Recoiling Black Holes in Merging Galaxies: Relationship to AGN Lifetimes, Starbursts, and the M-sigma Relation
MMon. Not. R. Astron. Soc. , 000–000 (0000) Printed 24 October 2018 (MN L A TEX style file v2.2)
Recoiling Black Holes in Merging Galaxies: Relationship to AGNLifetimes, Starbursts, and the M BH − σ ∗ Relation
Laura Blecha (cid:63) , Thomas J. Cox , Abraham Loeb , & Lars Hernquist Harvard University, Department of Astronomy, 60 Garden St., Cambridge, MA 02138, USA Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 9110
24 October 2018
ABSTRACT
Gravitational-wave (GW) recoil of merging supermassive black holes (SMBHs) may influ-ence the co-evolution of SMBHs and their host galaxies. We examine this possibility usingSPH/N-body simulations of gaseous galaxy mergers, including SMBH accretion, in whichthe merged BH receives a recoil kick. This enables us to follow the trajectories and accretionof recoiling BHs in self-consistent, evolving merger remnants. In contrast to recent studieson similar topics, we conduct a large parameter study, generating a suite of over 200 sim-ulations with more than 60 merger models and a range of recoil velocities ( v k ). With this,we can identify systematic trends in the behavior of recoiling BHs. Our main results are asfollows. (1) BHs kicked at nearly the central escape speed ( v esc ) may oscillate on large or-bits for up to a Hubble time, but in gas-rich mergers, BHs kicked with up to ∼ . v esc maybe confined to the central few kpc of the galaxy, owing to gas drag and steep central poten-tials. (2) v esc in gas-rich mergers may increase rapidly during final coalescence, in whichcase recoil trajectories may depend sensitively on the timing of the BH merger relative to theformation of the central potential well. Delays of even a few × yr in the BH merger timemay substantially suppress recoiling BH motion for a fixed kick speed. (3) Recoil eventsgenerally reduce the lifetimes of bright active galactic nuclei (AGN), but short-period recoiloscillations may actually extend AGN lifetimes at lower luminosities. (4) Bondi-Hoyle ac-cretion dominates recoiling BH growth for v k / v esc < ∼ . − . ; for higher v k , the BH accretesprimarily from its ejected gas disk, which we model as a time-dependent accretion disk. (5)Kinematically-offset AGN may be observable either immediately after a high-velocity recoilor during pericentric passages through a gas-rich remnant. In either case, AGN lifetimes maybe up to ∼ Myr (for ∆ v > km s − ), though the latter generally have higher luminosi-ties. (6) Spatially-offset AGN can occur for v k > ∼ . − . v esc (for ∆ R > kpc); thesegenerally have low luminosities and lifetimes of ∼ − Myr. (7) Rapidly-recoiling BHsmay be up to ∼ times less massive than their stationary counterparts. These mass deficitslower the normalization of the M BH − σ ∗ relation and contribute to both intrinsic and overallscatter. (8) Finally, the displacement of AGN feedback after a recoil event enhances centralstar formation rates in the merger remnant, thereby extending the starburst phase of the mergerand creating a denser, more massive stellar cusp. Key words: black hole physics – gravitational waves – accretion, accretion disks – galaxies:kinematics and dynamics – galaxies: evolution – galaxies: active
Within the hierarchical structure formation paradigm, a significantfraction of galaxy growth occurs via successive mergers. Given theample evidence that most, if not all, local galaxies host centralsupermassive black holes (SMBHs; e.g., Kormendy & Richstone1995; Richstone et al. 1998; Ferrarese & Ford 2005), major galaxymergers (those with mass ratios q > ∼ . ) should inevitably result (cid:63) Email: [email protected] in the formation of SMBH binaries. The fate of these binaries issomewhat uncertain and likely depends on the conditions withintheir host galaxies. In highly spheroidal, gas-poor galaxies, thesebinaries may “stall” at separations of about a parsec for up to aHubble time (e.g., Begelman et al. 1980; Milosavljevi´c & Merritt2001; Yu 2002). In gas-rich galaxy mergers, however, gas is drivento the central region of the merging galaxies simultaneously withthe formation of the SMBH binary. Numerical simulations indi-cate that BH merger timescales may be much shorter than galaxymerger timescales in this case ( ∼ − yr from the hard binary c (cid:13) a r X i v : . [ a s t r o - ph . C O ] N ov Blecha et al. stage; e.g., Escala et al. 2005; Dotti et al. 2007). This implies thatthe SMBH binaries most able to accrete gas and produce electro-magnetic signatures are likely to be short-lived.To date, observations seem to confirm this scenario. Severalquasar pairs with kpc-scale separations have been found in merg-ing galaxies (Komossa et al. 2003; Bianchi et al. 2008; Comerfordet al. 2009b; Green et al. 2010). Recently, spectroscopic and pho-tometric observations have found that between − − − ofactive galactic nuclei (AGN) at z < ∼ . may in fact contain dualBHs with separations of ∼ kpc (Comerford et al. 2009a; Smithet al. 2010; Liu et al. 2010b,a; Smith et al. 2010; Fu et al. 2010).However, only one unambiguous case of a SMBH binary has beenfound, with a separation of ∼ pc (Rodriguez et al. 2006). Severaladditional objects have been identified as candidate SMBH bina-ries but are still unconfirmed (Sillanpaa et al. 1988; Komossa et al.2008; Dotti et al. 2009; Bogdanovi´c et al. 2009; Boroson & Lauer2009). Thus, it is clear that the large majority of AGN do not con-tain binary SMBHs, which suggests that any substantial populationof long-lived SMBH binaries must exist in gas-poor environmentswhere they are quiescent.If most binaries are therefore assumed to merge on reason-ably short timescales, then gravitational-wave (GW) recoil must bea common phenomenon throughout the merger history of galaxies.GW recoil is a natural consequence of gravitational radiation fromBH binary mergers (Peres 1962; Bekenstein 1973; Fitchett & De-tweiler 1984). If the binary system has any asymmetry – unequalmasses, spins or spin orientations – then gravitational waves areradiated asymmetrically, resulting in a net linear momentum fluxfrom the final BH at the time of merger. This causes the BH torecoil in the opposite direction. Whether these recoil kicks werelarge enough to be astrophysically interesting was uncertain until afew years ago, because accurate calculations of the recoil velocityrequire BH merger simulations using full general relativity. Thesesimulations have revealed that GW recoils may be quite large. Re-coil velocities up to km s − are possible for special configura-tions, which is far greater than galactic escape speeds (Campanelliet al. 2007a,b). The implication that SMBHs may spend substantialtime in motion and off-center has opened a new line of inquiry intothe ramifications for SMBHs and their host galaxies.A useful starting point for such inquiries would be the distribu-tion of recoil kick velocities, but this is quite difficult to ascertain inpractice. The final velocity depends sensitively on not just the massratio of the progenitor BHs, but on their spin magnitudes and orien-tations as well. The distributions of SMBH binary mass ratios andspins at various redshifts have been estimated using halo mergertrees and semi-analytical models of SMBH growth (e.g., Volonteriet al. 2003, 2005; King et al. 2008; Berti & Volonteri 2008). Thesedistributions depend on a number of model assumptions, however,and the BH spin orientations prior to merger are far more uncertainstill. Thus, based on recent results from BH merger simulations us-ing full numerical relativity (NR), several groups have calculatedkick probability distributions as a function of BH mass ratio for ei-ther fixed or random values of BH spin, with the assumption thatthe spins are randomly oriented (Schnittman & Buonanno 2007;Campanelli et al. 2007a; Baker et al. 2008; Lousto et al. 2010a,b;van Meter et al. 2010). Their results are in good agreement witheach other and imply that the fraction of high-velocity GW recoilsis substantial. This underscores the potential for recoil events to bean important component of galaxy mergers.It is quite possible, of course, that the spins of SMBH binariesare not randomly oriented, but are preferentially aligned in someway. Bogdanovi´c et al. (2007) have suggested that torques in a cir- cumbinary gas disk may align the BH spins with the orbital axisof the disk. In this case, the resulting in-plane kicks would havea maximum recoil velocity of < km s − , although spins thatbecame anti-aligned by the same mechanism could result in recoilvelocities up to 500 km s − (e.g., Gonz´alez et al. 2007; Campanelliet al. 2007a; Baker et al. 2008). Additionally, simulations by Dottiet al. (2010) demonstrate efficient spin alignment of merging BHsin the presence of a highly coherent accretion flow, although it isunclear how efficient this process might be in a gaseous environ-ment that includes, e.g., star formation. Kesden et al. (2010) haverecently demonstrated that BH spin alignment may instead occurvia relativistic spin precession, regardless of whether a gas disk ispresent. The aforementioned recoil kick probability distributionsare therefore upper limits on the actual distributions.Numerous possible consequences of GW recoil events havebeen discussed in the literature. GW recoils may have a large effectat high redshifts, where escape velocities of galaxies are smaller(e.g., Merritt et al. 2004; Madau & Quataert 2004; Volonteri 2007).This is a concern for attempts to understand, for example, the originof the z = 6 SDSS quasars (e.g., Fan et al. 2001, 2003). Volonteri& Rees (2006) suggest that growth of SMBHs at high z must oc-cur only in highly-biased halos. Using cosmological hydrodynamicsimulations, Sijacki et al. (2009) investigate BH growth in massivehigh- z halos, including the ejection of BHs with recoil velocitiesabove v esc . Their findings are consistent with the observed popula-tions of bright quasars at z = 6 , despite the effects of GW recoil.At lower redshifts, recoiling BHs may produce electromag-netic signatures. The main signatures we will focus on here arerecoiling AGN that are either spatially or kinematically offset fromtheir host galaxies (Madau & Quataert 2004; Loeb 2007; Blecha &Loeb 2008; Komossa & Merritt 2008a; Guedes et al. 2009). Otherpossible signatures include flares from shocks induced by fallbackof gas marginally bound to the ejected BH (Lippai et al. 2008;Shields & Bonning 2008; Schnittman & Krolik 2008), enhancedrates of stellar tidal disruptions (Komossa & Merritt 2008b; Stone& Loeb 2010), and compact stellar clusters around ejected BHs(O’Leary & Loeb 2009; Merritt et al. 2009).Thus far, no confirmed GW recoil events have been observed.An inherent challenge in observing offset quasars is that larger spa-tial or kinematic offsets are easier to resolve, but less gas will bebound to the recoiling BH at higher recoil velocities, so its AGNlifetime will be shorter. Bonning et al. (2007) conducted a searchfor kinematic offsets in SDSS quasar spectra and found a null resultat a limit of 800 km s − . Several recoil candidates have been pro-posed, but their extreme inferred velocities should be exceedinglyrare. Indeed, the recoil candidate with a 2600 km s − offset, pro-posed by Komossa et al. (2008), may in fact be a superposition oftwo galaxies (Heckman et al. 2009; Shields et al. 2009a) or a binarySMBH system (Dotti et al. 2009; Bogdanovi´c et al. 2009). Anothercandidate with an even higher (3500 km s − ) offset is most likelya double-peaked emitter (Shields et al. 2009b). Recently, Civanoet al. (2010) have suggested that an unusual galaxy discovered inthe COSMOS survey by Comerford et al. (2009b), which those au-thors proposed to be a dual SMBH system, may in fact be a re-coiling BH, as new spectra indicate a kinematic offset of 1200 kms − . This candidate has a less extreme velocity than the others, butfurther observations are needed to confirm the nature of this object.Additionally, the SMBH in M87 has recently been observed to bespatially offset by ∼ pc, which could possibly be explained by apast recoil event (Batcheldor et al. 2010).In addition to producing direct observational signatures, GWrecoil may play a role in the co-evolution of SMBHs and their c (cid:13)000
Within the hierarchical structure formation paradigm, a significantfraction of galaxy growth occurs via successive mergers. Given theample evidence that most, if not all, local galaxies host centralsupermassive black holes (SMBHs; e.g., Kormendy & Richstone1995; Richstone et al. 1998; Ferrarese & Ford 2005), major galaxymergers (those with mass ratios q > ∼ . ) should inevitably result (cid:63) Email: [email protected] in the formation of SMBH binaries. The fate of these binaries issomewhat uncertain and likely depends on the conditions withintheir host galaxies. In highly spheroidal, gas-poor galaxies, thesebinaries may “stall” at separations of about a parsec for up to aHubble time (e.g., Begelman et al. 1980; Milosavljevi´c & Merritt2001; Yu 2002). In gas-rich galaxy mergers, however, gas is drivento the central region of the merging galaxies simultaneously withthe formation of the SMBH binary. Numerical simulations indi-cate that BH merger timescales may be much shorter than galaxymerger timescales in this case ( ∼ − yr from the hard binary c (cid:13) a r X i v : . [ a s t r o - ph . C O ] N ov Blecha et al. stage; e.g., Escala et al. 2005; Dotti et al. 2007). This implies thatthe SMBH binaries most able to accrete gas and produce electro-magnetic signatures are likely to be short-lived.To date, observations seem to confirm this scenario. Severalquasar pairs with kpc-scale separations have been found in merg-ing galaxies (Komossa et al. 2003; Bianchi et al. 2008; Comerfordet al. 2009b; Green et al. 2010). Recently, spectroscopic and pho-tometric observations have found that between − − − ofactive galactic nuclei (AGN) at z < ∼ . may in fact contain dualBHs with separations of ∼ kpc (Comerford et al. 2009a; Smithet al. 2010; Liu et al. 2010b,a; Smith et al. 2010; Fu et al. 2010).However, only one unambiguous case of a SMBH binary has beenfound, with a separation of ∼ pc (Rodriguez et al. 2006). Severaladditional objects have been identified as candidate SMBH bina-ries but are still unconfirmed (Sillanpaa et al. 1988; Komossa et al.2008; Dotti et al. 2009; Bogdanovi´c et al. 2009; Boroson & Lauer2009). Thus, it is clear that the large majority of AGN do not con-tain binary SMBHs, which suggests that any substantial populationof long-lived SMBH binaries must exist in gas-poor environmentswhere they are quiescent.If most binaries are therefore assumed to merge on reason-ably short timescales, then gravitational-wave (GW) recoil must bea common phenomenon throughout the merger history of galaxies.GW recoil is a natural consequence of gravitational radiation fromBH binary mergers (Peres 1962; Bekenstein 1973; Fitchett & De-tweiler 1984). If the binary system has any asymmetry – unequalmasses, spins or spin orientations – then gravitational waves areradiated asymmetrically, resulting in a net linear momentum fluxfrom the final BH at the time of merger. This causes the BH torecoil in the opposite direction. Whether these recoil kicks werelarge enough to be astrophysically interesting was uncertain until afew years ago, because accurate calculations of the recoil velocityrequire BH merger simulations using full general relativity. Thesesimulations have revealed that GW recoils may be quite large. Re-coil velocities up to km s − are possible for special configura-tions, which is far greater than galactic escape speeds (Campanelliet al. 2007a,b). The implication that SMBHs may spend substantialtime in motion and off-center has opened a new line of inquiry intothe ramifications for SMBHs and their host galaxies.A useful starting point for such inquiries would be the distribu-tion of recoil kick velocities, but this is quite difficult to ascertain inpractice. The final velocity depends sensitively on not just the massratio