A BRIGHTEST CLUSTER GALAXY WITH AN EXTREMELY LARGE FLAT CORE

Understanding the central structure of A2261-BCG requires knowledge of whether or not the core hosts a central supermassive black hole. This problem will be considered at length later in the paper, but we note here that the center of the galaxy does harbor a radio source that is at least an order of magnitude more powerful than those associated with star-forming regions and is thus evidence in favor of an active galactic nucleus (AGN). The NRAO VLA Sky Survey (NVSS; Condon et al. 1998) finds a source at 1.4 GHz with an integrated flux of 5.3 ± 0.5 mJy that lies 63 east of the BCG position. No other NVSS sources are found within 245 of the BCG. Data from the Faint Images of the Radio Sky at Twenty Centimeters (FIRST) survey (White et al. 1997) reveals a 3.4 mJy source that is more coincident with the core, lying 16 west of the BCG position. The FIRST detection limit at the source position is 0.99 mJy beam⁻¹. No other FIRST sources are found within 192 of the BCG. Presumably the NVSS and FIRST detections closest to the BCG correspond to the same source. The two radio positions are 75 apart, which is less than a 2σ difference and is consistent with the different astrometric uncertainties for the two surveys. Unfortunately, the Very Large Array (VLA) sky survey data currently do not have sufficient angular resolution to determine whether one of the knots, or the core itself, may host the AGN (VLA FIRST resolution is 5'', NVSS resolution is 45'').

If the radio source is at the cluster redshift then the FIRST detection yields an absolute luminosity of 7.8 × 10³⁹ erg s⁻¹ at 1.4 GHz corresponding to L_1.4 GHz = 5 × 10²³ W Hz⁻¹. Hlavacek-Larrondo et al. (2012) also find a central source with luminosity 5.0 × 10³⁹ erg s⁻¹ at 5 GHz corresponding to L_5.0 GHz = 1 × 10²³ W Hz⁻¹. The radio fluxes are indicative of a mildly powerful FR I radio source typical of those seen in BCGs (e.g., Croft et al. 2007)

Apart from the radio source, there is also a faint 24 μm detection of 0.44 mJy (Hoffer et al. 2012), which would indicate either star formation or a hot dust torus around an AGN. As in the case of the radio observations, however, the angular resolution is probably too poor to distinguish whether or not the flux comes from the center of the core or any of the associated knots.

In contrast, optical spectra do not reveal any significant evidence of emission lines that may be associated with an AGN or cooling flow activity (the spectra are presented in the next subsection). Further, there are no known X-ray or EUV sources identified with any of the compact knots; the X-ray limit on any point source in the core is L_2–10 keV < 3.8 × 10⁴¹ erg s⁻¹ (Hlavacek-Larrondo et al. 2012). At the same time, it is typical for central radio source in BCGs not to have strong X-ray counterparts. A black hole mass of ∼10¹⁰ M_☉ is in general consistent with the power requirements associated with the ICM shock fronts seen in other clusters (e.g., McNamara et al. 2009); but for such high-mass black holes, the power needed for such shocks is only ∼0.001L/L_ed, which therefore implies that the black holes can be radiatively inefficient. Hlavacek-Larrondo et al. (2012) note that synchrotron cooling can strongly affect the X-ray luminosity from the most massive black holes since the cooling break occurs below X-ray wavelengths, making such massive black holes underluminous at X-ray wavelengths compared to their radio luminosity. For A2261-BCG in particular, Hlavacek-Larrondo et al. (2012) estimate an Eddington ratio of ∼10⁻⁶–10⁻⁸.

