11institutetext: Department of Astronomy & Astrophysics, 525 Davey Lab, The
Pennsylvania State University, University Park, PA 16802, USA; Institute for
Gravitation and the Cosmos, The Pennsylvania State University, University
Park, PA 16802, USA; Department of Physics, 104 Davey Laboratory, The
Pennsylvania State University, University Park, PA 16802, USA; 11email:
<EMAIL_ADDRESS>22institutetext: Department of Physics and Astronomy, Texas
A&M University, College Station, TX 77843-4242, USA; George P. and Cynthia
Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M
University, College Station, TX 77843-4242, USA; 22email:
<EMAIL_ADDRESS>
# Surveys of the Cosmic X-ray Background

W.N. Brandt and G. Yang corresponding author

###### Abstract

We provide a highly concise overview of what X-ray surveys and their
multiwavelength follow-up have revealed about the nature of the cosmic X-ray
background (CXRB) and its constituent sources. We first describe early global
studies of the CXRB, the development of imaging CXRB surveys, and the resolved
CXRB fraction. Second, we detail the sources detected in CXRB surveys
describing their identification, classification, and basic nature. Third,
since active galactic nuclei (AGNs) are the main contributors to the CXRB, we
discuss some key insights about their demographics, physics, and ecology that
have come from CXRB surveys. Finally, we highlight future prospects for the
field.

Keywords Surveys; Cosmic X-ray background; Cosmology: observations; Galaxies:
active; Galaxies; Galaxies: evolution; Galaxies: clusters; Galaxies: groups;
X-ray astronomy

##  1 Introduction

###  1.1 The Cosmic X-ray Background and Early Global Studies

The cosmic X-ray background (CXRB) was the first cosmic background discovered
(Giacconi et al. 1962). Broad-band spectral measurements showed the CXRB
peaked in intensity at 20–40 keV (see Fig. 1), and that its 3–50 keV spectrum
could be acceptably fit with a thermal bremsstrahlung model associated with a
hot, optically thin plasma with a temperature of $kT\approx 40$ keV (e.g.,
Marshall et al. 1980). Furthermore, early all-sky surveys showed the CXRB was
highly isotropic, indicating that it was primarily extragalactic in nature
(e.g., Schwartz 1980). These results led some to argue that the CXRB largely
originates in a hot intergalactic medium. However, such early interpretations
were definitively ruled out by tight constraints upon the Compton-scattering
distortion of the spectrum of the cosmic microwave background (e.g., Mather et
al. 1990).

Contemporaneously with these early global studies of the CXRB, increasingly
sensitive investigations with X-ray observatories were showing that many
extragalactic objects were significant X-ray emitters, including active
galactic nuclei (AGNs), galaxies, and galaxy clusters and groups (e.g.,
Giacconi 1981). These findings indicated that at least some of the CXRB must
arise from discrete sources, motivating the formation and growth of an
industry investigating the discrete-source contributions to the CXRB.

###  1.2 Imaging Surveys of the CXRB: A Very Brief Review

The discrete-source nature of much of the low-energy CXRB was supported as
imaging X-ray survey observations with Wolter telescopes, such as Einstein and
ROSAT, resolved increasing fractions of the CXRB below 2–3 keV (see Fig. 2
left). For example, long-exposure ROSAT surveys in the early-to-mid 1990’s
reached 0.5–2 keV flux limits of $\approx 10^{-15}$ erg cm-2 s-1 and resolved
$\approx 75$% of the soft CXRB into discrete sources with a sky density of
800–900 deg-2, the majority of which were identified as AGNs (e.g., Hasinger
et al. 1998; Schmidt et al. 1998). The nature of the CXRB near its high-energy
peak in intensity, however, remained much less clear. The unobscured and
mildly obscured AGNs mostly discovered in early low-energy surveys did not
appear to have the requisite spectral properties to explain the broad-band
CXRB spectrum, particularly its 20–40 keV peak. However, it was recognized
that additional highly obscured AGNs might be capable of explaining the CXRB
spectrum, as their photoelectric-absorption cutoffs would lie at higher
energies. Most notably, Setti & Woltjer (1989) put forward one of the first
“AGN synthesis models” for the CXRB making this point quantitatively, where
reasonable assumptions about, e.g., AGN obscuration levels, luminosities, and
redshift evolution were shown to be plausibly capable of producing the CXRB
spectrum. Such synthesis models, continually refined in light of new data,
have become a mainstay of CXRB surveys research, aiding with the
interpretation of observational results and making testable predictions for
new observations.

Figure 1: Broad-band spectrum of the CXRB measured by several missions and
experiments as labeled. Note the peak at 20–40 keV. From Cappelluti et al.
(2017).

The sensitive CXRB-surveys industry at energies above 2–3 keV took longer to
develop, largely owing to the technological challenges of focusing and
detecting higher energy X-rays. The ASCA mission performed multiple CXRB
surveys reaching limiting 2–10 keV fluxes of $\approx 5\times 10^{-14}$ erg
cm-2 s-1 at best, detecting up to $\approx 100$ sources deg-2 (e.g., Ueda et
al. 1998). The most sensitive ASCA surveys were source-confused owing to the
limited available angular resolution, making robust source identifications
often difficult. The BeppoSAX mission advanced CXRB surveys at 5–10 keV, owing
to its improved high-energy imaging capabilities, resolving 20–30% of the 5–10
keV CXRB (e.g., Comastri et al. 2001).

Figure 2:  Left: Flux limit vs. solid angle of sky coverage for 0.5–2 keV
surveys from Einstein and ROSAT (green), Chandra (blue), XMM-Newton (red), and
SRG eROSITA (purple). Encircled points represent serendipitous surveys. Some
of the surveys are labeled by name in regions where symbol crowding allows.
Updated from Brandt & Alexander (2015), which provides additional relevant
details. Right: Flux limit vs. solid angle of sky coverage for 8–24 keV
surveys from Swift BAT (red), NuSTAR (blue), and SRG ART-XC (purple).

The superb X-ray telescopes and detectors on Chandra and XMM-Newton, both
launched in 1999, revolutionized CXRB surveys over the $\approx 0.5$–10 keV
band, allowing multiple powerful surveys with up to $\approx 150$–600 times
(depending upon energy band) the sensitivity of previous X-ray missions (see
Fig. 2 left; e.g., Brandt & Alexander 2015). Large samples of up to $\approx
12,000$ sources per survey allowed robust statistical characterization of CXRB
source populations (see Fig. 3 left), and, owing to small 0.3–3′′ X-ray source
positional uncertainties, the majority of the sources could be reliably
matched to multiwavelength counterparts for further characterization. The
surveying capabilities of Chandra and XMM-Newton are, moreover, highly
complementary; e.g., Chandra excels at the highest sensitivity surveys (see
Fig. 2 left) owing to its sub-arcsecond imaging which provides a small source-
detection cell and largely avoids source confusion, while the larger photon-
collecting area of XMM-Newton provides critical spectroscopic information for
sources above its confusion limit. While Chandra and XMM-Newton still did not
directly cover the 20–40 keV CXRB peak, they did reveal many highly obscured
AGNs with strong signatures of nuclear Compton “reflection”. This added
support to the idea that such objects are largely responsible for the overall
CXRB spectrum, as formalized with improved AGN synthesis models (e.g., Gilli
et al. 2007; Ananna et al. 2019).

Over the past two decades, CXRB surveys at higher energies of 10–200 keV also
advanced dramatically (see Fig. 2 right). First, INTEGRAL and Swift BAT
(launched in 2002 and 2004, respectively) provided new coded-aperture all-sky
hard X-ray surveys that generated sizable AGN samples, mostly at $z\lower
2.0pt\hbox{$\,\buildrel\scriptstyle<\over{\scriptstyle\sim}\,$}0.5$, with much
reduced obscuration bias (e.g., Mereminskiy et al. 2016; Oh et al. 2018).
Then, in 2012, NuSTAR provided the first high-energy focusing X-ray telescopes
in orbit, and it became possible to conduct multiple CXRB surveys reaching up
to observed $\approx 16$–24 keV that explore the $\lower
2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}10$ keV sky
with about a one-hundred-fold improvement in sensitivity (e.g., Harrison et
al. 2016; Lansbury et al. 2017). These reached ever closer to the 20–40 keV
CXRB peak, still further confirming the presence of obscured AGNs capable of
explaining the CXRB spectrum. The AGNs detected in NuSTAR CXRB surveys mostly
lie at $z\approx 0.2$–3, and the combination of INTEGRAL, Swift BAT, and
NuSTAR allow AGNs to be surveyed at high rest-frame energies over most of
cosmic time (see Fig. 3 right).

Figure 3:  Left: Distribution of 2–10 keV luminosity vs. redshift for X-ray
sources, mostly AGNs, with spectroscopic or high-quality photometric redshifts
from several Chandra and XMM-Newton surveys (as labeled). The top and right
histograms show redshift and luminosity distributions, respectively. Note the
large sample sizes and wide coverage of luminosity-redshift space. From Ni et
al. (2021a). Right: Distribution of 10–40 keV luminosity vs. redshift for
X-ray sources, mostly AGNs, with spectroscopic or high-quality photometric
redshifts from the NuSTAR Serendipitous Survey and the Swift BAT survey (as
labeled). The two gray short-dashed lines indicate an observed X-ray flux
range covering two orders of magnitude, from $2\times 10^{-12}$ to $2\times
10^{-14}$ erg cm-2 s-1. The black long-dashed line indicates the evolution of
the “knee luminosity” of the X-ray luminosity function $(L_{\ast})$. Note the
wide coverage of luminosity-redshift space. From Lansbury et al. (2017).

