dynamics around supermassive black holes · 2013-12-16 · a. gualandris & d. merritt: dynamics...

arX

iv:0

708.

3083

v1 [

astr

o-ph

] 2

3 A

ug 2

007

Dynamics around supermassive black holes

By ALESSIA GUALANDRIS AND DAVID MERRITT

Department of Physics and Center for Computational Relativity and Gravitation, RochesterInstitute of Technology, Rochester, USA

The dynamics of galactic nuclei reflects the presence of supermassive black holes (SBHs) in manyways. Single SBHs act as sinks, destroying a mass in stars equal to their own mass in roughlyone relaxation time and forcing nuclei to expand. Formation of binary SBHs displaces a mass instars roughly equal to the binary mass, creating low-density cores and ejecting hyper-velocitystars. Gravitational radiation recoil can eject coalescing binary SBHs from nuclei, resulting inoffset SBHs and lopsided cores. We review recent work on these mechanisms and discuss theobservable consequences.

1. Characteristic scales

Supermassive black holes (SBHs) are ubiquitous components of bright galaxies andmany have been present with roughly their current masses (∼ 109M⊙) since very earlytimes, as soon as ∼ 1 Gyr after the Big Bang (Fan et al. 2003; Marconi et al. 2004).A SBH strongly influences the motion of stars within a distance rh, the gravitationalinfluence radius, where

rh =GM•

σ2c

; (1.1)

M• is the SBH mass and σc is the stellar (1d) velocity dispersion in the core. Using thetight empirical correlation between M• and σc:

(

M•

108M⊙

)

= (1.66± 0.24)

(

σc

200 km s−1

)α

, α = 4.86± 0.4 (1.2)

(Ferrarese & Ford 2005), this can be written

rh ≈ 18 pc

(

σc

200 km s−1

)2.86

≈ 13 pc

(

M•

108M⊙

)0.59

. (1.3)

While the velocities of stars must increase – by definition – inside rh, this radius isnot necessarily associated with any other observational marker. Such is the case at theGalactic center, for instance, where the stellar density exhibits no obvious feature atrh ≈ 3 pc. However the most luminous elliptical galaxies always have cores, regionsnear the center where the stellar density is relatively low. Core radii are of order rh inthese galaxies, and the stellar mass that was (apparently) removed in creating the coreis of order M•. These facts suggest a connection between the cores and the SBHs, andthis idea has motivated much recent work, reviewed here, on binary SBHs and on theconsequences of displacing SBHs temporarily or permanently from their central locationsin galaxies.An important time scale associated with galactic nuclei (not just those containing

SBHs) is the relaxation time, defined as the time for gravitational encounters betweenstars to establish a locally Maxwellian velocity distribution. The nuclear relaxation timeis (Spitzer 1987)

TR ≈0.34σ3

c

G2ρcm⋆ ln Λ(1.4a)

0

http://arxiv.org/abs/0708.3083v1

A. Gualandris & D. Merritt: Dynamics around supermassive black holes 1

Figure 1. Relaxation time, measured at the SBH influence radius, in a sample of early-typegalaxies (Cote et al. 2004), vs. the central stellar velocity dispersion. Filled symbols are galaxiesin which the SBH’s influence radius is resolved; the star is the Milky Way bulge. (From Merritt,Mikkola & Szell 2007).

≈ 1.2× 1010 yr

(

σc

100 km s−1

)3 (ρc

105M⊙pc−3

)−1 (m⋆

M⊙

)−1 (ln Λ

15

)−1

(1.4b)

with ρc the nuclear density and lnΛ the Coulomb logarithm. Figure 1 shows estimatesof TR measured at rh in a sample of early-type galaxies, assuming m⋆ = 1M⊙. A least-squares fit to the points (shown as the dashed line in the figure) gives

TR(rh) ≈ 2.5× 1013 yr

(

σ

200 km s−1

)7.47

≈ 9.6× 1012 yr

(

M•

108M⊙

)1.54

. (1.5)

“Collisional” nuclei can be defined as those with TR(rh) . 10 Gyr; figure 1 shows thatsuch nuclei are uniquely associated with galaxies that are relatively faint, as faint asor fainter than the Milky Way bulge, which has TR(rh) ≈ 4 × 1010 yr. Furthermore,relaxation-driven changes in the stellar distribution around a SBH are generally confinedto radii . 10−1rh, making them all but unobservable in galaxies beyond the Local Group(T. Alexander, these proceedings). But the relaxation time also fixes the rate of gravita-tional scattering of stars into the central “sink” – either a single or a binary SBH – andthis fact has important consequences for nuclear evolution in low-luminosity galaxies, asdiscussed below.

2. Core structure

The ‘core’ of a galaxy can loosely be defined as the region near the center where thedensity of starlight drops significantly below what is expected based on an inward ex-trapolation of the overall luminosity profile. At large radii, the surface brightness profilesof early-type galaxies are well fit by the Sersic (1968) model,

ln I(R) = ln Ie − b(n)[

(R/Re)1/n − 1

]

. (2.1)

2 A. Gualandris & D. Merritt: Dynamics around supermassive black holes

The quantity b is normally chosen such that Re is the projected radius containing one-half of the total light. The shape of the profile is then determined by n; n = 4 isthe de Vaucouleurs (1948) model, which is a good representation of bright elliptical (E)galaxies (Kormendy & Djorgovski 1989), while n = 1 is the exponential model, whichapproximates the luminosity profiles of dwarf elliptical (dE) galaxies (Binggeli, Sandage& Tarenghi 1984). An alternative way to write (2.1) is

d ln I

d lnR= −

b

n

(

R

Re

)1/n

, (2.2)

i.e. the logarithmic slope varies as a power of the projected radius. While there is noconsensus on why the Sersic model is such a good representation of stellar spheroids, apossible hint comes from the dark-matter halos produced in N -body simulations of hier-archical structure formation, which are also well described by (2.2) (Navarro et al. 2004),suggesting that Sersic’s model applies generally to systems that form via dissipationlessclustering (Merritt et al. 2005).Sersic’s model is known to accurately reproduce the luminosity profiles in some galaxies

over at least three decades in radius (e.g. Graham et al. 2003), but deviations oftenappear near the center. Galaxies fainter than absolute magnitude MB ≈ −19 tend tohave higher central surface brightness than predicted by Sersic’s model; the structureof the central excess is typically unresolved but its properties are consistent with thoseof a compact, intermediate-age star cluster (Carollo, Stiavelli & Mack 1998; Cote et al.

2006; Balcells et al. 2007). Galaxies brighter than MB ≈ −20 have long been knownto exhibit central deficits (e.g. Kormendy 1985a); these have traditionally been calledsimply “cores,” perhaps because a flat central density profile was considered a priorimost natural (Tremaine 1997).For about two decades, it was widely believed that dE galaxies were distinct objects

from the more luminous E galaxies. The dividing line between the two classes was put atabsolute magnitude MB ≈ −18, based partly on the presence of cores in bright galaxies,and also on the relation between total luminosity and mean surface brightness (Kormendy1985b). This view was challenged by Jerjen & Binggeli (1997), and in a compelling seriesof papers, A. Graham and collaborators showed that – aside from the cores – early-typegalaxies display a remarkable continuity of structural properties, from MB ≈ −13 toMB ≈ −22 (Graham & Guzman 2003; Graham et al. 2003; Trujillo et al. 2004).The connection between nuclear star clusters and SBHs, if any, is unclear; in fact it

has been suggested that the two are mutually exclusive (Ferrarese et al. 2006; Wehner& Harris 2006), although counter-examples to this rule probably exist, e.g. NGC 3384which contains a nuclear cluster (Ravindranath et al. 2001) and may contain a SBH(Gebhardt et al. 2003).Here we focus on the cores. The cores extend outward to a break radius rb that is

roughly a few times rh, or from ∼ 0.01 to ∼ 0.05 times Re. A more robust way ofquantifying the cores is in terms of their mass (i.e. light): the “mass deficit” (Milosavljevicet al. 2002) is defined as the difference in integrated mass between the observed densityprofile ρ(r) and an inward extrapolation of the outer profile, ρout(r), typically modelledas a Sersic profile (figure 2):

Mdef ≡ 4π

∫ rb

0

[ρout(r) − ρ(r)] r2dr. (2.3)

Figure 2 shows mass deficits for a sample of “core” galaxies, expressed in units of theSBH mass. There is a clear peak at Mdef ≈ 1M•, although some galaxies have muchlarger cores.


[t]

Figure 2. Left: Surface brightness profile in the R band of NGC 3348, a “core” galaxy. Thedashed line is the best-fitting Sersic model; the observed profile (points, and solid line) falls belowthis inside of a break radius rb ≈ 0′′.35. (From Graham 2004.) Right: Histogram of observed massdeficits for the sample of core galaxies in Graham (2004) and Ferrarese et al. (2006). (Adaptedfrom Merritt 2006a.)

The fact that core and SBH masses are often so similar suggests a connection betweenthe two. Ejection of stars by binary SBHs during galaxy mergers is a natural model(Begelman, Blandford & Rees 1980); the non-existence of cores in fainter galaxies couldthen be due to regeneration of a steeper density profile by star formation (e.g. McLaughlinet. al 2006) or by dynamical evolution associated with the (relatively) short relaxationtimes in faint galaxies (e.g. Merritt & Szell 2006). However the largest cores are difficultto explain via the binary model (Milosavljevic & Merritt 2001).

