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(Niedzielskietal.2009).. Kennedy&Keuyou2008). | \citep{dol09} \citep{nie09}. \citep{ida05,ken08}. |
. planets orbiting elauts stars tend to lave larec transit probabilities due to the size of the lost stars (Assetetal. 2009). | planets orbiting giants stars tend to have large transit probabilities due to the size of the host stars \citep{ass09}. |
. Cüant stars present significant challenges. however. to those who intend to monitor those stars for the purpose of detecting cxoplanetary transits. | Giant stars present significant challenges, however, to those who intend to monitor those stars for the purpose of detecting exoplanetary transits. |
A good exaniple is the planet orbiting ID 122130 (Sctiawanctal.200 1).. for which the combination of the 22.9 2. host star (daSilvaetal.2006). and the high ecceutricitv of the planetary orbit lead to a transit probability of ~32 | A good example is the planet orbiting HD 122430 \citep{set04}, for which the combination of the 22.9 $R_\sun$ host star \citep{das06} and the high eccentricity of the planetary orbit lead to a transit probability of $\sim 32$. |
ILowever. assmunme a Jupiter radius for the planet requires the wnambignous detection of a 1.9«10D transit depth. | However, assuming a Jupiter radius for the planet requires the unambiguous detection of a $1.9 \times 10^{-5}$ transit depth. |
Additionally. the uncertiiuty in the orbital paralcters of the planet means that a laree fransit window will need to be continuously monitored (aneetal. 2009).. | Additionally, the uncertainty in the orbital parameters of the planet means that a large transit window will need to be continuously monitored \citep{kan09b}. |
Finally. a photometric survey of giaut stars bv Πανetal.(2000). found that almost half of their salple exhibited low-level plotometric variability that would further complicate transit detection. | Finally, a photometric survey of giant stars by \citet{hen00} found that almost half of their sample exhibited low-level photometric variability that would further complicate transit detection. |
The planet orbiting iota Draconis (hereafter + Dra} presents a particularly iuterestiug case. | The planet orbiting iota Draconis (hereafter $\iota$ Dra) presents a particularly interesting case. |
The host star is a 2 eiaut. is very bright (V.= 3.29). and is frequently referred to by its other common aliases of ΠΟ 137759 and HIP 75158. | The host star is a K2 giant, is very bright $V = 3.29$ ), and is frequently referred to by its other common aliases of HD 137759 and HIP 75458. |
A thorough spectral analysis of this star was mndertaken by Sadakaueetal.(2005).. who fouud a uictallicity of =0.12. | A thorough spectral analysis of this star was undertaken by \citet{sad05}, who found a metallicity of [Fe/H] $= 0.12$. |
The planetary companion was discovered by |Fe/II]Frinketal.(2002).. and the orbit was further refined by Zechinelsteretal.(2008). whose radial velocity data revealed a linear trend over tine. | The planetary companion was discovered by \citet{fri02}, and the orbit was further refined by \citet{zec08}, whose radial velocity data revealed a linear trend over time. |
Tn addition to the lavee stellar radius. the planetary orbit is hiellv eccentric and the argument of periastrou (w~ 907) cusures that the periastron passage occurs approximately in the obscrver-star plane perpendicular to the line-ofsieht. | In addition to the large stellar radius, the planetary orbit is highly eccentric and the argument of periastron $\omega \sim 90\degr$ ) ensures that the periastron passage occurs approximately in the observer-star plane perpendicular to the line-of-sight. |
Tere we present new radial velocity data for + Dra b and an analysis of the photometric stability of the host star. | Here we present new radial velocity data for $\iota$ Dra b and an analysis of the photometric stability of the host star. |
These data are used to provide a well-coustrained transit ephemeris for the next LO vears and an assessienut of the feasibility of detecting a transit for the planetary colupanion. | These data are used to provide a well-constrained transit ephemeris for the next 10 years and an assessment of the feasibility of detecting a transit for the planetary companion. |
This analysis and discussionmay be used as a nbodol for how to consider the transit detection potential for cach of the planets orbiting eiaut stars. | This analysis and discussionmay be used as a model for how to consider the transit detection potential for each of the planets orbiting giant stars. |
to our AM-band data. since the reduction in sensitivity over L' (— 3mmag) is much greater than can be compensated for by the red colour of the quasar nucleus (L'Al=0.76 for a power law a=13: Neugebauer et 11987). | to our $M$ -band data, since the reduction in sensitivity over $L'$ $\sim 3$ mag) is much greater than can be compensated for by the red colour of the quasar nucleus $L'-M=0.76$ for a power law $\alpha=1.3$; Neugebauer et 1987). |
