Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.stsci.edu/science/preprints/prep1203/prep1203.ps Äàòà èçìåíåíèÿ: Wed Dec 17 19:34:44 1997 Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 14:15:59 2007 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: ngc 6251

RELICS OF NUCLEAR ACTIVITY:
DO ALL GALAXIES HAVE MASSIVE BLACK HOLES?
Invited Review for `Galaxy Interactions at Low and High Redshift',
Proceedings IAU Symposium 186, Kyoto, August 1997,
D. B. Sanders, J. Barnes, eds., Kluwer Academic Publishers.
ROELAND P. VAN DER MAREL
STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA
Abstract. The distribution of black hole (BH) masses M ffl in galaxies is
constrained by photometric and kinematic studies of individual galaxies,
and by the properties of the quasar population. I review our understanding
of these topics, present new results of adiabatic BH growth models for HST
photometry of elliptical galaxies with brightness profiles of the `core' type,
and discuss the implications of ground­based stellar kinematical data. It is
not yet possible to uniquely determine the BH mass distribution, but the
available evidence is not inconsistent with a picture in which: (i) a majority
of galaxies has BHs; (ii) there is a correlation (with large scatter) between
M ffl and spheroid luminosity L sph of the form M ffl ú 10 \Gamma2 L sph (solar B­band
units); and (iii) the BHs formed in a quasar phase through mass accretion
with efficiency ffl ú 0:05.
1. Introduction
Considerable evidence suggests that the energetic processes in active galax­
ies and quasars are due to the accretion of matter onto massive BHs.
Lynden­Bell (1969) already suggested that BHs may also be present in qui­
escent galaxies, such as the Milky Way, M31 and M32. This spurred efforts
to find BHs in nearby galaxies through kinematical studies, which have since
increased steadily in sophistication, both observationally and theoretically.
There are now convincing BH detections for at least a dozen galaxies, and
new detections are reported at an ever increasing rate. The techniques for
detecting BHs in individual galaxies have been reviewed by, e.g., Kormendy
& Richstone (1995, hereafter KR95), Ford et al. (1998) and Richstone
(1998). Here I address the more general question: do all galaxies have BHs?

2 ROELAND P. VAN DER MAREL
2. Quasar counts and evolution
Integration of quasar number counts yields the comoving energy density
in quasar light. Assuming that this energy is produced by accretion onto
massive black holes, one obtains the total mass per cubic Mpc that is col­
lected in black holes (So/ltan 1982). Division by the observed luminosity
density of galaxies (Loveday et al. 1992) yields an estimate of the average
black hole mass per unit luminosity: hM ffl i=hLi = 2:0 \Theta 10 \Gamma3 (0:1=ffl), where
ffl is the accretion efficiency (Chokshi & Turner 1992). [Throughout this
paper, H 0 = 80 km s \Gamma1 Mpc \Gamma1 , mass­to­light ratios are in solar units, and
luminosities are in the B­band.]
To address the BH mass distribution, one must model not only the total
energy budget of the quasar population, but also its evolution. Tremaine
(1996; also Faber et al. 1997, hereafter F97) presented a simple argument
based on the typical quasar lifetime to show that a model in which ev­
ery spheroid (bulge or elliptical) has a BH is consistent with the inferred
hM ffl i=hLi. Haehnelt & Rees (1993, hereafter HR93) presented a more de­
tailed model (in which BH formation is linked to hierarchical structure
formation) to fit the distribution of quasars as function of magnitude and
redshift. Their predicted BH mass distribution at the current time (their
Fig. 8) is consistent with a fraction f ú 0:3 of all galaxies having a BH.
The uncertainties in these estimates are considerable. The only conclu­
sion that can be drawn with some confidence is that a fraction f = 0:1--1 of
all galaxies is likely to contain BHs with M ffl =L = 10 \Gamma2 --10 \Gamma3 . The product
of these quantities, hM ffl i=hLi, is better constrained than either quantity
independently, but is still rather uncertain (if only due to the unknown ffl).