Most recently, in Fall 2019 eROSITA on Spektrum-Roentgen-Gamma (SRG) started
its 4-year program of surveying the entire 0.2–5 keV sky (e.g., Predehl et al.
2021). When completed, eROSITA will reach typical flux limits below 2 keV (a
0.5–2 keV flux limit of $\approx 1.5\times 10^{-14}$ erg cm-2 s-1) about 25
times deeper than those of ROSAT, which provided the previously most-sensitive
soft X-ray all-sky survey (see Fig. 2 left). Millions of extragalactic sources
are expected in the final eROSITA survey. After these are well characterized,
an enormous undertaking, they will allow studies of the bright source
populations of the CXRB with overwhelming statistics. SRG also carries ART-XC,
which is simultaneously conducting a sensitive 4–30 keV all-sky survey that
should ultimately surpass other comparable surveys in this band considering
angular resolution, sensitivity, and uniformity together (see Fig. 2 right);
the ART-XC survey should detect thousands of sources (e.g., Pavlinsky et al.
2021).

As shown in Fig. 2, the surveys conducted by the above-described missions have
effectively covered much of the 0.5–24 keV sensitivity vs. solid-angle
“discovery space” in a “wedding-cake” pattern (i.e., ranging from shallow,
wide-field surveys to deep, pencil-beam surveys).

###  1.3 The Currently Resolved CXRB Fraction

For almost 60 years, a key driver of X-ray astronomy has been to resolve the
CXRB. While this has not yet been fully accomplished, particularly at the
20–40 keV CXRB peak, enormous progress has been made, and it seems clear that
the CXRB indeed primarily arises from discrete point sources, largely obscured
AGNs.

Figure 4:  Left: Cumulative 0.5–2 keV number counts for the 7 Ms exposure of
the Chandra Deep Field-South broken down by source type as labeled. The bottom
panel shows the fractional contributions to the total number counts coming
from AGNs, galaxies, and stars. Note the large sky densities of X-ray sources,
AGNs, and galaxies detected, as well as the rapid rise of the galaxy number
counts at the faintest fluxes. From Luo et al. (2017). Right: Flux
contribution from resolved NuSTAR sources to the intensity of the 8–24 keV
CXRB, plotted as a function of 8–24 keV flux. At faint fluxes, NuSTAR is
resolving $\approx 35$% of the CXRB. From Harrison et al. (2016).

The deepest Chandra surveys, aided by a “bright-end correction” from wider
field surveys, resolve $\approx 80.9\pm 4.4$% and $\approx 92.7\pm 13.3$% of
the CXRB intensity in the 0.5–2 keV and 2–8 keV bands, respectively (e.g., Luo
et al. 2017). The Chandra source number counts reach $\approx 50,500$ deg-2
with securely identified AGNs making up $\approx 23,900$ deg-2 and the strong
majority of the resolved flux (see Fig. 4 left). Notably, at the faintest
0.5–2 keV fluxes galaxies slightly surpass the sky density of AGNs, and the
galaxy number counts continue rising quickly to the faintest flux levels
probed. While some of these galaxies likely contain unrecognized AGNs, it
seems clear that galaxies will be the numerically dominant X-ray source
population at still fainter fluxes. They are expected to contribute $\approx
5$% to the still-unresolved portion of the 0.5–2 keV CXRB; the rest likely
comes from Galactic contributions, clusters and groups, and perhaps very high-
redshift ($z\lower
2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}6$) black
holes.

At the important higher energies, NuSTAR surveys directly resolve $\approx
35$% of the 8–24 keV CXRB emission (see Fig. 4 right; e.g., Harrison et al.
2016), although most of the relevant NuSTAR sources are not detected above
$\approx 16$ keV. The high-energy NuSTAR number counts reach $\approx 120$
deg-2 and are strongly dominated by AGNs. At still higher energies (e.g.,
20–60 keV), only a few percent of the CXRB has been directly resolved (e.g.,
Krivonos et al. 2021).

##  2 Sources Detected in CXRB Surveys

###  2.1 CXRB Source Counterparts, Redshifts, and Classifications

Once an X-ray source has been detected in a CXRB survey, its basic nature must
be determined before it can be used for most scientific studies. In addition
to the X-ray data themselves, such source classification typically relies upon
both multiwavelength photometric imaging data covering as much of the source’s
spectral energy distribution (SED) as possible as well as optical/infrared
spectroscopic data. Such source-classification work is a fundamental, large,
challenging, and sometimes underappreciated component of the CXRB-surveys
industry.

Counterpart matching: To begin, the X-ray source must be matched correctly to
its true multiwavelength counterpart. Such matching is now generally done
statistically with likelihood-ratio or Bayesian techniques that balance
matching completeness vs. reliability (e.g., Sutherland & Saunders 1992;
Salvato et al. 2018), and the availability of high-quality multiwavelength
imaging data considerably helps with the matching process (e.g., in setting
statistical matching priors and accommodating counterparts with varied SEDs).
The matching process depends strongly upon the sky density of plausible
counterparts, and thus matching details vary substantially from survey-to-
survey (e.g., Swift BAT vs. deep Chandra surveys). In the commonly encountered
regime of faint (say, $i$-band magnitudes of $i\approx 20$–25) counterparts,
X-ray sources with positional uncertainties of 1–3′′ or better (e.g., from
Chandra or XMM-Newton) allow suitable counterpart identification for most
scientific purposes, provided high-quality multiwavelength imaging is
available (e.g., Marchesi et al. 2016; Luo et al. 2017; Ni et al. 2021a). In
the best cases, up to $\approx 98$% of the X-ray sources can be matched to
counterparts. For larger positional uncertainties in the faint-counterpart
regime, the robustness of the matching quickly declines, and caution is
warranted. In some cases, a CXRB survey with large X-ray positional
uncertainties will first be matched to another overlapping CXRB survey with
smaller positional uncertainties before multiwavelength counterpart
determination; e.g., the identification of NuSTAR sources in sky regions also
having Chandra or XMM-Newton coverage (e.g., Lansbury et al. 2017).

Redshift determination: Once a secure multiwavelength counterpart has been
found, a counterpart redshift must be determined for most scientific
applications (the X-ray data alone generally do not provide reliable
redshifts, though there are notable exceptions). Ideally, this is done with a
high-quality optical/infrared spectrum that identifies multiple spectral
features, and a wide variety of 1–10 m telescopes, often with multi-object
spectrographs, have been productively employed for spectroscopic follow-up of
CXRB survey sources. Spectroscopic redshifts for CXRB sources can generally be
obtained down to $i$-band magnitudes of $i=23$–24 with long exposures on large
telescopes, but at still fainter magnitudes the spectroscopic-redshift
completeness drops rapidly (e.g., see Fig. 5 left). In this regime, and when
spectroscopic follow-up at brighter magnitudes becomes prohibitively
expensive, photometric-redshift estimates are generally employed. After much
effort, it has now become possible to derive quality photometric redshifts
(with $\approx 1$–8% accuracy in $\Delta z/(1+z)$) for many of the AGNs found
in CXRB surveys that have sensitive photometric data broadly and densely
spanning the optical/infrared SED (e.g., see Fig. 5 right; e.g., Luo et al.
2017; Salvato et al. 2019; Ni et al. 2021a). However, photometric redshifts
for X-ray-selected AGNs generally have larger uncertainties and a higher
fraction of catastrophic mis-estimates than those for galaxies without active
nuclei. Broad-line AGNs particularly challenge photometric-redshift analyses
and have elevated uncertainties and catastrophic mis-estimates. In the best-
studied CXRB survey fields, the combination of spectroscopic and photometric
approaches now provide a redshift completeness above 95%, sufficient for
reliable conclusions about CXRB source populations over cosmic time.

Figure 5:  Left: The spectroscopic-redshift completeness for the Chandra
COSMOS-Legacy survey as a function of $i$-band magnitude. Note the rapidly
declining completeness toward faint $i$ magnitudes; this has been one
persistent challenge for CXRB survey investigations since the early 2000’s
(the low completeness at the brightest magnitudes arises largely because many
of these objects are Galactic stars which were not targeted
spectroscopically). From Marchesi et al. (2016). Right: Histogram of the
fractional difference between photometric redshifts and spectroscopic
redshifts for X-ray detected AGNs (excluding broad-line AGNs) in the 4.6 deg2
region around the Chandra Deep Field-South (W-CDF-S). $\sigma_{\rm NMAD}$ is a
robust estimator of the standard deviation, and $f_{\rm outlier}$ is the
fraction of catastrophic mis-estimates of redshift. Overall, this is a
representative example of the quality of AGN photometric redshifts when high-
quality multiwavelength data are available. From Ni et al. (2021a).

Source classification: A variety of measured properties are commonly employed
to sort CXRB survey sources having secure counterparts and redshifts into
classes such as AGNs, galaxies, clusters and groups, and transients. These
include

  1. 1.

X-ray luminosity, spectral shape, variability, and morphology;

  2. 2.

X-ray-to-optical/infrared flux ratio;

  3. 3.

Optical/infrared emission-line and continuum properties; and

  4. 4.