We are therefore convinced. that we have not made any spurious detection. and that we have not failed to detect any sources which are in reality brighter than our quoted limits. | We are therefore convinced that we have not made any spurious detection, and that we have not failed to detect any sources which are in reality brighter than our quoted limits. |
Ifthe standard interpretation of our nuclear sources as dust-obscured quasars is correct. they should have the colours of a quasar. modified by some amount of foreground reddening. | If the standard interpretation of our nuclear sources as dust-obscured quasars is correct, they should have the colours of a quasar, modified by some amount of foreground reddening. |
We therefore perform linear regression. accounting for upper limits in the manner of Isobe. Feigelson Nelson (1986). on the data of Section 3... | We therefore perform linear regression, accounting for upper limits in the manner of Isobe, Feigelson Nelson (1986), on the data of Section \ref{sec:nuclei}. |
“Phis analwsis produces. values for the intrinsic luminosity ancl extinction of cach nuclear source. | This analysis produces values for the intrinsic luminosity and extinction of each nuclear source. |
We adopt our own parametrization of the near-infrared. interstellar extinction. law. obtained by fitting a second-order polynomial to the data of Ricke Lebolsky (1985). | We adopt our own parametrization of the near-infrared interstellar extinction law, obtained by fitting a second-order polynomial to the data of Rieke Lebofsky (1985). |
This parametrization. by virtue of ignoring the optical data. provides a rather better fit to the longest. wavelengths than do those of llowarth (1983) ane Cardelli. Clavton Mathis (1989). | This parametrization, by virtue of ignoring the optical data, provides a rather better fit to the longest wavelengths than do those of Howarth (1983) and Cardelli, Clayton Mathis (1989). |
The intrinsic quasar spectrum is assumed to be that of an a=1.3 power law (Neugebauer et 11059). | The intrinsic quasar spectrum is assumed to be that of an $\alpha = 1.3$ power law (Neugebauer et 1987). |
Table 5. lists the extinctions and intrinsic luminosities we derive for the obscured quasars in the five radio galaxies with detected nuclear sources. | Table \ref{tab:exts} lists the extinctions and intrinsic luminosities we derive for the obscured quasars in the five radio galaxies with detected nuclear sources. |
These data are presented graphically in Fig. 12.. | These data are presented graphically in Fig. \ref{fig:irspec}. |
For 3€ 223 and 3€ 234. where the nucleus was detected: at all four wavelengths. we also. performed regression. with the spectral index as an additional free | For 3C 223 and 3C 234, where the nucleus was detected at all four wavelengths, we also performed regression with the spectral index as an additional free |
The resulting spectrum shows the detection of many lines due to methane in Triton's atmosphere, particularly at 2320-2330 nm (Fig. | The resulting spectrum shows the detection of many lines due to methane in Triton's atmosphere, particularly at 2320-2330 nm (Fig. |
1). | 1). |
This is the first observation of gaseous methane since its discovery by Voyager (Herbert and Sandel 1991). | This is the first observation of gaseous methane since its discovery by Voyager (Herbert and Sandel 1991). |
As for our study of Pluto's CH4, we constructed a direct line-by-line atmospheric model of Triton, integrated over angles and including solar lines reflected off Triton's surface as well as the telluric transmission (see details in Lellouch et al. | As for our study of Pluto's $_4$, we constructed a direct line-by-line atmospheric model of Triton, integrated over angles and including solar lines reflected off Triton's surface as well as the telluric transmission (see details in Lellouch et al. |
2009). | 2009). |
The spectrum was first modelled by assuming a single-temperature layer, with Triton's atmospheric methane mean temperature (T) and column density (a) as free parameters. | The spectrum was first modelled by assuming a single-temperature layer, with Triton's atmospheric methane mean temperature (T) and column density (a) as free parameters. |
We inferred T-50*7? K and a = 0.08+0.03 cm-am (Fig. | We inferred $^{+20}_{-15}$ K and a = $\pm$ 0.03 cm-am (Fig. |
2 on-line). | 2 on-line). |
The same analysis for Pluto had given T-90*75 Kanda- 0.757333 cm-am. | The same analysis for Pluto had given $^{+25}_{-18}$ K and a = $^{+0.55}_{-0.30}$ cm-am. |
This confirms that Pluto’s atmosphere is warmer than Triton’s, as a result of its higher methane abundance. | This confirms that Pluto's atmosphere is warmer than Triton's, as a result of its higher methane abundance. |
