Chandra Observations of Abell 2261 Brightest Cluster Galaxy, a Candidate Host to a Recoiling Black Hole

The galaxy cluster Abell 2261's brightest cluster galaxy (A2261-BCG hereafter) is perhaps the best place to look for a recoiling or ejected central supermassive black hole. Abell 2261 is a rich cluster with virial mass ${M}_{\mathrm{vir}}=(1.7\pm 0.2)\,\times {10}^{15}\,{M}_{\odot }\,{h}_{70}^{-1}$ within ${R}_{\mathrm{vir}}\approx 3\ {h}_{70}^{-1}$ Mpc (Coe et al. 2012). A2261-BCG has a number of properties that set it apart from most other galaxies. First, it has one of the largest cores in its stellar surface brightness profile. Early-type galaxies can be separated into two categories based on their surface brightness profiles: core and cusp (Lauer et al. 1995). Galaxies can have central brightness profiles that can be parameterized as a Nuker law,

$$\begin{eqnarray}&&I(r)={2}^{(\beta -\gamma )/\alpha }{I}_{b}{\left(\displaystyle \frac{{r}_{b}}{r}\right)}^{\gamma }{\left[1+{\left(\displaystyle \frac{r}{{r}_{b}}\right)}^{\alpha }\right]}^{(\gamma -\beta )/\alpha },\end{eqnarray} \tag{ 1 }$$

where I_b is the brightness at the core (or "break") radius, r_b, γ and β are the power-law indices for r ≪ r_b and r ≫ r_b, respectively, and α is an index that sets the sharpness of the break (Lauer et al. 1995). For γ > 0.5, a galaxy is considered a power-law galaxy. For γ < 0.3, it is considered a core galaxy. A2261-BCG has a core with γ = −0.01 and a cusp radius of ${r}_{\gamma }=3.2\ \mathrm{kpc}$ (Postman et al. 2012), where r_γ is the radius at which the local (negative) log-slope of the brightness profile is 1/2. Cores with negative values of γ are seen in only rare cases (Lauer et al. 2002), but imply that the central stellar density actually decreases as the center is approached. A2261-BCG thus has no central cusp in stellar density. A2261-BCG's core was the largest known at its time of discovery, and is still only smaller than those in Holm 15A, the brightest cluster galaxy in Abell 85 with ${r}_{\gamma }=4.6\ \mathrm{kpc}$ (López-Cruz et al. 2014) and IC 1101, the brightest cluster galaxy in A2029 with ${r}_{b}\,=4.2\ \mathrm{kpc}$ (Dullo et al. 2017). Both of those galaxies, however, have shallow surface brightness cusps, which imply that their stellar density profiles are formally divergent at their centers, as is standard for nearly all core-galaxies.

In addition to having an unusually large and flat core, the stellar core of A2261-BCG is offset from the center of the galaxy as determined by the galaxy's outer isophotes (Postman et al. 2012). The core's center is located 0.7 kpc to the SW of the outer isophote center, suggestive of a recent perturbation. Taken together, the extreme size and flatness of the core along with the offset suggest that A2261-BCG is a possible site of a past black hole–black hole merger.

Black hole binaries are the leading candidates for creating core profiles in galaxy centers (Begelman et al. 1980; Faber et al. 1997). As two galaxies merge, their central black holes may sink to the center of the merged system from energy loss via dynamical friction (e.g., Governato et al. 1994; Kazantzidis et al. 2005, but see also Tremmel et al. 2015). Eventually, enough energy is transferred from the black hole's orbits to the stars so as to gravitationally bind the two black holes in a binary system. At this point, a major loss of energy from the binary black hole's orbit comes from interactions from stars passing by the binary. As energy is transferred from the binary to the stars, the stars are flung out to large distances from the center of the galaxy. This process turns what may have been a central surface brightness power law into a core profile. Thus a binary is said to have "scoured" a core into the galaxy.

If there are enough stars on orbits close enough to the binary, sufficient energy can be extracted such that gravitational wave emission from the binary black hole system can lead to the black holes merging in less than a Hubble time. In the final stages of black hole coalescence, asymmetric emission of gravitational waves as a result of mass asymmetry or spin anisotropy can lead to recoil of the merged black hole at speeds of up to several thousand $\mathrm{km}\ {{\rm{s}}}^{-1}$ (Campanelli et al. 2007; González et al. 2007; Lousto & Zlochower 2011).

The properties of the stellar surface-brightness of the core are also thought to result from the properties of the binary, such as mass and mass ratio. Although determining precise values of the binary may be impossible (Lezhnin & Vasiliev 2019), it is reasonable to expect that an exceptionally flat and large core would result from a massive binary with mass ratio ($q\equiv {m}_{2}/{m}_{1}\leqslant 1$) close to unity. One intriguing possibility is that the ejection of the merged black hole actually causes the core to "rebound" due to the removal of the central mass, resulting in the core becoming even larger (Boylan-Kolchin et al. 2004; Merritt et al. 2004; Gualandris & Merritt 2008).

A number of different techniques all predict that the A2261-BCG should host a very massive black hole in its center. Based on the 3.2 kpc size of its core, A2261-BCG would be expected to host a black hole with mass $M\gt {10}^{10}\,{M}_{\odot }$ (Lauer et al. 2007). The M–σ relation (Kormendy & Ho 2013) and the M–L relation (McConnell et al. 2011) predict that the A2261-BCG black hole mass lies in the range of 6 × 10⁹ ${M}_{\odot }$ < M < 1.1 × 10¹⁰ ${M}_{\odot }$.

There are alternatives to binary core scouring to explain early-type galaxy cores, such as dissipationless collapse (Nipoti et al. 2006), thermal evaporation of cold gas via AGN feedback (Nipoti 2009), and the sinking of black holes post merger without binary formation (Goerdt et al. 2010). Despite these alternatives, core-scouring is generally considered the most likely, and thus the properties of A2261-BCG paint a picture in which a massive binary existed at one point.

