![]() | Annu. Rev. Astron. Astrophys. 1988. 26:
245-294 Copyright © 1988 by Annual Reviews. All rights reserved |
Previous reviews include Faber & Gallagher (69), Rood (156), Ostriker (132), Bekenstein (26), and Trimble (201).
4.1. Masses
Newtonian/general relativistic mechanics, with its simple and beautiful foundations, provides a logically consistent explanation of the observed kinematic properties of the members of the solar system. In extragalactic astronomy, however, perplexing inconsistencies exist between observed kinematic properties and theoretical expectations:
1. The following problem in Galactic astronomy seems to be amplified
in the extragalactic domain: The application in 1932 by J.H. Oort and
more recently (with updated methodology and data) by J. Bahcall
(7,
and references therein) of Newtonian dynamics to kinematic properties
of stellar tracers within about 200 pc of the Sun predicts a mass (the
dynamical mass
Mdyn) that is a factor of 2 larger than
that calculated
from a comprehensive accounting of identified stellar, gaseous, and
dust material in the solar neighborhood
(Mid). Included in the
inventory of identified matter are objects directly observed by means
of their electromagnetic signatures and objects plausibly inferred
from reasonable extrapolations of data guided by results from the
theory of stellar evolution. If we define a mass anomaly index by
xm = Mdyn/Mid - 1,
i.e. the fractional excess of the dynamical mass relative
to the identified mass, then
xm = 0 for the solar system but
xm 1
for the solar neighborhood.
2. The surface luminosity density of the disk of a spiral galaxy can
be approximated by an exponential function of radius with a disk scale
length of typically
hD a
few kiloparsecs. For radii less than approximately
2.5hD, the observed rotational curve,
i.e. rotational
velocity (deprojected radial velocity) vs. radius, appears to be
consistent with the model characterized by a constant M/L
(ratio of
mass to luminosity) and a distribution of mass identical to that of
light. However, for radii larger than about
2.5hD, the rotation curve
remains flat (constant rotational velocity) up to a limit of
approximately 10 hD (set by the current sensitivity for
detection of
the 21-cm spectral line of neutral hydrogen). If, within a radius of
2.5 hD, the dynamical mass and identified mass are
assumed to be
identical (a conservative assumption), then as the radius is
increased, the dynamical mass exceeds the identified mass by larger
and larger factors. The matter within 10 hD has a mass
anomaly of
xm
3.
These properties and other regularities and characteristic
numerical values of the rotation curves of spiral galaxies are
discussed in depth by Bahcall & Casertano
(8),
van Albada & Sancisi
(207),
Kent (101,
102),
and Athanassoula et al.
(6a).
3. Typically, the identified mass of a group of galaxies is well
approximated by the sum of the masses of its four or five most
luminous members. Operationally, a group is classified as compact or
loose according to whether a typical separation of two neighboring
group members is a small number of galaxy diameters or ~ 20 times
larger. Williams & Rood
(214)
recently found that typically
xm 15
for a loose group chosen from an especially carefully determined
sample. Using scaling arguments, they then found that typically
xm ~
0 for a compact group selected from the homogeneous and complete
sample obtained by Hickson
(89).
By applying improved data and more
sophisticated analytical procedures, P. Hickson (private
communication, 1987) obtains dynamical parameters suggesting that
typically xm
4 for compact groups.
4. The Coma cluster contains hundreds of luminous member galaxies and possesses the symmetry and radial distribution of galaxies expected from a system in Newtonian gravitational equilibrium. Therefore, in 1933 Zwicky (219) was surprised to find that the mass of this cluster derived according to these assumptions from kinematic data applied to the virial theorem is much larger than the mass estimated to be contained within its entire galaxy content. In 1936, results for the Virgo cluster by Smith (185) confirmed this effect. Nevertheless, uncertainties in the data and analyses were sufficiently large to engender skepticism about the physical nature of the effect (152). But by 1972, the homogeneity of the data base had improved considerably, recently discovered optically luminous inter-galactic material (59a) was added to the inventory of mass contributors, and the analytical techniques were diversified to include model-fitting as well as virial theorem techniques which all gave consistent results (161). A general agreement developed that the effect is real. Over the last decade, the optical data base continued to improve (102a), and X-ray-emitting intergalactic ionized gas was discovered, which contributes a mass comparable to that contributed by the galaxies themselves (68, 76, 123). Results of the recent comprehensive dynamical analysis by Kent & Gunn (102a) indicate that the mass anomaly index for the Coma cluster is xm ~ 15, a value that is typical for rich clusters. In accordance with results of the discussion by Blumenthal et al. (28), we note that rich clusters and loose groups have similar mass anomaly indices.
5. The values of typical xm estimated above appear to be
related to
the class of extragalactic object under study. But even within a given
class, available evidence suggests that there is a physical range of
xm. For example, although typically
xm ~ 15 for loose groups,
Williams (213)
finds from accurate data for the six most luminous
galaxies in the IC 698 group that
xm
0. Is xm correlated with other
physical properties of an extragalactic object such as radius,
velocity dispersion, number of members, number density, mass, or mass
density? We have reason to be optimistic that the suggestive results
of early work
(100c,
157,
159,
159a,
162)
will soon be superseded by
definitive results made possible by modern computer technology and the
accurate and extensive modern data base.
Recently, several new techniques have been introduced to gain information about the distribution of dynamical mass for galaxies with special structural characteristics: (a) Some SO galaxies contain polar rings (which intersect the galactic rotational axis); measurements are being made of kinematic properties of polar rings to determine the angular dependence of the dynamical mass distribution in these galaxies (207a, 212). (b) Mass estimates for elliptical galaxies from the broadening of composite stellar spectral lines are uncertain partly because the effective ellipticities of the stellar orbits are unknown. However, the velocity vectors of the particles constituting a gas in thermal equilibrium are isotropic, and some elliptical galaxies reveal themselves in X-ray emission as an ionized gas with a thermal spectrum. Nevertheless, the mass of a galaxy derivable from properties of this gas is sensitive to its radial temperature gradient, which requires a next-generation X-ray detector for accurate measurement (68, 76, 169). (c) Some elliptical galaxies contain many shells of matter in their outer parts; Hernquist & Quinn (88) have developed techniques that apply properties of an array of shells to probe the distribution of dynamical mass in the outer parts of these galaxies. (d) Structural parameters of low-surface-brightness dwarf galaxies represent extremes that differ considerably from typical structural parameters of the spiral, SO, and elliptical galaxies ordinarily studied. Aaronson (1) determined definitive dynamical masses of dwarf galaxies from accurately determined kinematic properties of samples of well-chosen member stars. (e) The gravitational lensing of quasars offers unique possibilities for probing the mass distribution of galaxies and clusters of galaxies at large redshifts [see (132) for references].
Heisler et al. (87) [see also Bahcall & Tremaine (9a)) have presented three alternatives to the virial theorem for estimating the masses of groups of galaxies. The various uncertainties in real data contribute differently to the overall uncertainty in the dynamical masses provided by each of the four mass estimators. As a valuable consistency check, all four techniques should generally be applied to determine the dynamical mass of a group of galaxies.
Over the last several decades, a large part of the electromagnetic spectrum has become accessible to telescopic observation. This has led to the discovery of neutral and ionized intergalactic gas clouds in small groups of galaxies (14a, 163, 214) and ionized gas in rich clusters (76, 169) in amounts that are small compared with the amounts needed to resolve mass anomalies. After long-term intensive and diversified observational efforts to increase the inventory of identified masses, the mass anomalies continue to remain perplexing and formidable.