The error bars on the inferred mean methane temperature are such that it is not possible to constrain the methane vertical distribution. | The error bars on the inferred mean methane temperature are such that it is not possible to constrain the methane vertical distribution. |
Instead, we used the Voyager-determined thermal structure (temperature vs altitude, Krasnopolsky et al., | Instead, we used the Voyager-determined thermal structure (temperature vs altitude, Krasnopolsky et al., |
1993) and methane vertical profile (Herbert and Sandel 1991, ingress UV occultation profile). | 1993) and methane vertical profile (Herbert and Sandel 1991, ingress UV occultation profile). |
The latter shows a decrease of the | The latter shows a decrease of the |
and is included in the recorded spectra. | and is included in the recorded spectra. |
For this reason, contamination by emission lines originating in the often bright, extended nebulae surrounding WR stars is often a concern. | For this reason, contamination by emission lines originating in the often bright, extended nebulae surrounding WR stars is often a concern. |
SCORE’ss small 1”x2” slit excludes most of this nebular emission, leading in some cases to significant differences between spectra of the same variable WR star observed with both ISO and | s small $1\arcsec\times2\arcsec$ slit excludes most of this nebular emission, leading in some cases to significant differences between spectra of the same non-variable WR star observed with both ISO and (cf. |
WR146 in ? vs. ?,, as described in §44.2 of the ((cf. | WR146 in \citet{Willis1997} vs. \citetalias{2001AJ....121.2115S}, as described in 4.2 of the latter). |
While we know of no cases in which neon or other latter).abundances computed using ISO data were affected by this type of contamination, the sspectra of fainter WR stars used here should be relatively less affected by nebular emission. | While we know of no cases in which neon or other abundances computed using ISO data were affected by this type of contamination, the spectra of fainter WR stars used here should be relatively less affected by nebular emission. |
For a uniform, spherical, but clumped wind with terminal velocity vo; and constant volume filling fraction ó (0€6 1), as depicted in Fig. 2,, | For a uniform, spherical, but clumped wind with terminal velocity $v_{\infty}$ and constant volume filling fraction $\delta$ $0\le\delta\le1$ ), as depicted in Fig. \ref{fig:windmodel}, , |
the mass loss rate can be written: where µ is the mean atomic mass per ion, and n is the number density of the ionized gas. | the mass loss rate can be written: where $\mu$ is the mean atomic mass per ion, and $n$ is the number density of the ionized gas. |
Defining the standard A=TanMHMUoc, the density can be expressed as: The dominant radiative output of the wind at mid-infrared and longer wavelengths is free-free emission (?).. | Defining the standard $\mathcal{A}\equiv \frac{\dot{M}}{4\pi\mu
m_Hv_{\infty}}$, the density can be expressed as: The dominant radiative output of the wind at mid-infrared and longer wavelengths is free-free emission \citep{Wright1975}. |
The free-free optical depth along a particular line of sight through the clumped wind to the observer is where the reduced free-free opacity K(v,T)Kpp/MMe, Ye is the number of electrons per ion, and we have made use of the 1/r? density profile of Eq. 2.. | The free-free optical depth along a particular line of sight through the clumped wind to the observer is where the reduced free-free opacity $\mathcal{K}(\nu,T)=\kappa_{ff}/nn_e$ , $\gamma_e$ is the number of electrons per ion, and we have made use of the $1/r^2$ density profile of Eq. \ref{eq:2}. |
Assuming a constant, thermal source function, and integrating over cylinders of constant impact parameter b thus constant free-free optical depth), we recover ?"s (andinfrared/radio free-free flux expression, modified to include the effects of clumping via the fill factor ó: where D is the distance to the star, g, is the frequency dependent free-free Gaunt factor, and Z is the rms average charge per ion. | Assuming a constant, thermal source function, and integrating over cylinders of constant impact parameter $b$ (and thus constant free-free optical depth), we recover \citeauthor{Wright1975}' 's infrared/radio free-free flux expression, modified to include the effects of clumping via the fill factor $\delta$: where $D$ is the distance to the star, $g_\nu$ is the frequency dependent free-free Gaunt factor, and $Z$ is the rms average charge per ion. |
Most WR. mass loss rate estimates are derived from radio measurements of the free-free emission using Eq. 4.. | Most WR mass loss rate estimates are derived from radio measurements of the free-free emission using Eq. \ref{eq:4}. |
