Recoiling Supermassive Black Holes: a search in the Nearby Universe

Recoiling Supermassive Black Holes: a search in the Nearby Universe

Abstract

The coalescence of a binary black hole can be accompanied by a large gravitational recoil due to anisotropic emission of gravitational waves. A recoiling supermassive black hole (SBH) can subsequently undergo long-lived oscillations in the potential well of its host galaxy, suggesting that offset SBHs may be common in the cores of massive ellipticals. We have analyzed HST archival images of 14 nearby core ellipticals, finding evidence for small ( pc) displacements between the AGN (locating the SBH) and the center of the galaxy (the mean photocenter) in 10 of them. Excluding objects that may be affected by large-scale isophotal asymmetries, we consider six galaxies to have detected displacements, including M87, where a displacement was previously reported by Batcheldor et al. [2010]. In individual objects, these displacements can be attributed to residual gravitational recoil oscillations following a major or minor merger within the last few Gyr. For plausible merger rates, however, there is a high probability of larger displacements than those observed, if SBH coalescence took place in these galaxies. Remarkably, the AGN-photocenter displacements are approximately aligned with the radio source axis in four of the six galaxies with displacements, including three of the four having relatively powerful kpc-scale jets. This suggests intrinsic asymmetries in radio jet power as a possible displacement mechanism, although approximate alignments are also expected for gravitational recoil. Orbital motion in SBH binaries and interactions with massive perturbers can produce the observed displacement amplitudes but do not offer a ready explanation for the alignments.

Subject headings:
black hole physics – gravitational waves – galaxies: nuclei – galaxies: active – galaxies: interactions
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1. Introduction

Supermassive black holes (SBHs) have long been identified as the engines of active galactic nuclei (AGNs). More recently, compelling evidence has been amassed that they are present in the centers of almost all galaxies [Kormendy & Richstone, 1995, Ferrarese & Ford, 2005] and furthermore that the growth of the SBH is intimately linked to galaxy evolution (Ferrarese & Merritt, 2000, Gebhardt et al., 2000; see Alexander & Hickox, 2012 for a recent review).

As a consequence of energy losses due to dynamical friction, SBHs are generally expected to reside at the large-scale potential minimum of the host galaxy. Nevertheless, there are several mechanisms that seem capable of displacing the SBH from its equilibrium position [Batcheldor et al., 2010, hereafter B10]. Most recently, interest has focused on gravitational recoil resulting from the coalescence of an SBH-SBH binary [e.g., Favata, Hughes & Holz, 2004, Merritt et al., 2004, Campanelli et al., 2006, Baker et al., 2006]. Other possibilities include orbital motion of SBH-binaries [Komossa, 2006], asymmetric radio jets [Shklovski, 1982] and interactions with massive perturbers such as globular clusters, or massive molecular clouds.

The first two of these mechanisms, in particular, might be expected to occur as an inevitable consequence of galaxy evolution. Cold dark matter hierarchical cosmologies predict that galaxies experience multiple mergers during their lifetime [e.g., Coles & Lucchin, 2002, Springel et al., 2005], with minor mergers being more common than major mergers [e.g. Hilz et al., 2012]. When two galaxies merge, their central SBHs are expected to form a binary system [Begelman, Blandford & Rees, 1980] at the center of the merged system due to dynamical friction. Further tightening of the binary ensues through three-body interactions with stars, or gravitational drag from gas [Merritt & Milosavljević, 2005, Mayer et al., 2007], until finally, energy loss due to gravitational wave emission irreversibly drives the two SBHs to coalescence12.

In the final stage of SBH-binary coalescence, anisotropic emission of gravitational waves will, in general, impart a recoil velocity to the coalesced object [Bekenstein, 1973]. Following a recent breakthrough allowing the orbits of spinning black holes to be computed to coalescence [Pretorius, 2005, Campanelli et al., 2006, Baker et al., 2006], numerical relativity simulations have produced recoil velocities km s, even reaching km s for certain spin configurations [Campanelli et al., 2007, González et al., 2007, Tichy & Marronetti, 2007, Lousto & Zlochower, 2011, Lousto et al., 2012]. Such velocities would cause large displacements of the coalesced SBH from the center of the galaxy or, in the most extreme cases, eject it entirely from the host [Merritt et al., 2004, Campanelli et al., 2007a, Volonteri, Gúltekin & Dotti, 2010].

Recoils exceeding the escape velocity of the host galaxy are expected to be relatively rare [e.g., Lousto et al., 2012, hereafter L12] and, more frequently, the SBH will undergo damped oscillations in the galaxy potential. -body simulations [Gualandris and Merritt, 2008, hereafter GM08] have shown that moderately large kicks ( few km s, sufficient to eject the SBH from the core13 but not from the galaxy) result in long-lived oscillations which damp on a timescale Gyr. GM08 identified three dynamical phases for the particular case where the SBH is initially displaced beyond the core radius ( pc). In “phase I” the SBH undergoes damped harmonic motion at amplitudes greater than the core radius. These oscillations are damped relatively quickly ( yr) by dynamical friction. “Phase II” is characterized by oscillations of amplitude  pc between the SBH and the stellar core about the center of mass, which persist for up to Gyr. Finally, in “phase III”, the SBH has reached thermal equilibrium with the surrounding stars and experiences Brownian motion, signifying the end of the event.

Large gravitational recoil kicks would have a variety of observable consequences. In the case of SBHs associated with AGNs, most of the accretion disk and broad emission line gas will remain bound for recoils with velocities  km s and such systems might be observed as a displaced, or velocity-shifted AGNs [e.g., Merritt et al., 2004, Madau & Quataert, 2004, Loeb, 2007, Bonning, Shields & Salviander, 2007, Zanotti et al., 2010]. Stars moving with orbital velocities would also remain bound to the SBH after the kick, so that a recoiling SBH would be associated with a “hypercompact stellar system” of high internal velocity dispersion [Merritt et al., 2009].

Possible spectroscopic signatures of recoiling SBHs have been identified in a few individual active galaxies [Komossa et al., 2008, Shields et al., 2009, Robinson et al., 2010, Steinhardt et al., 2012], which would indicate large (  km s) kick velocities. In addition, systematic searches of large SDSS AGN samples have revealed objects that exhibit velocity shifts  km s between the broad and narrow lines [Bonning, Shields & Salviander, 2007, Eracleous et al., 2012, Tsalmantza et al., 2011]. Some of these may be recoiling SBHs, or SBH binaries, but alternative explanations for the shifts involving extreme broad line region kinematics cannot be excluded. Perhaps the most interesting case is that of CIS-42, a galaxy which hosts two compact optical sources separated by kpc and also exhibits a large velocity shift ( km s) between broad and narrow H emission lines [Civano et al., 2010, 2012, Blecha et al., 2012].

The gravitational recoil candidates discovered to date have been identified on the basis of anomalously large velocity shifts (  km s) or a large spatial offset ( kpc). If they are indeed recoiling SBHs, we are observing them during the early stages in their dynamical evolution following a large kick; that is, during the large amplitude phase I oscillations of GM08, if the SBH remains bound to the galaxy. However, special configurations of the progenitor binary are required to produce large kicks, which are therefore expected to be relatively rare events (L12) and furthermore, the subsequent large amplitude phase I oscillations are relatively short-lived.

On the other hand, the -body simulations of GM08 predict that, following a recoil kick sufficiently large to remove the SBH from the galaxy core, the decaying oscillations persist in phase II for 1 Gyr, comparable with the time between galaxy mergers [Hopkins et al., 2010, hereafter H10]. This suggests that low amplitude SBH displacements resulting from post-merger SBH binary coalescence should be relatively common in the cores of bright elliptical galaxies. Thus, rather than searching for short-lived phase I oscillations following rare large kicks, an alternative approach to studying the incidence of SBH binary coalescence is to look for phase II oscillations in nearby ellipticals.

Spectroscopic identification of phase II oscillations would be extremely difficult, if not impossible, as the associated velocity shifts would be comparable with gas motions due to rotation, or flows or turbulence driven by the AGN, or starburst activity. However, it is feasible to directly detect small-amplitude displacements between the AGN and the galaxy photocenter in high spatial resolution images of nearby galaxies. We recently analyzed archival Hubble Space Telescope Advanced Camera for Surveys images of the active giant elliptical M87 and found a projected offset of  pc () between the stellar photocenter and the AGN (B10; we note, however, that Gebhardt et al. 2011 did not find a significant offset in their near-infrared integral field spectroscopy data).

Here we describe a photometric analysis of archival HST images of 14 nearby (d<100 Mpc), bright ellipticals hosting low-luminosity AGNs, with the aim of directly measuring spatial offsets comparable with the core radius of the galaxy (typically  pc). Our method consists in measuring the relative positions of the AGN point source and the photocenter of the inner 2-3 kpc of the galaxy, assuming that the former marks the SBH position and the latter the minimum of the galactic potential. As long as the AGN is bright enough to be easily detected and faint enough that it does not overwhelm the host galaxy, it is possible to perform standard photometric analysis to locate the photocenter. The “displacement” is then computed as the relative distance between the AGN and photocenter.

The plan of this paper is as follows: in §2 we describe the sample; §3 describes the analysis methods used to determine the photocenter, SBH position and offset, and their uncertainties; in §4 the measured displacements are presented for each galaxy. In §5, we discuss the results in the context of gravitational recoil and other possible displacement mechanisms. Finally, our conclusions are summarized in §6. The results for selected galaxies are discussed in more detail in an Appendix.

2. The sample

The sample selected for this study consists of 14 nearby, regular, core elliptical galaxies which host AGNs and for which HST images obtained with ACS, NICMOS2, WFPC2 or WFC3 are available in the Hubble Legacy Archive (HLA).

HST observations have revealed that the central light distribution in nearly all nearby early type galaxies can be described by a singular surface brightness profile: as , where . The slope of the innermost surface brightness distribution is bimodal in the sense that there is a paucity of galaxies which have . Hence, early type galaxies have been classified in two families: “core galaxies”, which have a shallower () inner cusp within a “break” (or “core”) radius r pc, and “power law galaxies”, which have a steep cusp () continuing into the HST resolution limit [Lauer et al., 1995]. These classifications correlate with several other galaxy properties [e.g., Faber et al., 1997], in particular, core galaxies are on average more luminous than power-law galaxies, with essentially all bright () ellipticals having cores.

