceivable that, It is conceivable that895Annihilation radiation at y-ray frequencies offers one of the most exciting. prospects for non-gravitational detection of cold dark matter. and is expected if the dark matter consists of supersymmetric particles (e.g.2222222222222?..,"Annihilation radiation at $\gamma$ -ray frequencies offers one of the most exciting prospects for non-gravitational detection of cold dark matter, and is expected if the dark matter consists of supersymmetric particles \citep[e.g.][]{Berezinsky1994,Berezinsky2003,Bergstrom1998,Stoehr2003,Koushiappas2004,896Colafrancesco2007,Diemand2007,Kuhlen2008,Pieri2008,sp08a,Strigari2008,jeltema10,ackermann10,Zavala2010}."897 Much effort is being devoted to searching for this signal around the Milky Way's dwarf companions. in particular using the Fermi satellite (2)..," Much effort is being devoted to searching for this signal around the Milky Way's dwarf companions, in particular using the Fermi satellite \citep{abdo}."898 Predictions for the properties of the annihilation radiation rely on a detailed understanding of the structure of cold dark matter haloes which can be gained only through high-resolution numerical simulations of halo formation., Predictions for the properties of the annihilation radiation rely on a detailed understanding of the structure of cold dark matter haloes which can be gained only through high-resolution numerical simulations of halo formation.899 The structure of galaxy-mass cold dark matter haloes has been investigated in considerable depth (e.g.2222???) showing that the radial distribution of low-mass subhaloes. and thus of annihilation radiation. is much less centrally concentrated than that of the dark matter as a whole.," The structure of galaxy-mass cold dark matter haloes has been investigated in considerable depth \citep[e.g.][]{Diemand2007,diemand08,Kuhlen2008,sp08a,sp08b,Anderson2010,Kamionkowski2010}900 showing that the radial distribution of low-mass subhaloes, and thus of annihilation radiation, is much less centrally concentrated than that of the dark matter as a whole."901 In the Milky Way. this results in the dominant subhalo contribution to the annihilation radiation coming from large galactrocentric distance and so appearing almost uniform across the sky to an observer on Earth (23...," In the Milky Way, this results in the dominant subhalo contribution to the annihilation radiation coming from large galactrocentric distance and so appearing almost uniform across the sky to an observer on Earth \citep{sp08a}."902 This same effect causes the annihilation radiation from an external galaxy cluster to appear much less centrally concentrated than the distribution of galaxies., This same effect causes the annihilation radiation from an external galaxy cluster to appear much less centrally concentrated than the distribution of galaxies.903 As we show below. this has significant implications for the optimal strategy for detecting the annihilation signal.," As we show below, this has significant implications for the optimal strategy for detecting the annihilation signal."904" In this paper we present some of the largest high-resolution simulations of cluster haloes to date (the Phoenix Project) and use them to investigate the detailed structure of the dark matter distribution in clusters and its halo-to-halo variation,", In this paper we present some of the largest high-resolution simulations of cluster haloes to date (the Phoenix Project) and use them to investigate the detailed structure of the dark matter distribution in clusters and its halo-to-halo variation.905 We use these data. together with data from the Aquarius set of galaxy halo simulations (2).. to predict the expected y-ray annihilation radiation from cluster haloes which we compare to the expected annihilation radiation from giant and satellite galaxy haloes.," We use these data, together with data from the Aquarius set of galaxy halo simulations \citep{sp08b}, to predict the expected $\gamma$ -ray annihilation radiation from cluster haloes which we compare to the expected annihilation radiation from giant and satellite galaxy haloes."906 As we were completing this work. ? and ? posted preprints investigating. amongst other things. the y-ray annihilation radiation expected from galaxy clusters.," As we were completing this work, \cite{Pinzke11} and \cite{sanchez}907 posted preprints investigating, amongst other things, the $\gamma$ -ray annihilation radiation expected from galaxy clusters."908 The luminosity and spatial distribution of this radiation depend sensitively on the properties of surviving dark matter subhaloes down to the limiting mass of the cold dark matter power spectrum. which may be in the range 10.? to 10.AL. (22).," The luminosity and spatial distribution of this radiation depend sensitively on the properties of surviving dark matter subhaloes down to the limiting mass of the cold dark matter power spectrum, which may be in the range $10^{-6}$ to $10^{-12}M_\odot$ \citep{Hofmann2001,Green05}."909 For their analysis. ?. relied on an extrapolation of scalings based on published results for simulations of galactic," For their analysis, \cite{Pinzke11} relied on an extrapolation of scalings based on published results for simulations of galactic"910 , 911Most of the data in Table 1 relate to the light curve maximum.,Most of the data in Table 1 relate to the light curve maximum.912 Both ascending and descending branches of the light curve are not fully covered., Both ascending and descending branches of the light curve are not fully covered.913 The observations during these phases come mostly from the survey by Hartmanetal. (2006)., The observations during these phases come mostly from the survey by \citet{h1}.914. The survey presents observations when the star had a brightness between 22 and 25 mag in the R band., The survey presents observations when the star had a brightness between 22 and 25 mag in the $R$ band.915 The accuracy of these observations (Hartmanetal.2006) varies from 0.04 mag at R = 22 mag to 0.37 mag at R = 25 mag., The accuracy of these observations \citep{h1} varies from 0.04 mag at $R$ = 22 mag to 0.37 mag at $R$ = 25 mag.916 'To search for periodicities we used a method proposed by Lafler&Kinman(1965) which is based on the phase dispersion minimization.," To search for periodicities we used a method proposed by \citet{l1}917 which is based on the phase dispersion minimization."918 In this search we used only the observations inR band because they represent the best sampling among the total data set., In this search we used only the observations in band because they represent the best sampling among the total data set.919 The periodogram was calculated in the period range between 200 and 7000 days (Fig., The periodogram was calculated in the period range between 200 and 7000 days (Fig.920 2)., 2).921" The output parameter there is the inverse dispersion value 1/0 described by Lafler&Kinman (1965),, maxima in the periodogram correspond to dispersion minima."," The output parameter there is the inverse dispersion value $1/\theta$ described by \citet{l1}, maxima in the periodogram correspond to dispersion minima."922 There are essentially no peaks with period values less than 200 days., There are essentially no peaks with period values less than 200 days.923 This range of periods is not shown in the figure., This range of periods is not shown in the figure.924 A period of 665 days shows the highest amplitude., A period of 665 days shows the highest amplitude.925 There are two lower amplitude peaks at 3500 and 406 days (Fig., There are two lower amplitude peaks at 3500 and 406 days (Fig.926 2)., 2).927" However, these periods give much worse light curves."," However, these periods give much worse light curves."928 Longer periods contradict with the fast changes of brightness on ascending and descending branches of the light curve (Hartmanetal.2006)., Longer periods contradict with the fast changes of brightness on ascending and descending branches of the light curve \citep{h1}.929. The phased light curve in the R band is presented in Fig., The phased light curve in the $R$ band is presented in Fig.930 3., 3.931 It was calculated with the following light elements Figure 3 shows that we do not resolve and possibly not even cover the minimum of the light curve., It was calculated with the following light elements Figure 3 shows that we do not resolve and possibly not even cover the minimum of the light curve.932 The star in minimum brightness is not brighter than R = 25.4 mag., The star in minimum brightness is not brighter than $R$ = 25.4 mag.933 The total amplitude of the variability is bigger than 7 mag in the R band., The total amplitude of the variability is bigger than 7 mag in the $R$ band.934 Also the ascending branch is not well covered., Also the ascending branch is not well covered.935" Therefore, the epoch of the maximum can only be constrained to +5 days."," Therefore, the epoch of the maximum can only be constrained to $\pm5$ days."936" However, it is obvious that the light curve of this Mira variable is asymmetric, the ascending branch is steeper than the descending one."," However, it is obvious that the light curve of this Mira variable is asymmetric, the ascending branch is steeper than the descending one."937 We tried to refine the maximum in the light curve using archival observations of the infrared satellite Spitzer (McQuinnetal.2007).., We tried to refine the maximum in the light curve using archival observations of the infrared satellite Spitzer \citep{m2}.938" In five observations on 2004 January 09, July 22, August 16, and 2005 January 21 and August 25, the star varied in the range of 14.24 — 