Direct Gravitational Imaging of Intermediate Mass Black Holes in Extragalactic Halos
aa r X i v : . [ a s t r o - ph . C O ] J a n Mon. Not. R. Astron. Soc. , 1–7 (0000) Printed 8 June 2018 (MN L A TEX style file v2.2)
Direct Gravitational Imaging of Intermediate Mass BlackHoles in Extragalactic Halos
Kaiki Taro Inoue ⋆ Valery Rashkov † Joseph Silk , , ‡ and Piero Madau § Department of Science and Engineering, Kinki University, Higashi-Osaka, 577-8502, Japan Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 Institut d’Astrophsique de Paris, UMR 7095, CNRS, UPMC Univ. Paris VI, 98 bis boulevard Arago, 75014 Paris, France Department of Physics and Astronomy, The Johns Hopkins University Homewood Campus, Baltimore, MD 21218, USA Beecroft Institute for Particle Astrophysics and Cosmology, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford, OX1 3RH, UK
ABSTRACT
A galaxy halo may contain a large number of intermediate mass black holes (IMBHs)with masses in the range of 10 − M ⊙ . We propose to directly detect these IMBHs byobserving multiply imaged QSO-galaxy or galaxy-galaxy strong lens systems in thesubmillimeter bands with high angular resolution. The silhouette of an IMBH in thelensing galaxy halo would appear as either a monopole-like or a dipole-like variationat the scale of the Einstein radius against the Einstein ring of the dust-emitting regionsurrounding the QSO. We use a particle tagging technique to dynamically populate aMilky Way-sized dark matter halo with black holes, and show that the surface massdensity and number density of IMBHs have power-law dependences on the distancefrom the center of the host halo if smoothed on a scale of ∼ . . ∼ M ⊙ in a lensing galaxy thatharbours a O (10 ) M ⊙ supermassive black hole in its nucleus. Key words: cosmology: theory - gravitational lensing - black hole physics - galaxies:formation
Recent observations of off-nuclear ultraluminous X-raysources (ULXs) suggest the presence of intermediate massblack holes (IMBHs) not only in the neighborhood of thegalaxy nucleus but also in star clusters far out in thegalactic halo (Matsumoto et al. 2001; Roberts et al. 2004;Farrell et al. 2009; Jonker et al. 2010). A large populationof IMBHs might reside inside a galaxy halo, perhaps theleftover population of initial “seed” holes that never grewinto the supermassive variety (SMBHs ) hosted today inthe nuclei of massive galaxies. The mechanism of seed for-mation is unknown. Seed holes may be produced by the di-rect collapse of 10 − M ⊙ primordial gas clouds, by the ⋆ E-mail:[email protected] † E-mail:[email protected] ‡ E-mail:[email protected] § E-mail:[email protected] Here a “SMBH” means a black hole (BH) residing at the centerof a main parent halo. If the host halo habouring the BH belongsto a more massive parent halo, we call it an “IMBH”. collapse of the first nuclear star clusters, or be the rem-nants of 10 M ⊙ Population III stars (e.g. Loeb & Rasio1994; Madau & Rees 2001; Devecchi & Volonteri 2009). Ifwe could directly observe the abundance, spatial distribu-tion, and masses of IMBHs inside extragalactic halos, wewould be able to constrain the process of SMBH seed for-mation that has hitherto been veiled in mystery.We propose here to directly detect IMBHs by observ-ing multiply imaged QSO-galaxy or galaxy-galaxy lens sys-tems in the submillimeter band with high angular resolu-tion ( . . c (cid:13) Kaiki Taro Inoue, Valery Rashkov, Joseph Silk, Piero Madau
In this paper, we estimate the feasibility of mappingIMBHs in forthcoming observations. In Section 2, we de-scribe a particle tagging technique to dynamically populatethe N-body
Via Lactea II (VLII) extreme-resolution simu-lation with IMBHs, and derive semi-analytic formulae fordescribing the surface mass and number density of IMBHsin the host halo. In Section 3, we estimate the strong lens-ing probability due to IMBHs in a lensing galaxy. We thendescribe the extended source effects and observational fea-sibility of direct detection in the QSO-galaxy lensing sys-tem RXJ1131-1231. We summarise our results in Section 4.In what follows, we assume a concordant cosmology with amatter density Ω m = 0 . b = 0 . Λ = 0 . H = 70 , km / s / Mpc, which are obtained from the observedCMB, the baryon acoustic oscillations, and measurement of H . VLII, one of the highest-resolution N-body simulations ofthe assembly of a Milky Way-sized galaxy halo to date(Diemand et al. 2008), provides an ideal set-up for the studyof formation of IMBHs. VLII follows the hierarchical assem-bly of a dark halo of mass M = 2 × M ⊙ at redshift z = 0 within r = 402 kpc (the radius which encloses anaverage mass density 200 times the mean cosmological mat-ter density), with just over a billion particles and a forceresolution of 40 pc. The