Core galaxies are promising systems in which to search for SBH binaries or SBHs displaced by gravitational wave-induced recoils. They are bright ellipticals which are often the dominant components of clusters or groups and are thus likely to have experienced a recent major merger leading to the formation of an SBH binary. The shallow inner surface brightness profile indicates a mass deficit relative to that implied by inward extrapolation of the steeper brightness profile prevailing at larger radii. This is predicted as a natural consequence of depopulation of the inner region of the galaxy by 3-body interactions between an SBH binary and stars crossing the orbit of the binary [“loss-cone stars” Merritt & Milosavljević, 2005]. Therefore, “flat” inner surface brightness profiles have been proposed as a clear footprint of the formation of a tightly bound SBH binary [e.g., Faber et al., 1997, Merritt, 2006].

In addition, core galaxies tend to have regular photometric structures, and hence well-defined photocenters. In order to accurately locate the position of the SBH, we further require that each galaxy hosts a low luminosity AGN visible as a point source in the HST images.

In order to resolve the low amplitude offsets between photocenter and AGN expected in the phase II oscillations predicted by GM08, we select only galaxies within 100 Mpc.

The sample analyzed in this work was extracted from a sample of 29 core elliptical galaxies previously studied by Capetti and Balmaverde, in a series of three articles [Capetti & Balmaverde, 2005, Balmaverde & Capetti, 2006, Capetti & Balmaverde, 2006, hereafter CB05, BC06 and CB06 respectively]. CB05 compiled a radio-flux limited sample of AGNs in early type hosts by selecting radio-detected sources from the VLA surveys of Wrobel & Heeschen [1991] and Sadler et al. [1989]. The former is a northern sample of 216 early-type galaxies extracted from the CfA redshift survey [Huchra et al., 1983], with the following criteria: declination ; photometric magnitude ; heliocentric velocity km s; morphological Hubble type . The latter is a similar southern sample of 116 E and S0 galaxies with declination . Both were observed at 5 GHz with a flux limit of mJy.

The 65 objects with available archival HST images were classified as core or power-law galaxies on the basis of the slopes of their nuclear brightness profile as obtained by fitting a broken power law (the so-called “Nuker law”; Lauer et al. 1995; CB05; CB06). For the purpose of this study, we focus on the core galaxies listed in Table 1 of BC06 and impose two additional selection criteria, based on visual inspection of HST images: (i) the presence of an optically bright central point-like source (a low luminosity AGN); (ii) the absence of heavy nuclear obscuration and other photometric irregularities.

The 14 galaxies selected for this study are listed in Table 1 together with their distances, core radii and details of the archival data sets that were retrieved for photometric analysis. The sample includes two galaxies (NGC 4696 and 5419) that exhibit double nuclei, separated by . In these cases, it is not known which of the two point sources is the AGN and therefore we assume that the brightest is the AGN (although we have measured displacements relative to both).

The radio source properties, including the total power at 5 GHz and the position angle of any extended structure, are summarized in Table 2.

Galaxy Distance r r Instrument Pixel Scale ID
(1) (2) (3) (4) (5) (6) (7) (8) (9)
NGC 1399 sbf 2.19 (189) 0.99 (86) WFPC2/PC/F606W 0.05 8214
WFPC2/PC/F814W 0.05 5990
WFC3/IR/F110W 0.09 11712
WFC3/IR/F160W 0.09 11712
NGC 4168 UGC 7203 sbf 2.02 (303) 0.09 (14) WFPC2/PC/F702W 0.05 6357
NGC 4261 UGC 7360 sbf 1.62 (237) 0.428 (62) NICMOS2/F160W 0.05 7868
NGC 4278 UGC 7386 sbf 0.97 (83) 0.334 (29) ACS/WFC/F850LP 0.05 10835
WFPC2/PC/F814W 0.05 5454
NICMOS2/F160W 0.05 7886
NGC 4373 sbf 1.19 (269) 0.167 (32) WFPC2/PC/F814W 0.05 5214
NGC 4486 UGC 7654 (M87) sbf 9.41 (733) 1 (78) ACS/HRC/F606W 0.025 B10
ACS/HRC/F814W 0.025 B10
NICMOS2/F110W 0.05 7171
NICMOS2/F160W 0.05 7171
NICMOS2/F222M 0.05 7171
WFPC2/PC/F814W 0.05 8592
NGC 4552 UGC 7760 sbf 0.49 (36) 0.48 (35) WFPC2/PC/F814W 0.05 6099
NGC 4636 UGC 7878 sbf 3.44 (219) 0.297 (19) WFPC2/PC/F814W 0.05 8686
NGC 4696 sbf 1.4 (251) 0.2 (36) ACS/WFC/F814W 0.05 9427
NGC 5419 D 2.11 (499) 0.38 (90) WFPC2/PC/F555W 0.05 6587
NGC 5846 UGC 9706 sbf 1.52 (183) 0.25 (30) WFPC2/PC/F814W 0.05 5920
IC 1459 sbf 1.82 (258) 0.43 (60) WFPC2/PC/F814W 0.05 5454
IC 4296 sbf 1.44 (347) 0.32 (77) ACS/HRC/F625W 0.025 9838
WFPC2/PC/F814W 0.05 5910
NICMOS2/F160W 0.05 7453
IC 4931 vvir 0.99 (403) 0.13 (51) WFPC2/PC/F814W 0.05 8683

Note. – (1) Source name; (2) name as it appears in BC06 if different than the name given in the first column; (3) adopted distance in Mpc (from the HyperLeda extragalactic database); (4) method used to determine the distance: “sbf”, surface brightness fluctuation; “vvir”, from radial velocity, corrected for Local Group infall into Virgo; “D”, size-sigma relation [Dressler et al., 1987]; (5) core radius as derived by CB05, in arcsec (pc); (6) SBH influence radius (/) in arcsec (pc). Central velocity dispersions are given in Table 8. Black hole masses have been derived from the relation given in Ferrarese & Ford [2005]; (7) HST instrument/camera/filter used; (8) pixel scale in arcseconds/pixels as determined from direct measurement on the frames; (9) proposal identification number. B10: this is a combined image, see Table 1 in B10 for further details. A WFC3/IR image is available for NGC 4696, however the complex nuclear features and the pixel size of the camera do not allow us to infer the SBH position with the precision necessary for this work.

Table 1THE SAMPLE
Galaxy Radio Source Nature of the galaxy
Scale PA Comments
NGC 1399 10 kpc Linear, almost symmetric. Dominant component of Fornax cluster.
NGC 4168 - - Unresolved radio emission E2 in Virgo cluster.
NGC 4261 30 kpc Linear, symmetric lobes. W jet brighter than E. Massive E in the outskirts of Virgo cluster.
NGC 4278 1.4 pc S-shaped, inner jet brightest to the N. Large E near the center of Coma I cloud.
NGC 4373 - - Compact radio source. Outskirts of Hydra-Centaurus supercluster.
NGC 4486 1.5 kpc Linear on kpc scale. Virgo Cluster BCG.
NGC 4552 0.5 pc Twin pc-scale extension. Massive E in Virgo cluster.
NGC 4636 1 kpc Z shaped. No radio lobes. Massive E in the outskirts of Virgo cluster.
NGC 4696 1.6 kpc Broad, one sided on pc-scale. Centaurus Cluster BCG.
NGC 5419 - - Low surface brightness radio relic. Dominant component of group S753.
NGC 5846 - - Complex morphology. Dominant component of group [HG82]50.
IC 1459 - - Compact source. Giant E in group [HG82]15.
IC 4296 240 kpc Linear, NW component slightly brighter. Giant E, BCG of group A3565.
IC 4931 - - - BCG of A3656.

Note. – (1) Optical identification; (2) approximate length of the radio jet/extension; (3) position angle (degrees E of N); (4) total power at 5 GHz [ W]; (5) comments on the radio source morphology; (6) comments on the nature of the galaxy. This value is computed for the inner 25 pc. References: Slee et al. [1994], Wrobel & Heeschen [1991], Wrobel [1991], Sadler et al. [1989], Shurkin et al. [2008], Cavagnolo et al. [2010], Giroletti et al. [2005], Baade & Minkowski [1954], Nagar et al. [2002], Stanger & Warwick [1986], Taylor et al. [2006], Killeen et al. [1986a], Jones et al. [2000]. [HG82]: Huchra & Geller [1982].

Table 2NOTES ON THE RADIO SOURCES OF INDIVIDUAL GALAXIES

3. Data Analysis

Broad-band images of the sample galaxies acquired with ACS, NICMOS2, WFPC2 and WFC3 were retrieved from the Hubble Legacy Archive (HLA), giving preference to images obtained with the highest spatial resolutions and red filters (i.e., F606W and longer wavelengths).

Whenever available, several images taken with different instruments and filters, covering both optical and NIR bands, were obtained for each galaxy. A list of the images analyzed for each galaxy is given in Table 1. No additional processing steps were applied beyond the standard HLA reduction pipeline. As the goal of our analysis is simply to determine the relative positions of the isophotal center of the inner few kiloparsecs of the galaxy and the AGN point source within each individual image, this is sufficient for our purposes.

Each image was analyzed according to the following main steps: (1) a mask was constructed to block image defects and distorting features such as dust lanes, jets or bright stars and globular clusters; (2) elliptical isophotes were fitted to the galaxy surface brightness distribution and the photocenter computed as the flux-weighted average of the isophote centers; (3) the position of the point source (assumed to locate the SBH) was determined by fitting a gaussian profile. See §3.1 and §3.2 for a more detailed description of these procedures. Sky subtraction was not performed as a uniform background will not affect the photometric analysis and in many cases it is not possible to measure the sky background as the galaxy covers the frame.

3.1. The inner photocenter

Each image was analyzed with the IRAF task ellipse [Jedrzejewski, 1987], which was used to fit elliptical isophotes to the surface brightness distribution. The first step was to construct an image mask in order to minimize distortions due to image defects and intrinsic photometric irregularities such as dust features, optical or NIR knots associated with jets, globular clusters, foreground stars, etc. If an exposure time map (the “weight image”) was provided in the retrieved data set, this was used as an initial mask to eliminate cosmic rays, bad pixels, null areas and other image frame blemishes. Applying the initial mask, a first run of ellipse was performed to create a zeroth-order photometric model. To account for intrinsic irregularities in the surface brightness distribution, we then created a second mask by subtracting the zeroth-order photometric model from the original image and masking residuals exceeding , where is the standard deviation of the residual image and n is a clipping parameter.

To allow ellipse to find the photometric peak, the central region was unmasked and a new run performed. This process was iterated, adjusting n in order to map distorting features in the maximum possible detail. The iteration was terminated when the mask converged and further runs did not add any significant detail.