14.97 mag, 14.16 — 14.64 mag, and 13.66 - 14.04 mag in the 3.6, 4.5, and 8 um bands, respectively."," In five observations on 2004 January 09, July 22, August 16, and 2005 January 21 and August 25, the star varied in the range of 14.24 – 14.97 mag, 14.16 – 14.64 mag, and 13.66 - 14.04 mag in the 3.6, 4.5, and 8 $\,\umu$ m bands, respectively."939 A maximum is found during July/August 2004 corresponding to phases in the interval 0.18-0.22 according to Equation 1., A maximum is found during July/August 2004 corresponding to phases in the interval 0.18–0.22 according to Equation 1.940" Therefore the infrared maximum seems not to be in phase with the optical maximum exactly, but it is very close to it (see Fig."," Therefore the infrared maximum seems not to be in phase with the optical maximum exactly, but it is very close to it (see Fig."941 3)., 3).942 The calibrated spectrum of [HBS2006] 40671 in the 4300 - 7880 sspectral region is shown in Fig., The calibrated spectrum of [HBS2006] 40671 in the 4300 - 7880 spectral region is shown in Fig.943 4., 4.944 Molecular TiO bands dominate in the spectrum., Molecular TiO bands dominate in the spectrum.945 We classify the star as an rich (M-type or O Mira) star (Smak1964;Jaschek& 1987).," We classify the star as an oxygen-rich (M-type or O Mira) star \citep{s3,j1}."946. Strong narrow emission lines of hydrogen are present as well; this is typical for Mira stars during maximum light., Strong narrow emission lines of hydrogen are present as well; this is typical for Mira stars during maximum light.947 Using the spectrum we estimate a contribution of the TiO bands into the star brightness in B and V bands., Using the spectrum we estimate a contribution of the TiO bands into the star brightness in $B$ and $V$ bands.948 They are 6(B)= —0.28 mag and 6(V)= —0.16 mag., They are $\delta(B) = -$ 0.28 mag and $\delta(V) = -$ 0.16 mag.949 These values agree with the spectral type M1 — M2 (Smak1964)., These values agree with the spectral type M1 – M2 \citep{s3}.950. We have also determined the spectral type of the star using [TiO]: and [TiO]2 indices introduced by O'Connell(1973) and measured in our calibrated spectrum., We have also determined the spectral type of the star using $_1$ and $_2$ indices introduced by \citet{o1} and measured in our calibrated spectrum.951" The spectral indices were derived from fluxes measured in 30 bbandpasses centered at three wavelengths each for [TiO]: (6125, 6180 and 6370 A)) and for [TiO]2 (7025, 7100 and 7400 A)) as [TiO];=+0.52 and [TiO]2=+0.55, respectively."," The spectral indices were derived from fluxes measured in 30 bandpasses centered at three wavelengths each for $_1$ (6125, 6180 and 6370 ) and for $_2$ (7025, 7100 and 7400 ) as $_1 = +0.52$ and $_2 = +0.55$, respectively."952 These index values correspond to spectral class M3., These index values correspond to spectral class M3.953" Such a spectrum is natural for Mira variables in maximum light, while in the minimum they have usually later spectra."," Such a spectrum is natural for Mira variables in maximum light, while in the minimum they have usually later spectra."954 The Ha emission line of [HBS2006] 40671 is very narrow and not resolved in our spectrum., The $\alpha$ emission line of [HBS2006] 40671 is very narrow and not resolved in our spectrum.955 Its equivalent width is EW = 9A., Its equivalent width is EW = 9.956. For Ha we measure a heliocentric radial velocity of —440+15 km/s. That this high radial velocity is not caused by calibration problems was verified by measuring the radial velocity of the [ΟΠ 46300 sky line which was determined as as expected., For $\alpha$ we measure a heliocentric radial velocity of $-440 \pm15$ km/s. That this high radial velocity is not caused by calibration problems was verified by measuring the radial velocity of the [OI] $\lambda$ 6300 sky line which was determined as as expected.957" Also, at a distance of ~1.'6 from"," Also, at a distance of $\sim 1.\arcmin6$ from"958these terms to deviate from zero.,these terms to deviate from zero.959 Alternatively. also wrong input parameters of the ring (which are Hattening q. position angle E and the coordinates of the centre of the ellipse) will result in specific patterns in these ternis. see e.g. van cer Ixruit Allen (1978).. Schoenmakers et al.," Alternatively, also wrong input parameters of the ring (which are flattening $q$, position angle $\Gamma$ and the coordinates of the centre of the ellipse) will result in specific patterns in these terms, see e.g. van der Kruit Allen \nocite{1978ARA&A..16..103V}, Schoenmakers et al."960 and also Ixrajnovié et al., \nocite{1997MNRAS.292..349S} and also Krajnović et al.961 for details., \nocite{2006MNRAS.366..787K} for details.962" Pherefore. the fattening and position angle of each ring are determined by minimising 5,.55 and es along that ring."," Therefore, the flattening and position angle of each ring are determined by minimising $s_1, s_3$ and $c_3$ along that ring."963 Ehe centre is kept constant and is chosen to coincide with the position of maximal (lux in the galaxy., The centre is kept constant and is chosen to coincide with the position of maximal flux in the galaxy.964 Figure 3. shows the properties of the elliptic rings that were fitted to the aand VLA velocity fields. and Figure 4. shows the resulting harmonic terms.," Figure \ref{fig:kinthree} shows the properties of the elliptic rings that were fitted to the and VLA velocity fields, and Figure \ref{fig:kinhigh} shows the resulting harmonic terms."965 The datapoints of the VLA data are separated by approximately one beanisize., The datapoints of the VLA data are separated by approximately one beamsize.966 Error bars were calculated by constructing LOO Monte Carlo realisations of the velocity fields. where the measurement errors. of the maps were taken into account.," Error bars were calculated by constructing 100 Monte Carlo realisations of the velocity fields, where the measurement errors of the maps were taken into account."967 )oth the position angles and the inclinations of the rings show some variation in the Miele. but are very stable in the VLA field.," Both the position angles and the inclinations of the rings show some variation in the field, but are very stable in the VLA field."968 The dashed line in the top two panels of Figure 3. indicates the mean value of the position angleand inclination of the cata. which are D—4+1 and -60-42.," The dashed line in the top two panels of Figure \ref{fig:kinthree}969 indicates the mean value of the position angleand inclination of the data, which are $\Gamma = 47 \pm 1^\circ$ and $i = 60 \pm9702^\circ$."971llere. E is the »oxition angle of the receding side of the galaxy. measured forth through East.," Here, $\Gamma$ is the position angle of the receding side of the galaxy, measured North through East."972 Phe systemic velocities (lower panel of Figure 3)) have been corrected. for barvecntric motion and are in good agreement., The systemic velocities (lower panel of Figure \ref{fig:kinthree}) ) have been corrected for barycentric motion and are in good agreement.973 For the field we find a svstemic velocity of 1801283.+.. while or the VLA field. we find. 188825.," For the field we find a systemic velocity of $1891 \pm 3$, while for the VLA field we find $1888 \pm 2$."974 Phe dashed ines give both these mean velocities., The dashed lines give both these mean velocities.975 Both the inclination and the systemic velocity that we find are in agreement with xevious studies (Cinzano Van der Alarel1994.. Emisellom: et al. 2003..," Both the inclination and the systemic velocity that we find are in agreement with previous studies (Cinzano Van der Marel\nocite{1994MNRAS.270..325C}, Emsellem et al. \nocite{2003MNRAS.345.1297E},"976 Ixrajnovié et al. 2005))., Krajnović et al. \nocite{2005MNRAS.357.1113K}) ).977 The harmonic terms are shown in Figure 4.., The harmonic terms are shown in Figure \ref{fig:kinhigh}. .978 All terms are normalised with respect to ej., All terms are normalised with respect to $c_1$ .979 From e; we see that the, From $c_1$ we see that the980out of the 1 arcmin extraction radius.,out of the 1 arcmin extraction radius.981 The spectral fitting was performed with NSPEC v10., The spectral fitting was performed with XSPEC v10.982 Phe spectra were rebinned such that cach resultant channel had. at. least 20. counts per bin (source|background). which permitted. us to use V mininizations [or spectral fitting.," The spectra were rebinned such that each resultant channel had at least 20 counts per bin (source+background), which permitted us to use $\chi^2$ minimizations for spectral fitting."983 Due to considerable contamination from the Galactic background as well as some uncertainties in the low energy calibration of ( George 1998) we restricted our spectral analysis to the 0.8-8.0 keV οποιον band., Due to considerable contamination from the Galactic background as well as some uncertainties in the low energy calibration of ( George 1998) we restricted our spectral analysis to the 0.8-8.0 keV energy band.984 Above S keV the signal-to-noise crops rapidly and thus we choose to ignore these data., Above 8 keV the signal-to-noise drops rapidly and thus we choose to ignore these data.985 Since the photons from the individual QSOs are too few to eive reliable spectra. clues for the properties of cach 050 come from their hardness ratios (HIIS).," Since the photons from the individual QSOs are too few to give reliable spectra, clues for the properties of each QSO come from their hardness ratios (HR)."986 Hore we define the hardness ratio as h-s/h|s. where h and s are the total number of countμα in the 2-10. keV. ancl 1-2 keV. bands respectively.," Here