3. Massive binaries

A typical mass ratio for galaxy mergers in the local Universe is ∼ 10 : 1 (e.g. Sesanaet al. 2004). To a good approximation, the initial approach of the two SBHs can thereforebe modelled by assuming that the galaxy hosting the smaller BH spirals inward under theinfluence of dynamical friction from the fixed distribution of stars in the larger galaxy.Modelling both galaxies as singular isothermal spheres (ρ ∼ r−2) and assuming that thesmaller galaxy spirals in on a circular orbit, its tidally-truncated mass is m2 ≈ σ3

2r/2Gσwhere σ2 and σ are the velocity dispersion of the small and large galaxy respectively(Merritt 1984). Chandrasekhar’s (1943) formula then gives for the orbital decay rate andinfall time

dr

dt= −0.30

Gm2

σrln Λ, tinfall ≈ 3.3

r(0)σ2

σ32

(3.1)

where lnΛ has been set to 2. Using (1.2) to relate σ and σ2 to the respective SBH massesM1 and M2, this becomes

tinfall ≈ 3.3r(0)

σ

(

M2

M1

)−0.62

, (3.2)

i.e. tinfall exceeds the crossing time of the larger galaxy by a factor∼ q−0.6, q ≡ M2/M1 6

1. Thus for mass ratios q & 10−3, infall requires less than ∼ 102Tcr ≈ 1010 yr. This mass


ratio is roughly the ratio between the masses of the largest (∼ 109.5M⊙) and smallest(∼ 106.5M⊙) known SBHs and so it is reasonable to assume that galaxy mergers willalmost always lead to formation of a binary SBH in a time less than 10 Gyr. Thisconclusion is strengthened if the effects of gas are taken into account (e.g. Mayer et al.2007).Equation (3.1) begins to break down when the two SBHs approach more closely than

∼ rh, the influence radius of the larger hole, since the orbital energy of M2 is absorbedby the stars, lowering their density and reducing the frictional force. In spite of thisslowdown, N -body integrations (Merritt & Cruz 2001; Merritt & Milosavljevic 2001;Makino & Funato 2004; Berczik et al. 2005) show that the separation between the twoSBHs continues to drop rapidly until the binary semi-major axis is a ≈ ah, where

ah ≡Gµ

4σ2≈

1

4

q

(1 + q)2rh (3.3a)

≈ 3.3pcq

(1 + q)2

(

M1 +M2

108M⊙

)0.59

(3.3b)

and µ ≡ M1M2/(M1 +M2) is the binary reduced mass. At this separation – the “hardbinary” separation – the binary’s binding energy per unit mass is ∼ σ2 and it ejects starsthat pass within a distance ∼ a with velocities large enough to remove them from thenucleus (Mikkola & Valtonen 1992; Quinlan 1996).What happens next depends on the density and geometry of the nucleus. In a spherical

or axisymmetric galaxy, the mass in stars on orbits that intersect the binary is small,. M1+M2, and the binary rapidly ejects these stars; no stars then remain to interact withthe binary and its evolution stalls (figure 3). In non-axisymmetric (e.g. triaxial) nuclei, themass in stars on centrophilic orbits can be much larger, allowing the binary to continueshrinking past ah. And in collisional nuclei of any geometry, gravitational scattering ofstars can repopulate depleted orbits. These different possbilities are discussed in moredetail below.If the binary does stall at a ≈ ah, it will have given up an energy

∆E ≈ −GM1M2

2rh+

GM1M2

2ah(3.4a)

≈ −1

2M2σ

2 + 2(M1 +M2)σ2 (3.4b)

≈ 2(M1 +M2)σ2 (3.4c)

to the stars in the nucleus, i.e., the energy transferred from the binary to the stars isroughly proportional to the combined mass of the two SBHs. The reason for this counter-intuitive result is the ah ∝ M2 dependence of the stalling radius (3.3): smaller infallingBHs form tighter binaries. Detailed N -body simulations (Merritt 2006a) verify that themass deficit generated by the binary in evolving from ∼ rh to ∼ ah is a weak function ofthe mass ratio,

Mdef,h ≈ 0.4(M1 +M2)( q

0.1

)0.2

(3.5)

for 0.025 . q . 0.5. A mass deficit of ∼ 0.5M• is still a factor ∼ 2 too small to explain theobserved peak in the Mdef/M• histogram (figure 2). On the other hand, bright ellipticalgalaxies have probably undergone numerous mergers, and the proportionality betweenMdef and M1 + M2 (rather than, say, M2) implies that the mass deficit following Nmergers is ∼ 0.5N times the accumulated BH mass. Mass deficits in the range 0.5 .

Mdef/M• . 1.5 therefore imply 1 . N . 3 mergers, consistent with the number of


[t]

Figure 3. Early evolution of binary SBHs in N-body galaxies, for different values of the binarymass ratio, M2/M2 = 0.5, 0.25, 0.1, 0.05, 0.025 (left to right). The upper horizontal line indicatesrh, the influence radius of the more massive hole. Lower horizontal lines show ah (3.3), the“hard-binary” separation. The evolution of the binary slows drastically when a ≈ ah; in a real(spherical) galaxy with much larger N , evolution would stall at this separation. The smaller theinfalling BH, the farther it spirals in before stalling. (Adapted from Merritt 2006a.)

major mergers expected for bright galaxies since the epooch at which most of the gaswas depleted (e.g. Haehnelt & Kauffmann 2002). Hierarchical growth of cores tends tosaturate after a few mergers however making it difficult to explain mass deficits greaterthan ∼ 2M• in this way. An effective way to enlarge cores still more is to kick the SBHout, at least temporarily, as discussed in §4.

The first convincing evidence for a true, binary SBH was recently presented by Rodriguez et al. (2006),who discovered two compact, flat-spectrum AGN at the center of a single elliptical galaxy,with a projected separation of ∼ 7 pc. This is consistent with the radius at formation ofa ∼ 107.5M⊙ binary (1.3), or the stalling radius for a binary of at least ∼ 109.3M⊙ (3.3).Rodriguez et al. estimate a binary mass of ∼ 108M⊙ but with considerable uncertainty.All other examples of “binary” SBHs in single galaxies have separations ≫ rh (Komossa2006).

Even in a spherical galaxy, the stalling that occurs at a ≈ ah can be avoided if starscontinue to be scattered onto orbits that intersect the binary (Valtonen 1996; Yu 2002;Milosavljevic & Merritt 2003). Such “collisional loss-cone repopulation” requires thatthe two-body (star-star) relaxation time at r ≈ rh be less then ∼ 1010 yr; according to(1.5), this is the case in galaxies with M• . 106M⊙, i.e. at the extreme low end of theSBH mass distribution. Collisional loss cone repopulation is therefore irrelevant to theluminous galaxies that are observed to have cores but may be important in the mass


Figure 4. Short-term (a) and long-term (b) evolution of a massive binary in a series of N-bodyintegrations. Vertical axis is the inverse semi-major axis (i.e. energy) of the binary, computedby averaging several independent N-body runs; different curves correspond to different values ofN , the number of “star” particles. The evolution of the binary is independent of N until a ≈ ah

(horizontal line); thereafter the evolution rate is limited by how quickly stars are scattered ontoorbits that intersect the binary, and decreases with increasing N . (From Merritt, Mikkola &Szell 2007.)

range (M• . 107M⊙) of most interest to space-based gravitational wave interferometerslike LISA (Hughes 2006).N -body simulation would seem well suited to this problem (e.g. Governato, Colpi &

Maraschi 1994; Makino 1997; Milosavljevic & Merritt 2001; Makino & Funato 2004).The difficulty is noise – or more precisely, getting the level of noise just right. In a realgalaxy there is a clear separation of time scales between an orbital period, and the timefor stars to be scattered onto depleted orbits: the first is typically much shorter thanthe second which means that orbits intersecting the binary will remain empty for manyperiods before a new star is scattered in. This is called the “empty loss cone” regimeand it implies that supply of stars to the binary will take place diffusively. In an N -body simulation, however, N is much smaller than its value in real galaxies and orbitsare repopulated too quickly. This is the reason that binary evolution rates in N -bodysimulations typically scale as N−α, α < 1 rather than the ∼ T−1

R ∼ N−1 dependenceexpected if stars diffused gradually into an empty loss cone (Merritt & Milosavljevic2003). Figure 4 provides an illustration: early evolution of the binary, until a ≈ ah, isN -independent; formation of a hard binary then depletes the loss cone and continuedhardening occurs at a rate that is a decreasing function of N , though less steep thanN−1.An alternative approach is based on the Fokker-Planck equation. Both single and

binary SBHs can be modelled as “sinks” located at the centers of galaxies (Yu 2002).The main differences are the larger physical extent of the binary (∼ G(M1 +M2)/σ

2 vs.GM•/c

2) and the fact that the binary gives stars a finite kick rather than disrupting orconsuming them completely. However the diffusion rate of stars into a central sink variesonly logarithmically with the size of the sink (Lightman & Shapiro 1978), and a hardbinary ejects most stars well out of the core with V ≫ σ, so the analogy is fairly good.


Figure 5. Evolution of a binary SBH in a collisional nucleus, based on a Fokker-Planck modelthat allows for evolution of the stellar distribution (Merritt, Mikkola & Szell 2007). Left:Probability of finding the binary in a unit interval of ln a. From left to right, curves are forM1 + M2 = (0.1, 1, 10, 100) × 106M⊙. Solid (dashed) curves are for M2/M1 = 1(0.1). Opencircles indicate when the rate of energy loss to stars equals the loss rate to gravitational waves;filled circles correspond to an elapsed time since a = ah of 1010 yr. For the two smallest valuesof M•, the latter time occurs off the graph to the right. Right: Total time for a binary to evolvefrom a = ah to gravitational wave coalescence as a function of binary mass. The thick (black)curve is for M2/M1 = 1 and the thin (blue) curve is for M2/M1 = 0.1. Dotted curves show thetime spent in the gravitational radiation regime only.

The Fokker-Planck equation describing nuclei with sinks is (Bahcall & Wolf 1977)

∂N

∂t= 4π2p(E)

∂f

∂t= −

∂FE

∂E−F(E, t). (3.6)

Here N(E, t) = 4πp(E)f(E, t) is the distribution of stellar energies, f(E, t) is the phasespace density and p(E) is a phase-space volume element. The first term on the RHS of(3.6) describes the response of f to the flux FE of stars in energy space due to encounters.The second term, −F , is the flux of stars into the sink, which is dominated by scatteringin angular momentum (Frank & Rees 1976). A proper treatment of the latter termrequires a 2d (energy, angular momentum) analysis, but a good approximation to F canbe derived by assuming that the distribution of stars has reached a quasi steady-statenear the loss cone boundary in phase space (Cohn & Kulsrud 1979). If the sink is abinary SBH, a second equation is needed that relates the flux of stars into the loss coneto the rate of change of the binary’s semi-major axis:

d

dt

(

1

a

)

=2〈C〉

a(M1 +M2)

∫

F(E, t)dE (3.7)

with 〈C〉 ≈ 1.25 a dimensionless mean energy change for stars that interact with thebinary.Both terms on the RHS of (3.6) imply changes in a time ∼ TR. The first term on its

own implies evolution toward the Bahcall-Wolf (1976) “zero flux” solution, ρ ∼ r−7/4.