Given the same assumptions of atomic parameters of the wind (Z, µ. Ye), it is apparent that, in the absence of information about the clumping fill factor 6, therate, Mss=Μ/νὸ, is derived. | Given the same assumptions of atomic parameters of the wind $Z$, $\mu$, $\gamma_e$ ), it is apparent that, in the absence of information about the clumping fill factor $\delta$, the, $\dot{M}_{scl}\equiv\dot{M}/\sqrt{\delta}$, is derived. |
For fine structure lines arising from ions with ground states consisting of only two energy levels, the fractional abundance of the ion by number,jnj, can be calculated straightforwardly from the observed line flux by neglecting all other transitions. | For fine structure lines arising from ions with ground states consisting of only two energy levels, the fractional abundance of the ion by number, can be calculated straightforwardly from the observed line flux by neglecting all other transitions. |
Following ?,, the flux due to a given line transitioncan be written: where Αμ is the Einstein emission coefficient for the line in question, and m, is the density of the ions populating the upper level of the transition. | Following \citet{Barlow1988}, the flux due to a given line transitioncan be written: where $A_{ul}$ is the Einstein emission coefficient for the line in question, and $n_u$ is the density of the ions populating the upper level of the transition. |
Z used here (lromHaeusel&Zdunik1990a) is roughly the average charge of the uuclei actually present. | $Z$ used here \citep[from][]{haensel90b} is roughly the average charge of the nuclei actually present. |
A self-consistent calculation of the crust composition. aud the resultine phase diagraiu. is required to couclusively determine if laver cake melting actually occurs. | A self-consistent calculation of the crust composition, and the resulting phase diagram, is required to conclusively determine if layer cake melting actually occurs. |
There are three inain couclusious presented in this work. | There are three main conclusions presented in this work. |
First. for neutron stars accreting ‘apidly enough for the accreted hydrogen aud helium to burn stably. most of the leat released iu he crust [lows into the core. | First, for neutron stars accreting rapidly enough for the accreted hydrogen and helium to burn stably, most of the heat released in the crust flows into the core. |
As a result. the thermal prolile in the inner crust is nearly inclepeudenut ol the temperature at the top of the crust. | As a result, the thermal profile in the inner crust is nearly independent of the temperature at the top of the crust. |
Secoud. if the crust lattice is very impure. there is a uaximnur in temperature at deusities greater than neutron drip. where the heating occurs. | Second, if the crust lattice is very impure, there is a maximum in temperature at densities greater than neutron drip, where the heating occurs. |
The peak eniperature in the crust in tliis case is set by the ability of the crust to carry tlie generated nuclear uminosity iuward [rom the reaction shell aud is relatively iuseusitive to the core temperature. | The peak temperature in the crust in this case is set by the ability of the crust to carry the generated nuclear luminosity inward from the reaction shell and is relatively insensitive to the core temperature. |
Third. heating the inner crusi to temperatures zz8x105IN might melt. t1le Crust ---in thin layers where electron captures have reduced the lonic charge. | Third, heating the inner crust to temperatures $\approx 8\ee{8}\K$ might melt the crust in thin layers where electron captures have reduced the ionic charge. |
There are several consequences of these results. | There are several consequences of these results. |
Because a fluid layer ¢oes not support shear stress. the strain inthe crust must vanish in these melt lavers. | Because a fluid layer does not support shear stress, the strain in the crust must vanish in these melt layers. |
This will limit tje quadrupole that ean ye induced by thermal perturbatious to the electron capture rate (Bildsten1998) if these captures occur above the melt laver. | This will limit the quadrupole that can be induced by thermal perturbations to the electron capture rate \citep{bildsten98:gravity-wave} if these captures occur above the melt layer. |
Iu addition. the fluid layers can. clissipate roatioual energy. eitler hrough. hydrodsuamical or maguetolydrodyuamical processes. aud thus οςjntribute to balauciug he accretion torque acting on the stellar surface. | In addition, the fluid layers can dissipate rotational energy, either through hydrodynamical or magnetohydrodynamical processes, and thus contribute to balancing the accretion torque acting on the stellar surface. |
The electrical conductiviy Of an accreted crust is reduced. both because of erust heating (Urpin&Ceppert1995:GeppertUrpin1991) aud yecause of crust impurities (Brown&Bildsten1995). | The electrical conductivity of an accreted crust is reduced, both because of crust heating \citep{urpin95,geppert94} and because of crust impurities \citep{brown98a}. |