The details of the image reduction and co-addition of the A2261 HST observations are given in Postman et al. (2012) and Coe et al. (2012). The analyses of the BCG profile here are based on the F606W and F814W HST CLASH images. The Advanced Camera for Surveys (ACS) photometry is on the AB magnitude system but we will express much of the reduced photometry in the rest-frame V band (Vega-based) for compatibility with the Lauer et al. (2007a) analysis of central galaxy photometry. We use a suite of Bruzual & Charlot (2003, hereafter BC03) synthetic stellar population models to derive linear photometric transformations from the observed, extinction-corrected ACS/WFC magnitudes and colors to the rest-frame Johnson V band, V_o. The BC03 models used to empirically derive the transformation equations have the following parameters: exponential star formation rate e-folding times, τ, of 0 Gyr (SSP model), 0.2 Gyr, 0.6 Gyr, and 1.0 Gyr; metallicities of 0.25 Z_☉, 1.0 Z_☉, and 2.5 Z_☉; and ages from 2 Gyr to the age of the universe at the cluster redshift in 0.5 Gyr intervals. These models more than span the range of observed cluster galaxy spectral energy distributions (SEDs). To compute photometric transformations, we take the BC03 SEDs for each of the above models and compute the observed photometry and colors at the cluster redshift and then use the same SEDs to compute the rest-frame Johnson V magnitude. The transformation equation parameters are then derived using a linear least-squares fitting procedure. In addition, we compute an evolution correction, c_ev, from a BC03 τ = 0.6 Gyr solar metallicity model with a formation epoch of z = 4.5. The transformation equation is

$$\begin{eqnarray} V_o &=& ({\rm F814W} + c_{{\rm ev},{\rm F814W}}) + 0.5186 \nonumber\\ && \times ({\rm {\rm F606W} - {\rm F814W}} + c_{{\rm ev},{\rm F606W}} - c_{{\rm ev},{\rm F814W}}) + 0.1764\nonumber\\ &=& ({\rm F814W}) + 0.5186 \times ({\rm F606W - F814W}) + 0.4213, \end{eqnarray} \tag{ 1 }$$

where F606W and F814W are the Galactic extinction-corrected ACS/WFC measurements in AB-magnitudes, c_{ev, F606W} = 0.256, c_{ev, F814W} = 0.233, and V_o is on the Vega system. The extinction corrections used are 0.127 mag and 0.079 mag for the F606W and F814W filters, respectively. The rms scatter about the transformation equation shown in Equation (1) is 0.006 mag. We tested the robustness of the method by computing similar transformations for F625W and (F625W–F814W) and for F850LP and (F814W–F850LP). They yield the same rest-frame V_o values to within ±0.01 magnitudes.

The total luminosity of A2261-BCG was determined by fitting its surface photometry with an r^1/4 law. This is consistent with the methodology in Lauer et al. (2007a), which will be used to provide the context for the present galaxy. The BCG is highly luminous with a total absolute magnitude of −24.70 in the V band (see Table 1). Because we want to compare this to the z = 0 sample of BCGs, this luminosity includes an evolutionary correction of +0.26 mag to account for the aging of the stellar population since the z = 0.22 epoch. Even then, A2261-BCG is among the most luminous BCGs known (Postman & Lauer 1995).

Four sources fall within the outskirts of the core. Their coordinates and photometric properties are summarized in Table 1. The brightest source, "Knot 3," is well resolved. Its profile was measured simultaneously with the BCG (as is described in Section 3.1) and has a roughly exponential form. The close pair of compact sources northeast of the core center, Knots 1 and 2, are both marginally resolved with 005 half-intensity radii. The faint source south of the core, Knot 4, is unresolved. The photometric errors in Table 1 given here include both the random and estimated systematic errors. The random errors (photon shot noise, read noise, dark current) are in the range 0.005–0.010 mag. The systematic errors are relatively small but still about 2–4 times larger than the corresponding random errors. This is due to spatial variations in the background level after the BCG model is subtracted from the image. To estimate the amplitude of the systematic error we compared the knot photometry derived from the BCG-subtracted image with that derived by using a local sky subtraction (instead of BCG subtraction) where the background is estimated from an annulus with an inner radius of 06 and an outer radius of 12 centered on each knot. The two measures of the photometry typically agree to within 0.015–0.020 mag. Based on this, we adopt 0.018 mag as an estimate of the systematic error.