Once the final mask was constructed, ellipse was re-run with the mask applied to determine the photocenter of the galaxy. Elliptical isophotes were fitted between minimum and maximum values of the semi-major axis (SMA) which were usually determined by the core radius (r) and the image size, respectively. In almost all cases, the minimum SMA was set equal to or greater than the value of r as determined by CB05; Table 1. This was typically ″, or  pc. In some cases, where a dusty disk is present in the center of the galaxy, the initial SMA was chosen such that the inner ellipse is larger than the disk. The only exception was NGC 4486 (M 87), which has a very large core. In this case, we adopted the SMA range 1–3″ used by B10, who found that isophotes within 1″ are influenced by the AGN point source. The maximum SMA was that of the largest ellipse that completely fits within the image area – that is, only complete isophotes were fitted. This limits our isophotal analysis to the inner few kiloparsecs of each galaxy; the SMA of the outermost ellipse fit varies in the range kpc.

Between these limits, a series of ellipses was fitted to the 2-D surface brightness distribution, with the SMA being increased by two pixels at each step. Each fit returned values of the position angle, eccentricity and the pixel coordinates of the center of the ellipse. Finally, the photocenter was obtained as the flux-weighted average of the centers of the elliptical annuli generated by ellipse:

(1)

where and are the photocenter coordinates of the i-th isophote and is a weight, given by the product of the area of the annulus defined by neighbouring isophotes, with the mean intensity within the annulus.

To assess the sensitivity of the mean photocenter to the weighting method, we computed an alternative weight function using the flux enclosed within each successive elliptical isophote. For comparison, the two weight functions are plotted as a function of SMA in Fig.1, for the NICMOS image of NGC 4261. The annular flux method produces an approximately uniform weight distribution beyond the innermost region (SMA ), but typically decreases slowly at large SMA values. Not surprisingly, the enclosed flux method produces weights that increase monotonically with SMA, thus assigning much greater weight to the outer, fainter isophotes. This may be an undesirable characteristic in that isophotal distortions which may be present at fainter surface brightness levels (due to interactions with nearby companions, for example) might unduly influence the mean photocenter. Nevertheless, for the sources in our sample, the photocenters computed using the two methods are consistent within the errors in all cases. This result reflects the rather regular nature of the sample galaxies at the wavelengths under consideration.

We explored alternative methods for the measurement of the photocenter position, namely a moment based technique and a 2-D decomposition of the surface brightness distribution. In the first case, the photocenter position is obtained by weighting the coordinate of each pixel by its own intensity. This method seems to be particularly sensitive to the masking details and to the presence of asymmetries in the light distribution. The second approach, performed with the GALFIT surface brightness fitting program [Peng et al., 2002], requires, at least in some cases, multiple components for a successful fit (e.g. two or more Sérsic profiles) casting doubt on the physical meaning of the recovered photocenter and the errors associated with it.

The IRAF task ellipse was specifically built to fit the light profile of elliptical galaxies with minimal assumptions; the results obtained seem to be weakly dependent on the masking details and errors associated with the fitted parameters have been thoroughly studied [Busko, 1996]. Therefore, we prefer to adopt the photocenter position determined with this approach.

Figure 1.— Alternative weighting functions for the mean photocenter, derived from the NICMOS2/F160W image of NGC 4261. Both functions are normalized to their maximum values. Solid line: each isophote center is weighted by the light content of the corresponding elliptical annulus. Dashed dotted: each isophote center is weighted by the light content enclosed by the ellipse of the corresponding SMA.

3.2. The SBH position

We make the key assumption that the point-like source near the center of each galaxy is an AGN, which therefore locates the position of the SBH (see §5 for a detailed discussion of this assumption).

The AGN point sources are bright enough to be easily detected, but in our sample they are not so bright that the point spread function dominates the host galaxy. In order to determine the position of the SBH, we proceeded as follows. First, a median filtered version of the image was subtracted from the original producing a residual map in which the AGN is a prominent feature14. In the second step, we used the IRAF task center to fit gaussians to the marginal distributions of the residual point source along the x and y axes.

3.3. The photocenter–AGN displacement

For each image of each galaxy, the x and y components of the displacement were measured as the difference in pixels between the x and y co-ordinates of the photocenter and the AGN point source. The significance of the displacement is classified in two steps, considering the x and y components separately. Displacements smaller than 3, where is the error on the displacement (Section 3.4.1), are considered non-significant. If the displacement exceeds we make a further classification based on the distribution of the isophote center coordinates produced by ellipse. For each coordinate, x and y, the inter-quartile range (IQR, the difference between the upper and lower quartiles) of the isophote centers was computed. The corresponding displacement is then assigned significance levels of “null”, “low”, “intermediate” or “high” depending on its magnitude relative to the IQR:

  • null, IQR

  • low, 0.8 IQR IQR

  • intermediate, 1.6 IQR IQR

  • high, IQR.

The threshold values are based on the fact that, for a normal distribution, 0.8 IQR is equivalent to 1. For an ideal, symmetric galaxy the isophotes would be concentric, giving IQR = 0. Any irregularities in the surface brightness distribution will cause a dispersion in the centers of the fitted elliptical isophotes, resulting in a non-zero IQR. Hence, by normalizing to the IQR, we allow for uncertainties in the recovered offsets due to asymmetric surface brightness distributions arising from, for example, dust lanes or tidal distortions.

3.4. Errors and biases

Position uncertainties

The final error on the measured projected displacement is the combination of the uncertainties in the positions of the photocenter and the AGN point source. As the photocenter is determined by fitting elliptical isophotes, it is important to understand if the errors provided by ellipse are reasonable and robust. To investigate this, we used ellipse to analyze synthetic galaxy images constructed with GALFIT. We also used these simulated galaxies to estimate the uncertainties on both the AGN and photocenter positions.

The model images were constructed by fitting a Sérsic profile and a nuclear point source (a PSF generated with Tiny Tim, Krist 1993) to selected galaxies in our sample. We used NGC 4261 and 4278 to build models of NICMOS images, IC 1459 for WFPC2 images, NGC 1399 for WFC3 and IC 4296 for ACS images. The resulting model surface brightness distributions were populated with gaussian random noise so as to match the signal-to-noise ratio (SN) of the original galaxy image15. Four realizations of each synthetic galaxy image were generated and each realization was analyzed using the methods described in Sections 3.1 and 3.2, superposing the masks obtained from the corresponding real galaxy images.

Ellipse errors: for each isophote fit, the “true error” on the isophote center is computed as the difference between the position returned by ellipse and the known photocenter of the synthetic galaxy (i.e., the center position of the Sérsic component fitted by Galfit). These “true errors” are compared to the errors on the positions of the isophote centers returned by ellipse in Fig.2. The “true” error distribution is slightly broader than that of the ellipse errors, but both distributions are highly peaked, with of fits producing errors pixels. A detailed study by Busko [1996] of the errors returned by ellipse shows that errors on ellipticity, position angle and center position are unbiased and accurate when the radial gradient relative error16 is less than . This condition is satisfied for our sample galaxies.

Figure 2.— Error distributions for the co-ordinates of isophote center positions derived from ellipse fits to sixteen simulated galaxy images. For each galaxy, a series of ellipses was fitted to the surface brightness distribution, incrementing the SMA by two pixels at each step, as described in Sec. 3.1. The errors returned by the IRAF ellipse task are compared with the “true errors”, defined as the difference between the known position of the center of the model galaxy and the center position returned by the ellipse fit. The errors on each isophote center returned by ellipse are broadly consistent with the true errors. The error distributions combine results from all sixteen simulated galaxy images. The model images were derived from Galfit fits to the following data: NGC 4261/NICMOS2, IC 1459/WFPC2-PC, NGC 1399/WFC3-IR, IC 4296/ACS-HRC.

Position errors: the “true errors” on the (,) coordinates of the AGN and galaxy photocenter positions were also determined for each realization of the synthetic galaxy images, where the true error in each case is defined as the difference between the known positions of the AGN and photocenter (i.e., the positions returned by Galfit) and the values recovered using our analysis methods.

For signal-to-noise ratios characteristic of our data (), the distributions of the “true errors” on the AGN and photocenter positions derived from both the ACS and WFPC2 synthetic galaxy images are narrow and confined within pixel. We therefore adopt pixel as a conservative estimate of the uncertainty on both the AGN and photocenter positions derived from ACS and WFPC2 data. The “true error” obtained from the WFC3 and NICMOS2 images exhibit broader distributions, with tails extending to pixels. We therefore adopt the median values of the “true errors” as the uncertainties for WFC3 and NICMOS2 data, yielding 0.2 pixels for the photocenter position in both cameras and respectively 0.1 and 0.2 pixels for the AGN.

These uncertainties represent the precision with which we can determine the AGN and photocenter positions for an ideal galaxy, in an image with noise characteristics representative of our data. The adopted uncertainties are summarized in Table 3, together with the equivalent angular distances and linear distances corresponding to the closest and furthest of our sample galaxies.

Precision ACS WFPC2 NICMOS2 WFC3
HRC WFC PC WF
0.1 pxl 2.5 5 5 10 9 mas
0.2 0.3 0.3 0.6 0.6 pc
1 2 2 4.1 3.7 pc
0.2 pxl 10 18 mas
0.6 1.1 pc
4 7.3 pc

Note. – Values are given in mas (first row), in pc at the nearest galaxy (13 Mpc, second row) and at the farthest (84 Mpc, third row). Similarly for the other rows. Values for NICMOS2 are computed for a pixel scale of 005/pixel.

Table 3PRECISION ON ISOPHOTAL CENTER AND AGN POSITION

Minimum detectable displacement: the uncertainties on the AGN and photocenter coordinates determine the minimum detectable displacement. We require a 3 detection for a displacement to be considered significant. Combining the uncertainties on the photocenter and AGN in quadrature, the error on each component of the displacement is pxl, for ACS and WFPC2 data, pxl for WFC3, and pxl for NICMOS2 data. Therefore, the minimum displacements considered significant are pxl, for ACS and WFPC2, pxl for WFPC3, and pxl for NICMOS2.

Possible biases

Asymmetric surface brightness distributions: the galaxies in our sample were selected to be symmetric and regular, based on visual inspection of the images. However, in some cases, the galaxy extends beyond the edges of the frame and/or is not centered in the image frame. To eliminate the possibility of spurious offsets due to truncation of isophotes by the frame edge, the upper limit on the SMA range used in the surface brightness fits is taken to be that of the largest ellipse that fits completely within the frame (Sec. 3.1).

In addition, subtle intrinsic asymmetries might be present that were not revealed by visual inspection. As discussed by Jedrzejewski [1987], asymmetric surface brightness distributions (such as large-scale lopsidedness in the isophotes) will cause shifts in the isophote centers, which in turn will increase the IQR. Therefore, intrinsic surface brightness asymmetries (or other irregularities) will tend to reduce the level of significance assigned to any measured displacement (Sec. 3.3).