3. BH detections
HR93 predict a direct connection between M ffl and the galaxy formation
redshift z form (galaxies that form later have smaller BHs), but not between
M ffl and galaxy luminosity. Spirals form later than ellipticals, and are there­
fore predicted to have smaller BHs. Observations appear to confirm this;
e.g., the (active) galaxies M87 and NGC 1068 have similar luminosities,
but M ffl is 10 2:5 times larger in M87 (cf. Figure 1a below). Observations do
not rule out a correlation between M ffl and the spheroid luminosity of the
host (KR95). This may indicate that M ffl and L sph depend similarly on a
common underlying parameter (e.g., z form , as in the models of HR93), or
alternatively, that there is a physical link between BHs and spheroids.
Figure 1a shows M ffl versus L sph for all currently available BH mass de­
terminations inferred from: (\Theta) radio observations of water masers; (ffi) ion­
ized gas kinematics of nuclear disks; (\Lambda) time variability of broad double­
peaked Balmer lines; and (ffl) stellar kinematical studies that included aniso­

RELICS OF NUCLEAR ACTIVITY 3
Figure 1. Measurements of black hole mass M ffl versus spheroid luminosity Lsph . Arrows
indicate upper limits. (a; left) `Secure' BH detections obtained with various techniques,
as indicated by different symbols and discussed in x3. References are included in the bibli­
ography; where necessary, spheroid/total luminosity ratios were estimated from the Hub­
ble type and the relation in Simien & de Vaucouleurs (1986). (b; middle) M ffl values for
all core galaxies in F97 with MB! \Gamma20, inferred from models of adiabatic BH growth for
HST photometry (x4; van der Marel 1998, in preparation). M87 and NGC 3379 are the two
core galaxies for which secure kinematic determinations are also available (cf. panel a).
NGC 1600 is discussed in x5. (c; right) M ffl determinations from axisymmetric f(E; Lz )
models for ground­based stellar kinematical observations of elliptical galaxies (Mg98).
Circles: `core' galaxies; triangles: `power­law' galaxies; open symbols: galaxies in Virgo.
Galaxies already included in the left panel are omitted. For NGC 4486B and 4594 the
presence of a BH has been suggested previously on the basis of isotropic models. The M ffl
values in panel a are typically believed to have j\Delta log M ffl j Ÿ 0:3. The accuracy of the M ffl
measurements in panels b and c is dominated by systematic uncertainties in the model
assumptions, as discussed in x4, 5 and 6. In particular, mild radial velocity anisotropy
would lower the values in panel c. The solid line in each panel is the `reference model' dis­
cussed in the x3. It has M ffl = 1:4 \Theta 10 \Gamma2 Lsph , and fits the constraints from quasar number
counts for an assumed accretion efficiency ffl = 0:05. The long­dashed line in the right­
most panel is an alternative model. It has M ffl = 6:0 \Theta 10 \Gamma3 Msph (with Msph / Lsph 1:18 ,
cf. Mg98), and fits the constraints from quasar number counts for ffl = 0:022. The dashed
line in the left panel indicates those M ffl for which r ffl = 0:1 00 at D = 10 Mpc.
tropic modeling (studies with only isotropic models are discussed in x6).
There is indeed a correlation, but the scatter is large (¸ 2 dex at fixed
L sph ) and selection bias may be important. The dashed line shows the M ffl
for which the BH sphere of influence, r ffl ' GM ffl =oe 2 , extends 0:1 00 at a
distance D = 10 Mpc (oe is determined by L sph through the Faber­Jackson
relation). BHs below this line can be detected only in galaxies closer than
10 Mpc, and in galaxies in which kinematical tracers can be observed at
resolutions ! 0:1 00 (e.g., water masers).
The solid line shows the predictions of one possible model that is consis­
tent with the hM ffl i=hLi from quasar number counts. This `reference model'
assumes that every spheroid has a BH with M ffl / L sph . Approximately 30%
of the light from galaxies is due to spheroids (Schechter & Dressler 1987). So
for an assumed accretion efficiency ffl = 0:05 this yields M ffl = 1:4 \Theta 10 \Gamma2 L sph ,
which reproduces the trend in the data.