Finding any evidence of current or previous binary black hole systems is salient for gravitational wave studies, especially low-frequency experiments such as pulsar timing arrays (PTAs; Hobbs 2013; Desvignes et al. 2016; Verbiest et al. 2016; Aggarwal et al. 2019) and the Laser Interferometer Space Antenna (LISA Amaro-Seoane et al. 2017). The current electromagnetic evidence for unambiguous binary black holes is relatively sparse. The strongest candidate is 0402+379, which has strong evidence based on VLBI observations with proper motion measurements (Rodriguez et al. 2009; Bansal et al. 2017), but extensive searches for additional such objects have not produced more examples (Burke-Spolaor 2011). Other candidates exist but are less compelling as alternative explanations exist. Cyg A was reported to contain a transient secondary source in infrared (Canalizo et al. 2003) and radio (Perley et al. 2017) observations, with the most likely interpretation being an infalling stripped galaxy with an accreting black hole, but the 460 pc projected separation may indicate that it is not gravitationally bound and is, instead, a dual AGN. OJ287 has a light curve that may be explained as a binary system (Valtonen et al. 1988, 2011; Laine et al. 2020) or a precessing BL Lac jet (Tanaka 2013). A number of optical light curves from time-domain surveys such as Pan-STARRS (Hodapp et al. 2004; Chambers et al. 2016), Catalina Real-Time Transient Survey (Drake et al. 2009), and Palomar Transient Factory (Law et al. 2009; Rau et al. 2009) show variability that has been claimed to be periodic and thus evidence for a binary system (Graham et al. 2015; Liu et al. 2015; Charisi et al. 2016), but these sources have also been explained as displaying typical AGN variability (Vaughan et al. 2016) or having an SED consistent with a single AGN (Foord et al. 2017). AGN with velocity-offset broad line regions are evidence for low-mass-ratio binaries (Eracleous et al. 2012; Runnoe et al. 2015, 2017), but the complexities of broad line regions make any interpretation difficult (Eracleous et al. 2012). For the case of 0402+379, the projected separation is 7 pc, which puts it well out of the regime of gravitational wave emission and thus does not answer the question of whether black holes actually merge. Thus any evidence for black hole binaries is noteworthy, and evidence of black hole mergers is critical.

We have pursued evidence of a recoiling or ejected black hole in A2261-BCG as it would indicate that a binary black hole had existed and merged. In particular, we have focused our past efforts on the core region of A2261-BCG, including targeted studies of four stellar knots¹⁰ near the center of the galaxy (Postman et al. 2012). A recoiling black hole is expected to take with it a cloak of stars that are tightly bound to it. One of the stellar knots could be the expected cloak of stars bound tightly to the recoiling black hole. We used observations of A2261-BCG with the Karl G. Jansky Very Large Array (VLA) to look for core radio emission coming from one of the stellar knots but found only evidence of old jet activity (Burke-Spolaor et al. 2017). We also used HST/STIS spectroscopy of the northern three stellar knots to look for stellar velocity dispersions that would indicate the presence of a massive object. The velocity dispersions measured in two of the knots were modest, and the third knot was poorly constrained because of low signal-to-noise ratio (S/N; Burke-Spolaor et al. 2017). The fourth (southern) knot is too faint to attempt HST spectroscopy in a reasonable amount of time.

In this paper we use deep Chandra X-ray observations to look for evidence of accretion onto a large black hole at the core of A2261-BCG. As discussed above, we expect the galaxy to at one time have hosted a $\sim {10}^{10}\,{M}_{\odot }$ black hole, and if the black hole has never suffered a recoil or if the recoil is modest (below ∼750 $\mathrm{km}\,{{\rm{s}}}^{-1}$), then it will remain in the galaxy's core. Accretion onto a black hole above an Eddington ratio of about f_Edd > 10⁻⁶ will be visible as an X-ray point source. We focus our search for such emission at six locations of interest: the locations of the four stellar knots, which may be hosting a recoiling supermassive black hole, the optical center of the BCG, which is the expected site of a nonrecoiled black hole, and the location of radio emission found by Burke-Spolaor et al. (2017), which is the location of previous AGN activity.

In Section 2, we describe the Chandra observations and our treatment of the data reduction, paying close attention to astrometric registration. We present our analysis of the X-ray data in Section 3, including image and spectral fitting, finding no evidence for an X-ray point source. We discuss our results in Section 4 and suggest a potential way forward with high-spatial resolution infrared integral-field spectroscopy. Throughout this paper, we assume a cosmology with ${{\rm{\Omega }}}_{m}=0.3$, Ω_Λ = 0.7, and ${H}_{0}=70\ \mathrm{km}\ {{\rm{s}}}^{-1}\ {\mathrm{Mpc}}^{-1}$. The redshift of A2261-BCG is z = 0.2233, corresponding to a luminosity distance of ${D}_{L}=1109\ \mathrm{Mpc}$ and an angular diameter distance of ${D}_{A}=741\ \mathrm{Mpc}$, at which distance 1'' subtends $3.59\ \mathrm{kpc}$.

Table 1 summarizes the three Chandra data sets that we use in our search for an X-ray signature of the central black hole in A2261-BCG. The two archival data sets (ObsId 550 and 5007) were part of Guaranteed Time Observations (GTO) to measure the Sunyaev–Zeldovich effect and cluster gas properties (Bonamente et al. 2006; Baldi et al. 2007; Maughan et al. 2008; Hlavacek-Larrondo & Fabian 2011). Our new observations¹¹ were specifically designed to search for a low-luminosity accreting black hole in A2261-BCG. For scheduling purposes, our program was split into two observations (ObsIDs 20413 and 21960). Below we use the ObsID to identify an individual observation, if necessary. The aim points for each observation are listed in Table 1.