we define the hardness ratio as h-s/h+s, where h and s are the total number of counts, in the 2-10 keV and 1-2 keV bands respectively."987 In the case where there was no detection in the 1-2 keV band. we estimate the 30 upper limit following Ixraft et al. (," In the case where there was no detection in the 1-2 keV band, we estimate the $\sigma$ upper limit following Kraft et al. ("9881991).,1991).989 We test for possible svstematic biases that mav arise due to the combined energy. and. raclia dependence of the PSE. by splitting the entire sample into sources lving within the 12-arcmin radius from the center of the CIS and those lving beyond.," We test for possible systematic biases that may arise due to the combined energy and radial dependence of the PSF, by splitting the entire sample into sources lying within the 12-arcmin radius from the center of the GIS and those lying beyond."990 Additionally. we ereatec simulated spectra of sources Iving at various distances from the center and estimated their hardness ratio.," Additionally, we created simulated spectra of sources lying at various distances from the center and estimated their hardness ratio."991 No trend in LR with ofl-axis angle is apparent at any Dux and spectra shape., No trend in HR with off-axis angle is apparent at any flux and spectral shape.992 In fig., In fig.993 1 the hardness ratio of cach object versus the observed Dux in the 2-10 keV band is shown., 1 the hardness ratio of each object versus the observed flux in the 2-10 keV band is shown.994 The hardness ratios for four dillerent power-law models assuming Galactic absorption are shown (left hand scale)., The hardness ratios for four different power-law models assuming Galactic absorption are shown (left hand scale).995 Ehe right hand scale indicates the expected spectrum in the case ofE—1.9 for different absorbing column densities., The right hand scale indicates the expected spectrum in the case of $\Gamma=1.9$ for different absorbing column densities.996 One interesting result is that although our objects are optically classified as QSOs. he data require a mocerate absorption (l1077cmE 7) in order to reproduce the Hat spectra observed.," One interesting result is that although our objects are optically classified as QSOs, the data require a moderate absorption $\sim 10^{22} \rm cm^{-2}$ ) in order to reproduce the flat spectra observed."997 “Phe number of sources with [lat spectra increases towards faint Duxes. (and rence the mean spectrum llattens) suggesting the emergence ofa hard X-ray QSO population.," The number of sources with flat spectra increases towards faint fluxes, (and hence the mean spectrum flattens) suggesting the emergence of a hard X-ray QSO population."998 This is in agreement with orevious results by Ueda (1999) as well as results from. jard. X-ray selected type LAGN with ancl (Della Ceca (1999): Fiore 2001)., This is in agreement with previous results by Ueda (1999) as well as results from hard X-ray selected type I AGN with and (Della Ceca (1999); Fiore 2001).999 In addition our result is in agreement with the iarcdness ratio analysis of ~ LOO hard X-ray selected sources ov Giomuami 2000., In addition our result is in agreement with the hardness ratio analysis of $\sim$ 100 hard X-ray selected sources by Giommi 2000.1000 Aefore interpreting this result. we examined. whether he observed flattening is due to systematic elfects., Before interpreting this result we examined whether the observed flattening is due to systematic effects.1001 As our sources are [aint a possible source of svsteniatic errors is the ickground: subtraction., As our sources are faint a possible source of systematic errors is the background subtraction.1002 Since the spectrum of the X-ray rackerouncd is Hat (D.— 1.4). any over-subtraction of the rackerouncl will produce a Hat spectrum.," Since the spectrum of the X-ray background is flat $\Gamma\sim$ 1.4), any over-subtraction of the background will produce a flat spectrum."1003 This cllect will be apparent at faint sources close to the limit of the survey. since at this faint limit. the sources have Iuxes comparable o that of the background.," This effect will be apparent at faint sources close to the limit of the survey, since at this faint limit, the sources have fluxes comparable to that of the background."1004 At higher Ηχος this ellect will be negligible., At higher fluxes this effect will be negligible.1005 Another source of systematic elfects. suggested by Della Ceca 1999. may be due to spectral bias in the source selection.," Another source of systematic effects, suggested by Della Ceca 1999, may be due to spectral bias in the source selection."1006 They. showed that for sources with same Hux but different spectra. different number of counts will be detected.," They showed that for sources with same flux but different spectra, different number of counts will be detected."1007 As we approach the (tux limit of the survey. sources with a favourable spectrum will be detected. whereas sources with the same Ilux but with an unfavourable spectrum will be missed.," As we approach the flux limit of the survey, sources with a favourable spectrum will be detected, whereas sources with the same flux but with an unfavourable spectrum will be missed."1008 However they showed that in the case of the CUS. this selection. cllect favours the detection. of steep spectrum sources.," However they showed that in the case of the GIS, this selection effect favours the detection of steep spectrum sources."1009 In addition to this. it is clear from lig.," In addition to this, it is clear from Fig."1010 1 that the hardening of the spectra is observed in the xiehter data as well., 1 that the hardening of the spectra is observed in the brighter data as well.1011 Phe last two arguments give support o the reality of the observed. trend., The last two arguments give support to the reality of the observed trend.1012 The Uattenine could be attributed το intrinsic absorption., The flattening could be attributed to intrinsic absorption.1013 Indeed. a relatively small amount of absorption («10cm 7)) could easily vield an effective index of P—1.5.," Indeed, a relatively small amount of absorption $<10^{22}$ ) could easily yield an effective index of $\Gamma\sim 1.5$ ."1014 Some high redshift. QSOs with high column densities jave been found in the HELLAS 5-10 keV. survey (Fiore et al., Some high redshift QSOs with high column densities have been found in the HELLAS 5-10 keV survey (Fiore et al.1015 2000) ancl elsewhere. (Georgantopoulos et al., 2000) and elsewhere (Georgantopoulos et al.1016 1999. Bovle et al.," 1999, Boyle et al."1017 19905. Halpern ct al.," 1998, Halpern et al."1018 1998. Akivama et al.," 1998, Akiyama et al."1019 2000. Reeves & Turner 2000).," 2000, Reeves $\&$ Turner 2000)."1020 Hecently. Norman 2001. detected a further example of a tvpe LL OSO in the Doep Ficld South: CDE-8 202.," Recently, Norman 2001, detected a further example of a type II QSO in the Deep Field South; CDF-S 202."1021 Llowever the surveys have failed to detect a large number of clear-cut examples of this population of object as vet., However the surveys have failed to detect a large number of clear-cut examples of this population of object as yet.1022 As we have redshifts for our sample we can explore further the origin of us spectral Hattening., As we have redshifts for our sample we can explore further the origin of this spectral flattening.1023 For example. Vikhlinin (1995) gsugeested that absorbed QSO spectra may originate due to amped Lye clouds associated. with protogalaxies.," For example, Vikhlinin (1995) suggested that absorbed QSO spectra may originate due to damped $Ly\alpha$ clouds associated with protogalaxies."1024 We plot 10 hardness ratio versus the redshift in Fig., We plot the hardness ratio versus the redshift in Fig.1025 2., 2.1026 There is no clear trend for spectral evolution with redshift., There is no clear trend for spectral evolution with redshift.1027 We then Samined whether the Dlattening of the spectrum is due to μα»ectral evolution with luminosity., We then examined whether the flattening of the spectrum is due to spectral evolution with luminosity.1028 We plot the hardness ratio versus the 2-10 keV luminosity in Fie., We plot the hardness ratio versus the 2-10 keV luminosity in Fig.1029 3., 3.1030 Again no trend for spectral evolution with luminosity is apparent., Again no trend for spectral evolution with luminosity is apparent.1031 Lore we derive the average X-ray spectrum stacking together 16 QSOs photons in cach field., Here we derive the average X-ray spectrum stacking together the QSOs photons in each field.1032 Firstly we fit the data alone in the 0.8-S.0 keV energy band. forcing the two CIS detectors to have the same normalisations and. we tie 10 spectral index for the power-law component to take the same value in all data sets.," Firstly we fit the data alone in the 0.8-8.0 keV energy band, forcing the two GIS detectors to have the same normalisations and we tie the spectral index for the power-law component to take the same value in all data sets."1033 We find that a single power law IL) with P=1.56£0.18 for 47=104.89/99 degrees of reedom (d.o.L), We find that a single power law (PL) with $\Gamma=1.56\pm0.18$ for $\chi^2=104.89/99$ degrees of freedom (d.o.f.)1034 with the hydrogen column density fixed to 1e Galactic value (in the range of 1.710776087.1.9107'cm7 ) is à reasonable fit. in perfect with the hardness ratio analvsis.," with the hydrogen column density fixed to the Galactic value (in the range of $1.7\times10^{20} \rm cm^{-2}-1.9\times10^{20} \rm cm^{-2}$ ) is a reasonable fit, in perfect with the hardness ratio analysis."1035 We then fit the data., We then fit the data.1036 Again. we tie the spectral index for the power-law component to take the same value in all data sets. over the 0.5-2.0 keV range.," Again, we tie the spectral index for the power-law component to take the same value in all data sets, over the 0.5-2.0 keV range."1037 We fit the data with a single power-law component and we obtain a slope of b=2.32+0.2 (\7=170.23/173 d.o.