of the progenitor BHs, but on their spin magnitudes and orien-tations as well. The distributions of SMBH binary mass ratios andspins at various redshifts have been estimated using halo mergertrees and semi-analytical models of SMBH growth (e.g., Volonteriet al. 2003, 2005; King et al. 2008; Berti & Volonteri 2008). Thesedistributions depend on a number of model assumptions, however,and the BH spin orientations prior to merger are far more uncertainstill. Thus, based on recent results from BH merger simulations us-ing full numerical relativity (NR), several groups have calculatedkick probability distributions as a function of BH mass ratio for ei-ther fixed or random values of BH spin, with the assumption thatthe spins are randomly oriented (Schnittman & Buonanno 2007;Campanelli et al. 2007a; Baker et al. 2008; Lousto et al. 2010a,b;van Meter et al. 2010). Their results are in good agreement witheach other and imply that the fraction of high-velocity GW recoilsis substantial. This underscores the potential for recoil events to bean important component of galaxy mergers.It is quite possible, of course, that the spins of SMBH binariesare not randomly oriented, but are preferentially aligned in someway. Bogdanovi´c et al. (2007) have suggested that torques in a cir- cumbinary gas disk may align the BH spins with the orbital axisof the disk. In this case, the resulting in-plane kicks would havea maximum recoil velocity of < km s − , although spins thatbecame anti-aligned by the same mechanism could result in recoilvelocities up to 500 km s − (e.g., Gonz´alez et al. 2007; Campanelliet al. 2007a; Baker et al. 2008). Additionally, simulations by Dottiet al. (2010) demonstrate efficient spin alignment of merging BHsin the presence of a highly coherent accretion flow, although it isunclear how efficient this process might be in a gaseous environ-ment that includes, e.g., star formation. Kesden et al. (2010) haverecently demonstrated that BH spin alignment may instead occurvia relativistic spin precession, regardless of whether a gas disk ispresent. The aforementioned recoil kick probability distributionsare therefore upper limits on the actual distributions.Numerous possible consequences of GW recoil events havebeen discussed in the literature. GW recoils may have a large effectat high redshifts, where escape velocities of galaxies are smaller(e.g., Merritt et al. 2004; Madau & Quataert 2004; Volonteri 2007).This is a concern for attempts to understand, for example, the originof the z = 6 SDSS quasars (e.g., Fan et al. 2001, 2003). Volonteri& Rees (2006) suggest that growth of SMBHs at high z must oc-cur only in highly-biased halos. Using cosmological hydrodynamicsimulations, Sijacki et al. (2009) investigate BH growth in massivehigh- z halos, including the ejection of BHs with recoil velocitiesabove v esc . Their findings are consistent with the observed popula-tions of bright quasars at z = 6 , despite the effects of GW recoil.At lower redshifts, recoiling BHs may produce electromag-netic signatures. The main signatures we will focus on here arerecoiling AGN that are either spatially or kinematically offset fromtheir host galaxies (Madau & Quataert 2004; Loeb 2007; Blecha &Loeb 2008; Komossa & Merritt 2008a; Guedes et al. 2009). Otherpossible signatures include flares from shocks induced by fallbackof gas marginally bound to the ejected BH (Lippai et al. 2008;Shields & Bonning 2008; Schnittman & Krolik 2008), enhancedrates of stellar tidal disruptions (Komossa & Merritt 2008b; Stone& Loeb 2010), and compact stellar clusters around ejected BHs(O’Leary & Loeb 2009; Merritt et al. 2009).Thus far, no confirmed GW recoil events have been observed.An inherent challenge in observing offset quasars is that larger spa-tial or kinematic offsets are easier to resolve, but less gas will bebound to the recoiling BH at higher recoil velocities, so its AGNlifetime will be shorter. Bonning et al. (2007) conducted a searchfor kinematic offsets in SDSS quasar spectra and found a null resultat a limit of 800 km s − . Several recoil candidates have been pro-posed, but their extreme inferred velocities should be exceedinglyrare. Indeed, the recoil candidate with a 2600 km s − offset, pro-posed by Komossa et al. (2008), may in fact be a superposition oftwo galaxies (Heckman et al. 2009; Shields et al. 2009a) or a binarySMBH system (Dotti et al. 2009; Bogdanovi´c et al. 2009). Anothercandidate with an even higher (3500 km s − ) offset is most likelya double-peaked emitter (Shields et al. 2009b). Recently, Civanoet al. (2010) have suggested that an unusual galaxy discovered inthe COSMOS survey by Comerford et al. (2009b), which those au-thors proposed to be a dual SMBH system, may in fact be a re-coiling BH, as new spectra indicate a kinematic offset of 1200 kms − . This candidate has a less extreme velocity than the others, butfurther observations are needed to confirm the nature of this object.Additionally, the SMBH in M87 has recently been observed to bespatially offset by ∼ pc, which could possibly be explained by apast recoil event (Batcheldor et al. 2010).In addition to producing direct observational signatures, GWrecoil may play a role in the co-evolution of SMBHs and their c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies host galaxies. Strong empirical correlations exist between SMBHmass and properties of the host galaxy bulge, including the bulgeluminosity, mass, and stellar velocity dispersion (e.g., Kormendy& Richstone 1995; Magorrian et al. 1998; Gebhardt et al. 2000;Ferrarese & Merritt 2000; Merritt & Ferrarese 2001; Tremaineet al. 2002; Marconi & Hunt 2003). These correlations are well-reproduced by galaxy formation models in which much of BH andgalaxy bulge growth occurs via successive mergers, and in whichmerger-triggered BH fueling is self-regulated via AGN feedback(e.g., Silk & Rees 1998; Wyithe & Loeb 2003; Di Matteo et al.2005; Hopkins et al. 2006a). However, because GW recoil eventsmay occur simultaneously with this rapid BH accretion phase, re-coils could significantly disrupt the coordinated growth of BHs andgalaxy bulges. In particular, GW recoil may contribute to scatter inthe M BH − σ ∗ relation caused by ejected (Volonteri 2007) or boundrecoiling (Blecha & Loeb 2008; Sijacki et al. 2010) BHs; we willexamine the latter possibility in greater detail. It is also unclear apriori what effects, if any, GW recoil may have on the host galaxiesthemselves. In purely collisionless galaxies, Boylan-Kolchin et al.(2004) and Gualandris & Merritt (2008) have shown that bound re-coiling BHs may scour out a stellar core. In gas-rich galaxy merg-ers, copious of amounts of cold gas are driven to the central galacticregion during coalescence, triggering a luminous starburst such thatthe galaxy may appear as a ULIRG (Sanders et al. 1988a; Sanders& Mirabel 1996). Feedback from a central AGN may terminatethe starburst phase by expelling gas and dust from the central re-gion (e.g., Hopkins et al. 2006a, 2008b; Somerville et al. 2008).We will investigate whether observable starburst properties or gasand stellar dynamics may be affected by the sudden displacementof this central AGN via recoils (see also recent work by Sijackiet al. 2010).Our current work was initiated as a follow-up of Blecha &Loeb (2008), hereafter BL08. BL08 explored the trajectories andaccretion of BHs on bound orbits in a static potential with stellarbulge and gaseous disk components. They found that recoil kicks < ∼ v esc could produce long-lived ( > ∼ Gyr) oscillations of the BH;similar results were found by Gualandris & Merritt (2008), Kornre-ich & Lovelace (2008) & Guedes et al. (2009). BL08 also demon-strated that GW recoil can affect SMBH growth even when the BHis not ejected entirely from the host galaxy. By removing accretingBHs from the central dense region and thereby limiting the BH’sfuel supply, BHs receiving recoil kicks > ∼ . v esc may be less mas-sive than stationary BHs.In the present study, we use hydrodynamic simulations to self-consistently calculate the dynamics and accretion of recoiling BHsin realistic merger remnant potentials. We simulate galaxy merg-ers using GADGET-3 (Springel 2005), an SPH/N-body code, andapply a recoil kick to the BH at the time of BH merger. Due tothe detailed initial conditions and many free parameters involved insuch merger simulations, we conduct a large parameter study withdozens of galaxy merger models and a wide range of kick veloci-ties. Each merger model is simulated with at least one kick velocityand also with no recoil kick, for comparison. With this suite of re-coil simulations, we are able to observe trends in the behavior of re-coiling BHs in different environments. When paired with our time-dependent, sub-resolution models for recoiling BH accretion, thisapproach allows us to, for example, determine velocity-dependentrecoiling AGN lifetimes and estimate the effect of GW recoil onscatter in the M BH − σ ∗ relation.As this paper was in the final stages of preparation, two papersappeared that also involve hydrodynamic simulations of recoilingBHs in galaxy merger remnants (Guedes et al. 2010; Sijacki et al. 2010). However, each study used only a few simulations, probingonly a small part of parameter space. Guedes et al. (2010) used re-sults of three merger simulations as initial conditions, and ran hy-drodynamic simulations of recoiling BHs in these merger remnantsfor a short time. These initial trajectories were used to calibratesemi-analytic calculations of the recoil trajectory in the remnantpotential. A range of kick velocities was tested in each of the threemerger models used. Sijacki et al. (2010) simulate recoils in an iso-lated, stable disk galaxy; they also use this galaxy model as theinitial condition for a full merger simulation with GW recoils. Bothstudies also include prescriptions for accretion onto recoiling BHs.We provide a comparison of our results to the findings of these pa-pers in § § § §
3, the general characteristics of ourgalaxy merger simulations with stationary central BHs (i.e., no re-coil kicks). We discuss the variation in merger dynamics and rem-nant morphologies between models. In §
4, the dynamics of recoil-ing BHs are discussed. We describe the general characteristics ofrecoil trajectories and trends between models in § § § § § § § § M BH − σ ∗ relations derived fromour set of no-recoil simulations and our set of high-velocity recoilsimulations, and discuss implications for the observed M BH − σ ∗ relation. Finally, in § § For our simulations of galaxy mergers, we employ the smoothedparticle dynamics (SPH) code
GADGET-3 (Springel 2005), whichconserves both energy and entropy (Springel & Hernquist 2002).The code includes radiative cooling as well as a subresolutionmodel for a multiphase interstellar medium (ISM) (Springel &Hernquist 2003) that accounts for star formation and supernovafeedback. In addition, the code models BHs as gravitational “sink”particles that contain a BH seed and a gas reservoir. The reservoiris replenished by stochastic accretion of neighboring gas particles,but the actual accretion rate onto the BH is calculated smoothly us-ing the Bondi-Hoyle-Lyttleton formula with locally-averaged val-ues for the density and sound speed. Because the gas around the BHcannot be resolved at higher densities below the spatial resolutionlimit, the accretion rate calculated from these values is multipliedby a constant factor. Following other authors, we assume a value of100 for this factor (e.g. Springel et al. 2005b; Hopkins et al. 2006b;Johansson et al. 2009). Angular momentum is conserved duringaccretion of gas particles, but because this is a stochastic processowing to the finite mass resolution, we also introduce an analytic c (cid:13) , 000–000 Blecha et al.
Initial model parameters Resulting merger quantitiesModel q M tot M disk f gas R peri θ φ θ φ t mrg v esc ( t mrg ) v esc , max % diff.[ M (cid:12) ] [ M (cid:12) ] [kpc] [deg] [deg] [deg] [deg] [Gyr] [km s − ] [km s − ] q1fg0.6a 1.0 272.1 11.16 0.6 7.1 30 60 -30 45 1.55 1258 1494 18.7 q1fg0.5a 1.0 272.1 11.16 0.5 7.1 30 60 -30 45 1.58 1157 1568 35.6q1fg0.4a 1.0 272.1 11.16 0.4 7.1 30 60 -30 45 1.60 1102 1472 33.6 q1fg0.3a 1.0 272.1 11.16 0.3 7.1 30 60 -30 45 1.63 1118 1337 19.6 q1fg0.3b 1.0 272.1 11.16 0.3 14.3 30 60 -30 45 2.01 1165 1256 7.8q1fg0.3c 1.0 272.1 11.16 0.3 7.1 150 60 -30 45 1.70 1113 1264 13.6q1fg0.3d 1.0 272.1 11.16 0.3 7.1 150 0 -30 45 1.69 1152 1271 10.4q1fg0.3e 1.0 272.1 11.16 0.3 7.1 90 60 -30 45 1.76 970 1194 23.1q1fg0.3M20w 1.0 5442 223.1 0.3 19.4 30 60 -30 45 1.54 2555 2727 6.7q1fg0.3M10x 1.0 2721 111.6 0.3 15.4 30 60 -30 45 1.69 2067 2290 10.8q1fg0.3M0.1y 1.0 27.21 1.116 0.3 3.3 30 60 -30 45 1.60 457 641 40.3q1fg0.3M0.05z 1.0 13.61 0.5578 0.3 2.7 30 60 -30 45 2.00 338 497 47.0q1fg0.2a 1.0 272.1 11.16 0.2 7.1 30 60 -30 45 1.67 1049 1182 12.6 q1fg0.1a 1.0 272.1 11.16 0.1 7.1 30 60 -30 45 1.72 876 931 6.3 q1fg0.1b 1.0 272.1 11.16 0.1 14.3 30 60 -30 45 2.09 921 923 0.2q1fg0.1c 1.0 272.1 11.16 0.1 7.1 150 60 -30 45 1.80 891 956 7.3q1fg0.1d 1.0 272.1 11.16 0.1 7.1 150 0 -30 45 1.82 863 906 5.0q1fg0.1e 1.0 272.1 11.16 0.1 7.1 90 60 -30 45 1.84 860 918 6.7q1fg0.1M10x 1.0 2721 111.6 0.1 15.4 30 60 -30 45 1.74 1924 2033 5.7q1fg0.04a 1.0 272.1 11.16 0.04 7.1 30 60 -30 45 1.76 823 848 3.1 q1fg0a 1.0 272.1 11.16 0.0 7.1 30 60 -30 45 1.84 772 790 2.3 q0.9fg0.4a 0.9 258.5 10.60 0.4 7.1 30 60 -30 45 1.61 1104 1455 31.8q0.9fg0.3a 0.9 258.5 10.60 0.3 7.1 30 60 -30 45 1.65 1154 1337 15.9q0.9fg0.1a 0.9 258.5 10.60 0.1 7.1 30 60 -30 45 1.74 866 918 6.1q0.75fg0.4a 0.75 238.1 9.762 0.4 7.1 30 60 -30 45 1.69 1113 1302 17.1q0.75fg0.3a 0.75 238.1 9.762 0.3 7.1 30 60 -30 45 1.73 1090 1225 12.3q0.75fg0.1a 0.75 238.1 9.762 0.1 7.1 30 60 -30 45 1.83 810 867 7.1q0.667fg0.4a 0.667 226.8 9.297 0.4 7.1 30 60 -30 45 1.68 1086 1219 12.3q0.667fg0.3a 0.667 226.8 9.297 0.3 7.1 30 60 -30 45 1.73 883 1166 32.1q0.667fg0.1a 0.667 226.8 9.297 0.1 7.1 30 60 -30 45 1.85 846 847 0.1 q0.5fg0.6a 0.5 204.1 8.368 0.6 7.1 30 60 -30 45 1.88 914 1116 22.1 q0.5fg0.5a 0.5 204.1 8.368 0.5 7.1 30 60 -30 45 1.89 963 1076 11.7q0.5fg0.4a 0.5 204.1 8.368 0.4 7.1 30 60 -30 45 1.95 893 983 10.1q0.5fg0.4b 0.5 204.1 8.368 0.4 14.3 30 60 -30 45 2.46 965 1060 9.8q0.5fg0.4c 0.5 204.1 8.368 0.4 7.1 150 60 -30 45 1.90 1024 1112 8.6q0.5fg0.4d 0.5 204.1 8.368 0.4 7.1 150 0 -30 45 1.90 1061 1117 5.2 q0.5fg0.3a 0.5 204.1 8.368 0.3 7.1 30 60 -30 45 1.97 993 994 0.1 q0.5fg0.3b 0.5 204.1 8.368 0.3 14.3 30 60 -30 45 2.45 920 1003 9.0q0.5fg0.3c 0.5 204.1 8.368 0.3 7.1 150 60 -30 45 1.97 1012 1017 0.5q0.5fg0.3d 0.5 204.1 8.368 0.3 7.1 150 0 -30 45 1.92 1014 1069 5.4q0.5fg0.3e 0.5 204.1 8.368 0.3 7.1 90 60 -30 45 2.05 915 1126 23.1q0.5fg0.3f 0.5 204.1 8.368 0.3 7.1 90 0 0 0 1.94 978 1029 5.2q0.5fg0.3g 0.5 204.1 8.368 0.3 7.1 60 60 150 0 2.23 805 820 1.9q0.5fg0.3h 0.5 204.1 8.368 0.3 7.1 0 0 0 0 1.84 927 1111 19.8q0.5fg0.3i 0.5 204.1 8.368 0.3 7.1 180 0 0 0 1.84 1028 1146 11.4q0.5fg0.3j 0.5 204.1 8.368 0.3 7.1 180 0 180 0 2.09 823 930 13.0q0.5fg0.3k 0.5 204.1 8.368 0.3 7.1 10 0 -10 0 1.84 1046 1087 4.0q0.5fg0.3M10x 0.5 2041 83.68 0.3 15.4 30 60 -30 45 2.02 2081 2070 -0.5q0.5fg0.2a 0.5 204.1 8.368 0.2 7.1 30 60 -30 45 2.02 830 862 3.8 q0.5fg0.1a 0.5 204.1 8.368 0.1 7.1 30 60 -30 45 2.12 777 798 2.7 q0.5fg0.1b 0.5 204.1 8.368 0.1 14.3 30 60 -30 45 2.56 812 813 0.1q0.5fg0.1c 0.5 204.1 8.368 0.1 7.1 150 60 -30 45 2.12 811 813 0.2q0.5fg0.1d 0.5 204.1 8.368 0.1 7.1 150 0 -30 45 2.12 814 810 -0.5q0.5fg0.1M10x 0.5 2041 83.68 0.1 15.4 30 60 -30 45 2.07 1737 1737 0.0q0.5fg0.04a 0.5 204.1 8.368 0.04 7.1 30 60 -30 45 2.18 740 748 1.0 q0.5fg0a 0.5 204.1 8.368 0 7.1 30 60 -30 45 2.30 689 706 2.4 q0.333fg0.4a 0.333 181.4 7.438 0.4 7.1 30 60 -30 45 2.28 810 816 0.7q0.333fg0.3a 0.333 181.4 7.438 0.3 7.1 30 60 -30 45 2.38 856 858 0.3q0.333fg0.1a 0.333 181.4 7.438 0.1 7.1 30 60 -30 45 2.57 741 744 0.3q0.25fg0.4a 0.25 170.1 6.974 0.4 7.1 30 60 -30 45 2.94 829 830 0.1q0.25fg0.3a 0.25 170.1 6.974 0.3 7.1 30 60 -30 45 2.90 852 852 -0.1q0.25fg0.1a 0.25 170.1 6.974 0.1 7.1 30 60 -30 45 3.18 722 725 0.3 Table 1.