Table 1.  Observation Log

Obsid	MJD	R.A.	Decl.	Exposure	Mode	Detector
		(J2000)		(ks)
550	51494	17h22m27 60	+32°07'3720	9.06	VFAINT	ACIS-I
5007	53018	17h22m27 20	+32°07'5800	24.32	VFAINT	ACIS-I
20413a	58441	17h22m27 20	+32°07'5730	45.49	FAINT	ACIS-S
21960a	58459	17h22m27 20	+32°07'5730	49.44	FAINT	ACIS-S

Note.

^aOur data from the Chandra program associated with proposal 19700260 were split into two separate exposures for a total of approximately 100 ks.

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Our data reduction follows standard techniques with subpixel event repositioning techniques. All data were re-reduced using the Chandra Interactive Analysis of Observations (CIAO) v4.11 software package (Fruscione et al. 2006) and version 4.8.2 of the CALDB calibration database. Subpixel events were achieved using the energy-dependent sub-pixel event repositioning algorithm (EDSER; Li et al. 2004) from within the standard chandra_repro reprocessing, which also generates the bad pixel files and level 2 event files. We examined each observation individually for flares and removed intervals in which the count rate outside of obvious source areas was more than 3σ from the mean count rate across each observation. The new data show the cluster X-ray emission extends to 135'' (725 kpc) with a total of 1.7 × 10⁵ counts in this area.

2.1. Astrometric Registration

We separate our analysis into three components. We first present our analysis of the X-ray image and fits to the hot gas morphology in Section 3.1. We then analyze and fit the spectra of the irregular annuli recovered from the image fitting in Section 3.2. Finally we look for evidence of X-ray point sources in excess of the cluster gas with spectral fits to the X-ray emission at the locations of interest using the annuli spectra as background in Section 3.3.

3.1. Image Fitting

The combined X-ray image of A2261 shows a moderately disturbed morphology. Figure 1 shows that the X-ray emission is obviously noncircular, and examination of the isophotes shows that the eccentric isophotes are not concentric. At scales larger than ∼30'' the eccentric isophotes are elongated along an axis roughly 40° east of north with an eccentricity of e ≈ 0.5. At scales smaller than ∼30'', the isophotes are elongated along the north–south direction with an eccentricity of e ≈ 0.4. The outer isophotes are centered at a location approximately 8'' to the northwest of the inner isophote centers.

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Using the aspect-corrected merged Chandra data set, we performed two-dimensional fits to the imaging data with Sherpa (Freeman et al. 2001). To account for the noncircularity and nonconcentricity, we fit the imaging data with a sum of three two-dimensional, eccentric beta models with independent central locations. That is, each component has elliptical isophotes with eccentricity e and position angle θ, centered at a position x₀, y₀, with a value that depends on r, the distance from the center, as $A{[1+{(r/{r}_{0})}^{2}]}^{-\alpha }$, where A is the amplitude, r₀ is a core radius, and α is the index of the beta function. The resulting fit (Figure 1(c)) matches the majority of the apparent visual properties of the data. In particular, the centers of the inner and outer (as determined by having small and large r₀, respectively) beta model components are separated by about 12'' to the northwest and there is significant eccentricity in the outer component, aligned at 35^◦ east of north. Similarly, we plot the residuals divided by the square root of the number of data counts (or by 1 when no counts) in Figure 1(d). The distribution of scaled residuals is approximately symmetric about zero, with a median of −0.36 and rms 0.74. The best-fit parameters and uncertainties are provided in Table 2, the central portion is shown in detail in Figure 2 with knot locations identified in Table 3.

Table 2.  Imaging Best Fit

Parameter	Component 1	Component 2	Component 3
r0	${36}_{-12}^{+3}$	${431}_{-168}^{+36}$	${548}_{-96}^{+391}$
x0	${4288.0}_{-0.4}^{+0.6}$	${4301.2}_{-0.8}^{+4.2}$	${4308.5}_{-1.8}^{+2.0}$
y0	${4048.4}_{-0.6}^{+0.5}$	${4043.0}_{-2.0}^{+0.7}$	${4061.7}_{-1.8}^{+2.9}$
e	${0.09}_{-0.04}^{+0.03}$	${0.11}_{-0.02}^{+0.03}$	0.12 ± 0.02
θ	${4.5}_{-0.2}^{+0.3}$	${2.61}_{-0.08}^{+0.13}$	$-{0.96}_{-0.09}^{+0.07}$
A	${8.4}_{-0.2}^{+1.2}$	${2.6}_{-0.6}^{+0.1}$	${0.99}_{-0.07}^{+0.03}$
α	${2.9}_{-1.3}^{+0.9}$	${33}_{-4}^{+16}$	${4.1}_{-0.5}^{+2.9}$

Note. Parameters from the joint fit. Locations and distances are measured in pixels, with the location $(4288.0,4048.4)$ corresponding to J2000 coordinates of 17:22:27.3, +32:07:57.54 with positive x in the west direction and positive y in the north direction. The position angle θ is in radians measured north of west, and the amplitude, A, is measured in units of normalized counts.

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3.2. Spectral Fitting

We fit spectral models of A2261 as well to determine if there is any excess hard emission at the location of the stellar knots, which would be indication of accretion onto a compact object. Because there is significant X-ray emission from the cluster gas, it is necessary to model it. First, we split the X-ray data into different annular regions; second, we fit the X-ray spectra to the projected annular regions; and third, we attempt to fit to the deprojected volume emission regions. We detail each of these in turn.

