Supermassive Black Holes and Kinematics of Disc Galaxies
aa r X i v : . [ a s t r o - ph . C O ] A ug Supermassive Black Holes and Kinematicsof Disc Galaxies
A. V. Zasov, A. M. Cherepashchuk, and I. Yu. Katkov
Sternberg Astronomical Institute, Moscow State University, Moscow, Russia
Abstract
The statistical relations between the masses of supermassive black holes (SMBHs) in diskgalaxies and the kinematic properties of their host galaxies are analyzed. We use the radialvelocity profiles for several galaxies obtained earlier at the 6-m telescope of the Special As-trophysical Observatory of the Russian Academy of Sciences parallel with the data for othergalaxies taken from the literature. We demonstrate that the SMBH masses correlate well withthe velocities of rotation of disks at a fixed distance R ≈ kpc ( V ), which characterize themean density of the central region of the galaxy. The SMBH masses correlate appreciablyweaker with the asymptotic velocity at large distances from the center and with the angularvelocity at the optical radius R . We suggest that the growth of the SMBH occurs insideof the forming ”classical” bulge during a monolithic collapse of gas in the central kpc-sizeregion of the protogalaxy. We have also found a correlation between the SMBH mass and thetotal (indicative) mass of the galaxy M within the optical radius R , which includes bothbaryonic and ”dark” mass. The masses of the nuclear star clusters in early-type disk galaxies(based on the catalog of Seth et al.) are also scaled with the dynamical mass M , whereasthe correlations with the luminosity and velocity of rotation of galaxies are practically absentfor them. For a given M the masses of the nuclear clusters are, on average, nearly order ofmagnitude higher in S0–Sbc galaxies than in late-type galaxies. Recent studies of supermassive black holes (SMBHs) in the nuclei of galaxies have developedalong two directions—investigation of the effects of strong gravitation near the event horizons ofSMBHs (see, for example, [1, 2, 3]) and analyses of SMBH demographics (see, for example, [4]).Demographic studies require analysis of the relationship between the characteristics of the centralSMBHs and the kinematic properties of the host galaxies. Information about the history andevolution of SMBHs is ”coded” in the morphological and kinematic characteristics of the galaxies,making studies of galaxy kinematics with known central SMBH masses very promising. Studiesof spiral and lenticular galaxies play a special role here, since measurements of the rotationalvelocities of the gas and/or stars in the disks provide direct information about the distributions ofthe density and angular momentum.It is well known that the masses of SMBHs are closely correlated with the parameters of theirhost spheroidal systems (an elliptical galaxy or the bulge of a disk galaxy), and comprise a specifiedfraction of the total mass of the spheroidal component (about 10 − ), while the role of the diskis not obvious [5, 6, 7]. Since the rapid growth of a central black hole occurs in an early periodin the history of a galaxy, when the bulge and disk have just formed in the gravitational well of1he massive dark halo, we would expect the black-hole mass to be correlated not only with theparameters of the bulge, but also with the halo mass and the rotational velocity at large distancesfrom the center, V F AR , which determines the virial mass of the galaxy. A relationship betweenthe SMBH mass and the virial mass of the galaxy is predicted in numerical cosmological models[6, 9, 10, 11] (see also references therein), although the observational data remain controversial.Known relations between the SMBH masses and general properties of the host galaxies are basedprimarily on data for elliptical and lenticular galaxies. Unfortunately, the number of disk galaxiesthat have both reliable black-hole masses M BH estimates and detailed measurements of theirkinematic characteristics (circular velocity, stellar-velocity dispersion, etc.) is rather small. Thishas forced to use indirect estimates for demographic studies of SMBHs: inferring the asymptoticrotational velocities of galaxies from their empirical dependencies on the central stellar-velocitydispersions [6], and estimating the SMBH masses M BH from their connection with the stellar-velocity dispersions σ [12]. However, in this case the resulting relationship between the rotationalvelocity of the disk and M BH can simply result from correlations between the indirect methods usedto determine these two parameters. In [13] we demonstrated that the