The Consequences of the Cosmic Star-Formation Rate: X-ray Number Counts
A. Ptak\altaffilmark{1}
R. Griffiths
We discuss the observable consequences for the detection of galaxies in the X-ray bandpass resulting from a peak in the cosmic star-formation rate at a redshift $>$ 1. Following White \& Ghosh, we assume a large evolution in the X-ray/B luminosity ratio at $z \sim 0.5-1.5$ resulting from the X-ray binaries that have evolved from stars formed at $z > 1-2$. Using the HDF-N redshift survey data and the locally observed X-ray/B luminosity ratio as a guide, we estimate a median X-ray flux (2-10 keV) on the order of $8 \times 10^{-18}$ \ergcms ~for galaxies in the HDF-N, which is consistent with a signal derived from a stacking analysis of the HDF-N Chandra data by Brandt et al. (2001). We also predict the number counts in deep X-ray surveys expected from normal galaxies at high redshift. %We also estimate that at fluxes of below $X \times 10^{-18}$ %\ergcm galaxies will begin will begin to dominate AGN in number counts, %with a %number density of $\sim 5 %arcmin^{-2}$. %Assuming a linear extent of 10 kpc, these galaxies will %have an X-ray angular extent on the order $\sim 1.2''$, meaing that it is %possible that Chandra will be able to marginally resolve them in ultra-deep %exposures. %The large increase in the %relative population of %star-forming dwarf and irregular galaxies with redshift observed in optical %surveys implies that on the order of $\sim 50\%$ of these galaxies should %exhibit soft thermal spectral components similar to those observed in nearby %starburst galaxies such as M82 and ultra-luminous IR galaxies.
xrb_gal_evolution_preprint.tex
%\documentstyle[aasms4]{article}
\documentclass{aastex}
\usepackage{emulateapj5}
%\documentclass[preprint2]{aastex}

\newcommand {\cps} {counts s$^{-1}$}
\newcommand {\ergs} {erg s$^{-1}$}
\newcommand {\ergcms} {erg cm$^{-2}$ s$^{-1}$}
\slugcomment{Accepted for publication in ApJL}
\begin{document}
\title{The Consequences of the Cosmic Star-Formation Rate: X-ray Number Counts}
 
\author{A. Ptak\altaffilmark{1}, R. Griffiths}
\affil{Carnegie Mellon University, Dept. of Physics, Pittsburgh, PA 15213}
%\email{ptak@pha.jhu.edu}
\author{N. White}
\affil{NASA/GSFC LHEA, Greenbelt, MD 20771}
\author{P. Ghosh}
\affil{Tata Institute of Fundamental Research, Bombay 400 005, India}
\altaffiltext{1}{Present address: The Johns Hopkins University,
Dept. of Physics and Astronomy, 3400 N. Charles St., Baltimore, MD
21218; ptak@pha.jhu.edu}
\begin{abstract}
We discuss the observable consequences for the detection of galaxies 
in the X-ray bandpass resulting from
a peak in the cosmic star-formation rate at a redshift $>$ 1.  Following White
\& Ghosh, we assume a large evolution in the X-ray/B luminosity ratio at
$z \sim 0.5-1.5$
resulting from the X-ray binaries that have evolved from stars formed at $z
> 1-2$. Using the HDF-N redshift survey data and the locally observed
X-ray/B luminosity ratio as a guide, we estimate a median X-ray flux (2-10
keV) on the order of $8 \times 10^{-18}$ \ergcms ~for galaxies in the HDF-N,
which is consistent with a
signal derived from a stacking analysis of the HDF-N Chandra data by Brandt
et al. (2001).  We also predict the number counts in deep X-ray surveys
expected from normal galaxies at high redshift.
%We also estimate that at fluxes of below $X \times 10^{-18}$ 
%\ergcm galaxies will begin will begin to dominate AGN in number counts, 
%with a
%number density of $\sim 5  
%\rm arcmin^{-2}$.  
%Assuming a linear extent of 10 kpc, these galaxies will
%have an X-ray angular extent on the order $\sim 1.2''$, meaing that it is
%possible that Chandra will be able to marginally resolve them in ultra-deep
%exposures.
%The large increase in the
%relative population of 
%star-forming dwarf and irregular galaxies with redshift observed in optical
%surveys implies that on the order of $\sim 50\%$ of these galaxies should
%exhibit soft thermal spectral components similar to those observed in nearby
%starburst galaxies such as M82 and ultra-luminous IR galaxies.  
\end{abstract}
\keywords{evolution-galaxies:evolution--X-rays: galaxies--X-rays}
\section{Introduction}

The X-ray emission of nearby normal spiral
galaxies has been observed to be dominated
by X-ray binaries (XRB; see Fabbiano 1989 for a
review).  There is a strong correlation between the optical and X-ray
luminosities of galaxies which is also consistent with an XRB population
dominating the X-ray emission (i.e., assuming that XRB constitute an ~ constant fraction of stars in a galaxy).   Deep optical, IR and sub-mm surveys suggest that the peak of 
the cosmic star-formation lies at redshifts on the order of 1-2 or more
\citep{bla99}.  White \& Ghosh (1998, hereafter WG98) predicted that X-ray
binaries that form from this early star-formation activity should result in
the enhancement of X-ray emission in galaxies, most notably around a redshift
of 0.5-1.0 as the massive stars supernova forming low-mass X-ray binaries
(LMXRBs) containing neutron stars. or blackholes  The
LMXRBs containing neutron stars in turn evolve to form millisecond radio
pulsars (MRP), resulting in the observed 
distribution of XRB and MRP in the Galaxy and nearby galaxies.   Further
modeling by Ghosh \& White (2001; hereafter GW01) has been undertaken to
refine their previous 
results, with the primary improvement being the use of more recent
star-formation rate (SFR) history estimates (e.g., Blain et al. 1999).  These
more recent SFR history estimates take into account sub-mm data which is
sensitive to dusty (and hence obscured) high-redshift galaxies that would be
missed by optical/UV surveys.  The main impact of these modifications is that
the current estimate of the enhancement of X-ray flux from galaxies (due to
LMXRB) peaks at $z \sim 1.5$ rather than $z \sim 1.0$.  The modeling of WG98
and GW01 also includes the predictions for enhancements of high-mass X-ray
binaries (HMXRB).  We defer evaluation of the HMXRB enhancement for future
work, but note here that since HMXRB have a much shorter evolutionary time
scale than LMXRB, the HMXRB enhancement (along with other effects of starburst
activity) would closely track the SFR history and therefore occur at higher
redshifts than the LMXRB enhancement discussed here.

