A Radio Relic and a Search for the Central Black Hole in the Abell 2261 Brightest Cluster Galaxy

2.1.1. CLASH Imaging

2.1.2. New Spectroscopy

Spectra of knots 1, 2, and 3 were obtained using the Space Telescope Imaging Spectrograph (STIS) from 2015 July 31 to 2015 August 1. We used the G750L grating and the $52^{\prime\prime} \times 0\buildrel{\prime\prime}\over{.} 5$ slit. The initial pointing was centered on the brightest knot (knot 3 at R.A. $=\,{17}^{{\rm{h}}}{22}^{{\rm{m}}}$2714 and decl. = +32°07'5759 (J2000)). The observations were performed with an ORIENT angle of 1305, allowing all three knots to be observed simultaneously (Figure 1). We integrated for a total of eight orbits (total exposure time of 19,100 s) and acquired 16 exposures. The eight-orbit integration sequence was executed as two visits, with 300 s acquisition exposures done at the start of orbits #1 and #5 to ensure precise slit alignment. Four small pointing shifts (each 02 in size and parallel to the long dimension of the slit) were made over the course of four orbits to allow for the rejection of hot/bad pixels in the dispersion direction. The same shifts were repeated for the second set of four orbits.

Zoom In Zoom Out Reset image size

The STIS data were reduced by performing the subtraction of the variable herring-bone pattern noise, bias correction, and pixel-based charge transfer inefficiency (CTI) correction on the raw science data sets, then running the remainder of the calstis processing steps to produce the final CTI-corrected 2D flat-fielded images. The removal of the herring-bone pattern noise, a known issue with STIS since it resumed operations in 2001 using its Side-2 electronics, was done using the procedures outlined in Jansen et al. (2010). The 2D flat-fielded images were then shifted along the spatial axis using the Pyraf task sshift to remove the offsets from the dithers done between each orbit. The individual images were co-added using the ocrreject routine, which is designed to detect and remove cosmic rays in STIS CCD data as well as co-add input images. The benefits of using ocrreject to combine the data are twofold: (1) an error array that is proportional to the square root of the output science image, but smaller by a factor that depends upon the square root of the number of non-rejected input values used to compute the science pixel values, is produced and (2) it allowed us to use all 16 exposures to ensure robust cosmic-ray rejection. The final 1D spectrum for each knot was extracted using the x1d routine, which also applies the STIS flux and wavelength calibrations to produce a co-added 1D spectrum in ${F}_{\lambda }$ units of erg s⁻¹ cm⁻² Å⁻¹. The wavelength range of the extracted 1D spectra runs from 5257 to 10249 Å, with a dispersion of 4.87 Å per pixel.

The average signal-to-noise ratio (S/N) per resolution element (resel) in the 1000 Å wide range centered on the redshifted NaD doublet feature (centered at 7218 Å at the redshift of z = 0.2248 for A2261) for the extracted spectra from knots 1, 2, and 3 is 8.6, 7.7, and 10.7, respectively. The predicted per-resolution-element S/N estimates from the HST exposure calculator were about a factor of 1.8 higher than the achieved values. The large difference between the observed and predicted S/N is primarily due to the significant number of pixels lost to cosmic-ray contamination (even with 16 independent exposures) and, to a lesser degree, by residual noise left after the CTI and pattern noise corrections are applied. However, without applying those corrections, the observed S/N would have been much worse.

We fitted the extracted, normalized STIS spectra to estimate the stellar velocity dispersion in the knots. We used pPXF, the penalized pixel fitting code of Cappellari & Emsellem (2004). For each knot spectrum, we logarithmically rebinned in wavelength so that it matched that of the MILES library spectra (Vazdekis et al. 2010). To match the spectra, we convolved the higher-resolution spectra with a Gaussian with variance equal to the difference in the variance of our observations and the template spectra. We tried various schemes of binning the spectrum but found they made little difference to our final results. Thus, the effective resolution is $250\,\mathrm{km}\,{{\rm{s}}}^{-1}$. We similarly tried a variety of multiplicative and additive polynomials to account for any residual continuum shape but there was no significant improvement to the fits. Because of the low S/N of our data, we fit only the first two moments (velocity, V, and velocity dispersion, σ) of the line-of-sight velocity distribution relative to the recessional velocity of A2261.

A major concern for our fits to data of low S/N is spurious effects of template mismatch. In order to take this into consideration, we used the full MILES library. By using the entire library, we are ensuring that whatever the stellar population of the knots, we have included the proper stellar template. If we had not included the correct stellar template, then at low S/N the penalized pixel fitting method is more likely to find spurious solutions.