£.)., We fit the data with a single power-law component and we obtain a slope of $\Gamma =2.32 \pm 0.2$ $\chi^2 = 170.23/173$ d.o.f.).1038 Over the full 0.1-2.0 keV range a single power-law gives a poor fit (D=2.44 with v=690/333 clo)., Over the full 0.1-2.0 keV range a single power-law gives a poor fit $\Gamma = 2.44$ with $\chi^2 = 690/333$ d.o.f.).1039 A joint fit over the 0.5-8.0 keV energy, A joint fit over the 0.5-8.0 keV energy1040we can evaluate the integral directly from the observed transit curves: we use the stacked transit curves (Figure I).,we can evaluate the integral directly from the observed transit curves; we use the stacked transit curves (Figure 4).1041" We also calculate that £,,=0:785Dοἱ0.000997. where eds the tangential velocity of the planet in its orbit. P is orbital period. aud. D is the planct’s diaineter."," We also calculate that $t_{\phi} = 0.785 D/vP = 0.000997$, where $v$ is the tangential velocity of the planet in its orbit, $P$ is orbital period, and $D$ is the planet's diameter."1042 The factor of 0.785 allows for the fact that the average chord across a circular plauet is less than the diameter., The factor of $0.785$ allows for the fact that the average chord across a circular planet is less than the diameter.1043 The παΊσα iuteeration of the Figure L1 transits vields ὅξε=0.001037 in flux units where Εν=1., The numerical integration of the Figure 4 transits yields $\delta F_t = 0.001037$ in flux units where $F_{obs} =1$.1044 This value applies to the fiux deficit over a range of longitude defined by the augular extent of the planet at disk ceuter (between the two blue meridians on Figure 8)., This value applies to the flux deficit over a range of longitude defined by the angular extent of the planet at disk center (between the two blue meridians on Figure 8).1045 Over that longitude ranec. the total flux deficit due to star spots is (ou average). about," Over that longitude range, the total flux deficit due to star spots is (on average), about."1046" Because 22,Πz:OATS. the applies to a range of about 0.118 raciaus."," Because $2R_p/R_s \approx 0.118$, the applies to a range of about 0.118 radians."1047 There are 26 such wedges of longitude on the entire Earth-facing hemisphere of the star., There are 26 such wedges of longitude on the entire Earth-facing hemisphere of the star.1048 Neglecting limb effects. the total star spot flux deficit could be as large as," Neglecting limb effects, the total star spot flux deficit could be as large as."1049 Qur second broad step asstuues that the average size aud abundance of star spots is independent of disk position. but that the projected area - heuce the flux deficit - of star spots decreases as cos0. where 0 is the angular longitude distance from disk ceuter.," Our second broad step assumes that the average size and abundance of star spots is independent of disk position, but that the projected area - hence the flux deficit - of star spots decreases as $\cos1050\theta$, where $\theta$ is the angular longitude distance from disk center."1051 Our second step will therefore integrate over longitude (0) to obtain the total flix deficit for the eutire Earth-facing hemisphere of the star., Our second step will therefore integrate over longitude $\theta$ ) to obtain the total flux deficit for the entire Earth-facing hemisphere of the star.1052 Thus: where is the longitude interval covered by the planct caving trausit., Thus: where $\theta_p$ is the longitude interval covered by the planet during transit.1053"0, This integration vields Fy=1.0176£,,5..", This integration yields $F_0 = 1.0176 F_{obs}$.1054 So we calculate that the star spots on ILAT-P-11 cause the observed stellar fiux to be. on average. lower by compared to au uuspotted star of the same radius and spectral type.," So we calculate that the star spots on HAT-P-11 cause the observed stellar flux to be, on average, lower by compared to an unspotted star of the same radius and spectral type."1055 The peak-to-peak variations seen in the stellar rotational light curve are about in the WNepler data., The peak-to-peak variations seen in the stellar rotational light curve are about in the Kepler data.1056 This is somewhat smaller than because the broad distribution of the spots in longitude reduces thei signature in the rotational light curve., This is somewhat smaller than because the broad distribution of the spots in longitude reduces their signature in the rotational light curve.1057 We note that BLO found a significantly smaller peal-to-peak rotational lieblit curve amplitude J). but their photometry was obtained 1- to 2-vears carlicr than our Ixepler data.," We note that B10 found a significantly smaller peak-to-peak rotational light curve amplitude ), but their photometry was obtained 1- to 2-years earlier than our Kepler data."1058 The ucthodology described above makes approximations that depend on the fortuitous geomoetrv wherein HAT-P-11b crosses nearly perpendicular to he stellar equator., The methodology described above makes approximations that depend on the fortuitous geometry wherein HAT-P-11b crosses nearly perpendicular to the stellar equator.1059 Moreover. we also retained the approximation of uecelecting stellar lib darkenius.," Moreover, we also retained the approximation of neglecting stellar limb darkening."1060 We lieve that a inore general formialisii could be developed oue the same line of reasoniusg. that could be applied to ess stronely inclined planets; aud. could iuclude realistic LBub darkening.," We believe that a more general formalism could be developed along the same line of reasoning, that could be applied to less strongly inclined planets, and could include realistic limb darkening."1061 That gencralization is bevond the scope 6 this paper. aud we will utilize our current estimate of he total spot flux deficit of ILAT-P-11 when interpreting our results in the next Section.," That generalization is beyond the scope of this paper, and we will utilize our current estimate of the total spot flux deficit of HAT-P-11 when interpreting our results in the next Section."1062 Ow MCAIC fits produce excellent aerecuent with the Isepler data (Figure 6)., Our MCMC fits produce excellent agreement with the Kepler data (Figure 6).1063 The retrieved paramcters agree closely whether we solve for limb darkening. or fix the cocfücients at their Nawucz model atmosphere values.," The retrieved parameters agree closely whether we solve for limb darkening, or fix the coefficients at their Kurucz model atmosphere values."1064 Moreover. the retrieved linear cocficicnt iu the former case (α=0.6260011. Table 1) is in excellent agreement with the model atinosphere value (0.6179).," Moreover, the retrieved linear coefficient in the former case $u = 0.626 \pm0.014$, Table 1) is in excellent agreement with the model atmosphere value $0.6179$ )."1065 We conclude that the ILAT-P-11 system paraincters derived from the Isepler AICAIC fits are robust. aud not modelcepeudeut via limb darkening.," We conclude that the HAT-P-11 system parameters derived from the Kepler MCMC fits are robust, and not model-dependent via limb darkening."1066 INuutsonetal.(2007) reached a simulay conclusion in their analysis of IST observations of 22097.)Lah.," \citet{knutson}1067 reached a similar conclusion in their analysis of HST observations of 209458b."1068 The \? value for the best fit solution shown on Fieure 6 is (17 for the in-transit poiuts. for 112 deerces of freedom.," The $\chi^2$ value for the best fit solution shown on Figure 6 is 417 for the in-transit points, for 112 degrees of freedom."1069 Thus. the eror bars based purely on I&epler photometric precision nist be increased by a factor of 2 to account for the imperfect precision of star spot removal.," Thus, the error bars based purely on Kepler photometric precision must be increased by a factor of 2 to account for the imperfect precision of star spot removal."1070 That factor was applied in the ΑΙΟΝΤΟ fits. as noted iu Sec.," That factor was applied in the MCMC fits, as noted in Sec."1071 5.2., 5.2.1072 Both the J-baud aud B-baud transits imply linear lind darkening coefücieuts (4 iu Table 1) that are in reasonable agreement with model atinosphere values. but they do liut that liamh darkeuiug for the real star could vary more strongly with waveleneth than the model atmosphere predicts.," Both the J-band and B-band transits imply linear limb darkening coefficients $u$ in Table 1) that are in reasonable agreement with model atmosphere values, but they do hint that limb darkening for the real star could vary more strongly with wavelength than the model atmosphere predicts."1073 The AICAIC posterior distribution for 4 in the D-baud (uot illustrated) peaks at unitv. aud values excecding unity are unplysical.," The MCMC posterior distribution for $u$ in the B-band (not illustrated) peaks at unity, and values exceeding unity are unphysical."1074 The I-sided Cassia distribution has σ=0.080. so our result (Table 1. uv= 0.080) falls the model atmosphere value (0.562) bv Lasso.," The 1-sided Gaussian distribution has $\sigma =10750.080$, so our result (Table 1, $u=1.000 \pm0.080$ ) falls the model atmosphere value $0.862$ ) by $1.8\sigma$."1076" The J-baud result (a=0.086+0.065) sinularly falls below the model atinosphere