Table 3.  X-Ray Point Source Upper Limits

Location	x	y	99% Limit
			($\mathrm{erg}\ {{\rm{s}}}^{-1}\ {\mathrm{cm}}^{-2}$)
Knot 1	1.41	0.05	$2.9\times {10}^{-16}$
Knot 2	2.50	0.00	$2.7\times {10}^{-16}$
Knot 3	3.96	0.05	$2.7\times {10}^{-16}$
Knot 4	3.94	−3.46	$4.3\times {10}^{-16}$
Optical center	2.61	−1.37	$2.3\times {10}^{-16}$
Radio emission	5.74	0.77	$2.0\times {10}^{-16}$

Note. Upper limits to X-ray emission from the locations listed. The locations are identified by name and with their coordinates in units of 0492 pixels relative to (4288.0,4048.4), which corresponds to J2000 coordinates of 17:22:27.3, +32:07:57.54. The radii of the circular regions used in the X-ray analysis were all 1.04 pixels, except for knot 4, which was 1.25 pixels. The last column lists the 99% confidence upper limit to the restframe 2–7 keV flux, assuming a Γ = 2 power-law source with only Galactic absorption.

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Because of the nontrivial nature of the isophotes, we fit spectral models to annular regions as determined by isophote contours of the best-fit models. The annuli are well approximated by elliptical boundaries, with varying center locations, eccentricity, and position angle. The ellipses defining the annuli are presented in Table 4 in the Appendix, along with the number of X-ray counts in each annulus.

We did two X-ray spectral fits: first on each of the annular regions without deprojection, and then with an approximate deprojection of the three-dimensional spheroidal volumes that project to make the annular regions observed. The advantage of the former approach is that it is straightforward while the advantage of the latter is that it allows inference of the underlying physical regions. In both cases, we jointly fit each of the four observations, using their own individual response functions to properly account for the change in instrument behavior over time and the difference between ACIS-I and ACIS-S. Fits were performed with XSPEC v12.10.1f using C-stat statistics.

For the projected case, each annular region is fitted with an intrinsically absorbed APEC model with a Galactic absorption value of $3.19\times {10}^{20}\ {\mathrm{cm}}^{-2}$ and a redshift fixed at z = 0.2233. The spectral model we used produced good results at all annuli. After doing an inital Levenberg-Marquett minimization to find best-fit parameters for each annulus, we computed the 68% confidence intervals on each parameter with Markov Chain Monte Carlo (MCMC) runs. The best-fit and parameters and their uncertainties are presented in Table 5 in the Appendix.