correlation between M BH and the asymptotic rotational velocity is appreciably “looser” than the one which was obtainedfrom the indirect data [6, 12]. In view of the poor statistic data, this conclusion needs to beverified.We limit our consideration here to disk galaxies. In contrast to elliptical systems, their disks arerotationally supported, so their velocities of rotation may give a good idea of the mass containedinside the chosen radius R . It enables to estimate the total mass within R depending only weaklyon the adopted model for the matter distribution. We were provided with data from a program ofspectral observations obtained on the 6-m telescope of the Special Astrophysical Observatory ofthe Russian Academy of Sciences, for galaxies with the most reliably determined masses for theircentral black holes. The first results of these observations carried out in 2006–2009 were presentedin [14]. To increase the number of objects for our study, we also use here the kinematic parametersfor other disk galaxies with known M BH based on data taken from the literature. In recent studies of the formation of SMBHs and the growth of their masses, three importantproblems have been prominent.1. The problem of the very fast growth of the SMBH masses ( M BH ) at high redshifts (at leastfor massive galaxies and quasars). This rapid growth is implied by the discovery of more than tenquasars with very high redshifts z ≈ − [31, 32], as well as the gigantic SMBH masses (upto × M J ) for some objects at z ≈ [33]. This probably suggests the direct formation ofinitial black holes with masses of – M J in the inner regions of forming galaxies, although thisscenario requires a mechanism that can slow the rapid cooling of the gas and its transformation intostars (see the diskussion of this problem and references to original studies in [34]). The growth of M BH at high redshifts apparently overtakes the growth of their bulges, whose masses increase moreslowly. This conclusion has emerged from both numerical calculations of cosmological evolution[35, 36] and direct analysis of observations of quasars [37] and Seyfert galaxies [38].2. The relationship between the central black holes and the nuclear clusters (NCs) remainsunclear; the latter are observed in the centers of both spiral and elliptical galaxies and, as a rule,have modest luminosities. Both of these formations are often unified under the term ”centralmassive object” (CMO). As a rule, the masses and sizes of the NCs exceed the most massive2lobular clusters in the Galaxy, and have more complex star-formation histories, which are differentfor different galaxies and do not correspond to a single star-formation bursts [39]. The two typesof СМО (SMBH and NC) can exist independently of each other, although several galaxies wherethey are observed together are known [16, 40]. In all such cases, the black-hole mass exceeds themass of the NC.3. A key problem is to explain the observed correlations between the mass of the SMBH and/orNC and the bulge properties such as M BH − σ dependence. The SMBH masses statisticallydepend not only on the velocity dispersion, but also on the structure of the bulge. It was foundthat the masses of the central black holes in pseudobulges are, on average, a factor of a few lowerthan in galaxies with classical bulges or E galaxies, for the same central velocity dispersions [42].There may also exist an analogous difference for the NCs, which are, on average, less massive inlate-type galaxies, for a specified mass of the stellar population of the galaxy [16]: for the samestellar-velocity dispersion, M BH is, on average, several times higher for classical bulges than forpseudobulges [42].The difference in the SMBH masses for galaxies with classical bulges and pseudobulges isan important fact. Pseudobulges have lower central brightness concentrations, higher degrees offlattening, and more fast rotation. They are often considered to be false bulges—the result of”heating” of the inner region of the disk (for example, due to the evolution of an existing orformerly existing bar, or during a redistribution of the angular momentum of baryonic matter inthe disk), while classical bulges are usually considered to result from mergers in the early stagesof evolution of the galaxy. Pseudobulges are possessed by late-type Sc–Sd galaxies and someearlier-type galaxies with small bulges, with Sersic parameters n ≤ [44, 45]. Below we considera possibility that at least one of the key parameters determining the growth rate and final massof the SMBH in a young galaxy is not the type of