A test of these X-ray evolution models would be to evolve the local universe
X-ray luminosity function and derive the number counts of galaxies expected at
given flux levels (i.e., in a logN-logS diagram) for comparison with deep
X-ray surveys.  Unfortunately, the X-ray luminosity function of nearby
galaxies is not known directly because the typical X-ray flux of galaxies is
of order of $\log F_X = -13$ -- $-14 \rm \ ergs \ cm^{-2} \ s^{-1}$ which
is below the limiting flux of existing X-ray all-sky surveys (e.g, the ROSAT
All-Sky Survey has a limiting flux on the order of 
$\log F_{0.5-2.0 \rm keV} \sim -12$ -- $-13 \ \rm  \ ergs \ cm^{-2} \
s^{-1}$; Voges et al. 1999).  Here we take an alternative approach which is to
use the known X-ray/optical luminosity correlation given in \citet{dav92},
determined from Einstein
data, to estimate the X-ray luminosities and fluxes of galaxies in the HDF-N,
where optical luminosities and redshifts have been established.  Since the
expected X-ray flux of high-redshift galaxies is low, \citet{bra01}
performed a stacking analysis of a {\it Chandra} observation of the HDF-N.  We
show 
below that the X-ray flux distribution derived from our analysis is consistent
with the galaxy flux signal detected by {\it Chandra}.  A secondary goal of
this 
paper is to estimate the logN-logS distribution of galaxies (based on the
HDF-N) in order to predict X-ray number counts that could be detected by more
sensitive surveys.

\section{Methodology}
%In order to make a reasonable estimate of X-ray number counts expected from
%a deep survey due to (non-AGN) galaxies with enhanced X-ray emission, we used
%the Hubble Deep Field redshift survey presented in \citet{coh00}.  
As discussed above, our main goal is to estimate the X-ray flux and luminosity
for galaxies based on their optical luminosity, the X-ray/optical luminosity
correlation and X-ray luminosity evolution models.
The HDF-N ``proper'' sample presented in \citet{coh00} contains redshifts and
R-magnitudes for 125 galaxies spanning $\rm 4.75 \ arcmin^{2}$.
%The redshift
%distribution is shown in Figure 1.
%\begin{figure}[htbn]
%\plotone{hdf_z.ps}
%\caption{The redshift distribution of the HDF-N galaxies.}
%\end{figure}
The X-ray/optical correlation given in \citet{dav92} is based on B-band
luminosities, so accordingly the observed R-band magnitudes must be converted
to rest-frame B-band magnitudes.  
%To get an initial estimate of the X-ray luminosity
%We converted the observed R magnitudes to rest-frame B luminosities by
We used the k-correction plots in \citet{fre94} which include R to B band
corrections based on optical and UV observations of galaxies 
(which we caution only extends to z=0.6), from which we derived the B-band
luminosity for each galaxy (we used $H_0 = 70 \rm \ km \ s^{-1} \ Mpc^{-1}$
and
$q_0 = 0.1$ throughout this paper). Here we are primarily interested in the
mean properties of galaxies and accordingly did
not segregate by galaxy type, which we differ to future work (see also below).
The k-corrections as a function of galaxy type vary by $\sim 1$ magnitude,
which is somewhat larger than the scatter found for control galaxies by
\cite{fre94}, and accordingly we assume an uncertainty of 1 magnitude.

%In order to convert the observed I magnitudes to rest-frame B magnitudes, we
%fit a linear model to the ``k+color'' plot in CFRS VI in the z<1.0 and z>1.0 
%redshift regimes, resulting in B magnitudes in the AB system ($\rm B_AB$).
%After setting $\rm m_b = B_AB + 0.17$, we converted from $\rm m_b$ to flux
%using (based on NED values for some nearby galaxies):
%\begin{equation}
%\rm f_B = 10^{-(m_b + 55.928)/2.5} \times (6.81 \times 10^{14}) \times 
%(0.7 \times 10^{3}) \ ergs \ cm^{-2} \ s^{-1}
%\end{equation}
%The resulting distribution in B luminosity ($\rm L_B$) is shown in Figure 2.
%\begin{figure}[htbn]
%\plotone{B_hist.ps}
%\caption{The derived distribution in B luminosity for the CFRS galaxies.}
%\end{figure}

