###### Abstract

Pairs of active galactic nuclei (AGN) are observational flags of merger-driven
SMBH growth, and represent an observable link between galaxy mergers and
gravitational wave (GW) events. Thus, studying these systems across their
various evolutionary phases can help quantify the role mergers play in the
growth of SMBHs as well as future GW signals expected to be detected by pulsar
timing arrays (PTAs). At the earliest stage, the system can be classified as a
“dual AGN" where the SMBHs are gravitationally unbound and have typical
separations $<$30 kpc, and at the latest stage the system can be classified as
a “binary AGN" where the two massive host galaxies have likely been
interacting for hundreds of megayears to gigayears. However, detecting and
confirming pairs of AGN is non-trivial, and is complicated by the unique
characteristics of merger-environments. To date, there are less than 50 X-ray
confirmed dual AGN and only 1 strong binary AGN candidate. _AXIS_ will
revolutionize the field of dual AGN: the point-spread-function (PSF), field-
of-view (FOV), and effective area ($A_{eff}$) are expected to result in the
detection of hundreds to thousands of new dual AGN across the redshift range
$0<z<4$. The _AXIS_ AGN surveys will result in the first X-ray study that
quantifies the frequency of dual AGN as a function of redshift up to $z=3.5$.
_This White Paper is part of a series commissioned for the AXIS Probe Concept
Mission; additional AXIS White Papers can be found at theAXIS website with a
mission overview here_.

xx 1 5 Tracking SMBH mergers from kpc to sub-pc scales with AXIS Adi Foord
1,2†, Nico Cappelluti 3, Tingting Liu 4, Marta Volonteri 5, Melanie Habouzit
6,7, Fabio Pacucci8,9, Stefano Marchesi10,11,12, Nianyi Chen13, Tiziana Di
Matteo13, Labani Mallick14,15,16,‡, Michael Koss17 Firstname Lastname,
Firstname Lastname and Firstname Lastname<EMAIL_ADDRESS>
###### Contents

  1. 1 Introduction
    1. 1.1 Detecting Dual AGN
    2. 1.2 Detecting Binary AGN
  2. 2 The Power of _AXIS_ for AGN Pair Studies
    1. 2.1 The Blind Search for Dual AGN in _AXIS_ AGN Surveys
  3. 3 Quantifying the Rate of Dual AGN to High-z
  4. 4 Observations of SMBH binaries and mergers in X-rays
    1. 4.1 Periodicity, chirping, and merger signatures
    2. 4.2 Spectral hardening and double broad Fe lines
    3. 4.3 Synergies with other EM observatories
  5. 5 Population Statistics with AGN Pairs
    1. 5.1 Constraining Binary SMBH hardening timescales
      1. 5.1.1 Dual AGN
      2. 5.1.2 Binary AGN

###### List of Figures

  1. 1 Dual AGN as viewed by _Chandra_ and _AXIS_
  2. 2 Properties of Dual AGN detected by _AXIS_
  3. 3 The Frequency of Dual AGN Across Redshift
  4. 4 Binary AGN Detections with _AXIS_
  5. 5 Redshift versus Physical Separation for Dual AGN Detections

##  1 Introduction

Supermassive black holes (SMBHs) with masses of $10^{6}-10^{9}$ $M_{\odot}$
are ubiquitous in most massive galaxies, and classical hierarchical galaxy
evolution predicts that the later stages of galaxy evolution are governed by
mergers (e.g., White & Rees (1978)). As a result, galaxy mergers provide a
favorable environment for the assembly of active galactic nuclei (AGN) pairs
(Volonteri et al., 2003).

“Dual AGN" are pairs of AGN in the earliest phases of the galaxy merger, where
the SMBHs are gravitationally unbound. They have typical separations $<$ 30
kpc and can be in a single galaxy or an interacting system. The SMBHs will
sink toward the center of the stellar distribution on the dynamical friction
time scale. For typical values of the physical parameters governing the system
(such as the maximum impact parameter $b_{max}=$5 kpc and $v\approx\sigma=$200
km s-1), the inspiral time is only 3 Gyr, and any $10^{8}$ SMBH sitting within
$\sim$10 kpc of the center of a typical galaxy will spiral to the center
within a Hubble time. These inspiral times are expected to vary as a function
of the merging environment. They may be shorter for eccentric orbits, where
the SMBH can pass through higher density regions with stronger drag forces
Binney & Tremaine (1987); while computational analyses have shown that most
minor mergers (e.g., with stellar mass ratios less than 0.1) will not result
in close ($<10$ kpc) SMBH pairs forming within a Hubble time (Tremmel et al.,
2018).

The system can evolve into a SMBH binary (SMBHB), the final stage of a galaxy
merger, where the two massive host galaxies have likely been interacting for
hundreds of megayears to gigayears (Begelman et al., 1980). The merging system
is classified as a binary when the SMBHs are gravitationally bound in a
Keplerian orbit, and for a wide range SMBH masses and host galaxy environments
this occurs at orbital separations $<$10 pc (Mayer et al., 2007; Dotti et al.,
2007; Khan et al., 2012). As the last stage before coalescence, SMBHBs
represent an observable link between galaxy mergers and gravitational wave
(GW) events. The closest pairs (at sub-pc separations, or at $\sim
10^{3}-10^{4}$ Schwarzschild radii) are strong emitters of low-frequency (nHz)
GWs that are expected to dominate the GW background accessible to pulsar
timing arrays (PTAs; Burke-Spolaor et al. (2019)), which are sensitive to
massive SMBHs ($10^{7}-10^{9}M_{\odot}$). They are also direct precursors to
GW events detectable by future space-based laser interferometers such as the
Laser Interferometer Space Antenna (LISA), which are sensitive to massive
black hole (MBH) binaries with $10^{4}-10^{7}M_{\odot}$ (Sesana et al., 2007;
Luo et al., 2016b; Amaro-Seoane et al., 2023). The link between pairs,
binaries, and GW astrophysics, and the importance of detecting more systems,
is becoming increasingly stronger with recent PTA results finding evidence of
a stochastic GW background consistent with a population of SMBHBs (e.g.,
(Agazie et al., 2023b; Antoniadis et al., 2023; Reardon et al., 2023; Xu et
al., 2023)).