The second term implies that a mass of order ∼ M• will be scattered into the sink ina time of TR(rh). When the sink is a binary SBH, the binary responds by ejecting theincoming stars and shrinking, according to (3.7). As a result, changes in the structure ofthe nucleus on a relaxation time scale (e.g. growth of a core) are directly connected tochanges in the binary semi-major axis.Numerical solutions to (3.6), (3.7) (including also the effects of a changing gravitational

potential) have been presented by Merritt et al. (2007). The solutions are well fit by

ln(aha

)

= −B

A+

√

B2

A2+

2

A

t

TR(rh)(3.8)

where t is defined as the time since the binary first became hard (a = ah), and thecoefficients A ≈ 0.016, B ≈ 0.08 depend weakly on the binary mass ratio. Including theeffect of energy lost to gravitational radiation:

d

dt

(

1

a

)

=d

dt

(

1

a

)

stars

+d

dt

(

1

a

)

GR

(3.9)

allows one to compute the time to full coalescence, Tcoal. Figure 5 shows Tcoal (rightpanel), and the time spent by the binary in unit intervals of ln a prior to coalescence (leftpanel), as functions of binary mass. The time to coalescence is well fit by

Y = C1 + C2X + C3X2, (3.10a)

Y ≡ log10

(

Tcoal

1010yr

)

, (3.10b)

X ≡ log10

(

M1 +M2

106M⊙

)

. (3.10c)

with

M2/M1 = 1 : C1 = −0.372, C2 = 1.384, C3 = −0.025 (3.11a)

M2/M1 = 0.1 : C1 = −0.478, C2 = 1.357, C3 = −0.041. (3.11b)

Based on the figure, binary SBHs would be able to coalesce via interaction with starsalone in galaxies with M• . 2×106M⊙. ForM1+M2 & 107M⊙, evolution for 10 Gyr onlybrings the binary separation slightly below ah; in such galaxies the most likely separationto find a massive binary (in the absence of other sources of energy loss) would be nearah.The core continues to grow as the binary shrinks, but the mass deficit is not related in

a simple way to the mass in stars “ejected” by the binary (e.g. Quinlan 1996). Rather itresults from a competition between loss of stars to the binary, represented by −F(E, t),and the change in N(E, t) due to diffusion of stars in energy, represented by −∂FE/∂E.As the mass deficit increases, so do gradients in f , which increases the flux of stars towardthe center and counteracts the drop in density. In principle the two terms could balance,but at some distance from the center the relaxation time is so long that local FE(E) mustdrop below the integrated loss term

∫∞

E F(E)dE – stars can not diffuse in fast enough toreplace those being lost to the binary and the density drops. The Fokker-Planck solutionsshow that the mass deficit increases with binary binding energy as

Mdef,c ≈ 1.7 (M1 +M2) log10 (ah/a) (3.12)

again with a weak dependence on M2/M1. The mass deficit at the onset of the gravita-


tional radiation regime is found to be

Mdef,c ≈ (4.5, 3.5, 2.6, 1.6)(M1 +M2) (M2/M1 = 1) (3.13a)

≈ (3.4, 2.6, 1.7, 0.9)(M1 +M2) (M2/M1 = 0.1) (3.13b)

for M1+M2 = (105, 106, 107, 108)M⊙. These values should be added to the mass deficits(3.5) generated during formation of the binary when predicting core sizes in real galaxies.Are such mass deficits observed? Only a handful of galaxies in the relevant mass range

(Mgal . 1010M⊙) are near enough that their cores could be resolved even if present; ofthese, neither the Milky Way nor M32 exhibit cores. Also, as noted above, many low-luminosity spheroids have compact central excesses rather than cores. These facts donot rule out the past existence of massive binaries in these galaxies however. (1) Binaryevolution might have been driven more by gas dynamical torques than by ejection ofstars; gas content during the most recent major merger is believed to be a steep inversefunction of galaxy luminosity (Kauffmann & Haehnelt 2000). (2) Star formation cancreate a dense core after the two SBHs have coalesced (Mihos & Hernquist 1994). (3) Atwo-body relaxation time short enough to bring the two SBHs together would also allowa Bahcall-Wolf cusp to be regenerated in a comparable time after the two SBHs combine,tending to erase the core (Merritt & Szell 2006).From the point of view of physicists hoping to detect gravitational waves, it is disap-

pointing that this model only guarantees coalescence at the extreme low end of the SBHmass distribution. (Astronomers hoping to detect binary SBHs may take the oppositepoint of view.) Fortunately, there is no dearth of ideas for overcoming the “final parsecproblem” and allowing binary SBHs to merge efficiently, even in massive galaxies:Non-axisymmetric geometries. Real galaxies are not spherical nor even axisym-

metric; parsec-scale bars are relatively common and departures from axisymmetry areoften invoked to enhance fueling of AGN (e.g. Shlosman et al. 1990). Orbits in a triaxialnucleus can be “centrophilic,” passing arbitrarily close to the center after a sufficientlylong time (Poon & Merritt 2001, 2004). This implies feeding rates for a central binarythat can approach the “full loss cone” rate in spherical geometries, or

d

dt

(

1

a

)

≈ 2.5Fcσ

r2h(3.14)

if the fraction Fc of centrophilic orbits is large (Merritt & Poon 2004). While Fc isimpossible to know in any particular galaxy, even small values imply much larger feedingrates than in a diffusively-repopulated loss cone. Figure 6 shows results from N -bodysimulations that support this idea.Secondary slingshot. Stars ejected by a massive binary can interact with it again

if they return to the nucleus on nearly-radial orbits. The total energy extracted fromthe binary via this “secondary slingshot” will be the sum of the discret energy changesduring the interactions. Milosavljevic & Merritt (2003) showed that a mass M⋆ of starsinitially in the binary’s loss cone causes the binary to evolve as

1

a≈

1

ah+

4

rhln

(

1 +t

t0

)

, t0 =2µσ2

M⋆〈∆E〉P (E) (3.15)

in the absence of diffusive loss cone repopulation, where 〈∆E〉 is the specific energy changeafter one interaction with the binary,E is the initial energy and P (E) is the orbital period.The secondary slingshot runs its course after a few orbital periods. Sesana et al. (2007)sharpened this analysis by carrying out detailed three-body scattering experiments andrecording the precise changes in energy of stars as they underwent repeated interactions


Figure 6. Efficient merger of binary SBHs in barred galaxies. Plots are based on N-bodysimulations (no gas) of equal-mass binaries at the centers of galaxy models, with and withoutrotation. (a) Spherical models. The binary hardening rate declines with increasing N , as infigure 4, implying that the evolution would stall in the large-N limit. (b) Binary evolution ina flattened, rotating version of the same galaxy model. At t ≈ 10, the rotating model forms atriaxial bar. Binary hardening rates in this model are essentially independent of N , indicatingthat the supply of stars to the binary is not limited by collisional loss-cone refilling as in thespherical models. This is currently the only simulation that follows two SBHs from kiloparsecto sub-parsec separations and that can be robustly scaled to real galaxies. (From Berczik et al.2006.)

with the binary. They inferred modest (∼ ×2) changes in 1/a due to the secondary sling-shot, but their assumption of a ρ ∼ r−2 density profile around the binary was probablyover-optimistic; such steep density profiles are never observed and even if present initiallywould be rapidly destroyed when the binary first formed.Bound subsystems. As noted above, recent observational studies have greatly in-

creased the number of galaxies believed to harbor compact nuclear star clusters; inferredmasses for the clusters are comparable with the mass that would normally be associatedwith a SBH. It is not yet clear whether these subsystems co-exist with SBHs, but ifthey do, they could provide an extra source of stars to interact with a massive binary.Zier (2006, 2007) explored this idea, assuming a steeply rising density profile around thebinary, ρ ∝ r−γ , at the time that its separation first reached ∼ ah. Zier concluded that acluster having total mass ∼ M1+M2, distributed as a steep power law, γ & 2.5, could ex-tract enough energy from the binary to allow gravitational wave coalescence in less than10 Gyr. N -body tests of this hypothesis are sorely needed; as in the Sesana et al. (2007)study, Zier’s approach did not allow him to self-consistently follow the effect of formationof the binary on the surrounding mass distribution.Masive perturbers. In a nucleus containing a spectrum of masses, the gravitational

scattering rate is proportional to

m =

∫

n(m)m2dm∫

n(m)mdm(3.16)

(e.g. Merritt 2004). Perets et al. (2007) argued that “massive perturbers” near the center


of the Milky Way – massive stars, star clusters, giant molecular clouds – are sufficientlynumerous to dominate m, implying potentially much higher rates of gravitational scatter-ing into a central sink than in the case of solar-mass perturbers. Perets & Alexander (2007)extended this argument to galaxies in general, emphasizing in particular the early stagesfollowing a galactic merger, and concluded that collisional loss cone repopulation wouldbe sufficient to guarantee coalescence of binary SBHs in less than 10 Gyr for all butthe most massive binaries. As in the studies of Sesana et al. (2007) and Zier (2007),Perets & Alexander (2007) optimistically assumed a steep (ρ ∝ r−2) density profilearound the binary, in spite of N -body studies showing rapid destruction of the cusps.Their arguments for massive perturbers in giant E galaxies are also rather speculative.

Multiple SBHs. An extreme case of a “massive perturber” is a third SBH, whichmight scatter stars into a central binary (Zhao et al. 2002), or perturb the binary di-rectly, driving the two SBHs into an eccentric orbit and shortening the time scale forgravitational wave losses (Valtonen et al. 1994; Makino & Ebisuzaki 1994; Blaes et al.