Galaxy merger models. Boldface entries denote those for which we have varied v k . Fiducial-mass merger models are labeled as q[ value ]fg[ value ][ orb ],where “q” is the galaxy mass ratio, “fg” is the initial gas fraction, and each letter orb corresponds to a specific orbit (“a” being our “fiducial” configuration).High- and low-mass models are denoted by q[ value ]fg[ value ]M[ factor ][ orb ], where “M” is the ratio of the primary galaxy mass to the fiducial mass.c (cid:13)000
Galaxy merger models. Boldface entries denote those for which we have varied v k . Fiducial-mass merger models are labeled as q[ value ]fg[ value ][ orb ],where “q” is the galaxy mass ratio, “fg” is the initial gas fraction, and each letter orb corresponds to a specific orbit (“a” being our “fiducial” configuration).High- and low-mass models are denoted by q[ value ]fg[ value ]M[ factor ][ orb ], where “M” is the ratio of the primary galaxy mass to the fiducial mass.c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies accretion drag force ( ∝ ˙ M v ) calculated from the Bondi accretionrate at each timestep. These prescriptions are described in more de-tail in Springel et al. (2005b).We note that, as in all hydrodynamic simulations involving BHaccretion, the exact nature of the accretion on sub-resolution scalesis unknown, so it is necessary to assume a sub-resolution model.While the validity of the Bondi-Hoyle-Lyttleton formula (with amultiplicative factor) in our framework is indeed an assumption,few constraints exist on the gas flow from large scales down tothe BH. The Bondi-Hoyle-Lyttleton model provides a physically-motivated approximation of the gas captured by a BH, including aBH in motion, and its extensive use in the literature helps to placeour work in a larger context of galaxy evolution studies. We furtherassume that the accretion factor remains constant even after a GWrecoil event. This latter assumption is justified in that the spatial res-olution limit, which motivates the use of this factor, always remainsconstant. Furthermore, owing to the sink-particle treatment of BHsin the code, the accretion factor does not determine the amount ofgas bound to the BH at each timestep; it influences only how thisgas is accreted onto the BH. From a practical standpoint, using thesame accretion prescription throughout enables a more direct com-parison between recoiling and stationary BHs – one of the maingoals of this study.Because we are presently interested in GW recoil, we al-low for an arbitrary velocity to be added to the remnant BH atthe time of the BH merger, t mrg . To more easily compare recoilevents in different merger models, we scale this velocity to thecentral escape speed at the time of merger, v esc ( t mrg ). We de-fine v esc = (cid:112) − x BH ) at each timestep, i.e., the escape speed atthe position of the BH, which is close to the position of the potentialminimum in the absence of a recoil kick. Campanelli et al. (2007a),Baker et al. (2008), & van Meter et al. (2010) have all fit distri-butions to the data from full NR simulations of BH mergers, withresults in good agreement. For major mergers ( . < q < , therange we consider in our simulations), high spins ( a = a = 0 . ),and randomly-distributed spin orientations, van Meter et al. (2010)find that 69.8% of recoil kicks will be above 500 km s − and 35.3%will be above 1000 km s − . If the BH spin magnitudes are also ran-domly distributed ( ≤ a , a ≤ ), the these fractions are 41.6%and 13.5%. Our fiducial-mass merger simulations (described be-low) have v esc = 689 − km s − , and we also use low-masssimulations with v esc as low as 338 km s − . The NR results indi-cate that there is a substantial probability of BHs in these modelsreceiving kicks up to ∼ v esc . In our high-mass simulations, how-ever, v esc = 1737 − km s − , so the probability of recoilevents with v k ∼ v esc is much lower in these models.We also slightly modify the treatment of BH mergers in thecode. In the standard GADGET prescription, the BHs merge whenthey are separated by less than a gravitational softening length( a sep < R soft ) and have a relative velocity v rel < . c s , where c s is the local sound speed. If, as can happen in gas-rich merg-ers, the central escape velocity is increasing rapidly when the BHsmerge, small variations in t mrg can result in very different BH tra-jectories (see Fig. 8). In order to reliably compare results fromdifferent simulations, we therefore force the BHs to merge at agiven time that is predetermined as follows. We define the “coa-lescence time” t coal as the earliest time after which the BH binaryis tight enough that it could plausibly merge. Given the numeri-cal uncertainties near the spatial resolution limit, we generouslychoose t coal to be the time when the BH separation falls below a sep = 10 R soft (and v rel < . c s , as before). For reference, R soft = 80 pc in our fiducial-mass simulations (see below). Then, restarting the simulation slightly before t coal , we force the BHsto merge at a predetermined time t mrg ≥ t coal . t mrg can then bevaried as a free parameter, allowing us to systematically probe therange of possible BH merger times. In practice, this is only neces-sary for nearly equal-mass, gas-rich mergers in which v esc variessignificantly throughout the merger. In other cases the results areinsensitive to the choice of merger time, so t mrg is simply chosento be t coal .For the majority of our simulations, we use the same to-tal mass, . × M (cid:12) , for the primary galaxy, and scalethe secondary to yield the desired mass ratio. The exception is asmall subset of simulations with lower and higher total mass, de-scribed below. For all of our “fiducial mass” simulations, we use agravitational softening length of R soft = 80 pc for baryons and R soft , DM = 240 pc for the dark matter (DM). In each galaxy,4.1% of the total mass is in a baryonic disk component. The pri-mary galaxy has N halo = 4 . × DM halo particles, and for f gas = 0 . it has N disk = 3 . × disk particles, with equal num-bers of gas and star particles. In all other models, N halo and N disk are set such that the same particle mass resolution is maintained foreach component ( m star = 4 . × M (cid:12) , m gas = 2 . × M (cid:12) ,& m halo = 5 . × M (cid:12) ).Each galaxy is given a single BH particle, which as previouslystated, consists of a “seed” BH along with a gas reservoir fromwhich an accretion rate is calculated smoothly. We use a small ini-tial seed mass for the BH, . × M (cid:12) , in accordance with the M BH - M bulge (Magorrian et al. 1998) relation, because our initialgalaxies are pure disks with no bulge component. We find that ourresults are insensitive to the choice of seed mass. The total massof this hybrid particle is the “dynamical” mass of the BH; this isthe mass that is used for gravitational force calculations. This dy-namical BH mass is set to − of the total galaxy mass initially.This value is chosen such that the seed mass and dynamical masshave similar values by the time of the recoil kick, to avoid a dis-parity between the mass used for gravitational forces and that usedfor accretion physics of the recoiling BH. To help ensure that theBH remains in the center of the galaxy prior to the BH merger andrecoil kick, we set the accretion drag force equal to its value forEddington-limited accretion prior to the BH merger (though theactual accretion rate is still calculated self-consistently based onthe Bondi-Hoyle formula). Once the BHs merge, the accretion dragforce is calculated using the actual Bondi-Hoyle accretion rate forthe remainder of the simulation.Our set of fiducial-mass simulations covers a wide range ofgalaxy mass ratios and gas fractions, but in order to probe the ef-fects of GW recoil on black hole - host galaxy relationships, aswe do in § M . For the lower-mass runs,we maintain the same number of particles as in the fiducial simula-tions, such that higher mass resolution is achieved. Accordingly, wereduce the softening lengths in these simulations by ( M/M ) / .For the higher-mass runs ( M × & M × ), an increase in par-ticle number by this factor would be prohibitively computationallyexpensive, so we instead increase the particle number by a factorof 5 in each case, compromising a factor of 2 and 4 in mass res-olution, respectively. In the latter case, we maintain a reasonable M BH /M particle ratio by increasing the initial dynamical mass by afactor of 10.In order to evaluate the sensitivity of our results to numericalartifacts such as the choice of mass resolution, softening length, c (cid:13) , 000–000 Blecha et al.
Figure 1.
Fiducial example of a galaxy merger with BHs but no recoil kick(model q0.5fg0.3a). The gas distribution at time of BH merger (1.97 Gyr) isshown in both the x - y ( top ) and x - z ( bottom ) projections, with the densityscale shown on the right-hand side. The black solid and green dotted linesshow the pre-merger path of the BHs corresponding to the larger and smallergalaxies, respectively. The filled dots denote the BH positions at 500 Myrintervals. The black-and-white dot indicates the position of the merged BHat the moment of merger. and integration accuracy, we have run a number of additional sim-ulations in which we systematically vary these parameters. In ad-dition to these tests, two of the models included in our results havehigher mass resolution (and correspondingly higher spatial reso-lution) than our fiducial runs: our low-mass merger models havethe same number of particles as our fiducial-mass models and thushave 10 and 20 × higher mass resolution. Higher mass and spatialresolution reduce the noisiness of the potential, and varying the res-olution changes the detailed structure of the gas, especially in thehighest density regions. Higher integration accuracy also reducesnumerical noise. Consequently, the exact trajectory, and hence thesettling time, of a given recoil event will be affected to some extentby these numerical factors. However, the variation in recoil trajec-tories for different choices of resolution and integration accuracyare small compared to the differences for varying kick speed andmerger remnant properties. We also define the settling radius of theBH to be R soft to avoid sensitivity of our conclusions to the BHmotion in the innermost galaxy region where the softened potentialmay dominate. Most importantly, for all choices of mass resolu- Figure 2.
For the same simulation shown in Fig. 1 (model q0.5fg0.3a), theevolution of following quantities throughout the simulation is shown, fromtop to bottom: BH accretion rate ( ˙ M BH ), global star formation rate, nor-malized galaxy gas fraction ( f gas /f gas , ), BH mass ( M BH ), and BH sep-aration prior to merger. Vertical lines indicate the time of BH merger. tion, spatial resolution, and integration accuracy parameters tested,the qualitative behavior of the recoiling BHs and the relative differ-ences between simulations are robust. Therefore our main resultsdo not depend on these numerical factors.Table 1 lists the parameters for the galaxy merger models wehave constructed. We have tested a total of 62 different galaxymerger models in which we vary the galaxy mass ratio ( q ), the gasfraction ( f gas ), the orbital configuration. 55 of these models use the“fiducial” primary galaxy mass, and for easier reference we assigneach of these a name given by q[ value ]fg[ value ][ orb ], where “q”denotes the galaxy mass ratio, “fg” denotes the initial gas fraction,and each letter orb is identified with a specific orbital configuration.The remaining seven models have higher or lower total mass andare referred to by q[ value ]fg[ value ]M[ factor ][ orb ], where “M” de-notes the total galaxy mass relative to the equivalent fiducial-massgalaxy.In all cases, the orbital configuration is specified by six pa-rameters, and the galaxies are initially set on parabolic orbits. Thechoice of impact parameter for the first pericentric passage, R peri ,and initial galaxy separation, a i , determine the initial orbital en-ergy and angular momentum. In our fiducial-mass models, we set a i = 143 kpc and R peri = 7 . kpc, except for orbit “b”, which has R peri = 14 . kpc. In our high- and low-mass models, a i and R peri are scaled such that a i is the same fraction (0.625) of the virial ra- c (cid:13)000
For the same simulation shown in Fig. 1 (model q0.5fg0.3a), theevolution of following quantities throughout the simulation is shown, fromtop to bottom: BH accretion rate ( ˙ M BH ), global star formation rate, nor-malized galaxy gas fraction ( f gas /f gas , ), BH mass ( M BH ), and BH sep-aration prior to merger. Vertical lines indicate the time of BH merger. tion, spatial resolution, and integration accuracy parameters tested,the qualitative behavior of the recoiling BHs and the relative differ-ences between simulations are robust. Therefore our main resultsdo not depend on these numerical factors.Table 1 lists the parameters for the galaxy merger models wehave constructed. We have tested a total of 62 different galaxymerger models in which we vary the galaxy mass ratio ( q ), the gasfraction ( f gas ), the orbital configuration. 55 of these models use the“fiducial” primary galaxy mass, and for easier reference we assigneach of these a name given by q[ value ]fg[ value ][ orb ], where “q”denotes the galaxy mass ratio, “fg” denotes the initial gas fraction,and each letter orb is identified with a specific orbital configuration.The remaining seven models have higher or lower total mass andare referred to by q[ value ]fg[ value ]M[ factor ][ orb ], where “M” de-notes the total galaxy mass relative to the equivalent fiducial-massgalaxy.In all cases, the orbital configuration is specified by six pa-rameters, and the galaxies are initially set on parabolic orbits. Thechoice of impact parameter for the first pericentric passage, R peri ,and initial galaxy separation, a i , determine the initial orbital en-ergy and angular momentum. In our fiducial-mass models, we set a i = 143 kpc and R peri = 7 . kpc, except for orbit “b”, which has R peri = 14 . kpc. In our high- and low-mass models, a i and R peri are scaled such that a i is the same fraction (0.625) of the virial ra- c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies dius, R , and a i / R peri = 20 . We denote these orbits with lettersw - z to differentiate them from the orbits a - k of our fiducial-massmergers. Note that the orbital parameters do not remain constant asthe merger progresses, owing to energy losses via dynamical fric-tion. The angles ( θ , φ ) and ( θ , φ ) determine the initial orbitalphase and inclination, respectively, of each galaxy. These angles,as well as R peri for each galaxy model are given in Table 1. Ourfiducial merger orbit (orbit “a”) is a “generic” orbit, in that no sym-metries exist in the initial orientation angles of the disks. Note thatmany of these orbits are identical to those used in Cox et al. (2006)and Robertson et al. (2006a).For each model, we run a merger simulation in which the BHsare not allowed to merge. From this we can determine t coal , whichis used to set t mrg . Then, restarting slightly before t mrg , we simu-late both a merger with no recoil kick and a merger with v k / v esc =0 . . For the models shown in boldface in Table 1, we also simu-late recoil kicks with v k / v esc = 0 . , . , . , . , . , . , . , and1.2. Each simulation is run for 2.9 Gyr after t mrg . Finally, using theq0.5fg0.3a model, we simulate a small sample of recoil kicks withvarying kick orientation ( θ k , φ k ), the results of which are discussedin § We begin by examining galaxy merger simulations with no GW re-coil kick given to the BHs. Some basic characteristics of a galaxymerger simulation with q = 0 . and f gas = 0 . (our “fiducial”merger, model q0.5fg0.3a) are illustrated in Figs. 1 & 2. Fig. 1shows the gas distribution at the time of BH merger, as well asthe paths of the two BHs prior to merger. The gas distributionis very irregular, with distinct tidal streams. The inner region ofthe merger remnant is also lumpy and irregular. In other words,the initial disk structure of the progenitors has been destroyed bythe merger, and the remnant is still highly disturbed at the timeof BH coalescence. Fig. 2 shows the BH accretion and star for-mation throughout the simulation as well as the evolution of theBH separation prior to merger. This example illustrates some char-acteristics that are generic to our galaxy merger simulations. Si-multaneous bursts of star formation and BH accretion occur afterthe first close pericentric passage and at final coalescence (Mihos& Hernquist 1994b, 1996) as the result of gas inflows caused bygravitational torques (Barnes & Hernquist 1991, 1996). As we shalldemonstrate, these gas inflows can greatly influence the dynamicsof ejected black holes by deepening the central potential and byproviding additional drag force. Note that because our simulationsinclude star formation throughout, the gas fraction at the time ofBH merger is significantly lower than its initial value; in the exam-ple shown, 60% of the initial gas has been consumed by t mrg . Bythe end of the simulation, 2.9 Gyr after the merger, almost 80% ofthe gas has been depleted by star formation, and the BH accretionrate is very low. In our other merger models, 47-80% of the initialgas is depleted by the time of BH merger, and 62-88% is depletedby the end of the simulation. The final black hole mass in this ex-ample ( . × M (cid:12) ) is also typical of our fiducial-mass mergers.Fig. 3 shows gas and stellar density distributions of this fidu-cial (q0.5fg0.3a) model and five other merger models. Each plotshows gas and stellar density from three different projections.These examples are chosen to illustrate the generic nature of themorphological features mentioned above. In all cases, the mergerremnants are visibly disturbed and lumpy. Tidal tails are ubiqui-tous, though their size and density varies. Higher- f gas mergers have more compact remnants (Robertson et al. 2006b; Dekel & Cox2006; Hopkins et al. 2008a; Hopkins & Hernquist 2010a). Lower- q mergers are less strongly disrupted; a disk-like structure can beseen in the x − z orientation of model q0.25fg0.3a. A special caseis shown in the lower-right corner of Fig. 3. Model q0.5fg0.3h hasa coplanar orbit with both galaxies rotating prograde to the orbitalmotion. Due to the highly aligned orbit, the disk structure of theprogenitor galaxies is preserved in this merger remnant; tidal fea-tures are visible only from the face-on ( x − y ) projection. Our other“highly aligned” orbits (i, j, & k) result in similar remnant mor-phologies; they are included in our suite of merger models mainlyfor comparison, as mergers generally will not have such carefulalignment.As mentioned in §
2, in nearly equal-mass, gas rich merg-ers, the potential well in which the BH sits may deepen rapidlyduring final coalescence. Once the merger is complete, the rem-nant central potential will become shallower as the central stellarregion begins to relax. The phase of rapid v esc fluctuation coin-cides with the time of BH coalescence and may therefore affectrecoiling BH dynamics. Fig. 4 shows the evolution of the BH es-cape speed ( v esc ) for four merger simulations without recoil kicks.The solid lines denote t mrg and v esc ( t mrg ), while the dotted linesdenote the maximum (post-merger) value of v esc and the time atwhich it occurs. The difference between v esc ( t mrg ) and v esc , max is small in all except the top left panel, which shows the q1fg0.4amerger. It is clear that the escape speed, and hence the trajectory,of a kicked BH in this model will depend on whether the kick oc-curs at t coal or at some slightly later time. However, the sharp in-crease of v esc occurs only in gas-rich, nearly-equal-mass mergers.The other three panels in Fig. 4 show v esc vs. t for a sample of sim-ulations with lower q and f gas ; in these models, v esc is much lessvolatile during and after the BH merger. Moreover, the exampleshown in Fig. 4 is not the most gas-rich of our merger models butis chosen because of the large difference between v esc ( t coal ) and v esc , max , 34%. Larger differences between these quantities yieldlarger uncertainty in our results for BH dynamics when the recoilkick is assigned at t mrg = t coal . The final four columns in Table 1give t mrg , v esc ( t mrg ), v esc , max , and the fractional difference be-tween v esc ( t mrg ) and v esc , max for each merger model. All merg-ers with f gas < . have < ∼ difference between v esc ( t mrg )and v esc , max , and mergers with q < . have < difference.Therefore, while our results for nearly equal-mass, gas-rich merg-ers are subject to the assumption that the BH merger occurs on ashort timescale, the results for our other models are insensitive tothe merger time. We explore further the case of gas-rich, q ∼ mergers in § A universal feature of our recoil trajectories is that they havelow-angular-momentum orbits, which occurs because the centrally-concentrated baryonic component of the galaxy dominates the BHtrajectories even when they extend far into the halo. Consequently,we refer throughout the paper to the trajectories as “oscillations” ofthe BH about the galactic center. We see this clearly in Fig. 5, whichshows the trajectories of BHs kicked with v k / v esc = 0 . − . foreight different merger models. Also readily apparent in these plotsis the variation in BH oscillation amplitude and duration betweenmodels. For a fixed value of v k / v esc , BHs travel further from the c (cid:13) , 000–000 Blecha et al.
Figure 3.
Projected gas (yellow/red) and stellar (blue) density distributions for six different merger models, shown at the time of BH merger in each case. Theblack-and-white dot indicates the position of the BH in each panel. The spatial scale of all panels is 86 kpc, and the projection ( x - y , x - z , or y - z ) is labeled oneach panel. The models shown are (clockwise from top left, also labeled on each plot) q0.5fg0.3a, q1fg0.3a, q1fg0.3c, q0.5fg0.04a, q0.25fg0.3a, & q0.5fg0.3h. galactic center in mergers with lower q and f gas . In the q1fg0.6amodel, BHs kicked with v k = 0 . v esc ( = 878 km s − ) travel < kpc from the galactic center, while in the collisionless q1fg0amodel, the same v k / v esc allows the BH to travel ten times further.Note that scaling the kick speeds to v esc is important for deter-mining the trends between galaxy models; v esc ( t mrg ) for all of ourmodels ranges from − km s − ( − km s − forthe fiducial-mass models). The trend toward smaller recoil oscilla-tion amplitude for higher f gas occurs because higher gas fractionsresult in more compact remnants that have higher central densities, and these remnants also have larger available supplies of gas. Bothfactors contribute to steeper central potentials and increased gasdrag and dynamical friction. We can also see from Fig. 5 that recoiloscillations are slightly larger for lower q , though the trend is moreevident in higher- f gas remnants. Higher mass ratio mergers createstronger perturbations that drive gas more efficiently to the galax-ies’ central regions, further contributing to the steep potentials andhigh densities.We can see these trends more clearly in Fig. 6. The topplot shows the maximum galactocentric distance of each orbit in c (cid:13)000
Projected gas (yellow/red) and stellar (blue) density distributions for six different merger models, shown at the time of BH merger in each case. Theblack-and-white dot indicates the position of the BH in each panel. The spatial scale of all panels is 86 kpc, and the projection ( x - y , x - z , or y - z ) is labeled oneach panel. The models shown are (clockwise from top left, also labeled on each plot) q0.5fg0.3a, q1fg0.3a, q1fg0.3c, q0.5fg0.04a, q0.25fg0.3a, & q0.5fg0.3h. galactic center in mergers with lower q and f gas . In the q1fg0.6amodel, BHs kicked with v k = 0 . v esc ( = 878 km s − ) travel < kpc from the galactic center, while in the collisionless q1fg0amodel, the same v k / v esc allows the BH to travel ten times further.Note that scaling the kick speeds to v esc is important for deter-mining the trends between galaxy models; v esc ( t mrg ) for all of ourmodels ranges from − km s − ( − km s − forthe fiducial-mass models). The trend toward smaller recoil oscilla-tion amplitude for higher f gas occurs because higher gas fractionsresult in more compact remnants that have higher central densities, and these remnants also have larger available supplies of gas. Bothfactors contribute to steeper central potentials and increased gasdrag and dynamical friction. We can also see from Fig. 5 that recoiloscillations are slightly larger for lower q , though the trend is moreevident in higher- f gas remnants. Higher mass ratio mergers createstronger perturbations that drive gas more efficiently to the galax-ies’ central regions, further contributing to the steep potentials andhigh densities.We can see these trends more clearly in Fig. 6. The topplot shows the maximum galactocentric distance of each orbit in c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies Figure 4. BH v esc vs. time for a sample of four galaxy merger simulations with no recoil kick imparted to the BH. ( v esc ≡ (cid:112) − x BH ) .) In each panel, thetwo curves represent v esc of each BH prior to merger. After the merger, the escape speed of the remnant BH is shown. The solid vertical and horizontal linesmark the time of BH merger, t mrg , and the BH escape speed at that time, v esc ( t mrg ). The dotted vertical and horizontal lines denote the (post-merger) time ofthe maximum escape speed and its value. Top left panel: q1fg0.4a; top right panel: q0.5fg0.4d; lower left panel: q0.333fg0.4a; lower right panel: q1fg0.04a.