Moderate resolution spectroscopy of the BCG exists from the Sloan Digital Sky Survey (SDSS) DR8 and from the Gemini Observatory data archive. The Gemini data are deep long-slit spectra with GMOS-N from the program GN-2008A-Q-103 (PI: Chris Bildfell). The A2261 observations were obtained on 2008 March 16. The GMOS-N long-slit, with 075 width, was placed on the BCG and oriented at a position angle that intersects two of the three bright knots in the northern part of the core (but not the brightest one). The spectra are split into dual red and blue channels to optimize sensitivity. The full spectral range is ∼4140–6040 Å with a spectral resolution of R ∼ 1000 at the blue end. The one-dimensional co-added GMOS spectrum is shown in Figure 2.

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We measured the stellar velocity dispersion (σ) within the core of A2261-BCG from the GMOS spectrum using the IDL code pPXF developed by Cappellari & Emsellem (2004), which fits a linear combination of template spectra to the observed galaxy spectrum to minimize template mismatch. The template spectra are provided by the Vazdekis et al. (2010) single burst models for a range of ages and metallicities, which are based on the empirical MILES stellar library (Sánchez-Blázquez et al. 2006).

The fits are computed separately in the red and blue channel spectra, covering rest-frame wavelengths 3700–4150 Å and 4250–4700 Å, respectively in order to avoid regions near the chip edges where the wavelength solution is less reliable. The bright skyline at the 5682–5688 Å Na doublet is masked in the fitting procedure, and the fits are computed weighting all pixels equally. We find consistent values of σ = 393 ± 13 km s⁻¹ on the blue side and σ = 380 ± 8 km s⁻¹ on the red side. The higher-order non-Gaussian velocity moments H3 and H4 derived from the fits are negligible. We therefore adopt σ = 387 ± 16 km s⁻¹ as an estimate of the ensemble stellar velocity dispersion, including systematic errors. The Gemini velocity dispersion value is in excellent agreement with the 388 ± 19 km s⁻¹ velocity dispersion estimate from the DR8 SDSS database. This is among the highest central velocity dispersion values known.

The surface brightness profile of A2261-BCG was measured from the F814W image deconvolved with 20 cycles of Lucy (1974)–Richardson (1972) deconvolution to correct for the blurring of the point spread function (PSF). The deconvolved image of the core is given in Figure 3. Deconvolution works well on HST images for recovering estimates of the intrinsic light distributions of galaxies (Lauer et al. 1998, 2005). Given the angularly large and flat profile of the A2261-BCG core, the effects of deconvolution in the present context are extremely modest. The increase in the central surface brightness within the core after deconvolution is only ∼3%, with similar effect on the measured angular size of the core. The real import of deconvolution for A2261-BCG is to recover the forms of the compact sources falling around the core, and to reduce the effects of their scattering "wings" on the core, itself.

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Figure 3 also shows the residuals obtained after a two-dimensional model reconstructed from the brightness profile of the core was subtracted from the image. The profile for r > 05 was measured using the Lauer (1986) algorithm (operating in the xvista image processing system), which solves for the overlapping light distributions of multiple galaxies; the high-resolution algorithm of Lauer (1985) was used interior to this. The surface brightness profile is presented in Figure 5. The profile ratifies the visual impression that the core is essentially flat. In contrast to the typical central structure of most elliptical galaxies (but not all; see Lauer et al. 2002), there is no sign of any rising cusp in starlight as r → 0. The lack of a cusp actually made it difficult to determine the precise center of the galaxy. We did this by taking an intensity centroid over the entire core.