These B luminosities were then converted to X-ray luminosities using the
$\rm L_{0.5-4.5 \ keV}/L_B$ relation given in \citet{dav92}.
Assuming a power-law spectrum with a photon index of 1.8 and neutral
absorption $N_H < 10^{21} \ \rm cm^{-2}$ (the galactic column towards the
HDF-N is $1.6 \time 10^{20} \rm cm^{-2}$; Stark et al. 1992), which is
consistent with an 
XRB-dominated spectrum and the observed 2-10 keV X-ray spectra of nearby
galaxies (c.f., Ptak et al. 1999 and references therein), $F_{2-10 \rm \
keV} = F_{0.5-4.5 \rm \ keV}$ to within $\sim 
15\%$. Similarly, these same spectral assumptions also imply a $F_{0.5-2.0 
\rm keV}$ flux that is $\sim (0.5-0.6)F_{0.5-4.5 \ \rm keV}$ (at redshifts
exceeding 0.5, $F_{0.5-2.0 \ \rm keV} = 0.55 F_{0.5-4.5 \ \rm keV}$ for all
$N_H < 10^{21} \ \rm cm^{-2}$) and we adopt 1.0 and 0.55 as the conversion
factor to
the 2.0-10.0 keV and 0.5-2.0 keV bandpasses.  We also note
that the stellar evolution models we are concerned with here are relevant only
on long look-back time scales, and therefore only the lower-mass, older stellar
populations have a significant impact in our analysis.   
Ignoring the younger stellar populations
biases our results in the sense of underestimating the expected X-ray flux
for starburst systems which tend to exhibit enhanced
supernovae and high-mass X-ray binary populations (see Fabbiano 1989).
Since the \citet{dav92} correlation was performed using all
galaxies types, the differing amount of X-ray production as a function of
galaxy type inherently contributes to the scatter of the correlation.
Accordingly, the results of this paper should be accurate in a statistical
sense but should not be applied to any individual galaxy.  
%We expect this type of spectrum to be typical, for both galaxies and
%AGN, except for highly-absorbed type-II AGN and ultraluminous starburst
%galaxies which will likely have flatter spectra which are more likely to
%exhibit spectra with a photon index $\sim 1.0$.  X-ray source are
%observed to have harder spe ctra such along these lines at fainter fluxes
%(c.f., Giacconi et al. 2000, Griffiths et al. 2001) which is consistent with
%these populations becoming more prominent at higher redshifts. We
%conservatively set $F_{2-10 \ \rm keV} = F_{0.5-4.5 \rm \ keV}$ to facilitate
%comparison with deep X-ray 
%survey results, noting that at the faint end our galaxy fluxes may be
%underestimated by a factor of ~ 2.

The resultant B and X-ray luminosity distributions
derived from this procedure are shown in Figure 1.  The errors given in
this figure are derived from a Monte-Carlo approach in which the conversion
to the B and X-ray bandpasses was repeated (1000 iterations) with gaussian
deviates with a standard deviation of 1 magnitude added to the resulant B
magnitudes and gaussian deviates with standard deviation of 1 added to the log
X-ray luminosities (i.e., simulating an order-of-magnitude scatter in
$L_X/L_B$).   Errors derived in this way were comparable to the counting
errors that would be expected in each histogram bin (i.e., $\sqrt{N}$,
where N = the number of galaxies in a given histogram bin).  
The mean galaxy 
$L_{2-10 \rm \ keV}$ is $3.8 \times 10^{39}$ \ergs, which is comparable to the mean value for
passive galaxies given in \citet{geo99} of
$3.2 \times 10^{39}$ \ergs (after adjusting to our values of $H_0$ and $q_0$).
These values are somewhat lower than other nearby galaxies X-ray luminosity
estimates (e.g., Fabbiano, Trinchieri, \& McDonal 1984) however it should
noted that here and in \citet{geo99} active (including narrow-line) and
starburst galaxies have not been (explicitly) included in the analyses.
% FIGURE 1
\begin{figure*}[htbn]
\epsscale{1.5}
\plottwo{hdf_10kpc_L_B_10jul01.eps}{hdf_10kpc_f0.5-2.0_f2-10_L_X_10jul01.eps}
\caption{The estimated B-band (left) and X-ray luminosities (right)
for the HDF-N galaxies.  The error bars shown are derived from simulations
that incorporate a 1 magnitude uncertainty in the k-corrections and an order of magnitude uncertainty in the X-ray/optical flux ratio.  
The X-ray luminosity distribution is given for the unevolved case (solid line
and points) as well as that derived from the ``Peak-M'' (dashed line) and
``Gaussian'' (dotted line) evolution models.}
\end{figure*}

%As a consistency check, the $L_X$/$L_B$ correlation in Geogantopoulos,
%Basilakos, \& Plionis (1999; astro-ph 9902037; hereafter GBP) is shown
%together with the 
%values used for the CFRS galaxies in Figure 4.  Evidently, DJF found a higher
%value of $L_X$/$L_B$ than GBP for most values of GBP did, who based their
%analysis of Einstein fluxes associated with the Luis, Filippenko \& Sargent
%(1997) sample of nearby galaxies.  However, the average estimated X-ray
%luminosity of a CFRS galaxy in our analysis is $5.7 \times 10^{40}$ \ergs,
%to be compared with mean values of $L_X$ of $2.0 \times 10^{39}$ \ergs and
%$7.9 \times 10^{39}$ ergs for norma/HII and LINER galaxies, respectively, in
%the GBP sample.  Note that the mean luminosity for CFRS galaxies includes some
%degree of {\it optical} evolution (the mean redshift is $\sim 0.5$), which of
%course would be expected to result in a higher mean X-ray luminosity estimate.
%\begin{figure}
%\plotone{lx_vs_lb.ps}
%\caption{The estimated X-ray luminosity for the CFRS galaxies (prior to the
%application of any $L_X/L_B$ evolution) compared to the estimates given for
%local galaxies, as a function of $L_B$, in GBL.}
%\end{figure}

