Annu. Rev. Astron. Astrophys. 1988. 26: 245-294
Copyright © 1988 by . All rights reserved

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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 appeq 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 appeq 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 appeq 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 appeq 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 appeq 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 appeq 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.

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