At radii well outside the core, HST-based surface brightness profiles become vulnerable to systematic sky measurement errors and so on due to the low-intensity levels of the outer isophotes, the angularly small pixels, and limited fields of the cameras. To better characterize the envelope of A2261-BCG, we augmented the ACS photometry with surface photometry measured from a ground-based R-band image obtained with the Suprime-Cam imager on the Subaru 8 m telescope. The Subaru-derived profile was scaled to match the ACS profile over 5'' < r < 8'', then blended with it over the same interval, and used solely as the brightness distribution for r > 8''. The Subaru profile extends to ∼24'' and equivalent V-band surface brightnesses fainter than 25 mag arcsec⁻².

Despite the smooth structure of the profile, the residuals within the core show a number of interesting features. In addition to the presence of the four sources noted earlier, the residuals show a dipole-like pattern outside the central flat portion of the profile. The simplest interpretation is that the core is slightly displaced from the center of the surrounding envelope by ∼02 (0.7 kpc) toward position angle ∼300°. This conclusion is supported by the contour map of the core, shown in Figure 4. The contour lines outside of the core to the SW are clearly spaced closer together than those in the NE direction.

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We describe the profile with a "Nuker law" (Lauer et al. 1995),

$$\begin{equation} I(r)=2^{(\beta -\gamma)/\alpha }I_b\left({r_b\over r}\right)^{\gamma } \left[1+\left({r\over r_b}\right)^\alpha \right]^{(\gamma -\beta)/\alpha }, \end{equation} \tag{ 2 }$$

which models the surface brightness distribution as a "broken" power law. The envelope profile has the form I(r) ∼ r^−β as r → ∞, while the inner cusp has I(r) ∼ r^−γ as r → 0, with the transition radial scale provided by the "break radius," r_b. The "speed" of transition between the envelope and inner cusp is provided by α, while I_b, the surface brightness at r_b gives the overall intensity normalization.

The best-fitting Nuker law is plotted in Figure 5 and has the parameters γ = −0.01,β = 1.56, α = 2.41 ± 0.18,r_b = 120, and I_b of 19.72 in F814W(AB). The fit was conducted for r < 8'', beyond which the envelope falls away slightly faster than a pure power law with radius. As can be seen, the fit over this domain is excellent, with an rms residual of 0.02 mag. The parameters are not strongly dependent on the domain of the profile fitted, in any case. For a fit conducted limited to r < 37, or half of the nominal domain, r_b = 115 is recovered, only a 4% decrease from the nominal value. The break radius, r_b, corresponds to the point of maximum logarithmic curvature, and thus can also be estimated by non-parametric methods. Lauer et al. (2007a) did this for a large sample of core galaxies presented in Lauer et al. (2005), finding the Nuker-fit and non-parametric measurements to agree well over a large range in angular core size, with no biases.

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The negative γ actually implies that the surface brightness decreases slightly as r → 0. We also performed a Nuker fit forcing γ = 0, which is essentially identical to the nominal fit, but for the central point. In this case, we recover β = 1.55, α = 2.50,r_b = 130, and I_b of 19.72. The γ = 0 model falls right on the upper error bar of the central point and thus coincidentally serves as a 1σ confidence bound on the central profile.

The center of A2261-BCG may have a luminosity density profile that actually decreases as r → 0. This occurs in a number of galaxies including a few BCGs (Lauer et al. 2002, 2005). An Abel inversion of the Nuker model for A2261-BCG with γ = −0.01 indeed shows that r = 0 corresponds to a local minimum in stellar density (Figure 6). Even inversion of the γ = 0 model of the brightness profile formally implies a ∼4% decrease in luminosity density at the HST resolution limit. This can be understood as a consequence of the lack of a cusp in combination with a sharply defined core. With a generic surface brightness profile of the form I(r)∝(1 + r^α)^−β/α (both α and β positive), the derivative of the profile has the form I(r)'∝r^α for r ≪ 1. When used with the standard Abel transform, this implies a formal density of zero at r = 0, when α > 2, a condition satisfied for the A2261-BCG brightness profile.