2002; Volonteri et al. 2003; Iwazawa et al. 2006; Hoffman & Loeb 2007). The likelihoodof multiple-SBH systems forming is probably highest in the brightest E galaxies sincemassive binaries are most likely to stall (low stellar density, little gas) and since largegalaxies experience the most frequent mergers. Here again, more N -body simulations,including post-Newtonian terms, are needed; among other dynamical effects that couldthen be self-consistently included are changes in core structure, and BH-core oscillationslike those described in the next section.

Gas. The same galaxy mergers that create binary SBHs can also drive gas into thenucleus, and there is abundant observational evidence for cold (e.g. Jackson et al. 1993;Gallimore et al. 2001; Greenhill et al. 2003) and hot (e.g. Baganoff et al. 2003) gas near thecenters of at least some galaxies. Dense concentrations of gas can substantially acceleratethe evolution of a massive binary by increasing the drag on the individual BHs (Escalaet al. 2004, 2005; Dotti et al. 2007). The plausibility of such dense accumulations of gas,with mass comparable to the mass of the SBHs, is unclear however (e.g. Sakamoto et al.

1999; Christopher et al. 2005). Large-scale galaxy merger simulations (Kazantzidis et al.2005; Mayer et al. 2007) show that the presence of gas leads to more rapid formationof the massive binary, but these simulations still lack the resolution to follow the binarypast a ≈ rh and so have nothing relevant to say (yet) concerning the final parsec problem.

As this summary indicates, many possible solutions to the “final parsec problem” exist,but none is guaranteed to be effective in all or even most galaxies. The safest bet is thatboth coalesced and uncoalesced binary SBHs exist, but with what relative frequency isstill anyone’s guess.

4. SBH/IBH binaries

Secure dynamical evidence exists for SBHs in the mass range 106.5 . M•/M⊙ . 109.5

(Ferrarese & Ford 2005) and compelling arguments have been made for BHs with masses105 . M•/M⊙ . 107 in active nuclei (Greene & Ho 2004). Binary mass ratios as extremeas 1000 : 1, and possibly greater, are therefore to be expected. This possibility hasreceived most attention in the context of intermediate-mass black holes (IBHs) in theMilky Way, where they could form in dense star clusters like the Arches or Quintupletbefore spiralling into the center and forming a tight binary with the ∼ 3.5× 106M⊙ SBH(Portegies Zwart & McMillan 2002; Hansen & Milosavljevic 2003).


Figure 7. Left: N-body simulations of the inspiral of IBHs into the center of the Milky Way.Solid lines show the separation between the two BHs and dashed lines are theoretical predictionsthat ignore loss-cone depletion or changes in the structure of the core. Smaller IBHs spiralin farther before “stalling”; the MIBH = 103M⊙ simulation ends before the stalling radiusis reached. (From Baumgardt, Gualandris & Portegies Zwart 2006.) Right: Evolution beyonda = ah, based on the Fokker-Planck model of Merritt, Mikkola & Szell (2007). Dashed linesindicate when the evolution time due to gravitational radiation losses is less than 10 Gyr.

The predicted hard-binary separation for a SBH/IBH pair is (3.3)

ah ≈ 0.5mpc( q

10−3

)

(

M•

3.5× 106M⊙

)0.59

, q ≡MIBH

M•

. (4.1)

This separation – ∼ 102 AU – is comparable to the periastron distances of the famous“S” stars (Eckart et al. 2002; Ghez et al. 2005). Dynamical constraints on the existence ofan IBH at this distance from the SBH are currently weak (Yu & Tremaine 2003; Hansen& Milosavljevic 2003; Reid & Brunthaler 2004). Figure 7a shows N -body simulationsdesigned to mimic inspiral of IBHs into the Galactic center. The figure confirms theexpected slowdown in the inspiral rate at a separation ∼ ah. Figure 7b plots evolutionarytracks for the same three IBH masses as in the left panel, based on the Fokker-Planckmodel of Merritt et al. (2007). For MIBH . 103M⊙, evolution of the binary is dominatedby gravitational wave losses already at a = ah.The same inward flux of stars that allows the binary to shrink also implies an outward

flux of stars ejected by the binary. The latter are a potential source of “hyper-velocitystars” (HVSs), stars moving in the halo with greater than Galactic escape velocity (Hills1988). The relation between the stellar ejection rate and the binary hardening rate, whena 6 ah, is given by (3.7) after rewriting it as

Thard ≡ ad

dt

(

1

a

)

≈2.5

M•

× flux; (4.2)

here “flux” is the total mass in stars per unit time, from all energies, that are scatteredinto (and ejected by) the binary. Combining (4.2) with (3.8), the flux is

∼ 5.0M•

TR(rh)

[

1 +5t

TR(rh)

]−1/2

(4.3a)


Figure 8. Left: Creation of a core by inspiral of IBHs into the Galactic center. The initialdensity profile is shown by the solid line. Green (dotted) line shows the core 10 Myr afterthe 104M⊙ IBH has merged with the SBH; almost no change occurs during this time. (FromBaumgardt, Gualandris & Portegies Zwart 2006.) Right: Fokker-Planck model showing how thecusp regenerates due to two-body scattering, on Gyr timescales. (Adapted from Merritt, Mikkola& Szell 2007.)

. 350M⊙yr−1 (4.3b)

where the second line uses values appropriate to the Galactic center. Relating the to-tal ejected flux to the number of HVSs that would be observed is not straighforward;for instance, only a fraction (. 10%) would be ejected with high enough velocity tostill be moving faster than ∼ 500 km s−1 after climbing through the Galactic potential(Gualandris et al. 2005; Baumgardt et al. 2006), and targeted searches for HVSs onlydetect certain stellar types so that knowledge of the stellar mass function is also required(Brown et al. 2006).

Inspiral of the IBH creates a core of radius ∼ 0.05 pc ≈ 1′′ (figure 8a). Such a coremight barely be detectable at the center of the Milky Way from star counts. There isno clear indication of a core (Schoedel et. al 2007), but if the inspiral occurred morethan a few Gyr ago, star-star gravitational scattering would have gone some way toward“refilling” the region depleted by the binary (Merritt & Wang 2005; Merritt & Szell 2006;figure 7b). In this case, however, the ejected stars would almost all have moved beyondthe range of HVS surveys by now.

The angular distribution of the ejected stars has been proposed as a test for their origin;unlike other possible sources of HVSs, a SBH/IBH binary tends to eject stars parallel tothe orbital plane or, if the orbit is eccentric, in a particular direction (Levin 2006; Sesanaet al. 2006). In two N -body simulations of IBH inspiral however (Baumgardt, Gualandris& Portegies Zwart 2006; Matsubayashi et al. 2007), the orientation of the binary beganto change appreciably, in the manner of a random walk, after it became hard. This wasdue to “rotational Brownian motion” (Merritt 2002): torques from passing stars – thesame stars that extract energy and angular momentum from the binary – also changethe direction of the binary’s orbital angular momentum vector. In one hardening time


|a/a| of the binary, its orientation changes by

∆θ ≈ q−1/2

(

m⋆

M•

)1/2(

1− e2)−1/2

(4.4a)

≈ 9.0◦( q

10−3

)−1/2(

M•

106m⋆

)−1/2[

(

1− e2)−1/2

5

]

. (4.4b)

(The eccentricity dependence in (4.4b) is approximate; the numerical coefficient in thisequation has only been confirmed by detailed scattering experiments for e = 0.) In bothof the cited N -body studies, the binary eccentricity evolved appreciably away from zerobefore the orientation changes became signficant. Rotational Brownian motion mightnot act quickly enough to randomize the orienation of a SBH/IBH binary in a time of∼ 108 yr, the flight time from the Galactic center to the halo, unless perturbers moremassive than Solar-mass stars are present near the binary however (Merritt 2002; Perets& Alexander 2007).

5. Kicks and cores

After seeming to languish for several decades, the field of numerical relativity has re-cently experienced exciting progress. Following the breakthrough papers of Pretorius (2005),Campanelli et al. (2006) and Baker et al. (2006a), several groups have now successfullysimulated the evolution of binary BHs all the way to coalescence. The final inspiral isdriven by emission of gravitational waves, and in typical (asymmetric) inspirals, a netimpulse – a “kick” – is imparted to the system due to anisotropic emission of the waves(Bekenstein 1973; Fitchett 1984; Favata et al. 2004). Early arguments that the magni-tude of the recoil velocity would be modest for non-spinning BHs were confirmed by thesimulations, which found Vkick . 200 km s−1 in the absence of spins (Baker et al. 2006;Gonzalez et al. 2007a; Herrmann et al. 2007). The situation changed dramatically fol-lowing the first (Campanelli et al. 2007a) simulations of “generic” binaries, in which theindividual BHs were spinning and tilted with respect to the orbital angular momentumvector. Kicks as large as ∼ 2000 km s−1 have now been confirmed (Campanelli et al.