A second concern for fits to low S/N is the proper accounting of measurement uncertainties in the spectrum. We ran a series of Monte Carlo simulations to create realizations of the spectrum based on the 1D error spectrum after rebinning. The simulated data were fitted for each knot. For each knot spectrum, we ran 1000 realizations and took the median and 68% interval for the V and σ parameters of the fit, weighting them by the reciprocal of the square of the formal fit uncertainties. This weighting scheme ensures that poor fits have less influence on the final results than good fits. All had median results for the velocity dispersion to be very similar to the best-fit results.

The results of our fitting are presented in Table 1. Column 2 in this table is the velocity offset relative to a fiducial redshift of z = 0.22331. Column 3 is the derived velocity dispersion. For each knot, the results are expressed as the median values from our Monte Carlo simulations with the 68% interval of the parameter distributions for the uncertainties. We plot the 1D spectra with their best fits in Figure 2.

Zoom In Zoom Out Reset image size

Table 1.  A2261 Knot Velocity Offsets and Dispersions

	Velocity Offseta	Velocity Dispersiona
Object	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)
Knot 1	$-{74}_{-90}^{+65}$	${175}_{-59}^{+101}$
Knot 2	$-{117}_{-97}^{+98}$	${168}_{-63}^{+66}$
Knot 3	$-{58}_{-55}^{+62}$	${209}_{-46}^{+39}$

Note.

^aThe values given are the weighted medians with uncertainties coming from the weighted 16% and 84% of the Monte Carlo distributions. The best-fit model spectra used a mixture of stellar templates from the MILES library. Although the modeling procedure can use any of the stars from the full library, in practice only a few templates contribute the most. The non-negligible contributions in decreasing order of relative weights (i) to knot 1 come from G156−031, HD 187216, and HD 200779; (ii) to knot 1 come from UCAC2 21686546, HD 001326B, 2MASS J15182262+0206397, HD 199799, HD 042474, and HD 183324; and (iii) to knot 3 come from 2MASS J15182262+0206397, UCAC2 21686546, HD 12632, G171−010, HD 097907, BD+060648, 2MASS J05240938−2433300, HD 042474, and HD 023194.

Download table as:  ASCIITypeset image

In the spectra for knots 2 and 3, we find no significant evidence for a velocity dispersion larger than that expected for a galaxy with a black hole mass of $\lesssim 6\times {10}^{8}\,{M}_{\odot }$. The knot 1 velocity dispersion measurement is highly uncertain, however, and we cannot rule out the hypothesis that knot 1 is hosting the ejected A2261-BCG black hole.

The velocity offsets of the observed knots are significantly less than the velocity dispersions of A2261-BCG and the A2261 cluster (see Section 1). The knot velocity offsets are consistent with them being cluster members, and they are consistent with potentially being bound to A2261-BCG as well. However, in Section 4, we show that the knot velocity offsets are also consistent with the range of predicted initial kick velocities for an SMBH ejection event.

Stellar masses for the four knots are computed using the iSEDfit package (Moustakas et al. 2013). Input photometry for the iSEDfit analysis was obtained from 13 broadband images obtained from the CLASH HST Treasury program. All CLASH filters including, and redwards of, F390W were used for our SED fitting. For knots 1, 2, and 4, we used 0364 (1.31 kpc) diameter apertures and for knot 3 we used a 052 (1.87 kpc) diameter aperture. A local background subtraction was performed around each knot in each filter to account for underlying sky and BCG flux contamination. To compute the stellar masses, we generate a grid of 20,000 model spectra using a range of synthetic stellar populations (Bruzual & Charlot 2003), two different initial mass functions (IMFs; Salpeter 1955; Chabrier 2003), and the Calzetti dust extinction law (Calzetti et al. 2000). We then compute the grid of model photometry obtained by convolving the model spectra with HST filter response functions to generate a posterior probability distribution for the parameter space. We adopted a star formation history consisting of an initial burst followed by an exponentially decaying star formation rate (e.g., the BC03 tau model). Table 2 gives the best-fit stellar mass estimates derived for the knots for each of the two assumed IMF models.