simulation was performed with theparallel tree-code PKDGRAV2 (Stadel 2001). PKDGRAV2uses a fast multipole expansion technique in order to calcu-late the forces with hexadecapole precision, and an adaptiveleapfrog integrator. Expected to harbor a thin disk galaxy,VLII was selected to have no major mergers after z = 1.At the present epoch, VLII has a cuspy density profile andexhibits rich galactic substructure - the main host’s halocontains over 20,000 surviving subhalos with masses greaterthan 10 M ⊙ .Central black holes are added to subhalos followingthe particle tagging technique detailed in Rashkov & Madau(2013) and quickly summarized here. In each of 27 snapshotsof the simulation, choosen to span the assembly history ofthe host between redshift z = 27 .
54 and the present, allsubhalos are identified and linked from snapshot to snap-shot to their most massive progenitor: the subhalo tracksbuilt in this way contain all the time-dependent structuralinformation necessary for our study. We then identify thesimulation snapshot in which each subhalo reaches its max-imum mass M halo before being accreted by the main hostand tidally stripped. In each subhalo, the 1% most tightlybound dark matter particles are then “tagged” as stars atinfall, following a set of simple prescriptions calibrated toreproduce the observed luminosity function of Milky Waysatellites and the concentration of their stellar populations(Rashkov et al. 2012). We then measure the stellar line-of-sight velocity dispersion, σ ∗ , in each subhalo, and tag themost tightly bound central particle as a black hole of mass M BH according to an extrapolation of the M BH − σ ∗ relation of Tremaine et al. (2002), M BH = 8 . × M ⊙ (cid:16) σ ∗
100 km s − (cid:17) . (1)For stellar systems with σ ∗ − , a minimum seedhole mass of 100 M ⊙ is assumed. Any evolution of the taggedholes after infall is purely kinematical in character, as theirsatellite hosts are accreted and disrupted in an evolvingMilky Way-sized halo. Black holes do not increase in massafter tagging, and are tracked down to the z = 0 snapshot.We assume that IMBHs only form in subhalos with a massat infall > M s min = 10 M ⊙ .The merging process that produces each subhalo priorto its infall into the main host halo is important, as blackhole binaries may form in the process. The asymmetric emis-sion of gravitational waves produced during the coalescenceof a binary black hole system is known to impart a velocitykick to the system that can displace the hole from the centerof its host. The magnitude of the recoil will depend on thebinary mass ratio and the direction and magnitude of theirspins, and follows the prescriptions detailed in Guedes et al.(2011). When the kick velocity is larger than the escapespeed of the host halo, a hole may be ejected into inter-galactic space before becoming a Galactic IMBH. IMBHsthat would have formed in halos whose merger history pointsto a kick event are therefore excluded from the final catalog(see Rashkov & Madau 2013 for details).Since some of the subhalos will fall on trajectories thatbring them closer to the center of the main VLII host, theymight be completely disrupted after infall, leaving freely-roaming (“naked”) holes. Depending on the minimum halomass that allows the formation of an IMBH, the numbers offormed, kicked, and stripped IMBHs will be different. Figure1 shows an image of the projected distribution of IMBHs intoday’s Galactic halo according to the above prescriptions.We find 1,070 naked IMBHs and 1,670 holes residing in darkmatter satellites that survived tidal stripping. There are 50IMBHs more massive than 10 M ⊙ , and about 2,500 holesat the minimum mass of 100 M ⊙ (of which 950 are naked).Naked holes are more concentrated towards the inner haloregions as a consequence of the tidal disruption of infallingsatellites. Indeed, within 10 kpc, most MBHs are naked. To generalize the numerical results of the previous section,we shall assume in the following that the distribution ofIMBHs inside a lensing galaxy halo is spherically symmet-ric, and that the surface mass density σ m and the surfacenumber density σ n are described by the following “universalprofiles”, σ m ( r ) = σ m (0)(( r/r c ) + 1) exp[ r/r ∗ ] , (2) σ n ( r ) = σ n (0)( r/r c + 1) exp[ r/r ∗ ] , (3)where r c represents a core radius and r ∗ denotes a cut-off ra-dius at which the density starts to decay exponentially withincreasing r . The “universal profiles” are much steeper thanthose of a singular isothermal sphere (SIS). Subhalos hostingIMBHs can be massive enough to experience dynamical fric-tion, spiral in toward the center of the main host, be totally c (cid:13) , 1–7 irect Gravitational Imaging of Intermediate Mass Black Holes in Extragalactic Halos Figure 1.