2007b; Gonzalez et al. 2007b; Tichy & Marronetti 2007), and scaling arguments basedon the post-Newtonian approximation suggest that the maximum kick velocity wouldprobably increase to ∼ 4000 km s−1 in the case of maximally-spinning holes (Campanelliet al. 2007b). The most propitious configuration for the kicks appears to be an equal-massbinary in which the individual spin vectors are oppositely aligned and oriented parallelto the orbital plane. For unequal-mass binaries, the maximum kick is

Vmax ≈ 6× 104km s−1 q2

(1 + q)4(5.1)

where q ≡ M2/M1 6 1 is the binary mass ratio and maximal spins have been assumed(Campanelli et al. 2007c). Orienting the BHs with their spins perpendicular to the orbitalangular momentum may seem odd (Bogdanovic, Reynolds & Miller 2007), but there isconsiderable evidence that SBH spins bear no relation to the orientations of the gas disksthat surround them (e.g. Kinney et al. 2000; Gallimore et. al. 2006) and this is presumablyeven more true with respect to the directions of infalling BHs. Galaxy escape velocitiesare . 3000 km s−1 (Merritt et al. 2004), so gravitational wave recoil can in principleeject coalescing SBHs completely from galaxies.Detailed N -body simulations show that the motion of a SBH that has been kicked


Figure 9. Left: Core oscillations in an N-body simulation of ejection of a SBH from the centerof a galaxy; the kick velocity was 60% of the escape velocity. Contour plots show the stellardensity at equally spaced times, spanning ∼ 1/2 of the SBH’s orbital period. Filled circles arethe SBH and crosses indicate the location of the (projected) density maxima. (From Gualandris& Merritt 2007.) Right: Surface brightness contours of three “core” galaxies with double or offsetnuclei, from Lauer et al. (2005). Top: NGC 4382; middle: NGC 507; bottom: NGC 1374.

with enough velocity to eject it out of the core, but not fast enough to escape the galaxyentirely, exhibits three distinct phases (Gualandris & Merritt 2007):• Phase I: The SBH oscillates with decreasing amplitude, losing energy via dynamical

friction each time it passes through the core. Chandrasekhar’s theory accurately repro-duces the motion of the SBH in this regime for values 2 . ln Λ . 3 of the Coulomblogarithm, if the gradually-decreasing core density is taken into account.• Phase II: When the amplitude of the motion has decayed to roughly the core radius,

the SBH and core begin to exhibit oscillations about their common center of mass (fig-


Figure 10. Evolution of the SBH kinetic energy following a kick of 60% the central escape veloc-ity, in two N-body simulations of a galaxy represented by N stars, with N = (2.5×105, 2×106).The mass of the SBH, and the total mass of the galaxy, are the same in the two simulations;all that varies is the mass of the “star” particles. The right-hand panel shows binned values ofV 2. Most of the elapsed time is spent in SBH/core oscillations like those illustrated in figure 9.Eventually, the SBH’s kinetic energy decays to the Brownian value, shown as the horizontal

dashed lines in the right panel. The Brownian velocity scales as m1/2⋆ and so is smaller for larger

N . Scaled to a 3× 1010M⊙ galaxy, the time to reach the Brownian regime would be ∼ 108 yr.(Adapted from Gualandris & Merritt 2007.)

ure 9). These oscillations decay exponentially (figure 10), but with a time constant thatis 10− 20 times longer than would be predicted by a naive application of the dynamicalfriction formula.• Phase III: Eventually the SBH’s kinetic energy drops to an average value

1

2M•V

2• ≈

1

2m⋆v

2⋆ (5.2)

i.e. to the kinetic energy of a single star. This is the regime of gravitational Brownianmotion (Bahcall & Wolf 1976; Young 1977; Merritt et al. 2007).A natural definition of the “return time” of a kicked SBH is the time to reach the

Brownian regime. Unless the kick is very close to the escape velocity, the return time isdominated by the time spent in “Phase II;” during this time, the SBH’s energy decaysroughly as

E ≈ Φ(0) + Φ(rc)e−(t−tc)/τ (5.3)

(Gualandris & Merritt 2007); tc is the time when the SBH re-enters the core whose radiusis rc. The damping time in the N -body simulations, τ , is

τ ≈ 15σ3c

G2ρcM•

(5.4a)

≈ 1.2× 107yr

(

σc

250km s−1

)3 (ρc

103M⊙pc−3

)−1 (M•

109M⊙

)−1

, (5.4b)

with ρc and σc the core density and velocity dispersion respectively. The number of decaytimes required for the SBH’s energy to reach the Brownian level is ∼ ln (M•/m⋆) ≈ 20,


Figure 11. Left: Points show projected density profiles computed from N-body models af-ter a kicked SBH has returned to the center, for three different values of the kick velocity(Vkick = (0.2, 0.4, 0.8) × Vesc). Each set of points is compared with the best-fitting core-Sersicmodel (lines). The insert shows a zoom into the central region. Right: Mass deficits generatedby kicked SBHs. The differents sets of points correspond to different galaxy models. (Adaptedfrom Gualandris & Merritt 2007.)

implying that a kicked SBH will remain significantly off-center for a long time, as longas ∼ 1 Gyr in a bright galaxy with a low-density core.In fact, asymmetric cores are rather common. These include off-center nuclei (Bin-

gelli et al. 2000; Lauer et al. 2005); double nuclei (Lauer et al. 1996); and cores witha central minimum in the surface brightness (Lauer et al. 2002). Three examples, fromLauer et al. (2005), are reproduced here on the right side of figure 9; all are luminous“core” galaxies, and each strikingly resembles at least one frame from the N -body mon-tage on the left. The longevity of the “Phase II” oscillations makes the kicks a plausiblemodel for the observed asymmetries. This explanation is probably not appropriate forthe famous double nucleus of M31, since M31 is not a “core” galaxy, and since one ofthe brightness peaks in M31 (the one associated with the SBH) lies essentially at thegalaxy photocenter; Figure 9 suggests that an oscillating SBH would typically (thoughnot always) be found on the opposite side of the galaxy from the point of peak brightness.The M31 double nucleus has been successfully modelled as a clump of stars on eccentricorbits which maintain their lopsidedness by virtue of moving deep within the Keplerianpotential of the SBH (Tremaine 1995).The kicks are quite effective at inflating cores (Merritt et al. 2004; Boylan-Kinchin

et al. 2004). Figure 11, from Gualandris & Merritt (2007), illustrates this: the mass deficitgenerated by the kick is approximately

Mdef,k ≈ 5M• (Vkick/Vesc)1.75

. (5.5)

Even modest kicks can generate cores substantially larger than those produced duringthe formation of a massive binary (∼ 1M•; eq. 3.5). Furthermore, this mechanism ispotentially effective in even the most luminous galaxies, unlike the relaxation-drivenmodel for core growth discussed above (eq. 3.12) which only applies to nuclei with shortrelaxation times. Gravitational radiation recoil is therefore a tenable explanation forthe subset of luminous E galaxies with large mass deficits (figure 2). An alternativeexplanation for the over-sized cores (Lauer et al. 2007) postulates that the SBHs in these


galaxies are “hypermassive,” M• & 1010M⊙ and that the cores are a consequence ofslingshot ejection by a massive binary.The kicks have a number of other potentially observable consequences, including spa-

tially and/or kinematically offset AGN (Madau & Quataert 2004; Haehnelt et al. 2006;Merritt et al. 2006; Bonning et al. 2007) and distorted or wiggling radio jets (Gualandris& Merritt 2007). Many of these manifestations were first discussed by R. Kapoor in aremarkably prescient series of papers (Kapoor 1976,1983a,b,1985).

6. Black-hole-driven expansion

The growth of a core around a shrinking, binary SBH was discussed above: beyonda certain radius, the relaxation time becomes so long that the encounter-driven flux ofstars toward the center cannot compensate for losses to the binary, forcing the densityto drop. A similar process takes place around a single SBH (Shapiro 1977; Dokuchaev1989): stars coming too near are consumed, or disrupted, and the density drops. Thiseffect is absent from the classical equilibrium models for stars around a BH (e.g. Bahcall& Wolf 1976; Cohn & Kulsrud 1978) since these solutions fix the phase-space density farfrom the BH, enforcing an inward flux of stars precisely large enough to replace the starsbeing consumed by the sink. In reality, the BH acts as a heat source, in much the sameway that hard binary stars inject energy into a post-core-collapse globular cluster andcause it to re-expand.A simple model that produces self-similar expansion of a nucleus containing a SBH can

be constructed by simply changing the outer boundary condition in the Bahcall & Wolf (1976)problem from f(0) = f0 to f(0) = 0. One finds that the evolution after ∼one relax-ation time can be described as ρ(r, t) = ρc(t)ρ

∗(r), with ρ∗(r) slightly steeper than theρ ∼ r−7/4 Bahcall-Wolf form; the normalization drops off as ρc ∝ t−1 at late times.Figure 12 shows the results of a slightly more realistic calculation in a model designed tomimic the nearby dE galaxy M32. After reaching approximately the Bahcall-Wolf form,the density drops in amplitude with roughly fixed slope for r . rh. This example suggeststhat the nuclei of galaxies like M32 or the Milky Way might have been ∼ a few timesdenser in the past than they are now, with correspondingly higher rates of stellar tidaldisruption and stellar collisions.Expansion due to a central BH has been observed in a handful of studies based on

fluid (Amaro-Seoane et al. 2004), Monte-Carlo (Shapiro & Marchant 1978; Marchant& Shapiro 1980; Freitag et al. 2006), Fokker-Planck (Murphy et al. 1991), and N -body(Baumgardt et al. 2000) algorithms. All of these studies allowed stars to be lost into ordestroyed by the BH; however most adopted parameters more suited to globular clustersthan to nuclei, e.g. a constant-density core. Murphy et al. (1991) applied the isotropic,multi-mass Fokker-Planck equation to the evolution of nuclei containing SBHs, includingan approximate loss term in the form of (3.6) to model the scattering of low-angular-momentum stars into the SBH. Most of their models had what would now be consideredunphysically high densities and the evolution was dominated by physical collisions be-tween stars. However in two models with lower densities, they reported observing signifi-cant expansion over 1010 yr; these models had initial central relaxation times of Tr . 109

yr when scaled to real galaxies, similar to the relaxation times near the centers of M32and the Milky Way. The ρ ∼ r−7/4 form of the density profile near the SBH was ob-served to be approximately conserved during the expansion. Freitag et al. (2006) carriedout Monte-Carlo evolutionary calculations of a suite of models containing a mass spec-trum, some of which were designed to mimic the Galactic center star cluster. After thestellar-mass BHs in their models had segregated to the center, they observed a roughly


Figure 12. Black-hole-driven expansion of a nucleus; this Fokker-Planck model was given pa-rameters such that the density at the end is similar to what is currently observed in the nucleusof M32, with a final influence radius rh ≈ 3 pc. The left panel shows density profiles at constanttime intervals after a Bahcall-Wolf cusp has been established; the right panel shows the evolutionof the density at 0.1 pc as a function of Macc, the accumulated mass in tidally-disrupted stars.As scaled to M32, the final time is roughly 2× 1010 yr. This plot suggests that the densities ofcollisional nuclei like those of M32 and the Milky Way were once higher, by factors of ∼ a few,than at present. (From Merritt 2006b.)

self-similar expansion. Baumgardt et al. (2004) followed core collapse in N -body modelswith and without a massive central particle; “tidal destruction” was modelled by simplyremoving stars that came within a certain distance of the massive particle. When the“black hole” was present, the cluster expanded almost from the start and in an approxi-mately self-similar way. These important studies notwithstanding, there is a crucial needfor more work on this problem in order to understand how the rates of processes likestellar tidal disruption vary over cosmological times (e.g. Milosavljevic et al. 2006).