Table 2.  Best-fit Stellar Mass Estimates and Knot Central Size Estimates

	Mass within Rm	Mass within Rm
	(Salpeter IMF)	(Chabrier IMF)	Rm	HWHMa	HWHMb
Object	(${10}^{10}\,{M}_{\odot }$)	(${10}^{10}\,{M}_{\odot }$)	(kpc)	(arcsec)	(kpc)
Knot 1	${0.64}_{-0.08}^{+0.09}$	${0.37}_{-0.05}^{+0.05}$	0.66	≤0.047	≤0.17
Knot 2	${0.54}_{-0.07}^{+0.08}$	${0.31}_{-0.04}^{+0.05}$	0.66	≤0.043	≤0.15
Knot 3	${1.70}_{-0.20}^{+0.24}$	${0.98}_{-0.12}^{+0.15}$	0.94	≤0.053	≤0.19
Knot 4	${0.16}_{-0.02}^{+0.02}$	${0.09}_{-0.01}^{+0.01}$	0.66	≤0.041	≤0.15

Notes.

^aThe half-width at half-maximum (HWHM) of the central light distribution is derived from the deconvolved F814W CLASH image. See Section 2.3 for details. ^bAssumes 3.593 kpc arcsec⁻¹ at z = 0.22331, i.e., assumes the knots reside in the BCG core.

Download table as:  ASCIITypeset image

Upper limits on the sizes of the knots are also given in Table 2. The size estimates are the half-width at half-maximum (HWHM) values of the central light distribution of each knot derived from their profiles measured in a deconvolved F814W CLASH image. The image deconvolution was performed by identifying an unsaturated star in the F814W image as our PSF reference and then applying 20 iterations of the Lucy–Richardson deconvolution technique (Richardson 1972; Lucy 1974). The profile for each knot was then measured using the high-resolution PROFILE routine (Lauer 1985a) in the xvista image processing package. The HWHM values derived for the central light distributions are almost certainly all upper limits. The HWHM values in Table 2 are given in both arcseconds and kiloparsecs, adopting the projected scale of 3.593 kpc arcsec⁻¹ at z = 0.22331. All four knots have central light HWHM sizes that are equal to or less than 190 pc. We emphasize that these HWHM values are not the same as the effective radius. For example, knot 3 is clearly a fully resolved galaxy but the HWHM of the central light distribution reveals that its nuclear light distribution remains unresolved at HST's angular resolution.

Bonfini & Graham (2016) report the existence of a fifth knot in close proximity to knot 3. We do not model knot 5 as a separate entity. Bonfini & Graham (2016) report that knot 5 is significantly less massive any of the other knots by at least a factor of 10 and is a factor of 150 times less massive than knot 3. The STIS spectrum of knot 3 would have included all the light from knot 5 as well. The S/N of knot 5 would have been far too low for its kinematics to contribute in any way to the kinematic parameters we derived for knot 3.

We measured the observed $F475W-F814W$ and $F814W-F160W$ colors for knots 1 through 4 while preparing the input photometry for our stellar mass estimation described in Section 2.3. The colors of the four knots and those of the BCG (within its central 23.5 kpc) are shown in Figure 3. The colors shown are corrected for local Galactic extinction using the results from Schlegel et al. (1998). Knot 4 is the bluest and Knot 2 the reddest. The four knots are located near the periphery of the red sequence in this color–color space. All four knots are at the red end of the $(F475W-F814W)$ red sequence color distribution although they have $(F814W\,-F160W)$ colors that are consistent with the bulk of the red sequence galaxies. Although we cannot put strong constraints on the age or metallicity of the knots, the SED fitting results suggest that knots 3 and 4 are likely to have subsolar metallicity. Specifically, the probability that the stellar populations of knots 3 and 4 are subsolar are 0.93 and 0.91, respectively, for the Salpeter and Chabrier IMF. Our models do not provide any significant constraints on the metallicity of knots 1 and 2.

Zoom In Zoom Out Reset image size

If the knots are the stripped nuclei of initially larger early-type cluster galaxies, then they would be expected to be somewhat redder than the average red sequence cluster member. Elliptical galaxies are observed to have color gradients with the general trend of the stellar population becoming slightly bluer as one moves out to larger radii. Specifically, the observed color gradients in ellipticals (Tamura et al. 2000) are ${\rm{\Delta }}(F606W-F814W)/{\rm{\Delta }}\mathrm{log}(r)\sim -0.06$ in the redshift range $0.2\lesssim z\lesssim 0.3$. The origin of color gradients in elliptical galaxies appears to be predominantly due to a decrease in the metallicity of the stellar population with increasing radius from the galaxy center. The arrow in Figure 3 shows the direction in which elliptical $(F475W-F814W)$ and $(F814W-F160W)$ colors would change, on average, as one moves from a region corresponding to the size scale of the knots (~0.25 kpc) out to a radius of ~2–3 kpc, corresponding to the effective radius of a cluster elliptical. The trend denoted by the arrow corresponds to ${\rm{\Delta }}(F475W-F814W)=-0.16$ mag and ${\rm{\Delta }}(F814W-F160W)=-0.058$ mag for ${\rm{\Delta }}(F606W-F814W)/{\rm{\Delta }}\mathrm{log}(r)=-0.06$ and ${\rm{\Delta }}\mathrm{log}(r)=1$. If the knots are the nuclei of stripped early-type galaxies, then their progenitors are consistent with being red sequence members of Abell 2261.