Plot of the distribution of IMBHs in the simulated Milky Way-sized halo. Each dot represents the position of an IMBH (left).The threshold of the minimum subhalo mass required for the formation of a seed hole is assumed to be M s min = 10 M ⊙ . The projecteddensity of dark matter in the VLII simulation is plotted in a zoom-up image, where the size of each disk is proportional to the log ofthe BH mass (right). stripped of their dark matter, and deposit a naked IMBHinto the center of the main host. As shown in Figure 2, mostof IMBHs at r .
10 kpc are naked. We find that the surfacemass density at r .
10 kpc is not significantly affected by M s min .The constants σ m (0) and σ n (0) can be estimated asfollows. First, each halo is approximated as a sphericallysymmetric object with virial radius r . We assume thatwithin r the halo density profile is given by that of anSIS with one dimensional velocity dispersion σ v . Then wehave r ( z ) = σ v H ( z ) p
50 Ω m ( z ) , (4)where Ω m ( z ) and H ( z ) are the matter density parameterand the Hubble parameter at redshift z , respectively. Theinitial size of the halo is then r ini ≈ / r . (5)The correlation between the stellar velocity dispersion σ v and mass M SMBH of the supermassive black hole at the cen-ter is approximately given by (cid:18) M SMBH M ⊙ (cid:19) ∼ β × (cid:18) σ v
200 km/s (cid:19) α , (6)where β = O (1) and 4 < α <
5. The mass of the SMBHat the nucleus of the Milky Way is M SMBH = 4 × M ⊙ .Then, the velocity dispersion of the spheroidal componentis σ v = 88 km/s and r = 3 . × kpc at z = 0 providedthat α = 4 .
24 and β = 1 .
32 (G¨ultekin et al. 2009). We alsoassume that the total mass of IMBHs within r is given by M IMBH ( < r ) = fM SMBH , where f = 0 . −
1. Then fromequations (2) and (6), we have σ m (0) ≈ βf (cid:0) σ v /
200 km/s (cid:1) α πr c (cid:0) ln ( r /r c ) + 1 / (cid:1) × M ⊙ . (7)If we adopt f = 0 .
2, the analyticaly estimated surface massdensity σ m fits the simulated values well (see Fig. 2). Wefind that the surface mass density in the neighborhood ofthe center does not change much even if one changes thethreshold M s min .Second, we assume that the seed of an IMBH is formedat a redshift of z = 20 inside a host halo with a mass of M > M s min , and each seed grows almost independently. Thenthe approximated virial radius of the halo is ˜ r ( z = 20) =3 . × pc. Assuming an SIS profile, the maximal circu-lar velocity of a host halo is estimated as V max = √ σ v =10 H ˜ r = 12 km/s. At z = 20, the number density of subha-los with maximal velocity larger than V max is approximatelygiven by n ( > V max ) = AV max ,A ( z = 20) = 1 . × (cid:18) h − Mpc / (km/s) (cid:19) − , (8)provided that V max ≪ r ini ( z = 20) = 1 .