value (0.2L1) by ο,1σ.", The J-band result $u=0.086\pm0.065$ ) similarly falls the model atmosphere value $0.244$ ) by $2.4\sigma$.1077 If ciscrepanucies in model atiuosphliere predictious for uv do vary with wavelength iu this fashion (stronger at short-A. weaker at long-A). we would not necessarily expect a significant effect in the EKepler band. because it lies intermediate in waveleneth between our B- aud J-band data.," If discrepancies in model atmosphere predictions for $u$ do vary with wavelength in this fashion (stronger at $\lambda$, weaker at $\lambda$ ), we would not necessarily expect a significant effect in the Kepler band, because it lies intermediate in wavelength between our B- and J-band data."1078 Moreover. any such systematic variation should be coufiriued using transits of larser plaucts. exlibiting deeper transits. where ereater precidon iu derived lub darkening can be achieved.," Moreover, any such systematic variation should be confirmed using transits of larger planets, exhibiting deeper transits, where greater precision in derived limb darkening can be achieved."1079 We note that here is observational precedent for limb darkening at short wavelengths to be stronger than model atinosphliere xedietious (Tingleyctal.9006)., We note that there is observational precedent for limb darkening at short wavelengths to be stronger than model atmosphere predictions \citep{tingley}.1080.. We plan additional simultaneous D- aud J-baud observations. of eiaut. planet rausits.," We plan additional simultaneous B- and J-band observations, of giant planet transits."1081 Our results for the J-band transit are inconsistent with he I&epler results as regards the planetary radius., Our results for the J-band transit are inconsistent with the Kepler results as regards the planetary radius.1082" Iu. J-ud. we find that R,/Re is lwger than the Kepler solution. (0.0627. 0.0589). aud the differeuce is more hau 5 times the precision of the J-band measureineut."," In J-band, we find that $R_p/R_s$ is larger than the Kepler solution $0.0627$ $0.0589$ ), and the difference is more than 5 times the precision of the J-band measurement."1083 We regard the IKepler result as definitive. so we consider tow this discrepancy can be explained.," We regard the Kepler result as definitive, so we consider how this discrepancy can be explained."1084 Oue potential explanation of a discrepant radius iu J-van is that it reflects a true variation of the planctary radius with wavelength. due to atmospheric opacity.," One potential explanation of a discrepant radius in J-band is that it reflects a true variation of the planetary radius with wavelength, due to atmospheric opacity."1085 However. the difference here secs inplausibly large. aud we prefer a more mundane explanation.," However, the difference here seems implausibly large, and we prefer a more mundane explanation."1086 The trausit of ILAT-P-11b is relatively long in duration (2.3 hours). aud shallow (0.00[).," The transit of HAT-P-11b is relatively long in duration (2.3 hours), and shallow (0.004)."1087 Cirouud-based infrared photometry can be subject to baseline fluctuations caused by tellure water vapor absorption at the edges of the JITIS baudpasses., Ground-based infrared photometry can be subject to baseline fluctuations caused by telluric water vapor absorption at the edges of the JHK bandpasses.1088 The longer the duration of a transit event. the more seusitive it is to baseline effects; because the adopted baseline has to spur a longer interval.," The longer the duration of a transit event, the more sensitive it is to baseline effects, because the adopted baseline has to span a longer interval."1089 Also. a given baseline error will have a ereater relative effect for shallow transits.," Also, a given baseline error will have a greater relative effect for shallow transits."1090" Teuce. ILAT- is particularly prone to baseline errors. aud we reearcd the F,/Pt valuefrou our J-band MC'MC fits as unreliable at the level of accuracy needed for meaningful comparison"," Hence, HAT-P-11 is particularly prone to baseline errors, and we regard the $R_p/R_s$ valuefrom our J-band MCMC fits as unreliable at the level of accuracy needed for meaningful comparison"1091that since particles only move a clistance ~τίς{1}x1/2 downstream before losing an appreciable fraction of their energy. the effects induced by spherical svimmetry are expected io become more important at low energies.,"that since particles only move a distance $\sim u_{2}\tau_{loss,2}(E)\propto 1/E$ downstream before losing an appreciable fraction of their energy, the effects induced by spherical symmetry are expected to become more important at low energies."1092 It is likely however (hat (he assumption of stationaritv breaks down before the spherical geometry leads to important. effects. but this should be checked case by case.," It is likely however that the assumption of stationarity breaks down before the spherical geometry leads to important effects, but this should be checked case by case."1093 We proposed a semi-analytical calculation of the process of diffusive acceleration of electrons al a non-relativistic shock in the presence of svnchrotron (or inverse Compton scattering) losses., We proposed a semi-analytical calculation of the process of diffusive acceleration of electrons at a non-relativistic shock in the presence of synchrotron (or inverse Compton scattering) losses.1094 The calculation returns the spectrum of electrons at the shock and at any location upstream and downstream for an arbitrary choice of the momentum dependence of the diffusion coelficient., The calculation returns the spectrum of electrons at the shock and at any location upstream and downstream for an arbitrary choice of the momentum dependence of the diffusion coefficient.1095 The results of the calculations for the spectrum at the shock have been illustrated lor tlhiree cases: 1) diffusion constant in momentum (D(p)=Dy). 2) Dolun ditfusion (D(p)x p). and 3) IXolmogorov diffusion (D(p)xp! ).," The results of the calculations for the spectrum at the shock have been illustrated for three cases: 1) diffusion constant in momentum $D(p)=D_{0}$ ), 2) Bohm diffusion $D(p)\propto p$ ), and 3) Kolmogorov diffusion $D(p)\propto p^{1/3}$ )."1096a For the space dependence of the spectrum and the integrated electron spectra we restricted for simplicity to cases 1) and 2)., For the space dependence of the spectrum and the integrated electron spectra we restricted for simplicity to cases 1) and 2).1097 While confirming the results of previous caleulations for the simple case of a constant diffusion coelficient. our results can be easily obtained for any choice of the diffusion coefficient.," While confirming the results of previous calculations for the simple case of a constant diffusion coefficient, our results can be easily obtained for any choice of the diffusion coefficient."1098 Most results illustrated here are referred to (he case of Dohm diffusion and to dilferent compression [actors at the shock., Most results illustrated here are referred to the case of Bohm diffusion and to different compression factors at the shock.1099 While the slope at low momenta is the standard test particle slope. depending only upon the compression factor. the shape of the cutoff. which is determined by (he onset of svinchrotron losses. depends on the adopted diffusion coefficient.," While the slope at low momenta is the standard test particle slope, depending only upon the compression factor, the shape of the cutoff, which is determined by the onset of synchrotron losses, depends on the adopted diffusion coefficient."1100" It is exponential (x exp[-p/pu]) for D(p)=Dy and approaches a xexp[-(p/paY] lor Bohm diffusion. where py is related (o p,,,, through Eq. 25.."," It is exponential $\propto \exp\left[ -p/p_{0}\right]$ ) for $D(p)=D_{0}$ and approaches a $\propto \exp\left[ -(p/p_{0})^{2}\right]$ for Bohm diffusion, where $p_{0}$ is related to $p_{max}$ through Eq. \ref{eq:p0pmax}."1101 The importance of these calculations for the description of (he phenomenology of supernova remnants. and possibly other classes of sources. is evident: for supernova remnants the svuchrotron X-ray. enussion is now resolved both spectrally and spatially aud its careful description could allow to access precious information on the acceleration process.," The importance of these calculations for the description of the phenomenology of supernova remnants, and possibly other classes of sources, is evident: for supernova remnants the synchrotron X-ray emission is now resolved both spectrally and spatially and its careful description could allow to access precious information on the acceleration process."1102 For instance. if the magnetic field is indeed. aniplilied by. accelerated particles (mainly. protons) al the shock. the masini energy of the electron component is determined by svnchrotron losses. while if no amplification occurs. the maximum energy could be determined by the linite age (or spatial size) of the accelerator. as it is for protons.," For instance, if the magnetic field is indeed amplified by accelerated particles (mainly protons) at the shock, the maximum energy of the electron component is determined by synchrotron losses, while if no amplification occurs, the maximum energy could be determined by the finite age (or spatial size) of the accelerator, as it is for protons."1103 The (wo cases result in, The two cases result in1104The complex magneticOo ποια structure and dynanues ↕∐↴∖↴∏∐↴∖↴↻∪↑↻↸∖∐∏∐∐⋝↥⋅⋜∥∖∙↕∐↕≯⋯⊳↑↑∐∖↖↽↸∖↥⋅⋅↖↽↸∖⊼↕↴∖↴↑↸∖∐↸⊳↸∖∪↕⋟ ↻↸∖∐∏∐∐⋝↥⋅⋜∥∖∙↻↥⋅↸∖↴∖↴↸∖∐↑↴∖↴↸∖↖↽↸∖↥⋅⋜↕↕∪∏↑↴∖↴↑⋜⋯≼∐∐∶,"The complex magnetic field structure and dynamics in sunspot penumbrae, in