A similar possibility is that the outer isophotes are distorted by tidal interactions with nearby galaxies. As our analysis is confined to the inner few kiloparsecs, such interactions are unlikely to significantly affect our results. Nevertheless, we have verified that the photocenter position does not change significantly when recomputed excluding isophote centers corresponding to ellipse SMAs greater than 85, 90 and 95% of that of the largest complete ellipse that fits within the image frame.

Isophote twists and PSF effects: core galaxies are often characterized by strong isophote twisting at radii interior to the core radius, [Lauer et al., 2005]. In addition, the inner isophotes are distorted by the point spread function; TINY TIM simulations show that for the HST instruments used, the PSF can affect the region within a radius r pixels. As typically r, we mitigate both effects by setting r as the minimum SMA for the ellipse fits.

Lopsided stellar nuclei (LSN): observations of the nuclear regions of nearby galaxies have revealed the presence of double nuclei with separations in the range 1–10 pc [Lauer et al., 1993, 1996, 2005, Thatte et al., 2000, Debattista et al., 2006]. One explanation for such configurations is that lopsided stellar orbit distributions tend to persist within the SBH sphere of gravitational influence since orbits do not precess in Keplerian potentials and are not, therefore, axisymmetrized by phase mixing [Peiris & Tremaine, 2003]. The best studied example is M31, in which the components of the double nucleus are separated by ( pc). Peiris & Tremaine [2003] proposed a model for M31 in which the nucleus consists of an eccentric disk of stars orbiting the SBH, the latter being coincident with the fainter component.

The WFPC2 Planetary Camera (with which most of the images studied here were obtained) resolves spatial separations of pc only for galaxies within 20 Mpc. It is possible, therefore, that some of the galaxies in our sample harbor unresolved double nuclei. This will not affect the determination of the galaxy photocenter, since the core is excluded from the isophote fitting. However, if the unresolved nuclei are of unequal brightness as in M31, this could result in a systemic error in the AGN position which may approach the PSF FWHM ( pixels). This in turn would result in a spurious displacement.

4. Results

The results of the photometric analysis are presented in Table 4, where we list the (x, y) pixel co-ordinates of the mean photocenter and the point source, the magnitudes of the corresponding components of the displacement, the direction of each displacement component on the sky and the significance level of the displacement, determined as outlined in Sec. 3.3.

Figures 3 and 4 illustrate examples of the results for galaxies in which, respectively, no significant displacement was found (NGC4373, Fig. 3) and in which the measured displacement is considered significant (NGC 4486, Fig. 4). In each figure, the top row of panels shows the original image and the residual images after subtraction of, respectively, the isophotal model generated by ellipse fits and a median filtered image. In the middle row are plotted the surface brightness profile and the and pixel coordinates of the isophotal centers, all as functions of the ellipse SMA. The positions of the photocenter and the AGN point source are also plotted. The leftmost panel of the bottom row is a scatter plot showing the distribution of the isophote centers, colour coded according to SMA. The locus of the cumulative mean photocenter position, computed outwards from the inner SMA limit, is also shown as a solid black line. The last two panels show the distributions of the () isophote center co-ordinates. The co-ordinates of the mean photocenter and the AGN point source are also plotted in all three panels. Similar figures for the remaining galaxies are presented in the Appendix (Sec. C), where the results for individual galaxies are also described in more detail (Sec. B).

In the case of NGC 4373, the and components of the displacement are and thus consistent with zero. In the case of the ACS/HRC F814W image of NGC 4486, both the and components of the displacement are significant at the level and their magnitudes are IQR and accordingly classified as having a “high” significance level (Table 4).

For four galaxies, two or more images obtained with different instruments and/or filters were analyzed, providing various combinations of wavelength and spatial resolution. The photocenter displacements in milliarcseconds, relative to the AGN point source, are plotted for these cases in Fig. 5a. There are two galaxies, NGC 4696 and 5419, in which a second point-like brightness peak is present. In these cases, the following discussion refers to the displacement relative to the primary point source (the brightest, which we take to be the AGN), unless otherwise noted.

AGN–photocenter displacements exceeding the minimum detectable value (i.e., significant at 3 level; Sec. 3.4.1) were measured in at least one direction ( or ), in at least one image, for ten out of the 14 galaxies in the sample: NGC 1399, 4168, 4278, 4486 (M87), 4636, 4696, 5419, 5846, IC 4296, and IC 4931. In the remaining galaxies, NGC 4261, 4373, 4552, and IC 1459, the AGN and photocenter are coincident within the position uncertainties ().

The distribution of the isophote center co-ordinates provides an indication of the systematic uncertainty arising from photometric distortions due to effects such as those outlined in Sec. 3.4.2. As discussed in Sec. 3.3, we assign a significance level for each measured displacement based on its magnitude relative to the IQR, which characterizes the width of the isophote center distribution. Three galaxies exhibit displacements (in at least one direction, in one image) IQR, that we classify as having intermediate or high significance. These are NGC 4278, 4486 (M87) and 5846. Three more have displacements classified as having low significance: NGC 1399, 5419 and IC 4296 (IQR).

In the two double nucleus galaxies, the photocenter position is much closer to the primary point source than the secondary. The offsets (relative to the primary) are pxl, but given the large IQR in NGC 4696 the displacement is classified as not significant in this case. In neither galaxy does the photocenter lie between the two “nuclei” (Fig. 5b, 25 and 26).

For the galaxies where multiple images were analyzed, the displacements in mas derived from the different images are consistent to within for two of the four galaxies (NGC 1399 and 4278).

In the remaining two galaxies (NGC 4486 and IC 4296), the results from one or more images differ significantly from the others (Fig. 5a). In IC 4296, the offset measured from the red (F814W) WFPC2 image is significantly different from those measured from the ACS-F625W and NICMOS2 F160W images, which are consistent to within . This galaxy has a warped dusty disk oriented approximately E-W, extending either side of the nucleus but it seems unlikely that this structure is the cause of the discrepancy, the origin of which remains unclear.

Several ACS, NICMOS2 and WFPC2 images were analyzed for NGC 4486 (M87). For the ACS red optical image (F814W) we recover the B10 result, which indicates that the photocenter is displaced by  mas to the north-west of the nucleus. A smaller but less significant offset in approximately the same direction is measured from the WFPC2 F814W image. However, the photocenters derived from the NICMOS2 F110W, F160M and F222W image are consistent with the AGN position. As discussed in detail in Appendix B, the origin of these differences is unclear. Neither dust, nor the prominent optical jet (also visible in the NIR) appear to provide satisfactory explanations. The central region of the galaxy where the isophote fitting was performed () appears to be free of large scale dust features. The masking procedure should prevent the jet from distorting the isophote fits but in any case, even when the fits were repeated with different levels of masking and even with no mask at all, no significant differences in the mean photocenter position were found. As there is no compelling reason to favor or discard the results from any given image, we compute a weighted average displacement.

Whether classified as significant, or not, the measured angular photocenter displacements are always small, typically a few mas and almost without exception mas. The only cases that exceed 100 mas are the displacements relative to the secondary point sources in the two double nucleus galaxies. Disregarding these, the projected linear displacements are all  pc. Therefore, for every galaxy analyzed, the measured displacement is a small fraction of the galaxy core radius; as a fraction of , the range in displacement magnitude is approximately 1–10%.

In our previous analysis of NGC 4486 (B10), we found that the galaxy photocenter (in ACS and WFPC images) is displaced in approximately the same direction as the jet, implying that the SBH is displaced in the counter-jet direction. It is therefore of interest to compare the direction of the measured photocenter displacements with the radio source axis for this sample. In Table 5 we give the position angle (PA) of the radio source, for those galaxies in which jets or jet-like extended structures have been observed, along with the PA of the measured displacement (as derived from the x, y components). Five galaxies are associated with relatively powerful, extended ( kpc) radio sources: NGC 1399, 4261, 4486, 4696 and IC 429617. Of these, NGC 4486 (M 87; 3C 274), NGC 4261 (3C 270) and IC 4296 (PKS 1333-33) are Fanaroff-Riley Type I (FRI) radio sources, characterized by prominent twin jets ending in kiloparsec-scale lobes [Fanaroff & Riley, 1974]. All three also have parsec-scale jets approximately aligned with the kpc-scale structure.

In NGC 4486, the displacement PA derived from our reanalysis of the ACS F814W image agrees with the B10 result. The direction of the weighted mean displacement, derived from displacements obtained from all the images, is also closely aligned with the jet direction. We find a similar result for IC 4296. As already noted, the results from the ACS and NICMOS2 images are consistent and indicate a displacement to the NW. If the discrepant WFPC2 result is disregarded, the weighted mean of the ACS and NICMOS2 displacements yields a PA only different from that of the large-scale radio axis, with the photocenter displaced on the side of the brighter north-western jet.

The displacement measured in NGC 4261 is not considered to be significant (). Nevertheless, the derived PA is consistent (albeit within the large uncertainty) with that of the radio axis, and again, the offset is in the direction of the brighter western jet.

NGC 1399 also has an FRI-like radio source morphology with a well-defined axis in PA. The measured displacement (classified as low significance) has a consistent PA with a value of . NGC 4696, is one of the galaxies with two optical point sources. Its large scale radio source does not exhibit well-defined jets, but is elongated approximately E–W over  kpc, with the ends of both “arms” bending south. At parsec scales there is a compact core with a one-sided jet emerging to the SW in PA. However, it is not clear which of the two optical nuclei hosts the core radio source [Taylor et al., 2006], complicating the comparison with the photocenter displacement. If the secondary point source is identified as the AGN, then the photocenter, which is close to the primary point source, is displaced approximately in the counter-jet direction. On the other hand, if the primary point source is indeed the AGN, the displacement (which, in any case, is classified as having “null” significance) would be almost perpendicular to the jet.

Three more galaxies have relatively weak, small radio sources that have jet-like features or elongations on sub-kiloparsec scales. The measured photocenter displacements are not aligned with the radio source axis in NGC 4552 or NGC 4636. NGC 4278 has a compact ( pc) source consisting of a core with jet-like features emerging along a SE–NW axis on either side. These features gradually bend to the east and west, respectively, becoming fainter and more diffuse. The weighted mean photocenter position is displaced approximately in the initial direction of the SE jet. According to Giroletti et al. [2005]’s analysis of this source, the jet axis is closely aligned with our line of sight, with the SE component being the oppositely directed counter-jet.