Radio morphology and core surface brightness.

Further discussion of these approaches is given in, e.g., Brandt & Alexander
(2015). Additionally, SED fitting codes can be used, e.g., to assess if
significant AGN power appears present (e.g., Pouliasis et al. 2020; Yang et
al. 2020). In most cases, several independent approaches are utilized to
cross-check classifications, thereby providing reliably classified samples.

###  2.2 Main Extragalactic Source Types

Classification of CXRB survey sources reveals a wide variety of source types,
and below we will briefly describe the main extragalactic populations
discovered.

AGNs: AGNs are the energetically dominant source type detected in all CXRB
surveys, and they also dominate numerically in all but the 1–2 deepest 0.5–2
keV surveys (where galaxies appear to dominate numerically). Their primary
X-ray emission is thought to be largely created via Compton up-scattering in
an accretion-disk “corona” in the immediate vicinity of the supermassive black
hole (SMBH), but X-rays may also arise from the accretion disk itself (at low
energies) or jets. CXRB surveys are extremely effective at discovering AGNs
for three key reasons:

  1. 1.

Luminous AGNs appear almost universally to produce substantial X-ray emission,
typically making up 1–20% of the total power emitted;

  2. 2.

The penetrating nature of high-energy X-rays allows detection of the common
obscured systems that are often missed at other wavelengths, and any X-ray
biases against obscured systems decline with increasing redshift; and

  3. 3.

X-rays provide superior contrast between AGN light and host-galaxy starlight,
thereby minimizing confusion between the two.

These three points together explain why deep X-ray surveys have discovered the
highest sky density of AGNs, up to 23,900 deg-2, compared to any other
wavelength (see Fig. 4 left).

The variety of CXRB surveys conducted (see Fig. 2) have discovered AGNs in
significant numbers from the local universe to $z\approx 5$, thereby allowing
studies of AGN properties over most of cosmic time (e.g., see Fig. 3). Even at
high redshifts of $z\approx 2$–5, deep CXRB surveys allow the discovery of
many moderate-to-low luminosity AGNs, comparable to the well-studied Seyfert
galaxies in the local universe (e.g., Vito et al. 2018). The full range of AGN
X-ray luminosity commonly found across CXRB surveys spans an impressive five
orders of magnitude, $L_{\rm X}=10^{41}$–$10^{46}$ erg s-1, and optical
counterpart magnitudes span $i_{\rm AB}\approx 14$–28.

As expected from the shape of the CXRB, X-ray surveys reveal vast numbers of
obscured AGNs at all redshifts, with a generally higher fraction of obscured
AGNs being found by progressively higher energy surveys. X-ray spectral
fitting of the obscured systems finds intrinsic absorption column densities
spanning $N_{\rm H}=10^{21}$–$10^{24.5}$ cm-2 and frequently reveals X-ray
absorption complexity (e.g., partially covering or ionized absorption). There
are also unobscured systems having intrinsic $N_{\rm H}$ consistent with zero.
The AGN column density distribution generally appears log-normal in form with
a peak around $N_{\rm H}=10^{23.5}$ cm-2 (e.g., Ueda et al. 2014; Liu et al.
2017) when averaged over wide ranges of redshift and luminosity (note the
$N_{\rm H}$ distribution depends upon both of these quantities; see §3.2).

Consistent with the wide ranges of AGN luminosity and X-ray absorption level,
the optical/infrared appearances of AGNs from CXRB surveys are varied, ranging
from obvious blue, broad-line AGNs to elusive AGNs that are host dominated and
challenging to distinguish from normal galaxies (e.g., Luo et al. 2010; Hickox
& Alexander 2018). The X-ray unobscured vs. obscured classifications do not
always map simply onto the classical optical type 1 vs. type 2
classifications, though there is generally respectable correspondence (e.g.,
Merloni et al. 2014; Koss et al. 2017).

Much additional information about the AGNs from CXRB surveys is given in §3.

Figure 6: Redshift dependence of $L_{\rm 2-10\rm\ keV}({\rm LMXB})/M_{\star}$
and $L_{\rm 2-10\rm\ keV}({\rm HMXB})/{\rm SFR}$ derived from stacking
analyses of $z\approx 0$–2.5 galaxies with sensitive X-ray coverage (using
samples as labeled). The dashed blue curves show the best-fit relations, and
the dotted red curves show predicted evolution from one population model of
XBs. From Lehmer et al. (2016).

Galaxies: Galaxies are significant contributors to the 0.5–7 keV source number
counts at the faint fluxes probed by deep CXRB surveys. They most prominently
contribute in the 0.5–2 keV band but also materially contribute from 2–7 keV.
Galaxies numerically dominate over AGNs in the X-ray number counts below 0.5–2
keV fluxes of $\approx 10^{-17}$ erg cm-2 s-1 (see Fig. 4 left); a similar
situation is found in deep radio surveys reaching below a few mJy. The
detected X-ray emission primarily originates from the accreting X-ray binary
(XB) populations inhabiting these galaxies (including ultraluminous X-ray
sources). Below $\approx 1$–2 keV, hot gas emission often contributes
materially as well, arising from, e.g., supernova remnants, starburst-driven
outflows, and hot interstellar media. Unrecognized SMBH activity (e.g., from
low-luminosity or elusive highly obscured AGNs) inevitably also contributes in
some systems.

The X-ray detected galaxies in deep CXRB surveys typically lie at $z\approx
0$–1.5 (e.g., Luo et al. 2017), and they thereby allow the evolution of galaxy
X-ray source populations to be investigated over the last $\approx 70$% of
cosmic time. These galaxies generally have X-ray luminosities of $L_{\rm
X}=10^{39}$–$10^{42}$ erg s-1 and relatively soft X-ray spectra with effective
power-law photon indices of $\Gamma=1.7$–2.2. They include both late-type and
early-type morphologies, and they span wide ranges of stellar mass
($M_{\star}$) and star-formation rate (SFR).

Stacking-based analyses with deep CXRB surveys have allowed systematic studies
of normal-galaxy X-ray source populations over the redshift range $z\approx
0$–3 (e.g., Lehmer et al. 2016), and these have shown that average galaxy
$L_{\rm X}$ over cosmic time is a function of at least $M_{\star}$ (primarily
relating to low-mass XBs; LMXBs), SFR (primarily relating to high-mass XBs;
HMXBs), and redshift. The redshift evolution leads to generally rising $L_{\rm
X}$ at higher redshift with scaling relations of $L_{\rm 2-10\rm\ keV}({\rm
LMXB})/M_{\star}\propto(1+z)^{2-3}$ and $L_{\rm 2-10\rm\ keV}({\rm HMXB})/{\rm
SFR}\propto(1+z)$; see Fig. 6. The upward $L_{\rm X}$ evolution for LMXBs and
HMXBs is respectively attributed to declining galaxy stellar ages and
metallicities (e.g., Fornasini et al. 2020), although further investigations
of these putative drivers are required.

Figure 7:  Left: The X-ray luminosity function of $z<1.2$ clusters/groups from
COSMOS (gray crosses) and the Extended Chandra Deep Field-South (black crosses
and dots). For comparison, the dashed and dotted curves show the local X-ray
luminosity function in the Northern and Southern hemispheres, respectively,
from the ROSAT All-Sky Survey. From Finoguenov et al. (2015). Right: Example
X-ray light curve of a FXRT found serendipitously in a Chandra CXRB survey
observation of the Chandra Deep Field-South. The middle panel shows the ratio
between the data and broken power-law model fit in the upper panel. The lower
panel shows the X-ray hardness ratio. Based on its detailed properties, this
FXRT has been proposed to be powered by a magnetar resulting from a binary
neutron star merger. From Xue et al. (2019).

Galaxy clusters and groups: Galaxy clusters and groups are detected in
significant numbers (up to $\approx 400$ deg-2) in CXRB surveys below $\approx
10$ keV, standing out owing to their spatial extension and relatively soft
X-ray spectra. Their X-ray emission arises from their hot
intracluster/intragroup media (ICM/IGM) via a combination of bremsstrahlung,
line radiation, and recombination emission; AGNs present in the cluster/group
also often contribute to the total X-ray luminosity. The ICM generally
outweighs the optically visible galaxies in clusters by a factor of $\approx
1.5$–10, yet it is very difficult to observe at non-X-ray wavelengths; in
groups the IGM often has a mass comparable to or less than that of the
galaxies.

CXRB surveys have discovered thousands of clusters/groups with $L_{\rm
X}\approx 10^{41}$–$10^{45}$ erg s-1 from $z\approx 0$–1 and an increasing
number at $z\approx 1$–2 and beyond (e.g., see Fig. 7 left; e.g., Böhringer et
al. 2004; Finoguenov et al. 2015; Adami et al. 2018; Liu et al. 2021a). These
span masses of $M_{500}\approx(0.1$–20)$\times 10^{14}$ M⊙ ($M_{500}$ is the
mass within $r_{500}$, the radius within which the mean density is equal to
500 times the critical density).

Cluster/group samples from CXRB surveys have provided key insights into the
$\Lambda$CDM cosmology via measurements of, e.g., the baryonic mass fraction
and the evolution of cluster number counts (e.g., Allen & Mantz 2020). The
eROSITA survey should soon deliver $\lower
2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}10^{5}$
clusters extending to $z\lower
2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}1$, and these
will ultimately provide precision cosmological constraints (e.g., Predehl et
al. 2021).