\subsection{Evolution in $L_X/L_B$}
We proceed now assuming that the ratio $\rm L_X/L_B$ evolves as a result of an
excess of X-ray binaries at earlier epochs.  
%Our evolution model is 
%\begin{equation}
%L_X/L_B(z) = L_X/L_B(0) \times 10^{1.6exp[-(z-1.0)^2]-0.6}
%\end{equation}
%This function is plotted in Figure 5.  
We use the evolutionary models ``Peak-M'' and ``Gaussian'' given in
\citet{gho01}, 
plotted in Figure 2.  Both models are based on fits to the observed
star-formation rate using optical/UV observations, however the ``Gaussian''
model also includes a
component with a Gaussian functional form that takes into account the
evolution of the IR luminosity 
function using IR and sub-mm data (c.f., Blain et al. 1999).
These models only take into account the relative change
in X-ray luminosity as a function of redshift, however in this paper we are
attempting to derive the X-ray luminosities of galaxies based on the
rest-frame B-band 
luminosity.  Accordingly, any optical evolution must be taken into
account explicitly before we could apply our X-ray evolution models.  
To this end, we took the mean and standard deviation of the
B-band luminosities in redshift bins large enough to contain at least 20
galaxies and fit $\log L_B$ as a function of z with a linear model
(also shown in Figure 2).  The X-ray luminosities were evolved by
multiplying them by the ratio $E_X(z)/E_B(z)$, where $E_X(z)$ and $E_B(z)$ are
the X-ray and optical (after normalizing to z=0) evolution models shown in
Figure 2.  The net amount of optical evolution derived in this way amounts to
only a factor of $\sim 2$ from a redshift of 0 to 1.
% FIGURE 2
\begin{figure*}[htbn]
\plottwo{pranab_models_10jul01_z_vs_L_X.eps}{l_b_evol_resized.ps}
\caption{(left) Evolution models ``Peak-M'' (solid line) and
``Gaussian'' (dashed line) for the 
X-ray luminosity of normal galaxies, normalized at z=0, from
\citet{gho01}. (right) Observed evolution in mean B-band luminosity
for the HDF-N galaxies, with the linear fit to $\log L_B$ versus z plotted
as a solid line.  The error bars shown were derived by the dispersion of
luminosities in each redshift bin.}
\end{figure*}

\section{Results}
Applying these procedures, the mean
2-10 keV X-ray galaxy flux increased from $2.3 \times 10^{-18}$ \ergcms~ to 4.2
and $8.4 \times 10^{-18}$ 
\ergcms~ and the mean 2-10 keV X-ray luminosity increased from $3.8 \times
10^{39}$ \ergs~ to 5.3 and $19. \times 10^{39}$ \ergs~ for the ``Peak-M'' and
``Gaussian''
models, respectively (with 0.5-2.0 keV values a factor of 0.55 lower as
discussed above).  The distribution of $L_X$ and $F_X$ (before and after 
including evolution) is shown in Figures 1 and 3.  The flux density implied is
4.3 and $7.8 \times 10^{-13} \ \rm ergs \ s^{-1} \ cm^{-2} \ deg.^{-2}$ in the
0.5-2.0 keV and 2-10 keV bandpasses, or 2-4\% of the 2-10 keV X-ray
background.  \citet{kun01} find that the extra-galactic X-ray backround in the
1-2 keV bandpass is $\sim 5.7 \times 10^{-12} \ \rm ergs \ s^{-1} \ cm^{-2} \
deg.^{-2}$.  With same spectral assumptions discussed above, $F_{1-2 \rm
\ keV} \sim 0.3F_{0.5-4.5 \ \rm keV}$, implying a 1-2 keV flux density of $\sim
2.3  \times 10^{-13} \ \rm ergs \ s^{-1} \ cm^{-2} \ deg.^{-2}$, or $\sim
4\%$ of the observed 1-2 keV background.
% Tozzi et al. cites Mush. (2000) for flux dens. (1-2 keV) =
% 5.3e-13/sq. deg./0.12 or 4.4e-12/sq. deg. 
We repeated our analysis after only including
galaxies with redshifts in the range of 0.5-1.0 (55 galaxies) which 
resulted in a mean 2-10 keV X-ray
flux of $\sim 7.0 \times 10^{-18}$  \ergcms (indicating that our results are
dominated by galaxies in this redshift range).  
%We also repeated our analysis
%using the ``Peak-M'' model for comparison. This SFR model only includes fits
%to optical/UV data and is the SFR profile used in \citet{whi98}.  This
%resulted in a mean X-ray flux of $4.3 \times 10^{-18}$ \ergcms~ and a mean
%X-ray luminosity of $5.3 \times 10^{39}$ \ergs, or an effect that is a factor
%of $\sim 2$ smaller than the ``Gaussian'' model.
% FIGURE 3
\begin{figure*}[htbn]
\epsscale{0.8}
\plotone{hdf_10kpc_f0.5-2.0_f2-10_F_X_10jul01.eps}
\caption{0.5-2.0 keV and 2-10 keV flux distributions predicted for 
HDF-N galaxies.   The lines and errors are defined as in Figure 1.}
\end{figure*}