Figure 3.— Example of a galaxy where the displacement is not significant. NGC 4373, WFPC2/PC - F814W, scale=/pxl. First row - left to right: the galaxy Log(counts s), note that the color scale is adjusted to highlight the presence of the nuclear point source, emission is present over the whole field of view; galaxy after subtraction of the isophotal model; galaxy after subtraction of the median filter. Second row - surface brightness profile in counts s; second and third panels: and coordinates of the isophotal centers versus semi-major axis length. Blue diamond: AGN; red bullet: photocenter. The blue diamond and the red bullet are not positioned both at SMA=0 to make the figure clear and avoid superpositions. Third row - scatter plot of the isophote centers. The solid line (near the photocenter) is the cumulative photocenter computed including progressively all data from the core radius outward. Different colors for the data points are used to represent the centers of isophotes with SMA length in a given range. Defining : green: , orange: , brown: . Second and third panels: histograms of the distributions of the and coordinates of the isophotal centers.

Figure 4.— Example of a galaxy where the displacement is significant. NGC 4486 (M 87), ACS/HRC/F814W, scale=/pxl. Caption as in Fig.3.
Galaxy Instrument region Offset Dir Type
HST IQR PC NPS [pxl] [mas] [IQR] [pc]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)
NGC 1399 WFPC2/PC - F606W [2.5:15] 0.19 520 0.1 519.9 0.1 0.1 0.14 5 7 0.5 0.7 0.4 0.6 W non sig
0.28 465.4 0.1 465 0.1 0.4 0.14 20 7 1.4 0.5 1.7 0.6 N low
WFPC2/PC - F814W 0.29 502.9 0.1 502.9 0.1 0 0.14 0 7 0 0.5 0 0.6 - non sig
0.27 438.6 0.1 438.3 0.1 0.3 0.14 15 7 1.1 0.5 1.3 0.6 N non sig
WFC3/IR - F110W 0.13 759.9 0.2 759.7 0.1 0.2 0.22 18 20 1.5 1.7 1.6 1.8 W non sig
0.14 725.4 0.2 725.3 0.1 0.1 0.22 9 20 0.7 1.6 0.8 1.8 N non sig
WFC3/IR - F160W 0.18 759.9 0.2 759.7 0.1 0.2 0.22 18 20 1.1 1.2 1.6 1.8 W non sig
0.08 725.4 0.2 725.4 0.1 0 0.22 0 20 0 2.8 0 1.8 - non sig
NGC 4168 WFPC2/PC - F702W [2.1:8.5] 1.76 409.6 0.1 408.9 0.1 0.7 0.14 35 7 0.4 0.1 5 1 W null
1.47 425.1 0.1 424.6 0.1 0.5 0.14 25 7 0.3 0.1 4 1 N null
NGC 4261 NICMOS2 - F160W [1.7:7.5] 0.08 200 0.2 199.6 0.2 0.4 0.3 20 15 5 3.7 2.9 2.2 W non sig
0.26 182.3 0.2 182.1 0.2 0.2 0.3 10 15 0.8 1.1 1.5 2.2 N non sig
NGC 4278 ACS/WFC - F850LP [1.2:9.1] 0.31 1165.6 0.1 1166.4 0.1 0.8 0.14 40 7 2.6 0.5 3.4 0.6 E high
0.83 3160 0.1 3161.1 0.1 1.1 0.14 55 7 1.3 0.2 4.7 0.6 S low
WFPC2/PC - F814W 0.44 370.2 0.1 370.6 0.1 0.4 0.14 22 7 1 0.3 1.9 0.6 E low
0.87 357.3 0.1 359 0.1 1.7 0.14 84 7 1.9 0.2 7.2 0.6 S int
NICMOS2 - F160W 0.26 245.8 0.2 246.4 0.2 0.6 0.3 30 15 2.3 1.2 2.6 1.3 E non sig
0.62 224.8 0.2 225.8 0.2 1 0.3 50 15 1.6 0.5 4.3 1.3 S int
NGC 4373 WFPC2/PC - F814W [1.2:10] 0.58 2328.7 0.1 2328.8 0.1 0.1 0.14 5 7 0.2 0.2 2 2.7 E non sig
0.16 870.7 0.1 870.8 0.1 0.1 0.14 5 7 0.6 0.9 2 2.7 S non sig
NGC 4486 ACS/HRC - F606W [1:3] 2.78 419.1 0.1 682.1 0.1 1.4 0.14 35 4 0.5 0.1 2.7 0.3 W null
0.98 417.7 0.1 679.5 0.1 2.6 0.14 65 4 2.7 0.1 5.1 0.3 N high
ACS/HRC - F814W 1.03 553.1 0.1 549.6 0.1 3.5 0.14 87 4 3.4 0.1 6.8 0.3 W high
0.8 551.8 0.1 549.9 0.1 1.9 0.14 47 4 2.4 0.1 3.6 0.3 N high
NICMOS2 - F110W 0.42 207.2 0.2 206.8 0.2 0.4 0.3 20 15 1 0.7 1.6 1.2 W non sig
0.96 277.9 0.2 277.7 0.2 0.2 0.3 10 15 0.2 0.3 0.8 1.2 N non sig
NICMOS2 - F160W 0.65 207.5 0.2 207.4 0.2 0.1 0.3 5 15 0.2 0.5 0.4 1.2 W non sig
0.76 277.8 0.2 277.7 0.2 0.1 0.3 5 15 0.1 0.4 0.4 1.2 N non sig
NICMOS2 - F222M 0.51 207.6 0.2 207.2 0.2 0.4 0.3 20 15 0.8 0.6 1.6 1.2 W non sig
0.59 277.3 0.2 277.9 0.2 0.6 0.3 30 15 1 0.5 2.3 1.2 S non sig
WFPC2/PC - F814W 0.42 448.3 0.1 447.6 0.1 0.7 0.14 35 7 1.7 0.3 2.7 0.6 W low
0.58 517.2 0.1 517 0.1 0.2 0.14 10 7 0.3 0.2 0.8 0.6 N non sig

Note. – (1) Optical name; (2) instrument/camera/filter on HST; (3) lower and upper limit, in arcseconds, of the region analyzed; (4) inter-quartile range in pixel, this is the difference between 75th and 25th percentile of the isophotal center dataset; (5) photocenter position in pixel on the frame; (6) nuclear point source position in pixels; (7 - 8) offset of the isophotal center with respect to the nuclear point source in pixels and milliarcseconds; (9) offset in pixel normalized by the corresponding IQR; (10) offset in pc; (11) direction of the offset; (12) type of displacement as defined in §3.3. : for further details see Table 1 in B10.

Table 4MEASURED PROJECTED OFFSETS
Galaxy Instrument region Offset Dir Type
HST IQR PC NPS1 NPS2 [pxl] [mas] [IQR] [pc]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)
NGC 4552 WFPC2/PC - F814W [1:15] 0.42 538.9 0.1 538.7 0.1 0.2 0.14 10 7 0.5 0.3 0.7 0.5 W non sig
0.89 500.8 0.1 500.4 0.2 0.4 0.23 20 12 0.4 0.3 1.5 0.9 N non sig
NGC 4636 WFPC2/PC - F814W [4:14] 0.94 698 0.1 697.4 0.1 0.6 0.14 30 7 0.6 0.2 1.9 0.5 W null
0.93 569.9 0.1 570 0.1 0.1 0.14 5 7 0.1 0.2 0.3 0.5 S non sig
NGC 4696 ACS/WFC - F814W [1.5:16] 2.15 1582.9 0.1 1583.4 0.1 0.5 0.14 25 7 0.2 0.07 4.5 1.3 E null
3.78 2977.6 0.1 2977.8 0.1 0.2 0.14 10 7 0.05 0.04 1.8 1.3 S non sig
1586.1 0.1 3.2 0.14 160 5 1.5 0.05 29 1.3 E low
2973.2 0.1 4.4 0.14 220 5 1.2 0.03 39 1.3 N low
NGC 5419 WFPC2/PC - F555W [2:13.5] 0.5 398.4 0.1 397.8 0.1 0.6 0.14 30 7 1.2 0.3 7 2 W low
0.22 447.6 0.1 447.8 0.1 0.2 0.14 10 7 0.9 0.6 2 2 S non sig
397.1 0.1 1.3 0.14 65 7 2.6 0.2 15 2 W high
442.5 0.1 5.1 0.14 255 7 23.2 0.5 60 2 N high
NGC 5846 WFPC2/PC - F814W [1.6:15.8] 0.84 519.5 0.1 518.2 0.4 1.3 0.4 65 21 1.6 0.5 7.8 2.5 W int
1.05 466 0.1 466.4 0.1 0.4 0.14 20 7 0.4 0.1 2.4 0.9 S null
IC 1459 WFPC2/PC - F814W [2.5:15] 0.42 536.4 0.1 536.7 0.1 0.3 0.14 15 7 0.7 0.3 2.1 1 E non sig
0.50 510.5 0.1 510.7 0.1 0.2 0.14 10 7 0.4 0.3 1.4 1 S non sig
IC 4296 ACS/HRC - F625W [1.5:6.5] 0.49 833.3 0.1 832.6 0.2 0.7 0.22 18 6 1.4 0.4 4.2 1.2 W low
0.38 785.3 0.1 784.8 0.1 0.5 0.14 13 4 1.3 0.3 3 0.6 N low
WFPC2/PC - F814W 0.39 551.5 0.1 552 0.18 0.5 0.2 25 10 1.3 0.5 6 2 E non sig
0.13 515 0.1 514.9 0.18 0.1 0.2 5 10 0.8 1.6 1 2 N non sig
NICMOS2 - F160W 0.13 420.8 0.2 420.6 0.2 0.2 0.3 13 14 1.9 2.2 2.8 3.2 W non sig
1.07 253.4 0.2 252.7 0.1 0.7 0.2 37 11 0.7 0.2 8.3 2.5 N null
IC 4931 WFPC2/PC - F814W [1:15] 1.29 403.6 0.1 404.1 0.1 0.5 0.14 25 7 0.4 0.1 10 3 E null
0.66 505.9 0.1 505.8 0.1 0.1 0.14 5 7 0.2 0.2 2 3 N non sig

Note. – (1) Optical name; (2) instrument/camera/filter on HST; (3) lower and upper limit, in arcseconds, of the region analyzed; (4) inter-quartile range in pixel, this is the difference between 75th and 25th percentile of the isophotal center dataset; (5) photocenter position in pixel on the frame; (6) and (7) nuclear point source position in pixels; (8 - 9) offset of the isophotal center with respect to the nuclear point source in pixels and milliarcseconds; (10) offset in pixel normalized by the corresponding IQR; (11) offset in pc; (12) direction of the offset; (13) type of displacement as defined in §3.3.

