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X-Ray Emission from a Supermassive Black Hole Ejected from the Center of a Galaxy

X-Ray Emission from a Supermassive Black Hole Ejected from the Center of a Galaxy
Yutaka Fujita

arXiv:0808.1726v1 [astro-ph] 12 Aug 2008

Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan ABSTRACT Recent studies have indicated that the emission of gravitational waves at the merger of two black holes gives a kick to the ?nal black hole. If the supermassive black hole at the center of a disk galaxy is kicked but the velocity is not large enough to escape from the host galaxy, it will fall back onto the the disk and accrete the interstellar medium in the disk. We study the X-ray emission from the black holes with masses of ? 107 M⊙ recoiled from the galactic center with velocities of ? 600kms?1 . We ?nd that their luminosities can reach 1039 ergs?1 , when they pass the apastrons in the disk. While the X-ray luminosities are comparable to those of ultra-luminous X-ray sources (ULXs) observed in disk galaxies, ULXs observed so far do not seem to be such supermassive black holes. Statical studies could constrain the probability of merger and recoil of supermassive black holes. Subject headings: black hole physics — ISM: general — galaxies: nuclei — Xrays: general



Recently, studies in numerical general relativity have shown that merged binary black holes can have a large recoil velocity through anisotropic emission of gravitational waves (e.g. Gonz?lez et al. 2007; Campanelli et al. 2007). The maximum velocity would reach a ? 4000 km s?1 , although the actual distribution of kick velocities is very uncertain. The discovery of such recoiled black holes is important for studies about the growth of black holes as well as the general relativity. Supermassive black holes ( 106 M⊙ ) at the centers of disk galaxies would be kicked through this mechanism. Although they would be bright just after the kick because of the emission from the accretion disk carried by the black holes, they would soon get dim as the disk is consumed by the black holes (Loeb 2007). However, if the kick velocity of a black

–2– hole is not large enough to escape from the host galaxy, it will eventually fall back onto the galactic disk. If the time-scale of dynamical friction is large enough, it will revolve around the galactic center many times before it ?nally spirals into the galactic center. When the black hole passes the galactic disk, it will accrete the interstellar medium (ISM) in the disk (Blecha & Loeb 2008). The accretion of the surrounding gas onto an isolated black hole has been studied by several authors (Fujita et al. 1998; Agol & Kamionkowski 2002; Mii & Totani 2005; Mapelli, Ferrara & Rea 2006, and references therein). Most of the previous studies focused on stellar mass (? 10M⊙ ) or intermediate mass black holes (IMBHs; ? 103 M⊙ ). The accretion rate and thus the luminosity of a black hole depend on the mass of the black hole and the density of the gas surrounding it (see equation [7]). Since the mass of a stellar-mass black hole is small, its luminosity becomes large enough to be observed only when it plunges into a high density region such as a molecular cloud. On the other hand, in this letter, we show that a recoiled supermassive black hole can shine even in the ordinary region of a galactic disk because of its huge mass.



We calculate the orbit of a recoiled black hole in a ?xed galaxy potential. The galaxy potential consists of three components, which are Miyamoto & Nagai (1975) disk, Hernquist spheroid, and a logarithmic halo: Φdisk = ? GMdist , √ 2 + (a + 2 + b2 )2 R z GMsphere , r+c z q


Φsphere = ?

(2) + d2 , (3)

1 2 Φhalo = vhalo ln R2 + 2

where R (= x2 + y 2) and z are cylindrical coordinates aligned with the galactic disk, and √ r = R2 + z 2 . We adopt the parameters for the Galaxy. We take Mdisk = 1.0 × 1011 M⊙ , Msphere = 3.4×1010 M⊙ , a = 6.5 kpc, b = 0.26 kpc, c = 0.7 kpc, d = 13 kpc, and q = 0.9; vhalo is determined so that the circular velocity for the total potential is 220 km s?1 at R = 7 kpc (see Law et al. 2005). We solve the equation of motion for the supermassive black hole: v = ??Φ , ˙ (4)