% \section{Number Counts and Simulation}
% In order to increase the field size beyond 112 $\rm arcmin^2$ we selected
% galaxies at random from the CFRS list at a density of $564/112 \sim 5 \rm
% arcmin^{-2}$.  In order to accomidate the entire ACIS-S field of view we
% simulated a 90' by 90' regions, or $\sim 41,000$ sources.
% During this process, we introduced an order of magnitude
% scatter to the $L_X/L_B$ ratio (as observed in the DJF correlations) by
% adding a Gaussian deviate logarithmatically.  Similarly, we assumed that
% the X-ray extent of each galaxy was 5 kpc (the half-light radius of the
% typical MDS galaxy at a redshift of 0.5) with a scatter of a factor of 2
% (applied in the same fashion).  The resultant distribution of sizes is
% shown in Figure 6. These figures show that while arcsecond resolution will
% be good enough to resolve several galaxies in a large field, given the
% typical size of an X-ray field of view (i.e., 10' or so), sub-arcsecond
% resolution will be necessary to resolve a typical galaxies at these redshifts.
% \begin{figure}[htbn]
% \plottwo{size_hist.ps}{size_fx.ps}
% \caption{(left) The distribution of half-light radii expected for the X-ray
% extents of the CFRS-type galaxies.  (right) The X-ray extent as a function
% of X-ray flux for a 90' by 90' field.}
% \end{figure}
% 
% The logN-logS distribution expected from the above discussion is shown in
% Figure 7. The points give the distribution of the original CFRS sample prior
% to introducing the scatter in $L_X/L_B$, while the solid line shows the
% distribution of resulting from the selection procedure describe above (in
% effect, incorporating scattter numerically).  Also shown are logN-logS
% distributions derived from the ASCA 2-10 keV luminosity function given in
% Boyle et al. (1998) (shown with a dot-dash line), representing AGN, and
% the distribution resulting from converting the IR luminosity function given in
% Saunders et al. (1989), converted to the X-ray bandpass using the IR/X-ray
% correlation in Green, Anderson \& Ward (1992).  The ASCA 2-10 keV number
% counts overestimate the XRB by $\sim 50\%$, so the extrapolation down to these
% fluxes is obviously not physical.  Accordingly, in the simulation below we
% adopted a logN-logS relation based on the Cagnoni et al. survey from $5
% \times 10^{-14}$ \ergcms, the Hassinger et al. Lockman Hole survey from $2
% \times 10^{-15} - 5 \times 10^{-14}$ \ergcms (converted to the 2-10 keV
% bandpass), and a flatish power-law below $2 \times 10^{-15}$.  These flux
% ranges are based on the limitng fluxes of the respective surveys (i.e, $F_X
% \sim 10^{-15}$ \ergcms in the 0.5-2.0 keV Lockman Hole survey).
% (These two curves were
% computed for the 2-10 keV bandpass, but for $\Gamma = 1.8, N_H = 3 \times
% 10^{20}$, these two fluxes are equal.)  From these figures it is evident that
% the optically-driven X-ray number count estimates exceed the IR-driven X-ray
% number count estimates at fluxes below $\sim 3 \times 10^{-15}$ \ergcms.
% Physically, this would correspond to X-ray sources being detected with an
% optical but no IR counterpart.  This is problematic since it is would be
% difficult to obscure IR emission and not optical emission, although other
% selection effects may be contributing (i.e., the limiting sensitivity of the
% CFRS and IRAS surveys).
% To first order the
% ratio of the two curves gives an estimate of the X-ray emission due to
% on-going starburst activity (in the IR case) and past, evolved starburst
% activity, which has sense resulted in old stellar populations and X-ray
% binaries.  Both estimates exceed the AGN number counts below $\sim 2 \times
% 10^{-16}$ \ergcms.  The current 0.5-2.0 keV flux limit in a deep survey is
% $10^{-15}$ \ergcms, where AGN completely dominate both estimates.
% The galaxy and AGN counts comprise $\sim 11\% (2.2 \times 10^{-12} \rm \ ergs
% \ cm^{-2} \ s^{-1} \ deg^{-2})$ and $\sim 87\% (1.7 \times 10^{-11} \rm \ ergs
% \ cm^{-2} \ s^{-1} \ deg^{-2})$ of the XRB.
% \begin{figure}[htbn]
% \plotone{xray_lognlogs.ps}
% \caption{logN-logS distributions.  The points give the results of the direct
% estimate of the X-ray fluxes of the CFRS galaxies.  The solid line shows the
% results of resampling the X-ray fluxes over a wider field of view, and also
% incorporates the scatter in the $L_X/L_B$ correlation.  The dashed line gives
% the logN-logS estimate based on the IR luminosity function (see text).  The
% dot-dashed line gives the logN-logS estimate based on the ASCA 2-10 keV
% luminosity function (in effect, an extrapolation based on the ASCA logN-logS
% relation), which as shown overstimates the XRB.  THe dot-dot-dot-dash line
% shows a composite logN-logS relation based on various surveys, exptrapolated 
% to lower fluxes to comprise $\sim 85\%$ of the XRB.}
% \end{figure}
% 
% \subsection{AXAF ACIS-S}
% \subsubsection{Images}
% The effective area of AXAF ACIS-S is $\sim 400$ times smaller than that
% proposed for the final mirror configuration on XEUS.  However, the AXAF
% field of view is considerably larger than the $\sim 5-10'$ FOV of the
% Wide-Field Imager (WFI) on XEUS, which only comprise the center-most of the 6
% ACIS-S CCDs.  We performed a 1 Ms simulation using the AXAF simulator {\sc
% MARX}.  The results is shown in Figure 8.  The non-AGN galaxies are shown in
% red and the AGN galaxies are shown in blue.  The non-AGN galaxies were
% simulated with a spectrum of $N_H = 3 \times 10^{20}$, $\Gamma = 1.8$,
% and the AGN where simulated with 50\% having a spectrum of $N_H = 1 \times
% 10^{20}$, $\Gamma 
% = 1.0$ (highly-absorbed, redshifted Sy 2s), 25\% with $N_H = 1 \times
% 10^{20}$,
% $\Gamma = 2.0$ (Sy 1s), and 25\% with $N_H = 3 \times 10^{21}$, $\Gamma =
% 1.7$ (moderately aborbed Sy 2s).  This combination of spectra results in a
% 2-10 keV slope of $\sim 1.4$.
% The WFPC2 FOV
% ($\sim 2.5'$ on
% each side) is shown in green for comparison.  The FOV of Constellation-X will
% be on this order.  The area of the Constellation-X is on the order of 36 times
% that of ACIS-S, so a similiar number of counts would be expected in a $\sim
% 30$ ks Constellation-X observation.
% \begin{figure}[htbn]
% %\plotone{cfrs_x_y_flux_spec_size_z_27jan99_b5.ps}
% \caption{A 1 Ms ACIS-S simulation based on the logN-logS curves shown in
% Figure 7 for non-AGN galaxies (red) and AGN (blue).  }
% \end{figure}
% 
% \subsubsection{Spectra}
% The above simulation assumes that the sources will have a spectrum similiar
% to an unabsorbed power-law with $\Gamma = 1.8$, absorbed by a Galactic
% column of $\sim 3 \times 10^{20} \rm \ cm^{-2}$.  This is also the spectrum
% observed in type-I AGN.  It is likely, based both on the IR-driven number
% counts and the observed positive evolution of irregular and peculiar galaxies
% in the MDS, that a large fraction of these galaxies will have a significant
% thermal component in their spectra.  To test the level at which this component
% could be constrained, we used the best-fitting model for the ASCA spectrum of
% M82 and simulated it redshifted to z=0.5 (without any evolution).  This
% resulted in a 0.5-4.5 keV flux of $2 \times 10^{-17}$ \ergcms, which is
% typical of the galaxies discussed above.  A 100 ks XEUS observation would
% constrain the temperature of the thermal flux in this case to within $15\%$.
% XXX Also discuss fits with soft component scaled by 0.1, 0.5, and 2.0XXX.
% \begin{figure}[htbn]
% %\plotone{m82_xp8_wfi_zcevmkl5pl_z0.5_100ks_pl.ps}
% \caption{The residuals from a power-law fit to a 100 ks XEUS CCD spectrum of
% M82 at z=0.5}
% \end{figure}
We proceed now to the question of the numbers of galaxies expected
to be detected as a function of flux in ultra-deep {\it Chandra}, 
{\it XMM-Newton}, or
future X-ray surveys.  To address this, we derived the ``logN-logS''
number count distribution (i.e., the number of galaxies exceeding flux S as a
function of flux)
implied by our analysis, shown in Figure 4, using the HDF-N area sited above. 
%The galaxy data points flatten
%below $F_X = 10^{-18}$ \ergcms~ due to the redshift completeness limit in Cohen
%et al. (2000) at R=24, and accordingly only data points above this flux limit
%should be considered complete. 
The galaxy number counts have been corrected for spectroscopic completeness
using Figure 1 from \citet{coh00}.
This figure also shows the 
fits to the 0.5-2.0 keV and 2-10 keV HDF-S logN-logS distrubitions
\citep{toz01} (note that these curves are extrapolations below fluxes of $\sim
10^{-16}$ and $10^{-15} \rm \ ergs \ cm^{-2} \ s^{-1}$ for the soft and hard
bands, respectively).
The 2-10 keV HDF-S logN-logS in the $S=10^{-15} - 5 \times
10^{-14}$ \ergcms~ 
range is in good agreement with the HDF-N logN-logS curve given in
\citet{gar01}, where fluctuation analysis implies that the logN-logS curve 
flattens somewhat below $S=1.0 \times 10^{-15}$ \ergcms.  The total (i.e.,
including AGN) source densities determined by \citet{bra01} are marked
which also implies a flattening of the X-ray logN-logS.  Note that the results
of the stacking analysis in \citet{bra01} cannot be plotted on this
diagram since by design the analysis was done around optically-detected
galaxies without significant X-ray counterparts and hence the area is
not well defined.
%The dotted-line shows
%an extension of the Chandra logN-logS below this flux limit assuming that the
%slope flattens from -1 to -0.5.  The dot-dashed line shows a fit to the data
%points above $10^{-18}$ \ergcms, extrapolated to lower fluxes, and the dashed
%line shows a fit similarly derived from 
%We repeated our analysis with an alternative evolution model (model
%``Peak-M'' in \citet{gho01}) for comparison.  
%Figure 4 also shows the logN-logS derived assuming the ``Peak-M'' SFR model
%rather than the ``Gaussian'' model.
Depending on the amount that the AGN logN-logS flattens, the total X-ray 
logN-logS may become dominated by normal galaxies at fluxes below 
$\log F_X = -17$ -- $-18$ \ergcms, particularly in the soft band.  
% FIGURE 4
\begin{figure*}
\epsscale{2.0}
\plottwo{gal_lognlogs_0.5-2.0kev_19jul.ps}{gal_lognlogs_2.0-10.0kev_19jul.ps}
\caption{The logN-logS for galaxies derived from the HDF-N estimates for the
``Gaussian'' (diamonds) and ``Peak-M'' evolution models in the 0.5-2.0 kev
(left) and 2.0-10.0 keV (right) bandpasses.  The solid lines give the
logN-logS double power-law fit
from \citet{toz01} based on the Chandra observation of the HDF-S (note that
this logN-logS includes all contributions to number counts).   
The square points mark the source density determined
in the 500 ks Chandra HDF-N observation \citep{bra01}. $F_X = 10^{18}$
\ergcms~ corresponds to $R\sim24$.}
\end{figure*}