###  1.1 Detecting Dual AGN

Commonly measured empirical trends between the supermassive black hole mass
($M$) and host-galaxy bulge velocity dispersion ($\sigma$) and luminosity
($L$) $-$ i.e., the $M$–$\sigma$ and $M$–$L$ relations $-$ suggest that AGN
play vital roles in shaping the properties of galaxies across cosmic time
(Magorrian et al., 1998; Ferrarese & Merritt, 2000; Tremaine et al., 2002;
Gültekin et al., 2009; McConnell & Ma, 2013). Galaxy mergers are believed to
be a key process supporting the various SMBH-galaxy scaling relations (Jahnke
& Macciò, 2011; Hopkins et al., 2006; Sobral et al., 2015). Theoretically,
there are many reasons to expect a link between gas-rich, similar-mass mergers
and the accretion of material onto at least one of the supermassive black
holes (e.g., Volonteri et al. (2003); Hopkins et al. (2006)). Tidal forces
between galaxies can introduce gravitational torques that effectively
dissipate the specific angular momentum of material from large-scale gas
reservoirs and transport significant quantities down to scales in which SMBHs
can accrete (Barnes & Hernquist, 1991; Di Matteo et al., 2008; Anglés-Alcázar
et al., 2017). This can result in enhanced periods of SMBH growth, regulation
of the host galaxy’s properties, and relations such as $M$–$\sigma$ and
$M$–$L$ emerging (e.g., Wyithe & Loeb (2003); Di Matteo et al. (2005)).

However, observationally, the connection between galaxy mergers and SMBH
activity remains poorly understood; various studies have found conflicting
results regarding whether mergers are responsible for, or even correlated
with, SMBH activity (Urrutia et al., 2008; Koss et al., 2010; Ellison et al.,
2011; Schawinski et al., 2012; Treister et al., 2012; Satyapal et al., 2014;
Villforth et al., 2014; Glikman et al., 2015, 2018; Fan et al., 2016; Weston
et al., 2017; Barrows et al., 2018; Goulding et al., 2018; Onoue et al.,
2018). The activity of AGN is likely obscuration and merger-stage dependent
Kocevski et al. (2015); Koss et al. (2016); Weston et al. (2017).
Consequently, past measurements were likely complicated by (1) sensitivity and
angular resolution of available instruments, (2) identification of galaxy
mergers at high-z, and (3) intrinsic properties of merging SMBHs and their
host galaxies (such as, AGN variability and gas/dust obscuration). One of the
best ways to analyze the possible ties between merger environments and SMBH
activity is to study systems with unique observational flags of merger-driven
SMBH growth – or dual AGN. By detecting pairs of SMBHs across a wide range of
redshift, we can observationally measure the role (or lack thereof) that
mergers play in enhancing SMBH growth across cosmic time.

Direct detection of emission associated with two accreting SMBHs requires both
angular resolution (1 kpc corresponds to angular separations less than 1at
$z>0.1$) and sensitivity. Radio observations can resolve radio-emitting cores
on the smallest spatial scales Rodriguez et al. (2006); Rosario et al. (2010);
Fu et al. (2015); Tingay & Wayth (2011); Deane et al. (2014); Gabányi et al.
(2014); Wrobel et al. (2014a, b); Müller-Sánchez et al. (2015); Kharb et al.
(2017); however, this technique is only efficient for the minority of AGN
pairs that are expected to be radio-bright Hooper et al. (1995). Optical
selection techniques are affected by optical extinction and contamination from
star formation, which is especially problematic when observing highly-obscured
mergers Kocevski et al. (2015); Koss et al. (2016); Ricci et al. (2017);
Blecha et al. (2018); De Rosa et al. (2018); Koss et al. (2018); Lanzuisi et
al. (2018); Torres-Albà et al. (2018). As a result, confirmation of most AGN
pairs has been made via X-ray observations (e.g., NGC 6240; Komossa et al.
(2003)), and most studies leverage Chandra’s superior angular resolution to
discover closely-separated dual AGN Koss et al. (2012); Foord et al. (2019,
2021a). However, there are less than 50 directly detected pairs of X-ray AGN
candidates to date (see, e.g., Chen et al. (2022a)) as the majority of
Chandra-detected dual AGN are restricted to the local universe ($z<0.1$).
High-z Chandra survey studies have resulted in non-detections Sandoval et al.
(in prep.) due to the small field of view with a high spatial resolution
($<1.5\arcsec$) and sensitivity.

###  1.2 Detecting Binary AGN

Despite the strong theoretical case for the existence of SMBHBs, their
observational evidence has been elusive. Currently, the only widely-accepted
SMBHB is at a projected separation of 7.3 pc (in the radio galaxy 0402+379 at
$z=0.055$) where the two nuclei are directly resolved via very long baseline
interferometry (Rodriguez et al., 2006) and their proper motion is
statistically significant over the course of $\sim$ a decade (Bansal et al.,
2017). However, 0402+379 is not representative of the low-frequency GW sources
emitting in the PTA or LISA band, since its separation is much wider and its
GW inspiral timescale is much longer than a Hubble time. Indeed, direct
observations cannot resolve the vast majority of SMBHBs in the GW-dominated
regime of orbital evolution (which corresponds to $\sim$ centi- to milli-
parsec separations), and even the Event Horizon Telescope can only resolve
$\sim$ pc scales except for the most nearby systems. Therefore, the
electromagnetic (EM) search for SMBHBs requires _indirect_ observations from
which the presence of a binary can be inferred.