We thank H. Baumgardt, A. Graham and T. Lauer for permission to reproduce fig-ures from their published work, and A. Graham for comments on the manuscript. Weacknowledge support from the National Science Foundation under grants AST-0420920and AST-0437519 and from the National Aeronautics and Space Administration undergrants NNG04GJ48G and NNX07AH15G.

REFERENCES

Amaro-Seoane, P., Freitag, M., & Spurzem, R. 2004 Accretion of stars on to a massiveblack hole: a realistic diffusion model and numerical studies. Mon. Not. R. Astron. Soc.352, 655–672.

Armitage, P. J., & Natarajan, P. 2002 Accretion during the Merger of Supermassive BlackHoles. Astrophys. J. Letts. 567, L9–L12.

Baganoff, F. K., et al. 2003 Chandra X-ray spectroscopic imaging of Sagittarius A* and thecentral parsec of the Galaxy. Astrophys. J. 591, 891–899.

Bahcall, J. N., & Wolf, R. A. 1976 Star distribution around a massive black hole in aglobular cluster. Astrophys. J. 209, 214–232.

Bahcall, J. N., & Wolf, R. A. 1977 The star distribution around a massive black hole in aglobular cluster. II Unequal star masses. Astrophys. J. 216, 883–907.


Baker, J. G., Centrella, J., Choi, D.-I., Koppitz, M., & van Meter, J. 2006aGravitational-wave extraction from an inspiraling configuration of merging black holes.Phys. Rev. Letts. 96, 111102.

Baker, J. G., Centrella, J., Choi, D.-I., Koppitz, M., van Meter, J. R., & Miller,M. C. 2006b Getting a kick out of numerical relativity. Astrophys. J. 653, L93–L96.

Balcells, M., Graham, A. W., & Peletier, R. F. 2007 Galactic Bulges from Hubble SpaceTelescope NICMOS Observations: Central Galaxian Objects, and Nuclear Profile Slopes.Astrophys. J. 665, 1084–1103.

Batcheldor, D., Marconi, A., Merritt, D., & Axon, D. J. 2007 How Special Are BrightestCluster Galaxies? The Impact of Near-Infrared Luminosities on Scaling Relations for BCGs.Astrophys. J. 663, L85-L88.

Baumgardt, H., Gualandris, A., & Portegies Zwart, S. 2006 Ejection of hypervelocitystars from the Galactic Centre by intermediate-mass black holes. Mon. Not. R. Astron. Soc.372, 174–182.

Baumgardt, H., Makino, J., & Ebisuzaki, T. 2004 Massive black holes in star clusters. I.Equal-mass clusters. Astrophys. J. 613, 1133–1142.

Begelman, M. C., Blandford, R. D., & Rees, M. J. 1980 Massive black hole binaries inactive galactic nuclei. Nature 287, 307–309.

Bekenstein, J. D. 1973 Gravitational-Radiation Recoil and Runaway Black Holes. Astro-phys. J. Letts. 183, 657–664.

Berczik, P., Merritt, D., & Spurzem, R. 2005 Long-Term Evolution of Massive Black HoleBinaries. II. Binary Evolution in Low-Density Galaxies. Astrophys. J. 633, 680–687.

Berczik, P., Merritt, D., Spurzem, R., & Bischof, H.-P. 2006 Efficient Merger of BinarySupermassive Black Holes in Nonaxisymmetric Galaxies. Astrophys. J. Letts. 642, L21–L24.

Binggeli, B., Barazza, F., & Jerjen, H. 2000 Off-center nuclei in dwarf elliptical galaxies.Astron. Ap. 359, 447–456.

Binggeli, B., Sandage, A., & Tarenghi, M. 1984 Studies of the Virgo Cluster. I - Photometryof 109 galaxies near the cluster center to serve as standards. Astron. J. 89, 64–82.

Blaes, O., Lee, M. H., & Socrates, A. 2002 The Kozai Mechanism and the Evolution ofBinary Supermassive Black Holes. Astrophys. J. 578, 775–786.

Boker, T., Sarzi, M., McLaughlin, D. E., van der Marel, R. P., Rix, H.-W., Ho, L. C.,& Shields, J. C. 2004 A Hubble Space Telescope Census of Nuclear Star Clusters in Late-Type Spiral Galaxies. II. Cluster Sizes and Structural Parameter Correlations. Astron. J.127, 105–118.

Bogdanovic, T., Reynolds, C. S., & Miller, M. C. 2007 Alignment of the Spins of Super-massive Black Holes Prior to Coalescence. Astrophys. J. Letts. 661, L147–L151.

Bonning, E. W., Shields, G. A., & Salviander, S. 2007 Recoiling black holes in quasars.ArXiv e-prints, 705, arXiv:0705.4263.

Boylan-Kolchin, M., Ma, C.-P., & Quataert, E. 2004 Core Formation in Galactic Nucleidue to Recoiling Black Holes. Astrophys. J. 613, L37–L40.

Brown, W. R., Geller, M. J., Kenyon, S. J., & Kurtz, M. J. 2006 A successful targetedsearch for hypervelocity stars. Astrophys. J. Letts. 640, L35–L38.

Campanelli, M., Lousto, C. O., Marronetti, P., & Zlochower, Y. 2006 Accurate Evo-lutions of Orbiting Black-Hole Binaries without Excision. Phys. Rev. Letts. 96, 111101.

Campanelli, M., Lousto, C. O., Zlochower, Y., Krishnan, B., & Merritt, D. 2007aSpin flips and precession in black-hole-binary mergers. Phys. Rev. D 75, 064030.

Campanelli, M., Lousto, C., Zlochower, Y., & Merritt, D. 2007b Large Merger Recoilsand Spin Flips from Generic Black Hole Binaries. Astrophys. J. 659, L5–L8.

Campanelli, M., Lousto, C. O., Zlochower, Y., & Merritt, D. 2007c Maximum Gravi-tational Recoil. Phys. Rev. Letts. 98, 231102.

Carollo, C. M., Stiavelli, M., & Mack, J. 1998 Spiral Galaxies with WFPC2. II. TheNuclear Properties of 40 Objects. Astron. J. 116, 68–84.

Chandrasekhar, S. 1943 Dynamical friction. I. General considerations: the coefficient of dy-namical friction. Astrophys. J. 97, 255–273.

Christopher, M. H., Scoville, N. Z., Stolovy, S. R., & Yun, M. S. 2005 Astrophys. J.622, 346–365.

http://arxiv.org/abs/0705.4263


Cohn, H., & Kulsrud, R. M. 1978 The stellar distribution around a black hole - Numericalintegration of the Fokker-Planck equation. Astrophys. J. 226, 1087–1108.

Cote, P., et al. 2004 The ACS Virgo Cluster Survey. I. Introduction to the Survey. Astro-phys. J. Suppl. 153, 223–242.

Cote, P., et al. 2006 The ACS Virgo Cluster Survey. VIII. The Nuclei of Early-Type Galaxies.Astrophys. J. Suppl. 165, 57–94.

de Vaucouleurs, G. 1948 Recherches sur les Nebuleuses Extragalactiques. Annalesd’Astrophysique 11, 247–287.

Dokuchaev, V. I. 1989 The evolution of a massive black-hole in the nucleus of a normal galaxy.Sov. Astron. Letts. 15, 167–170.

Dotti, M., Colpi, M., Haardt, F., & Mayer, L. 2007 Mon. Not. R. Astron. Soc. 582,956–962.

Eckart, A., Genzel, R., Ott, T., & Schodel, R. 2002 Stellar orbits near Sagittarius A*.Mon. Not. R. Astron. Soc. 331, 917–934.

Escala, A., Larson, R. B., Coppi, P. S., & Mardones, D. 2004 The role of gas in themerging of massive black holes in galactic nuclei. I. Black hole merging in a spherical gascloud. Astrophys. J. 607, 765–777.

Escala, A., Larson, R. B., Coppi, P. S., & Mardones, D. 2005 The role of gas in themerging of massive black holes in galactic nuclei. II. Black hole merging in a nuclear gasdisk. Astrophys. J. 630, 152–166.

Fan, X., et al. 2003 A survey of z¿5.7 quasars in the Sloan digital sky survey. II. Discovery ofthree additional quasars at z¿6. Astron. J. 125, 1649–1659.

Favata, M., Hughes, S. A., & Holz, D. E. 2004 How Black Holes Get Their Kicks: Gravita-tional Radiation Recoil Revisited. Astrophys. J. Letts 607, L5–L8.

Ferrarese, L., et al. 2006 A Fundamental Relation between Compact Stellar Nuclei, Super-massive Black Holes, and Their Host Galaxies. Astrophys. J. Letts 644, L21–L24.

Ferrarese, L., & Ford, H. 2005 Supermassive Black Holes in Galactic Nuclei: Past, Presentand Future Research. Sp. Sci. Rev. 116, 523–624.

Fitchett, M. J.1983 The influence of gravitational wave momentum losses on the centre ofmass motion of a Newtonian binary system. Mon. Not. R. Astron. Soc. 203, 1049–1062.

Frank, J., & Rees, M. J. 1976 Effects of massive central black holes on dense stellar systems.Mon. Not. R. Astron. Soc. 176, 633–647.

Freitag, M., Amaro-Seoane, P., & Kalogera, V. 2006 Stellar remnants in galactic nuclei:mass segregation. Astrophys. J. 649, 91–117.

Gallimore, J. F. et al. 2001 The nature of the nuclear H2O masers of NGC 1068: Reverber-ation and evidence for a rotating disk. Astrophys. J. 556, 694–703.

Gallimore, J. F., Axon, D. J., O’Dea, C. P., Baum, S. A., & Pedlar, A. 2006 A Surveyof Kiloparsec-Scale Radio Outflows in Radio-Quiet Active Galactic Nuclei. Astron. J. 132,546–569.