Table 4MEASURED PROJECTED OFFSETS (continued)
Galaxy PA (deg)
jet displacement
NPS1 NPS2
kpc-scale jets:
NGC 1399 low
NGC 4261 () non significant
NGC 4486 ()
NGC 4696 ()
IC 4296 (158 8) low
pc-scale jets:
NGC 4278
NGC 4552 low
NGC 4636 null

Note. – Photocenter position angles are computed with respect to the nuclear point source. Angles increase east of north. When multiple values have been derived from different images an error weighted mean is computed. Values in parenthesis indicate the supplementary angles (i.e. ). The significance changes for different instruments (see Table 4). This value changes to when only WFPC2 results are considered. This value changes to when only ACS and NICMOS2 results are considered. See Table 2 for references on the radio jet PA.

Table 5RADIO JET AND PHOTOCENTER POSITION ANGLES

Figure 5a Offset of the isophotal center with respect to the SBH as measured on different instruments, at different frequencies. Each photocenter is centered on an ellipse whose axes represent the IQR of the isophote centers dataset used to derive the photocenter. Error bars represent the error on the offset. The diamond marks the origin of the reference frame (SBH position).

Figure 5b As in Fig.5a for the galaxies showing a double nuclear point source. The offset of the fainter nuclear point source with respect to the SBH is marked with a diamond and the label NPS2.

5. Discussion

In this section we will examine our key assumption that the SBH position is marked by the nuclear point source. We will then discuss the possible origins of the observed offsets. Most of the displacement mechanisms considered below have been previously discussed in B10. Nevertheless, we summarize them here in order to provide context for our new results.

5.1. The AGN nature of the nuclear point sources

Our sample of 14 core elliptical galaxies was selected from the 26 (out of 29) studied by BC06 that were identified as containing AGN based on the presence of i) an unresolved optical or X-ray source; ii) an “AGN-like” optical spectrum, or iii) radio jets. Most of our sample of 14 exhibit two or more AGN signatures in addition to the presence of a radio source and optical point source nucleus. Optical or UV variability has been detected in HST observations of NGC 4486 [Perlman et al., 2003], NGC1399 [O’Connell et al., 2005], NGC4552 [Cappellari et al., 1999, Maoz et al., 2005] and NGC 4278 [Cardullo et al., 2009]. Hard X-ray point sources have been detected in NGC 4261, 4278, 4486, 4552, 5419 and IC 1459 [González-Martín et al., 2009]. Weak broad H lines (NGC 4278, 4636 and NGC 4168), or emission line ratios indicative of AGN photoionization (NGC 4261, 4486, 4552, 5846) have also been detected in several galaxies [Ho et al., 1997]. In addition, the radio sources in most objects feature compact ( pc) cores (NGC 1399, 4168, 4373, 4552, 5419, IC 1459) and/or parsec or kpc-scale jets (NGC 4261, 4278, 4486, 4696, IC 4296; see Appendix B for references). Only IC 4931, which by comparison has been relatively little studied, lacks supporting evidence indicating the presence of an AGN in the form of X-ray, radio or line emission.

There is, therefore, plenty of evidence that these galaxies (with the possible exception of IC 4931) host AGNs. However, it does not necessarily follow (except in cases where optical/UV variability has been observed) that the optical or NIR point sources are themselves manifestations of the AGN, rather than, for example, nuclear star clusters. Low luminosity radio loud AGNs are thought to be powered by radiatively inefficient accretion flows [see, for example, Ho, 2008, Balmaverde et al., 2008, and references therein], with most of the accretion power channeled into the kinetic energy of the radio jets. Detailed studies of NGC4486 [Di Matteo et al., 2003], IC 1459 [Fabbiano et al., 2003] and IC 4296 [Pellegrini et al., 2003] show that this is the case for at least three galaxies of our sample.

In low luminosity radio galaxies, the optical, near infrared and X-ray luminosities of the nuclei correlate tightly with the core radio luminosity, implying a common origin in non-thermal emission from the jet [Chiaberge et al., 1999, Capetti & Balmaverde, 2005, Baldi et al., 2010]. This is supported by polarization measurements: Capetti et al. [2007] found that the optical nuclei of the nine nearest FR I radio galaxies in the 3C catalogue, including two galaxies from our sample, NGC 4486 (M87, 3C 274) and NGC 4261 (3C 270), have high polarizations (%), which they attribute to synchrotron emission. The optical or UV variability of the point sources in NGC 4486 and three other galaxies, noted above, is also consistent with jet synchrotron emission. More generally, BC06 found that their sample of core elliptical galaxies, from which this sample is drawn, also exhibit optical-radio and X-ray-radio correlations and indeed form a continuous distribution with the radio galaxies, extending these correlations to lower luminosities. Therefore, there is direct evidence, in the form of optical polarization and/or optical/UV variability that the nuclear sources in five of our sample galaxies are produced by synchrotron emission associated with the radio core source, presumably the base of the jet. It is reasonable to assume, given the correlations found by BC06, that the same is true for the rest of the sample.

The base of the jet is, in turn, very close to the SBH. Arguably the best studied jet is that of M87. Using multifrequency observations made with the Very Long Baseline Array, Hada et al. [2011] were able to show that the radio core at 43 GHz is located within 14-23 Schwarzchild radii of the SBH and accretion flow. In the optical, the lower optical depth should move the peak of the emission even closer to the SBH.

In summary, we contend that there are good reasons to believe that the optical or near-infrared point sources in our galaxies reveal the position of the SBH.

5.2. Recoiling SBHs

Here we consider if the measured SBH displacements are consistent with residual oscillations due to gravitational recoils generated by coalescence of an SBH binary.

GM08 used N-body simulations to study the post recoil dynamical evolution of an SBH in representative core elliptical galaxy potentials. They found that when the recoil velocity is sufficient to eject the SBH from the core ( in the range of the escape velocity, ), the subsequent motion is characterized by three phases. The initial large-amplitide (r) oscillations are damped relatively quickly ( yr) by dynamical friction (phase I). When the amplitude becomes comparable with the core radius, , the SBH and the stellar core undergo long-lived oscillations about their center of mass, which persist for Gyr (phase II). Finally, the SBH reaches thermal equilibrium with the stars, experiencing low-amplitude Brownian motion (phase III).

As our measured displacements are 0.1 , it is highly unlikely that they represent phase I oscillations. This would require either fortuitous timing (the SBH would have to be caught whilst passing through or close to the equilibrium position) and/or orientation (the oscillation direction would have to be closely aligned with the line of sight) for each galaxy. We also rule out phase III Brownian motion due to interactions with individual stars, which will produce negligibly small amplitudes in real galaxies (GM08). The possibility of Brownian oscillation due to interactions with massive perturbers is discussed in Section 5.3. Here, we focus on phase II which, as already noted, is characterized by long-lived damped oscillations at amplitudes .

In this phase, the characteristic damping time is given by GM08 as:

(2)

where the approximation on the right-hand side makes use of the M- relation [Ferrarese & Ford, 2005], being the 1D stellar velocity dispersion, with pc) and km s. For our galaxies, eq. 2 yields values of in the range  Gyr, with an average of 1.2 Gyr (Table 8). The rms amplitude of the SBH motion with respect to the galaxy center is expected to evolve as:

(3)

where is the time at which the oscillation amplitude has decayed to a scale comparable to the core radius (B10).

Simulations indicate that the galaxy merger rate is a strong function of redshift and galaxy mass [e.g., Fakhouri et al., 2010, H10]. The merger rate for brightest cluster galaxies has recently been determined observationally by Lidman et al. [2013], who find mergers per Gyr at , implying a mean time between mergers of  Gyr18. If we take this as representative of our sample, equations 2 and 3 together suggest that a “typical” rms displacement (ignoring projection effects) is . This suggests that larger displacements than were actually observed might be expected if due to post gravitational recoil oscillations.

However, equation 3 describes the oscillation amplitude rather than the instantaneous displacement and moreover the above estimate does not account for projection effects, or the range in damping timescales characterizing our sample galaxies, or for variations in the merger rate. In order to investigate in more detail the likelihood of obtaining the observed displacements in our sample, if they result from post-recoil oscillations, we have constructed a simple Monte-Carlo simulation based on the GM08 N-body simulations. Details of the method are given in Appendix A. However, we start from the assumption that, after any kick large enough to move the SBH beyond the core radius, the distance, R, of the SBH from the center of the galaxy is given by:

(4)

where is the elapsed time since the kick, i.e., the time since the last merger, is the damping time given by eq.2 and is the SBH oscillation frequency calculated from eq. A2. We set , since phase II begins when the oscillation amplitude is roughly equal to the core radius. We then suppose that each galaxy is observed at a random time, , since its last merger, where the probability that the merger occurred at time follows an exponential distribution characterized by a mean time-between-mergers, . This distribution is sampled to generate corresponding values of , which are then projected onto the sky plane assuming that the recoil kicks have random directions. The distribution of projected displacement for each galaxy is then used to compute the probability, , of observing a displacement larger than that actually measured, given a kick of sufficient magnitude.

These probabilities were computed for two values of the mean time between mergers: = 5.0 Gyr and = 0.4 Gyr, which were derived from the galaxy merger rate models of H10 for redshifts , mass ratios and galaxy masses and , respectively (see Appendix A for details). The two values of are representative of the mass range covered by our sample, and illustrate the effect on the displacement probabilities of the strong galaxy mass dependence of the merger rate.

The probabilities, , are listed for each galaxy in Table 6 for both values of . The probabilities of observing a projected displacement exceeding distance are plotted as functions of in Figures 7a and 7b, for each galaxy, along with the observed displacement.

As would be expected, the smaller value of results in larger values of ; clearly if , there is a greater chance of observing a large displacement than when . For  Gyr, for all but two galaxies (NGC 4278 and NGC 4552) and for all 6 galaxies that have masses  M (for which this value of is presumably most relevant). On the other hand, for  Gyr, all but four galaxies have , including five of the six having displacements considered significant at the level of IQR (the exception is M87, for which ).

Considering the sample as a whole, the probability of not observing a displacement larger than those actually measured in any of the galaxies in the sample is simply . For  Gyr, this is negligibly small, . Even for  Gyr, , indicating that it is statistically unlikely that larger displacements were not observed, given the occurrence of a recoil kick sufficient to trigger phase II oscillations.

However, it is unlikely that all the galaxies in the sample experienced a recoil kick big enough to move the SBH beyond the core radius. Assuming that the potential experienced by the SBH can be approximated as a harmonic potential (), we estimated the kick velocity required to displace the SBH out to the core radius for each galaxy, obtaining values in the range  km s, with an average of km s (the values for each galaxy are listed in Table 8).