As Tables 1 and 2 suggest, knots 2 and 3 are photometrically and kinematically consistent with the properties of small galaxies. Their velocity dispersions are between 168 and 209 km s⁻¹, and they have stellar masses of $3.1\times {10}^{9}$ and $9.8\times {10}^{9}$ ${M}_{\odot }$, respectively (using a Chabrier IMF). The velocity dispersions of knots 2 and 3 are inconsistent at the $\gtrsim 2\sigma$ level with systems containing a black hole with mass comparable to that predicted for A2261-BCG, ${M}_{\bullet }\gtrsim 5.6\times {10}^{9}$ ${M}_{\odot }$, which would have yielded an observed stellar velocity dispersion in excess of 330 km s⁻¹ (Kormendy & Ho 2013). Figure 4 shows the predicted range in velocity dispersion for the estimated range in the A2261-BCG black hole mass discussed in Section 1. As noted above, the large errors in the velocity dispersion of knot 1 mean that we cannot rule out the hypothesis that it is hosting a high-mass black hole.

Zoom In Zoom Out Reset image size

As reported by Postman et al. (2012), A2261-BCG was detected by the FIRST survey (Becker et al. 1995) as an unresolved 1.4 GHz radio source with a flux of 3.4 mJy, 16 west of the galaxy's position; this is just under a factor of two of the galaxy core radius. We thus collected wide-band continuum data from the VLA to obtain:

• 1.  
  accurate reference frame ties to the available Subaru optical image (Postman et al. 2012) to determine whether the offset position was genuine;
• 2.  
  a resolved image of the radio feature to assess its nature morphologically; and
• 3.  
  an estimate of the jet age through radio spectral aging (e.g., Carilli et al. 1991).

Data were collected under project code VLA/15A-061 in A-configuration in two frequency ranges. The first was 3.976–8.024 GHz (C-band; ${f}_{\mathrm{avg}}=5.873\,\mathrm{GHz}$ after flagging, hereafter "6 GHz"), which provided 03 imaging resolution. The second was 7.976–11.896 GHz (X-band; ${f}_{\mathrm{avg}}\,=9.937\,\mathrm{GHz}$, hereafter "10 GHz"), which provided 02 resolution. Both frequency setups used standard 2 MHz channel widths and 2 s sampling. The standard primary calibrator 3C 286 was used for flux density and bandpass calibration, and source J1735+3616 was used as a phase calibrator. To gain sufficient sensitivity, observations were performed in two epochs and then concatenated to create a single data set per frequency band. Given the extended emission in the source, we do not expect any significant intrinsic variability between the two epochs.

The 6 GHz observations were performed on 2015 July 11 and 13, giving a total of 6.27 hr on-source time. At 10 GHz, the observations were made on 2015 June 25 and 27; 6.70 hr were spent on source at this frequency. We utilized the standard VLA pipelines to calibrate the data, and performed manual flagging and imaging with the CASA software package. Table 3 provides the resulting image noise, measurement, and beam parameters.

Table 3.  VLA Imaging Results

Band	${f}_{\mathrm{center}}$	σ	Peak	Int.	Beam Size	Beam	Source Size	Source	Linear
	(GHz)	(μJy)	(μJy)	(μJy)	(mas)	P.A. (deg)	(mas)	P.A. (deg)	Extent (kpc)
C	5.873	2.1	132.4 ± 6.8	483 ± 31	530 × 360	68.0	$950\pm 70\times 470\,\pm$ 60	135 ± 5	3.45
X	9.937	1.2	23.4 ± 1.9	158 ± 14	340 × 220	72.0	$840\pm 80\times 490\,\pm$ 60	126 ± 9	3.05