4 ROELAND P. VAN DER MAREL
4. Surface­brightness profiles
HST observations of early­type galaxies have revealed central surface bright­
ness cusps that fall in two categories (F97), `power­laws' (showing no clear
break) and `cores' (showing a clear break). Cusps can be explained as a
consequence of the influence of a BH on surrounding stars (Young 1980,
hereafter Y80). Properties of cusps around BHs depend on M ffl , initial con­
ditions (Quinlan et al. 1995, hereafter Q95) and two­body relaxation (Bah­
call & Wolf 1976). Cusps may also be due to processes unrelated to BHs
(KR95), and they can also be destroyed (Quinlan & Hernquist 1997). Ob­
served cusps therefore do not uniquely constrain the BH masses in galaxies.
Nonetheless, simple models of adiabatic BH growth for observed pho­
tometry of M87 (Young et al. 1978; Lauer et al. 1992; Crane et al. 1993) and
several other galaxies imply BH masses that agree well with kinematic de­
terminations. I have therefore started a study of adiabatic BH growth mod­
els for a large sample of galaxies with published HST photometry. These
models may be particularly relevant for core galaxies, for which the observed
break in the brightness profile may be associated with an originally homoge­
neous core. I have used the software of Q95 to fit the photometric models of
Y80 to all core galaxies in the sample of F97 with MB ! \Gamma20 (van der Marel
1998, in preparation). The models fit well in the central few arcsec (RMS
residual ¸0:05 mag/arcsec 2 ), and the photometrically inferred M ffl appear
meaningful: the kinematically determined M ffl for M87 and NGC 3379 (see
Figure 1a) are reproduced to within 0:12 and 0:50 dex, respectively.
Figure 1b shows the results for the whole sample. The M ffl are remark­
ably consistent with the kinematical detections in Figure 1a, and show a
similar trend with L sph . So despite their simplicity, it may well be that the
Y80 models capture the essence of surface brightness cusps in core galax­
ies. The prevalence of these cusps would then imply that most or all core
galaxies have BHs, with M ffl / L sph as suggested by Figure 1b.
5. Stellar kinematics and velocity dispersion anisotropy
Stellar motions often provide the only kinematical tool to study BH masses
in quiescent galaxies, but the well­known degeneracy between M ffl and ve­
locity dispersion anisotropy (Binney & Mamon 1982) is still a major com­
plication. This degeneracy can be resolved when high resolution HST data
are available (e.g., van der Marel et al. 1997; Gebhardt et al. 1998), but
such data are not yet available for many galaxies. Lower resolution ground­
based data are plentiful, but more ambiguous to interpret. I use the case of
NGC 1600, an E3 core galaxy with no significant rotation, to illustrate this.
Ground­based kinematical data with ¸ 2 00 resolution (Jedrzejewski &
Schechter 1989) show a mildly peaked velocity dispersion profile, and HST

RELICS OF NUCLEAR ACTIVITY 5
Figure 2. Predictions of spherical dynamical models for NGC 1600 that reproduce HST
and ground­based photometry (F97; Peletier et al. 1990). The abscissa in each panel
is log([M ffl =\Upsilon] + C), where log C j 7:425; i.e., approximately logarithmic in (M ffl =\Upsilon)
for (M ffl =\Upsilon) AE C, and M ffl = 0 on the left boundary. The ordinate is oe r =oe t , increasing
logarithmically from 1=3 to 3. For each (M ffl =\Upsilon; oe r =oe t ), the stellar mass­to­light ratio
\Upsilon was chosen to minimize the ü 2 of the fit to the kinematical data of Jedrzejewski &
Schechter (1989). (a; left) Contours of ü 2 . The first two contours correspond to the 1oe
and 2oe level, as calculated from the statistic \Deltaü 2 . The heavy contours show the 3oe region.