Intuitively, the orbital motion of a binary may imprint on the EM emission of
the system as a periodic variation of the flux. This possible binary signature
has in fact been studied extensively by analytic calculations and numerical
simulations, and the physical mechanisms by which an AGN hosting an SMBHB (or
a “binary AGN”) can vary periodically include: BH-disk impact (Lehto &
Valtonen, 1996; Ivanov et al., 1998), modulated accretion (e.g. MacFadyen &
Milosavljević (2008); Shi et al. (2012); Noble et al. (2012); D’Orazio et al.
(2013); Farris et al. (2014); Gold et al. (2014)), relativistic Doppler boost
(D’Orazio et al., 2015), and self-lensing (D’Orazio & Di Stefano, 2018).
Systematic searches for periodically varying AGN in large optical time-domain
surveys have yielded hundreds of binary candidates (e.g. (Graham et al.,
2015b, a; Charisi et al., 2016; Liu et al., 2015, 2019; Chen et al., 2020,
2022b)), while similar searches in X-rays have been less than successful due
to the pointed nature of most X-ray observations and the depth and observing
cadence of current surveys (e.g., (Liu et al., 2020)). Yet, X-rays are a more
direct tracer of gas in the immediate vicinity of the BHs (the so-called
“minidisks”) at the inspiral stage (e.g., Tang et al. (2018); d’Ascoli et al.
(2018)), i.e., when the optical emission originates from further out in the
system and may become decoupled from the binary motion (e.g., (Krauth et al.,
2023)). Hence, the most direct link between the growth of SMBHs and and their
mergers is best established (in the electromagnetic regime) with observations
at short wavelengths (especially X-rays).

In addition to tracking binary-induced periodicity, which has also been
predicted in the optical bands, X-rays can _uniquely_ probe signatures such as
X-ray spectral hardening (Roedig et al., 2014; Farris et al., 2015) and double
broad Fe K$\alpha$ lines (Sesana et al., 2012; Jovanović et al., 2014). These
signals are often accompanied by distinct emissions in other wavebands,
suggesting strong synergies between an X-ray telescope and other
observatories, including optical ground-based time-domain surveys such as LSST
($\sim 2025-2035$). More excitingly, EM observations of SMBHBs will also
enable multi-messenger science in the low-frequency GW regime, which has
recently been opened up by the PTA experiments (e.g., (Agazie et al., 2023b)).
If this gravitational wave background originates from a cosmic population of
SMBHBs (Agazie et al., 2023a), individual binaries could be detected as single
sources by PTAs by $\sim 2030$ (Rosado et al., 2015; Kelley et al., 2018). In
the mid-2030s, LISA will start probing GW sources in the mHz range, among
which are the mergers of massive black holes (MBHs; $\sim
10^{4}-10^{7}M_{\odot}$). These low-frequency GW detectors will prompt
searches for EM counterparts in localized sky areas; at the same time, EM-
detected SMBHBs can be used in the joint search for GW signals in PTA data or
serve as “verification binaries” for LISA111X-ray observations will be crucial
for identifying LISA counterparts. See AXIS white paper ”Prospects for Time-
Domain and Multi-Messenger Science with AXIS” for a summary of multi-messenger
science with SMBHBs and the synergies of AXIS with low-frequency GW
detectors.. The rich, multi-wavelength, and multi-messenger science of MBHBs
and MBH mergers, therefore, demands a sensitive X-ray telescope operating at
the $\sim$ same time as the suite of EM and GW observatories in the 2030s.

##  2 The Power of _AXIS_ for AGN Pair Studies

The _AXIS_ point-spread-function (PSF), field-of-view (FOV), and effective
area ($A_{eff}$) are expected to result in the detection of hundreds to
thousands of new dual AGN across the redshift range $0<z<4$ (see Reynolds et
al. (2023)). Currently, large-scale blind searches for X-ray dual AGN are
hampered by the large dependence of _Chandra_ ’s PSF on the off-axis angle
(OAA). The shape and size of the High-resolution Mirror Assembly PSF varies
significantly with source location in the telescope field of view, as well as
the number of photons. Between 0$<$ OAA $<$8, the 90% encircled energy radius
grows from $\sim$2to 6. The point spread function becomes difficult to model
above OAA values of 3Sandoval et al. (in prep.), and consequently, off-axis
point sources are frequently misconstrued as extended or having a multi-
component structure. On top of this, putative dual AGN with angular
separations $>1$are difficult to detect at OAA$>$3, as the angular separation
becomes smaller than the semi-major axis of the PSF. Although the proposed on-
axis angular resolution of _AXIS_ (PSF Half Energy Width$=$1.5) is marginally
larger than _Chandra_ ’s on-axis angular resolution (PSF Half Energy
Width$=$0.8), the field-of-view average PSF is stable as a function of
increasing off-axis angle (1.6up to OAA$=$7.5) and is significantly smaller
than _Chandra_ ’s field-of-average ($\sim$5up to OAA$=$7.5on ACIS-I).

The _AXIS_ PSF, coupled with $A_{eff\mathrm{,~{}1~{}keV}}=4200$ cm2 and
$A_{eff\mathrm{,~{}6~{}keV}}=830$ cm2 (compared to ACIS at launch with
$A_{eff\mathrm{,~{}1~{}keV}}=500$ cm2 and $A_{eff\mathrm{,~{}6~{}keV}}=200$
cm2), and a 24diameter active field of view (compared to ACIS-I with 16square
field of view) will revolutionize the field of dual AGN. A single 300 ks
exposure with AXIS yields a sample size of 1000 AGN for which blind dual AGN
searches down to 1.5can be carried out. In comparison, with a 300 ks ACIS-I
observation, it is expected that less than 20 AGN will be detected within the
field that has a PSF $<$1.5.