. LP the crust is as impwe as considered here. he timescale for Olunic decay over a pressure scalelieight is much less (by a factor of 100) than the low timescale. for much of the crust. | If the crust is as impure as considered here, the timescale for Ohmic decay over a pressure scaleheight is much less (by a factor of 100) than the flow timescale, for much of the crust. |
As a result. the inward advection of magnetic [flux (Ixonar is reduced in importance. | As a result, the inward advection of magnetic flux \citep{konar97} is reduced in importance. |
Thermomaguetic ellects. such as current clrift (Ceppert&Urpin19901) aud the battery ellect (e.g..Blandford.Applegate.&Heruquist.1982).. will be comparatively more important. however. because of the greater thermal gradieut. | Thermomagnetic effects, such as current drift \citep{geppert94} and the battery effect \citep*[e.g.,][]{blandford83}, will be comparatively more important, however, because of the greater thermal gradient. |
In recent vears. attention has been giveu to other. more efficient. cooling mechanisms. | In recent years, attention has been given to other, more efficient, cooling mechanisms. |
The direct. Urea process cau operate if the proton fraction is [n]ϱ‘eater than 0.115 (Lattimer or if hyvperous are present (Prakashetal. 1992).. | The direct Urca process can operate if the proton fraction is greater than 0.148 \citep{lattimer91} or if hyperons are present \citep{prakash92:_rapid_delta}. . |
Other exotic mechanisms may be possible. includiug pion condensates (οσαetal.1991).. kaon condensates (Brownetal.1988).. or quark uatter (Iwamoto1952).. | Other exotic mechanisms may be possible, including pion condensates \citep{umeda94}, kaon condensates \citep{brown88:_stran}, or quark matter \citep{iwamoto82:_neutr}. |
The exotic mechauisius have the same temperature dependeuce as the direct. Urea (x. 7?) but are weaker. | The exotic mechanisms have the same temperature dependence as the direct Urca $\propto T^6$ ) but are weaker. |
Although none of the hydrostatic st"uctures cousidered iu his paper has an interior proton fraction large enough to activate the direct Urea. some form of enhanced cooling could operate. | Although none of the hydrostatic structures considered in this paper has an interior proton fraction large enough to activate the direct Urca, some form of enhanced cooling could operate. |
However. tlie crust temperature would still femmain high 1.2)) if he crust were very impure. | However, the crust temperature would still remain high \ref{sec:Simple-expr-crust}) ) if the crust were very impure. |
Direct observational couseqtences ofthe core 1eutriuo emissivityv are | Direct observational consequences ofthe core neutrino emissivity are |
our conclusions. | our conclusions. |
Firstly. we have seen that the presence of a high mass galaxy within a region if size /? does not uniquely specify the value of the overdensity 9. | Firstly, we have seen that the presence of a high mass galaxy within a region if size $R$ does not uniquely specify the value of the overdensity $\delta$. |
Rather we obtain a probability density (which is Gaussian in shape) and work with the value where this probability is maximum. | Rather we obtain a probability density (which is Gaussian in shape) and work with the value where this probability is maximum. |
In reality. however. the actua value of ὁ could be different and this may possibly affect the predicted luminosity function. | In reality, however, the actual value of $\delta$ could be different and this may possibly affect the predicted luminosity function. |
Note that the luminosity function a the brighter end is almost independent of the details of reionization history. and this. in principle. can be used for constraining the value of 9. | Note that the luminosity function at the brighter end is almost independent of the details of reionization history, and this, in principle, can be used for constraining the value of $\delta$. |
The effect of feedback can then be studied using the faint enc of the luminosity function. | The effect of feedback can then be studied using the faint end of the luminosity function. |
The radiative feedback prescription used in this paper is based on a Jeans mass calculation (2).. | The radiative feedback prescription used in this paper is based on a Jeans mass calculation \citep{2005MNRAS.361..577C}. |
However. alternate prescriptions for feedback exist in literature. e.g. ?. and hence the shape of the luminosity function at faint ends as predicted by our mode may not be robust. | However, alternate prescriptions for feedback exist in literature, e.g., \citet{2000ApJ...542..535G} and hence the shape of the luminosity function at faint ends as predicted by our model may not be robust. |