Download table as:  ASCIITypeset image

FIRST images indicated, to low significance, that there was a radio component offset from the BCG's core. Our new higher-resolution images (Figure 5) confirm this offset. We find the radio centroid to be 180 ± 025 from the photometric center of the optical core.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To verify that an inaccurate radio/optical reference frame tie could not be the cause of the offset, in our data we identified two field sources detected in both our VLA image and the Subaru image (an R-band image from Suprime-cam; Postman et al. 2012). The positions of the optical centroid and the unresolved radio core component of these galaxies, and their radio/optical positional differences, are reported in Table 4. In the same table, we show A2261-BCG's fitted radio position (fitting the X-band data for a single Gaussian source) and the core's peak optical pixel location after the knots have been removed. We thus find the offset of the radio source to be significant and not due to a reference frame error.

We can also assess the probability that this radio source is a projected association and not a genuine one. The galaxy lies in the center of a dense cluster, and so general radio counts will likely underestimate this number. We thus measure the radio source count directly from the A2261-BCG field using an image out to the FWHM image at C-band, which has the larger field of view of the two frequencies. The C-band field of view is 0.01 deg². There were three objects in this field with flux densities equal to or larger than the flux density of the A2261-BCG radio source, including the A2261-BCG radio source itself. Thus, the count is $R(\gtrsim 140\,\mu \mathrm{Jy})\simeq 300\,{\deg }^{-2}$ in this field. The radio offset is 6.5 kpc (180), which subtends a circular aperture around the core center of area $3.9\times {10}^{-7}\,{\deg }^{2}$. A radio source of this flux density had a probability of $1.2\times {10}^{-4}$ of being in the galaxy core by chance; we are thus confident that the radio detection is related to the core.

One further possibility is that we are seeing a weakly lensed (magnified) background galaxy. Although the source is also not radially elongated, as we might naively expect for a weakly lensed object, this might be due to structural complexity in the lensed galaxy and/or the BCG itself. However, the radio source lies within a nominal Einstein radius for this object (~8'', assuming a point mass, z = 0.3 of the background galaxy, and ${M}_{2500}\simeq {10}^{14}\,{M}_{\odot }$ for the BCG), making significant magnification unlikely. Future work will have to investigate this possibility further using more complex modeling of the mass distribution in the large, flat core in which this radio source resides.

The radio luminosity of this source is ~5 × 10²³ W Hz⁻¹, as determined from the FIRST flux density. The most compact component at the C-band has a brightness temperature of ${T}_{{\rm{B}}}\gt 1.4\times {10}^{3}$ K. The emission appears to cover a projected linear extent of around $1\times 3.5\,\mathrm{kpc}$, with a projected centroid offset of 6.5 kpc from the core. Using our new flux measurements and previous lower-frequency measurements by Hogan (2014), we find a spectral index of $\alpha =-1.5\pm 0.1$, in agreement with their fit of the lower-frequency data only. Figure 7 shows a resolved two-point spectral index map of our 6 and 10 GHz data across the full extent of the radio emission. Although there is substantial error on the indices in this map (~0.5–1 on source), it is clear that there are no flat-spectrum subcomponents in the observed emission that could feasibly represent a presently active nuclear black hole.

Zoom In Zoom Out Reset image size

The spectrum and morphology of this emission are strong evidence that the radio object is in fact relic emission, whose steep slope is indicative of an aged population of synchrotron-emitting electrons (e.g., Scheuer & Williams 1968; Carilli et al. 1991). Relics encompass a range of morphologies and properties; however, as argued by Feretti et al. (2012), compact relics without sharp edges that are resident in the cores of galaxies are interpreted either as a fading jet component from a source that is no longer active, or as a "radio phoenix," which can arise due to compression shocks during a merger that re-energizes plasma from a previously emitting radio jet (e.g., Ensslin et al. 1998). However, the central location of this emission and the lack of other larger-scale emission directly related to the BCG appear to imply that this relic marks an active nucleus shut-off event. We cannot isolate what caused the central object to cease its activity; it could simply have run out of fuel, or it could be a merger- or recoil-induced quenching of the radio emission.

The limited size of the emission suggests that either the black hole's activity was short lived (such that it had insufficient time to grow to a large radio source) and/or that any radio emission that extended beyond the central regions of the galaxy faded more quickly due to lower pressure and magnetic field strength (and thus only the central regions are visible now).