Figure 1: Dual AGN as viewed by _Chandra_ and _AXIS_

A dual AGN with $L_{X,~{}\mathrm{0.5-8~{}keV}}=5\times 10^{43}$ erg s-1 at
$z=3$, with $r=1.5\arcsec$ (11.8 kpc) and a flux ratio of 0.5 (the secondary
AGN has a luminosity of $L_{X,~{}\mathrm{0.5-8~{}keV}}=2.5\times 10^{43}$ erg
s-1). We simulate a 300 ks observation with both _Chandra_ and _AXIS_ as a
function of increasing off-axis angle (OAA), from on-axis (0) to highly off-
axis (7.5). On-axis, _Chandra_ observes 18 counts associated with the dual
AGN, while _AXIS_ observes 150. We show the size of the point spread function
in a black dashed line. Given the stability of the shape and size of the
_AXIS_ point spread function, together with the enhanced effective area and
field of view, a single 300 ks _AXIS_ pointing results in the sensitivity to
detect over 20$\times$ more dual AGN than possible with a similar _Chandra_
pointing.

###  2.1 The Blind Search for Dual AGN in _AXIS_ AGN Surveys

The _AXIS_ AGN surveys will result in the first X-ray study that quantifies
the frequency of dual AGN as a function of redshift up to $z=3.5$. In
particular, 10,000 X-ray AGN detected within a deep and intermediate survey
field will yield hundreds of new dual AGN detections; including data from a
serendipitous wide-area survey from Guest Observer observations could increase
the detection number to the thousands. AXIS plans to follow a “Wedding cake”
strategy to perform its extragalactic surveys: (1) a deep 7 Ms observation of
a single AXIS pointing ($\sim$0.16 deg2, or $\sim$24$\times$24 square arcmin);
and (2) an intermediate-area (2.5 deg2) and intermediate-depth (375 ks
exposure per pointing). An AXIS Serendipitous field built via combining Guest
Observer observations (assuming 20 Ms of guaranteed non-Galactic plane time,
with a median of 50 ks per pointing) could cover 50 deg2 with a sensitivity
$\sim$10-16 erg s-1 cm-2 (see $\ast$ cite Seeding White Paper $\ast$) for more
details on the surveys.

We use results from end-to-end _AXIS_ simulations with the SIXTE tool, as
described in Cappelluti et al. (2023). Briefly, simulations have been
performed using the Monte Carlo code Simulation of X-ray Telescopes (SIXTE;
Dauser et al. (2019)). SIXTE simulates X-ray observations by modeling the
arrival time, energy, and position of each photon based on the unique
telescope input parameters (i.e., effective area, field of view, point spread
function, vignetting, read-out properties, redistribution matrix). The input
catalog for the _AXIS_ survey simulations is based on the Gilli et al. (2007)
AGN population synthesis model. AGN have been simulated down to a 0.5–2 keV
luminosity L0.5-2=1040 erg s-1 and up to redshift $z=$3\. In the high-redshift
regime (i.e., at $z>$3, where the AGN space density starts declining), a mock
catalog built from the Vito et al. (2014) $z>$3 AGN luminosity function is
used. The catalogs used are available online at
http://cxb.oas.inaf.it/mock.html in FITS format and ready to be used within
SIXTE.

From the mock _AXIS_ AGN fields, we select AGN that meet the following
criteria: $L_{X,~{}\mathrm{0.5-8~{}keV}}>10^{42}$ erg s-1; $n$, the number of
0.5$-$8 keV counts, $>50$; and $OAA<10\arcmin$. We imposed these cuts to form
a sample of AGN where we can easily find dual AGN. For example, if $n<50$,
assuming a standard flux-ratio of $\sim 0.1$ Koss et al. (2010), the secondary
will be contributing $<$5 X-ray counts. Our luminosity and OAA cuts follow a
similar reasoning: below $10^{42}$ erg s-1 we may suffer from contamination
from bright X-ray binaries and/or ultra-luminous X-ray sources, and at
$OAA<10\arcmin$ the average _AXIS_ PSF half energy width (HEW) is 1.6. After
imposing these cuts, we have a sample of $\sim$10,000 X-ray AGN. In Fig. 2, we
show the distributions of $z$ and $n$ of our _AXIS_ sample.

We compare these distributions to those for X-ray AGN from publicly available
wide and deep Chandra fields: X-UDS (Chandra imaging of the Subaru-XMM
Deep/UKIDSS Ultra Deep Survey field; Kocevski et al. (2018)), AEGIS-XD
(Chandra imaging of the central region of the Extended Groth Strip; Nandra et
al. (2015)), CDF-S (Chandra Deep Field-South; Luo et al. (2016a)), and the
COSMOS-Legacy survey (Civano et al. (2016)). Here, we include AGN that satisfy
the following criteria: $L_{X,~{}\mathrm{0.5-8~{}keV}}>10^{42}$ erg s-1; $n$,
the number of 0.5$-$8 keV counts, $>50$; and $OAA<4\arcmin$. In particular,
the _Chandra_ PSF HEW at 4is close to 3. Between _AXIS_ and _Chandra_ , the
samples are significantly different as a function of their size, redshift, and
X-ray counts. In comparison to the 10,000 X-ray detected AGN by _AXIS_ , the
_Chandra_ sample size is composed of 428 AGN that span a shorter redshift
range and have far fewer counts (with the majority of X-ray AGN at $z<2.5$ and
with $n_{counts}<200$)

Figure 2: Properties of Dual AGN detected by _AXIS_

We show the distributions for redshift and number of 0.5$-$8 keV counts
($n_{counts}$) associated with a sample of AGN from an _AXIS_ deep (5 Ms
observation of a single _AXIS_ pointing) and intermediate (300 ks exposure per
pointing) survey from which we can analyze for the presence of a dual AGN. We
include X-ray AGN that meet the following criteria:
$L_{X,~{}\mathrm{0.5-8~{}keV}}>10^{42}$ erg s-1; $n$, the number of 0.5$-$8
keV counts, $>50$; and $OAA<10\arcmin$. We include $z$ and $n_{counts}$
information for publicly available wide and deep Chandra fields: X-UDS
(Chandra imaging of the Subaru-XMM Deep/UKIDSS Ultra Deep Survey field;
Kocevski et al. (2018)), AEGIS-XD (Chandra imaging of the central region of
the Extended Groth Strip; Nandra et al. (2015)), CDF-S (Chandra Deep Field-
South; Luo et al. (2016a)), and the COSMOS-Legacy survey (Civano et al.
(2016)).