\section{Discussion}
We have estimated the X-ray fluxes of galaxies in the Hubble Deep Field using
the known X-ray/B-band luminosity correlation and taking evolution in the
X-ray binary population of the galaxies into account (using the ``Gaussian''
and ``Peak-M'' models in GW01).  Here we are only attempting to estimate the
LMXRB contribution to the galaxy fluxes, which should dominate the X-ray
fluxes unless significant starburst and/or AGN activity is present.
The mean 2-10 keV X-ray
flux that the Gaussian model predicts is $\sim 8.2 \times 10^{-18}$  \ergcms~
which can 
be compared with $\sim 1.7 \times 10^{-17}$ \ergcms ~obtained from a stacking
analysis of a 500 ks {\it Chandra} observation of the HDF-N (converted to the
2-10 keV bandpass from a signal of $2.3 \times 10^{-17}$ \ergcms~ in the
0.5-8.0 keV bandpass assuming the same spectrum as discussed above) determined
by \citet{bra01}.  The ``Peak-M'' model predicts a mean X-ray flux a factor of
$\sim 3.5$ lower than the ``Gaussian'' model.
%Given the 
%uncertainties (most notably the large scatter in the nearby galaxy
%X-ray/optical correlation), this excellent agreement may be biased by
%selection effects. 
The ``Gaussian'' model is therefore predicting a signal which is a factor of
$\sim 2$ less than the signal observed, although we note that \citet{bra01}
selected optically-bright galaxies (a sample of 11) for their stacking
analysis, and our estimate of the mean galaxy X-ray luminosity 
(prior to the application of any
evolution) is evidently somewhat lower than that assumed by \citet{bra01} but
is nevertheless consistent with other estimates.  In both the hard and soft
bandpass, we are predicting that galaxies make up $\sim 4\%$ of the X-ray
background down to a flux of $\sim 10^{-18} \ \rm ergs \  cm^{-2} \ s^{-1}$.
%For comparison, \citet{hel01} predict that starburst
%galaxies likely constitute up to $\sim 20-25\%$ of the hard X-ray backgound.
% One idea... optically-bright HDF galaxies are effectively UV selected and
%hence have little dust extinction.  But that should also bias things towards
%a lower amount of dust extinction but should also be selecting on younger
%stellar populations.