bulge, but rather the mean density of matter(initially gas) in the central, kpc-size part of the observed bulge. It is the density of matter whichdetermine the gravitational contraction time of gas, the rate at which the gas is transformed intostars, and the accretion rate onto the CMO. M BH and the Angular Velocity of the CentralRegion The mean density of the inner region of a galaxy within a radius R is proportional to the squareof the angular velocity V /R at this distance. Therefore, it makes sense to test for the existenceof a universal (for bulges and pseudobulges) correlation between the SMBH mass and the angularvelocity, for which we will use the circular velocity at a fixed distance R = R b . The choice of R b is fairly arbitrary. Here, we choose the velocity V corresponding to R b = 1 kpc. First, thisis the characteristic size of the dynamically and/or chemically decoupled nuclear regions of diskgalaxies. Second, as a rule, the finite angular resolution of observations hinders determination ofthe shape of the rotation curve with the desired accuracy at distances closer to the center. Third,noncircular motions of gas associated with peculiarities of the inner structures of galaxies (bars,spirals, rings, inclined disks, active nuclei) are frequently observed within the central kiloparsec.Note that the first attempts to identify and study the kinematic properties of the inner kpc-sizeregions in galaxies with active nuclei were undertaken by Afanas’ev, who plotted the rotationalvelocity of the gas against the mean volume luminosity of the bulge at this distance [46, 47].3igure 1a compares the masses of the central black holes M BH and the rotational velocitiesV1 of parent galaxies at R b ≈ ◦ . Forthe most slowly rotating galaxy (NGC 428), we used the mass of the nuclear star cluster (takenfrom the data pr5esented by Seth et al. [16]) instead of the black-hole mass which is unknown.The relationship is preserved, but appears looser if to replace V1 onto the velocity of rotationat a maximal distance from the center V F AR where it is measured, or asymptotic velocity (Fig.1b). However, this conclusion is not too convincing because for the galaxies considered here thevelocities at large R are estimated with larger uncertainties than the velocities at a fixed distance.To increase the statistics, we used published data on the rotation curves of galaxies with knownblackhole masses. Figure 2 presents the diagram analogous to Fig. 1a for an appreciably largernumber of objects (see Table), whose black-hole masses have been estimated using the most reliablemethods: reverberation mapping and the resolved kinematics method, in the optical or the radioranges (the latter is from observations of megamasers). We have also included several galaxieswith model SMBH masses based on optical line-of-sight velocity measurements with very highangular resolution (NGC 404, NGC 524, NGC 3368, NGC 4435). We have only upper limits onthe blackhole masses for M33, NGC 4435, and IC 342. The lowest upper limit of M BH in thediagram is that for М33. For galaxies with measured masses for both the central black holes andthe NCs the latter are indicated by asterisks. In these cases pairs of corresponding mass valuesare joined by vertical lines. The rotational velocities were estimated from the rotation curvescited in the ”Bibliographical catalog of galaxy kinematics” in the HYPERLEDA database (see alsoreferences in [13]). When several rotation curves were available, we gave preference to the onethat was traced most certainly in the inner region of the galaxy. The characteristic uncertaintiesare illustrated by the cross in the lower-right corner of the figure. The uncertainties in the SMBHmasses were taken to be a factor of two (0.3 dex) [48, 49] if a larger uncertainty was not indicatedin the source, while the uncertainties in the velocities were taken to be 25% ( ∼ . dex). Theempty circles in Fig. 2 denote galaxies with pseudobulges. The latter include late-type galaxies(Sc and later) and earlier-type galaxies for which the presence of a pseudobulge is indicated byphotometry (following [42, 45]).It follows from Fig. 2 that the black-hole masses are indeed correlate with the angular velocityof the disk at R ≈ kpc, at least for galaxies whose velocities of rotation exceed 200 km/s. Afterexclusion of M33, the correlation coefficient is r = M BH on Other Kinematic Parameters The relationship between the SMBH mass and the rotational velocity becomes less tight if thelatter velocity corresponds to the outer parts of the observed rotation curve V F AR , where