Transients: CXRB surveys have played a role in serendipitously discovering new
types of extragalactic X-ray transients. This dates back to at least the ROSAT
All-Sky Survey, which discovered multiple tidal disruption event (TDE)
candidates and other galactic giant X-ray outbursts, some of which remain
poorly understood (e.g., Komossa 2015). Chandra and XMM-Newton surveys have
discovered other extragalactic transients, including the revelation of a new
population of fast X-ray transients (FXRTs) with durations of $\approx 5000$ s
and relatively faint X-ray fluxes (e.g., see Fig. 7 right; e.g., Yang et al.
2019a; Quirola-Vásquez et al., in prep). FXRTs may be binary neutron-star
merger events that form magnetars, off-axis gamma-ray bursts, and/or TDEs
involving the disruption of a white dwarf by an intermediate mass black hole.
The eROSITA survey is now discovering new X-ray selected TDEs and other
transients.

##  3 Insights on the AGN Population from CXRB Surveys

As described in §2, AGNs are the energetically dominant contributors to the
CXRB and usually dominate numerically in CXRB surveys as well. Therefore, in
this section we will present some key insights about AGN demographics,
physics, and ecology revealed by CXRB surveys.

###  3.1 AGN Demographics

Pre-Chandra/XMM-Newton era: The AGN luminosity function (LF) describes the AGN
comoving number density as a function of luminosity and redshift. Since the
discovery of the first AGNs, the LF has attracted intense investigations.
Early studies before $\approx 1990$ were largely limited to the LF’s luminous
end (i.e., quasars, $\approx 10$–100 deg-2) selected by optical surveys (see,
e.g., Hartwick & Schade 1990 for a review). These studies established that the
number density of quasars peaks at $z\approx 2$–3, despite the relatively
large uncertainties at high redshifts ($z\gtrsim 3$).

ROSAT, thanks to its unprecedented sensitivity (at the time; see §1.2) from
0.1–2.4 keV and large field of view ($2^{\circ}$ diameter), delivered several
key results that fundamentally shaped our understanding of AGN demographics.
The ROSAT Deep Survey detected discrete X-ray sources reaching a surface
density of $\approx 800$–900 deg-2, most ($\gtrsim 80\%$) of which are AGNs
(e.g., Hasinger et al. 1998; Schmidt et al. 1998). ROSAT enabled the first
comprehensive studies of the AGN X-ray luminosity function (XLF; e.g., Miyaji
et al. 2000). These favored luminosity-dependent density evolution (LDDE)
models, such that more luminous AGNs evolve more strongly as a function of
redshift. Similar to the optical/radio results, the ROSAT-based XLF rises
sharply from $z=0$ to $z\approx 2$–3. However, the XLF was poorly constrained
at higher redshifts, and the inferred X-ray AGN number density was consistent
with a constant at $z\gtrsim 3$. The XLF could account for 60–90% (depending
upon the specific LDDE model) of the 0.5–2 keV CXRB, indicating that the
observed soft CXRB largely originates from distant AGNs.

Redshift evolution of AGN number density: Thanks to their order-of-magnitude
sensitivity improvements compared to previous missions, Chandra and XMM-Newton
have significantly pushed forward studies of AGN demographics. Their deepest
surveys have detected an enormously dense AGN population, reaching a sky
density of 23,900 deg-2 (e.g., Luo et al. 2017). This density is more than 1
and 2 orders of magnitude higher than those of ROSAT-detected AGNs and SDSS
quasars, respectively (e.g., Hasinger et al. 1998; Palanque-Delabrouille et
al. 2013).

Chandra and XMM-Newton are able to detect a fairly complete AGN sample over
wide luminosity, redshift, and obscuration ranges (see Fig. 3 left), allowing
detailed characterization of the AGN XLF. The most outstanding feature of the
AGN XLF is so-called “AGN downsizing”: the number density of higher luminosity
AGNs peaks at higher redshift (e.g., Cowie et al. 2003; Ueda et al. 2014; Aird
et al. 2015). For example, AGNs with $L_{X}\approx 10^{45}$ erg s-1 and
$L_{X}\approx 10^{43}$ erg s-1 peak at $z\approx 2.5$ and $z\approx 1$,
respectively. Fig. 8 (left) displays the number-density evolution for AGNs
within different luminosity ranges, where downsizing is apparent. Similar
downsizing behavior has also been found among optically and radio-selected
AGNs (e.g., Croom et al. 2009; Rigby et al. 2011). The AGN-downsizing behavior
suggests that more-massive SMBHs today generally form earlier in cosmic
history. Interestingly, a similar phenomenon has also been found in studies of
galaxy formation: in the local universe, more-massive galaxies tend to have
older stellar populations than less-massive ones (e.g., Thomas et al. 2005);
observations of distant galaxies have directly demonstrated this galaxy-
downsizing picture (e.g., Cowie et al. 1996; Juneau et al. 2005). The
evolutionary similarity between AGNs and galaxies suggests some fundamental
links between SMBH and stellar growth (see §3.3).

AGN downsizing behavior poses a significant theoretical challenge. In the
framework of the $\Lambda$CDM universe, dark-matter halos form hierarchically,
i.e., low-mass halos form first and they merge into massive halos later in
cosmic time (e.g., White & Rees 1978; Blumenthal et al. 1984). A
straightforward scenario is that SMBH and galaxy growth also follow this
hierarchical path, because they evolve in the central regions of dark-matter
halos. However, the observed AGN and galaxy downsizing appear to go against
this scenario, and thus downsizing phenomena are often described as “anti-
hierarchical”. Modern cosmological simulations can roughly yield the trend of
downsizing by involving physical mechanisms of AGN feedback (e.g., Scannapieco
et al. 2005; Sijacki et al. 2015; Volonteri et al. 2016). However, further
work is needed to reproduce the observed AGN XLF across all redshifts and
luminosities (e.g., Rosas-Guevara et al. 2016; Habouzit et al. 2019).

Figure 8:  Left: Number-density evolution at $z=0$–5 of AGNs within different
X-ray luminosity ranges from the best-fit XLF model of Aird et al. (2015). The
shaded regions indicate model uncertainties (99% confidence level). The data
points are from Miyaji et al. (2015). The number-density evolution shows a
clear “downsizing” pattern, such that more luminous AGNs peak at higher
redshifts. From Aird et al. (2015). Right: High-redshift AGN number-density
evolution. The solid large circles are based on the observed AGNs in Vito et
al. (2018), with different colors indicating the best-fit models. The lowest
luminosity bin is moderately affected by incompleteness, and the empty circles
are corrected for this effect. For higher luminosity bins, the incompleteness
effect should be negligible. The smaller data points are from different
studies as labeled. The gray stripes represent galaxy number densities, scaled
by a factor of 0.02. The number density of AGNs at all luminosities decreases
sharply toward higher redshifts at $z>3$, similarly to massive galaxies. From
Vito et al. (2018).

High-redshift AGNs attract particular attention, because they are closely
related to the seeding and early formation of SMBHs. One of the most important
lessons from Chandra and XMM-Newton is that the AGN number density declines
sharply as a function of redshift at $z\gtrsim 3$ (e.g., Barger et al. 2003;
Silverman et al. 2008), which was not shown with the ROSAT data (see above).
Fig. 8 (right) displays the AGN number density evolution at $z>3$. Adopting a
power-law functional form of $(1+z)^{-\gamma}$, the power-law index describing
the number-density decline is $\gamma\approx 6$–9, depending on the AGN
luminosity. This means there are $\approx 30$–150 times fewer AGNs at $z=6$
than at $z=3$. X-ray stacking analyses indicate that low-luminosity AGNs
undetected by the deepest Chandra surveys contribute negligibly to the total
cosmic accretion power (e.g., Vito et al. 2016). Given the weak AGN activity
at high redshifts, AGNs are unlikely the dominant sources driving cosmic
hydrogen reionization (e.g., Parsa et al. 2018; Vito et al. 2018; Ananna et
al. 2020).

While Chandra and XMM-Newton sample X-ray photons up to $\approx 10$ keV,
NuSTAR and Swift BAT can detect photons at higher energies ($\approx 3$–79 keV
for NuSTAR; 14–195 keV for Swift BAT). This allows them to detect and
characterize some heavily obscured AGNs, which could be very faint in lower-
energy bands (e.g., Alexander et al. 2013; Civano et al. 2015; Harrison et al.
2016; Lansbury et al. 2017). Studies based on the NuSTAR and Swift BAT surveys
suggest that the Compton-thick ($N_{\rm H}\lower
2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}10^{24}$ cm-2)
fraction among all AGNs is $\approx 60\%$, a few times higher than some
earlier results (e.g., Ananna et al. 2019). Fig. 9 (left) compares the
Compton-thick fractions from NuSTAR and Swift BAT vs. those from different XLF
models.

The ongoing eROSITA all-sky survey (see §1.2) will be particularly helpful for
constraining the XLF at $z\approx 0$ and the luminous end of high-redshift XLF
(e.g., Wolf et al. 2021). The eROSITA team has released a $\approx 140$ deg2
survey field, eFEDS (see Fig. 2 left; Brunner et al. 2021). Fig. 9 (right)
compares the $z\approx 6$ XLF constrained by eFEDS with those extrapolated
from lower-$z$ XLF models. The eFEDS data point appears to be higher than most
of the model values, but the uncertainty is still too large for a firm
conclusion. The full eROSITA release in the future will clarify whether the
discrepancy is statistically significant or not.