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Given, however, the modest central decrease in density implied by even the γ = −0.01 model, which just occurs near the resolution limit, it is not possible to say with confidence if A2261-BCG is yet another example of a "hollow core." At the same time there is no sign of any centrally rising cusp in central surface brightness, and an even constant density core over nearly two decades in radius is unusual (see the collection of core density profiles in Lauer et al. 2007b).

Figure 7 shows that the core of A2261-BCG is the largest core yet seen among extensive surveys of local galaxies. The figure is an adaptation of a figure in Lauer et al. (2007a), which shows the relationship between the core "cusp radius," r_γ, and the total V-band luminosity, L_V, for a composite sample of HST studies of the central structure of early-type galaxies (Lauer et al. 1995, 2005; Faber et al. 1997; Quillen et al. 2000; Ravindranath et al. 2001; Rest et al. 2001; Laine et al. 2002).¹⁵ The Laine et al. (2002) study, in particular, is focused on the central structure of BCGs and is thus particularly useful for placing the core of A2261-BCG in context.

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The cusp radius is the angular or physical scale at which the local logarithmic slope of the surface brightness profile reaches a value of −1/2, as the profile transitions from the steep envelope to the shallower inner cusp. In terms of the Nuker-law parameters,

$$\begin{equation} r_\gamma \equiv r_b\left({1/2-\gamma \over \beta -1/2}\right)^{1/\alpha }. \end{equation} \tag{ 3 }$$

This scale was first introduced by Carollo et al. (1997) and adopted in the analysis of Lauer et al. (2007a), who demonstrated that it gave tighter relationships between the core and global properties of the galaxies than the direct use of the break radius, r_b, did.

For A2261-BCG, the γ = −0.01 Nuker-law fit yields r_γ = 089  ±  002 or 3.2  ±  0.1 kpc at the distance of A2261-BCG (the γ = 0 fit also gives r_γ = 089). As a check, this value is consistent with a simple estimate of r_γ = 090, made by fitting a parabola to the core over 07 < r < 14. The corresponding "cusp brightness," I_γ, the surface brightness at r_γ, is 19.52 mag arcsec⁻² (F814W) or 20.29 in the rest-frame V band corrected for interstellar extinction. As shown in Figure 7, this r_γ is over twice as large as the largest BCG cores seen in the Laine et al. (2002) sample. It is also three times larger than the large core in MS0735.6+7421-BCG noted by McNamara et al. (2009). The A2261-BCG core falls on the high side of the Lauer et al. (2007a) relation between core size and total galaxy luminosity,

$$\begin{equation} \log (r_\gamma /{\rm pc})=(1.32\pm 0.11)(-M_V-23)/2.5+2.28\pm 0.04. \end{equation} \tag{ 4 }$$

The scatter in log (r_γ) about this relation is 0.35 dex; A2261-BCG falls 0.33 dex above the relation, corresponding to a 1.0σ deviation.

If cores are created by the scouring action of a binary black hole, and the core size is indicative of the mass of the binary, then the implied black hole mass for A2261-BCG must be extremely large. McConnell et al. (2011) recently identified two black holes with masses 10¹⁰ M_☉ or greater in the BCGs A1367-BCG (= NGC 3842) and A1656-BCG (= NGC 4889), which have cusp radii of only 0.3 kpc and 0.7 kpc, respectively (Lauer et al. 2007a), implying that M_• in A2261-BCG is yet larger than that found in those two galaxies.