a curveof rotation reaches maximum or a plateau (Fig. 3a). Thus, our conclusions do not support thepresence of a tight correlation between the black-hole masses and circular velocities of galaxies farfrom the center.This correlation also nearly disappears when we plot M BH against the angular velocity of thedisk at the optical radius R = R (where R is the radius corresponding to the surface brightness25 m /arcsec in the B band) instead of R = 1 kpc (Fig. 3b). Since the observed rotation curves of4ur sample galaxies reach R in only a few cases, the velocities of rotation were taken from theHYPERLEDA database; in most cases, they were based on the H I linewidth measurements.The ”classical” dependence of the masses of the black holes (and of several NCs in the samegalaxies) on the central stellar velocity dispersion σ (taken from the HYPERLEDA database),presented in Fig. 3c. In general, this plot looks rather similar to the diagram “ M BH -V1” (Fig. 2),although galaxies with pseudobulges (open circles) are shifted in this case.Note that although the relation between M BH and V is due to the same factors as the depen-dence of M BH on the central velocity dispersion σ , the former does not simply reduce to the latter.First, observational estimates of σ are the result of averaging of chaotic stellar velocities along theline of sight. The velocity dispersion falls with distance from the center, and the result dependson the adopted radius for the averaged region. This radius has been determined in different waysin different studies, and is usually related to the effective radius of a galaxy in some way. Second,in contrast to the rotational velocity, σ is not related to either the mass or the mean densityof the system; translation to the latter requires the construction of a dynamical model and, ingeneral case, taking into account the rotation of a bulge, which is usually badly known. Finally,measurement and interpretation of the velocity dispersion becomes especially complex for galaxieswith small bulges, where two dynamically distinct components contribute to σ – the bulge and thedisk. The effect of the disk is especially important in the presence of a young stellar populationwith a low velocity dispersion. At the same time, although the circular velocity of the disk at agiven distance R is often measured with lower accuracy than σ , the former has a simpler universalinterpretation, and in all cases characterizes the total mass of matter within the chosen radius. M BH and the Luminosity and Mass of the Galaxy Figure 4 plots the mass of the central black hole against the total luminosity L V and theindicative mass M = V F AR R /G , which is close to the total mass of the galaxy within theoptical radius R . As expected, the mass of the CMOs is very loosely connected with the totalluminosity of galaxy. Indeed, black-hole mass is known to closely tied with the mass and luminosityof the spheroidal component of a galaxy only [5, 49] (see also references therein). However, thereis an overall trend for all galaxies to increase M BH with total mass M (the correlation coefficientfor the logarithmic plot is r = 0 . ). Note that a bulge mass contribution to M is usually small.The linear regression fit in Fig. 4 has the form log M BH = a log M + b, (1)where a = − . ± . , b = 1 . ± . (without including the galaxies with upper limits for M BH ).In contrast to the total luminosity of the galaxy, which is closely correlated with its rotationalvelocity (the Tully–Fisher relation), M depends on the masses of both the baryonic components(stars, gas) and the dark halo, with their contributions being comparable within the optical radius(see, for example, [50]). Ferrarese et al. [41] show the existence of a similar dependence betweenthe mass of the CMO and the quantity M gal ∼ R e σ e /G , where σ e is the stellar-velocity dispersionwithin the effective radius R e , which contains half the total luminosity of an elliptical galaxy or thebulge of a spiral galaxy. However, their conclusions of [41] were based mainly on data for ellipticalgalaxies. 5 CMOs IN GALAXIES WITH CLASSICAL BULGES ANDPSEUDOBULGES
