Evidence for a massive BH in the S0 galaxy NGC 4342

Abstract

We present axisymmetric dynamical models of the edge-on S0 galaxy NGC 4342. A combination of observations from the ground and with the Hubble Space Telescope (HST) has shown that NGC 4342 rotates rapidly and has a strong central increase in velocity dispersion. We construct simple two-integral Jeans models as well as fully general, three-integral models. The latter are built using a modified version of Schwarzschild's orbit-superposition technique. The two-integral Jeans models suggest a black hole (BH) mass between 3 and 6x10^8 Msun, depending on the data set used to constrain the model, but they fail to fit the details of the observed kinematics. The three-integral models can fit all ground-based and HST data simultaneously, but only when a central BH is included. Models without BH are ruled out to a confidence level better than 99.73 per cent. We determine a BH mass of 3x10^8 Msun. This corresponds to 2.6 per cent of the total mass of the bulge, making NGC 4342 one of the galaxies with the highest BH mass to bulge mass ratio currently known. The models that best fit the data do not have a two-integral phase-space distribution function. They have rather complex dynamical structures: the velocity anisotropies are strong functions of radius reflecting the multi-component structure of this galaxy. The best fit model without BH tries to fit the high central velocity dispersion by placing stars on radial orbits. The measured rotation velocities, however, restrict the amount of radial anisotropy such that the central velocity dispersion measured with the HST can only be fit when a massive BH is included in the models.

Full text

Page 1

arXiv:astro-ph/9805324v1 26 May 1998
submitted to the Astrophysical Journal
Evidence for a massive BH in the S0 galaxy NGC 4342
Nicolas Cretton
Leiden Observatory, PO Box 9513, 2300 RA Leiden, The Netherlands
Frank C. van den Bosch1
Department of Astronomy, University of Washington, Seattle, WA 98195, USA2
1Hubble Fellow
2Previously at Leiden Observatory, PO Box 9513, 2300 RA Leiden, The Netherlands.

Page 2

– 2 –
ABSTRACT
We present axisymmetric dynamical models of the edge-on S0 galaxy NGC 4342.
This small low-luminosity galaxy harbors, in addition to its outer disk, a bright nuclear
stellar disk. A combination of observations from the ground and with the Hubble
Space Telescope (HST) has shown that NGC 4342 rotates rapidly and has a strong
central increase in velocity dispersion.
We construct simple two-integral Jeans models as well as fully general, three-
integral models. The latter are built using a modified version of Schwarzschild’s
orbit-superposition technique developed by Rix et al. and Cretton et al. These models
allow us to reproduce the full line-of-sight velocity distributions, or ‘velocity profiles’
(VPs), which we parameterize by a Gauss-Hermite series. The modeling takes seeing
convolution and pixel binning into account.
The two-integral Jeans models suggest a black hole (BH) mass between 3 and
6 × 108M⊙, depending on the data set used to constrain the model, but they fail
to fit the details of the observed kinematics. The three-integral models can fit all
ground-based and HST data simultaneously, but only when a central BH is included.
Models without BH are ruled out to a confidence level better than 99.73 per cent. We
determine a BH mass of 3.0+1.7
cent confidence levels. This corresponds to 2.6 per cent of the total mass of the bulge,
making NGC 4342 one of the galaxies with the highest BH mass to bulge mass ratio
currently known.
The models that best fit the data do not have a two-integral phase-space distribution
function. They have rather complex dynamical structures: the velocity anisotropies
are strong functions of radius reflecting the multi-component structure of this galaxy.
When no central BH is included the best fit model tries to fit the high central
velocity dispersion by placing stars on radial orbits. The high rotation velocities
measured, however, restrict the amount of radial anisotropy such that the central
velocity dispersion measured with the HST can only be fit when a massive BH is
included in the models.
−1.0× 108M⊙, where the errors are the formal 68.3 per
Subject headings: black hole physics — galaxies: elliptical and lenticular, cD —
galaxies: individual (NGC 4342) — galaxies: kinematics and dynamics — galaxies:
nuclei — galaxies: structure.