A last, but more tenuous, possibility for the origin of the relic in this core is that it is old emission that originated from the extended active galactic nucleus that exists approximately 25 northwest of the BCG, in a direction about 45° from north. Note that this is the object referred to as a "field spiral" in Table 4, as identified in the Subaru image. This plasma may have been re-energized due to sloshing or shocks from ongoing cannibalization in the A2261-BCG core. The other radio object, at J2000 R.A., decl. J17:22:17, +32:09:13, has emission that extends from its central bright source outwards in a general direction toward the core of A2261-BCG, as shown in the maps of Sommer et al. (2017). The direction of the core of that object in general agrees with the offset direction of the radio source with the A2261-BCG photometric centroid. If one draws a line from the BCG center through its resident relic, it points generally down the barrel of the other galaxy's axis and through its central bright source. Although this is suggestive, it does not imply direct causality.

We also explored whether this object could be explained as a medium-sized symmetric object (MSO), a kiloparsec-scale radio source representing an intermediate stage in the evolution of extragalactic radio sources from parsec scales (compact symmetric objects, CSOs) to classical Faranoff-Riley II sources (Fanti et al. 1995; Readhead et al. 1996). This interpretation would favor the presence of an offset SMBH, resident somewhere within the offset location of the radio emission. The principal objection to this explanation is that this source is significantly underluminous relative to the expectations for MSOs. CSOs and MSOs show well-defined scalings of luminosity and size, with objects having a size scale of order 1 kpc expected to have spectral luminosities of order 10²⁷ W Hz⁻¹ at 5 GHz (Fanti et al. 1995; Readhead et al. 1996; Tremblay et al. 2016). In contrast, the spectral luminosity of this source at 5 GHz is approximately $7\times {10}^{22}$ W Hz⁻¹. Although the scatter in this relation is large (~1 dex), it is insufficient to accommodate this difference. A secondary objection is that this source is spectrally anomalous relative to most CSOs and MSOs, which both tend to have a flat-spectrum core and only a small fraction of the source with a spectral slope as steep as −1.5. Even in the regions where spectral indices are steeper than this, these regions are typically at the edges of the source, rather than being the entire source (Tremblay et al. 2016). Finally, CSOs and MSOs tend to be made up of a set of compact objects rather than be dominated by a continuous, resolved component, as this object is.

We can place a limit on the age of the radio component in this galaxy using synchrotron aging models, e.g., Harwood et al. (2013). These typically model the broadband radio spectrum with a double power law, with a break frequency (${f}_{{\rm{b}}}$) above which the aging electrons have a steep spectrum, and below which the spectrum exhibits a more standard ($\alpha \simeq -0.7$) injection value. In these models, ${f}_{{\rm{b}}}$ and the ambient magnetic field in the radio lobe (B) can be used to estimate the time since last electron acceleration, $t=1610\,{B}^{-3/2}{f}_{{\rm{b}}}^{-1/2}$ Myr, with B in μG and ${f}_{{\rm{b}}}$ in GHz (c.f. Pacholczyk 1970; Ensslin et al. 1998).

From Figure 6, there appears to be no clear low-frequency spectral break down to the lowest data point at 326 MHz (Rengelink et al. 1997). Given the steep spectrum across these frequencies that is well-fit to a single power law, we therefore infer that the break frequency is ${f}_{{\rm{b}}}\lt 326\,\mathrm{MHz}$. We also require a magnetic field to translate this to a limit on relic age. In the absence of any determinations of the magnetic field in A2261-BCG, Figure 8 shows the inferred range of relic age estimates for break frequencies ranging from 10 MHz to 326 MHz as a function of magnetic field strength. The implication is that the relic must be very old (>10s of Myr), have an uncharacteristically high magnetic field, or both. The very low spectral break implied for this source implies a magnetic field in the relic on the order of 2 μG if the relic is aged 1 Gyr, and 15 μG for a more typical relic age of 50 Myr.

Zoom In Zoom Out Reset image size

We can estimate the magnetic field by assuming equipartition between magnetic energy and relativistic particle energy. Following Pacholczyk (1970) and assuming that there is equal energy in heavy particles and a filling factor of 1 (i.e., the magnetic field occupies the whole region rather than being in filaments), the minimum value of the total energy is reached when

$$\begin{eqnarray}&&{B}_{\min }={(9{c}_{12})}^{2/7}{R}^{-6/7}{L}^{2/7},\end{eqnarray} \tag{ 1 }$$