Fig. 5, normalized to the half-mass effective radius of the galaxy( R max / R eff ). The bottom plot shows the settling time, t settle , de-fined as the time when the apocentric distance of the BH oscil-lations, relative to the stellar center of mass, falls below R soft .This definition is chosen to avoid following BH trajectories below ascale where their oscillations may be dominated by numerical noiseor gravitational softening. We find that our conclusions are not sen-sitive to the exact definition of t settle . Note that for some high-velocity recoils (for all recoils in the collisionless simulations), wehave only lower limits on t settle , because in these cases the BH didnot settle by the end of the simulation.In the top panel of Fig. 6, the curves for a given f gas lie nearlyon top of each other. This supports our assertion that the initialgas fraction is more important than the mass ratio in determining R max / R eff for a given v k / v esc . By normalizing these quantities. weessentially isolate the effects of gas drag or potential shape fromvariation in galaxy size or central potential depth. One can easilysee from Fig. 6 that, especially for lower v k / v esc , a gas fraction ≥ can reduce the amplitude of BH oscillations by up to anorder of magnitude with respect to a purely collisionless system.Note that R max / R eff is at least as large for f gas = 0 . as it isfor f gas = 0 . , opposite the trend we expect if gas drag dominatesthe BH trajectories. However, galaxies with higher f gas generallyhave higher star formation rates, so systems with initial gas frac-tions of . − . will have similar amounts of gas by the timeof the BH merger. Furthermore, as previously stated, higher gas fractions yield more concentrated merger remnants (smaller R eff ).Combined, these effects result in similar R max / R e for recoils inmergers with initial f gas = 0 . − . .As discussed in §
2, the recoil trajectories may be sensitiveto numerical parameters such as resolution or integration accuracy.In particular, because R eff is of the order of a few kpc, recoilingBHs with R max /R eff < ∼ . spend substantial time at or below thespatial resolution limit. R max and t settle are therefore approximatein these cases. The BH settling times are also susceptible to possi-ble inaccuracies in dynamical friction forces due to our finite massresolution, which is likely to result in underprediction of the trueamount of dynamical friction. However, we can predict that theeffect of this uncertainty on our results is likely to be small; inour lower-mass galaxy mergers, which have × and × bettermass resolution, BHs kicked near the escape speed still experi-ence very little dynamical friction and have very long wanderingtimes. Even if dynamical friction is still underestimated in thesehigher-resolution runs, it is clear that in general, recoils near theescape speed will result in wandering times of at least a few Gyr,and that in gaseous mergers, recoiling BHs with v k < ∼ . v esc re-main within the central kpc of the galaxy. Finally, because we usethe same mass resolution in all of our simulations (excepting thelow/high mass runs), the relative trends that we find between dif-ferent galaxy models are robust.We expect some variation in R max for different merger or-bits as well. In the set of eleven different orbital configurations we c (cid:13) , 000–000 Blecha et al.
Figure 5.
In each plot, BH recoil oscillation amplitudes are shown for varying kick velocities within a single model. The x -axis is the time after the BH merger, t − t mrg . The color-coded numbers on each plot indicate v k / v esc for each curve. Galaxy models shown are, from left to right and top to bottom: q1fg0.6a,q0.5fg0.6a, q1fg0.3a, q0.5fg0.3a, q1fg0.1a, q0.5fg0.1a, q1fg0a, q0.5fg0a. c (cid:13)000
In each plot, BH recoil oscillation amplitudes are shown for varying kick velocities within a single model. The x -axis is the time after the BH merger, t − t mrg . The color-coded numbers on each plot indicate v k / v esc for each curve. Galaxy models shown are, from left to right and top to bottom: q1fg0.6a,q0.5fg0.6a, q1fg0.3a, q0.5fg0.3a, q1fg0.1a, q0.5fg0.1a, q1fg0a, q0.5fg0a. c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies Figure 6. R max /R eff ( top window ) and t settle ( bottom window ) are plot-ted versus v k / v esc for the eight models whose trajectories are shown inFig. 5. t settle is defined as the time after the BH merger at which the apoc-entric distance of the BH orbits drops below R soft . Arrows denote lowerlimits on t settle in cases when the BH has not settled by the end of thesimulation (defined as t mrg + 2 . Gyr). simulated with q = 0 . & f gas = 0 . , the central escape speedsat t mrg vary from − km s − . Since the total mass in allof these simulations is constant, the variation in v esc reflects dif-ferences in the central concentration, and hence the steepness ofthe potential well. We simulate recoil trajectories in each of thesewith v k / v esc = 0 . , and find that R max / R eff = 4 − . Based onthis example, we see that the merger orbit alone can influence theremnant central potential well enough to change the amplitude ofrecoil trajectories by a factor of ∼ .Fig. 7 shows two examples of recoil trajectories in three dif-ferent projections as well as R ( t ) . The top plot shows a recoil eventwith v k / v esc = 0 . , which in this model (q0.5fg0.3a) correspondsto v k ≈ km s − . Note that the orbit is highly non-planar; itlooks similar in all three projections. The orbit is also centrophilic,which as we have noted is common to all of our recoil simulations.The average orbital period is short, ∼ × yr, and t settle ∼ Myr, such that the BH settles to the center well before the end ofthe simulation.Recoil events with velocities near v esc produce long-lived ( > Gyr), large-amplitude BH oscillations. Many of these oscillationsstill have large amplitudes at the end of the simulation, 2.9 Gyr af-ter the BH merger, so we have only lower limits on t settle . Thebottom plot in Fig. 7 illustrates this type of recoil event, againfor the q0.5fg0.3a model. The trajectory shown has a kick speedof v k / v esc = 0 . , so v k ≈ km s − . The amplitude of these Figure 7.
Top four windows: trajectory for the v k / v esc = 0 . recoil sim-ulation with the q0.5fg0.3a model. Bottom four windows: trajectory forthe v k / v esc = 0 . recoil simulation with the q0.5fg0.3a model. In eachcase, the four windows show the trajectories in the x − y , x − z , and y − z projections, as well as the BH’s galactocentric distance versus time. Notethe greatly different spatial scales of the two simulations. oscillations is ∼ kpc, almost two orders of magnitude greaterthan in the lower- v k example. Although the BH only completesfive orbits before the end of the simulation, we can see that againthere is no evidence for a preferred orbital plane; the orbit is three-dimensional. Because the oscillation amplitude is so large andshows no sign of damping out by the end of the simulation, it islikely that such an orbit will not return to the galaxy center within aHubble time, and certainly not within the mean time between majorgalaxy mergers. Such BHs essentially can be considered “lost” tothe galaxy. If in other cases the BHs do return to the galactic center c (cid:13) , 000–000 Blecha et al. after several Gyr and another galaxy merger has taken place in themeantime, the returning and new BHs could form another binary.In recoil events with v > v esc , the rapidly recoiling BH canonly take a small amount of gas with it; only gas that is orbitingthe BH with v orb > ∼ v k stays bound to the BH when it is ejected.The accretion timescale and luminosity of these ejected disks isdiscussed in § v − .) These escaping BHsare therefore likely to wander indefinitely, undetected, through in-tergalactic space. As illustrated in Fig. 4, v esc can increase significantly during coa-lescence in equal-mass, gas-rich mergers. To better understand howthis may affect BH trajectories, we have run a series of simulationswith the BH merger (and recoil kick) occurring at sequentially latertimes using model q1fg0.4a. The v esc evolution of model q1fg0.4ais replotted in the top window of Fig. 8, with the fiducial mergertime, t mrg = t coal , marked by the solid black line and the subse-quent merger times tested marked by black dashed lines. We havetested simulations with each of these merger times twice, oncewith v k = 1000 km s − and once with v k / v esc ( t mrg ) = 0 . . Byconducting the second experiment we are normalizing to the evolv-ing depth of the central potential well, which helps us to separatethe gravitational and drag effects on the trajectories.Fig. 8 shows R max for the BH orbits in each of these varying- t mrg simulations, with the v k = 1000 km s − simulations in themiddle panel and the v k / v esc ( t mrg ) = 0 . simulations in the bot-tom panel. As v esc increases from 1100 km s − at t coal to al-most 1500 km s − at its maximum, the amplitudes of BH trajec-tories from constant- v k recoil events decrease by more than twoorders of magnitude. However, the bottom panel of Fig. 8 showsthat when v k is set to a constant fraction of the escape speed,the BHs kicked from deeper potential wells (larger v esc ) still havesmaller-amplitude trajectories, but the variation is much less se-vere than when v k = constant. The variation that persists even forfixed v k / v esc can be attributed to the enhanced gas drag and dy-namical friction, as well as the steeper central potential well, thatresult from the rapid formation of the central dense cusp. At verylate merger times, − Myr after t coal , the opposite trendis seen. The amplitude of constant- v k trajectories increases by al-most an order of magnitude from the minimum at t coal + 70 Myrto the value at t coal + 500 Myr. This is partly because the centralpotential becomes shallower as the merger remnant begins to relax.The same trend occurs at late times in the constant- v k / v esc simula-tions, because the potential well also becomes less steep, and gasdrag becomes less efficient as more of the gas is consumed in starformation. We note that merger times up to t coal + 500 Myr areincluded here only for illustrative purposes; in reality, such delayedmergers are probably unrealistic in gas-rich systems.If the BHs are able to merge rapidly, before the central po-tential reaches its maximum depth, another interesting effect canoccur. During the period of rapid central potential evolution, thetimescale on which v esc increases is typically much shorter thanthe timescale for a recoiling BH orbit to decay via gas drag or dy-namical friction. Consequently, on its first several pericentric pas-sages through the central region, the BH encounters an increas-ingly deep potential well, and its velocity is actually boosted by (cid:10) (cid:5) (cid:1)(cid:16)(cid:1)(cid:14)(cid:11)(cid:15)(cid:1)(cid:10) (cid:3)(cid:8)(cid:2) (cid:12)(cid:9) (cid:6)(cid:7)(cid:4) (cid:13)(cid:1) Figure 8.
Top window: v esc is plotted as a function of t − t coal for theq1fg0.4a merger simulation. The portion shown here is a zoom-in of thetop-left window in Fig. 4. The solid vertical line denotes t coal , and thedashed vertical lines denote the subsequent merger times used to test vari-ation in t mrg . Middle window: R max /R eff is plotted versus BH mergertime for the set of delayed-merger simulations done using model q1fg0.4a.Each recoiling BH in these simulations is assigned a recoil kick of kms − . Bottom window:
Same as middle window, but for a set of simula-tions in which the kick speed in km s − varies, but is held to a con-stant value of v k / v esc ; in every case v k / v esc = 0 . . The x -axis rangesfrom t mrg = t coal to t mrg = t coal + 500 Myr. a small amount, such that the ratio v BH / v esc is roughly constant onsubsequent pericentric passages. Because only v BH in creases, not v BH / v esc , the BH’s galactocentric distance is not boosted beyondits initial maximum, R max , and once the rapid potential evolutionceases, drag forces become dominant and the velocity begins to de-cay. This effect is by design short-lived, and it is strongest whenthe BH orbital timescale is short, such that the BH orbit is domi-nated by the dynamics of the inner galaxy region. These velocityboosts are therefore mostly an interesting illustration of the sensi-tivity of recoil dynamics to the BH merger time, although we willsee some implications of this effect for the recoiling AGN lifetimescalculated in § × yr in the BH mergermay significantly reduce the amplitude and duration of recoilingBH oscillations. Based on results from numerous hydrodynamicsimulations of binary BH inspiral (e.g., Escala et al. 2005; Dotti c (cid:13) , 000–000 ecoiling Black Holes in Merging Galaxies Figure 9.
Top window: distribution of R max for our set of ( θ, φ ) (cid:54) = (0,0) simulations, normalized to R max (0, 0) for each correspond-ing v k / v esc value. The set of simulations includes runs with v k / v esc = (cid:104) P orb (0 , (cid:105) . et al. 2007), we have good reason to believe that BHs in gas-richsystems merge efficiently in general, but the merger time of a givenBH binary is impossible to predict with this precision. By assum-ing t mrg = t coal in our simulations, we exclude the possibility ofdelayed mergers, but we also take steps to ensure that this has aminimal effect on our results. First, only a small number of oursimulations have large variation in v esc . In these cases, we see bycomparing Figs. 6 & 8 that the variation in oscillation amplitudesfor a given v k / v esc due to evolving central density (less than a factorof 10) is generally much less than the variation for different valuesof v k / v esc (up to three orders of magnitude). All of the analysis inthis study is presented in terms of v k / v esc . Therefore, the dramaticsuppression of recoil trajectories with fixed v k , while an importantresult in itself, does not affect our other conclusions. Most of our recoiling BHs have v k > ∼ km s − , in which casetheir kicks will be oriented out of the orbital plane of the binary(Campanelli et al. 2007a,b; Lousto & Zlochower 2009). However,because the BH binary inspiral occurs on sub-resolution scales inour simulations, the binary orbital angular momentum vector can-not be predicted. Furthermore, the galactic disk structure of themerger progenitors is disrupted by major mergers (see Fig. 3),except when the galaxies have nearly coplanar orbits. In genericmergers, there is no obvious reference direction in which to ori-ent the recoil kick with respect to the progenitors’ initial structure.Clearly, on certain recoil trajectories (i.e., along tidal tails or centralclumps) a BH will encounter denser gaseous regions than on oth-ers. However, it is unclear a priori whether these density variations are sufficient to cause significant variation in BH recoil trajectories.In most of our simulations, we simply orient the recoil kick alongthe z -axis of the simulation, ( θ k , φ k ) = (0 , , in the coordinatesystem with respect to which the initial galaxy orbits are assigned.Here, we examine a subset of simulations with varying kick orien-tation to determine the sensitivity of our results to this choice.We test a sample of different kick orientations with threedifferent values of v k / v esc (0.6, 0.8, & 0.9) in our q1fg0.3a andq0.5fg0.3a merger models. As a gauge of how the BH trajecto-ries differ among this sample, we calculate the maximum galac-tocentric distance ( R max ) and average orbital period ( (cid:104) P orb (cid:105) ) ofthe BH in each simulation. Fig 9 shows the distributions of thesequantities, normalized to R max and (cid:104) P orb (cid:105) of the ( θ k , φ k ) = (0, 0)simulations for each corresponding v k / v esc value. The q0.5fg0.3adistributions peak slightly below 1.0 and the q1fg0.3a distributionspeak slightly above 1.0, but the combined histogram is distributedfairly evenly around unity. In other words, the ( θ k , φ k ) = (0, 0)kick orientation is not a “special” direction. The overall variationin R max / R max (0, 0) for each model is less than a factor of 4. Incontrast, Fig. 5 shows that R max is almost two orders of magni-tude higher for v k / v esc = 0 . than for . . Clearly, the amplitudeand duration of BH oscillations depends much more strongly onthe kick magnitude than its direction, and we need not concern our-selves too much with our choice of kick orientation. Fig. 10 compares the BH accretion and star formation historiesfor simulations of the q0.5fg0.3a merger model with v k = 0 and v k / v esc = 0 . − . . The top windows in Fig. 10 show thateven kicks with v k / v esc = 0 . − . produce qualitatively differ-ent AGN lightcurves (as inferred from ˙ M BH ) than in the zero-kickcase, although the final BH masses are similar. In these cases, thepeaks in accretion rate at coalescence ( t ≈ Gyr) are slightly lowerdue to the sudden removal of the BHs from the highest-density re-gion. However, the BHs remain within 1 kpc of the galactic center,and accretion continues through the end of the simulation at higherrates than in the zero-kick case. Thus, although the total mass ac-creted is about the same for v k / v esc = 0 − . , the active lifetimeis longer when a recoil kick occurs.In the v k / v esc = 0 . simulation, the BH accretion cuts offmore sharply at t mrg and is subsequently highly variable, due tothe larger-amplitude, longer-lived BH oscillations. Unlike the BHswith lower-velocity recoils, this BH attains a noticeably lower finalmass than its zero-kick counterpart.For recoil kicks > ∼ . v esc , the BH accretion cuts off sharplyat t mrg , and the BH subsequently accretes very little gas as it trav-els on large, long-period orbits that extend well into the halo. Thesehigh-velocity recoil events therefore reduce the AGN lifetime. Ad-ditionally, the BH mass is essentially frozen at its value at t mrg ,which is about half that of the stationary BH mass. If the BH doesreturn to the galaxy center after several Gyr, most of the galaxy’sgas will have been consumed in star formation, so the BH will re-main undermassive. In the galaxy merger models we have used, theBH mass deficits for high-velocity recoils versus no recoil rangefrom a factor of ∼ (almost no deficit) to ∼ . These BH massdeficits and their implications are discussed in § t AGN ) c (cid:13) , 000–000 Blecha et al.
Figure 10.