(b; middle) Contours of \Upsilon, increasing linearly. (c; right) Contours of M ffl , increasing
logarithmically. Heavy curves in panels b and c indicate contours for which the value
of \Upsilon or log M ffl is indicated. Contours of \Upsilon and ü 2 are approximately parallel, so \Upsilon is
well determined independent of the anisotropy, log \Upsilon = 1:02. By contrast, contours of
M ffl and ü 2 are approximately perpendicular, so there is a strong degeneracy between
M ffl and anisotropy. In all panels, a heavy horizontal bar indicates those isotropic models
with a BH that are acceptable at the 1oe level, and a heavy vertical bar indicates those
anisotropic models without a BH that are acceptable at the 1oe level.
photometry shows a shallow (F97), marginally significant (Byun et al. 1996;
Gebhardt et al. 1996), surface brightness cusp. I construct spherical dynam­
ical models (adequate for the present purpose) following the approach of
van der Marel (1994, hereafter vdM94). I solve the Jeans equation for a
given velocity anisotropy profile profile, oe r =oe t (r) (where 2oe t 2 j oe 2
` + oe 2
OE ),
project and convolve the results, and compare with the data in a ü 2 sense.
The normalization of the dispersion profile is determined by the stellar
mass­to­light ratio \Upsilon, and its shape is determined by oe r =oe t and M ffl =\Upsilon.
Figure 2 shows the fitted ü 2 , M ffl and \Upsilon in the (M ffl =\Upsilon; oe r =oe t ) parameter
space, for models with constant oe r =oe t . The valley in the ü 2 contours shows
that a one­parameter family of (M ffl =\Upsilon; oe r =oe t ) combinations fits the data.
An isotropic model requires a very massive BH, log M ffl = 9:85, but only
modest anisotropy, oe r =oe t = 1:18, is required to fit the data without a BH.
Models that are radially anisotropic at all radii may not correspond to a
positive phase­space distribution function (DF) (vdM94), or may not be
stable (Stiavelli et al. 1993), so I also constructed models in which the core
is isotropic, and in which there is a smooth transition at the break radius of
the surface brightness profile (r b = 3:12 00 ) to a value (oe r =oe t ) main character­
istic of the main body. Models with log M ffl !10:01 are still all acceptable at

6 ROELAND P. VAN DER MAREL
the 1oe level. The best fit with no BH has (oe r =oe t ) main = 1:45, and the best
fit with log M ffl = 9:15, as suggested by adiabatic BH growth (Figure 1b),
has (oe r =oe t ) main = 1:30. So in the absence of independent constraints on the
velocity dispersion anisotropy, the data do not significantly constrain M ffl .
Our understanding of the velocity anisotropy in galaxies is only rudi­
mentary. Ellipticals and bulges with power­law brightness profiles have low
to intermediate luminosity (F97), and are flattened by rotation. The tensor
virial theorem indicates that they may be isotropic. Any anisotropic model
with the same average (oe 2
R + oe 2
OE )=oe 2
z is also viable, but both M32 (van der
Marel et al. 1998) and the Galactic Bulge (Evans & de Zeeuw 1994) have
indeed been shown to be nearly isotropic. By contrast, core galaxies like
NGC 1600 have intermediate to high luminosity, and little rotation (F97).
Detailed studies of three individual galaxies (Merritt & Oh 1997; Rix et
al. 1997; Gerhard et al. 1998) are consistent with mild radial anisotropy,
oe r =oe t = 1:2--1:4, with a possible transition to isotropy at small radii. Such
a velocity distribution can be produced by dissipationless collapse (van Al­
bada 1982). Mild radial anisotropy is also consistent with studies of the
ratio of major to minor axis kinematics (van der Marel 1991) and line­
of­sight velocity profile shapes (Bender et al. 1994) in a larger sample of
core galaxies, and is also seen in the Galactic halo in the solar neighbor­
hood (oe r =oe t = 1:5 \Sigma 0:2; Beers & Sommer­Larsen 1995). So it appears that
power­law galaxies may be approximately isotropic and that core galaxy
may be mildly radially anisotropic, but neither result is firmly established.