Page 3

– 3 –
1.Introduction
Several lines of evidence suggest that active galactic nuclei (AGNs) are powered by accretion
onto a super-massive black hole (BH) (Lynden-Bell 1969; Rees 1984). The much higher
volume-number density of AGNs observed at redshift z ≈ 2 than at z = 0, suggests that many
quiescent (or ‘normal’) galaxies today must have gone through an active phase in the past, and
therefore harbor a massive BH as well. Such a BH will significantly influence the dynamics of the
galaxy inside a radius of influence, rBH= GMBH/σ2, where σ is a characteristic velocity dispersion
of the stars in the center. In particular, hydrostatic equilibrium requires that the rms velocities of
the stars surrounding a massive BH follow an r−1/2power-law (Bahcall & Wolf 1976; Young 1980).
Since the late 70s, combined imaging and spectroscopy of the central regions of galaxies has
suggested that massive BHs should be present in a number of early-type galaxies (see Kormendy
& Richstone 1995 for a review). Conclusive dynamical evidence for the presence of a central BH
requires that a model with a BH can fit all observations (photometric and kinematic), and that no
model without a BH can provide an equally good fit. Such conclusive evidence can only be inferred
from observations that probe well inside the radius where the BH dominates the dynamics. Up to
a few years ago, most claimed BH detections were based on observations with spatial resolutions
of similar size as the radii of influence of the inferred BH masses (Rix 1993). This, together
with the limited amount of freedom in the models used to interpret the data, has hampered an
unambiguous proof for the presence of these BHs (i.e., the observed kinematics could not be
confronted with all possible dynamical configurations without a BH). Often spherical models
were used even when the observed flattening was significant. If the models were axisymmetric,
the distribution function (hereafter DF) was often assumed to depend only on the two classical
integrals of motion, energy and vertical angular momentum; f = f(E,Lz). This implies that the
velocity dispersions in the radial and vertical directions are equal (i.e., σR= σz). It is well-known
that strong radial anisotropy in the center of a galaxy results in a high central velocity dispersion,
mimicking the presence of a massive BH (cf. Binney & Mamon 1982). Conclusive evidence for
a BH therefore requires that one can rule out radial anisotropy as the cause of the high velocity
dispersions measured, and models must thus be sufficiently general.
Recently two major breakthroughs have initiated a new era in the search for massive BHs in
normal galaxies. First of all, we can now obtain kinematics at much higher spatial resolution (down
to FWHM ∼ 0.1′′), using specially-designed spectrographs, such as the Subarcsecond Imaging
Spectrograph (SIS) on the Canada-France Hawaii Telescope, or the Faint Object Spectrograph
(FOS) and STIS aboard the HST. This allows us to probe the gravitational potential much closer
to the center, where the BH dominates the dynamics. Not only has this improved the evidence
for massive BHs in several old BH-candidate galaxies (M31, Ford et al. 1998; M32, van der Marel
et al. 1997, 1998; M87, Harms et al. 1994, Macchetto et al. 1997; NGC 3115, Kormendy et
al. 1996a; NGC 4594, Kormendy et al. 1996b), but it has also provided new cases (M84, Bower
et al. 1998; NGC 3377, Kormendy et al. 1998; NGC 3379, Gebhardt et al. 1998; NGC 4261,
Ferrarese, Ford & Jaffe 1996; NGC 4486B, Kormendy et al. 1997; NGC 6251, Ferrarese, Ford &
Jaffe 1998; and NGC 7052, van der Marel & van den Bosch 1998). Secondly, the revolutionary
increase in computer power has made it possible to investigate a large number of fully general,