The same quantities for model q0.5fg0.3a are plotted as in Fig. 2, but here they are shown for simulations with v k / v esc = 0 . − . in addition tothe v k = 0 case. The red lines in the ˙ M BH plots (top row) correspond to the accretion rate calculated from our ejected-disk model as described in § v k (cid:54) = 0 plots, the v k = 0 curves are drawn again with dashed lines, except for the ˙ M BH plots where the dashed lines are omitted for clarity. for both stationary and recoiling BHs in six different galaxy mod-els for which we have varied v k . Fig. 11 shows the results, withcolored lines indicating t AGN for recoiling BHs as a functionof v k and black horizontal lines indicating t AGN for a station-ary BH in the corresponding merger model. In order to differ-entiate between bright AGN and low-luminosity AGN, we calcu-late t AGN assuming three different definitions of an “active” BH.The thick solid lines in the figure are calculated assuming the BHis an AGN when L bol > L Edd , and the thin solid lines as-sume L bol > L Edd . Because these quantities depend on the BHmass, we use an absolute luminosity value for our third AGN def-inition: L bol > L min (denoted by the dashed lines in Fig. 11). Wechoose L min = 3 . × L (cid:12) , which is . L Edd for a M (cid:12) BH.In these models, the low-luminosity AGN lifetime is gener-ally enhanced by moderate-velocity recoil events, and the brightAGN lifetime is generally reduced. Although the details depend onthe model parameters and kick speed, in all models, t AGN falls offsteeply at high v k / v esc , when the BH is ejected far enough from thecenter on large enough orbits that Bondi accretion becomes inef- fective. This corresponds to the accretion behavior seen in the lastcolumn of Fig. 10 ( v k / v esc = 0 . ).For smaller v k , such that the BH is confined to the central fewkpc, the dependence of t AGN on the nature of the merger remnantis more complex. We examine first the relatively gas-poor models(those with initial f gas = 0 . ). In the q1fg0.1a model, t AGN is en-hanced only for v k / v esc ≤ . and falls precipitously at higher v k .In the q0.5fg0.1a model, recoil events always reduce the AGN life-time. Merger remnants with less gas have smaller central gas reser-voirs to fuel the BH during pericentric passages, and their shallowercentral potentials result in larger BH orbits, which have fewer peri-centric passages. Consequently, in gas-poor remnants, t AGN willgenerally be lower for recoiling BHs than for stationary BHs.In gas-rich merger remnants, t AGN is more readily enhancedby GW recoil. Stationary BHs in gas-rich mergers typically expe-rience a bright AGN phase due to the rapid inflow of cold gas tothe central region, which is terminated when the AGN feedbackenergy heats the surrounding gas enough to quench the BH fuel-ing. Fig. 11 shows that although GW recoil shortens this brightAGN phase, the low-luminosity t AGN is enhanced for recoil kicks c (cid:13) , 000–000 ecoiling Black Holes in Merging Galaxies Figure 11.
AGN lifetimes ( t AGN ) of recoiling BHs with v k / v esc = 0 . − . , compared to t AGN for v k = 0 in six different galaxy models. In each plot,the black lines indicate the stationary AGN lifetimes and the colored lines indicate the recoiling BH lifetimes at each value of v k / v esc . The models shownare (from top left): q1fg0.6a (red), q1fg0.3a (blue), q1fg0.1a (green), q0.5fg0.6a (magenta), q0.5fg0.3a (cyan), and q0.5fg0.1a (gold), as indicated in the plotlabels. The different line types denote t AGN according to three different definitions of an “active” BH. For the thin and thick solid lines, t AGN is defined as thetime for which the BH luminosity L bol > and L Edd , respectively. The dashed lines show t AGN for which L bol > L min , where L min = 3 . × L (cid:12) , or . L Edd for a M (cid:12) BH. In all cases L bol is calculated from the Bondi-Hoyle accretion rate as described in the text. No cuts have been appliedto t AGN based on the BH settling time, t settle , so in some cases t AGN includes accretion that occurs after the BH settles back to the galactic center. as high as v k / v esc = 0 . . In these cases, the recoiling BHs are ontightly-bound orbits and can accrete gas during their numerous pas-sages through the central dense region. Because they remain in mo-tion, however, their feedback energy is spread over a much greatervolume than for stationary BHs. As a result, the gas encounteredby the recoiling BHs never heats up enough to completely cut offthe BH fuel supply, and the BH has a longer lifetime as a low-luminosity AGN. In contrast to the traditional “feast or famine”model of merger-triggered AGN fueling, these short-period recoil-ing BHs are more inclined to “nibble”. We can see evidence of this displaced AGN feedback throughits effect on star formation. The bottom row of Fig. 10 shows thedepletion of gas throughout each simulation, normalized to the ini-tial gas fraction, and the dotted lines show the v k = 0 curve in eachof the other plots. It is evident that slightly less gas remains at theend of each higher- v k simulation. In the merger with a stationaryBH, this gas is accreted or expelled from the galactic center viafeedback, but when the central BH is removed, the gas continuesbe consumed by star formation. Although in this example the starformation rate enhancement is small and difficult to discern from c (cid:13) , 000–000 Blecha et al. examining the SFR evolution alone, the effect can be much largerin higher- q , f gas mergers. We explore in § t AGN may be enhanced by GWrecoil for low-luminosity AGN, we emphasize that the bright AGNphase (
L > L Edd ) is always shorter for recoiling BHs than forstationary BHs, or at best roughly equal. This is a direct result ofthe peak accretion episode being disrupted at the time of the recoilkick. The important consequence of this is that the total accretedBH mass is never enhanced by GW recoil in our simulations. Formoderate recoil speeds, the BH mass deficit relative to a stationaryBH is generally slight, but we find that the effect of recoil is always to decrease the final BH mass. The implications of this finding arediscussed in § v k = 0 ,the two main accretion episodes are associated with the periods ofrapid star formation. This means that the AGN luminosity may bedifficult to distinguish from the starburst luminosity, and the AGNmay also be dust-obscured for at least part of its active phase. IfGW recoil allows the AGN to remain active long after the starburstis complete, such an AGN might be more readily observable, be-cause it would no longer be competing with the starburst luminosityand may also be less dust-obscured. We have seen that moderate-velocity recoils in gas-rich remnantsmay allow efficient accretion from ambient gas. However, a BHmoving rapidly or in a low-gas-density region is unlikely to sweepup much gas from its surroundings, and we would expect the prob-ability of observing this type of active BH to be low. Indeed, in oursimulations, the Bondi accretion rate of the BH rapidly declinesfollowing a large recoil kick (see Fig. 10). The possibility not ac-counted for in our simulations is that, if the BH is surrounded byan accretion disk at the time of recoil, some amount of this gas mayremain bound to the recoiling BH. We therefore implement an ana-lytic model to calculate the BH accretion rate from this ejected gasdisk, based on the BH mass and accretion rate at the moment ofrecoil.The BH carries with it the part of the accretion disk where v orb > ∼ v k ; i.e., it will carry a disk with radius approximately R ej ∼ GM BH /v k2 . This is a reasonable approximation if the BHis kicked directly out of the orbital plane of the disk, as is the casewhen v k > ∼ km s − and the BH orbital plane is aligned withthat of the disk. If the accretion rate from this ejected disk is highenough, such a system could potentially be seen as an offset AGNvia either resolved spatial offsets or offset spectral lines. BL08 pre-dicted accretion timescales of < ∼ − Myr for the type of re-coiling BHs we consider here ( M BH ∼ − M (cid:12) ; v k ∼ − km s − ), assuming a constant- ˙ M model. Here, we im-prove on these estimates by calculating a time-dependent accretionrate for the ejected disk.We assume the innermost region of the gas disk is well-modeled by a viscous, Keplerian, thin disk (specifically, an α -disk,Shakura & Sunyaev (1973)). The evolution of the disk surface den-sity, Σ , can be described by a diffusion equation: ∂∂t Σ( R, t ) = 3
R ∂∂R (cid:104) R / ∂∂R (cid:0) ν Σ R / (cid:1)(cid:105) , (1)where ν is the kinematic viscosity (see, e.g., Lynden-Bell & Pringle1974; Pringle 1981). The steady-state solution is recovered when the left-hand side of the equation vanishes, but this is not the casefor our ejected disk, which is no longer fed at its outer radius. Exactanalytic solutions to Eq. (1) can be found when ν scales only withradius (Lynden-Bell & Pringle 1974), but in the α -disk model, ν isa function of both R and Σ . Pringle (1991) has derived self-similarsolutions to this equation for viscosity scaling as ν ∝ Σ m R n .These solutions assume a disk with no inner radius, so for our casewe must neglect the finite inner disk radius at the innermost sta-ble circular orbit of the BH ( R ISCO ), as well as the possibility ofa circumbinary gap in the disk that persists after the BH merger.This should not affect our results, however, as the ejected disk willbe much larger than the ISCO ( R ej /R ISCO > ), and the gapis expected to refill on a timescale of years (Milosavljevi´c & Phin-ney 2005; Tanaka & Menou 2010). For an α -disk in which viscos-ity is assumed to scale with gas pressure and the opacity equalsthe electron-scattering value ( κ es ≈ . cm g − ), the viscosity isgiven by ν = C R Σ / , (2) C ≡ (cid:18) k B αµ m p (cid:19) / (cid:16) κ es σ SB G M BH (cid:17) / . In this equation k B is Boltzmann’s constant, α is the thin-disk vis-cosity parameter, µ is the mean molecular weight, m p is the protonmass, and σ SB is the Stefan-Boltzmann constant. This correspondsto the self-similar solution of Pringle (1991) with m = 2 / , n = 1 (see also Cannizzo et al. 1990): Σ( R, t )Σ = (cid:16) tt (cid:17) − / f (cid:20)(cid:16) RR (cid:17) (cid:16) tt (cid:17) − / (cid:21) , (3) f [ u ] ≡ (28) − / u − / (1 − u / ) / . The arbitrary constants Σ , t , and R satisfy t − = C Σ / R . (4)Integrating Eq. (3) yields a time-dependent expression for diskmass: M d ( t ) = (28) / π R Σ (cid:16) tt (cid:17) − / . (5)From this we obtain the time-dependent accretion rate: ˙ M d ( t ) = −
316 (28) / π R Σ t (cid:16) tt (cid:17) − / . (6)We determine Σ , t , and R using Eq. (4) along with the con-ditions that M d ( t (cid:48) ) = M ej and ˙ M d ( t (cid:48) ) = ˙ M mrg , where t (cid:48) = t + t sim − t mrg , t sim is the time in the simulation, M ej is theejected disk mass, and ˙ M mrg is the Bondi accretion rate calculatedin the simulation at the time of merger. The mass evolution of thedisk is therefore given by: M d ( t (cid:48) ) = M ej (cid:18) t (cid:48) t (cid:19) − / , (7) ˙ M d ( t (cid:48) ) = ˙ M mrg (cid:18) t (cid:48) t (cid:19) − / , (8) t = 316 M ej ˙ M mrg . (9)We can calculate the initial radius and mass of the ejected diskusing the multi-component, self-gravitating disk model of BL08.The calculation takes as input the kick velocity, BH accretion rate,and BH mass at the time of the merger. Note that because we use c (cid:13)000
316 (28) / π R Σ t (cid:16) tt (cid:17) − / . (6)We determine Σ , t , and R using Eq. (4) along with the con-ditions that M d ( t (cid:48) ) = M ej and ˙ M d ( t (cid:48) ) = ˙ M mrg , where t (cid:48) = t + t sim − t mrg , t sim is the time in the simulation, M ej is theejected disk mass, and ˙ M mrg is the Bondi accretion rate calculatedin the simulation at the time of merger. The mass evolution of thedisk is therefore given by: M d ( t (cid:48) ) = M ej (cid:18) t (cid:48) t (cid:19) − / , (7) ˙ M d ( t (cid:48) ) = ˙ M mrg (cid:18) t (cid:48) t (cid:19) − / , (8) t = 316 M ej ˙ M mrg . (9)We can calculate the initial radius and mass of the ejected diskusing the multi-component, self-gravitating disk model of BL08.The calculation takes as input the kick velocity, BH accretion rate,and BH mass at the time of the merger. Note that because we use c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies the accretion rate calculated in the code as input, the normaliza-tion of the ejected-disk accretion rate is subject to the same as-sumptions as is the Bondi-Hoyle accretion rate (see § R ej lies in the region of the disk that is self-gravitating but still strongly dominated by the BH potential (i.e.,Zone II of the BL08 model). Quantitatively, R ej for our fiducial-mass simulations is between . − . Schwarzschild radii, or ∼ . − . pc. The corresponding mass of the ejected disk, M ej ,is . − . M (cid:12) ( . − . M (cid:12) for our fiducial-mass models).We use these quantities as initial conditions for the ejecteddisk model outlined above. The timescale for the accretion rate (andmass) decay, t , ranges between . − . yr. t depends on M ej and ˙ M mrg , which in turn depend on v k and the galaxy model pa-rameters. Specifically, t decreases with increasing v k , f gas , and q . After a time t , the accretion rate has dropped by a factor of − / ≈ . (note that the time in Eqns. 9 is defined such that t (cid:48) = t at t mrg ). By the end of our simulations, about − ofthe disk mass has been consumed. This corresponds to an increasein the BH mass of ∆ M = 0 . − ( . − for v k / v esc = 0 . simulations only). As expected, these values of ∆ M are somewhatlower than the result of BL08, ∆ M ≈ M BH . BL08 consid-ered kick speeds as low as 100 km s − ; their result also assumedthat the entire disk mass was accreted and that the accretion wasEddington-limited at the time of BH merger.Fig. 10 demonstrates that except in high- v k simulations wherethe average orbital timescale is long ( v k > ∼ . v esc ), the ejected-disk accretion is typically insignificant compared to the Bondi ac-cretion of the oscillating BH. Of course, the BH may still carry anaccretion disk during this phase, but the accretion will be more ac-curately characterized by the highly-variable Bondi rate calculatedfrom the local density and sound speed than by an isolated-diskmodel. Therefore, our analytic ejected-disk model becomes impor-tant only for high-velocity recoils in which the Bondi accretion ratedrops sharply after the kick. Below, we discuss the AGN lifetimesresulting from the combined accretion models, as well as the feasi-bility of observing offset AGN. In Fig. 12, we show 2 examples of the ∆ R , ∆ v phase space oc-cupied by recoiling BHs. The left and right panels show simula-tions of the q0.5fg0.3a model with v k / v esc = 0 . & 0.9, respec-tively. ∆ R is the binned spatial offset of the BH from the stel-lar center of mass, and ∆ v is the binned kinematic offset fromthe stellar center-of-mass velocity. The contour shading shows,for each ∆ R , ∆ v bin, the amount of time spent at that location( ∆ t , top windows), the total AGN energy output ( ∆ E bol , middlewindows), and the average bolometric luminosity (cid:104) L bol (cid:105) (bottomwindows). L bol is determined at each timestep from the relation L bol = (cid:15) rad ˙ M BH c , where the radiative efficiency (cid:15) rad is 0.1 un-less ˙ M BH < .
01 ˙ M Edd , in which case the system is considered ra-diatively inefficient, and (cid:15) rad = 0 . M BH / (0 .
01 ˙ M Edd ) (Narayan& McClintock 2008).The v k / v esc = 0 . recoiling BH, which settles back to thegalaxy center in ∼ Myr, fills a corner of the phase space.The ∆ t contours peak at low velocities, as these represent apocen-tric passages where the BH spends the most time. (cid:104) L bol (cid:105) is above L (cid:12) throughout the simulation, with peak values > L (cid:12) .Unlike the ∆ t contours, (cid:104) L bol (cid:105) peaks at high velocities, becausethe BH has the highest accretion rates immediately after the kick and during pericentric passages. The total bolometric energy out-put per ∆ R , ∆ v bin, which is the product of these two distribu-tions, accordingly peaks at both high ∆ R , ∆ v and low ∆ R , ∆ v .Instead of emitting all of its AGN feedback energy from a singlecentral point in the galaxy, the BH distributes this energy through-out the central kpc, as discussed in § v k = 0 BH in the same mergermodel (see Fig. 11).In contrast to this example, the v k / v esc = 0 . recoiling BH oc-cupies a narrow track in the phase space, as it completes only a feworbits and does not experience much drag. The ∆ t and (cid:104) L bol (cid:105) con-tours in this example illustrate an inherent difficulty in observingrapidly-recoiling BHs: the brightest luminosities occur just afterthe kick, when the BH velocities are highest, but this is also wherethe BH spends the least amount of time. Still, the BH has luminosi-ties > ∼ L (cid:12) for ∆ R up to 10 kpc. Further analysis is required todetermine the observability of the recoiling BHs in both of theseexamples, as well as those in our other simulations.Fig. 13 shows the AGN lifetimes, t AGN , in six merger modelsfor which we have varied v k . AGN lifetimes in the top two windowsinclude only the Bondi accretion rate, while t AGN in the bottomtwo windows includes the accretion from our ejected-disk model aswell. Unlike the lifetimes in Fig. 11, here we also apply a cut to theAGN lifetime such that only activity that occurs while the BH is re-coiling is shown: t AGN < t settle . We calculate t AGN using each ofthe three AGN definitions described previously. The solid lines inthe figure correspond to AGN defined as L bol > (3% , L Edd ,and the dashed lines correspond to L bol > L min . The shaded re-gions of the plot show the range of values between these definitions.As before, we choose L min = 3 . × L (cid:12) = 1 . × erg s − .A notable feature in Fig. 13 is that the peak AGN lifetimes forrecoiling BHs are quite long, > Myr, even for kick speeds near1000 km s − in some cases. Note also that in the lower- f gas merg-ers, t AGN peaks at the lowest v k / v esc , but in the gas-rich merg-ers the peak value is v k / v esc = 0 . − . . This reflects the factthat we have defined t AGN < t settle in these plots. In the gas-rich mergers, gas drag quickly damps out the low- v k trajectories,and t AGN is limited by t settle . For higher v k / v esc , gas drag is lessefficient and t AGN is instead limited by the gas supply available tothe BH.In all cases, the AGN lifetimes that include only Bondi ac-cretion (Fig. 13, top windows) fall sharply to < Myr forlarge v k / v esc . This demonstrates that Bondi accretion is inefficientwhen the BH is kicked far from the dense central region. How-ever, when we also allow for BH accretion from its ejected disk(Fig. 13, bottom windows), the ejected-disk accretion enhancesthe active lifetime for high v k / v esc recoils by more than an orderof magnitude. In the examples shown, t AGN for low-luminosityAGN is 3 - 14 Myr even for kicks as high as 1.2 v esc . For evenhigher kick speeds, t AGN will slowly decay as the trend in theplot indicates, owing to the decreasing ejected disk mass. The rel-atively slow decay of t AGN with increasing v k occurs partly be-cause, as opposed to a constant- ˙ M accretion model, here t AGN de-pends on the fraction of disk accreted before the BH luminos-ity falls below the “AGN” limit. In addition, the disk mass in theself-gravitating regime has a fairly weak ( r / ) dependence on ra-dius, so M ej ∝ /v k . Recall, however, that the probability of re-coil events with kick velocities (cid:29) km s − is quite small(Schnittman & Buonanno 2007; Campanelli et al. 2007a; Bakeret al. 2008; Lousto et al. 2010b; van Meter et al. 2010); this morethan the BH’s fuel supply limits the chances of observing a recoilevent with v k (cid:29) v esc . c (cid:13) , 000–000 Blecha et al.
Figure 12.