–3– where v= (vx , vy , vz ) is the velocity of the black hole, and Φ = Φdisk + Φsphere + Φhalo . The density of the disk is given by √ √ b2 Mdisk aR2 + (a + 3 z 2 + b2 )(a + z 2 + b2 )2 √ ρdisk = (5) 4π [R2 + (a + z 2 + b2 )2 ]5/2 (z 2 + b2 )3/2 (Miyamoto & Nagai 1975). We assume that part of the disk consists of the ISM; its density is represented by ρISM = fISM ρdisk and fISM = 0.2. The circulation velocity of the disk is given by ?Φ . (6) vcir = r ?r The accretion rate of the ISM onto the supermassive black hole is given by the BondiHoyle accretion (Bondi 1952): m = 2.5πG2 ˙ m2 ρISM BH , 2 (c2 + vrel )3/2 s (7)

where mBH is the mass of the black hole, cs (= 10 km s?1 ) is the sound velocity of the ISM, and vrel is the relative velocity between the black hole and the surrounding ISM. We assume that the orbit of the black hole is con?ned on the x-z plane (vy = 0). Thus, the relative 2 2 2 2 velocity is simply given by vrel = vx + vcir + vz . The X-ray luminosity of the black hole is given by LX = η mc2 , ˙ (8) where η is the e?ciency. Since the accretion rate is relatively small for the mass of the black hole, the accretion ?ow would be a radiatively ine?cient accretion ?ow (RIAF; Ichimaru 1977; Narayan 2005). In this case, the e?ciency follows η ∝ m for LX 0.1LEdd , where LEdd ˙ is the Eddington luminosity (e.g. Kato, Fukue & Mineshige 1998). Therefore, we assume that η = ηEdd for m > 0.1mEdd and η = ηEdd m/(0.1mEdd ) for m < 0.1mEdd , where mEdd = ˙ ˙ ˙ ˙ ˙ ˙ ˙ 2 LEdd /(c ηEdd ) (Mii & Totani 2005). We assume that ηEdd = 0.1. We solved equation (4) by Mathematica 6.0 using a command NDSolve. The black hole is ejected on the x-z plane at t = 0. The direction of the ejection changes from θ = 0? to 90? , where θ = 0? corresponds to the z-axis. We calculate the orbit until t = tmax , which is chosen to be much larger than the period of revolution and to be smaller than the time-scale of dynamical friction. The latter is estimated to be
3 vrel vrel tdf = = vrel ˙ 4πG2 mBH ρ ln Λ


(Binney & Tremaine 2008), where ρ is the total density (disk+sphere+halo). The halo component does not much a?ect the dynamical friction. Since N-body simulations for a spherically symmetric potential showed that the Coulomb logarithm is ln Λ ? 2–3 (Gualandris & Merritt

–4– 2008), we take ln Λ = 2.5. The e?ects of dynamical friction on orbits in a complex potential like the one we adopted would be complicated and ideally should be studied with highresolution N-body simulations. Thus, equation (9) should be regarded as a rough estimate of the time-scale of the dynamical-friction.