6. Isotropic models for stellar kinematical data
Magorrian et al. (1998, hereafter Mg98) studied 36 (mostly) elliptical galax­
ies for which HST photometry and ground­based stellar kinematics have
been published. Each galaxy was modeled with the Jeans equations, as­
suming an f(E; L z ) DF (the axisymmetric generalization of a spherical
isotropic model). Figure 1c shows the BH masses that best fit the observed
kinematics. BHs are required in nearly all galaxies, with M ffl ú 6 \Theta 10 \Gamma3 M sph
(long­dashed line), consistent with quasar number counts if the accretion
efficiency ffl = 0:022. This is the first dynamical study that addresses a
large sample in a homogeneous way while including HST photometry. It
establishes the important fact that the presence of a BH in every spheroid
is consistent with kinematical data, and that the required BH masses are
consistent with quasar counts for a reasonable value of ffl.
Nonetheless, the Mg98 results are not unique. Of the 29 galaxies that
require a BH under the f(E; L z ) hypothesis, 19 are core galaxies with simi­
lar data as for NGC 1600. Mg98 find log M ffl = 10:07 for NGC 1600, but the
results in x5 showed that all M ffl smaller than this are equally acceptable.

RELICS OF NUCLEAR ACTIVITY 7
So the Mg98 models may have overestimated the masses and/or prevalence
of BHs. This would not violate the constraints from quasar counts: if one
assumes a higher ffl = 0:1, one may decrease all M ffl by a factor 4:5, or
remove the BHs in 78% of the galaxies.
Two core galaxies in the sample have M ffl determinations from inde­
pendent sources. Neither is well fit by an f(E; L z ) model. For M87, Mg98
infer the same M ffl as inferred from HST gas kinematics, but only if the
data outside 5 00 are ignored. For NGC 3379, Mg98 infer an M ffl that exceeds
the more accurate determination of Gebhardt et al. (1998) by a factor 7.
Independent of whether one views these comparisons as reasonable or poor
agreement, it leaves open the question whether f(E; L z ) models return the
correct result for galaxies that may not have a (significant) BH.
One may wonder whether the correlation between M ffl and L sph inferred
by Mg98 can be explained if the M ffl values were partly spurious. This is
in fact the case. For galaxies that are radially anisotropic, isotropic mod­
els will fit the observed dispersion gradients by invoking BHs for which
r ffl j GM ffl =oe 2 is similar to the observational resolution. This predicts a
correlation of M ffl with distance of the form r ffl ú 2 00 , which is not inconsis­
tent with the Mg98 results. The more distant galaxies in the sample are the
most luminous. So this predicts not only the correlation of M ffl with L sph ,
but also that this correlation should be weaker for the galaxies in Virgo
(which are all at the same distance), as seen in Figure 1c.
Actual measurements of the velocity anisotropy are required to establish
whether or not the M ffl inferred by Mg98 are correct. Either way, the M ffl in
Figure 1c are 4.5 times higher than those in Figure 1b, averaged over the 14
galaxies common to both samples. So either the photometric measurements
are too low (not impossible, cf. the uncertainties discussed in x4), or the
Mg98 results are too high (which would require mild radial anisotropy that
is not inconsistent with our understanding of core galaxies, cf. x5).
7. Conclusions
Our understanding of the BH mass distribution is still incomplete, partly
due to a lack of complete representative samples that cover quiescent and
active galaxies of all Hubble types, and partly due to persistent uncer­
tainties in the correct interpretation of photometric and kinematic data.
However, it is clear that we are finding BHs in the correct mass range to
explain quasar fueling and evolution, to within the uncertainties.
I thank Gerry Quinlan for kindly allowing me to use his adiabatic BH growth
software. This work benefited from discussions with Eric Emsellem, Tod Lauer,
John Magorrian, Scott Tremaine and Tim de Zeeuw. It was supported by STScI
grant HF­1065.01­94A and an STScI Fellowship. STScI is operated by AURA Inc.,
under NASA contract NAS5­26555.

8 ROELAND P. VAN DER MAREL
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