L12 have studied kick velocity distributions for “hang-up” kicks, which arise in binary configurations where the SBH spins are partially aligned with the orbital angular momentum by pre-merger accretion. For spin magnitude and orientation distributions derived from accretion simulations and a mass ratio distribution based on galaxy merger studies (including both minor and major mergers), they generate probability distributions for the magnitude of the recoil velocity for two extreme cases of “hot” and “cold” gas disks (i.e., corresponding to adiabatic indices and , respectively). The former regime is likely to be most applicable to the ellipticals in our sample and in this case, probabilities range from % for kicks km s to % for kicks km s. Our Monte-Carlo simulation assumes that the coalescence event produces a recoil large enough to produce phase II oscillations (i.e., the values given in Table 8). As the probabilities are conditional on the occurrence of a kick of sufficient magnitude, the probability that both events will occur is . There is thus a smaller probability of observing a displacement larger than actually measured for each galaxy. Using the kick probabilities given by L12, we find that the probability of not observing a displacement larger than those actually measured in the entire sample is for  Gyr and for  Gyr.

As the merger rate increases with redshift, we may have underestimated the time-between-mergers by integrating over the redshift range . However, the higher value of used in the simulation implies a merger rate ( mergers Gyr) consistent with that given by the models of H10 for galaxies at (see their Fig. 3). The rate for major mergers is a factor 2–3 lower than the rate for major and minor mergers combined, which we used to estimate . However, although the magnitude of the recoil velocity is a function of SBH mass ratio (with the largest recoils occurring for mass ratios characteristic of major mergers), even small () mass ratios are capable of producing kicks km s, large enough to trigger phase II oscillations in our galaxies [Lousto et al., 2010]. Minor mergers were, in any case, included in computing the kick velocity distribution presented by L12.

Thus, even allowing for the distribution of kick velocities, the Monte-Carlo simulation suggests that it is highly likely that displacements larger than those actually measured would have been observed in this sample if each galaxy has experienced at least one merger leading to an SBH-binary coalescence and gravitational recoil within the last few Gyr. In fact, our simulations suggest that  Gyr, corresponding to a merger rate mergers Gyr, is required for a % chance of not observing larger displacements in the sample.

If, indeed, the formation of a binary SBH is an inevitable outcome of galaxy mergers, explanations must be sought in the evolution of the binary or that of the recoiling SBH. Possibilities include (1) the binary stalls before reaching the radius at which gravitational wave emission drives rapid coalescence; (2) if coalescence occurs, the mass ratio or spin-orbit properties of the binary are such as to typically preclude recoil velocities large enough to displace the SBH to the core radius ( km s); or (3) the damping time for the recoil oscillations may be shorter than predicted by the pure N-body simulations.

Alternatively, it is possible that galaxy mergers are much more infrequent than inferred from studies based on the current CDM framework [see Kroupa, 2014, and references therein for a detailed discussion].

Although our results imply that SBH displacements due to gravitational recoil are much less common than might be inferred from theoretical considerations, this does not preclude the possibility that observed displacements in individual galaxies are due to recoil oscillations. Indeed, the values listed in Table 6 indicate that for  Gyr, the chance of not observing a larger displacement, given a sufficiently large kick, is % for all objects having a displacement considered significant. Even for  Gyr, there are still three of these galaxies for which . The likelihood that the recovered offset is due to SBH coalescence is discussed for individual galaxies in Appendix B.

Assuming that the measured displacements are indeed due to phase II recoil oscillations, we have used eq. 3 to estimate the merger epoch for those galaxies with displacements rated at least as “low significance” in terms of the isophote centroid IQR. Allowing for the time taken for the SBH binary to form and subsequently coalesce in the center of the merged galaxy, and for phase I oscillations, the elapsed times since the merger are typically several Gyr, comparable with the mean time between galaxy mergers estimated here for galaxy masses , and consistent with the observationally determined merger rate for brightest cluster galaxies [Lidman et al., 2013].

Eq.2, used to estimate the SBH damping time, relies on the - relation [Ferrarese & Ford, 2005]. To test the dependence of our result on the value adopted for we use eq.6 in Lauer et al. [2007] to estimate SBH masses using the - relation (see Table 9 and Appendix A for more details). Using these alternative masses, and taking into account the kick velocity distribution computed by L12, we derive new values for obtaining , instead of 8, for  Gyr and 0.14 instead of 0.05 for  Gyr. The likelihood of our result is somewhat increased for t = 5 Gyr, however there is still a large probability of finding displacements larger than those measured, leaving our basic conclusion unchanged.

No useful constraints can be obtained on the merger epoch from consideration of the time necessary to replenish the stellar population of the core. This is roughly the relaxation time, , at the influence radius of the central SBH, which can be estimated as:

(5)

Merritt [2013, eq. 3.5]. Given that the measured velocity dispersion is always  km s in the centers of our galaxies (see Table 8), it is clear that the replenishment time is much longer than the timescales involved in the SBH merger-recoil event ( yr).

In general, coalescence of an SBH-binary results in a re-orientation of the SBH spin axis, leading to a sudden flip in the direction of the associated radio jet [Merritt & Ekers, 2002]. Therefore, the radio source morphology may act as a “signpost” of SBH coalescence. However, powerful extended radio sources have lifetimes yr [e.g., Parma et al., 1999, O’Dea et al., 2009, Antognini, Bird & Martini, 2012], much shorter than the time-between-mergers, even for massive galaxies. Thus even if a spin flip took place, morphological traces of this event, such as a change in jet direction, would not necessarily be evident in the current (post-coalescence) radio source. The radio source properties of individual galaxies are discussed in Appendix B.

It is notable that in four of the six galaxies in which significant displacements have been found, the displacements are also approximately aligned with the radio jet axis (Section 4 and Table 5). This number includes three of the four that have powerful kpc-scale jets (Section 4 and Table 5), suggesting jet power asymmetries as a possible displacement mechanism (as discussed below). However, such alignments do not necessarily argue against gravitational recoil. In their statistical study of the coalescence of spinning black hole binaries Lousto et al. [2010] find that the recoil velocity is preferentially aligned (or counter-aligned) with the orbital angular momentum of the progenitor binary and moreover, that the spin direction distribution of the recoiling SBH peaks at an angle of to the orbital angular momentum (for an equal mass progenitor binary; the probability distribution is broader and peaks at larger angles for smaller mass ratios). This suggests, assuming that the jet traces the spin axis of the recoiling SBH, a tendency for the displacement to be somewhat, but not greatly, misaligned with the jet axis, consistent with what is observed in these objects.

Galaxy d [] p(t = 0.4 Gyr) p(t = 5 Gyr)
NGC 1399 0.01 0.75 0.11
NGC 4168 0.02 0.98 0.89
NGC 4261 0.01 0.94 0.23
NGC 4278 0.1 0.36 0.04
NGC 4373 0.01 0.99 0.58
NGC 4486 0.01 0.99 0.85
NGC 4552 0.05 0.10 0.01
NGC 4636 0.01 0.99 0.69
NGC 4696 0.02 0.97 0.42
NGC 5419 0.02 0.97 0.46
NGC 5846 0.04 0.90 0.25
IC 1459 0.01 0.92 0.21
IC 4296 0.01 0.97 0.37
IC 4931 0.03 0.95 0.46

Note. – Probability to observe a projected displacement larger than the value actually observed in this work (in units of core radii) at a random time after the last kick. Probabilities are computed for a mean time between galactic mergers t = 0.4 Gyr and 5 Gyr. The symbol “” indicates 3 offsets that were classified as “null” after the normalization for the co-ordinates IQR. The symbol “” indicates offsets that do not reach the 3 level.

Table 6PROBABILITIES

5.3. Other displacement mechanisms

We now consider several other mechanisms that may plausibly produce SBH displacements.

1. Asymmetric jets: if the AGN jets are intrinsically asymmetric in power output, the resulting net thrust can push the SBH away from the original equilibrium position [Shklovski, 1982, Saslaw & Whittle, 1988]. Kornreich & Lovelace [2008] determine the SBH acceleration for this scenario:

(6)

where and 19, is the mass accretion rate, M the Eddington accretion rate, the accretion luminosity and is the jet luminosity. For asymmetrical, oppositely directed jets is the difference in the luminosities of the two jets.

Under the assumption that the restoring force from the galaxy is negligible (a reasonable approximation for the low-density cores of “core galaxies”), Eq. 6 can be integrated to obtain an expression for the displacement:

(7)

where is the time over which the SBH is accelerated to produce an offset r.

The best candidates for jet thrust displacements are the four galaxies (NGC 1399, 4261, 4486 and IC 4296) that have relatively powerful kpc-scale jets (Section 4 and Table 2). Of these, we did not detect a significant displacement in NGC 4261, which has an FR I radio source. NGC 4486 and IC 4296 also host FR I radio sources and NGC 1399 has an FR I-like morphology, despite its relatively low power. Interestingly, all three of these galaxies exhibit photocenter displacements that are at least approximately (within 20) in the jet direction (Table 5). This implies that the SBH is displaced relative to its equilibrium position in the counter-jet direction, as might be expected if the displacements are related to intrinsic asymmetries in jet power. NGC 4486 (M87) has already been discussed in detail by B10, who concluded that a jet power asymmetry amounting to % of the accretion luminosity can explain the observed displacement, for a radio source lifetime yr. We find similar results in the cases of NGC 1399 and IC 4296, where the observed displacement can be produced for a jet asymmetry % of the Bondi accretion luminosity, again for a radio source lifetime  yr (See Appendix B for details).

A close alignment between the displacement and the (initial) jet direction is also found for the low power pc-scale radio source in NGC 4278. In this case, Giroletti et al. [2005]’s interpretation of the radio data implies that the photocenter is displaced in the counter-jet direction, with the jet axis being closely aligned with the line of sight. Assuming that the SBH is displaced along the jet axis, the de-projected magnitude of the displacement would be pc. Nevertheless, it seems possible that this could result from jet thrust, if sustained for yr (Appendix B).

The double nucleus galaxy NGC 4696 does not show well-defined jets on kpc scales, but has a one-sided pc-scale jet in PA. The displacement relative to the brighter nucleus is considered non-significant because of the large IQR. However, as already noted, it is not known which of the two optical nuclei hosts the AGN producing the radio jet. If it is the fainter nucleus, the photocenter displacement is approximately in the counter-jet direction, which is not consistent with jet acceleration of the SBH (which would cause the SBH to be displaced in the counter-jet direction).

The remaining two objects which exhibit displacements considered to be significant (NGC 5419 and 5846) do not have well-defined jets on either parsec or kiloparsec scales.