Table 5.  Spectral Fits

Annulus	${N}_{{\rm{H}}}$		$\mathrm{log}{F}_{X}$		kT		$Z/{Z}_{\odot }$		C-stat
	Proj.	Deproj.	Proj.	Deproj.	Proj.	Deproj.	Proj.	Deproj.
1	${9.5}_{-9.3}^{+2194.9}\times {10}^{-8}$	$(8.4\pm 0.7)\times {10}^{-9}$	−13.20 ± 0.02	$-{12.82}_{-0.03}^{+0.04}$	${7.87}_{-1.25}^{+1.80}$	${7.65}_{-0.46}^{+0.55}$	${1.23}_{-0.40}^{+0.55}$	1.18 ± 0.06	1300.0
2	${2.8}_{-1.9}^{+2.8}\times {10}^{-2}$	$(1.0\pm 0.1)\times {10}^{-2}$	−13.04 ± 0.02	$-{12.91}_{-0.05}^{+0.04}$	${6.14}_{-0.65}^{+0.84}$	${5.70}_{-0.44}^{+0.50}$	${0.79}_{-0.23}^{+0.27}$	0.57 ± 0.03	1400.6
3	${2.0}_{-1.3}^{+2.2}\times {10}^{-2}$	$(1.4\pm 0.1)\times {10}^{-6}$	−12.76 ± 0.01	−12.40 ± 0.02	${7.51}_{-0.79}^{+0.84}$	8.31 ± 0.77	${0.43}_{-0.13}^{+0.16}$	0.35 ± 0.03	1692.4
4	${1.4}_{-1.0}^{+1.7}\times {10}^{-2}$	${3.3}_{-0.2}^{+0.1}\times {10}^{-9}$	−12.73 ± 0.01	$-{12.54}_{-0.05}^{+0.04}$	${7.25}_{-0.66}^{+0.74}$	${6.97}_{-0.48}^{+0.54}$	${0.70}_{-0.17}^{+0.21}$	0.95 ± 0.05	1710.1
5	${2.6}_{-1.7}^{+2.6}\times {10}^{-2}$	$(2.7\pm 0.3)\times {10}^{-2}$	−12.68 ± 0.01	$-{12.46}_{-0.05}^{+0.04}$	${8.44}_{-0.97}^{+1.26}$	${12.45}_{-0.95}^{+0.85}$	${0.37}_{-0.13}^{+0.15}$	0.020 ± 0.001	1757.4
6	${4.8}_{-2.5}^{+2.7}\times {10}^{-2}$	$(1.1\pm 0.1)\times {10}^{-1}$	−12.62 ± 0.01	$-{12.41}_{-0.05}^{+0.03}$	${7.43}_{-0.73}^{+0.86}$	${5.66}_{-0.40}^{+0.38}$	${0.36}_{-0.11}^{+0.13}$	${0.31}_{-0.04}^{+0.03}$	1719.3
7	${6.0}_{-2.6}^{+2.5}\times {10}^{-2}$	${4.5}_{-0.2}^{+0.3}\times {10}^{-2}$	−12.544 ± 0.010	$-{13.02}_{-0.16}^{+0.12}$	${6.66}_{-0.54}^{+0.73}$	${5.50}_{-0.35}^{+0.41}$	${0.47}_{-0.11}^{+0.12}$	1.26 ± 0.08	1803.7
8	${3.8}_{-2.0}^{+2.1}\times {10}^{-2}$	${3.7}_{-0.3}^{+0.2}\times {10}^{-2}$	$-{12.413}_{-0.009}^{+0.008}$	$-12.20\pm 0.02$	${7.84}_{-0.66}^{+0.69}$	${8.51}_{-0.62}^{+0.64}$	${0.36}_{-0.09}^{+0.11}$	${0.29}_{-0.03}^{+0.02}$	1873.2
9	${4.7}_{-1.8}^{+1.9}\times {10}^{-2}$	${5.9}_{-0.6}^{+0.5}\times {10}^{-2}$	−12.271 ± 0.007	$-{12.35}_{-0.04}^{+0.03}$	${7.71}_{-0.53}^{+0.57}$	${7.30}_{-0.56}^{+0.54}$	${0.45}_{-0.08}^{+0.09}$	${0.55}_{-0.05}^{+0.03}$	2043.0
10	$(3.4\pm 1.4)\times {10}^{-2}$	$(3.1\pm 0.3)\times {10}^{-2}$	−12.047 ± 0.006	$-11.78\pm 0.01$	${8.21}_{-0.44}^{+0.51}$	${8.44}_{-0.42}^{+0.52}$	0.27 ± 0.06	0.21 ± 0.01	2100.6
11	$(3.8\pm 1.6)\times {10}^{-2}$	${5.0}_{-0.4}^{+0.3}\times {10}^{-2}$	−12.183 ± 0.007	$-12.32\pm 0.04$	${8.12}_{-0.51}^{+0.57}$	${7.56}_{-0.56}^{+0.43}$	0.31 ± 0.08	0.38 ± 0.02	2056.9
12	$(2.6\pm 1.4)\times {10}^{-2}$	$(4.4\pm 0.3)\times {10}^{-2}$	−12.095 ± 0.006	$-{11.93}_{-0.02}^{+0.01}$	${7.77}_{-0.45}^{+0.49}$	${7.99}_{-0.49}^{+0.41}$	${0.26}_{-0.06}^{+0.07}$	0.29 ± 0.02	2172.3
13	${6.7}_{-2.0}^{+2.3}\times {10}^{-2}$	${9.3}_{-0.5}^{+0.4}$	−12.306 ± 0.008	$-{14.31}_{-0.51}^{+0.62}$	${8.31}_{-0.67}^{+0.87}$	${13.67}_{-1.18}^{+1.05}$	${0.41}_{-0.09}^{+0.10}$	${2.12}_{-0.25}^{+0.20}$	2003.8
14	$(3.9\pm 1.9)\times {10}^{-2}$	$(3.4\pm 0.3)\times {10}^{-2}$	$-{12.254}_{-0.008}^{+0.007}$	$-12.21\pm 0.03$	${9.35}_{-0.76}^{+0.93}$	${12.87}_{-1.17}^{+1.06}$	${0.26}_{-0.08}^{+0.09}$	0.29 ± 0.02	2113.5
15	${2.3}_{-1.4}^{+1.6}\times {10}^{-2}$	$(4.9\pm 0.3)\times {10}^{-3}$	−12.195 ± 0.007	$-12.29\pm 0.03$	${8.45}_{-0.55}^{+0.65}$	${7.57}_{-0.43}^{+0.52}$	${0.38}_{-0.08}^{+0.09}$	0.44 ± 0.03	2096.2
16	${1.9}_{-1.2}^{+1.5}\times {10}^{-2}$	$(7.0\pm 0.5)\times {10}^{-3}$	−12.113 ± 0.006	$-{12.22}_{-0.03}^{+0.02}$	${10.09}_{-0.79}^{+1.08}$	${13.79}_{-0.77}^{+0.63}$	${0.20}_{-0.08}^{+0.09}$	0.020 ± 0.001	2200.8
17	${2.0}_{-1.2}^{+1.3}\times {10}^{-2}$	${3.2}_{-0.2}^{+0.3}\times {10}^{-2}$	$-{11.958}_{-0.005}^{+0.006}$	$-11.96\pm 0.01$	${10.00}_{-0.65}^{+0.87}$	${11.25}_{-0.73}^{+0.70}$	0.27 ± 0.08	0.28 ± 0.02	2133.1
18	$(4.7\pm 1.9)\times {10}^{-2}$	${9.1}_{-0.7}^{+0.5}$	$-{12.045}_{-0.006}^{+0.007}$	$-{14.58}_{-0.32}^{+0.56}$	${9.99}_{-0.90}^{+1.15}$	${5.64}_{-0.37}^{+0.44}$	0.28 ± 0.10	0.020 ± 0.002	2413.7

Note. Results of spectral fits to the X-ray data with 1σ uncertainties. Spectral fitting was done two different ways: analysis of the projected annuli (under the "Proj." columns) and a deprojected analysis (under the "Deproj." columns) assuming that the elliptical annuli deprojected as if they were concentric. The model parameters are the redshifted, intrinsic absorption column in units of ${10}^{22}\ {\mathrm{cm}}^{2}$ (${N}_{{\rm{H}}}$), the logarithmic 0.3–7 keV flux in units of $\mathrm{erg}\ {{\rm{s}}}^{-1}\ {\mathrm{cm}}^{-2}$ ($\mathrm{log}{F}_{{\rm{X}}}$), the temperature of the collisional plasma of the APEC model in units of keV (kT), and the abundance relative to solar (Z/Z_⊙). The final column lists C-stat values per 2097 degrees of freedom for each annulus for the best fits of the projected models. The deprojected fit, which was fitted to all annuli simultaneously, had best-fit C-stat of 35441.6 for 37800 degrees of freedom. In the projected case, the annuli fits are independent of each other, but for the deprojected case, all parameter uncertainties are correlated. The statistical uncertainties shown in the table come from the MCMC runs and are marginalized over all other parameters. In addition to the statistical uncertainties, there are systematic uncertainties to the deprojected fits arising from using a concentric model for nonconcentric data. Thus the full uncertainty is larger than what is shown and likely a large effect for the scatter seen in the profiles of Figure 3.