In contrast to early-type galaxies, late-type Sbc–Sd galaxies always possess pseudobulges, while,as a rule, earlier type galaxies contain classical bulges or both types of bulges. Therefore, thedivision of galaxies into early and late morphological types can be viewed as a division into objectswith classical bulges and pseudobulges (although this identification is not perfect). Hu [42] notedthat the SMBH masses in galaxies with pseudobulges (i.e., in late-type galaxies) are systematicallylower than those in early-type galaxies, for the same velocity dispersion. This is illustrated forour sample of galaxies in Fig. 3c, where we compare the masses of black holes and several nuclearclusters with the central velocity dispersion taken from the HYPERLEDA database. However,galaxies with the two types of bulges are well mixed in the diagram where M BH is plotted vs. V (Fig. 2). This suggests that, for a given mean density of matter within the central kpc-size region, M BH , or more generally the CMO mass, does not depend, or depends only weakly, on the type ofa bulge.The difference between galaxies with bulges and pseudobulges, or between galaxies of earlyand late types, is especially clear when considering the stellar masses of the NCs, which wasdemonstrated by Seth et al. [16]: nuclear clusters in the early type galaxies are more massive.As in the case of the blackholes, there is essentially no correlation between the masses of nuclearclusters and the velocities of rotation of their parent galaxies. This is illustrated by Fig. 5a,where the masses of NCs are plotted against the velocities of rotation of galaxies taken fromHYPERLEDA (they are obtained mainly from the HI linewidths). Galaxies with disk inclinations i < ◦ were excluded due to uncertainty in the estimated corrections for the disk inclination. Theempty symbols indicate galaxies of type Sc or later (i.e., galaxies with pseudobulges or withoutany appreciable bulges). However, as in the case of the SMBHs, there is a correlation betweenthe NC masses and the total dynamical masses of the galaxies within the optical radius M (Fig.5b), which is especially clearly manifests for S0–Sbc galaxies (correlation coefficient r = 0 . ).The correlation with galaxy mass is weak or absent for late-type galaxies possessing only small(pseudo)bulges (empty circles). The masses of the NCs are, on average, a factor of six lower thanin the earlier-type galaxies.Earlier, Seth et al. [16] found a similar relation between the NC mass and the total mass ofstellar population of a galaxy, estimated from its luminosity (in the B band) and color index (seeFig. 2 in [16]). The mass values found from photometry and on the base of circular velocities arenot identical, since the kinematically found mass is the sum of masses of visible components anda dark halo, while the photometric mass relates only to stellar population, being calculated undercertain assumptions about the initial stellar mass function and the star-formation history. It isstriking that the difference between early- and late-type galaxies in Fig. 5b reveals itself appreciablyclearer than the similar relation based on the masses of stellar population alone presented by Sethet al. [16].To resume, both SMBHs and NCs masses depend weakly on the linear or angular velocities ofrotation of the disks at large radii, but they correlated with the angular velocity within the centralkiloparsec, and also with the mass of a galaxy within the optical radius. We have confirmedthat galaxies with pseudobulges, which are primarily late-type spiral galaxies, have appreciablyless massive NCs, on average, for the same integrated characteristics of the galaxy and the samestellar-velocity dispersion [41]. 6 DISCUSSION
The genetic relationship between the central black-holes and stellar clusters is obvious: theirmasses are correlated with the mass or stellar-velocity dispersion of the bulge in the same way.However, the attempts to explain how the formation of one could be connected with the presence ofthe other encounter considerable difficulties. The ratio of the NC and SMBH masses encompassesa very large range. As a rule, in galaxies with low-luminosity bulges, M BH < M NC [41], while theopposite is true for large bulges [18]. There also exist galaxies with high luminosity in which thereexist a SMBH, but no NC is observed. Partially it can be explained by the difficulties in detectingstar clusters against the bright background of the nucleus of a massive galaxy (although it is hardto ”hide” a star cluster with a mass of M J ), but this is more likely associated with an earlycessation to the growth of NCs in galaxies with the most massive black holes. A key factor here isthe difference in the conditions for the growth of the masses of SMBHs and NCs.The correlation between the masses of SMBHs and NCs with the properties of bulges ratherthan the disks of their parent galaxies suggest that both types of CMOs arise from the same gasmedium as the stars in the central part of bulges, but via different processes