%A telescope with m$^2$ effective areas will likely be able to directly observe
%the galaxies and confirm these number count estimates.  
The best test of these models would be the direct detection of high-z galaxies
in the X-ray bandpass, obviously with sufficient spectroscopic 
identification to
rule out an AGN contribution to the X-ray flux.  
This would require an X-ray detection sensitivity on the order of $10^{-17}$
\ergcms, which would imply an exposure on the order of 10 Ms for 
{\it Chandra}
(i.e., the effective exposure in the stacking analysis was 5 Ms), while even
such a large exposure would be insufficient for {\it XMM-Newton} to reach these
detection sensitivites (due to {\it XMM-Newton} becoming background-limited at
very large exposures).  Optical (and, to a lesser extent, IR) spectroscopic 
identifications
could possibly miss highly-obscured AGN or low-luminosity AGN which would
produce enhanced 
X-ray fluxes relative to normal galaxies. A simple expectation is that the
X-ray emission of galaxies would be extended (on spatial scales comparable to
the optical emission), while the X-ray image of galaxies dominated by AGN
would of course be unresolved.  The half-light radius 
of galaxies in the HST Medium Deep Survey was typically $\sim 0.1-1.0''$,
with a median value around $0.6''$ \citep{rat99}.  Arcsecond resolution will
therefore be necessary to detect any extension to galaxies.
%However, note that in such an ultra-deep survey, galaxies would likely be
%detected which are still dominated by HMXRB.  HMXRB tend to have harder
%spectra than LMXRB, and so these galaxies would be expected to have harder
%spectra.  However, obscured AGN are also expected to be more numerous at
%higher redshifts and AGN spectra are observed to harden on
%average as a function of redshift \citep{gri01}, limiting the use
%of X-ray spectral shape as a discriminant of galaxies and AGN in deep surveys.

%Large-angle serendipitous source surveys based on the Chandra and XMM-Newton
%archives should serve to provide a more direct measure of the optical/X-ray
%correlation as well as estimate the X-ray luminosity function in the 2-10 keV
%bandpass.  Since this analysis strongly depends on the  , which would considerable improve the accuracy of X-ray galaxy
%evolution predictions.  

% Since galaxies and AGN are likely to have similiar spectral properties, and
% spectral analysis requires a large number of counts, an easier way to
% distinguish galaxies from an AGN in a deep survey image 
% would be to check to source extension.  Figure 5 shows the expected angular
% extent of the X-ray emission of the 
% galaxies assuming that the XRB are distributed over a region with a linear
% extent of 10 kpc, including a factor of 2 dispersion in the linear sizes.
% This figure implies that 1'' or so resolution would be sufficient to resolve
% galaxies.  We caution that these size estimates may be overly
% optimistic.  Most of the X-ray binaries in spirals galaxies such as M31 are
% concentrated in the kpc-sized bulge region, although it is plausible that the
% binaries settled in the bulges there over Hubble time scales. A less
% model-depenmdent constaint is the fact that the typical size of galaxies in
% the Medium Deep Survey is only 0.7'' (ref XXX), and it is probably unlikely
% that galaxies would have a larger X-ray extent than optical extent.
% 
\acknowledgements
We thank the referee, Paulo Tozzi for useful comments that strengthened
this paper.  This research was
partly funded by NASA contract NAS8-38252 to Pennsylvania State University. 