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For the deprojected case, the entire cluster emission is fitted simultaneously using the XSPEC projct model to combine the volumes, which are determined by deprojecting the elliptical annuli into prolate ellipsoidal shells. The deprojection requires that the elliptical annuli be concentric. Despite the fact that the elliptical annuli are not concentric, we proceed as if they were all centered on the innermost region. This assumption is unlikely to make a large difference as the change in center is small compared to the semiminor axes of the larger ellipses (Table 4), but it is formally incorrect. We again use an absorbed APEC model with the same Galactic absorption and redshift as before. The best-fit parameters and their 68% confidence intervals were determined with MCMC runs and again presented in Table 5 in the Appendix.

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We plot profiles of the parameters in Figure 3. Although there are differences between the projected fits and deprojected fits, they show the same general trends. The profiles show a few interesting trends across radius. First, the surface brightness profile of the projected case is smooth because the regions were selected based on the isophotes. We compare the X-ray surface brightness profile to the stellar light profile in Figure 4. The intrinsic absorption column shows a potential change from higher values at radii r > 40 kpc to values consistent with no intrinsic absorbing column, though with significant uncertainties in the inner region because of the lower number of counts arising from the fact that the area is smaller. In any event, the overall absorption is modest. The temperature of the collisional plasma shows a steady increase from the inner regions of 6 to 9 keV at 200 kpc. Finally the metallicity shows significant enhancement inside of 10 kpc compared to the rest of the cluster gas.

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3.3. X-Ray Point Sources

Either there is no 10¹⁰ ${M}_{\odot }$ black hole in any of the four stellar knots, the optical center, or the site of radio emission; or any such black hole is accreting below an Eddington fraction of 10⁻⁶. We find no excess X-ray emission attributable to a point source in any of the four stellar knots near the galaxy core center, which for two of the knots is consistent with our past spectroscopic findings of low-mass (<6 × 10⁸ ${M}_{\odot }$) black holes (Burke-Spolaor et al. 2017). It is, of course, possible to find excess emission that could be attributed to a point source at many locations in the image, but, without a specific location to search, the chance of a spurious signal is high. Thus, we restrict our search for excess emission to only the locations of interest. As mentioned in Section 3.1, we are able to place limits on any accretion arising from the locations of interest. Given the size of A2261-BCG, a black hole with mass following either the M–σ or M–L relations would be near 10¹⁰ ${M}_{\odot }$. Assuming a bolometric correction of 10 for hard X-ray, our flux limits correspond to emission at 10⁻⁶ of Eddington for a 10¹⁰ ${M}_{\odot }$ black hole. Given the range of bolometric corrections for hard X-rays at low accretion rates and the uncertainties associated with estimating black hole masses in such extreme environments, this Eddington fraction limit can only be considered an order-of-magnitude estimate.

The fact that we find an upper limit to the Eddington fraction of f < 10⁻⁶ does not preclude a black hole from existing in any of the locations we searched. Eddington fractions below 10⁻⁶ are plausible for systems such as A2261-BCG. Most BCGs do not show bright X-ray AGN at their centers (Sun 2009; Donahue et al. 2020). There has been considerable research into low-luminosity AGN. By necessity, this research tends to focus on nearby sources such as Sgr A* (Baganoff et al. 2003), analogs of which cannot be detected outside of the Local Group. Similarly, Soria et al. (2006) studied several elliptical galaxies with black holes having masses smaller than 6 × 10⁸ ${M}_{\odot }$ emitting in X-rays at fractions of Eddington below $\mathrm{log}({L}_{{\rm{X}}}/{L}_{\mathrm{Edd}})=-6.96$. Their sample includes NGC 821, which was studied in detail by Pellegrini et al. (2007) to have a 0.3–8 keV nuclear luminosity of $2.8\times {10}^{38}\ \mathrm{erg}\ {{\rm{s}}}^{-1}$. M87 is the nearest central dominant galaxy in a large galaxy cluster and has a large black hole ($M=6.6\times {10}^{9}\,{M}_{\odot }$, Gebhardt et al. 2011) emitting at a small fraction of Eddington (Di Matteo et al. 2003). It is possible to infer the presence of a black hole from analysis of the cluster X-ray emission, but this requires well resolving the central kiloparsec region, which is not possible for A2261 (Russell et al. 2018).

For comparison, Gültekin et al. (2012) and Gültekin et al. (2019) looked at nearly all galaxies with direct, dynamical black hole mass measurements as part of a broader study of the fundamental plane of black hole accretion. Within their sample of black holes, they found that ${L}_{{\rm{X}}}/{L}_{\mathrm{Edd}}$ ranged from 10⁻¹⁰ to 10⁻², with roughly 60% below 10⁻⁶. The sample of galaxies is biased toward low accretion rates and quiescent AGN by the nature of needing to avoid a bright AGN when measuring stellar velocity distributions at the center. If A2261-BCG were closer and/or had a tip-tilt star, it would similarly be a target for black hole mass estimation and could therefore be considered as broadly coming from the same parent distribution of galaxies. On the other hand, the sample contained few BCGs, which may have qualitatively different fueling environments than other black hole hosts, and there are not enough known 10¹⁰ ${M}_{\odot }$ black holes to draw broad conclusions.