where R is the source depth, L is the luminosity, and where in CGS units ${c}_{12}=1.7\times {10}^{8}$ is a factor that depends on the radio spectrum and a lower and upper frequency cutoff, assumed here to be 10 MHz and 100 GHz, respectively (e.g., Harris et al. 1993). Note that 10 MHz is a standard choice for a lower cutoff, while the choice of upper frequency cutoff does not greatly effect the results (between choices of 1 GHz and 100 GHz, ${B}_{\min }$ varies by $\lt 0.5\,\mu {\rm{G}}$). For a radio relic depth of ~3 kpc, we find that the equipartition magnetic field is ~15 μG. Note that because the equipartition field is most sensitive to the size of the source and because this radio source is compact when compared to other radio relics, the magnetic field in this object is about one to two orders of magnitude higher than more diffuse radio relics (e.g., Giovannini et al. 1993). This is large, but perhaps unsurprising, given the location of this relic in proximity to the core of this BCG.

It is tempting to trace the jet axis's alignment back to A2261-BCG's optical core position or to one of the knots. However, based on the likely age of the jet and mobility of the knots, we conclude that the relative positioning of the radio and optical components cannot be meaningfully interpreted.

The knots were put forward by Postman et al. (2012) as candidates for stellar knots cloaking a recoiling SMBH. Based on the photometric and spectroscopic similarity to the BCG itself, we are now confident that these knots are in fact resident members of the A2261-BCG core. In Section 2.5, we demonstrated that knots 2 and 3 are consistent with being likely cannibalized small galaxies, and given their low velocity dispersions of 168–209 $\mathrm{km}\,{{\rm{s}}}^{-1}$ are no longer candidate HCSSs for a roaming SMBH. Thus, we are left with knots 1 and 4 as HCSS candidates; however, based strictly on their colors, knots 1 and 4 could feasibly also be interpreted as stripped cluster members. As previously discussed, our large error bar on knot 1 only rules out the HCSS hypothesis at a $\sim 1.5\sigma$ level and thus measurements of higher S/N are still required to rule out the hypothesis confidently.

Based on our new measurements, we can attempt some consistency checks to further investigate knots 1 and 4 as potential HCSS candidates. Merritt et al. (2009) formulated a relationship between the total mass of stars bound to the black hole ${M}_{{\rm{s}}}$, black hole mass ${M}_{\bullet }$, host galaxy velocity dispersion σ, and initial kick velocity ${V}_{{\rm{k}}}$:

$$\begin{eqnarray}&&\displaystyle \frac{{V}_{{\rm{k}}}}{1000\,\mathrm{km}\,{{\rm{s}}}^{-1}}\simeq 0.21\left(\displaystyle \frac{\sigma }{200\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{{M}_{{\rm{s}}}}{{M}_{\bullet }}\right)}^{-2/5}\,.\end{eqnarray} \tag{ 2 }$$

Through various mass estimate methods, Postman et al. (2012) found agreement that the central SMBH in A2261-BCG is on the order of ${M}_{\bullet }\sim {10}^{10}\,{M}_{\odot }$, while its velocity dispersion is $\sigma =387\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Using the stellar mass estimates of Table 2 and the above equation, under the hypothesis that knot 1 is a stellar cloak, this formulation implies kick velocities between 480–600 $\mathrm{km}\,{{\rm{s}}}^{-1}$. For knot 4, we obtain kick velocities in the range 850–1100 $\mathrm{km}\,{{\rm{s}}}^{-1}$, assuming different IMFs.

We would not expect the velocity offset of an observed cloak to exceed this kick velocity; it is likely to be less due to the misalignment with the line of sight and dampening of the SMBH velocity over time. Knot 1 appears to be well within these values despite the large error on its dynamical measurements. Should future observations permit a dynamical assessment of knot 4, if it represents an HCSS, we would likewise not expect its velocity offset from the core to exceed the kick velocity.

We can use the HCSS size prediction of Merritt et al. (2009) to note that for kick velocities in the range 480–600 $\mathrm{km}\,{{\rm{s}}}^{-1}$, the HCSS size is predicted to be up to around 200 pc or 005 in our images, and therefore this range of velocities is consistent with the HWHM for knot 1, $\leqslant 0.047$, reported earlier. Thus, this comparison demonstrates consistency with an HCSS model, but not conclusive support. For knot 4, velocities in the range 850–1100 $\mathrm{km}\,{{\rm{s}}}^{-1}$ predict smaller effective radii of between 30 and 60 pc, or up to 0015.