Figure 9:  Left: The Compton-thick fraction among all $z<0.07$ AGNs as a
function of 8–24 keV flux. The data points are estimated from NuSTAR or Swift
BAT data. Different curves are derived from different XLF models as labeled.
NuSTAR and Swift BAT data are helpful for constraining the Compton-thick
population. From Ananna et al. (2019). Right: The X-ray luminosity function at
$z\approx 6$. The thick black data point is derived from eFEDS. The curves
represent model-extrapolated XLFs from the literature as labeled, with
uncertainties indicated by the colored shaded areas and error bars. The eFEDS
data point appears to be higher than most of the model values. The full
eROSITA release will clarify if this possible discrepancy is statistically
significant. From Wolf et al. (2021).

X-ray missed AGNs: Although X-ray observations have several advantages for AGN
detection (see §2.2), even deep CXRB surveys may still miss some AGNs powered
by actively growing SMBHs. Multiwavelength identifications of these X-ray
missed AGNs are critically important, because complete AGN samples are
necessary to draw an unbiased picture of SMBH formation and evolution. There
are mainly two types of AGNs that might be missed by X-ray selection: one is
intrinsically X-ray weak, and the other is heavily obscured. We discuss these
two types of objects separately below.

Some luminous quasars like PHL 1811 have been found to have weak X-ray
emission, more than 10 times below the expectations from the $L_{X}-L_{UV}$
relation for typical AGNs (e.g., Leighly et al. 2007; Luo et al. 2014). The
weak X-ray emission appears to be intrinsic, as spectral analyses suggest
these particular quasars are X-ray unobscured. However, such X-ray weak
objects appear rare, consisting of only a few percent of SDSS quasars (e.g.,
Gibson et al. 2008; Pu et al. 2020). Considering this rarity, our general
understanding of AGN demographics appears largely unaffected by the
intrinsically X-ray weak population.

Compared to intrinsic X-ray weakness, heavy obscuration is a more common cause
of incompleteness of X-ray surveys. When obscuration reaches above the
Compton-thick level, even hard X-rays are significantly suppressed due to
Compton scattering and subsequent photoelectric absorption. Despite AGN-
demographics studies to correct for the incompleteness caused by selection
biases against Compton-thick sources, these efforts must make strong
assumptions about several key factors such as $N_{\rm H}$ distribution above
$10^{24}$ cm-2 and X-ray spectral shapes (e.g., Ueda et al. 2014; Aird et al.
2015; Buchner et al. 2015; Ananna et al. 2019). The uncertainties associated
with these assumptions are a major obstacle to achieving the full picture of
AGN demographics, which could be quite different from our current
understanding. For example, the currently observed sharp decline of AGN
activity at $z\gtrsim 3$ (see Fig. 8 right) might be exaggerated by Compton-
thick obscuration (e.g., Yang et al. 2021b).

To address better the issue of X-ray incompleteness, it is important to
develop multiwavelength identification methods to effectively select Compton-
thick AGNs (see Brandt & Alexander 2015; Padovani et al. 2017; Hickox &
Alexander 2018 for reviews). One popular method is using broad-band mid-
infrared (MIR) photometry to capture AGN dust re-emission (e.g., Lacy et al.
2004; Donley et al. 2012). Another is using optical/IR spectroscopy to detect
high-ionization lines that are beyond typical star-formation ionization
energies (e.g., Steidel et al. 2002; Alexander et al. 2008). However, due to
the constraints of survey sensitivity and/or wavelength coverage, these
methods are generally limited to bright objects. Fortunately, JWST will soon
provide unprecedentedly deep IR imaging and spectroscopy. It may potentially
detect a significant population of Compton-thick AGNs and improve our
understanding of AGN demographics across cosmic history (e.g., Satyapal et al.
2021; Yang et al. 2021a,b).

###  3.2 AGN Physics

X-ray obscuration: In §2.2, we briefly introduced AGN X-ray obscuration
including its measurement, the basic $N_{\rm H}$ distribution, and its
relation to optical obscuration. In this section, we mainly focus on the
dependence of X-ray obscuration upon redshift, AGN luminosity, and host-galaxy
properties.

AGN X-ray obscuration shows significant cosmic evolution. The general trend is
that the obscuration rises strongly from $z=0$ to $z\approx 2$ (e.g., Buchner
et al. 2015; Liu et al. 2017). Fig. 10 (left) displays the obscured AGN
fraction as a function of redshift. For AGNs with $10^{43.5}<L_{X}<10^{44.2}$
erg s-1, the obscured fraction ($N_{\rm H}>10^{22}$ cm-2) increases from
$\approx 40\%$ at $z=0$ to $\gtrsim 80\%$ at $z=2$. The obscuration-redshift
relation is broadly consistent with the fact that the obscuring materials
(mainly cold gas) are more abundant in the earlier universe. Interestingly,
most studies of the Compton-thick AGN fraction have not found a significant
redshift dependence (e.g., Buchner et al. 2015; Ananna et al. 2019; Li et al.
2019; but also see Lanzuisi et al. 2018). However, the uncertainties are
large, especially considering detection incompleteness for the Compton-thick
population (e.g., Hickox & Alexander 2018). At high redshifts of $z\gtrsim 2$,
$N_{\rm H}$ measurements become challenging due to the general faintness of
high-redshift objects. However, studies have suggested that the obscuration-
redshift relation “saturates” at high redshifts, i.e., the obscured fraction
roughly remains constant at $z\gtrsim 2$ (e.g., Liu et al. 2017; Vito et al.
2018).

At a given redshift ($z\lower
2.0pt\hbox{$\,\buildrel\scriptstyle<\over{\scriptstyle\sim}\,$}3$), AGN X-ray
obscuration becomes weaker toward higher luminosities (e.g., Merloni et al.
2014; Liu et al. 2017). For example, at $z\approx 1.5$, the obscured fraction
drops from 75% at $L_{X}\approx 10^{43}$ erg s-1 to 40% at $L_{X}\approx
10^{44.5}$ erg s-1. This luminosity dependence can be understood within the
framework of the AGN-unification model, which envisages a toroidal obscuring
structure (e.g., Antonucci 1993; Netzer 2015). In this model, whether a
specific AGN is obscured depends on the viewing angle, and thus the obscured
fraction is numerically equivalent to the torus covering factor for an AGN
sample. It has been reasonably proposed that the torus covering factor is
negatively related to AGN luminosity (or Eddington ratio), because more
powerful central engines could blow away more obscuring materials via
radiation pressure and/or winds (a “receding torus”; e.g., Lawrence 1991;
Netzer 2015; Ricci et al. 2017). However, observations suggest that the
obscuration-luminosity anticorrelation may not hold for high-redshift
($z\lower 2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}3$)
AGNs, although the uncertainties are considerable (e.g., Vito et al. 2014,
2018; Buchner et al. 2015).

Since AGN activity is closely related to host-galaxy properties (see §3.3), it
is natural to wonder if AGN obscuration also depends upon galaxy properties.
Studies have not found a significant difference in host-galaxy $M_{*}$ or SFR
for X-ray obscured vs. unobscured AGNs (e.g., Merloni et al. 2014; Mountrichas
et al. 2021b; but also see Lanzuisi et al. 2017). Interestingly, studies
indicate that optical type 2 AGNs tend to have higher $M_{*}$ compared to type
1 AGNs, although these two classes have similar SFR distributions (e.g., Zou
et al. 2019; Mountrichas et al. 2021c). The different behaviors of X-ray and
optical obscuration suggest that they may have different physical origins.
However, robust measurements of host-galaxy properties can be challenging,
especially for luminous AGNs which outshine host starlight, and further
investigations are needed to test AGN obscuration-galaxy connections.

Multiwavelength energy distribution of X-ray, UV/optical, and IR: Modern
imaging surveys can effectively sample the SEDs for large numbers of
extragalactic sources. The investigation of AGN multiwavelength SEDs is an
effective way to gain insight into AGN physics, as they reflect the physical
structures of, e.g., the accretion disk and its corona.

Perhaps the most fundamental SED feature is the tight connection between
UV/optical and X-ray luminosities for type 1 AGNs. Conventionally, researchers
have used a quantity, $\alpha_{\rm ox}$, the SED slope between UV and
X-ray.111$\alpha_{\rm
ox}$$=0.3838\log\frac{L_{\rm\nu,2keV}}{L_{\nu,2500\textup{\AA}}}$, where
$L_{\nu,2500\textup{\AA}}$ and $L_{\rm\nu,2keV}$ are rest-frame 2500 $\AA$ and
2 keV monochromatic luminosities with units of erg s-1 Hz-1, respectively. It
has been found that $\alpha_{\rm ox}$ is tightly correlated with
$L_{\nu,2500\textup{\AA}}$ (e.g., Steffen et al. 2006; Just et al. 2007; Lusso
et al. 2010; Lusso & Risaliti 2016). Fig. 10 (right) displays an example of
this relation. The $\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relation has
an intrinsic scatter of only $\approx 0.1$ in $\alpha_{\rm ox}$, over more
than five orders of magnitude in $L_{\nu,2500\textup{\AA}}$. This scatter
translates to a factor of $\approx 2$–3 in terms of the
$L_{\rm\nu,2keV}$-$L_{\nu,2500\textup{\AA}}$ relation. The best-fit
$\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relation has a negative slope of
$\approx-0.14$, indicating that more luminous AGNs tend to have larger UV-to-
X-ray ratios. Studies have generally not found a significant redshift
evolution of the $\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relation up to
$z\approx 6$–7, indicating this relation is determined by some fundamental
accretion physics (e.g., Vito et al. 2019; Wang et al. 2021; see Fig. 10
right). Taking advantage of this apparent redshift independence, some
researchers have proposed to use quasars as “standard candles” to constrain
cosmological parameters (e.g., Lusso & Risaliti 2017).