High-resolution X-ray observations have shown that BCGs in general are unlikely to have a nuclear X-ray point source, despite other compelling evidence of an accreting black hole. In particular, Hlavacek-Larrondo & Fabian (2011) looked at a sample of BCGs (including A2261-BCG) in cool-core clusters with X-ray luminosities above ${L}_{{\rm{X}}}={10}^{45}\ \mathrm{erg}\ {{\rm{s}}}^{-1}$. Their sample had radio emission, indicating the BCG hosted an accreting black hole at least at some time in the past. None of the objects in their sample showed nuclear X-ray point sources. Hlavacek-Larrondo & Fabian (2011) identified several potential reasons for the lack of X-ray nuclei in galaxies with obvious AGN radio jets: (i) very massive black holes (i.e., $M\gt {10}^{10}\,{M}_{\odot }$) resulting in radiative power below the kinetic power inferred from the radio jets, (ii) X-ray emission originating in the jet and therefore Doppler suppressed out of the line of sight, (iii) alternative accretion mechanisms such as magnetically dominated accretion disks (Blandford & Payne 1982), (iv) a large column absorbing the X-ray emission of the AGN, and (v) AGN duty cycles that indicate radio jet emission coming from a different epoch than that probed by X-ray observations. Our VLA observations of A2261-BCG show that the radio emission with luminosity density ${L}_{\nu }\sim 5\times {10}^{30}\ \mathrm{erg}\ {{\rm{s}}}^{-1}\ {\mathrm{Hz}}^{-1}$ is indeed from an earlier epoch (at least 48 Myr old based on synchrotron aging) and that it is thus not necessarily a strong predictor of X-ray emission (Burke-Spolaor et al. 2017). That is, the radio emission is not evidence of a currently accreting black hole in A2261-BCG. The questions raised about obscuration are, however, still important, especially as A2261-BCG has been identified as a potentially centrally obscured source. We address these questions below.

We have determined that there is not significant obscuration preventing us from seeing black hole emission. Here, we describe the arguments in the literature advocating for a significant dust mass and cold gas at the center of A2261-BCG and our line of reasoning for why A2261-BCG is not heavily obscured. Bildfell et al. (2008) noted that its combined X-ray and optical properties were similar to those of blue-core, star-forming BCGs. They argued that because A2261-BCG had a red core, this indicated that there was significant star formation that was extincted and that this was consistent with an earlier measurement of $\sim {10}^{8}\,{M}_{\odot }$ of dust in the galaxy. This earlier measurement is due to Chapman et al. (2002) based on James Clerk Maxwell Telescope Submillimeter Common User Bolometer Array (JCMT/SCUBA) detection of significant emission at 450 and 850 μm. This emission, however, comes from a location that is about 35'' to the west of A2261-BCG. The SCUBA beam size is ∼15'' at 850 μm with JCMT pointing accuracy of about 2'' (Chapman et al. 2002), which puts the 850 μm emission close to a region of 100 and 160 μm emission as detected by Herschel/PACS (Rodríguez-Muñoz et al. 2019). Further, we do not find evidence of significant ongoing or recent star formation in A2261-BCG. First, Herschel/PACS 100 and 160 μm imaging shows no significant emission from A2261-BCG (Rodríguez-Muñoz et al. 2019). Second, the SDSS spectrum of A2261-BCG is devoid of Hα, O iii, or other star formation tracing lines, nor does the spectrum show evidence of strong Balmer absorption features. Without any positive observational evidence for recent star formation, the red core of A2261-BCG is not sufficient reasoning to argue in favor of a heavy absorption. Additionally, our analysis of optical BCG position relative to the X-ray peak gets a value of about ${R}_{\mathrm{off}}=5.7{h}_{70}^{-1}\ \mathrm{kpc}$ compared to the value of ${R}_{\mathrm{off}}=0.4{h}_{70}^{-1}\ \mathrm{kpc}$ due to Bildfell et al. (2008). Adopting our larger value puts A2261-BCG much closer to the rest of the normal red-core BCGs.

HST-resolution imaging also allows us to better see the inner stellar distribution and lack of dust lanes. A second line of reasoning by Bildfell et al. (2008) is the appearance of a double nucleus in their optical imaging as evidence for a dust lane. Their optical imaging was done with MegaCam on the Canada–France–Hawaii Telescope with 0186 pixels in 07 seeing. It is likely that the stellar knots seen in HST imaging appeared as a double nucleus. At higher resolution, the optical and infrared imaging show no evidence of dust, either. The HST UV, optical, and NIR imaging shows no central dust lanes or color gradients associated with dust obscuration (Postman et al. 2012). Additionally, an estimated 3σ upper limit to the 100 μm flux within the central 15 kpc is 0.24 mJy using the public Herschel science archive data products. The 0.2–2.0 μm spectral energy distribution of A2261-BCG also is well fit by models that have intrinsic extinction of ${A}_{V}\leqslant 0.35\ \mathrm{mag}$. All of these constraints suggest that we have a largely dust-free view of the center of A2261-BCG.

We also find no evidence for large amounts of cold gas in A2261-BCG. A final argument for heavy obscuration comes from the Spitzer 3.6–24 μm observations (Egami et al. 2006). The observations show extended emission with monochromatic luminosities of ∼10⁴²–${10}^{44}\ \mathrm{erg}\ {{\rm{s}}}^{-1}$. Hlavacek-Larrondo & Fabian (2011) argue that such infrared emission is to be expected as reprocessed emission by gas surrounding an AGN. The amount of emission seen in the Spitzer imaging, however, is consistent with extrapolations of the stellar population SED fitting with only a slight excess at 24 μm. Thus, the infrared emission is almost entirely starlight, indicating no evidence for excess cold gas in the system. Thus we conclude that we have a clear view of any accreting black hole, but no X-ray point source emission is seen. It is still possible, however, that a ${10}^{10}\,{M}_{\odot }$ black hole exists in one of the stellar knots of A2261-BCG but is accreting at such a low level that it does not produce sufficient X-ray emission to be noticeable above the cluster gas emission.