fact the very existence of penumbrae, present several outstanding puzzles in solar physics."1105↴⋁↻∏∐↕↸∖↴∖↴↕∐↴∖↴∪↕⋜∐⋅ ↻∐⋅↖↽↴∖↴↕↸⊳↴∖↴∙↽∕∏∐↴∖↴∱∎∐∐∖↴∖↴↑↥⋅⋯⊳⊓∐⋅↸∖⋜⋯≼⊔↑↴∖↴≼⋅↖⇁∐⋜⋯∐↸⊳↴∖↴⋜∐⋅↸∖↸∖↖↽↕≼∐∖∐∏⋅↖↽ a consequence of unobservable sub.surface processes that we do not understand theoretically., This fine structure and its dynamics are evidently a consequence of unobservable sub–surface processes that we do not understand theoretically.1106 One of the foremost. theoretical problems associated with sunspot peummbrac (and also unbrae) is the heating problem The bolometie brightuess of the penumbra is sole of the normal solar surface on average: even in the unbra it is still about20%., One of the foremost theoretical problems associated with sunspot penumbrae (and also umbrae) is the heating problem: The bolometric brightness of the penumbra is some of the normal solar surface on average; even in the umbra it is still about.1107. Carrving these heat fluxes requires large vertical velocities. of the order 12 laus. which must also be of the right correlation (upward hot. downward cool).," Carrying these heat fluxes requires large vertical velocities, of the order 1–2 km/s, which must also be of the right correlation (upward hot, downward cool)."1108 The observations do not fit this requirement., The observations do not fit this requirement.1109 The problem is most serious in the mubra. where vertical velocityintensity correlations are quite low compared to what is needed to carry the observed heat Hux (Beckers. 1977).," The problem is most serious in the umbra, where vertical velocity–intensity correlations are quite low compared to what is needed to carry the observed heat flux (Beckers, 1977)."1110 The velocities seen iu the peuuubra are larger. but mostly |iorizoutal {Beckers and Schrotter 1969. Tritschler et al.," The velocities seen in the penumbra are larger, but mostly horizontal (Beckers and Schrötter 1969, Tritschler et al."1111 2t601. Laughans et al.," 2004, Langhans et al."1112 2005a). with ittle upward inotiou iu the bright components of the fine structure.," 2005a), with little upward motion in the bright components of the fine structure."1113 There is lus a lie:ue flux problem in the »onunbra as well as iu the uiubra., There is thus a heat flux problem in the penumbra as well as in the umbra.1114 One obvious solution o the heat flux problem would be oasstune that the peuubra ds a very shallow structure. such that the observed reat flux can be carried mostly Nw oradiatiou from the convection zone below.," One obvious solution to the heat flux problem would be to assume that the penumbra is a very shallow structure, such that the observed heat flux can be carried mostly by radiation from the convection zone below."1115 Iowever. lis would imply that tιο field iu he peuunmbra is nearly rorizoutal. which is no consisteu with the observatiou hat most of the magretic flux of a sunspot actually crosses the solar surface| through he peuunibra. not the iubra.," However, this would imply that the field in the penumbra is nearly horizontal, which is not consistent with the observation that most of the magnetic flux of a sunspot actually crosses the solar surface through the penumbra, not the umbra."1116 The region below the peuunbra must be stronelv uaenetic. ax in the quaifitative ctuck peuunibra models of Jahu and Schinidt (1991).," The region below the penumbra must be strongly magnetic, as in the quantitative `thick penumbra' models of Jahn and Schmidt (1994)."1117 This rules out the shallow enunmbra model of Scluuidt et a. (, This rules out the shallow penumbra model of Schmidt et al. (11181986).,1986).1119 recent model of Thomas et al. (, recent model of Thomas et al. (11202002). which interprets the structure of the peuunibra as due to ‘turbulent puuipius.,"2002), which interprets the structure of the penumbra as due to `turbulent pumping'."1121 Tn the case of the wmbra. however. the heat flow problem has a well known solution: the spots apparently (at the surface) spaceΠιο magnetic field actually contains a deuse forest of ficldfree gaps below the surface (Parker 1979a).," In the case of the umbra, however, the heat flow problem has a well known solution: the spot's apparently (at the surface) space–filling magnetic field actually contains a dense forest of field–free gaps below the surface (Parker 1979a)."1122 The heat fux of the uubra is channeled through these gaps by fieldfree convection., The heat flux of the umbra is channeled through these gaps by field–free convection.1123 The contribution of the present paper is to take the logical step of asstuine that the pemuubra is equally eappy low its observed surface., The contribution of the present paper is to take the logical step of assuming that the penumbra is equally gappy below its observed surface.1124 We show how. besides solving he heat flow problem. this explains a number of other o»zzlue observations brought iuto sharp focus by the recent highresolution observations with the Swedish 1-u Solar Telescope (Scharmer ct al.," We show how, besides solving the heat flow problem, this explains a number of other puzzling observations brought into sharp focus by the recent high–resolution observations with the Swedish 1-m Solar Telescope (Scharmer et al."1125 2002. Langhaus ct al.," 2002, Langhans et al."1126 2005a)., 2005a).1127 A major conceptual advantage of the model is that it provides a imuch mere well defined framework for interpreting the observatious than modols referring more eenerically to some kind of maeuctoconvection., A major conceptual advantage of the model is that it provides a much more well defined framework for interpreting the observations than models referring more generically to some kind of magnetoconvection.1128 Before we discuss the model. we briefle review some of the older and more receut observational evidence aud the proposed interpretation (sects 2.. 3)).," Before we discuss the model, we briefly review some of the older and more recent observational evidence and the proposed interpretation (sects \ref{interp}, \ref{recinterp}) )."1129 Tn section 7 we present a simple potential (currentfree) feld model for the pemmmbra. which takes iuto account feldfree iutrusions just below the visible surface.," In section \ref{model} we present a simple potential (current--free) field model for the penumbra, which takes into account field–free intrusions just below the visible surface."1130 We show that this leads to a magnetic field with strong fluctuations iu inclination. azimuth angle aud streneth above the surface without the need to invoke currents in the observed lavers.," We show that this leads to a magnetic field with strong fluctuations in inclination, azimuth angle and strength above the surface without the need to invoke currents in the observed layers."1131 This maguetieo Ποια structure is such that it allows locally horizoutal or nearly horizontal magnetic fields. thereby providing a natural cuviromment for Evershed flows (for which we do uot claim to have," This magnetic field structure is such that it allows locally horizontal or nearly horizontal magnetic fields, thereby providing a natural environment for Evershed flows (for which we do not claim to have"1132and the data analysis technique 0]... with a reduction of the scatter after account for the ellect of cooling Hows in central cluster regions. 1]...,"and the data analysis technique \cite{WJF}, with a reduction of the scatter after account for the effect of cooling flows in central cluster regions \cite{AE99}."1133 At lower temperatures. evidence has been found for a steepening of the Liaw Zx relation below 1 keV 0]...," At lower temperatures, evidence has been found for a steepening of the $L_{bol}$ $T_X$ relation below 1 keV \cite{Pon96}."1134 As for the evolution of the Lou; £x relation. existent data out to z20.4. and. possibly. out tos~0.8 4]. are consistent with no evolution (i.e... 24%0).," As for the evolution of the $L_{bol}$ $T_X$ relation, existent data out to $z\simeq 0.4$ \cite{MS97} and, possibly, out to $z\sim 0.8$ \cite{RdC99} are consistent with no evolution (i.e., $A\simeq 0$ )."1135 Instead of assuming a unique massIuminosity conversion. in the following we will show how final constraints on cosmological parameters changes as the Lug x and AL x relations are varied.," Instead of assuming a unique mass–luminosity conversion, in the following we will show how final constraints on cosmological parameters changes as the $L_{bol}$ $T_X$ and $M$ $T_X$ relations are varied."1136" The RDCS subsample. that we will use in the following analysis. has a [ux of Si),=3.5»10Hcresὃνtem2 and contains SI clusters with measured redshifts out to z—(85 over a 33MES sq."," The RDCS subsample, that we will use in the following analysis, has a flux--limit of $S_{lim}=3.5\times 10^{-14}\fl$ and contains 81 clusters with measured redshifts out to $z=0.85$ over a 33 sq."1137 deg., deg.1138 area 0]., area \cite{RosIAP}.1139 In order to fully exploit the information provided by the RDCS. we resort to a maximumlikelihood approach. in which model predictions are compared to the RDCS cluster distribution on the (L.2) plane.," In order to fully exploit the information provided by the RDCS, we resort to a maximum–likelihood approach, in which model predictions are compared to the RDCS cluster distribution on the $(L,z)$ plane."1140 To this purpose. let o(L.z) e the PressSchechter based luminosity function. as predicted. by a given. model. so that ó(L.z)(dVfds) dzdL is the expected number density of clusters in t1e comoving volume clement (dVdz)dz and in the luminosity interval dL.," To this purpose, let $\phi(L,z)$ be the Press–Schechter based luminosity function, as predicted by a given model, so that $\phi(L,z)\,(dV/dz)$ $dz\,dL$ is the expected number density of clusters in the comoving volume element $(dV/dz)\,dz$ and in the luminosity interval $dL$."1141" Therefore. the expected. number of clusters in RDCS bving in the dzdL clement of the (L.z2) plane is A(z.