Interestingly. the presence of a "knee" in the luminosity function can be used to estimate the value of the halo mass below which star formation can be suppressed (which in turn can indicate the temperature) while the shape of the function below this knee should indicate the nature of feedback. | Interestingly, the presence of a “knee” in the luminosity function can be used to estimate the value of the halo mass below which star formation can be suppressed (which in turn can indicate the temperature) while the shape of the function below this knee should indicate the nature of feedback. |
This study can also be complemented with proposed for studying feedback using other observations. e.g.. 21 em observation (2) and CMBR (?).. | This study can also be complemented with proposed for studying feedback using other observations, e.g., 21 cm observation \citep{2008MNRAS.384.1525S} and CMBR \citep{2008MNRAS.385..404B}. |
Finally. we have neglected the presence of other sources of reionization. e.g.. metal-free stars. minihaloes. and so on. | Finally, we have neglected the presence of other sources of reionization, e.g., metal-free stars, minihaloes, and so on. |
It is expected that these sources would be too faint to affect the luminosity function in the ranges we are considering. | It is expected that these sources would be too faint to affect the luminosity function in the ranges we are considering. |
However. these sources may affect the thermal history of the medium. e.g. the metal-free stars would produce higher temperatures because of harder spectra. | However, these sources may affect the thermal history of the medium, e.g, the metal-free stars would produce higher temperatures because of harder spectra. |
In such cases. it is most likely that feedback would oceur at magnitude brighter than what we have indicated and hence would possibly be easier to detect. | In such cases, it is most likely that feedback would occur at magnitude brighter than what we have indicated and hence would possibly be easier to detect. |
GK acknowledges useful discussion with Prof. Jasjeet S. Bagla. | GK acknowledges useful discussion with Prof. Jasjeet S. Bagla. |
Computational work for this study was carried out at the cluster computing facility in the Harish-Chandra Research Institute (http://cluster.hrires.in/index.html). | Computational work for this study was carried out at the cluster computing facility in the Harish-Chandra Research Institute (http://cluster.hri.res.in/index.html). |
We would also like to thank the referee for suggestions that improved this paper's quality. | We would also like to thank the referee for suggestions that improved this paper's quality. |
As expressed in Equation (5)). the number density of ionizing shotons produced per unit time is related to the SFR density. which in turn depends on the SFR in each halo. given by Equation (4800). and the number density of haloes of a certain age. given by Equation (1)) for average regions. and by Equation (159) for overdense regions. | As expressed in Equation \ref{nnu}) ), the number density of ionizing photons produced per unit time is related to the SFR density, which in turn depends on the SFR in each halo, given by Equation \ref{global_sfr}) ), and the number density of haloes of a certain age, given by Equation \ref{nmzzc}) ) for average regions, and by Equation \ref{nmzzc_biased}) ) for overdense regions. |
We derive Equation (15)) in this appendix. | We derive Equation \ref{nmzzc_biased}) ) in this appendix. |
We denote the number density at redshift + of haloes formed between redshifts z, and z.|dz. with mass between À/ and A|dM. by NM.2.z,2)Md'z,.. | We denote the number density at redshift $z$ of haloes formed between redshifts $z_c$ and $z_c+dz_c$, with mass between $M$ and $M+dM$, by $N(M,z,z_c)dMdz_c$. |
This quantity is related to(1) the ormation rate at redshift ο, of haloes with mass between AJ and Al|dAl. denoted by NowM.2JdAL. and (2) the probability of their survival at redshift z. denoted by pouy(2.2). | This quantity is related to (1) the formation rate at redshift $z_c$ of haloes with mass between $M$ and $M+dM$, denoted by $\dot N_\mathrm{form}(M,z_c)dM$, and (2) the probability of their survival at redshift $z$ , denoted by $p_\mathrm{surv}(z,z_c)$. |
We calculate hese two quantities using a technique given by ?.. applied to an overdense region with overdensity ὁ and size 2. | We calculate these two quantities using a technique given by \citet{1994PASJ...46..427S}, applied to an overdense region with overdensity $\delta$ and size $R$ . |
Recall that in extended Press-Schechter theory (2).. the mass 'uncetion of dark matter haloes is detined as the comoving number density of haloes with mass between Af and AZ|dA. | Recall that in extended Press-Schechter theory \citep{1991ApJ...379..440B}, the mass function of dark matter haloes is defined as the comoving number density of haloes with mass between $M$ and $M+dM$ . |
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