that occur on differenttime scales. The depth of the potential well at the galactic center is of primary importance here.Classical bulges and pseudobulges probably formed at different times (the latter as a product ofthe evolution of the inner part of the disk). Pseudobulges rotate faster than the classical ones, and,since galaxies with this type of bulges are not distinguished in a M BH − V diagram, we concludethat the final mass of the central black hole is more closely related to the matter density in theinner kpc-size region than to the specific angular momentum of the bulge.The inner region of a galaxy containing the densest part of the bulge, with which we associatethe growth of the SMBH, should form within the first billion years, in the first and relatively shortstage of the galaxy formation. The presence of two stages in the formation of galaxies has beeninvestigated in a number of studies numerically modeling this process in a Λ CDM model of theUniverse (see, for example, [51, 52, 53]). According to the numerical simulations of Cook et al. [51],during the first, short phase in the formation of galaxies, there was a collapse of dark and baryonicmatter into the inner regions of the galaxies, leading to the formation of stellar spheroids (bulges)at z ≈ , after which there began a quieter and more prolonged stage of disk formation, which didnot influence the galactic centers. In the simple analytical model proposed by Xu et al. [52], thestellar bulge forms as a result of a gravitational monolithic compression of an isothermal gaseoussphere, which loses its stability in the gravitational field of the central cusp of the dark halo; thisprocess is accompanied by violent star formation, which sustains the growth of the central blackhole.Evidently, the formation of both the bulges of disk galaxies and the elliptical (E) galaxies is acomplex process. Baes et al. [54] separated the influence of the age and chemical composition onthe spectrum of the stellar population for elliptical galaxies, and concluded that the star-formationhistories are different for the inner and outer regions of a galaxy: the central region ( R ≈ . – kpc) has a steep metallicity gradient, and apparently formed as a result of a monolithic collapse ofgas, in contrast to more distant regions. The hydrodynamical computations of Pipino et al. [55]subsequently demonstrated the agreement between the observed metallicity gradients in E galaxiesand those expected for a monolithic collapse.Classical bulges of disk galaxies are similar to E galaxies: they are characterized by the similarrelations between the observable parameters [45]. So one can expect that the inner regions of diskgalaxies with the size of the order of a kiloparsec, containing the classical bulge, could also haveformed from gas compressed as a whole, without a participation of merging of smaller subsystems.A monolithic collapse of gas is natural to associate with the fast growth of the CMOs (SMBHs7nd/or NCs). As three-dimensional hydrodynamical computations show, the higher the gas density,the more intense the accretion of gas into the center of the forming galaxy and, as a consequence,the more massive the central object that is formed—a future SMBH [43].A high gas density in the inner part of a protogalaxy leads to intense star formation near thegalactic center. On the one hand, this process facilitates the growth of the black hole, since itprovides a source of turbulent motions in the gaseous medium (see, for example, [56]); on theother hand, it limits the growth of the black hole in time, since it depletes the supply of availablegas [43]. If the bulge has a low density and star formation occurs over an extended time, thecentral black hole is not able to grow effectively, and it remains to be a comparatively low-massobject. However, the growth of the bulge mass can continue for a long time after the growth ofthe black-hole has ceased — for example, as a consequence of mergers with small systems, or as aresult of dynamical heating of the inner region of the disk (in this case a pseudobulge may form).Numerical simulations of the growth of a bulge show that this scenario can explain the gradualemergence of the ratio between the bulge and SMBH masses [35]. Note that in galaxies whereboth types of bulges are observed (a more compact classical bulge and a pseudobulge) the mass ofthe black hole correlates with the mass of the classical bulge [59].The formation of a galaxy took place in the gravitational field of both dark halo and baryonicmatter. The role of dark matter in formation of CMOs