The $\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relation discussed above is
mainly investigated using type 1 AGN samples, where the AGN UV emission is
directly observable. Under the scheme of AGN unification, this relation should
also hold for the central engines of the type 2 population, despite their
obscuration. Based on this idea, Yang et al. (2020) developed a SED-fitting
code, x-cigale. x-cigale builds SED templates from X-ray to IR by applying the
$\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relation to physical AGN UV-to-IR
models, in which the intrinsic $L_{\nu,2500\textup{\AA}}$ is also known for
type 2 AGNs. Using x-cigale, studies have successfully fitted observed type 2
SEDs, supporting the AGN-unification scheme (e.g., Yang et al. 2020;
Mountrichas et al. 2021a; Toba et al. 2021). The fitted X-ray vs. MIR AGN
luminosities are also consistent with empirical AGN $L_{X}$-$L_{\rm 6\mu\rm
m}$ relations (see, e.g., Fig. 15 of Toba et al. 2021), indicating these
relations are physically driven by the $\alpha_{\rm
ox}$-$L_{\nu,2500\textup{\AA}}$ relation.

Some observational studies have suggested that the observed $\alpha_{\rm
ox}$-$L_{\nu,2500\textup{\AA}}$ relation might actually be driven by a more
fundamental connection between $\alpha_{\rm ox}$ and Eddington ratio (e.g.,
Lusso et al. 2010; Jin et al. 2012). The Eddington-ratio dependence is also
favored by some theoretical studies of the AGN disk-corona system (e.g., Cao
2009; Kubota & Done 2018). However, the dependence on Eddington ratio is still
controversial, likely due to the strong degeneracy with
$L_{\nu,2500\textup{\AA}}$ and the relatively large uncertainties in SMBH-mass
measurements (e.g., Shemmer et al. 2008; Liu et al. 2021b).

Figure 10:  Left: Redshift evolution of X-ray obscured AGN fraction at
$43.5<\log L_{X}<44.2$ (units: erg s-1). The red data points are from a
complete Compton-thin ($N_{\rm H}<10^{24}$ cm-2) sample, and the red curve is
the best fit. The blue points and curve are from a subsample with
spectroscopic redshifts; the green points and curve are from the sample plus
Compton-thick objects. The black and purple points are from the literature.
The obscured fraction rises sharply from $z=0$ to $z\approx 2$–3. From Liu et
al. (2017). Right: $\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relation. The
larger data points represent $z>6$ quasars, while the smaller data points and
blue shaded regions represent $z<6$ quasars. The downward-pointing triangles
indicate $\alpha_{\rm ox}$ upper limits. The lines are the best-fit relations
from the literature as labeled. The $z>6$ quasar sample is consistent with
these $\alpha_{\rm ox}$-$L_{\nu,2500\textup{\AA}}$ relations, which were
derived from $z<6$ quasars. From Vito et al. (2019).

X-ray variability: Modern X-ray surveys often obtain multiple exposures on the
same sky region to reach higher sensitivities. As a bonus, multiple exposures
also enable time-domain analyses on timescales from days to years. These
analyses can effectively reveal some essential physical properties of AGNs. It
has been proposed that a significant fraction of observed AGNs might be
powered by TDEs instead of normal gas accretion (e.g., Milosavljević et al.
2006). Whether an X-ray AGN is powered by a TDE or gas accretion can be
distinguished with long-term ($\sim$years) variability analyses. A TDE-powered
AGN likely will decay monotonically over time (except for the initial burst),
and the change in X-ray flux can reach orders of magnitude (e.g., Komossa
2015). In contrast, a normal AGN has stochastic variability with much milder
amplitudes. The long-lived Chandra and XMM-Newton missions allow the
characterization of AGN long-term variability.

Fig. 11 (left) compares the fluxes from two observational epochs separated by
$\approx 15$ years. The flux changes between the two epochs are stochastic
with amplitudes generally less than a factor of $\approx 2$–3. This result
suggests these AGNs are likely powered by normal gas accretion rather than
TDEs. Actually, systematic searches for TDEs in X-ray surveys indicate the
fraction of TDE-powered AGN is at most $\approx 1\%$ (e.g., Luo et al. 2008;
Zheng et al. 2017). The mild stochastic variability also indicates that novel
AGN phenomena such as “changing-look” events and emission-state changes are
rare, because those phenomena are often associated with large changes in X-ray
flux.

Figure 11:  Left: Observed AGN 0.5–7 keV flux comparison for two observational
epochs of the Chandra Deep-Field South separated by 15 years in the observed
frame. The AGNs are at redshifts of $\approx 0.6$–3.1 (10th–90th percentile).
The red dashed and dotted lines mark no variation and factor-of-two
variations, respectively. The flux variability appears to be stochastic, and
the amplitudes are $\lesssim 2$–3. Therefore, extreme events (e.g., TDEs and
changing-look AGNs) are rare even on a 15-year timescale. From Yang et al.
(2016). Right: AGN variability strength (normalized excess variance) vs. 2–10
keV luminosity. Different colors indicate different redshift ranges as
labeled. The small crosses represent individual sources. The large data points
indicate the binned results. AGN variability becomes weaker toward higher
luminosities. From Zheng et al. (2017).

From X-ray spectral analyses, it has been found that the observed distant AGN
X-ray flux variations are largely due to changes of the intrinsic luminosity
rather than obscuration (e.g., Yang et al. 2016; Falocco et al. 2017). This
finding means X-ray variability can be used to probe the central engine
properties. Deep-field observations have found X-ray variability amplitudes
are anti-correlated with luminosities, as is known in the local universe
(e.g., Lanzuisi et al. 2014; Yang et al. 2016; Zheng et al. 2017). Fig. 11
(right) displays this anti-correlation. By fitting the variability-luminosity
relation with physical models of power spectral density (PSD), researchers can
constrain SMBH masses and Eddington ratios for different samples and thereby
study the cosmic evolution of these fundamental properties (e.g., Paolillo et
al. 2017; Zheng et al. 2017).

Finally, timing analyses are a useful way to select AGNs. Deep X-ray surveys
can detect faint AGNs that have a similar luminosity level ($L_{X}<10^{42}$
erg s-1) to normal galaxies. It is often challenging to select these AGNs with
X-ray or multiwavelength methods (see §2.1) due to their similarity to normal
galaxies. However, if they are found to have significant X-ray variability,
then their AGN nature is revealed, because typical normal galaxies have
relatively constant light curves. Deep-field studies have successfully used
this method to identify low-luminosity AGNs, some of which are missed by other
selection methods (e.g., Young et al. 2012; Ding et al. 2018). Future powerful
observatories such as Athena and Lynx (see §4.1) will detect many more faint
X-ray sources than we have today, and the variability selection method will be
crucial for selecting low-luminosity AGNs among these sources.

###  3.3 AGN Ecology

From observations of local systems, SMBH masses are tightly correlated with
some host-galaxy properties such as bulge masses and velocity dispersions
(e.g., Kormendy & Ho 2013). These connections are surprising given that SMBH
masses are often negligible ($\lesssim$ a few thousandths) compared to the
host-galaxy masses. Therefore, some physical connections between SMBH growth
and host-galaxy properties likely exist, referred to here as “AGN ecology”.
X-ray surveys and their accompanying multiwavelength data offer an excellent
chance to study AGN-galaxy connections across cosmic history. We discuss the
topic of AGN-galaxy connections in this section, mainly focusing on recent
work not covered in Brandt & Alexander (2015).

Measurements of host-galaxy properties: Basic galaxy properties such as
$M_{*}$ and SFR can be estimated by modeling the observed broad-band SEDs from
the UV to IR. For optically selected quasars, the AGN component typically
outshines the host-galaxy component at UV-to-NIR (near-IR) wavelengths, posing
a significant challenge for SED decomposition. Fortunately, X-ray selected
AGNs, especially those with low-to-moderate luminosities ($L_{X}\lesssim
10^{44}$ erg s-1) and/or significant nuclear absorption, often have UV-to-NIR
SEDs dominated by starlight (see, e.g., Fig. 9 of Luo et al. 2010). Their
$M_{*}$ and SFR measurements are almost as straightforward as those of normal
galaxies. Even for luminous quasars, the X-ray fluxes can be used to constrain
their AGN component in SED modeling and thereby reduce the uncertainties in
the $M_{*}$ and SFR measurements (e.g., Yang et al. 2020; Mountrichas et al.
2021a).

Galaxy morphological measurements are challenging in general. Since broad-line
(BL) AGNs could have a significant contribution to the optical imaging, their
host-galaxy morphological measurements might be unreliable and/or heavily
biased. Therefore, morphological studies often focus on non-BL AGN hosts
(e.g., Yang et al. 2019b; Ni et al. 2021b). Even for non-BL AGNs’ host
galaxies, morphological measurements are technically challenging for ground-
based telescopes, as a $1^{\prime\prime}$ seeing translates to an $\approx 8$
kpc physical scale at $z=1$, comparable to the typical sizes of $L^{*}$
galaxies. For this reason, the morphological investigations of X-ray AGN hosts
often rely on HST imaging.