65 Mpc /h . Assuming thatall the halos with mass > M ⊙ contain an IMBH seed,the total number of IMBH seeds inside a lensing galaxy halo c (cid:13) , 1–7 Kaiki Taro Inoue, Valery Rashkov, Joseph Silk, Piero Madau M min s = M Ÿ r c = r c = r * =
100 kpc0.5 1.0 5.0 10.0 50.0100.00.01110010 r kpc Σ m M min s = M Ÿ r c = r * =
25 kpc0.5 1.0 5.0 10.0 50.0100.00.01110010 r kpc Σ m Figure 2.
Surface mass density of IMBHs in the simulated MilkyWay-sized halo. The dashed and dot-dashed curves correspondto the naked and the total (naked plus hosted-in-substructure)IMBHs in our numerical simulations, respectively. The solidcurves represent fitted “universal profiles” in which the totalmass of IMBHs coincides with that of our simulated results. Thiscurve is also obtained if we assume f = 0 .
2. The distribution ofsimulated IMBHs is smoothed by a Gaussian window function W ( r ) = exp[ − r / (2 r c )], where r c = 1 kpc. The total masses ofIMBHs (naked plus hosted-in-substructure) are 9 × M ⊙ (top)and 8 × M ⊙ (bottom). is estimated as N ( > V max = 12 km/s) = A ( z = 20)( V max = 12 km/s) × πr ini = 1 . × . (9)Note that N ( > V max ) is proportional to r . If the totalnumber of IMBHs within r does not change much, thenthe surface number density at the center is σ n (0) ≈ N ( > V max )2 πr r c . (10)Thus σ n (0) is proportional to r or σ v if r c does not de-pend on r . As shown in Figure 3, the “universal profile”fits the simulation well if the total number of IMBHs coin-cides with that of the simulation. If σ n (0) in equation (10) isused, however, the surface number density is systematicallyreduced by a factor of 2 − M min s = M Ÿ r c = r * =
100 kpc0.5 1.0 5.0 10.0 50.0 100.00.0010.010.1110 r kpc Σ n M min s = M Ÿ r c = r * =
25 kpc0.5 1.0 5.0 10.0 50.0 100.010 - - r kpc Σ n Figure 3.
Surface number density of IMBHs in the simu-lated Milky Way-sized halo. The dashed and dot-dashed curvescorrespond to the naked and the total(naked plus hosted-in-substructure) IMBHs in our numerical simulations, respectively.The solid curves represent fitted “universal profiles” in which thetotal number of IMBHs coincides with that of our simulated re-sults (bold solid) and that of our semi-analytically estimated val-ues (thin solid). The distribution of simulated IMBHs is smoothedby a Gaussian window function W ( r ) = exp[ − r / (2 r c )], where r c = 1 kpc. The Einstein angular radius θ E of a point mass with a mass M is written in terms of angular diameter distances: to thelens D L , to the source D S , and between the lens and thesource D LS as θ E ∼ × M M ⊙ ! D L D S /D LS Gpc ! − mas . (11)Therefore, a radio interferometer with resolution of 3 mascan easily resolve the distortion of an image within the Ein-stein ring for a point mass M ∼ M ⊙ .The strong lensing cross section due to an IMBH is pro-portional to M . Therefore, the lensing probability p is givenby the ratio between the surface mass density of IMBHsand that of a lensing galactic halo at r = r E = D L θ E . Fromequations (2) and (7), we have p = σ m (IMBH) σ m (SIS) (cid:12)(cid:12)(cid:12)(cid:12) r = r E ∝ σ αv σ v r E ∝ fσ α − v , (12)where σ m (IMBH) and σ m (SIS) denote the surface mass den- c (cid:13) , 1–7 irect Gravitational Imaging of Intermediate Mass Black Holes in Extragalactic Halos sity of IMBHs and that of an SIS, respectively. Similarly, themean mass ¯ M of an IMBH at r = r E satisfies¯ M = σ m (IMBH) σ n (IMBH) (cid:12)(cid:12)(cid:12)(cid:12) r = r E ∝ fσ α − v . (13)Thus the lensing probability and the Einstein radius arelarger for halos with larger velocity dispersion as long as α > D − / L , lens systems withsmall D L are more suitable as targets. If a perturber is spatially extended, then the lensing effectis different from that of a point mass. The density profileof a perturber can be reconstructed from a local mappingbetween the observed image and the non-perturbed imageobtained from the prediction of the macrolens. In fact, thepower of the radial density profile of the perturbers can bereconstructed from the perturbed images within the Ein-stein ring of the perturber (Inoue & Chiba 2005a). In thisway, one could make a distinction between an IMBH and aCDM subhalo. Furthermore, from distortion outside the Ein-stein ring of the perturber, the degeneracy between the per-turber mass and the distance can be broken provided thatthe Einstein radius of the perturber is sufficiently smallerthan that of the primary macrolens (Inoue & Chiba 2005b).The precise measurement of spatial variation in the surfacebrightness of lensed images provides us with plenty of infor-mation about the mass, abundance, and spatial distributionof IMBHs.