Page 4

– 4 –
three-integral models based on the orbit-superposition method (Schwarzschild 1979). In the past
decade, this method has been used to build a variety of spherical, axisymmetric and triaxial
models (e.g., Schwarzschild 1982; Pfenniger 1984; Richstone & Tremaine 1984, 1988; Zhao 1996).
Levison & Richstone (1985), Richstone & Tremaine (1985), and Pfenniger (1984) showed how to
include rotation velocities and velocity dispersions as kinematic constraints. More recently, Rix et
al. (1997) and Cretton et al. (1998) extended this modeling technique even further by fitting to
the entire velocity profiles (see also Richstone 1997). Van der Marel et al. (1997, 1998) used this
to build fully general, axisymmetric models of M32, and showed convincingly that M32 harbors
a massive BH. Recent review papers on this rapidly evolving field include Ford et al. (1998), Ho
(1998), Richstone (1998), and van der Marel (1998).
In many galaxies where the presence of a BH has been suggested, a nuclear disk, seen close
to edge-on, is present. These disks are either in gaseous form (M84, M87, NGC 4261, NGC 4594,
NGC 6251, NGC 7052), or made up of stars (NGC 3115). It is easier to detect BHs in edge-on
systems with disks, where one can use both the measured rotation velocities and the velocity
dispersions to determine the central mass density. It is therefore not surprising that BHs have
predominantly been found in galaxies with nuclear disks. Furthermore, nuclear disks allow a good
determination of the central mass density of their host galaxies. Gaseous disks have the advantage
that their kinematics can be easily measured from emission lines. Since gas in a steady-state
disk can only move on non-intersecting orbits, the measured rotation velocities of a settled gas
disk, in the equatorial plane of an axisymmetric potential, correspond to the circular velocities,
Vc(R) =
of the central potential gradient, and thus of the central mass density. However, often the gas
disks are not in a steady state; many show a distorted morphology (e.g. M87, see Ford et al. 1994),
and non-gravitational motion, such as outflow, inflow or turbulence can be present and complicate
the dynamical analysis (e.g., NGC 4261, Jaffe et al. 1996; NGC 7052, van den Bosch & van der
Marel 1995). Nuclear stellar disks do not suffer from this, but have the disadvantage that their
kinematics are much harder to measure. First of all, the kinematics have to be determined from
absorption lines rather than emission lines, and secondly, the line-of-sight velocity distributions, or
velocity profiles (VPs), measured are ‘contaminated’ by light from the bulge component. However,
van den Bosch & de Zeeuw (1996) showed that with sufficient spatial and spectral resolution
one can resolve the VPs in a broad bulge-component and a narrow disk-component. From these
VPs the rotation curve of the nuclear disk can be derived, providing an accurate measure for the
central mass density. Therefore, galaxies with an embedded nuclear disk (either gaseous or stellar)
observed close to edge-on are ideal systems to investigate the presence of massive BHs.
?RdΦ/dR. The rotation curve of a nuclear gas disk therefore provides a direct measure
In this paper we discuss the case of NGC 4342; a small, low-luminosity (MB = −17.47)
S0 galaxy in the Virgo cluster. The galaxy is listed as IC 3256 in both the Second and Third
Reference Catalogues of Bright Galaxies, since in the past it has occasionally been confused with
NGC 4341 and NGC 4343 (see Zwicky & Herzog 1966). At a projected distance of ∼ 30′′SE of
NGC 4342, a small galaxy is visible. It is uncertain whether this is a real companion of NGC 4342
or whether it is merely close in projection. HST images of NGC 4342 revealed both an outer disk,
as well as a very bright nuclear stellar disk inside ∼ 1′′(van den Bosch et al. 1994; Scorza & van
den Bosch 1998). It is a normal galaxy, with no detected ISM (Roberts et al. 1991), and with small

Page 5

– 5 –
color-gradients (van den Bosch, Jaffe & van der Marel 1998, hereafter BJM98). For its size and
luminosity, it does however reveal a remarkably large central velocity dispersion and a very steep
rotation-curve (see BJM98). Unfortunately, the spectral resolution of the available kinematic data
is insufficient to actually resolve the VPs in disk and bulge components. In order to determine
the central mass density in NGC 4342, we thus have to construct dynamical models of the entire
system: bulge and disk components. Here we present simple two-integral Jeans models as well as
fully general three-integral models, and we provide evidence for the presence of a central massive
dark object (MDO) of ∼ 3 × 108M⊙. Throughout this paper we assume the MDO to be a BH,
but we discuss alternatives in Section 7.2
In Section 2 we briefly discuss the data used to constrain the models and in Section 3 we
describe our mass model. In Section 4 we show the results of some simple two-integral modeling,
and we discuss its shortcomings. Section 5 describes the general outline of the three-integral
modeling technique. In Section 6 we discuss shortcomings of the velocity-profile parameterization
used when applied to dynamically cold systems, and present a modified approach. The results
of the three–integral modeling are discussed in Section 7. Finally, in Section 8, we sum up and
present our conclusions. Throughout this paper we adopt a distance of 15 Mpc for NGC 4342,
consistent with the distance of the Virgo cluster (Jacoby, Ciardullo & Ford 1990).
2.The data
All data used in this paper are presented and discussed in detail in BJM98. Here we merely
summarize.
2.1.Photometric data
BJM98 used the Wide Field and Planetary Camera 2 (WFPC2) aboard the HST to obtain
U, V and I band photometry of NGC 4342. The spatial resolution of these images is limited by
the HST Point Spread Function (FWHM ∼ 0.1′′) and the size of the pixels (0.0455′′× 0.0455′′).
The full field-of-view covers about 35′′× 35′′. Figure 1 shows contour plots at two different scales
of the I-band image. The presence of the nuclear disk is evident from the highly flattened, disky
isophotes inside 1.0′′.
2.2. Kinematic data
Using the ISIS spectrograph mounted at the 4.2m William Herschel Telescope (WHT) at La
Palma, BJM98 obtained long-slit spectra of NGC 4342 along both the major and the minor axis.
The spectra have a resolution of σinstr= 9kms−1, and were obtained with a slit width of 1.0′′under
good seeing conditions with a PSF FWHM of 0.80′′(major axis) and 0.95′′(minor axis). After
standard reduction, the parameters (γ,V,σ,h3,h4) that best fit the VPs were determined using