Contour plot of recoiling BH quantities ∆ t (top panels), ∆ E bol (middle panels), and (cid:104) L bol (cid:105) (bottom panels) in ∆ R , ∆ v space. (cid:104) L bol (cid:105) is theaverage bolometric BH luminosity per bin. The left panels are calculated from the q0.5fg0.3a merger simulation with v k / v esc = 0 . , and the right panels arefor the same merger model but with v k / v esc = 0 . . These findings illustrate the importance of BH accretion fromthe ejected disk for the lifetimes of rapidly-recoiling AGN. Alsocrucial, however, is the time-dependent nature of this accretion. Ifwe were to assume a simple constant- ˙ M model for the ejected-diskaccretion, we would greatly overpredict the lifetime of the brightAGN phase, and in some cases we would underpredict the lifetimeof the low-luminosity phase. We can calculate the discrepanciesbetween t AGN for a constant- ˙ M model and the lifetimes shownin Fig. 13, restricting the comparison to v k / v esc ≥ . to captureonly the simulations in which ejected-disk accretion is the domi-nant mode. ˙ M BH ( t mrg ) ≈ −
50% ˙ M Edd for all the modelsshown in Fig. 13 except q0.5fg0.1a. If we assumed the accretioncontinues at this rate for a time M ej / ˙ M BH ( t mrg ) in these models,we would overpredict t AGN for bright (
L > L Edd ) AGN bya factor of ∼ − . Conversely, t AGN for
L > L min would be underpredicted by a factor up to ∼ . In the q0.5fg0.1a model, ˙ M BH ( t mrg ) ≈
5% ˙ M Edd . In this case, t AGN for
L > L Edd would be overpredicted by a factor of ∼ − , depending onkick speed, and t AGN for
L > L min would also be overpredictedby a factor of ∼ − . Therefore, it is clear that inclusion of more realistic, time-dependent model for ejected-disk accretion, such asthe one presented here, is important for calculating the lifetimes andluminosities of rapidly recoiling AGN. Similarly, for lower-velocityrecoils, the BH + ejected-disk system clearly cannot be treated asisolated, because accretion from ambient gas is the dominant modeof AGN fueling.To determine whether these recoiling AGN could be distin-guished from their stationary counterparts, we need more informa-tion than simply the active lifetimes. Recoiling AGN could be iden-tified as such if during their active phase they are either kinemati-cally or spatially offset from their host galaxies; we will considerboth possibilities.The gas carried along with the recoiling BH is expected toinclude at least part of the BH’s broad-line (BL) region, becauseBL clouds reside deep within the potential well of the BH. Thenarrow-line (NL) region lies much further from the BH, so in gen-eral this gas will not be bound to the recoiling BH and will remainat the redshift of the host galaxy. A kinematically offset AGN couldtherefore be seen in a spectrum as a broad-line (BL) feature offsetfrom a narrow-line (NL) feature, if the recoiling AGN is able to il- c (cid:13) , 000–000 ecoiling Black Holes in Merging Galaxies Figure 13.
Active lifetimes of recoiling BHs as a function of v k . Results are shown for the same six galaxy models shown in Fig. 11, separated by massratio for clarity ( q = 1 on the left, q = 0 . on the right). On the left: q1fg0.6a (red), q1fg0.3a (blue), q1fg0.1a (green); on the right: q0.5fg0.6a (magenta),q0.5fg0.3a (cyan), and q0.5fg0.1a (gold). For each model, simulations were run for v k / v esc = 0 . − . . In all plots, the solid and dashed lines denote thethree different definitions of t AGN discussed in the text, and the shaded regions denote the range of values between these bounds. The upper and lower solidlines denote t AGN for L bol > and L Edd , respectively. The dashed lines show t AGN for L bol > L min , where L min = 3 . × L (cid:12) . UnlikeFig. 11, here we have applied cuts to t AGN such that only the active time t AGN < t settle is shown. In the top two windows, L bol is calculated from theBondi accretion rate only, while the bottom two windows show t AGN with the ejected-disk accretion model included as well. luminate NL clouds as it leaves the center of the galaxy. Otherwise,such a system might have a spectrum with no NLs and BLs thatare offset from the redshift of the host galaxy’s stellar light. Be-cause the physics of the NL region are not included in our analysis,we consider the velocity offset between the recoiling BH and thethe stellar center of mass. We calculate the AGN lifetime as before,based on the BH luminosity at each timestep, but in this case we areonly interested in the lifetime of offset
AGN; that is, we calculatethe time for which the BH is active and exceeds a minimum veloc-ity offset ∆ v min . We note that the limit ∆ v min is imposed on thephysical velocity difference between the BH and the host galaxy.The line-of-sight velocity seen by a typical observer will be lower,so the velocity-limited AGN lifetimes shown here are upper limits.Fig. 14 shows the results of our analysis for ∆ v min =500 km s − (top windows) and 800 km s − (middle windows).For ∆ v min = 500 km s − , the offset AGN lifetime for low- f gas , low- v k mergers is much smaller than the total AGN life-time in Fig. 13. v esc is relatively low in these models, so kickspeeds are also lower for fixed v k / v esc . In the q0.5fg0.1a merger,for example, v esc = 777 km s − , so the BH never exceeds the500 km s − limit for v k / v esc ≤ . . The offset AGN lifetimes for low v k / v esc in gas-rich models are a factor of 5-10 lower than the to-tal AGN lifetimes, but the peak lifetimes are still ∼ − Myr. Athigh v k / v esc ( ≥ . ), there is little difference between t AGN withor without the velocity cut. In these cases, the ejected disk domi-nates the BH accretion, and the BH speed is above 500 km s − fornearly all of the AGN phase.When ∆ v min is increased to 800 km s − , the AGN lifetimesdrop sharply for most merger models and kick speeds (see the mid-dle windows in Fig. 14). Only in the equal-mass, gas-rich modelsshown here (q1fg0.6a & q1fg0.3a) do the BHs appear as bright off-set AGN, and for only a narrow range of kick speeds. These twomodels have v esc > , such that BHs kicked with ∼ kms − may have tightly-bound orbits. In these cases the BHs makemany rapid pericentric passages through the dense central region,where they encounter an ample gas supply from which to accrete.Interestingly, in the q1fg0.6a and q1fg0.3a models, kicks < kms − ( ≤ . v esc ) have nonzero lifetimes in this plot. These are ex-amples of the phenomenon discussed in § v esc reaches its maximum, so the BHs receive mildvelocity boosts on subsequent passages through the increasinglydeep central potential well. c (cid:13) , 000–000 Blecha et al.
Figure 14.
The BH active lifetime is plotted in the same manner as in Fig. 13 and for the same galaxy models, but after minimum-velocity or minimum-separation cuts have been imposed. In all cases, both the Bondi accretion and the ejected-disk model are included in calculating L bol . The top two windowsshow the timescale for which the BHs are active and also have a velocity greater than 500 km s − relative to the host galaxy’s stellar center of mass. Themiddle two windows show t AGN for a minimum velocity of 800 km s − . The bottom two windows show t AGN for when the BH is spatially offset from thestellar center of mass by > kpc. In the other (lower- q , f gas ) models, the central region is lessdense, such that bound BHs have lower kick speeds and loweraccretion rates during pericentric passages. In these models, onlyejected-disk accretion is efficient at producing an offset AGN with ∆ v > km s − , which occurs only when the BHs are ejectedentirely from the host galaxy. These ejected AGN have lifetimes < Myr and low luminosities ( t AGN < Myr for
L > L Edd ). To be observed as a spatially-offset recoiling AGN, a recoilingBH must travel far enough from the galactic center to be resolvedas distinct point source before exhausting its fuel supply. As withthe velocity offsets, we define the spatial offsets relative to the stel-lar center of mass. The maximum galactocentric distance achievedby a recoiling AGN in any of our fiducial-mass simulations is ∼ kpc by our lowest-luminosity AGN definition and only ∼ kpc by c (cid:13)000
L > L Edd ). To be observed as a spatially-offset recoiling AGN, a recoilingBH must travel far enough from the galactic center to be resolvedas distinct point source before exhausting its fuel supply. As withthe velocity offsets, we define the spatial offsets relative to the stel-lar center of mass. The maximum galactocentric distance achievedby a recoiling AGN in any of our fiducial-mass simulations is ∼ kpc by our lowest-luminosity AGN definition and only ∼ kpc by c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies the strictest definition. In our high-mass simulations, which havelarger ejected disks, offsets > ∼ − kpc may be achieved while L > L min , but the maximum offset while
L > − L Edd is still only a few kpc. Offsets of ∼ kpc correspond to an an-gular separation of ∼ . at z = 0 . ; these could be resolvedwith HST/JWST as long as they are not observed edge-on. Offsets > ∼ − kpc could be resolved at this redshift with SDSS and
Chan-dra . To determine the lifetimes of the spatially-offset AGN in oursimulations, we impose a minimum-distance cut of ∆ R min = 1 kpc from the stellar center-of-mass, and we identify an offset AGNas one that simultaneously has ∆ R > ∆ R min and meets our AGN-luminosity criteria. The bottom windows of Fig. 14 show the resultsof this analysis. We find that above v k / v esc = 0 . − . (physi-cally, the kick speed above which R max exceeds 1 kpc), the offsetAGN lifetimes can be long, but only for low-luminosity AGN. Inthese models, t AGN ranges from − Myr for
L > L min , and . − Myr for
L > L Edd . In none of our simulations doesthe offset exceed R min for more than 1 Myr while its luminosity is > L Edd . The reason that spatially-offset AGN are only seen atlow luminosities is as follows. For recoiling BHs with short-periodoscillations, Bondi accretion is dominant, and most of the brightAGN activity occurs during pericentric passages with small ∆ R .For BHs on long-period orbits or escaping BHs, the ejected diskaccretion dominates. In this case the brightest AGN phase occurs asthe BH leaves of the central dense region, and once the BH passes ∆ R min , its luminosity has already begun a monotonic decay.We can conclude from Fig. 14 that in most of our models, low-luminosity recoiling AGN may be distinguishable via spatial off-sets > kpc for kick speeds > ∼ . − . v esc , but as kinematically-offset AGN with ∆ v min = 800 km s − , they may be distinguish-able only for kick speeds > ∼ v esc . These offset AGN generallyhave luminosities < ∼ L Edd , and their luminosity owes mainlyto accretion from the disk ejected with the BH. The exceptionsare equal-mass, gas-rich mergers (here, q1fg0.6a & q1fg0.3a), inwhich recoiling BHs on bound trajectories may experience multi-ple phases as bright (
L > L Edd ), kinematically-offset AGNaccreting from ambient gas during pericentric passages. This sce-nario can only occur in merger remnants with large central escapespeeds ( > ∼ − km s − ), such that BHs may receive kicks > ∼ km s − and still undergo short-period oscillations. In lower- q , lower- f gas mergers, the central gas density is lower, and the kickspeeds for bound trajectories are smaller, so this bright, velocity-offset phase does not occur. If kinematic offsets can be observedwith a resolution of 500 km s − instead of 800 km s − , velocity-offset-AGN lifetimes increase significantly, and measurable veloc-ity offsets can be attained for a much wider range of kick speeds.In the lowest q , f gas merger for which we have varied v k (theq0.5fg0.1a model), the offset AGN lifetimes are always < Myrfor
L > L lim and < Myr for
L > L Edd . Our q0.5fg0.1amodel has 10% gas initially, but by the time of the recoil kick only ∼ of the baryonic mass is in gas. We can conclude that mergerremnants with gas fractions lower than this and with q < ∼ . areunlikely to fuel bright offset AGN according to our criteria, at leastfor recoiling BHs with M BH ∼ M (cid:12) . Larger BHs will havelarger gas reservoirs and longer AGN lifetimes, and the reverse willbe true of smaller BHs. For example, in the q0.5fg0.1a model, a BHwith v k / v esc = 0 . has a velocity-offset ( ∆ v min = 800 km s − )AGN lifetime < Myr by all AGN criteria, while in the × moremassive q0.5fg0.1M10x model, the velocity-offset t AGN is 27 Myr(for
L > L min ). In general, larger BHs will have longer offset-AGN lifetimes for fixed v k / v esc . However, larger BHs are found in larger galaxies, where a higher kick speed is required to reachan appreciable fraction of the escape speed, and such kicks have alower probability of occurring. We discuss recoil kick probabilitiesfurther in § BH - σ ∗ Relation
Several authors have suggested that GW recoil may contribute toscatter in the observed black hole - host galaxy bulge relationsdue to ejected BHs (Volonteri 2007) or bound recoiling BHs thatleave the central galactic region (Blecha & Loeb 2008; Sijacki et al.2010). Volonteri (2007) used semi-analytic models to estimate theeffect of ejected BHs at high redshifts on the BH mass - bulge stel-lar velocity dispersion relation at z = 0 . In this work, we have al-ready demonstrated that, even when they remain bound to the hostgalaxy, recoiling BHs can undergo substantially different accretionhistories than their stationary counterparts, and that the resultingAGN lightcurves may also vary significantly as a function of kickspeed (see Figs. 10, 13, 14). Here, we attempt to quantify the ef-fect of individual GW recoil events on the M BH − σ ∗ relation. Be-cause we have simulated all of our merger models with both withno recoil kick and with v k = 0 . v esc , we are able to compare theM BH − σ ∗ relations that result from each of these samples. The fi-nal BH masses and LOS-averaged stellar velocity dispersions fromboth sets of simulations are plotted in Fig. 15; the right windowalso shows simulations with v k / v esc . − . . We include onlymodels with the fiducial merger orientation angles (orbits a & w -z) in this plot to avoid heavily weighting the fit toward the ( q , f gas )combinations for which we have varied the orbit.By examining the mass deficits of these recoiling BHs rela-tive to the stationary BHs in our simulations, we can quantify theinterruption to BH growth caused by GW recoil. Note that we areprobing only the effect of GW recoil on the growth of kicked BHs;the actual BH mass deficit resulting from BHs merging in a cos-mological framework may differ from these values. In particular,the v k = 0 . v esc simulations result in BH wandering times of atleast several Gyr, so in reality these BHs will be lost to the galaxyand never contribute to the M BH − σ ∗ relation. If the galaxy expe-riences subsequent mergers, especially minor mergers, the kickedBH may be replaced with a smaller BH from the incoming galaxy,creating a larger mass deficit. We also stress that the data plottedhere are not meant to represent a random sample, as we have variedparameters in a systematic way. Accordingly, the relations shownare not expected to reproduce the observed M BH − σ ∗ relation. Inparticular, the scatter in the v k = 0 relation (0.13 dex) is smallerthan the observed scatter ( ∼ . − . dex, e.g., Tremaine et al.2002; Aller & Richstone 2007; Hopkins et al. 2007b), owing to anumber of factors such as the single merger orbital configurationused in this plot, the constant feedback efficiency assumed for allsimulations, and small range of total galaxy mass spanned by themajority of our models. Furthermore, although scaling each kick to0.9 v esc essentially allows us to capture the maximum effect of asingle recoil event on BH growth, this does not reflect the fact that c (cid:13) , 000–000 Blecha et al.
Figure 15.
Left panel: M BH − σ ∗ relation for BHs with no recoil kicks (black circles) and with v k / v esc = 0 . (red triangles). M BH is in all cases the BHmass at the end of the simulation ( t mrg + 2 . Gyr) and σ ∗ is the stellar velocity dispersion averaged over 100 random sight lines, where error bars give therange of sampled values. All merger models with orbits a & w - z are shown. The solid black line is a least-square fit to the no-recoil data and the red dashedline is fit to the high-recoil data; the fit parameters are indicated on the plot. Right panel: same data as left panel, but also including data for the six mergermodels in which we have varied v k / v esc . The blue diamonds show these results for v k / v esc = 0 . − . , and the blue dot-dashed line is a fit to these data.The green triple-dot-dashed line is a fit to all data shown. in galaxies with lower escape speeds, large v k / v esc recoil eventswill occur more frequently than in massive galaxies. Such a trendwith galaxy mass would steepen the slope of the M BH − σ ∗ re-lation, though this would also depend on the distribution of othermerger parameters, such as q and f gas , with varying galaxy mass.Despite these limitations in comparing our simulations to the ob-served M BH − σ ∗ relation, our results provide substantial insightinto how GW recoil affects the growth of kicked BHs and the inher-ent complexities of this process. The relative differences in Fig. 15between the simulations with and without recoil are robust and caneasily be understood in physical terms.It can be seen by visual inspection of Fig. 15 that the effect ofhigh-velocity recoils is an overall downward offset in normaliza-tion and an increase in scatter. Because the LOS-averaged valuesof σ ∗ do not change significantly in the presence of a recoil kick,we focus our discussion on variation in the final BH mass.The downward shift in Fig. 15 reflects the fact that GW recoilalways reduces the final mass of a merged BH. We quantify the“mass deficit” of recoiling BHs relative to stationary BHs by cal-culating the fractional mass difference for each recoil simulationrelative to its v k = 0 counterpart, ( M fin (0) - M fin ( v k )) / M fin (0),where M fin is the final BH mass in each case. Fig. 16 shows themass deficit plotted versus v k for the six merger models discussedpreviously. The deficits generally increase with v k , though the de-tails vary substantially between models. In the q0.5fg0.1a model,recoiling BHs with v k = v esc have ∼ / lower final mass thando stationary BHs, while in the q1fg0.3a model, a v k = v esc recoilresults in a BH almost five times smaller than its stationary counter-part. Note also that the curves in Fig. 16 all level out at v k / v esc =0 . − . ; this marks the kick speed in each model above whichrecoiling BHs are unable to accrete more gas after their ejected Figure 16.