##  3 Quantifying the Rate of Dual AGN to High-z

AXIS will observationally constrain the frequency of X-ray dual AGN to within
3%, up to z=3.5, quantifying how (or if) mergers affect SMBH growth and galaxy
evolution. If mergers play no role in enhancing SMBH growth, the expected
frequency of dual AGN is predicted to be below 2% at all redshifts Aird et al.
(2019); Ventou et al. (2017); however, large-scale cosmological hydrodynamical
simulations that model the physics associated with SMBH accretion and mergers
and predict that the frequency of dual AGN should be a factor of two higher
Volonteri et al. (2022); Chen et al. (2023a), while nearby observations of
dual AGN predict a fraction four times as high Koss et al. (2012). The AXIS
deep and intermediate survey will detect a sample size of AGN large enough to
discern between a non-enhanced and a merger-enhanced fraction, down to angular
separations of 1.5$\arcsec$.

There have been many optical searches for quasar pairs in the high-redshift
Universe, where tens of candidates have been identified ($z>1$; e.g., Hennawi
et al. (2006); Myers et al. (2008); Hennawi et al. (2010); Kayo & Oguri
(2012); Eftekharzadeh et al. (2017)). Most recently, two of the highest-z dual
AGN candidates ($z>5$) were detected via optical spectroscopy and photometry
(Yue et al., 2021, 2023), and new observational techniques that leverage the
angular resolution of Gaia have been effective first steps for detecting the
dual AGN population at high-z (i.e., (Chen et al., 2023b), (Ciurlo et al.,
2020)). However, large surveys with wide-area coverage are necessary to find
large samples of dual AGN candidates. A handful of large surveys in the
optical regime have yielded constraints on the high-z dual AGN fraction.
Silverman et al. (2020) analyze double quasars resolved by the Hyper Suprime-
Cam (HSC) Subaru, where $\sim$100 dual AGN candidates were identified out to
$z=4.5$. Shen et al. (2023) analyze 60 Gaia-resolved double quasars to measure
the quasar pair statistics at $z>1.5$. Both studies find no evidence for
evolution across redshift, and significantly different dual AGN fractions
($\sim 0.26\pm 0.18$% vs. $\sim 6.2\pm 0.5\times 10^{-4}~{}$%). On top of
this, optical selection techniques for AGN are affected by optical extinction
and contamination from star formation, which is especially problematic when
observing highly-obscured mergers Kocevski et al. (2015); Koss et al. (2016);
Ricci et al. (2017); Blecha et al. (2018); De Rosa et al. (2018); Koss et al.
(2018); Lanzuisi et al. (2018); Torres-Albà et al. (2018); Foord et al.
(2021b).

To date, most predictions of the dual AGN fraction at high-$z$, and as a
function of $z$, have been carried out via cosmological simulations (Steinborn
et al., 2016; Rosas-Guevara et al., 2019; Volonteri et al., 2022; Chen et al.,
2023a).

The assumed physics, spatial, and mass resolution, as well as selection
criteria for dual AGN, vary across each simulation. In particular, results
from the Magneticum Pathfinder Simulations (Steinborn et al. 2016; box size =
182 cMpc3) resolve SMBH pairs down to 2-5 kpc; the The Evolution and Assembly
of GaLaxies and their Environment (EAGLE) simulations (Rosas-Guevara et al.
2019; box size = 100 cMpc3) resolve SMBH pairs down to 5 kpc; the Horizon-AGN
simulations (Volonteri et al. 2022; box size = 142 cMpc3) resolve SMBH pairs
down to 4 kpc; and ASTRID simulations (Chen et al. 2023a; box size = 369
cMpc3) resolve SMBH pairs with separations down to 4/(1+z). Both Horizon-AGN
and ASTRID include sub-grid dynamical friction modeling. A nearby
observational constraint using nearby ($z<0.05$) _Chandra_ observations places
a limit on spectroscopically confirmed X-ray dual AGN of $4.4_{-2.2}^{+4.5}\%$
Koss et al. (2012), and a high-z observational constraint analyzing _Chandra_
survey data at $2.5<z<3.5$ places an upper limit of $4.5\%$ Sandoval et al.
(in prep.).

In Fig. 3, we plot these two observational limits, as well as results from the
Horizon and ASTRID simulations Volonteri et al. (2022); Chen et al. (2023a).
Both the Horizon and ASTRID simulation results have been derived specifically
for _AXIS_ observations, i.e., each AGN in a pair has $L_{bo}>10^{43}$
(Eddington-ratios down to 0.1), and all dual AGN have separations
$1.5\arcsec<r<30$ kpc (via private communication). We also show the expected
fraction of X-ray dual AGN, assuming the observed X-ray incidence of single
AGN in galaxies Aird et al. (2019). We assume that each dual AGN is undergoing
a galaxy merger and weigh the X-ray incidence of a single AGN by the observed
galaxy merger fraction Ventou et al. (2017) to derive the observed dual AGN
fraction. Whereas the cosmological simulations include accretion physics
introduced by galaxy mergers, the observed dual AGN fraction represents the
statistical probability of detecting two X-ray AGN in a galaxy merger,
assuming that the probability of finding an X-ray AGN is not affected by the
merger environment.