Gebhardt, K., et al. 2003 Axisymmetric Dynamical Models of the Central Regions of Galax-ies. Astrophys. J. 583, 92–115.

Gerhard, O. 2001 The Galactic Center HE I Stars: Remains of a Dissolved Young Cluster?Astrophys. J. 546, L39–L42.

Gonzalez, J. A., Sperhake, U., Brugmann, B., Hannam, M., & Husa, S. 2007a MaximumKick from Nonspinning Black-Hole Binary Inspiral. Phys. Rev. Letts. 98, 091101.

Gonzalez, J. A., Hannam, M., Sperhake, U., Brugmann, B., & Husa, S. 2007b Su-permassive Recoil Velocities for Binary Black-Hole Mergers with Antialigned Spins.Phys. Rev. Letts. 98, 231101.

Governato, F., Colpi, M., & Maraschi, L. 1994 The fate of central black holes in merginggalaxies. Mon. Not. R. Astron. Soc. 271, 317–322.

Graham, A. W., Erwin, P., Trujillo, I., & Asensio Ramos, A. 2003 A New EmpiricalModel for the Structural Analysis of Early-Type Galaxies, and A Critical Review of theNuker Model. Astron. J. 125, 2951–2963.

Graham, A. W., & Guzman, R. 2003 HST Photometry of Dwarf Elliptical Galaxies in Coma,and an Explanation for the Alleged Structural Dichotomy between Dwarf and Bright El-liptical Galaxies. Astron. J. 125, 2936–2950.


Greene, J. E., & Ho, L. C. 2004 Active galactic nuclei with candidate intermediate-massblack holes. Astrophys. J. 610, 722–736.

Greenhill, L. J., et al. 2003 A warped accretion disk and wide-angle outflow in the innerparsec of the Circinus galaxy. Astrophys. J. 590, 162–173.

Gualandris, A. & Merritt, D. 2007 Ejection of Supermassive Black Holes from GalaxyCores. ArXiv e-prints, 708, arXiv:0708.0771.

Gualandris, A., Portegies Zwart, S., & Sipior, M. S. 2005 Three-body encountersin the Galactic Centre: the origin of the hypervelocity star SDSS J090745.0+024507Mon. Not. R. Astron. Soc. 363, 223–228.

Haehnelt, M. G., & Kauffmann, G. 2002 Multiple supermassive black holes in galacticbulges. Mon. Not. R. Astron. Soc. 336, L61-L64.

Haehnelt, M. G., Davies, M. B., & Rees, M. J. 2006 Possible evidence for the ejection ofa supermassive black hole from an ongoing merger of galaxies. Mon. Not. R. Astron. Soc.366, L22-L25.

Hansen, B. M. S., & Milosavljevic, M. 2003 The need for a second black hole at the Galacticcenter. Astrophys. J. 593, L77–L80.

Herrmann, F., Hinder, I., Shoemaker, D., & Laguna, P. 2007 Unequal mass binary blackhole plunges and gravitational recoil. Class. Quantum Gravity 24, 33–42.

Hills, J. G. 1988 Hyper-velocity and tidal stars from binaries disrupted by a massive Galacticblack hole. Nature 331, 687–689.

Hoffman, L., & Loeb, A. 2007 Dynamics of triple black hole systems in hierarchically mergingmassive galaxies. Mon. Not. R. Astron. Soc. 377, 957–976.

Holley-Bockelmann, K., Mihos, J. C., Sigurdsson, S., Hernquist, L., & Norman, C.2002 The Evolution of Cuspy Triaxial Galaxies Harboring Central Black Holes. Astro-phys. J. 567, 817–827.

Holley-Bockelmann, K., & Sigurdsson, S. 2006 A Full Loss Cone For Triaxial Galaxies.ArXiv Astrophysics e-prints, arXiv:astro-ph/0601520.

Hughes, S. A. 2006 A brief survey of LISA sources and science. In Laser Interferometer SpaceAntenna: 6th International LISA Symposium, AIP Conference Proceedings, vol. 873, pp.13–20.

Ivanov, P. B., Papaloizou, J. C. B., & Polnarev, A. G. 1999 The evolution of a super-massive binary caused by an accretion disc. Mon. Not. R. Astron. Soc. 307, 79–90.

Iwasawa, M., Funato, Y., & Makino, J. 2006 Evolution of massive black hole triples. I.Equal-mass binary-single systems. Astrophys. J. 651, 1059–1067.

Jackson, J. M. et al. 1993 Neutral gas in the central 2 parsecs of the Galaxy. Astrophys. J.402, 173–182.

Jerjen, H., & Binggeli, B. 1997 Are “Dwarf” Ellipticals Genuine Ellipticals? In The Natureof Elliptical Galaxies; 2nd Stromlo Symposium (ed. M. Arnaboldi, G. S. Da Costa, & P.Saha) ASP Conference Series, vol. 116, pp. 239–250.

Kapoor, R. C. 1976 Ejection of massive black holes from galaxies. Pramana 7, 334–343.Kapoor, R. C. 1983a On the hypothesis of ejection of supermassive black holes from centers of

galaxies and its application to quasar-galaxy associations. Astrophys. Sp. Sci. 93, 79–85.Kapoor, R. C. 1983b Some implications of escape of supermassive black holes from galactic

nuclei due to plasmoid ejection. Astrophys. Sp. Sci. 95, 425–429.Kapoor, R. C. 1985 Effect of dynamical friction on the escape of a supermassive black hole

from a galaxy. Astrophys. Sp. Sci. 112, 347–359.Kauffmann, G., & Haehnelt, M. 2000 A unified model for the evolution of galaxies and

quasars. Mon. Not. R. Astron. Soc. 311, 576–588.Kazantzidis, S., et al. 2005 The fate of supermassive black holes and the evolution of the

MBH-σ relation in merging galaxies: The effect of gaseous dissipation. Astrophys. J. Letts.623, L67–L70.

Kinney, A. L., Schmitt, H. R., Clarke, C. J., Pringle, J. E., Ulvestad, J. S., & An-tonucci, R. R. J. 2000 Jet Directions in Seyfert Galaxies. Astrophys. J. 537, 152–177.

Komossa, S. 2006 Observational evidence for binary black holes and active double nuclei.Memorie della Societa Astronomica Italiana 77, 733–771.

Kormendy, J. 1985a Brightness profiles of the cores of bulges and elliptical galaxies. Astro-phys. J. Letts. 292, L9–L12.


http://arxiv.org/abs/astro-ph/0601520


Kormendy, J. 1985b Families of ellipsoidal stellar systems and the formation of dwarf ellipticalgalaxies. Astrophys. J. 295, 73–79.

Kormendy, J., & Djorgovski, S. 1989 Surface photometry and the structure of ellipticalgalaxies. Ann. Rev. Astron. Ap. 27, 235–277.

Lauer, T. R., et al. 1993 Planetary camera observations of the double nucleus of M31. As-tron. J. 106, 1436–1447.

Lauer, T. R., et al. 1996 Hubble Space Telescope Observations of the Double Nucleus ofNGC 4486B. Astrophys. J. Letts. 471, L79–L82.

Lauer, T. R., et al. 2002 Galaxies with a central minimum in stellar luminosity density.Astron. J. 124, 1975–1987.

Lauer, T. R., et al. 2005 The Centers of Early-Type Galaxies with Hubble Space Telescope.V. New WFPC2 Photometry. Astron. J. 129, 2138–2185.

Lauer, T. R., et al. 2007 The Masses of Nuclear Black Holes in Luminous Elliptical Galaxiesand Implications for the Space Density of the Most Massive Black Holes. Astron. J. 662,808–834.

Levin, Y. 2006 Ejection of high-velocity stars from the Galactic center by an inspiralingintermediate-mass black hole. Astrophys. J. 653, 1203–1209.

Macfadyen, A. I., & Milosavljevic, M. 2006 ArXiv Astrophysics e-prints,arXiv:astro-ph/0607467

Madau, P., & Quataert, E. 2004 The Effect of Gravitational-Wave Recoil on the Demographyof Massive Black Holes. Astrophys. J. Letts. 606, L17–L20.

Makino, J. 1997 Merging of Galaxies with Central Black Holes. II. Evolution of the Black HoleBinary and the Structure of the Core. Astrophys. J. 478, 58–65.

Makino, J., & Ebisuzaki, T. 1994 Triple black holes in the cores of galaxies. Astrophys. J.446, 607–610.

Makino, J., & Funato, Y. 2004 Evolution of Massive Black Hole Binaries. Astrophys. J. 602,93–102.

Marchant, A. B., & Shapiro, S. L. 1980 Star clusters containing massive, central black holes.III - Evolution calculations. Astrophys. J. 239, 685–704.

Marconi, A., Risaliti, G., Gilli, R., Hunt, L. K., Maiolino, R., & Salvati, M. 2004Local supermassive black holes, relics of active galactic nuclei and the X-ray background.Mon. Not. R. Astron. Soc. 351, 169–185.

Matsubayashi, T., Makino, J., & Ebisuzaki, T. 2007 Orbital evolution of an IMBH in theGalactic nucleus with a massive central black hole. Astrophys. J. 656, 879–896.

Mayer, L., Kazantzidis, S., Madau, P., Colpi, M., Quinn, T., & Wadsley, J. 2007 RapidFormation of Supermassive Black Hole Binaries in Galaxy Mergers with Gas. Science 316,1874–1876.

McLaughlin, D. E., King, A. R., & Nayakshin, S. 2006 The M − σ relation for nucleatedgalaxies. Astrophys. J. Letts. 650, L37–L40.

Merritt, D. 1984 Relaxation and tidal stripping in rich clusters of galaxies. II. Evolution ofthe luminosity distribution. Astrophys. J. 276, 26–37.

Merritt, D. 2000 Black Holes and Galaxy Evolution. In Dynamics of Galaxies: from the EarlyUniverse to the Present (ed. F. Combes, G. A. Mamon & V. Charmandaris) ASP Confer-ence Series, vol. 197, pp. 221–230.

Merritt, D. 2002 Rotational Brownian motion of a massive binary. Astrophys. J. 568, 998–1003.

Merritt, D. 2004 Evolution of the dark matter distribution at the galactic center.Phys. Rev. Letts. 92, 201304.