The M_•–L and M_•–σ relations between nuclear black hole mass and galaxy luminosity (Dressler 1989; Kormendy & Richstone 1995; Magorrian et al. 1998) or velocity dispersion (Ferrarese & Merritt 2000; Gebhardt et al. 2000) give some guidance on what to expect for the central black hole mass in A2261-BCG, completely apart from its core structure. The M_•–L and M_•–σ (elliptical galaxy only sample) relations from the comprehensive analysis of Gültekin et al. (2009) predict M_• = 6 × 10⁹ M_☉ and 2 × 10⁹ M_☉, respectively. The analogous McConnell et al. (2011) M_•–L and M_•–σ relations, which as noted above include BCG black hole masses, predict somewhat higher values of 1.1 × 10¹⁰ M_☉ and 5 × 10⁹ M_☉. It should be noted that A2261-BCG is more luminous and has a higher velocity dispersion than any galaxy that actually has a black hole mass measurement, thus the predictions are extrapolations.

A different approach is to use the fundamental plane of black hole activity (Merloni et al. 2003), which derives M_• from a combination of 5 GHz core radio luminosity and 2–10 keV nuclear X-ray emission. Hlavacek-Larrondo et al. (2012) use this methodology to estimate M_• = 2.0^+8.0_−1.6 × 10¹⁰ M_☉ for A2261-BCG.

Unfortunately, estimates of black hole mass implied by the scale of the core, itself, in A2261-BCG will be even more uncertain extrapolations. Lauer et al. (2007a) presented a number of relationships between r_γ and M_•, based on how the sample of core galaxies with real M_• determinations was analyzed. If r_γ and M_• are fitted symmetrically, then Lauer et al. (2007a) find r_γ∝M^0.8_•, which predicts M_• ∼ 4 × 10¹⁰ M_☉ for A2261-BCG. If on the other hand M_• is treated as an independent variable, then Lauer et al. (2007a) find r_γ∝M^1.5_•, which predicts a more modest M_• ∼ 7 × 10⁹ M_☉. The large difference between the two estimates is due to the small number of systems contributing to the Lauer et al. (2007a) r_γ–M_• relationships and the large scatter between the two parameters.

An alternate approach advocated in several papers is to relate estimates of the "mass deficit," M_d, that is the mass in stars that was ejected to generate the core, to M_•. Unfortunately, this methodology at present also leads to large uncertainties in the estimated M_• for A2261-BCG. Kormendy & Bender (2009) derive a relationship between L_d and M_• for galaxies of the form L_d∝M_•, where L_d is the observed starlight rather than inferred mass deficit, and is measured by integrating the central difference between the observed surface brightness profile and an inward extrapolation of a Sérsic law fitted to the envelope of the galaxy.

The best fit of a Sérsic law to the envelope of A2261-BCG has n = 4.1, or essentially the classic r^1/4 law form. An r^1/4 law fitted to the envelope gives M_V ≈ −20.8, implying M_• ∼ 1.1 × 10¹⁰ M_☉, using the Kormendy & Bender (2009) relation. This later L_d is identical to M_V ≈ −20.8 derived by the simple estimate of "core luminosity," L_γ ≡ πI_γr²_γ used by Lauer et al. (2007a) as a proxy for L_d that avoids the need for the careful selection and evaluation of a "pre-scouring" reference surface brightness profile.

One intriguing possibility is that the large flat core has resulted from the central ejection of its nuclear black hole. In this scenario, the galaxy most likely had a large core to begin with, which would have been enlarged by the ejection of the central black hole. The large core would have been generated by a smaller black hole than that directly implied by the presumption that scouring by the binary black hole did all the work.

Merritt et al. (2004) and Boylan-Kolchin et al. (2004) show that a core can be generated directly in a "power-law" galaxy (a system that initially has a steep central cusp) when the components of a binary black hole merge and the remnant is ejected by the asymmetric emission of gravitational radiation. Gualandris & Merritt (2008) simulated this scenario, finding that the ejection can substantially enlarge a pre-existing core, leading to the inference of an exceptionally large mass deficit. Given the high luminosity of A2261-BCG, it is extremely likely that it would have a large core prior to any ejection of a central black hole. Gualandris & Merritt (2008) also show that the central stellar density profiles can become extremely flat after ejection of the black hole, similar to what is seen in Figure 6.