Using a sub-sample of 10,000 X-ray AGN from the _AXIS_ survey fields (see
Section 2.1), we can statistically (at the 95% C.L.) discern between predicted
merger- and secular-dominated dual AGN fractions, across $0<z<3.5$.
Interestingly, nearby observational constraints anchor the low-redshift X-ray
dual AGN fraction twice as high as the merger-triggered accretion models
predicated by the cosmological simulations. Assuming that the X-ray dual AGN
fraction scales similarly to those predicted by cosmological simulations, we
may expect the X-ray dual AGN fraction to peak at values closer to 8% at
$z=2$. This would amount to detecting hundreds of more dual AGN than
predicated by the cosmological simulations, and boost our population
statistics.

Figure 3: The Frequency of Dual AGN Across Redshift

Dual AGN fraction versus redshift. If mergers play no role in enhancing SMBH
growth, we may expect the frequency of dual AGN to be under 2% at all
redshifts (as estimated by the X-ray active fraction of galaxies and the
observed galaxy merger rate; Aird et al. (2019); Ventou et al. (2017)).
However, predictions from large-scale cosmological simulations (green squares
from Horizon-AGN Volonteri et al. (2022); purple circles from ASTRID Chen et
al. (2023a)) that model the physics associated with mergers and SMBH accretion
predict a dual AGN fraction twice as high (between $<1\%$ and up to $4\%$);
and nearby observational constraints anchor the low-redshift dual AGN fraction
at a factor of 4 higher ( 4% in the local universe). Previous X-ray analyses
quantifying the dual AGN fraction at both low and high redshift (brown
triangles) have resulted in non-detections and large-error bars, due to the
sample size of AGN as observed by _Chandra_ Koss et al. (2016); Sandoval et
al. (in prep.). Only _AXIS_ can statistically differentiate between the low-
and high-end predictions and constrain the dual AGN fraction up to $z=3.5$,
measuring whether galaxy mergers enhance SMBH growth over cosmic time.

##  4 Observations of SMBH binaries and mergers in X-rays

Progress in the past $\sim$ decade in numerical simulations of a SMBH binary
embedded in a circumbinary disk has drastically advanced our knowledge of its
configuration, accretion mechanisms, and the expected EM output. These
simulations have reached the general consensus that the binary torque carves
out an empty “cavity” in the circumbinary disk, which has a radius
approximately twice the binary separation. Nevertheless, gas flows into the
cavity through narrow streams and fuels the BHs via “minidisks,” which should
sufficiently power the BHs to radiate as luminously as regular AGN. This
distinctive configuration, which is coupled to the binary’s orbital motion,
produces a range of observational signatures that largely fall into one of two
categories: variability and spectral features.

###  4.1 Periodicity, chirping, and merger signatures

The orbital motion of the BHs can imprint periodic variations on the EM flux
of the binary system via mechanisms such as relativistic Doppler effects
D’Orazio et al. (2015), gravitational lensing (D’Orazio & Di Stefano, 2018),
modulated accretion onto the binary (e.g. (Noble et al., 2012; Farris et al.,
2014; Bowen et al., 2019; Noble et al., 2021)), out-flung streams of gas
hitting the cavity wall (Tang et al., 2018), and mass exchange between the
minidisks (Bowen et al., 2017). In the late inspiral stage where the binary
orbit is rapidly shrinking, the periodicity may still able to follow the
increasing orbital frequency, producing an EM “chirp” (e.g. (Tang et al.,
2018)). In order to distinguish these binary variability signatures from the
more likely occurrence of regular (single) AGN variability, at least two
observational requirements should be met: (1) Because of the rarity of binary
AGN, a survey should probe a sufficiently large volume (i.e., sky area and
depth) which samples a large number of AGN. Current observational and
theoretical work puts the occurrence rate of periodically varying binaries at
$\lesssim 10^{-4}$ per AGN (Liu et al., 2019; Kelley et al., 2019); detecting
binary AGN would thus require a sample size of at least $\sim 10^{4}$ AGN. (2)
Because regular AGN (powered by single BHs) are known to vary stochastically
and _aperiodically_ , at least a few cycles should be sampled in order to
distinguish true periodicity from a stochastic process (Vaughan et al., 2016).
Within each cycle, the periodic variation should be tracked with a high
sampling rate and high precision in order to faithfully characterize the
variation and to distinguish it from stochastic variability. Thus, depending
on SMBHB parameters, this corresponds to a sampling rate of $\sim$ hours –
days over a period of $\sim$ weeks – up to decades.

There have been searches in the Swift BAT dataset for X-ray periodicities,
with a few possible candidates (Severgnini et al., 2018; Serafinelli et al.,
2020). However, past work has shown that it is challenging to distinguish true
periodicity from stochastic AGN variability, especially when the measurement
errors are large; and the relatively small sample size of BAT AGN ($\sim$103)
may not be sufficient for discovering rare binary AGN. There may be
opportunities for discovery with eROSITA which surveys a much larger sample of
AGN; however, its sampling rate may not be well-matched to the periodic
timescales of the majority of SMBHBs Liu et al. (2020). AXIS will remedy both
issues, through a blind search among a large number of AGN (see next section),
and by targeting individual candidates to sample any periodicities with high
sensitivity. Observations of these periodicities (or EM chirps) can not only
identify SMBHBs, but will also enable us to study gas dynamics in extreme,
time-variable spacetime and the accretion disk structure of a binary BH
system, by testing the predictions of (magneto-) hydrodynamic simulations. In
certain binary models, intensive monitoring over a short time period can
extract even more science: for example, binary self-lensing flares encode
exquisite information about the binary disk structure and even BH shadow sizes
which cannot be resolved by very long baseline interferometry (Davelaar &
Haiman, 2022); this can be measured by sampling $\sim$ ten percent of the
orbit at a rate that is equivalent to $\sim$ 1 percent of the orbit.