To estimate the observational feasibility of direct detectionof IMBHs, we adopt a QSO-galaxy lensing system RXJ1131-1231 as a target since this system has a massive lensing haloat relatively small redshift. The redshifts of the source andthe lens are z S = 0 .
658 and z L = 0 .
295 (Sluse et al. 2003),respectively. To model the macro-lens, we adopt a singularisothermal ellipsoid (SIE) in a constant external shear fieldin which the isopotential curves in the projected surface per-pendicular to the line-of-sight are ellipses (Kormann et al.1994; Inoue & Takahashi 2012). The IMBHs inside the lens-ing halo are modeled as point masses. Using the observedmid-infrared fluxes, the position of the lensed images andthe centroid of the lensing galaxy, the velocity dispersionfor the best-fit model is estimated as σ v = 3 . × km/s.From the M − σ relation with α = 4 .
24 and β = 1 . r is M IMBH = 1 . f × M ⊙ . Then the lensing probabil-ity is p = 5 f × − . The mean mass of the IMBH at r = r E = 5 . h M IMBH i = 2 f × M ⊙ and thecorresponding Einstein radius is θ E = √ f mas. Therefore, ifthe angular resolution is < √ f mas, we would be able to de-tect an imprint of IMBHs in the lensed Einstein ring of dustemission if the lensed image has an area > f − mas .To estimate observational feasibility, we use the sim-ulated data of IMBHs for a Milky Way-sized halo with M s min = 10 M ⊙ and scale up the mass of each IMBH bya ratio between the total mass of the SMBH for RXJ1131-1231 (= 1 . × M ⊙ ) and that for the Milky Way-sized halo (= 4 × M ⊙ ). In this model, we find that the ratiobetween the mass fraction of all IMBHs to that of a SMBHin the center is f = 0 .
2. The most massive IMBH has a massof M IMBH = 7 × M ⊙ . Taking into account the logarith-mic correction to σ v in equation (7), the distance of eachparticle from the center is scaled up by a factor γ ≈ (cid:18) ln( σ v (RXJ1131) / ( √ H ( z = 0 . r c ))ln( σ v (MW) / ( √ H ( z = 0) r c )) (cid:19) / = 1 . , (14)where we assume that r c = 1 kpc. As shown in Figure 4,we find that massive “naked” IMBHs with masses in therange of O (10 − ) M ⊙ are observable if the radius of thedust emitting region around the QSO is ∼
500 Mpc and theangular resolution is < ∼ × mas . Thus we expect > O (10) “naked”IMBHs inside the lensed arc if f > . Based on numerical simulations of IMBH formation in aMilky-way sized halo, we have found that the surface massdensity and number density of IMBHs have power-law de-pendences on the distance from the center of the host haloif smoothed on scales of ∼ ∼ O (10 − ). Thenext generation submillimeter telescopes with high angularresolution ( . . ∼ M ⊙ .In addition to IMBHs in the lensing galaxy, SMBHswith a mass of & M ⊙ inside halos in the line-of-sight mayalso be observable, especially in systems that show anomaliesin the flux ratios (Inoue & Takahashi 2012). In this case,some distortion in the lensed image due to the host halo isexpected.By measuring the local distortion of lensed extendedimages with high angular resolution, we will be able to deter-mine the mass, abundance, and density profile of the IMBHspresent in the lensing galaxy. Direct detection of IMBHswill shed new light on the formation process of SMBH seedswhich has hitherto been shrouded from view. This work was supported by the NSF through grant OIA-1124453, and by NASA through grant NNX12AF87G. Thisresearch was also supported in part by ERC project 267117 c (cid:13) , 1–7 Kaiki Taro Inoue, Valery Rashkov, Joseph Silk, Piero Madau
Figure 4.