\begin{thebibliography}{}
\bibitem[Blain et al. (1999)]{bla99}Blain, A., Smail, I., Ivison, R., Kneib,
J.-P. 1999, \mnras, 302, 632
\bibitem[Brandt et al. (2001)]{bra01}Brandt, N., et al. 2001, \aj, in press
(astro-ph/0102411)
\bibitem[Cohen et al. (2000)]{coh00}Cohen, J. et al. 2000, \apj, 538, 29
\bibitem[David, Jones \& Forman (1992)]{dav92}David, L., Jones, C., \& Forman,
W. 1992, \apj, 388, 82
\bibitem[Fabbiano (1989)]{fab89}Fabbiano, G. 1989, \araa, 27, 87 
\bibitem[Frei \& Gunn (1994)]{fre94}Frei, Z. \& Gunn, J. 1994, \aj, 108, 1476
\bibitem[Georgantopoulos, Basilakos, \& Plionis (1999)]{geo99}Geogantopoulos,
I., Basilakos, S. \& Plionis, M. 1999, \mnras, 305, 31
\bibitem[Garmire et al (2001)]{gar01}Garmire, G. et al. 2001, in prep.
\bibitem[Ghosh \& White (2001)]{gho01}Ghosh, P. \& White, N. 2001, submitted
\bibitem[Kuntz, Snowden \& Mushotzky (2001)]{kun01} Kuntz, K., Snowden, S. \&
Mushotzky, R. 2001, \apj, 548, L119
\bibitem[Ptak et al. (1999)]{pta99}Ptak, A., Serlemitsos, P., Yaqoob, T.,
Mushotzky, R. 1999, \apjs, 120, 179
\bibitem[Ratnatunga, Griffiths, \& Ostrander (1999)]{rat99}Ratnatunga, K., Griffiths, R., \& Ostrander, E. 1999, \aj, 118, 86]
\bibitem[Voges et al. (1999)]{voh99}Voges, W., et al. 1999, \aa, 349, 389
\bibitem[White \& Ghosh (1998)]{whi98}White, N. \& Ghosh, P. 1998, \apjl, 504,
L31
\bibitem[Tozzi et al. (2001)]{toz01}Tozzi, P. et al. 2001, \apj, submitted (astro-ph/0103014)
\end{thebibliography}
%\clearpage
%\figcaption{The redshift distribution of the HDF-N galaxies.}
%\figcaption{The estimated B-band (left) and X-ray luminosities (right)
%for the HDF-N galaxies.  The error bars shown are derived from simulations
%that incorporate a 1 magnitude uncertainty in the k-corrections and an order of magnitude uncertainty in the X-ray/optical flux ratio.  
%The X-ray luminosity distribution is given for the unevolved case (solid line
%and points) as well as that derived from the ``Peak-M'' (dashed line) and
%``Gaussian'' (dotted line) evolution models.}
%\figcaption{(left) Evolution models ``Peak-M'' (solid line) and
%``Gaussian'' (dashed line) for the 
%X-ray luminosity of normal galaxies, normalized at z=0, from
%\citet{gho01}. (right) Observed evolution in mean B-band luminosity
%for the HDF-N galaxies, with the linear fit to $\log L_B$) versus z plotted
%as a solid line.  The error bars shown were derived by the dispersion of
%luminosities in each redshift bin.}
%\figcaption{0.5-2.0 keV and 2-10 keV flux distributions predicted for 
%HDF-N galaxies.   The lines and errors are defined as in Figure 1.}
%\figcaption{The logN-logS for galaxies derived from the HDF-N estimates for the
%``Gaussian'' (diamonds) and ``Peak-M'' evolution models in the 0.5-2.0 kev
%(left) and 2.0-10.0 keV (right) bandpasses.  The solid lines give the
%logN-logS double power-law fit
%from \citet{toz01} based on the Chandra observation of the HDF-S (note that
%this logN-logS includes all contributions to number counts).   
%The square points mark the source density determined
%in the 500 ks Chandra HDF-N observation \citep{bra01}. $F_X = 10^{18}$
%\ergcms~ corresponds to $R\sim24$.
%}

\end{document}

astro-ph0108302.extracted_bib
\begin{thebibliography}{}
\bibitem[Blain et al. (1999)]{bla99}Blain, A., Smail, I., Ivison, R., Kneib,
J.-P. 1999, \mnras, 302, 632
\bibitem[Brandt et al. (2001)]{bra01}Brandt, N., et al. 2001, \aj, in press
(astro-ph/0102411)
\bibitem[Cohen et al. (2000)]{coh00}Cohen, J. et al. 2000, \apj, 538, 29
\bibitem[David, Jones \& Forman (1992)]{dav92}David, L., Jones, C., \& Forman,
W. 1992, \apj, 388, 82
\bibitem[Fabbiano (1989)]{fab89}Fabbiano, G. 1989, \araa, 27, 87 
\bibitem[Frei \& Gunn (1994)]{fre94}Frei, Z. \& Gunn, J. 1994, \aj, 108, 1476
\bibitem[Georgantopoulos, Basilakos, \& Plionis (1999)]{geo99}Geogantopoulos,
I., Basilakos, S. \& Plionis, M. 1999, \mnras, 305, 31
\bibitem[Garmire et al (2001)]{gar01}Garmire, G. et al. 2001, in prep.
\bibitem[Ghosh \& White (2001)]{gho01}Ghosh, P. \& White, N. 2001, submitted
\bibitem[Kuntz, Snowden \& Mushotzky (2001)]{kun01} Kuntz, K., Snowden, S. \&
Mushotzky, R. 2001, \apj, 548, L119
\bibitem[Ptak et al. (1999)]{pta99}Ptak, A., Serlemitsos, P., Yaqoob, T.,
Mushotzky, R. 1999, \apjs, 120, 179
\bibitem[Ratnatunga, Griffiths, \& Ostrander (1999)]{rat99}Ratnatunga, K., Griffiths, R., \& Ostrander, E. 1999, \aj, 118, 86]
\bibitem[Voges et al. (1999)]{voh99}Voges, W., et al. 1999, \aa, 349, 389
\bibitem[White \& Ghosh (1998)]{whi98}White, N. \& Ghosh, P. 1998, \apjl, 504,
L31
\bibitem[Tozzi et al. (2001)]{toz01}Tozzi, P. et al. 2001, \apj, submitted (astro-ph/0103014)
\end{thebibliography}