{λατα,=pz.L) FaySG.{ανfdz)edzd"," Therefore, the expected number of clusters in RDCS lying in the $dz\,dL$ element of the $(L,z)$ plane is $\lambda(z,L)dzdL=\rho(z,L)$ $f_{sky}[S(z,L)](dV/dz) dzdL$."1142 lere fii is t1e fluxdependent RDCS sky.coverage., Here $f_{sky}$ is the flux–dependent RDCS sky–coverage.1143 The likelihood function.L. £ is define as the product of the probabilities of observing exactly one cluster in dzdL a each of the (2;.£;) positions occupied by the RDCS clusters. and of the proxioilities. of observing zero clusters in," The likelihood function ${\cal L}$ is defined as the product of the probabilities of observing exactly one cluster in $dz\,dL$ at each of the $(z_i,L_i)$ positions occupied by the RDCS clusters, and of the probabilities of observing zero clusters in"1144along the radio ring.,along the radio ring.1145 To balance the svuchrotrou and inverse Compton cooling of an electron population. this model would need to postulate a fine-tuned acceleration process that however must not fan out the well-coufined radio emission alone the arc.," To balance the synchrotron and inverse Compton cooling of an electron population, this model would need to postulate a fine-tuned acceleration process that however must not fan out the well-confined radio emission along the arc."1146" Model E: in this model. “radio tail” would outline the ballistic orbit of NGC M""mi."," Model 4: in this model, the “radio tail” would outline the ballistic orbit of NGC 1265."1147" To sustain such a helical orbit of NGC 1265 over ofο this model would require au undetectedο dark objectκα mass A>[κουωςcBNLOMAL, The change of the direction in the brighter part of the tail remains unexplainable aud there is also the problem iu explaining the coustaney of the spectra and the surface brightuess along the radio rug."," To sustain such a helical orbit of NGC 1265 over $360\degr$, this model would require an undetected dark object of mass $M\gtrsim M_\rmn{NGC~1265}\simeq11483\times10^{12}M_\odot$ orbiting the The change of the direction in the brighter part of the tail remains unexplainable and there is also the problem in explaining the constancy of the spectrum and the surface brightness along the radio ring."1149 Caven these difficultics. it is attractive to consider alternative possibilities that may explore the interaction between a radio galaxy with the outskirts of the Perseus ICAL.," Given these difficulties, it is attractive to consider alternative possibilities that may explore the interaction between a radio galaxy with the outskirts of the Perseus ICM."1150 This has been foreshadowed in a remark bv 7/— who speculate whether the large scale polarized structure that arches around the steep spectrmu tail of NGC 1265 is indeed the remains of an earlier phase of feedback., This has been foreshadowed in a remark by \citet{2005A&A...441..931D} who speculate whether the large scale polarized structure that arches around the steep spectrum tail of NGC 1265 is indeed the remains of an earlier phase of feedback.1151 Our work will demonstrate that this picture is uot only the simplest consisteut explanation for the radio morphology and spectruni but we also use it to indirectly inter the presence of a cluster shock wave and measure its properties.," Our work will demonstrate that this picture is not only the simplest consistent explanation for the radio morphology and spectrum, but we also use it to indirectly infer the presence of a cluster shock wave and measure its properties."1152 Previously. the morphology of a eiut radio galaxy has already: been used to iudirectly detect a large scale shock at an intersecting fhuneut of galaxies (7)— bv usine the radio galaxy as a giant cluster weather station (?)..," Previously, the morphology of a giant radio galaxy has already been used to indirectly detect a large scale shock at an intersecting filament of galaxies \citep{2001ApJ...549L..39E} by using the radio galaxy as a giant cluster weather station \citep{1998Sci...280..400B}."1153 Caavitationallv driven. supersouic flows of intergalactic eas follow these flaments toward estes B ealaxies that represent the knots of the cosmüc web a(?7)..," Gravitationally driven, supersonic flows of intergalactic gas follow these filaments toward clusters of galaxies that represent the knots of the cosmic web \citep{1996Natur.380..603B}."1154 The flows will inevitably collide aud. form Iaree-se shock waves (QU277)..," The flows will inevitably collide and form large-scale shock waves \citep{1998ApJ...502..518Q, 2000ApJ...542..608M, 2003ApJ...593..599R,1155 2006MNRAS.367..113P}."1156 OF exeat. interest is the subclass of accretion shocks that are thought to heat the barvous of the warnrot iuterealactie iiedium (IGAL) when they are accreted outo a ealaxy cluster., Of great interest is the subclass of accretion shocks that are thought to heat the baryons of the warm-hot intergalactic medium (IGM) when they are accreted onto a galaxy cluster.1157 Formation shocks have also beeu xoposed. as possible geueration sites of intergalactic naenetic fields (2??)..," Formation shocks have also been proposed as possible generation sites of intergalactic magnetic fields \citep{1997ApJ...480..481K, 1998A&A...335...19R, 2008Sci...320..909R}."1158 Prior to this work. ouly discrete ucreer shock waves have been detected im the N-ravs (es.T) and there was no characterization possible of he detailed flow properties iu the post-shock regime as ο test whether shear flowsthe necessary condition for eoncrating magnetic fieldsare preseut.," Prior to this work, only discrete merger shock waves have been detected in the X-rays \citep[e.g.,][]{2002ApJ...567L..27M} and there was no characterization possible of the detailed flow properties in the post-shock regime as to test whether shear flows—the necessary condition for generating magnetic fields—are present."1159 The structure of the paper is as follows., The structure of the paper is as follows.1160 In Section 2.. we prescut the basic picture of our model in a nutshell while we derive the detailed three-dimensional (3D) ecolctry of NGC 1265 within our model in Section 3..," In Section \ref{sec:idea}, we present the basic picture of our model in a nutshell while we derive the detailed three-dimensional (3D) geometry of NGC 1265 within our model in Section \ref{sec:geometry}."1161 Tn Section L. we work out the properties of the accretion shock onto the Perseus cluster iucludiug those of the post-shock flow aud preseut the implications for the παπιο warm-hot IGAL.," In Section \ref{sec:shock}, we work out the properties of the accretion shock onto the Perseus cluster including those of the post-shock flow and present the implications for the infalling warm-hot IGM."1162 Iu Section 5.. we carefully examine the wnderling plivsics as well as the lvcdvodvuamic stability. of our model aud discuss our findings in Section 6..," In Section \ref{sec:model}, we carefully examine the underlying physics as well as the hydrodynamic stability of our model and discuss our findings in Section \ref{sec:conclusions}."1163 Throughout this work. we use a IIubble constant of ff)=rüXkms‘AIpe," Throughout this work, we use a Hubble constant of $H_{0} = 70\,\rmn{km~s}^{-1}\rmn{Mpc}^{-1}$."1164" For the currently favored ACDAL cosmology with the prescut dav deusitv of total matter. O,,=0.28. aud the cosmological constant. O4=0.72. we obtain an angular diameter distance to Perseus (2=0.0179) of Daye=T5Mp: at this distance. 1 corresponds to 21.5kpc."," For the currently favored $\Lambda$ CDM cosmology with the present day density of total matter, $\Omega_m=0.28$, and the cosmological constant, $\Omega_\Lambda=0.72$, we obtain an angular diameter distance to Perseus $z=0.0179$ ) of $D_\rmn{ang}=75\,\rmn{Mpc}$; at this distance, $1\arcmin$ corresponds to $21.8\,\rmn{kpc}$."1165 N-vav data estimates a virial radius and mass for of LOMpe and Moy)=7.7«101A. (2).," X-ray data estimates a virial radius and mass for of $R_{200}=1.9\,\rmn{Mpc}$ and $M_{200}=7.7\times10^{14}M_\odot$ \citep{2002ApJ...567..716R}."1166" Before we preseut the idea of our model. we poiut out the main morphological aud Spectral properties of the ejut radio galaxy NGC 1265hrotronthat every model would have to explain: (1) The syuc surface brielituess. 5,. aud the spectral ides. a. between 19 aud 92 cm along the tail of NCC 1265uas (starting at the ealaxys head) show a characteristic jour (as shown in Fieure 2 of ?))