The reddest band ($H_{160}$) from HST allows morphological measurements up to
$z\approx 3$, above which the covered rest-frame wavelengths shift to the UV
and the “morphological k-correction” becomes strong (e.g., Taylor-Mager et al.
2007). JWST will be able to probe to higher redshifts thanks to its high-
resolution imaging ability at longer wavelengths ($\approx 0.6$–$5\ \mu$m for
NIRCam). There are various methods of making morphological measurements, e.g.,
Sérsic-profile fitting, concentration-asymmetry-clumpiness (CAS), and visual
classifications (see Conselice 2014 for a review). Visual classifications from
expert classifiers are often very time consuming. Fortunately, the advances of
machine-learning techniques in recent years allow effective visual-like
morphological classifications for large numbers of distant galaxies (e.g.,
Huertas-Company et al. 2015).

Host-galaxy stellar mass and star-formation rate: As we have discussed in
§3.1, both SMBH growth and galaxy stellar growth have the anti-hierarchical
behavior of downsizing. Also, the cosmic SMBH-accretion density and star-
formation density222 The total SMBH accretion rate and star-formation rate per
comoving volume, both in units of $M_{\odot}$ yr-1 Mpc-3. both peak at
$z\approx 2$ (see, e.g., Fig. 20 of Aird et al. 2015). These similarities
suggest a connection between AGN activity and star formation (SF).

One major challenge in studying the AGN-SF connection is “AGN flickering”.
From hydrodynamical simulations, AGNs are likely associated with strong short-
term ($\lesssim 10$ Myr) variability (e.g., Yuan et al. 2018). This temporal
behavior acts as “noise” in the analyses of SMBH cosmic evolution, for which
only long-term ($\gtrsim 100$ Myr) AGN strength is relevant. To overcome this
variability issue, Chen et al. (2013) and Hickox et al. (2014) proposed to use
sample-averaged SMBH accretion rate (BHAR, estimated from the combination of
direct X-ray detection and stacking) to approximate long-term average BHAR.
They found that sample-averaged BHAR is linearly correlated with galaxy SFR,
and interpreted this result as a tight universal connection between SMBH and
stellar growth over galaxy evolution timescales ($\gtrsim 100$ Myr). In this
scenario, long-term BHAR can be simply inferred from host-galaxy SFR alone.

Figure 12:  Left: Average BHAR-$M_{*}$ relation (AGN main sequence) for all
galaxies at different redshifts (as labeled). The dashed line represents the
best-fit relation based on a $z=0.5$–2 sample from the literature. At any
fixed $M_{*}$, BHAR rises toward high redshifts, but the redshift dependence
is stronger in more massive galaxies. From Yang et al. (2018a). Right: AGN
fraction (duty cycle) as a function of redshift for different $M_{*}$ bins.
$M_{*}$ increases from the leftmost to the rightmost panels. The blue and red
data points represent star-forming and quiescent galaxies, respectively. The
AGN-fraction difference between star-forming vs. quiescent samples depends on
redshift and $M_{*}$. From Aird et al. (2018).

On the other hand, deep-field studies have also found that the fraction of
AGN-hosting galaxies rises steeply as a function of stellar mass (e.g., Xue et
al. 2010; Aird et al. 2012; Bongiorno et al. 2012). This mass dependence
appears to challenge the AGN-SF connection above. This apparent paradox could
result from the SF main sequence, i.e., SFR and $M_{*}$ are positively
correlated among star-forming galaxies at a given redshift. For example, AGN
activity might be primarily related to SFR, while the apparent $M_{*}$
dependence might be a bias due to the SFR-$M_{*}$ main sequence, or vice
versa. To test this idea, Yang et al. (2017) performed partial-correlation
analyses, which control SFR ($M_{*}$) and investigate the dependence on
$M_{*}$ (SFR). Their result, somewhat surprisingly, indicates that sample-
averaged BHAR is mainly correlated with $M_{*}$, and the apparent BHAR-SFR
connection is a secondary relation caused by the SF main sequence. Similar
conclusions have also been reached by subsequent studies (e.g., Fornasini et
al. 2018; Ni et al. 2019). Observational works have also investigated the
effects of host-galaxy cosmic environments on BHAR when controlling for
$M_{*}$ (e.g, Powell et al. 2018; Yang et al. 2018b; Allevato et al. 2019;
Noordeh et al. 2020). The environmental dependence is generally weak, except
for the most massive clusters.

Motivated by the importance of $M_{*}$, studies have attempted to quantify the
BHAR dependence on $M_{*}$ at different redshifts (e.g., Georgakakis et al.
2017; Aird et al. 2018; Yang et al. 2018a).333The BHAR vs. $M_{*}$ relation is
sometimes called the “AGN main sequence”, in analogy with the well-known SF
main sequence (e.g., Mullaney et al. 2012). Such works often have to collect
large samples of AGNs, combining both deep and wide X-ray surveys to cover
AGNs from low-to-high luminosities. Fig. 12 (left) shows the resulting
BHAR-$M_{*}$ relation. At any fixed $M_{*}$, BHAR rises toward high redshifts,
likely reflecting the fact that AGN-accretion fuel (cold gas) is more abundant
in the earlier universe. However, the redshift dependence is stronger in more
massive galaxies, indicating that massive galaxies assemble their SMBH masses
earlier in cosmic history, compared to low-mass galaxies. This phenomenon is
broadly consistent with AGN downsizing (see §3.1), considering that more
massive galaxies generally have more massive SMBHs.

We caution that AGN activity could still have some “residual” dependence on
SFR, although $M_{*}$ is the main factor. Studies have also investigated the
AGN dependence on host-galaxy positions with respect to the SF main sequence
at a given $M_{*}$ (e.g., Aird et al. 2018, 2019; Masoura et al. 2018; Yang et
al. 2018a; Bernhard et al. 2019; Florez et al. 2020; Mountrichas et al.
2021b). Fig. 12 (right) displays this dependence, where galaxies are divided
into star-forming and quiescent populations. The resulting SF dependence is
quite complicated, apparently affected by both redshift and $M_{*}$. More
detailed studies found evidence suggesting the AGN activity might not be a
simple monotonic function of host-galaxy star formation. For example, AGN
activity drops from the starburst to the main sequence (MS) populations, but
it surprisingly appears to rise from the MS to the sub-MS populations (see,
e.g., Fig. 11 of Aird et al. 2019). This complexity suggests there might be
some “hidden parameters” beyond SFR and $M_{*}$ affecting SMBH growth. These
parameters could be related to galaxy morphology as we will discuss below.

Host-galaxy morphology: In local systems, SMBH masses are closely related to
host-galaxy morphology. For example, they are tightly correlated with bulge
masses, but are almost completely unrelated to galactic-disk masses (see
Kormendy & Ho 2013 for a review). Therefore, it is likely that AGN activity in
the distant universe also depends on host-galaxy morphology.

It has been long known that optically and X-ray selected AGNs can be found in
galaxies with a variety of morphological types, e.g., bulge-dominated,
irregular, and disk-dominated, since the first studies on this topic (e.g.,
Bahcall et al. 1997; Grogin et al. 2005). However, early works did not reach a
consensus on whether AGN activity is physically related to host-galaxy
morphologies, especially after controlling for the effects of stellar mass and
redshift as discussed above (e.g., Pierce et al. 2007; Kocevski et al. 2012).
One major reason for the disagreement among these works are the technical
challenges in morphological measurements (see above), which significantly
limited the sample sizes ($\lesssim 100$ X-ray AGNs).

The situation has been gradually improved with the advance of the HST CANDELS
survey (Grogin et al. 2011; Koekemoer et al. 2011), which has provided deep
$H_{160}$ imaging over five separate fields (total area $\approx 1000$
arcmin2). Based on the CANDELS data, robust morphological measurements and
classifications have been performed for $\approx 50,000$ galaxies up to
$z\approx 3$ (e.g., Huertas-Company et al. 2015). There are $\approx 1,000$
X-ray detections among these galaxies, thanks to the deep Chandra and XMM-
Newton exposures for the CANDELS fields.

Taking advantage of these large AGN and galaxy samples, Yang et al. (2019b)
revealed a tight correlation between sample-averaged BHAR and SFR for bulge-
dominated systems, and this BHAR-SFR correlation is largely unaffected by
$M_{*}$ (see Ni et al. 2019 for a similar conclusion). Fig. 13 (left) shows
this correlation. The best-fit relation has $\rm BHAR/SFR\approx 1/300$,
similar to the SMBH/bulge mass ratio observed in the local universe (e.g.,
Kormendy & Ho 2013). This similarity indicates that the BHAR-bulge SFR
relation could be the origin of the SMBH-bulge mass relation in local systems.
Yang et al. (2019b) also found that BHAR is not related to SFR for the non-
bulge-dominated sample, highlighting the key role of morphology. The bulge-
dominated systems only consist of $\approx 1/4$ of the massive ($\gtrsim
10^{10}\ M_{\odot}$) galaxy population. This explains why the strong BHAR-
bulge SFR relation was missed by the previous works that did not have
morphological information (e.g., Yang et al. 2017; Fornasini et al. 2018). The
BHAR-bulge SFR relation might also hold for the bulge component in bulge-plus-
disk systems. This can be tested if bulge SFR can be separated from disk SFR
by future high-resolution mid/far-IR imaging by, e.g., JWST and Origins.