The physical displacement of the core from the envelope center, noted above, is indicative of a local dynamical disturbance. This is likely to be a relatively recent event. An ejected black hole would be trailed by a strong dynamical-friction wake as it leaves the core. In effect, it would "pluck" the core, which would then oscillate for a few crossing times, t_c ∼ r_γ/σ or ∼10⁷ yr for A2261-BCG. At the same time, this need not mean that the ejection of the black hole, itself, needs to be as recent. If the ejected black hole remains on a radial orbit that periodically returns to the core, then the disturbance might only be due to a recent passage (D. Merritt 2012, private communication).

Real proof of the ejected black hole hypothesis would be to find direct evidence of the ejected black hole, itself. Merritt et al. (2009) show that the ejected black hole carries along with it a "cloak" of stars that had previously been closely bound to it. The ejected black hole and associated stars would somewhat resemble a globular cluster or ultracompact dwarf galaxy. The key diagnostic for such a system would be the extremely high velocity dispersion of the tightly bound stars. An obvious question then for the present case is if any of the four sources proximal to the core might be such an object.

An important point is that the stellar "cloak" is most likely to be considerably less massive than the black hole. For a black hole ejected from a core, Merritt et al. (2009) find

$$\begin{equation} {M_b\over M_\bullet }\approx 2\times 10^{-2}\left({\sigma \over 200 \ {\rm km\ s^{-1}}} \right)^{5/2}\left({V_k\over 10^3\ {\rm km\ s^{-1}}}\right)^{-5/2}, \end{equation} \tag{ 5 }$$

where M_b is the mass of stars bound to the black hole, σ is the velocity dispersion of the galaxy, and V_k is the "kick" velocity with which the newly merged binary black hole is ejected from the center of the galaxy. In the case of A2261-BCG with σ = 387 km s⁻¹, the coefficient in the above equation becomes 0.1. While we have echoed the nominal V_k = 1000 km s⁻¹ from Merritt et al. (2009), the real value depends on the unknown mass ratio and spins of the two black holes within the merging binary and can range from essentially zero to a few thousand km s⁻¹. The only way to constrain V_k better would be to identify the remnant and measure its line-of-sight velocity.

Merritt et al. (2009) also show that the effective radius of the cloak is also related to the kick velocity. For a black hole initially in a core,

$$\begin{equation} R_e\approx 43\left({M_\bullet \over 10^{10}\,M_\odot }\right) \left({V_k\over 10^3 \ {\rm km\ s^{-1}}}\right)^{-2} \rm {pc}. \end{equation} \tag{ 6 }$$

Given the expected scale and mass of the stellar cloak, the best candidate for an ejected black hole would be the least luminous of the four sources, the unresolved point source south of the core. The most luminous of the four sources has an implied luminosity of L_V ∼ 4 × 10⁹ L_☉ and a substantially larger physical extent than the number given above. When converted to a likely mass, the source carries a substantial fraction of the putative 10¹⁰ M_☉ black hole, thus not matching the expectation that M_b ≪ M_•. Morphologically, the source also resembles any number of other small galaxies visible within the neighborhood of the BCG. The two less luminous paired-sources, also north of the core, are more consistent with a possible cloak, but even their compact sizes are large for the expectations enumerated above.

Of course if V_k is large, and the ejection happened long ago, then the remnant would be unlikely to be within the core, and the candidate list would have to be extended to sources at much larger distances from the center of the BCG. The timescale for exiting the core is simply r_γ/V_k, which is likely to be substantially shorter than t_c. Conversely, a small kick favors larger and more extended cloaks, and increases the likelihood that the remnant would remain close to the core in the event that the kick was insufficient to unbind the black hole from the BCG, itself. If the offset core is indeed due to an ejected black hole, then the short lifetime of the offset would imply that the remnant should be relatively close-by.