."," Before we present the idea of our model, we point out the main morphological and spectral properties of the giant radio galaxy NGC 1265 that every model would have to explain: (1) The synchrotron surface brightness, $S_\nu$, and the spectral index, $\alpha$, between 49 and 92 cm along the tail of NGC 1265 (starting at the galaxy's head) show a characteristic behaviour (as shown in Figure 2 of \citealt{1998A&A...331..901S}) )."1167 In the first part ]of the tail. both quantities decline moderately mi a wav that is consistent with svuchrotron and inverse Compton cooling of a relativistic electron population that eot accelerated at the base or tle ier reeions of the jet. (," In the first part of the tail, both quantities decline moderately in a way that is consistent with synchrotron and inverse Compton cooling of a relativistic electron population that got accelerated at the base or the inner regions of the jet. ("1168"2) At the point of the tail where the twist changes in projection frou left- to right-hauced. both quantities experience a sudden dropwhile 4), changes by a factor of 10. à declines from 11 το 2.1. (","2) At the point of the tail where the twist changes in projection from left- to right-handed, both quantities experience a sudden drop—while $S_\nu$ changes by a factor of 10, $\alpha$ declines from $-1.1$ to $-2.1$ . ("1169"3) Finally. along the remaimime curved arc. 5, and a stay approximately constant on a total are leneth of lave=22ROL1zoTOOkpe. where R5150Xpe is the radius of m arc. &£&3/1 the projected arc leneth in uuits of 27 radius. iud &=Ph/(2zR)0. where h is the height of the 3D helix.","3) Finally, along the remaining curved arc, $S_\nu$ and $\alpha$ stay approximately constant on a total arc length of $l_\rmn{arc} = 2\pi R \xi \sqrt{1 + k^2}\gtrsim 700 \,\rmn{kpc}$, where $R\simeq150\,\rmn{kpc}$ is the radius of the arc, $\xi\simeq 3/4$ the projected arc length in units of $2\pi$ radians, and $k=h/(2\pi R)\geq0$, where $h$ is the height of the 3D helix."1170 This property is iu particular puzzlug. as there is no visible svuchrotrou cooling or fanning out of the dilute part of the tail visible.," This property is in particular puzzling, as there is no visible synchrotron cooling or fanning out of the dilute part of the tail visible."1171 These fiudiugs taken together sugeest the presence of two separate populations of relativistic clectrous eiviug vise to the bright aud the dim part of the tail. respectively. where the latter ιτ lave expericuced a coherent cucrectization over a length scale of 27~300kpe aud on a timescale that is shorter than the cooling time of the radio emittiug clectrous ofTancie$2.9«105vr.," These findings taken together suggest the presence of two separate populations of relativistic electrons giving rise to the bright and the dim part of the tail, respectively, where the latter must have experienced a coherent energetization over a length scale of $2 R\simeq 300\,\rmn{kpc}$ and on a timescale that is shorter than the cooling time of the radio emitting electrons of $\tau_\rmn{sync,\,ic} \lesssim 2.9\times 10^8\,\rmn{yr}$."1172 The presence of one radio tail that counects the two electron populations iu projection poiuts to a causally counected origin of the svuchrotron racdiatiug structure., The presence of one radio tail that connects the two electron populations in projection points to a causally connected origin of the synchrotron radiating structure.1173 The most natural explanation that combines these observational requirements are the reminders of two distinct epochs of active ealactic nucleus outbursts where the ost recent oue is still visible as a head-tail radio jet aud the older oue experienced a recent coliercut enereetization eveut., The most natural explanation that combines these observational requirements are the reminders of two distinct epochs of active galactic nucleus outbursts where the most recent one is still visible as a head-tail radio jet and the older one experienced a recent coherent energetization event.1174 Tu we propose that such an cuereizing event couldbe partienlay.provided |* the passage of a detached radio plasmabubble from a previous outburst throueh a shock wave.," In particular, we propose that such an energizing event could be provided by the passage of a detached radio plasma bubble from a previous outburst through a shock wave."1175 This passage transforms the plasiuabubble iuto a torus (vortex ring) and αλανασαν compresses and euereizes the agedelectron population to eut low surface brightness and steep-spectrunn radio ciussiow (as we detail below)., This passage transforms the plasma bubble into a torus (vortex ring) and adiabatically compresses and energizes the agedelectron population to emit low surface brightness and steep-spectrum radio emission (as we detail below).1176 If the shock crossing is oblique.," If the shock crossing is oblique,"1177northern rim.,northern rim.1178 Therefore. the CIE condition is justified and we will not further consider the VNEI model. (," Therefore, the CIE condition is justified and we will not further consider the VNEI model. ("1179(source #111) ts the brightest one among the four point sources near to the remnant center.,source 11) is the brightest one among the four point sources near to the remnant center.1180 We extracted its spectrum from a circular region with a radius of 10 aresec centered at the source position (cf., We extracted its spectrum from a circular region with a radius of 10 arcsec centered at the source position (cf.1181 Table 1)., Table 1).1182" The background spectrum was extracted from a nearby region from a circle of 10 aresec radius centered at RA=19""54'""23.234>, Dec=31°29/22.75"" (02000)."," The background spectrum was extracted from a nearby region from a circle of 10 arcsec radius centered at $19^{\rm h}54^{\rm m}23.234^{\rm s}$ , $31^{\circ}29'22.75""$ (J2000)."1183 After background subtraction. 54 net counts were avaliable for the spectral analysis of the source.," After background subtraction, 54 net counts were avaliable for the spectral analysis of the source."1184 Since the location of iis close to the edge of ACIS-I3 CCD. we computed the response files manually with the CIAO tools MKARF and MKRME.," Since the location of is close to the edge of ACIS-I3 CCD, we computed the response files manually with the CIAO tools MKARF and MKRMF."1185 The spectrum was binned dynamically so as to have at least 5 counts per bin., The spectrum was binned dynamically so as to have at least 5 counts per bin.1186 In view of the small photon statistic of these sources. we adopted the C—-statistic (Cash 1979) for all the fittings.," In view of the small photon statistic of these sources, we adopted the $C-$ statistic (Cash 1979) for all the fittings."1187 To better constrain the parameters. we fixed the hydrogen column density at the optical extinction inferred value (i.e. 4x107! em™).," To better constrain the parameters, we fixed the hydrogen column density at the optical extinction inferred value (i.e. $4\times10^{21}$ $^{-2}$ )."1188 Fitting with a power-law model results in a reasonable fit that yields a photon index of [22.7+0.4 and a normalization at 1 keV of 14701»107 photons keV! em™ s!., Fitting with a power-law model results in a reasonable fit that yields a photon index of $\Gamma=2.7\pm0.4$ and a normalization at 1 keV of $1.4^{+0.4}_{-0.3}\times10^{-5}$ photons $^{-1}$ $^{-2}$ $^{-1}$.1189 The best-fit column density is consistent with the values inferred from the spectra of the supernova remnant emission within the Io error bound., The best-fit column density is consistent with the values inferred from the spectra of the supernova remnant emission within the $1\sigma$ error bound.1190" The unabsorbed flux deduced for the best-fit power-law model parameters is f£,=4.5x107 ergs em s! in 0.5--8 keV. A blackbody model can describe the spectrum of this source equally well.", The unabsorbed flux deduced for the best-fit power-law model parameters is $f_{x}=4.5\times10^{-14}$ ergs $^{-2}$ $^{-1}$ in $0.5-8$ keV. A blackbody model can describe the spectrum of this source equally well.1191 The best-fit model implies a temperature of T=467x10°K., The best-fit model implies a temperature of $T=4.6^{+0.7}_{-0.6}\times10^{6}~K$.1192 The radius of the projected blackbody emitting area is in the range ~170—310 m and ~410—750 m for the adopted distances of 7 kpe and 17 kpe. respectively (see $33 for the discussion of the remnant distance).," The radius of the projected blackbody emitting area is in the range $\sim170-310$ m and $\sim410-750$ m for the adopted distances of 7 kpc and 17 kpc, respectively (see 3 for the discussion of the remnant distance)."1193" The unabsorbed flux deduced for the best-fit blackbody model is f,=2.6x107 ergs em™ s! in 0.5—8 keV. For the other three fainter central X-ray sources it Is interesting to compare their brightness and hardness with those ofCXOU195422.", The unabsorbed flux deduced for the best-fit blackbody model is $f_{x}=2.6\times10^{-14}$ ergs $^{-2}$ $^{-1}$ in $0.5-8$ keV. For the other three fainter central X-ray sources it is interesting to compare their brightness and hardness with those of.119497+312902.1.. To do so. we have prepared their spectra and the response files in the same way as we did forCXOU195422.," To do so, we have prepared their spectra and the response files in the same way as we did for."119597+312902.1.. Fixing the column density at ny=4x107 cm we obtained the photon indices by fitting a power-law model to their spectra., Fixing the column density at $n_{H}=4\times10^{21}$ $^{-2}$ we obtained the photon indices by fitting a power-law model to their spectra.1196 The fitted parameters are summarised in Table 3., The fitted parameters are summarised in Table 3.1197 The photon index provides a measure of the hardness of these X-ray sources., The photon index provides a measure of the hardness of these X-ray sources.1198 Whereas sources #99 and ((source #110) are as soft asCXOU195422.97+312902.1.. ((source #335) appears to show harder X-ray emission.," Whereas sources 9 and (source 10) are as soft as, (source 35) appears to show harder X-ray emission."1199 We have also computed the absorption-corrected fluxes from the inferred power-law parameters which are given in Table 3., We have also computed the absorption-corrected fluxes from the inferred power-law parameters which are given in Table 3.1200 Given the limited photon statistics of the central point sources. the spectral analysis is not very constraining.," Given the limited photon statistics of the central point sources, the spectral analysis is not very constraining."

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