Figure 13:  Left: The average BHAR-SFR relation for bulge-dominated galaxies.
The top and bottom panels are for different redshift bins. Each black data
point is estimated based on all galaxies in the corresponding SFR sample. To
assess the effects of stellar mass, each SFR sample is divided into
high-$M_{*}$ (blue) and low-$M_{*}$ (red) subsamples The BHAR does not appear
to be significantly affected by $M_{*}$ in general. The black lines represent
the best-fit relation (same in both panels). The strong BHAR-bulge SFR
relation suggests that SMBHs coevolve with bulges, consistent with
observations of local systems. From Yang et al. (2019b). Right: The average
BHAR-$\rm\Sigma_{1}$ relation for star-forming galaxies. Different colors
indicate different redshift bins. The lines and shaded areas are the best-fit
models and errors. In all three redshift bins, BHAR rises toward high
$\rm\Sigma_{1}$. From Ni et al. (2021b).

Besides morphological classifications, another common way to describe galaxy
shapes utilizes continuous quantities. Among these morphological quantities,
$\rm\Sigma_{1}$ (the projected central surface-mass density within 1 kpc) has
become increasingly popular among researchers, as observations have found
$\rm\Sigma_{1}$ is closely related to galaxy evolution (e.g., Barro et al.
2017). For AGN activity, studies have found AGN fraction is elevated among
high-$\rm\Sigma_{1}$ compact star-forming galaxies (e.g., Kocevski et al.
2017; Ni et al. 2019). This result is qualitatively consistent with the BHAR-
bulge SFR relation (Yang et al. 2019b), because bulge-dominated galaxies are
often compact. Ni et al. (2021b) further quantified the BHAR dependence on
$\rm\Sigma_{1}$ among star-forming galaxies, as displayed in Fig. 13 (right).
BHAR increases monotonically toward high $\rm\Sigma_{1}$ for all of the three
redshift bins investigated. The conclusion suggests a link between AGN
activity vs. host-galaxy gas content and/or gravitational potential well on
the central $\approx\ $ kpc scale, which are closely related to the quantity
$\rm\Sigma_{1}$.

Despite the recent significant progress on AGN links to host-galaxy properties
(especially morphology), we still lack a comprehensive and quantitative
description of how AGN activity depends on all the key properties including
(but not limited to) $M_{*}$, SFR, morphology, and redshift. Much larger
AGN/galaxy samples are needed to achieve this goal. The future is bright for
this fast-developing field, as many advanced multiwavelength survey telescopes
will begin operation. In addition to future X-ray telescopes (see §4.1), Rubin
will provide deep half-sky $ugrizy$ images for photometric redshifts, $M_{*}$,
and SFR measurements. JWST will open the window for high-redshift galaxies and
Compton-thick AGNs (see §3.1). Roman and Xuntian will allow large-scale
morphological measurements thanks to their efficient high-resolution imaging
capability.

##  4 Some Future Prospects and Other Relevant Reviews

###  4.1 Some Future Prospects for CXRB Surveys

Many fundamental science questions remain that can be best answered with
ongoing and new CXRB surveys, including the following:

  1. 1.

How do highly obscured SMBHs grow and provide feedback through the $z\approx
1$–4 galaxy formation era?

  2. 2.

How do SMBHs grow in the first galaxies at $z\approx 4$–10, and what are the
“seeds” for these SMBHs?

  3. 3.

What host-galaxy properties link most strongly to SMBH growth, and what does
this reveal about SMBH-galaxy co-evolution?

  4. 4.

How does large-scale cosmic environment, ranging from voids to superclusters,
relate to SMBH growth?

  5. 5.

What galaxy physical properties drive the observed cosmic evolution of their
X-ray binary populations, and how do these populations evolve at $z\approx
3$–10?

  6. 6.

What will a $\approx 10^{5}$-object X-ray cluster/group sample reveal about
the growth of the most massive cosmic structures, the cosmological model, and
dark energy?

  7. 7.

How did the ICM form and SMBHs grow in $z\lower
2.0pt\hbox{$\,\buildrel\scriptstyle>\over{\scriptstyle\sim}\,$}2$
protoclusters?

  8. 8.

What is the nature of faint X-ray transients in the distant universe?

The CXRB-surveys community is blessed to have multiple X-ray missions capable
of addressing these questions still operating, including Chandra, XMM-Newton,
INTEGRAL, Swift, NuSTAR, and SRG. These missions alone should ensure another
great decade of CXRB survey discoveries, particularly if they undertake
aggressive projects capable of exploring new “discovery space”. Moreover, the
vast archives of X-ray observations from these missions (e.g., note the
locations of the serendipitous surveys in Fig. 2) will be made immensely more
valuable as the extraordinary new data from complementary imaging and
spectroscopic surveys become available, such as those from Rubin, Xuntian,
SDSS, AAT, DESI, 4MOST, MOONS, PFS, Extremely Large Telescopes, JWST, Euclid,
Roman, ALMA, LMT TolTEC, the VLA, ASKAP, MeerKAT, and the SKA. These will
allow thousands of archival sensitive pointed X-ray observations and the all-
sky surveys to be systematically mined to address science questions
comprehensively with titanic X-ray source samples (e.g., Brandt & Vito 2017).

Figure 14:  Left: Grasp (the product of effective area and field of view) vs.
energy for the Einstein Probe Wide-Field X-ray Telescope (EP WXT), compared to
the grasps of some current and previous missions with focusing X-ray
telescopes. The large grasp of Einstein Probe should make it a powerful wide-
field transient survey facility. Updated from Zhao et al. (2014). Right: 0.5–2
keV flux limit vs. area for planned Athena CXRB surveys compared to a
selection of previous CXRB surveys (a half-energy width of the Athena point
spread function of $5^{\prime\prime}$ is assumed). Note the large areas that
Athena aims to cover to excellent sensitivity. Adapted from Marchesi et al.
(2020).

Einstein Probe, planned for launch in 2023, should greatly advance
understanding of transient sources within the 0.5–4 keV CXRB. It will utilize
Lobster-eye optics (covering $\approx 3600$ deg2) to perform a systematic
large-grasp survey of transients at an unprecedented combination of
sensitivity and cadence (e.g., see Fig. 14 left). Discovered transients will
be investigated with an on-board follow-up X-ray telescope.

Athena, selected for launch in $\approx 2034$, will be a potent mission for
$\approx 0.3$–10 keV CXRB surveys if it achieves its planned imaging point
spread function; e.g., covering several deg2 to 0.5–2 keV fluxes of $\approx
2\times 10^{-17}$ erg cm-2 s-1 (see Fig. 14 right) and providing sufficient
photon statistics for quality source characterization. Athena surveys will
hopefully provide a complete census of SMBH growth, including highly obscured
systems, out to $z\approx 8$–10.

Lynx, a candidate large NASA mission, aims to observe the seeds of the first
SMBHs directly as well as conduct much superb broader survey science. With
Chandra-like angular resolution and a collecting area $\approx 30$–50 times
that of Chandra, Lynx could detect $\approx 30,000$ M⊙ black holes at
$z\approx 10$ (with 0.5–2 keV fluxes of $\approx~{}5\times 10^{-19}$ erg cm-2
s-1; compare with Fig. 2 left). Seeding models (e.g., Population III remnants
vs. direct-collapse black holes) would be discriminated using the observed
X-ray luminosity function and host properties.

Additional impressive surveyors of the CXRB, including STAR-X, AXIS, and
HEX-P, are under active scientific development and will hopefully soon obtain
construction funding.

###  4.2 Other Relevant Reviews

Owing to page and reference limits, this overview has been highly concise.
Other useful relevant reviews published over the past decade include Treister
& Urry (2011), Brandt & Alexander (2015), Netzer (2015), Xue (2016), Padovani
et al. (2017), Hickox & Alexander (2018), Allen & Mantz (2020), Siemiginowska
& Civano (2020), and Krivonos et al. (2021).

##  5 Acknowledgments

We thank DM Alexander, CT Chen, L Klindt, BD Lehmer, B Luo, Q Ni, CJ Papovich,
and F Vito for helpful discussions. WNB acknowledges support from the V.M.
Willaman Endowment, NSF grant AST-2106990, NASA grant 80NSSC19K0961, and Penn
State ACIS Instrument Team Contract SV4-74018 (issued by the Chandra X-ray
Center, which is operated by the Smithsonian Astrophysical Observatory for and
on behalf of NASA under contract NAS8-03060). The Chandra ACIS Team Guaranteed
Time Observations (GTO) utilized were selected by the ACIS Instrument
Principal Investigator, Gordon P. Garmire, currently of the Huntingdon
Institute for X-ray Astronomy, LLC, which is under contract to the Smithsonian
Astrophysical Observatory via Contract SV2-82024. GY acknowledges support from
the NASA/ESA/CSA James Webb Space Telescope through the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Incorporated, under NASA contract NAS5-03127. Support
for program number JWST-ERS-01345 was provided through a grant from the STScI
under NASA contract NAS5-03127. GY acknowledges support from the George P. and
Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy at
Texas A&M University.

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