is poorly known. In generally acceptedcosmological schemes for galaxy formation, the virial mass of a galaxy, which is comprised primarilyby the dark halo, is determined by the value of circular velocity at large R , which is close to theobserved velocity V F AR [58]. Nevertheless, as it was shown above, the masses of CMOs correlatebetter with M than with V F AR . It is worth reminding that M is the total mass within theoptical radius of a galaxy, where the masses of baryonic and dark matter are usually comparable.Both types of compact objects – SMBH and NC – may begin to grow independently, increasingtheir masses more rapidly if the gas density in the central part of forming galaxy is higher.Thecorrelation between the masses of nuclear clusters and bulges is not as tight as it is for M BH (see[59]), which may reflect that the growth stage of the cluster lasts appreciably longer than thegrowth stage of the black hole. Nuclear clusters in E galaxies can increase their masses via theaccretion of gas with low angular momentum, and those in spirals – via the slow accretion of gasfrom the disk, or due to dynamical friction of massive objects in the disk (star clusters,massive gasclouds) [60, 61, 62]. Therefore, when the central black hole has only a modest mass (say, due toa low initial gas density), the NC can overtake the black hole in mass over billions of years, whilestill remaining comparatively low-mass (as in M33, for example). In galaxies with massive classicalbulges, and consequently with high-mass central black holes, a massive NC may not form, due tothe expected high activity of the nucleus; this apparently is the case in early-type high-luminositygalaxies. The main conclusions of this work are the following.1. The masses of supermassive black holes (SMBHs) in the nuclei of disk galaxies do not dependon the angular velocity of peripheral regions of the disk, but they correlate with the angular velocityof the inner kpc-size regions of galaxies, which characterizes the mean density of the matter there.Galaxies with classical bulges and pseudobulges probably form a single sequence, although betterstatistics are needed before firm conclusions can be drawn. Based on the idea of Baes et al. [54]and the model of Xu et al. [52], which propose that there should be a monolithic collapse ofmatter during the formation of the inner regions of galaxies, we suggest that such a collapse of8seudo-isothermal gas within a radius of R ≈ kpc is responsible for the rapid growth of mass ofthe central SMBH and the classical bulge in the initial period of a history of galaxy.2. Although a correlation between the SMBH mass M BH and the circular velocity V F AR at largedistances R can be traced, it is fairly loose, confirming our earlier conclusion [13]. Consequently,the velocity of rotation of the outer disk, which characterizes the total virial mass of the dark haloin modern models for galaxy formation, does not play the determining role in the formation of thecentral black hole. The same may also be true for nuclear star clusters (NCs).3. The masses of both the SMBHs and NCs are correlated with M = V far R /G , where M is the indicative total mass of a galaxy within the optical radius R . A similar relationfor elliptical galaxies, whose masses were crudely estimated based on their velocity dispersions,was demonstrated earlier by Ferrarese et al. [41]. This enables to suggest that the conditionsfor the formation of the central massive objects in both disk and E galaxies depend on the massof the galaxy within the optical radius, where the contributions of dark and baryonic matter arecomparable, rather than with the mass of a dark halo only.4. Nuclear stellar clusters in early-type spiral galaxies (S0–Sbc) are, on average, nearly anorder of magnitude more massive than those in later-type galaxies with the same values of M ,or than the SMBHs in these galaxies. It concords with the idea that the formation of SMBHs andNCs occurs on different time scales, and the masses of the NCs (if they managed to form close tothe black hole) apparently continue to grow after the growth of the SMBHs has ceased.5. At least for spiral galaxies with central black holes with comparatively modest masses, thetotal mass of the NC + SMBH correlates better with such parameters as the central angular velocityof a disk and the indicative mass M , than does the mass of SMBH alone. The authors thank A.V. Moiseev and V.L. Afanas’ev for obtaining the spectral observations onthe SAO 6-m telescope, and also O.K. Sil’chenko for interest in this work and valuable comments.