2. Stalled SBH binaries: in the aftermath of a galaxy-galaxy merger, the SBH binary orbit shrinks at first due to dynamical friction and subsequently through slingshot ejection of stars intersecting the orbit. Investigations of quasi-steady spherical models suggested that the evolution of the binary stalls at separations  pc, due to a paucity of interacting stars, rather than hardening to the point at which gravitational wave emission drives the final inspiral to coalescence [the so-called “final parsec problem”; e.g., Merritt & Milosavljević, 2005]. Based on -body simulations, Merritt [2006] estimated “typical” semi-major axes for stalled binaries, finding pc for an SBH mass ratio and pc for , respectively. If the binary center of mass is located at the photocenter, the displacements of the primary and secondary components would be and , respectively, giving   pc and  pc for (0.1). Thus stalled binaries could produce displacements comparable with our results, particularly if the secondary SBH is accreting and the mass ratio is near unity.

It has been argued that stalling can be avoided in galaxies containing significant amounts of nuclear gas [e.g., Escala et al., 2005, Cuadra et al., 2009, Mayer et al., 2007]. Even in purely stellar nuclei, N-body simulations sometimes find that evolution of the binary can continue efficiently due to the presence of centrophilic orbits [Khan et al., 2011, Preto et al., 2011, Gualandris & Merritt, 2012]. However the existing gas-dynamical simulations probably do not yet have enough spatial resolution to follow the binary’s evolution to sub-parsec scales, and the N-body simulations appear to not yet have large enough N that their results can be robustly extrapolated to the much larger-N regime of real galaxies [Vasiliev et al., 2014].

Another possibility, discussed by Antonini & Merritt [2012], is accretion of a less massive galaxy by a giant elliptical, such as NGC 4486, which has a pre-existing depleted core (presumably the result of the evolution of SBH binaries formed in previous mergers). In such situations, dynamical friction is very inefficient in the core due to the lack of stars moving slower than the sinking object. The orbital eccentricity can increase rapidly while the apoapsis hardly changes, resulting in a slowly evolving SBH binary in a highly eccentric orbit. The simulations presented by Antonini & Merritt [2012] indicate that in an M87-like core, a low mass ratio binary () can persist over a Hubble time in an increasingly eccentric orbit with a semi major axis  pc. If the secondary SBH is accreting, it will be visible as an off-center AGN; if both components of the SBH binary are accreting, a double nucleus might be observed (perhaps as in NGC 4696 and NGC 5419).

Helical distortion or “wiggling” of parsec-scale radio jets has been linked to putative SBH binaries in several AGNs, with the jet wiggles being variously attributed to orbital motion, precession of the accretion disk around the jet-emitting black hole or to geodetic precession [e.g., Begelman, Blandford & Rees, 1980, Roos et al., 1993, Katz, 1997, Romero et al., 2000, Lobanov & Roland, 2005]. However, the periods ( years) and separations ( pc) typically inferred from analyses of jet wiggles are much smaller than would be the case for a stalling binary. If the pc-scale displacements measured in this work are interpreted as SBH binary orbits, periods years are implied for total masses  M. Geodetic precession is insignificant at these separations. The wavelength of jet wiggles caused by orbital motion is given by , where is the apparent jet velocity (for a jet speed and inclination to the line of sight, ) and is the orbital period. Therefore, assuming , a pc-scale binary will produce very long wavelength wiggles in the jet ( kpc). In general, due to the combination of orbital and jet velocities, the jet will precess on the surface of a cone which, for a pc-scale binary of mass M will have a half-opening angle [see Equation 7 in Roos et al., 1993]. Thus, orbital motion would cause only small curvatures in the jet over kpc scales, which would be difficult to discern as the jet loses collimation, or to distinguish from jet bending due to environmental effects, such as ram pressure. This will also be the case for disk precession, since the precession period exceeds the orbital period. Therefore, although the jet morphology has been mapped in detail from pc to kpc scales for a number of our sample galaxies (see Table 2 for references), these observations are unlikely to provide unambiguous clues as to the presence, or not, of a stalled pc-scale binary.

3. Massive perturbers: galaxy centers host a variety of potential perturbers with masses ranging from (e.g., stellar mass black holes and neutron stars) to , such as giant molecular clouds and stellar clusters.

Gravitational interactions with these objects will cause the SBH to undergo a type of Brownian motion, with the amplitude of the root-mean-square displacement given by:

(8)

where is proportional to the second moment of the mass distribution of the massive perturbers:

with being the number of perturbers with masses in the range [Merritt, 2013, eq. 7.63].

The offsets measured in this work range from 0.01 to 0.1 , but are typically (Table 6). For a typical SBH mass of order M (Table 9), rms displacements can be generated by Brownian motion for M.

The mass functions of globular clusters, gas clumps and giant molecular clouds in the inner 100 pc of the Galaxy have been estimated by Perets et al. [2007]. For comparison, using the mass functions presented in their paper, we find that can be as high as M for a population of giant molecular clouds. The Milky Way, of course, is very different from the galaxies studied here. However, as recently discussed by Antonini & Merritt [2012], the low efficiency of dynamical friction in low density cores favors the formation of a population of stalling massive objects in the cores of giant ellipticals.

Therefore, it seems plausible that displacements of order those observed could result from Brownian motion due to a population of massive perturbers. In several galaxies, the observed displacements are approximately aligned with the kpc-scale radio jets. This suggests that the displacement is not random, at least in these cases, favoring other mechanisms (i.e, gravitational recoil or jet thrust) that are expected to offset the SBH in the jet direction. Nevertheless, we conclude that Brownian motion cannot be excluded as the cause of the displacement in any individual galaxy, particularly those where the offsets are not aligned with kpc-scale jets, i.e. NGC 4278, 5846 and 5419.

Galaxy Offset (pc) PA (deg) Suspected Origin
NPS1 NPS2 NPS1 NPS2 Gravitational Jet Stalling Massive
Recoil Thrust SBH-SBH Perturbers
NGC 1399 1.5 0.4 -17 16
NGC 4278 7.6 0.4 152 3
NGC 4486 4.3 0.2 307 1
NGC 5846 8.2 2.5 253 8
IC 4296 3.8 0.7 338 7
Galaxies with two nuclear sources
NGC 5419 252 13 346 2

Note. – Projected offsets of the photocenter with respect to the AGN and their possible origin. When multiple images have been analyzed, values presented here are the error weighted average. Position angles (PA) are given in degrees East from North. NPS = nuclear point source.

Table 7SUMMARY

6. Summary and Conclusions

We have analyzed HST archival images of 14 nearby core elliptical galaxies, each of which hosts a central point-like source associated with a low-luminosity AGN, in order to search for offsets between the AGN and the galaxy photocenter. Such AGN–photocenter displacements are possible signposts of gravitational recoils resulting from the coalescence of an SBH binary.

We find significant () differences between the positions of the nuclear optical (or NIR) point source and the mean photocenter of the galaxy, as determined from isophote fits, in ten of the 14 galaxies in the sample. Assuming that the mean photocenter locates the minimum of the galactic potential well and that the point source locates the position of the AGN and hence the SBH, these results imply that the SBH is displaced from its equilibrium position by angular distances ranging between 20 and 90 mas, or projected linear distances in the range  pc. As spurious offsets may occur as a result of large-scale isophotal asymmetries, only displacements of magnitude the inter-quartile range of the distribution of isophote center coordinates (equivalent to for a gaussian distribution) are considered “real”. There are six galaxies that exhibit displacements IQR with three of these (NGC 4278, NGC 4486 and NGC 5846) having displacements IQR (equivalent to ). In every case, the measured displacement of the SBH relative to the galaxy photocenter is a small fraction (1–10%) of the galaxy core radius, which is typically  pc, for these galaxies.

Approximate alignments between the SBH–photocenter displacements and the radio source axis were found in four of the six galaxies considered to have significant displacements, including three of the four that have FR I, or FR I-like radio sources with relatively powerful and well-defined kpc-scale jets. Indeed, in every case in which there is both a significant displacement and an unambiguous jet, the two are approximately aligned.

Lacking detailed knowledge of the merger history of the galaxies, or of the SBH binary parameters (such as mass ratio and spin configuration) that determine the recoil velocity, it is not possible to directly test the hypothesis that the displacements are caused by residual gravitational recoil oscillations. Instead, we used a simple Monte-Carlo model to investigate if the measured displacements are consistent with gravitational recoil. We find that the displacements in individual objects can plausibly be attributed to residual gravitational recoil oscillations following a major or minor merger within the last few Gyr. However, for plausible merger rates there is a high probability of larger displacements than actually observed, if SBH coalescence events took place in these galaxies.

That larger displacements were not observed suggests that the frequency of gravitational recoil kicks large enough to trigger long-lived oscillations is lower than predicted, perhaps because the evolution of the SBH binary typically results in a configuration that suppresses recoil kicks with velocities km s. Alternatively, the post-recoil oscillations may be damped more quickly than predicted by pure N-body simulations. In either case, gas may play an important role [e.g., Dotti et al., 2010, Sijacki, Springel & Haehnelt, 2011]. Otherwise, it is possible that galaxy mergers are much more infrequent than implied by the current CDM paradigm [Kroupa, 2014].

Several other mechanisms are capable of producing the observed displacements, with the observed alignments between the SBH–photocenter displacements and the radio source axis favoring jet acceleration in some objects. An approximate displacement–radio axis alignment is also expected for gravitational recoil, but not for orbital motion in pre-coalescence SBH binaries or interactions with massive perturbers. However, both of the latter mechanisms are capable of producing displacement amplitudes comparable to those observed and cannot be ruled out in individual objects.

In general, it is not possible to unambiguously distinguish between different mechanisms (including recoil) on the basis of the displacement measurements alone for individual galaxies. However, with a larger sample it may be possible to distinguish mechanisms using statistical arguments. Thus, for jet acceleration the displacement direction should be strongly correlated with the radio jet, with the amplitude correlating with jet power. In the case of gravitational recoil, a weaker correlation with jet direction might be expected. However, no such correlations are expected for binary SBH, or massive perturbers.

Acknowledgments

We wish to honor the memory of our great friend, colleague and mentor David Axon. We thank the anonymous referee for the valuable and timely comments that improved the paper. DL thanks E. Vasiliev, R. Mittal, F. Antonini and M. Richmond for helpful discussions. AM acknowledges support from the Italian National Institute for Astrophysics (INAF) through PRIN-INAF 2011 “Black hole growth and AGN feedback through the cosmic time” and from the Italian ministry for school, university and research (MIUR) through PRIN-MIUR 2010-2011 “The dark Universe and the cosmic evolution of baryons: from current surveys to Euclid”. DM was supported by the National Science Foundation under grant no. AST 1211602 and by the National Aeronautics and Space Administration under grant no. NNX13AG92G. Support for program AR-11771 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. We acknowledge the usage of the HyperLeda database (http://leda.univ-lyon1.fr) and the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Center (CADC/NRC/CSA).