Fractional mass deficit of recoiling BHs versus stationary BHsas a function of v k / v esc . M fin (0) and M fin ( v k ) are the final BH masses(at t mrg + 2 . Gyr) for stationary and recoiling BHs, respectively. The plotlegend lists the models shown. disk has been exhausted. The models with lower f gas achievethis limiting value at lower v k / v esc , owing to the lower gas dragand shallower potentials in these remnants. The blue diamonds in c (cid:13)000
Fractional mass deficit of recoiling BHs versus stationary BHsas a function of v k / v esc . M fin (0) and M fin ( v k ) are the final BH masses(at t mrg + 2 . Gyr) for stationary and recoiling BHs, respectively. The plotlegend lists the models shown. disk has been exhausted. The models with lower f gas achievethis limiting value at lower v k / v esc , owing to the lower gas dragand shallower potentials in these remnants. The blue diamonds in c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies Fig. 15 mark the positions of these varying- v k simulations on the M BH − σ ∗ relation. The points corresponding to lower v k / v esc lieclose to the no-recoil (black) line; those with higher v k have lowerBH masses.In Fig. 15, the normalization offset between the v k = 0 BHpopulation and the v k / v esc = 0 . population is 0.44 dex, and theoffset between v k = 0 and the total population is 0.22 dex. How-ever, it has been demonstrated that the normalization of the blackhole - galaxy bulge correlations depends on the efficiency of AGNfeedback (Di Matteo et al. 2005; Robertson et al. 2006c; Hopkinset al. 2007a). In our simulations, we assume a constant fraction(5%) of the BH’s bolometric luminosity couples to the surroundinggas as thermal energy. Stationary accreting BHs with lower feed-back efficiencies would grow larger before heating the surroundinggas enough to slow or halt accretion. Depending on how much ac-cretion occurs prior to versus after the BH merger, higher feedbackefficiencies could reduce the normalization offset between our re-coiling and stationary BH populations. In general, however, station-ary BHs will accrete more after the BH merger than recoiling BHs,so there is likely to be a non-zero downward shift in M BH − σ ∗ normalization caused by GW recoil.As previously stated, the disproportionate effect of recoilevents on galaxies with small v esc could have some effect onthe M BH − σ ∗ slope. In our simulations, where we have scaledkick speeds to v esc , there is no significant difference between the M BH − σ ∗ slope for recoiling versus stationary BHs. This is tobe expected, because the depth of the central potential well scalesmore or less self-similarly with total galaxy mass. We do, however,see a trend toward larger BH mass deficits for higher- q mergers,which arises because gas is driven more efficiently to the galaxycenters during coalescence, and recoiling BHs “miss” a larger ac-cretion phase when they are kicked out of this central dense region.The variation in BH mass deficits between merger models re-sults in larger intrinsic M BH − σ ∗ scatter for BH populations thathave undergone recoils. The correlation for the no-recoil samplehas a scatter of 0.13 dex, and the v k / v esc = 0 . correlation has ascatter of 0.24 dex. In other words, the high-recoil sample has al-most twice as much intrinsic scatter as the no-recoil sample. Thisincrease in scatter is a universal consequence of GW recoil; recoilevents essentially add an extra variable to the determination of fi-nal BH masses. As opposed to stationary BHs, the final mass ofrecoiling BHs depends not just on how much gas is available to beaccreted, but also when this accretion occurs relative to the timeof the kick. In mergers with no recoil, M BH is a strong functionof the amount of gas driven into the central region (i.e., the depthof the central potential well). The details and timing of the coldgas flow in galaxy mergers depend nontrivially on factors such as q , f gas , the galaxy orbits, and the star formation rate, so it is naturalthat larger intrinsic scatter is found in the final masses of recoilingBHs. If the kick speed is lower, such that the BH can settle back tothe center while an ample gas supply is still present, the BH massdeficit will be reduced, but the details of this late-phase accretionadd yet another element of unpredictability to the final value of theBH mass.In addition to the larger intrinsic M BH − σ ∗ scatter for a BHpopulation with fixed v k / v esc , we also anticipate an increase inoverall scatter caused by the range of kick speeds that would occurin a realistic population of BHs and by BHs that have undergonemultiple recoils through their formation history. The contributionof GW recoil to the total M BH − σ ∗ scatter is difficult to predictfrom our simulations; quantitative predictions would require fol-lowing detailed BH formation histories in a cosmological frame- work, which is beyond the scope of this paper. However, we at leastgain a sense of how a range of kick speeds affects the M BH − σ ∗ re-lation by plotting our varied- v k simulations along with the v k = 0 and v k / v esc = 0 . populations. The right panel in Fig. 15 shows thesame data as the left panel but also includes data for the simulationsin which we have varied v k / v esc (blue diamonds). The blue line isa fit to these points, and the green line is a fit to all data shown.The fit to all the data has a scatter of 0.25 dex, which as expected islarger than the scatter for the v k = 0 population.The most robust of our conclusions from this analysis is the in-crease in intrinsic M BH − σ ∗ scatter for BHs that have undergonea single recoil event, by a factor of ∼ in our simulations. Thisfinding suggests that GW recoil events may be a non-negligiblecontribution to the scatter in the observed M BH − σ ∗ relation, es-pecially because BHs at z = 0 may have undergone multiple recoilevents throughout their formation history. Fig. 17 compares the SFRs for simulations with no GW recoil(black dashed curve), with v k / v esc = 0 . (red solid curve), and withno BHs (blue dotted curve) in a gas-rich, equal-mass merger model(q1fg0.4a). It is clear that after the merger, the simulation with alarge recoil kick has a higher SFR than the simulation with v k = 0 .The post-merger SFRs are similar in the high-recoil case and in thesimulation with no BH at all. This same behavior can be seen inthe high-recoil simulations of model q0.5fg0.3a shown in Fig. 10,though to a lesser degree. These enhanced SFRs occur becausewhen the BH is removed from the center of the merger remnant,the AGN feedback is also displaced. The lack of central energyinput allows star formation to continue unhindered in this regionfor a longer time. We can actually see the effect of the recoilingAGN feedback on the instantaneous SFR in Fig. 17. The SFR curvefor the v k / v esc = 0 . simulation has a vaguely periodic shape; infact, each small trough in the SFR coincides with a pericentric pas-sage of the BH through the galactic center, which imparts a smallamount of feedback energy to the dense region. This supports theconnection between the recoiling BH dynamics and the galacticSFR, but the main consequence of the recoil event is that star for-mation is never as strongly quenched as when the BH does notrecoil. In the example shown in Fig. 17, the merger remnant witha stationary BH has almost twice the amount of gas at the end ofthe simulation as the merger with v k / v esc = 0 . . This correspondsto an increase in total star formation of . × M (cid:12) in the recoilsimulation, or ∼ increase in total stellar mass, solely due to thedisplacement of the BH and its feedback.In Fig. 18, we can clearly see the effect of this enhanced starformation on the remnant stellar density profile. The figure showsthe remnant stellar density profiles for the same three simulationsshown in Fig. 17, with v k = 0 (black curves), v k / v esc = 0 . (redcurves), and without BHs (blue curves). The results are further bro-ken down into the contribution from stars formed prior to the galaxymerger (“old” stars, thin curves) and those formed during merger-driven starbursts (“new” stars, thick curves). In all cases, the “new”stellar population dominates in the central kpc, but in the remnantwith a recoiling BH the central stellar density is almost twice thatof the remnant with a stationary BH. In fact, this stellar profile veryclosely resembles that of a remnant without a BH. Therefore, re-coil events in gas-rich mergers can prolong starburst phases, creat-ing denser and more massive stellar cusps. We have also examinedthe (unattenuated) U − B color evolution of the stellar componentin these no-recoil, large-recoil, and no-BH simulations. The colors c (cid:13) , 000–000 Blecha et al.
Figure 17.
Total star formation rate (SFR) vs. time for the q1fg0.4a mergermodel. The black dashed line represents the v k = 0 simulation, the redsolid line represents the v k / v esc = 0 . simulation, and the blue dotted linerepresents a simulation with no BHs. The vertical line marks the time of BHmerger in the simulations with BHs. Figure 18.
Final stellar density profiles (2.9 Gyr after t mrg ) for the samethree simulations shown in Fig. 17, with the same color coding. The thickcurves are the “new” stellar populations that formed during the merger andthat dominate within the central ∼ kpc, and the thin curves are the “old”stellar populations from the initial stellar disks of the progenitor galaxies.In each case, the black curves are the profiles for the v k = 0 simulation,the red curves represent the v k / v esc = 0 . simulation, and the blue curvesrepresent the simulation with no BHs. Poisson error bars are shown on thedensities in each radius bin. The vertical dotted line denotes the gravita-tional softening length (80 pc) in these simulations. in all three cases are similar; by the end of the simulation all have U − B ∼ , i.e., these merger remnants are entering the “green val-ley” in transition from blue to red. However, in the v k / v esc = 0 . and no-BH simulations, which have prolonged star formation, thestars are slightly bluer than in the no-recoil simulation. While thisdifference is small, ∼ . mag, it further demonstrates that inmerger remnants with rapidly-recoiling BHs, the (blue) starburstphase may be prolonged, and hence the transition to red ellipticalslightly delayed, solely due to the effect of GW recoil. In § opposite effect of one that has beenproposed for gas-poor mergers, where repeated BH oscillationsthrough the central region of the merger remnant may scour outa stellar core (Boylan-Kolchin et al. 2004; Gualandris & Merritt2008). Such core-scouring is expected to occur on scales of < ∼ Using the SPH/N-body code
GADGET-3 , we have generated a suiteof galaxy merger simulations both with and without a recoil kickapplied to the central SMBH at the time of BH merger. Owing tothe large range of parameters sampled, we were able to analyzesystematic trends in recoiling BH behavior with variation in galaxymass ratio, total galaxy mass, initial gas fraction, orbital configu-ration, and BH merger time. In addition, we have used a range ofrecoil kick velocities, which are scaled to the galactic central es-cape speed in each case. We followed the trajectories and accretionhistory of the recoiling BHs, as well as evolution of host galaxyproperties such as the star formation rate and depth of the centralpotential well. For the BH accretion, the Bondi-Hoyle accretionrates were used, but we also included a time-dependent model foraccretion from a gas disk carried along with the recoiling BH.
The recoiling BH trajectories in our simulations are character-ized by low-angular-momentum orbits (i.e., “oscillations” aboutthe galactic center) that are also highly three-dimensional. In otherwords, the baryonic component of the merger remnant dominatesthe BH orbits even if they extend well into the halo, but the unre-laxed nature of this remnant creates complicated BH trajectories.We find that the amplitude and duration of these oscillations varieswidely between different galaxy models and kick velocities; someBHs settle back to equilibrium at the galactic center within a fewMyr, while others may remain on large orbits through the halo fora Hubble time.The amplitude and duration of BH oscillations in a given re-coil event clearly depend on the central escape speed, i.e., the depthof the central potential well. However, by normalizing kick speedsin our simulations to v esc at the time of the kick, we are able to com-pare different galaxy models regardless of their escape speed. Wefind substantial variation in recoil trajectories between models evenfor fixed v k / v esc . Recoil oscillations are more readily suppressed inmergers with higher q and f gas . Such merger remnants are more c (cid:13)000
The recoiling BH trajectories in our simulations are character-ized by low-angular-momentum orbits (i.e., “oscillations” aboutthe galactic center) that are also highly three-dimensional. In otherwords, the baryonic component of the merger remnant dominatesthe BH orbits even if they extend well into the halo, but the unre-laxed nature of this remnant creates complicated BH trajectories.We find that the amplitude and duration of these oscillations varieswidely between different galaxy models and kick velocities; someBHs settle back to equilibrium at the galactic center within a fewMyr, while others may remain on large orbits through the halo fora Hubble time.The amplitude and duration of BH oscillations in a given re-coil event clearly depend on the central escape speed, i.e., the depthof the central potential well. However, by normalizing kick speedsin our simulations to v esc at the time of the kick, we are able to com-pare different galaxy models regardless of their escape speed. Wefind substantial variation in recoil trajectories between models evenfor fixed v k / v esc . Recoil oscillations are more readily suppressed inmergers with higher q and f gas . Such merger remnants are more c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies centrally concentrated and gas-rich, resulting in steeper central po-tential wells and increased gas drag and dynamical friction.In the models for which we have varied v k / v esc , we find that,with the exception of our collisionless simulations, recoiling BHswith v k / v esc = 0 . − . reach galactocentric distances < ∼ kpcand settle back to the center in < . Gyr. The corresponding rangeof kick speeds is 310-880 km s − .For large recoil velocities, GW recoil events can produce BHoscillations that persist through the end of our simulations, 2.9 Gyrafter the kick. The largest orbits can extend well into the galactichalo, with galactocentric distances up to ∼ kpc. In our modelsthese long-lived oscillations occur for kicks > ∼ . − . v esc , againdepending on the mass ratio and gas content of the merger.Furthermore, as illustrated in § q ∼ , the central escape speed may increase rapidly around thetime of BH binary coalescence. In this case, the trajectory of therecoiling BH may also depend on the time of the BH merger rela-tive to the formation time of the central density cusp. Of all the fac-tors influencing the BH trajectories, this is the most unpredictable,as it depends on the relative timing of two short-timescale pro-cesses. This adds an element of uncertainty to any attempt, includ-ing the current study, to model populations of recoiling BHs in gas-rich galaxies. Our assumption of rapid BH mergers ( t mrg = t coal )means that our BH oscillation amplitudes may be upper limits inmergers with strong v esc evolution. However, the effect of this un-certainty on the results presented here is limited, due to the rela-tively small number of merger models affected and our use of thenormalization v k / v esc .We have also tested whether recoil trajectories are affected bythe direction of the kick. Our generic merger remnants (those thatare not formed from highly-aligned galaxy orbits) are highly dis-turbed at the time of the BH recoil and therefore do not have disk-like structures, i.e., there is no “special” direction in which a recoil-ing BH would clearly experience much greater drag. Even with theclumpy, irregular density profiles of our merger remnants, we findthat the trajectories of recoiling BHs have little dependence on thekick direction. Much more important in determining the amplitudeand duration of recoiling BH oscillations is the magnitude of thekick velocity relative to the escape speed, along with the aforemen-tioned global galaxy properties such as the initial gas fraction andmass ratio. We note that there should indeed be a dependence ofthe recoil trajectory on the kick direction with respect to the planeof the accretion disk; recoils directed into the disk plane likely ex-perience more gas drag and have shorter oscillation timescales. Inaddition, (Rossi et al. 2010) have shown that the ejected disk massand AGN luminosity may depend strongly on the direction of therecoil kick with respect to the accretion disk plane. We do not re-solve this small-scale region in our simulations; however, recoilkicks > ∼ km s − will always be nearly perpendicular to the or-bital plane of the binary (Campanelli et al. 2007a,b; Lousto & Zlo-chower 2009), which is unlikely to be perpendicular to the orbitalplane of the accretion disk. Therefore, for the recoil velocities weconsider ( > ∼ km s − ), we can assume that the BH is unlikelyto be kicked directly into the accretion disk plane.We mention in § ∼ − kms − , should occur with fairly high probabilities. Even if the BHspin magnitudes are randomly distributed between 0 and 1, . of major mergers should have kicks above 500 km s − , and . should be above 1000 km s − . Furthermore, Lousto et al. (2010b)have conducted statistical analysis of GW recoil spins and kick speeds using post-Newtonian approximations calibrated to numeri-cal relativity results. They provide kick probability distributions forseveral mass ratio bins, which we can use to estimate the relativeprobability of “high” ( v k ∼ v esc ) or “moderate” ( v k ∼ . v esc )kick speeds in various merger models. Coincidentally, for mass ra-tios . ≤ q ≤ . and < ∼ v k < ∼ km s − , which rep-resent a large fraction of our fiducial-mass simulations, the kickprobability distribution is quite flat. For these models, the relativeprobability of a given kick speed between models, as well as therelative probability of high versus moderate v k in a given model, isroughly unity. In our highest-mass (q1fg0.3M20x) simulation, theprobability of a kick near v esc = 2500 km s − is about 10 timessmaller than the probability of a kick with 0.6 v esc and is also ∼ times smaller than the kick probability for v k ∼ v esc in the q1fg0.3amodel. For mergers with q < ∼ . , which we do not model in ourstudy, the kick distribution becomes heavily skewed toward veloc-ities < km s − .An important caveat to the interpretation of recoil kick prob-abilities is that the relevant velocity for observations is the line-of-sight (LOS) velocity, not the actual velocity. For random linesof sight, the probability of observing a given kick v k as a kine-matic offset > ∆ v min is therefore reduced by a factor P (∆ v LOS > ∆ v min ) = 1 − ∆ v min /v k . For example, about 20% of recoilswith v k = 1000 km s − will have ∆ v LOS > km s − .Lousto et al. (2010b) find that the overall probability distributionfor ∆ v LOS is lower than the v k distribution by a factor of between ∼ (for kicks > km s − ) and ∼ (for kicks > kms − ). Similarly, the probability of observing a recoiling BH withspatial offset ∆ R LOS > ∆ R min is (cid:112) − ∆ R / ∆ R ; i.e., amajority of spatial offsets > ∼ . R min will have LOS offsets ex-ceeding the minimum observable offset. The final coalescence of two merging, gas-rich galaxies typi-cally triggers both a burst of star formation and a phase of rapidBH accretion. Assuming the BHs themselves coalesce on a shorttimescale, the resulting recoil event coincides with a period of highactivity in the central region of the merger remnant. Thus, we ex-pect recoiling BHs in gas-rich mergers to have substantially dif-ferent accretion histories than their stationary counterparts. This isindeed the behavior seen in our simulations, with greater disruptionto the BH accretion history for higher kick velocities.Recoil events that produce short-period BH oscillations( v k / v esc ∼ . − . , depending on the merger model) cause the BHaccretion rate to drop at the time of the kick, thereby reducing thepeak luminosity of the BH. However, the BH remains in the centralfew kpc of the merger remnant where gas densities are large enoughthat Bondi-Hoyle accretion is efficient. Because the BH’s feedbackenergy is deposited in a much larger volume than for stationaryBHs, it is unable to heat the gas sufficiently to completely termi-nate the AGN phase. The recoiling BH may therefore experience alonger active phase by a factor of a few than its stationary counter-part, although at lower luminosities. This phase continues in somecases until the end of the simulation, 2.9 Gyr after the BH merger.Owing to the lower luminosities of these extended AGN phases, wefind that they do not increase the final BH mass relative to station-ary AGN. However, this type of accretion episode is distinct fromother merger-triggered AGN phases in that it is not accompaniedby a simultaneous starburst. The copious amounts of dust producedby starbursts can easily obscure an active central source, and the c (cid:13) , 000–000 Blecha et al. starburst luminosity may overwhelm the AGN luminosity. Recoil-ing AGN that continue accreting long after the starburst is completetherefore may be more easily observable.When recoil kicks are large enough to produce long-period( > ∼ Myr) BH oscillations ( v k / v esc > ∼ . − . depending onthe merger model), the Bondi-Hoyle accretion rate drops precipi-tously as the BH is rapidly ejected to a lower-density region. Eventhough the BH remains on a low-angular-momentum orbit and re-turns several times to the dense central region, its velocity is gener-ally too high during