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Soc. 411, 1803 (2011).12able 1: Black-hole (central cluster) masses and kinematic parameters for the galaxies considered № Galaxy M BH,NUCL , M ⊙ Source V1,km/s V F AR ,km/s σ ,km/s1 NGC 224 140 [15] 230 232 1702 NGC 404 (BH) 0.45 [16] - 200 -3 NGC 404 (NUCL) 10 [16] - 200 -4 NGC 598 (BH) <0.0015 [8] 60 130 375 NGC 598 (NUCL) 2 [17] 60 130 376 NGC 1023 44 [7] 130 - 2047 NGC 1068 8.3 [7, 19] 220 230 1998 NGC 1300 66 [20] 170 230 2299 NGC 2748 44 [20] 115 145 -10 NGC 3031 70 [7] 300 168 16111 NGC 3227 7.63 [21] 140 - 13312 NGC 3368 7.5 [22] 160 200 12813 NGC 3384 16 [7] 106 200 14814 NGC 3783 29.8 [23] 150 180 15515 NGC 3998 270 [24] 406 400 30416 NGC 4051 1.73 [21] 120 160 8417 NGC 4151 13.3 [23] 280 - -18 NGC 4258 39 [25, 7] 233 194 13419 NGC 4303 5 [25] 160 160 10920 NGC 4342 330 [7] 210 - 25121 NGC 4395 0.36 [26] 40 90 9022 NGC 4435 <7.5 [27] 160 - 15723 NGC 4593 15 [23] - - 19824 NGC 5128 49 [15] 250 170 12025 MW (BH) 3.7 [15] 220 230 -26 MW (NUCL) 30 [18] 220 230 -27 Circunus 1.7 [28] 130 152 -28 IC342 (BH) <0.5 [29] 80 218 7429 IC342 (NUCL) 6 [29] 80 218 7430 3C 120 30 [7] 100 280 10031 MRK 79 52.4 [23] - 150 13032 MRK 279 34.9 [23] 90 200 -33 NGC 428 (NUCL) 3.16 [16] 40 110 3034 NGC 524 830 [30] 290 320 25035 NGC 2787 41 [15] 170 220 20036 NGC 3245 210 [15] 150 200 21037 NGC 3516 31.7 [21] 115 180 15038 NGC 7457 3.5 [7] 58 130 6539 NGC 7469 12.2 [23] 100 120 130 M B H , M S un
30 300
2 3 4 5 6 7 8 910 (a)
100 V
FAR ,km/s10 M B H , M S un
80 200 400
1 2 3 4 5 6 7 8 9 10 (b)
Figure 1: Relationship between the SMBH mass (the NC mass for NGC 428) and (a) the circularvelocity at R ≈ V for Mrk 79.13 M B H , M S un M BH < 1500 M Sun
30 300
Figure 2: A comparison of masses of SMBHs (filled circles) and several NCs (asterisks) as with thecircular velocity of parent galaxies at R ≈
00 V
FAR ,km/s10 M B H , M S un
70 200 400 M BH < 1500 M Sun (a)
10 100V
FAR /R ,km s -1 kpc -1 M B H , M S un M BH < 1500 M Sun (b) σ ,km/s10 M B H , M S un M BH < 1500 M Sun
30 300 (c)
Figure 3: A plot of the masses of SMBHs and several NCs against (a) the circular velocity ofparent galaxies far from the center V F AR , (b) the angular velocity of the galaxy at the opticalradius R = R , and (c) the central velocity dispersion taken from HYPERLEDA database. Thenotation is the same as in Fig. 2. 15 .0 8.5 9.0 9.5 10.0 10.5 11.0 11.5log L V M B H , M S un M BH < 1500 M Sun (a) M ,M Sun M B H , M S un M BH < 1500 M Sun (b)
Figure 4: A comparison of the SMBH masses with (a) the total luminosities of parent galaxies L V and (b) the dynamical (indicative) masses within the optical radius M = V far R /G . Thenotation is the same as in Fig. 2. ROT ,km/s10 M NUC L , M S un (a) M ,M Sun M NUC L , M S un (b) Figure 5: (a) Diagram illustrating the absence of a correlation between the NC masses (taken from[16]) and the velocity of rotation (taken from HYPERLEDA). The filled symbols show S0–Sbcgalaxies and the empty symbols are for later-type galaxies. (b) Relation between the masses ofthe NCs and the dynamical masses M of parent galaxies. A comparison with Fig.4b shows thatthe nuclear clusters in S0-Sbc galaxies have higher (in the mean) masses of NCs than SMBHs fora given M25