Transient signals are also expected just prior to or shortly after the merger.
For instance, in the final $\sim$ days before coalescence, the X-ray bright
minidisks shrink as the binary separation shrinks and are eventually
disrupted, causing a sudden drop in X-ray flux $\sim$ a few orbits before
merger, while the optical flux, which is dominated by the outer circumbinary
disk, remains steady; the system then gradually re-brightens post-merger
(Krauth et al., 2023). Other simulations also show that the rapidly
inspiraling binary can decouple from the circumbinary disk which may also
cause a sharp decline in flux at short wavelengths (Dittmann et al., 2023).
The synergy here with an optical survey like LSST is clear: the candidate can
be identified by the sudden disappearance of its X-ray flux accompanied by a
steady optical emission. More importantly, this signature can, in principle,
be identified with as few as two observations (Krauth et al., 2023) and could
be the “smoking gun” signature of an MBHB approaching merger.

###  4.2 Spectral hardening and double broad Fe lines

As the accretion streams strike the minidisks, shock-heating produces bright
X-ray emission in excess of the conventional power-law X-ray spectrum of an
AGN (Roedig et al., 2014; Farris et al., 2015). This spectral hardening
signature may be distinguished by searching for excess luminosity in the X-ray
energy range or modeling the AGN X-ray spectrum, as in previous studies of
individual sources with Chandra and NuSTAR (Saade et al., 2020, 2023; Foord et
al., 2017, 2022). (Krolik et al., 2019) predicts that the all-sky number of
sources which exhibit this signature is $\sim 10^{2}$ at the $10^{-13}$ erg
cm-2 s-1 flux level, or $\sim 10^{4}$ for sources that are $\sim 100$ times
fainter. Thus, identifying this type of binary signature in blind searches is
feasible with the large number of AGN after combining the dedicated AXIS
surveys and serendipitous observations. The depth in the latter, serendipitous
field will reach $\sim$ 10-16 erg s-1 cm-2 in an $\sim$ 50 deg2 sky area
[ref], thus potentially yielding a large number of SMBHBs that display this
signature.

Figure 4: Binary AGN Detections with _AXIS_

We simulate a mock binary AGN with two broad iron lines separated by 0.4 keV
which corresponds a 109$M_{\odot}$ SMBHB at a sub-pc separation. The same
spectrum is observed with Chandra and AXIS with 20 ks, 40 ks, and 60 ks
exposure. Left panel: a more positive $\Delta C_{\rm stat}$ indicates that the
double-line model is statistically favored. The colored bands correspond to
the respective 1$\sigma$ distributions. For comparison purposes, the dotted
line marks a nominal detection threshold which corresponds to the approximate
$\Delta C_{\rm stat}$ achieved with a 60 ks Chandra observation, below which
the double iron line model is not favored at high confidence. Right panel: The
energy of the second line recovered by spectral fitting as a function of
exposure time. (The dashed line marks the true value.) Chandra is unable to
constrain its energy with 20 or 40 ks observations (consistent with the
marginal detections shown on the left); however, AXIS can constrain the
parameter to high precision with only 20 ks.

Additionally, X-ray signatures of a binary may also originate from the
minidisks themselves which produce fluorescent Fe K$\alpha$ lines. The line
energies are expected to be Doppler shifted in opposite directions as the
result of radial velocity changes, producing a double broad Fe line feature
which periodically oscillates with time (Sesana et al., 2012; Jovanović et
al., 2014). A past study with Swift XRT has revealed tantalizing evidence for
such a signature (Severgnini et al., 2018); however, since the spectrum was
effectively integrated over a significant fraction of the putative binary
period, the temporal information is lost. With AXIS’ large effective area at 6
keV (830 cm2), a double Fe line feature in a similar source could be
distinguished from noise fluctuations in a “snapshot” observation (and
ideally, its oscillation would be captured over several visits per orbit).
Meanwhile, resolving this broad line feature only requires a moderate energy
resolution at 6 keV ($\sim$ 0.1 keV), which is easily met by AXIS. Figure 4
shows an example where distinguishing between double- and single-line models
at the same statistical significance level requires $\sim$60 ks exposure with
Chandra, but only $\sim$20 ks with AXIS. Similarly, AXIS is able to recover
the energy of the second line with high precision, thereby constraining the
physical parameters of the system; by contrast, Chandra would require three
times the exposure time to achieve a comparable precision level.

###  4.3 Synergies with other EM observatories

Those X-ray emissions from binaries are usually accompanied by signatures at
UV, optical, and infrared wavelengths, offering opportunities to probe the
same SMBHB source across the EM spectrum. For instance, theory predicts that
excess X-ray emission can be produced by streams crossing the cavity and
striking the minidisks; the same cavity is expected to cause a deficit in the
UV due to the missing gas (e.g. (Roedig et al., 2014)). Other examples can be
found in the wavelength-dependent variability amplitudes or patterns (or
achromaticity) predicted by binary models (e.g. (D’Orazio et al., 2015;
D’Orazio & Di Stefano, 2018; Westernacher-Schneider et al., 2022)). In fact,
not only are multi-wavelength observations beneficial for the studies of
SMBHBs; they are _necessary_ in order to robustly distinguish binaries because
of the high occurrence rates of interlopers (namely, regular AGN). Therefore,
an X-ray telescope will be a powerful arbitrator of SMBHB candidates
discovered by other facilities in other wavebands, in addition to a
potentially powerful discovery engine on its own. For example, a number of
studies have been carried out with Chandra, XMM or NuSTAR to observe the X-ray
spectra and search for the predicted X-ray excess, or other peculiar features,
for a sample of SMBHB candidates that display possible optical periodicity
selected from ground-based time-domain surveys (e.g. (Foord et al., 2017;
Saade et al., 2020; Foord et al., 2022)). In $\sim$ 2032, the Rubin
Observatory LSST will be well into its ten-year operation and potentially will
have discovered $\sim$ a dozen to $\sim$ a hundred periodically varying SMBHBs
(Kelley et al., 2019, 2021). A similar follow-up study with an X-ray telescope
such as AXIS will examine the nature of these periodic sources and place
stringent tests on their binary hypothesis.