Finally, the approximate "sloshing timescale" of the A2261-BCG core is ~10⁷ yr (Postman et al. 2012). We can thus note that ignoring drag effects and galaxy potential, a recoiling SMBH may have travelled 5–6 kpc given the inferred kick velocities for knot 1, and 8.5–12 kpc for knot 4. This is consistent with the observed offset of knot 1 from the center of both the core and the photometric center of the galaxy envelope. Note that our support for knot 1 as an HCSS candidate differs from that of Postman et al. (2012) because they lacked knot mass estimates and thus had assumed ${V}_{{\rm{k}}}=1000\,\mathrm{km}\,{{\rm{s}}}^{-1}$.

We do not have sufficient S/N on our velocity distribution measurements to assess the non-Gaussianity of the spectral features, as discussed in Merritt et al. (2009). Thus, knot 1 and knot 4 (for which spectroscopy has not yet been performed) remain candidate stellar cloaks in the recoil scenario.

A2261 has two Chandra exposures of 10 and 25 ks (ObsIDs 550 and 5007, respectively), which do not conclusively reveal any accretion onto an SMBH. The X-ray flux in those data is dominated by 0.5–2 keV emission from hot cluster gas, showing a cooled core (Bauer et al. 2005). Above 2 keV, there is some emission, possibly a point source consistent with knot 4, although it is too faint to reliably distinguish it from cluster gas emission.

The age of the relic radio source can potentially be understood as a time marker for an event related to the disturbance of the central SMBH, and thus we are interested in understanding the age and nature of this relic. We limited the timescale of last electron energization in the radio source to $\gtrsim 50\,\mathrm{Myr}$. The existence of a relic in this BCG is interesting in itself and has a number of potential origins, as discussed in Section 3.3.

To investigate how atypical A2261-BCG's radio source properties are among BCGs, we compare it with the sample of Hogan et al. (2015), who systematically studied the radio properties of a large sample of BCGs (including A2261-BCG). In comparison with that sample, we find that the 1.4 GHz radio luminosity is typical of ~50% of BCGs. Strikingly, we appear to not detect a distinct core in this object down to a 3σ limit of $\lt 3.6\,\mu \mathrm{Jy}$ at 10 GHz. Although the non-detection of a core component in the Hogan (2014) sample was relatively common, their typical upper limit on core emission was on average a factor of >1000 less stringent than our limit. Nevertheless, they found that ~30% of their BCGs had clear spectrally identified radio cores, while 30% consisted of only non-core components (i.e., had upper limits on core emission, as in our case), and 30% were complete radio non-detections; see their Table C.1.

The most unusual thing about the radio relic in A2261-BCG is its central position combined with its small size and steep spectral index. We show the spectral index distribution in Figure 9 of 30% of the non-core BCGs in the Hogan sample. There are only a handful of targets in the sample with spectra comparable to or steeper than the central relic in A2261-BCG, and it is likely that given the large selection in Hogan (2014), there is some contamination from BCG-unrelated cluster relics included in this distribution. The distribution of core-dominated BCGs tend to center on indices closer to $\alpha \sim 0$. Therefore, it seems that the radio spectrum of A2261-BCG lies at the extremity of implied activity and jet ages for BCGs.

Zoom In Zoom Out Reset image size

The presumption behind our analysis of the A2261-BCG core is that the galaxy hosted a high-mass central black hole until perhaps relatively recently. We hypothesized that the black hole has been ejected and might be found in one of the knots or elsewhere in and around the core. Bonfini & Graham (2016), in contrast, suggest that the core was generated by the merger of A2261-BCG with a "stalled massive perturber," which would be the remnant central regions of another galaxy that merged with or was cannibalized by A2261-BCG. The orbital decay of the perturber "stalls" near the outer regions of a nearly constant-density core (as A2261-BCG has), leaving it to persist as one of the stellar knots.

It appears that the Bonfini & Graham (2016) scenario differs from ours mainly in whether or not A2261-BCG and any of the galaxies that merged with it possess central black holes. As we noted in the introduction, cores are generated in the standard picture as the end point of a "dry merger" of two galaxies that each possess a central black hole. Ejection of the central black hole in the merger occurs as one outcome when the binary black holes formed in the merger coalesces. Bonfini & Graham (2016) do not discuss the role or even the presence of the central black holes in their scenario, and indeed it appears that they are not included in the theoretical models of Goerdt et al. (2010) on which their discussion is based. In short, the Bonfini & Graham (2016) scenario presumes as we do that the core of A2261-BCG may not currently harbor a central black hole; however, they implicitly take this as an unexplained initial condition in contrast to our explicit hypothesis that the central black hole has been recently ejected.