these pericentric passages to allow for substan-tial gas accretion, and the gas is depleted by star formation betweensubsequent passages.In such high-velocity recoil events, a portion of the inner ac-cretion disk may remain bound to the BH. We account for this byassigning to each recoiling BH a time-dependent, isolated accretiondisk with a mass and initial accretion rate based on the BH mass,recoil velocity and the accretion rate at the time of the kick. Themass of these ejected disks is only a few percent of the BH mass,so they do not contribute significantly to the final BH mass. How-ever, the accretion from these disks does greatly extend the activelifetime of rapidly-recoiling BHs in the regime where Bondi-Hoyleaccretion is inefficient. We find that the AGN lifetime in our modelsmay increase from (cid:28) Myr to ∼ Myr when ejected-disk accre-tion is included, though these are generally low-luminosity AGN.The peak lifetimes in the Bondi-Hoyle regime are generally longerand correspond to brighter AGN, but for a fairly narrow range ofkick speeds. t AGN in the Bondi-Hoyle regime may be up to ∼ Myr for low-luminosity AGN and between ∼ − Myr forAGN accreting at − L Edd . From an observational standpoint, our primary interest is not the to-tal active lifetime, but rather the time for which the BH is active and can be distinguished as a recoiling BH. We find that kinematically-offset AGN – those that are luminous enough to be detected and have velocity offsets large enough to be spectrally resolved – occurin two distinct physical scenarios. In the first scenario, the recoil-ing AGN travel far from the galactic center and are powered byaccretion from the ejected disk. This occurs for recoil velocitiesnear or above the central escape speed. In our simulations, AGNwith velocity offsets > km s − have lifetimes < ∼ Myr inmost cases. In most of our galaxy models, recoiling AGN can onlymeet this velocity criterion for v k > v esc . For reference, the SDSSquasar study conducted by Bonning et al. (2007), which yielded anull result, had a spectral offset limit of 800 km s − .The other physical mechanism for producing kinematically-offset recoiling AGN is via multiple pericentric passages througha central dense region. Note that marginally-bound recoiling BHsmay also experience close passages, but these will be rapid and fewin number; the cumulative probability of observing such an eventis low. If a recoiling BH is able to settle back to the galaxy centerwithin ∼ . − Gyr, it will undergo many short-period oscilla-tions through the central region. In this case, the BH may be ableto accrete efficiently from the ambient gas during high-velocityclose passages, producing a kinematically-offset AGN. This sce-nario favors massive, gas-rich galaxies with high central densities:the larger the central escape speed and the steeper the potentialwell, the higher the velocity with which a BH can be kicked and stillremain tightly bound to the galaxy. In our q = 1 , gas-rich mergers,offset AGN with ∆ v > km s − can have lifetimes up to 100Myr, and may have lifetimes > ∼ Myr at bright ( > L Edd ) luminosities. Especially for these AGN, an increase of spectral res-olution to achieve a limit of 500 km s − could make a substan-tial difference; in our models, the lifetimes increase by a factor of ∼ − with this lower value of ∆ v min .The maximum spatial offset achieved by a recoiling AGN inour high-mass simulations is ∆ R = 112 kpc by our most gen-erous AGN definition ( L > . × erg s − ) and 3.2 kpc byour strictest definition ( > L Edd ), but for our fiducial-masssimulations these maximum offsets are only 15 and 1.3 kpc, re-spectively. To calculate spatially-offset AGN lifetimes, we requirea minimum offset ∆ R min = 1 kpc. Such an offset could be re-solved by HST or JWST at z < ∼ . , or by SDSS or Chandra at z < ∼ . . In our simulations, recoiling BHs achieve R max > kpc for v k / v esc > ∼ . − . . AGN lifetimes may be quite long nearthis threshold kick speed ( ∼ Myr), though only at low lumi-nosities. At higher kick speeds, lifetimes are generally ∼ − Myr and slowly decrease with higher v k , as less gas bound to therecoiling BHs.Based on our calculated AGN lifetimes, we conclude that forescaping BHs ( v k > v esc ), probabilities for observing recoils viaspatial offsets and kinematic offsets are similar. For recoiling BHson bound trajectories, velocity-offset AGN with high luminositiesare favored for massive, gas-rich galaxies ( q = 1 , f gas = 0 . − . in our models). Spatially-offset AGN with lower luminosities havesimilar lifetimes for all models. Recoiling BHs in merger remnantsthat are both gas poor ( f gas < ∼ . initially) and result from lower- q mergers ( q < ∼ / ) are not expected to produce long-lived offsetAGN. M BH − σ ∗ Scatter & Offset
We have demonstrated that recoiling BHs have lower final massesthan their stationary counterparts, though the mass deficit variesconsiderably with kick speed and merger remnant properties. Thismay affect the formation of the observed correlations betweenSMBHs and the bulges of their host galaxies. In particular, we con-sider the possible effects of these mass deficits on the observed M BH − σ ∗ relation by comparing the M BH − σ ∗ correlations of oursets of v k = 0 and v k = 0 . v esc simulations, as well as our simula-tions with varying v k . We do not find any evidence for a change in M BH − σ ∗ slope caused by recoils with fixed v k / v esc , but in a realis-tic population of galaxy mergers, galaxies with smaller v esc wouldbe disproportionately affected by recoils with v k near or above v esc .This could contribute to some steepening of the M BH − σ ∗ slope.In our simulations, we find that GW recoil events may contributeto a downward shift in normalization, an increase in overall scatter,and an increase in intrinsic scatter of the M BH − σ ∗ relation (seeFig. 15). The magnitude of these effects, particularly the normaliza-tion offset and total scatter, are sensitive to the galaxy populationconsidered and the detailed merger and recoil histories of the cen-tral BHs. Therefore, we cannot make quantitative predictions aboutthe contribution of GW recoil to the observed normalization andscatter of the M BH − σ ∗ relation; this would in fact be difficultto predict with any method. A more realistic approach involvingBH and galaxy populations derived from a cosmological frame-work would still be plagued with uncertainties in the recoiling BHmasses. We have shown that these masses are sensitive numerousfactors that do not lend themselves to semi-analytical modeling,including the (possibly evolving) central potential depth, the BHmerger timescale, and the detailed BH accretion history.Despite these uncertainties, the existence of a recoiling-BH c (cid:13)000
We have demonstrated that recoiling BHs have lower final massesthan their stationary counterparts, though the mass deficit variesconsiderably with kick speed and merger remnant properties. Thismay affect the formation of the observed correlations betweenSMBHs and the bulges of their host galaxies. In particular, we con-sider the possible effects of these mass deficits on the observed M BH − σ ∗ relation by comparing the M BH − σ ∗ correlations of oursets of v k = 0 and v k = 0 . v esc simulations, as well as our simula-tions with varying v k . We do not find any evidence for a change in M BH − σ ∗ slope caused by recoils with fixed v k / v esc , but in a realis-tic population of galaxy mergers, galaxies with smaller v esc wouldbe disproportionately affected by recoils with v k near or above v esc .This could contribute to some steepening of the M BH − σ ∗ slope.In our simulations, we find that GW recoil events may contributeto a downward shift in normalization, an increase in overall scatter,and an increase in intrinsic scatter of the M BH − σ ∗ relation (seeFig. 15). The magnitude of these effects, particularly the normaliza-tion offset and total scatter, are sensitive to the galaxy populationconsidered and the detailed merger and recoil histories of the cen-tral BHs. Therefore, we cannot make quantitative predictions aboutthe contribution of GW recoil to the observed normalization andscatter of the M BH − σ ∗ relation; this would in fact be difficultto predict with any method. A more realistic approach involvingBH and galaxy populations derived from a cosmological frame-work would still be plagued with uncertainties in the recoiling BHmasses. We have shown that these masses are sensitive numerousfactors that do not lend themselves to semi-analytical modeling,including the (possibly evolving) central potential depth, the BHmerger timescale, and the detailed BH accretion history.Despite these uncertainties, the existence of a recoiling-BH c (cid:13)000 , 000–000 ecoiling Black Holes in Merging Galaxies contribution to the M BH − σ ∗ correlation and its scatter is a nec-essary consequence of GW recoil events. In particular, we demon-strate that a universal effect of GW recoil is to increase the intrinsicscatter in BH masses. The disruption to BH accretion caused by arecoil event introduces an extra variable into the determination ofthe final BH mass, namely, the timing of the recoil kick relative tothe merger-induced burst of BH accretion (i.e. quasar phase). In ourrecoil simulations, the intrinsic M BH − σ ∗ scatter of our rapidly-recoiling BH population ( v k / v esc = 0 . ) is almost × the scatterin our stationary-BH population. This is the contribution to scattercaused solely by interruption of BH growth by a recoil kick; otherfactors not accounted for here could easily increase the contributionof GW recoil to M BH − σ ∗ scatter. While a more realistic popula-tion of BHs will have smaller average mass deficits resulting from arange of kick speeds, the BHs are also likely to have undergone nu-merous mergers and recoil events in the past, which would increasethe overall scatter. Subsequent merger events, in which an incomingBH may replace an ejected BH, could also increase scatter. The rel-atively small scatter of the empirical relation, 0.25 - 0.3 dex, placesconstraints on the contribution of GW recoil and, hence, on thefrequency of large v k / v esc recoil events. Similarly, a non-zero con-tribution of GW recoil to the observed scatter places constraints onthe contribution from other sources, such as redshift evolution ofthe M BH − σ ∗ relation (e.g., Haehnelt & Kauffmann 2000; Shieldset al. 2003; Robertson et al. 2006c). Previously, a model for galaxy evolution has been outlined in whichmergers play a central role (e.g., Hopkins et al. 2006a, 2008b;Somerville et al. 2008). In this picture, galaxies form originallyas disks, and the population of ellipticals is built up through timefrom mergers. Gas-rich mergers pass through intermediate phasesin which they host significant star formation and black hole activity,first as ULIRGs, then as quasars, and finally as dormant ellipticalgalaxies.There is a great deal of observational support for this scenario.Nearby ULIRGs are invariably associated with gas-rich mergers(Sanders et al. 1988a; Sanders & Mirabel 1996) and contain largequantities of molecular gas in their centers (Sanders et al. 1991),driving nuclear starbursts. Many display evidence for central AGNthrough their “warm” spectra (Sanders et al. 1988b), leading to theinterpretation that quasars are the descendants of ULIRGs. As thestarbursts and quasar activity fade, the merger remnant evolves intoa passive elliptical (Toomre & Toomre 1972; Toomre 1977), mak-ing the transition from blue to red. The relics of this process canbe seen in the central light concentrations in elliptical galaxies thatwere put into place during the starburst phase of their creation (e.g.,Mihos & Hernquist 1994a; Hopkins et al. 2008c), and correlationsbetween supermassive black holes and e.g. the central potentials oftheir hosts (Hopkins et al. 2007b; Aller & Richstone 2007).These fossil signatures, and the timing of the events that led totheir formation, are sensitive to the interplay between star forma-tion and black hole growth and the feedback processes that accom-pany each of these. In principle, black hole recoil could impact allof these phenomena to varying degrees, providing constraints onthe modeling we have presented here as well on the interpretationof the observations more generally.For example, some ULIRGs display evidence for significantAGN activity in the central starburst region. This is strong evi-dence that the BHs in these systems did not undergo rapid recoil events, and that any recoil motion was quickly damped out. How-ever, merger-triggered central AGN, particularly those in ULIRGs,may be dust-obscured or dwarfed by the luminous starburst. AGNthat are instead kicked out of the central region by a large recoilmay be more easily detected, provided a large enough region ofthe galaxy is observed. Additionally, we have shown that in somecases, bound recoiling AGN may have longer lifetimes than sta-tionary AGN. Such AGN may continue shining after the starburstis complete, which may also make them easier to observe.Moreover, in the simulations, at least, feedback from blackhole growth plays a significant role in quenching star formation (DiMatteo et al. 2005; Springel et al. 2005a), allowing the remnant toevolve from a blue, actively star-forming galaxy, to a red, quiescentobject. During this transition, the remnant can, for some period oftime, be classified as a K+A or E+A galaxy (Snyder 2010). If thecentral BH were ejected, star formation would linger at higher ratesthan for a stationary BH, extending the duration of the blue to redtransition, modifying the stellar populations, and ultimately yield-ing an elliptical with denser, more massive central stellar cusps. Ifthe BH did not eventually return to the nucleus, subsequent gas-poor mergers would be less strongly affected by BH scouring, ob-scuring the relationship between core and cusp ellipticals of thesame mass (Hopkins & Hernquist 2010b).Fig. 18 shows that if the BHs recoil at sufficiently high speed,the remnant relaxes to a state similar to what would have happenedhad the galaxies not had black holes. Compared to the case of noBH recoil, the remnants with recoiling BHs (or no BHs) have moremassive central stellar cusps. These more massive stellar cusps re-flect a more extended period of active star formation following fi-nal coalescence of the progenitor galaxies, lengthening the periodof time to make the blue to red transition. Furthermore, the reducedefficiency of AGN feedback means that the central regions wouldremain more heavily dust-obscured than if there were no BH re-coil, making the remnant less likely to be visible as a K+A galaxy(Snyder 2010) and potentially significantly reducing the number ofK+A galaxies expected to be observable as merger remnants.Using our suite of merger models, we can make some qual-itative predictions about the morphologies of recoiling BH hosts.Fig. 3 shows that our merger remnants have some common mor-phological features. In general, at the time of BH merger (and re-coil) the merging galaxies have undergone final coalescence (i.e.,they no longer have two distinct cores), but are still highly dis-turbed and have prominent tidal features. This is true even whenthe progenitor galaxies have low initial gas fractions (4%) or rela-tively small ratios (0.25). For minor mergers with q < . , the dis-ruption to the primary galaxy would be less pronounced, but suchmergers would also yield small GW recoil kicks. Highly-aligned(i.e. coplanar) galaxy merger orbits may result in remnants withregular disk structures (see Fig. 3), but these orbits should com-prise only a small fraction of major galaxy mergers. Therefore, weconclude that the majority of galaxy merger remnants that producelarge GW recoil events have single cores but are still tidally dis-turbed at the time of the recoil kick. Furthermore, we have shownthat the offset-AGN lifetimes for recoiling BHs in our simulationsare < Myr and are in most cases ∼ − Myr. Tidal struc-tures in these major merger remnants generally persist for at least afew hundred Myr, so it follows that most observable recoiling AGNshould be found in unrelaxed remnants that may still have visiblerings or tidal tails. c (cid:13) , 000–000 Blecha et al.
Shortly before this paper was completed, Guedes et al. (2010) andSijacki et al. (2010) completed independent studies of recoilingBHs in gaseous mergers. However, both of these papers are ex-ploratory in nature, in that only a few examples of galaxy merg-ers are studied. While there is agreement between these studies onsome fundamental conclusions, our large parameter study allowsus to expand upon these findings, connect them into a more coher-ent picture, and present some entirely new results. Here we give abrief comparison of this work to the work of Guedes et al. (2010)& Sijacki et al. (2010).Guedes et al. (2010) use one equal-mass and two minormerger remnants as initial conditions for their simulations. Themass and spatial resolution used are comparable to ours, thoughin their equal-mass merger, higher resolution is obtained at latestages via particle splitting. The merger orbits were coplanar andprograde, a configuration that results in highly disk-like remnants(see our Fig. 3). Recoils with a range of kick speeds were appliedto the BH, and after a brief initial phase, the BH trajectories werefollowed semi-analytically. We note that they use v k / v esc as low as0.14, while we use only v k > . v esc , such that the BHs do notspend most of their time at radii ∼ R soft .Sijacki et al. (2010) use isolated galaxy models as well as onegalaxy merger model for their recoiling BH simulations. Like oursimulations, theirs were performed using GADGET-3 , with similarspatial resolution. However, they use only one merger model, whichis massive and gas-rich, resulting in a remnant with a very high cen-tral escape speed (3500 km s − ) and steep central potential. Thismodel is therefore fairly extreme, in that recoils with v k ∼ v esc arerequired to eject the BH beyond the central few kpc.Despite the substantially different approaches of these twostudies and our own, a common finding is that gas inflow duringgalaxy mergers can create centrally-dense remnants that impart sig-nificant gas drag to recoiling BHs, thereby reducing the amplitudeand return time of their trajectories. That this effect remains impor-tant even for modest gas fractions ( < ∼ . ) illustrates the limitationsof modeling GW recoil dynamics in purely collisionless systems.Guedes et al. (2010) find that in their minor mergers, recoilingBHs exceed 600 km s − only for v k > v esc , and they do not cal-culate AGN lifetimes for escaping BHs. Kinematically-offset AGNhave lifetimes up to a few Myr in their q = 1 merger. Sijacki et al.(2010) note that velocity offsets up to 500 km s − may occur dur-ing the bright AGN phase in their isolated disk model, but do notdiscuss offset AGN in their merger model.Although they use similar values of L min and ∆ R min , Guedeset al. (2010) calculate longer spatially-offset AGN lifetimes than wefind in our models. The disparity in offset AGN lifetimes may arisepartly from the different dynamical treatments; Guedes et al. (2010)calculate the recoil trajectories semi-analytically, as opposed to ourN-body approach. Further, they assume ˙ M BH = ˙ M Edd for theejected-disk accretion rather than a time-dependent, isolated-diskmodel. They argue that spatially-offset AGN are naturally longer-lived than kinematically-offset AGN because the former occur nearapocenter and the latter near pericenter. However, we show that insome cases, kinematically-offset AGN may have longer lifetimes,because the BH is much more likely to be actively accreting duringpassages though the central dense region.As we have found in our recoil simulations, Sijacki et al.(2010) show that recoil events interrupt a phase of rapid BH ac-cretion in their gas-rich merger, causing a BH mass deficit relativeto a stationary BH. They note that BH mass deficits may introduce scatter into BH mass - host galaxy relationships, which we demon-strate robustly in § § q ∼ , gas-rich mergers. We eliminate much ofthis uncertainty in our simulations by scaling v k to v esc ( t mrg ). Thisapproach also enables a much clearer comparison between models.Also unique to our work is that we test a range of recoil kick di-rections in generic merger remnants, demonstrating that in general,the kick direction is less important for recoil trajectories than thekick magnitude.Another novel feature of our models is the inclusion of a time-dependent accretion disk around the recoiling BH. We also calcu-late recoiling AGN lifetimes using three different luminosity lim-its, which allows us to differentiate between bright and faint AGN.We learn from this analysis that some recoiling BHs may actuallyhave longer AGN lifetimes than stationary BHs, though at low lu-minosities. We also show that kinematically-offset AGN occur viatwo different mechanisms: repeated pericentric passages in mas-sive, gas-rich remnants, and ejected-disk accretion in high-velocityrecoils ( v k > v esc in our models). We demonstrate that spatially-offset AGN can occur for a wide range of kick speeds and mergermodels.Finally, we use our suite of simulations to construct M BH − σ ∗ relations for stationary and rapidly-recoiling BH populations. Wefind that GW recoil introduces a normalization offset and largeroverall and intrinsic scatter into this correlation.We have shown that recoiling BHs may be observable as offsetAGN; discoveries of these objects would both inform models ofhierarchical galaxy formation and constrain event rates for futuregravitational-wave observatories. In the meantime, the richly variedeffects of GW recoil on SMBHs and their host galaxies are not tobe discounted as important components of merger-driven galaxyevolution. ACKNOWLEDGEMENTS
This work was supported in part by NSF grant AST0907890 andNASA grants NNX08AL43G and NNA09DB30A (for A. L.) T. C.thanks the Keck Foundation for their support.
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