##  5 Population Statistics with AGN Pairs

The majority of dual AGN detected by AXIS will span physical separations below
20 kpc, a physical regime where merger-induced effects are believed to be
important to the SMBH growth Hopkins et al. (2007). In the nearby universe
($z=0.1$), _AXIS_ is capable of detecting dual AGN at $L_{X}>10^{41}$ erg s-1
at $r$<5 kpc; at $z=2$ _AXIS_ is capable of detecting dual AGN at
$L_{X}>10^{42}$ erg s-1 down to $r=12$ kpc; and at $z>5$ _AXIS_ is capable of
detecting dual AGN down to physical separations $r>10$ kpc. Assuming the dual
AGN fraction follows predictions from cosmological simulations, we expect the
deep and intermediate _AXIS_ survey to detect $\sim$200 dual AGN between
$0<z<4$. This detection sample is over a magnitude more than the expected dual
AGN detections from publicly available _Chandra_ fields ($\sim$10), assuming
similar luminosity and X-ray count thresholds.

In Fig. 5 we show distributions for redshift and physical separation
associated with a mock sample of dual AGN from an _AXIS_ deep (5 Ms
observation of a single _AXIS_ pointing) and intermediate (300 ks exposure per
pointing) survey. We include redshift and physical separations for a mock
sample of dual AGN detected via publicly available wide and deep Chandra
fields (see Fig. 2). Assuming the dual AGN fraction follows predictions from
cosmological simulations, we create a mock subsample of dual AGN in each
redshift bin with $L_{x}>10^{40}$ erg s-1. We assign a physical separation to
each dual AGN, sampling from a distribution of physical separations measured
for X-ray dual AGN in the nearby universe Koss et al. (2012). We note that our
ability to detect dual AGN in a given _AXIS_ observation can be amplified
using available statistical tools. In particular, tools such as BAYMAX Foord
et al. (2019, 2020, 2021a) can push analyses to angular separations
$\sim$0.8across a wide range of flux rations, corresponding to a physical
separation $r<7$ kpc at $z=1.6$ (where the angular diameter distance peaks).

Figure 5: Redshift versus Physical Separation for Dual AGN Detections

Distributions for redshift and physical separation associated with a mock
sample of dual AGN from an _AXIS_ deep (5 Ms observation of a single _AXIS_
pointing) and intermediate (300 ks exposure per pointing) survey. We include
redshift and physical separations for a mock sample of dual AGN detected via
publicly available wide and deep Chandra fields (see Fig. 2). Assuming the
dual AGN fraction follows predictions from cosmological simulations, we create
a mock subsample of dual AGN in each redshift bin. We assign a physical
separation to each dual AGN, sampling from a distribution of physical
separations measured for X-ray dual AGN in the nearby universe Koss et al.
(2012). For _AXIS_ , a dual AGN is detected if the angular separation is
larger than 1.5, while for _Chandra_ , a dual AGN is detected if the angular
separation is larger than 0.8.

###  5.1 Constraining Binary SMBH hardening timescales

####  5.1.1 Dual AGN

Most recently, results from PTAs such as NANOGrav have found evidence for a GW
background (GW frequencies between $\sim$ nHz and 100 nHz), with oscillations
of $\sim$ months to $\sim$ a decade Agazie et al. (2023b). The GW signal has
been compared to simulations of various SMBH binary populations, and based on
current measurements, the amplitude of the signal suggests that SMBHs may be
(1) more common or (2) more massive than previously thought. An important
component in breaking this degeneracy is a strong constraint on the overall
SMBH hardening timescale. In particular, the final signal of binaries detected
by PTAs is driven by mergers occurring at $z=0.3-0.8$, which correlate with
progenitor dual AGN at $<30$ kpc-scale separations at $z=1-3$ (see fig. 12 in
Agazie et al. (2023a)). Thus, constraining the frequency of dual AGN
detections at $z=1-3$, as a function of separation, will make a big impact on
future binary SMBH model inferences. In Fig. 5 we show current dual AGN
detections from _Chandra_ , which are mostly constrained to the nearby
universe, and expected dual AGN detections by _AXIS_. In particular, _AXIS_
will detect some of the highest-redshift dual AGN to date, over a large range
of physical separations.

####  5.1.2 Binary AGN

The discovery of $\sim$ a few dozen SMBHBs at different orbital periods would
provide an indirect test of their hardening timescales (Haiman et al., 2009).
In the GW-driven regime, the residence timescale $t_{\rm res}=t_{\rm
GW}=-R/(dR/dt)$ is the time a binary spends at a given separation $R$, or
equivalently, the corresponding orbital period $t_{\rm orb}$, and scales with
the period: $t_{\rm GW}\propto t_{\rm orb}^{8/3}$. Since the number of
binaries at a given orbital period is determined by the probability of
observing them at this stage: $N\propto(t_{\rm res}/t_{\rm Q})$, where $t_{\rm
Q}\sim 10^{7}$ yr is the typical quasar lifetime, this yields a simple scaling
relation between the fraction of sources and their periods in the GW regime:
$f\propto t_{\rm orb}^{8/3}$. Hence, with a sample of SMBHBs whose orbital
periods are measured from, e.g., EM periodicity, one can test the steep,
$t_{\rm orb}^{8/3}$ scaling relation due to GW inspiral. By contrast, a
shallower scaling relation would probe the timescale due to gas interactions.

###### Acknowledgements.

We kindly acknowledge the AXIS team for their outstanding scientific and
technical work over the past year. This work is the result of several months
of discussion in the AXIS-AGN SWG. AF thanks Stanford University for support
during the proposal writing phase. no multiple yes

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