The black hole is placed at the center of the galaxy at t = 0. Since we do not know the distributions of mass and initial velocity (v0 ) of the black hole, we consider situations in which the emission from it would be observed easily. That is, the luminosity of the black hole would be large, and the observable time would be long. We consider ?ve combinations of mBH and v0 shown in Table 1. If we take larger mBH and/or smaller v0 , the dynamical friction becomes more e?ective and the black hole quickly falls into the galaxy center. On the other hand, if we take smaller mBH and/or larger v0 , the luminosity of the black hole becomes too small to be observed (equation [7]). Moreover, the black hole is not bound to the galaxy, if v0 is too large. The dynamical friction is most e?ective when θ = 90? . In Table 1, we show the time-average of the time-scale, tdf θ=90? , for 0 < t < tmax and θ = 90? . Fig. 1 shows the orbit of the black hole when v0 = 600 km s?1 and θ = 80? . Fig. 2 shows the luminosity of the same black hole (mBH = 3 × 107 M⊙ ). In Table 1, we present the distance of the apastrons from the center of the galaxy (rmax ) when θ = 90? . It is to be noted that rmax is not much dependent on θ for a given v0 . We also present the maximum X-ray luminosity of the black hole (Lmax ) when θ = 90? in Table 1. For a given mBH and v0 , the X-ray luminosity is larger when θ is closer to 90? , because the orbit is included in the galactic disk, where ρISM is large. We found that for v0 600 km s?1 , the luminosity reaches its maximum when the black hole passes apastrons and when the apastrons reside in the disk of the galaxy. This is because v decreases, ρISM increases, and thus m increases there (equation [7]). On the other hand, ˙ ?1 for v0 ? 700 km s , the distance of the apastrons from the galactic center (rmax ) is always large (Table 1). Thus, even if apastrons reside in the disk, ρISM is small there. Therefore, the luminosity of the black hole reaches its maximum between the apastron and periastron, and Lmax is smaller compared with the models of v0 600 km s?1 (Table 1). Assuming that black holes are ejected in random directions at the centers of galaxies, we estimate the probability of observing black holes with luminosities larger than a threshold luminosity Lth . For given mBH and v0 , we calculate 91 evolutions of the luminosity by

–5– changing θ from 0? to 90? by one degree. Then, we obtain the period during which the relation LX > Lth is satis?ed for each θ, and divide the period by tmax . This is the fraction of the period during which the black hole luminosity becomes larger than Lth . We refer to this fraction as f (θ) and show it in Fig. 3 when mBH = 3 × 107 M⊙ , v0 = 600 km s?1 , and Lth = 3 × 1039 erg s?1 . We average f (θ) by θ, weighting with sin θ, and obtain the probability of observing black holes with LX > Lth . In Table 1, we present the probability P3e39 when Lth = 3 × 1039 erg s?1 ; for the parameters we chose, P3e39 ? 0–0.56. 4. Discussion

We have found that a supermassive back hole that had been recoiled at the center of a disk galaxy could be observed in the galactic disk with an X-ray luminosity of LX 1039 erg s?1 . One of the candidates of such objects is ultraluminous X-ray sources (ULXs) observed in disk galaxies (Colbert & Mushotzky 1999; Makishima et al. 2000; Mushotzky 2004). They are found in o?-nuclear regions of nearby galaxies and their X-ray luminosities exceed ? 3×1039 ergs?1 , which are larger than the Eddington luminosity of a black hole with a mass of ? 20M⊙ . If ULXs are stellar mass black holes, they might be explained by anisotropic emission (Reynolds et al. 1997; King et al. 2001), slim-disks (Watarai, Mizuno & Mineshige 2001) or thin, super-Eddington accretion disks (Begelman 2002). On the other hand, there is some evidence that they are IMBHs at least for some of them (Miller, Fabian & Miller 2004; Cropper et al. 2004). Considering their X-ray luminosities and o?-center positions, some of the ULXs might be the recoiled supermassive black holes. However, the fraction of supermassive black holes in the ULXs would not be large. Schnittman & Buonanno (2007) estimated that for comparable mass binaries with dimensionless spin values of 0.9, only ? 10% of all mergers are expected to result in an ejection speed of ? 500–700 km s?1 . Since the ejection speed is smaller for mergers with large mass ratios and smaller spin values, the actual fraction would be smaller. Moreover, in our model, the time-corrected probability of observing black holes with LX > ? ? 3 × 1039 erg s?1 is P3e39 0.1, where P3e39 is obtained by averaging min[ tdf θ , tage ]f (θ)/tage by θ, weighting with sin θ, and tage (? 10 Gyr) is the age of a galaxy (Table 1). Here, we note that tdf θ should be regarded as the upper-limit of the actual time-scale, because tdf should decrease through the dynamical friction every time the black hole passes the dense region of the galaxy. Furthermore, our model indicates that a traveling supermassive black hole needs to have a mass comparable to the one currently observed at the galactic center in order to have large LX . It is unlikely that a galaxy would have undergone many mergers of black holes with such masses. The number of such mergers that a galaxy has undergone