Although absence of evidence is not evidence of absence, our observations are consistent with no ${10}^{10}\,{M}_{\odot }$ black hole existing in any of the locations of the stellar knots. If there is no black hole in any of the stellar knots, then the questions regarding the location of the expected central black hole of A2261-BCG remain. One possibility is that a 10¹⁰ ${M}_{\odot }$ black hole exists at the local center of the galaxy and is accreting at a very low rate such that there is no obvious X-ray point source. Just as we cannot definitively ascertain whether there is a black hole in the stellar knots, we cannot definitely ascertain whether one exists at the center of the galaxy, either; but nor can we rule it out with the X-ray data. Another possibility is that the black hole did suffer a gravitational wave recoil of relatively high velocity ($\sim 1000\ \mathrm{km}\ {{\rm{s}}}^{-1}$) over 10 Myr ago and it has traveled over 10 kpc from the center. Looking at a wider radius of stellar knots suspected of being a recoiling black hole cloak would increase the chance of X-ray noise leading to an X-ray point source false positive.

The findings here are consistent in light of our past results, which as previously mentioned demonstrated through spectroscopy and stellar color analysis that two of the central stellar knots are likely to be low-mass group-member galaxies that are being stripped and cannibalized by the BCG. The existence of a relic radio source implies that there was at some point a sufficiently high accretion rate onto the black hole to support the formation of collimated jets, but the present lack of a bright X-ray core supports the conclusion that the radio source seen in this BCG represents relic emission.

It should be possible to definitively determine whether a black hole exists at the center of the A2261-BCG with JWST IFU observations and full Schwarzschild modeling of the galaxy. The central surface brightness of A2261-BCG is too low for HST to measure the stellar velocity dispersion in the central 025 region, and there are no tip-tilt stars available for ground-based adaptive optics IFS observations. With JWST it would be possible to get high S/N spectroscopy of the center of the galaxy to get stellar kinematics as well as to do so for the stellar knots. Although the stellar knots had spectra taken with HST/STIS, the hot pixels on STIS led to lower than expected S/N and may have compromised the ability to measure the stellar velocity dispersions of the knots. If a large black hole is present in any of the stellar knots, then it should be obvious in JWST spectroscopy. Similarly, if a 10¹⁰ ${M}_{\odot }$ black hole is either present or absent from the center of the galaxy, it would be straightforward to detect its presence with Schwarzschild modeling of the same data. If a large black hole were quickly removed from the center of the galaxy, the stars in the previous sphere of influence would react on a dynamical time.

We also note that the asymmetry in the X-ray morphology indicates a disturbance that is similar to the optical morphology disturbance. Both the X-ray and optical light have cores that are displaced with respect to the centers as determined by outer isophotes. The optical light, which traces starlight, and the X-ray light, which traces the hot gas, are similar in their amplitude and direction of displacement. The X-ray morphology could be evidence of "sloshing." Sloshing, the presence of asymmetric and/or spiral structure patterns in the hot gas in a cluster observed in some cool-core clusters (Markevitch et al. 2000, 2003; Clarke et al. 2004; Ghizzardi et al. 2010; Simionescu et al. 2010; Sanders et al. 2020), is thought to be a result of dark-matter substructure passing through the center of the cluster (Ascasibar & Markevitch 2006; ZuHone et al. 2010; Roediger et al. 2012). The X-ray emission located 33 southwest of the cluster core center may be evidence of this (Figure 5). Located at α = 17:22:12.5, δ = +32:06:43.4, there is extended emission in a roughly elliptical region extending 30'' × 20''. At a projected separation of approximately 700 kpc, this region contains several galaxies that are cluster members as determined by their redshift. Thus the X-ray and optical morphology—including the large and offset stellar core—could have both been an effect of cluster substructure interactions.

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In this work, we presented new 100 ks of Chandra observations of A2261-BCG. We fitted these new data along with 35 ks of archival data to determine the profile of X-ray emitting soft gas. Our analysis of the morphology of the X-ray gas showed evidence of a previous dynamical disturbance, consistent with the optical morphology. We also fitted the X-ray spectra of the extended emission, which yielded profiles showing a cool core with enhanced metallicity. Using our cluster gas profile as a background region, we fitted the X-ray spectra at the locations of the stellar knots, the optical center, and the location of the radio emission. Our analysis found that all of the locations of interest were consistent with no X-ray point sources. Synthesizing available information about A2261-BCG, while this galaxy should host a black hole with a mass potentially in excess of 10¹⁰ ${M}_{\odot }$ and contains multiple indications that it could have been the site of a past merger of two black holes, we find no evidence for such a black hole accreting above an Eddington fraction of f_Edd = 10⁻⁶.

K.G. acknowledges support provided by the National Aeronautics and Space Administration (NASA) through Chandra Award Numbers GO7-18087X, TM8-19007X, and GO8-19078X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical observatory for and on behalf of NASA under contract NAS8-03060. S.B.S. acknowledges support for this work by NSF grant #1815664. S.B.S. is a CIFAR Azrieli Global Scholar in the Gravity and the Extreme Universe program. The NANOGrav project receives support from National Science Foundation (NSF) Physics Frontier Center award number 1430284. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The results in this paper are based, in part, on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. This research has made use of NASA's Astrophysics Data System. This research used data products from the Herschel Science Archive. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

Facilities: HST - Hubble Space Telescope satellite, Chandra - , Subaru - , Herschel. -

Software: CIAO (Fruscione et al. 2006), Sherpa (Freeman et al. 2001; Doe et al. 2007), XSPEC (Arnaud 1996), matplotlib (Hunter 2007), astropy (Astropy Collaboration et al. 2013, 2018), xvista (Stover 1988).

In this appendix we present Table 4, which defines our annuli, and Table 5, which lists the results of our spectral fits. We also plot them in Figures 6, 7, and 8.

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