Merritt, D. 2006a Mass Deficits, Stalling Radii, and the Merger Histories of Elliptical Galaxies.Astrophys. J. 648, 976–986.

Merritt, D. 2006b Dynamics of galaxy cores and supermassive black holes. Rept. Prog. Phys.69, 2513–2579.

Merritt, D., Berczik, P., & Laun, F. 2007 Brownian Motion of Black Holes in Dense Nuclei.Astron. J. 133, 553–563.

Merritt, D., & Cruz, F. 2001 Cusp Disruption in Minor Mergers. Astrophys. J. Letts. 551,L41-L44.

Merritt, D., Graham, A. W., Moore, B., Diemand, J., & Terzic, B. 2006 Empirical

http://arxiv.org/abs/astro-ph/0607467


Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles andComparison with Parametric Models. Astron. J. 132, 2685–2700.

Merritt, D., Mikkola, S., & Szell, A. 2007 Long-Term Evolution of Massive Black HoleBinaries. III. Binary Evolution in Collisional Nuclei. ArXiv e-prints, 705, arXiv:0705.2745.

Merritt, D., Milosavljevic, M., Favata, M., Hughes, S. A., & Holz, D. E. 2004 Conse-quences of Gravitational Radiation Recoil. Astrophys. J. Letts. 607, L9–L12.

Merritt, D., Navarro, J. F., Ludlow, A., & Jenkins, A. 2005 A Universal Density Profilefor Dark and Luminous Matter? Astrophys. J. Letts. 624, L85–L88.

Merritt, D., & Poon, M. Y. 2004 Chaotic loss cones and black hole fueling. Astrophys. J.606, 788–798.

Merritt, D., Storchi-Bergmann, T., Robinson, A., Batcheldor, D., Axon, D., & CidFernandes, R. 2006a The nature of the HE0450-2958 system. Mon. Not. R. Astron. Soc.367, 1746–1750.

Merritt, D., & Szell, A. 2006 Dynamical cusp regeneration. Astrophys. J. 648, 890–899.Merritt, D., & Wang, J. 2005 Loss cone refilling rates in galactic nuclei. Astrophys. J. Letts.

621, L101–L104.Mihos, J. C., & Hernquist, L. 1994 Dense stellar cores in merger remnants. Astro-

phys. J. Letts. 437, L47–L50.Mikkola, S., & Valtonen, M. J. 1992 Evolution of binaries in the field of light particles and

the problem of two black holes. Mon. Not. R. Astron. Soc. 259, 115–120.Milosavljevic, M., & Merritt, D. 2001 Formation of galactic nuclei. Astrophys. J. 563,

34–62.Milosavljevic, M., & Merritt, D. 2003 Long-term evolution of massive black hole binaries.

Astrophys. J. 596, 860–878.Milosavljevic, M., Merritt, D., & Ho, L. C. 2006 Contribution of stellar tidal disruptions

to the X-ray luminosity function of active galaxies. Astrophys. J. 652, 120–125.Milosavljevic, M., Merritt, D., Rest, A., & van den Bosch, F. C. 2002 Galaxy cores as

relics of black hole mergers. Mon. Not. R. Astron. Soc. 331, L51–L54.Murphy, B. W., Cohn, H. N., & Durisen, R. H. 1991 Dynamical and luminosity evolution

of active galactic nuclei - Models with a mass spectrum. Astrophys. J. 370, 60–77.Navarro, J. F., et al. 2004, The inner structure of LCDM haloes - III. Universality and

asymptotic slopes. Mon. Not. R. Astron. Soc. 349, 1039–1051.Perets, H. B., Hopman, C., & Alexander, T. 2007 Massive perturber-driven interactions

between stars and a massive black hole. Astrophys. J. 656, 709–720.Perets, H. B., & Alexander, T. 2007 Massive perturbers and the efficient merger of binary

massive black holes. ArXiv e-prints, 705, arXiv:0705.2123Poon, M. Y., & Merritt, D. 2001 Orbital Structure of Triaxial Black Hole Nuclei. Astro-

phys. J. 549, 192–204.Poon, M. Y., & Merritt, D. 2004 A self-consistent study of triaxial black hole nuclei. Astro-

phys. J. 606, 774–787.Portegies Zwart, S. F., & McMillan, S. L. W. 2002 The runaway growth of intermediate-

mass black holes in dense star clusters. Astrophys. J. 576, 899–907.Pretorius, F. 2005 Evolution of Binary Black-Hole Spacetimes. Phys. Rev. Letts. 95, 121101.Pringle, J. E. 1991 The properties of external accretion discs. Mon. Not. R. Astron. Soc. 248,

754–759.Quinlan, G. D. 1996 The dynamical evolution of massive black hole binaries I. Hardening in

a fixed stellar background. New Astron. 1, 35–56.Ravindranath, S., Ho, L. C., Peng, C. Y., Filippenko, A. V., & Sargent, W. L. W.

2001 Central Structural Parameters of Early-Type Galaxies as Viewed with Nicmos on theHubble Space Telescope. Astron. J. 122, 653–678.

Ravindranath, S., Ho, L. C., & Filippenko, A. V. 2002 Nuclear cusps and cores in early-typegalaxies as relics of binary black hole mergers. Astrophys. J. 566, 801–808.

Redmount, I. H., & Rees, M. J. 1989 Gravitational-radiation rocket effects and galacticstructure. Comm. Astrophys. 14, 165–178.

Reid, M. J., & Brunthaler, A. 2004 The proper motion of Sagittarius A*. II. The mass ofSagittarius A*. Astrophys. J. 616, 872–884.

Rodriguez, C., Taylor, G. B., Zavala, R. T., Peck, A. B., Pollack, L. K., & Romani,




R. W. 2006 A Compact Supermassive Binary Black Hole System. Astrophys. J. 646, 623–632.

Sakamoto, K., Okumura, S. K., Ishizuki, S., & Scoville, N. Z. 1999 CO images of thecentral regions of 20 nearby spiral galaxies. Astrophys. J. Suppl. 124, 403–437.

Schodel, R., et al. 2007 The structure of the nuclear stellar cluster of the Milky Way. As-tron. Ap. 469, 125–146.

Sersic, J. L. 1968 Atlas de Galaxies Australes. Cordoba: Observatorio Astronomico.Sesana, A., Haardt, F., & Madau, P. 2006 Interaction of massive black hole binaries with

their stellar environment. I. Ejection of hypervelocity stars Astrophys. J. 651, 392–400.Sesana, A., Haardt, F., & Madau, P. 2007 Interaction of massive black hole binaries with

their stellar environment. II. Loss cone depletion and binary orbital decay. Astrophys. J.660, 546–555.

Sesana, A., Haardt, F., Madau, P., & Volonteri, M. 2004 Low-frequency gravitationalradiation from coalescing massive black hole binaries in hierarchical cosmologies. Astro-phys. J. 611, 623–632.

Shapiro, S. L., & Marchant, A. B. 1978 Star clusters containing massive, central black holes- Monte Carlo simulations in two-dimensional phase space Astrophys. J. 225, 603–624.

Shlosman, I., Begelman, M. C., & Frank, J. 1990 The fuelling of active galactic nuclei.Nature 345, 679–686.

Spitzer, L. 1987 Dynamical Evolution of Globular Clusters. Princeton University Press.Tichy, W., & Marronetti, P. 2007 Binary black hole mergers: large kicks for generic spin

orientations. ArXiv e-prints, arXiv:gr-qc/0703075Tremaine, S. 1995 An Eccentric-Disk Model for the Nucleus of M31. Astron. J. 110, 628–633.Tremaine, S. 1997 The centers of elliptical galaxies. In. Unsolved Problems in Astrophysics (ed.

J.N. Bahcall & J.P. Ostriker), pp. 137–158. Princeton University Press.Tremaine, S., et al. 2002 The Slope of the Black Hole Mass versus Velocity Dispersion Cor-

relation. Astrophys. J. 574, 740–753.Trujillo, I., Erwin, P., Asensio Ramos, A., & Graham, A. W. 2004 Evidence for a New

Elliptical-Galaxy Paradigm: Sersic and Core Galaxies. Astron. J. 127, 1917–1942.Valtonen, M. J., Mikkola, S., Heinamaki, P., & Valtonen, H. 1994 Slingshot ejections

from clusters of three and four black holes. Astrophys. J. Suppl. 95, 69–86.Valtonen, M. J. 1996, Are supermassive black holes confined to galactic nuclei? Comm. As-

trophys. 18, 191–206.Vicari, A., Capuzzo-Dolcetta, R., & Merritt, D. 2007 Consequences of Triaxiality for

Gravitational Wave Recoil of Black Holes. Astrophys. J. Letts. 662, 797–807.Volonteri, M., Haardt, F., & Madau, P. 2003 The assembly and merging history of super-

massive black holes in hierarchical models of galaxy formation. Astrophys. J. 582, 559–573.Wehner, E. H., & Harris, W. E. 2006 From Supermassive Black Holes to Dwarf Elliptical

Nuclei: A Mass Continuum. Astrophys. J. Letts. 644, L17–L20.Young, P. J. 1977 The black tide model of QSOs. II - Destruction in an isothermal sphere.

Astrophys. J. 215, 36–52.Yu, Q. 2002 Evolution of massive binary black holes. Mon. Not. R. Astron. Soc. 331, 935–958.Yu, Q., & Tremaine, S. 2003 Ejection of hypervelocity stars by the (binary) black hole in the

Galactic center. Astrophys. J. 599, 1129–1138.Zhao, H., Haehnelt, M. G., & Rees, M. J. 2002 Feeding black holes at galactic centres by

capture from isothermal cusps. New Astron. 7, 385–394.Zier, C. 2006 Merging of a massive binary due to ejection of bound stars. Mon. Not. R. As-

tron. Soc. 371, L36–L40.Zier, C. 2007 Merging of a massive binary due to ejection of bound stars - II. Mon. Not. R. As-

tron. Soc. 378, 1309–1327.

http://arxiv.org/abs/gr-qc/0703075

dynamics around supermassive black holes · 2013-12-16 · a. gualandris & d. merritt: dynamics...

Documents