–6– would be N 1. Thus, the probability that a galaxy has a traveling supermassive black hole with a luminosity comparable to that of ULXs is 1 × 10?2 . In fact, current radio observations seem to show that ULXs observed so far are not supermassive black holes. Our model predicts that the X-ray luminosity of a supermassive black hole traveling through the galaxy is comparable to the typical X-ray luminosity of a LINER (? 4 × 1039 –5 × 1041 erg s?1 ; Terashima et al. 2002). LINERs seem to show core radio emission and many even have detectable jets (Nagar et al. 2005). On the other hand, radio observations have shown that no ULX has been detected with a unresolved radio core (Mushotzky 2004). Moreover, it has been shown that the optical luminosities of ULXs tend to be smaller than their X-ray luminosities (e.g. Ptak et al. 2006), which is inconsistent with typical RIAF spectra (e.g. Yuan, Quataert & Narayan 2004). Thus, it is unlikely that most of the ULXs are the supermassive black holes traveling through the galaxies. However, the recoiled supermassive black holes could be found through future extensive surveys. Our model predicts that the X-ray luminous black holes should not be observed far from the centers of the host galaxies (say 10 kpc), because ρISM should be small there (§ 3). Our model also predicts that the relative velocity between the X-ray source and the surrounding ISM and stars is vrel vcir . If atomic line emission associated with the X-ray source is observed, the velocity could be estimated through the Doppler shift. Instead of X-rays, Maccarone (2005) argued that radio detections may be best to search for isolated accreting black holes. The detailed analysis of the spectra and the time variability would be useful to determine the masses of the black holes (Mushotzky 2004). In the future, statistical studies could observationally constrain the probability of the mergers of black holes and the recoil.



We have shown that a supermassive black hole ejected from the center of the host disk galaxy will return to the galactic disk, if the initial velocity is smaller than the escape velocity of the galaxy. The black hole accretes the surrounding ISM and the resultant X-ray luminosity can reach 1039 erg s?1 , when it passes the apastrons in the disk. Although the luminosity of a recoiled supermassive black hole is comparable to that of ultra-luminous X-ray sources (ULXs), it is unlikely that many of the observed ULXs are the supermassive black holes. I would like to thank the anonymous referee for useful comments. I am grateful to H. Tagoshi and T. Tsuribe for useful discussion. YF was supported in part by Grants-

–7– in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (20540269).

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A This preprint was prepared with the AAS L TEX macros v5.2.


Table 1. Model Parameters and Results mBH (M⊙ ) 3 × 106 1 × 107 1 × 107 1 × 107 3 × 107 3 × 107 3 × 107 v0 (km s?1 ) 500 500 600 700 500 600 700 tmax (Gyr) 0.3 0.3 1 2 0.3 1 2 tdf θ=90? (Gyr) 4.7 1.4 4.5 27 0.47 1.5 9.0 rmax (kpc) 1 1 3 13 1 3 13 Lmax (erg s?1 ) 1 × 1038 5 × 1039 5 × 1039 8 × 1037 1 × 1041 1 × 1041 2 × 1039 P3e39 ? P3e39

0 0.064 0.016 0 0.56 0.15 0

0 0.010 0.012 0 0.031 0.11 0

– 10 –

3 2 1

z kpc

0 1 2 3 4 3 2 1 0 1 2 3 4

x kpc
Fig. 1.— The orbit of a black hole for 0 < t < 1 Gyr when v0 = 600 km s?1 and θ = 80? .

1041 1040

L X erg s

1039 1038 1037 1036 0.0 0.1 0.2 0.3 0.4 0.5

t Gyr
Fig. 2.— The luminosity of a black hole for 0 < t < 0.5 Gyr when mBH = 3 × 107 M⊙ , v0 = 600 km s?1 and θ = 80? .

– 11 –

0.8 0.6 0.4 0.2 0.0 0 20 40 60 80

f (θ )

θ (deg)
Fig. 3.— The fraction of the period during which the black hole luminosity becomes larger than Lth , when mBH = 3 × 107 M⊙ , v0 = 600 km s?1 , and Lth = 3 × 1039 erg s?1 .



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