Simulated lensed images of RXJ1131-1231. The black dots in the top left panel show the positions of IMBHs in the lensinggalaxy and the dot size is proportional to log ( M IMBH ). The other panels show the contour and 3D maps of the surface brightnesscentered at the angular position of an IMBH with a mass of 1 . × M ⊙ that produces a “black hole”. We assume that the dustemitting region has a circular gaussian luminosity profile with a 1 σ radius r = 500 pc. The numbers of contours representing the surfacebrightness are 10 (top left), 25 (bottom left), 25 (top right). (DARK) hosted by Universit´e Pierre et Marie Curie - Paris6. REFERENCES
Devecchi B., Volonteri M., 2009, The Astrophysical Jour-nal, 694, 302Diemand J., Kuhlen M., Madau P., Zemp M., Moore B.,Potter D., Stadel J., 2008, Nature, 454, 735Farrell S. A., Webb N. A., Barret D., Godet O., RodriguesJ. M., 2009, Nature, 460, 73Guedes J., Madau P., Mayer L., Callegari S., 2011, TheAstrophysical Journal, 729, 125G¨ultekin K., Richstone D. O., Gebhardt K., Lauer T. R.,Tremaine S., Aller M. C., Bender R., Dressler A., Faber S. M., Filippenko A. V., Green R., Ho L. C., KormendyJ., Magorrian J., Pinkney J., Siopis C., 2009, The Astro-physical Journal, 698, 198Inoue K. T., Chiba M., 2003, The Astrophysical JournalLetter, 591, L83Inoue K. T., Chiba M., 2005a, The Astrophysical Journal,634, 77Inoue K. T., Chiba M., 2005b, The Astrophysical Journal,633, 23Inoue K. T., Chiba M., 2006, Annual reports by ResearchInstitute for Science and Technology, 18, 11Inoue K. T., Takahashi R., 2012, Monthly Notices of RoyalAstronomical Society, 426, 2978Jonker P. G., Torres M. A. P., Fabian A. C., Heida M.,Miniutti G., Pooley D., 2010, Monthly Notices of Royal c (cid:13) , 1–7 irect Gravitational Imaging of Intermediate Mass Black Holes in Extragalactic Halos Astronomical Society, 407, 645Klypin A. A., Trujillo-Gomez S., Primack J., 2011, TheAstrophysical Journal, 740, 102Kormann R., Schneider P., Bartelmann M., 1994, Astron-omy and Astrophysics, 284, 285Loeb A., Rasio F. A., 1994, The Astrophysical Journal,432, 52Madau P., Rees M. J., 2001, The Astrophysical JournalLetter, 551, L27Matsumoto H., Tsuru T. G., Koyama K., Awaki H.,Canizares C. R., Kawai N., Matsushita S., Kawabe R.,2001, The Astrophysical Journal Letter, 547, L25Rashkov V., Madau P., 2013, in preparationRashkov V., Madau P., Kuhlen M., Diemand J., 2012, TheAstrophysical Journal, 745, 142Roberts T. P., Warwick R. S., Ward M. J., Goad M. R.,2004, Monthly Notices of Royal Astronomical Society, 349,1193Sluse D., Surdej J., Claeskens J. F., Hutsemekers D., JeanC., Courbin F., Nakos T., Billeres M., Khmil S. V., 2003,Astronomy and Astrophysics, 406, L43Stadel J. G., 2001, Ph.D. Thesis,University of WashingtonTremaine S., Gebhardt K., Bender R., Bower G., DresslerA., Faber S. M., Filippenko A. V., Green R., GrillmairC., Ho L. C., Kormendy J., Lauer T. R., Magorrian J.,Pinkney J., Richstone D., 2002, The Astrophysical Jour-nal, 574, 740 c (cid:13)000