7.1 X-Rays and Globular Clusters

One of the first elliptical-like galaxies to be probed for DM was M87. This galaxy is actually a massive cD at the center of the Virgo cluster and is therefore not a typical elliptical. Fabricant, Lecar and Gorenstein (1980) and Binney and Cowie (1981) analyzed X-ray observations of this galaxy to determine its mass profile. The underlying assumption of these and similar studies is that the X-ray emission comes from thermal gas in hydrostatic equilibrium with the local gravitational potential. This idea can be expressed through yet another form of the virial theorem:

(7.1)

where P is the gas pressure, _g is the gas density, and the other symbols have their usual meanings. Combining this expression with the ideal gas law gives

(7.2)

(e.g. Fabricant and Gorenstein 1983) where T_g is the gas temperature. While Fabricant et al. (1980) and Binney and Cowie (1981) both found evidence for a large mass in the center of Virgo, they did not agree on whether it was associated with a dark halo around M87, or whether the mass was identified with the cluster as a whole.

This difference of opinion illustrates a problem in applying equation (7.2) to ellipticals. Specifically, current data provide poor information on the temperature profile of the X-ray gas. Without such information it is difficult to constrain the mass distribution. Stewart et al. (1984) attempted to overcome this problem by using both X-ray images and spectroscopy of M87 from the Einstein observatory. The X-ray spectroscopy provided limited constraints on the temperature profile. These authors concluded that a dark halo with a mass of about 3 x 10¹³ M surrounded M87, with a central density around 1.5 x 10^-2 M pc^-3.

These X-ray results subsequently received support from an analysis of the dynamics of globular clusters around M87. Huchra and Brodie (1987) obtained velocities and projected distances for some globulars in the huge system that surrounds M87 and found a dynamical mass for the galaxy of 6 x 10¹² M within 18 kpc of its center. If one extrapolates this dark halo assuming a mass distribution of the form M R, the globular cluster results converge to the X-ray results of Stewart et al. (1984). Within 18 kpc, Huchra and Brodie (1987) found (M/L_B) ~ 150. Even for stellar mass-to-light ratios at the upper end of accepted ranges, this suggests a dark-to-luminous mass ratio of at least 15.

A more recent study by Mould et al. (1990) using the kinematics of globular clusters around M87 broadly supports this conclusion. These authors find that mass models without dark halos do not fit the data. They carry out a similar study for NGC 4472 and find that, while a model without DM cannot be excluded, a more natural interpretation is that this galaxy is surrounded by a dark halo.

More representative ellipticals have also been studied using X-rays. Forman, Jones and Tucker (1985) selected a sample of 55 galaxies detected by Einstein of which 39 were suitable to analyze with equation (7.2). Forman et al. (1985) had the usual problem with the lack of a temperature profile, and assumed that the gas in these ellipticals was isothermal. On the basis of this somewhat shaky assumption they concluded that galaxies in their sample had dynamical masses of up to 5 x 10¹² M. The highest dark-to-luminous mass ratios in this sample were then around 10 or more, suggesting that M87 need not be exceptional in the mass and extent of its dark halo. However, the simplifying assumption of an isothermal gas distribution could in principle lead to inflated values of the total dynamical mass.

The uncertainty in the derived mass was illustrated by a similar study of the X-ray emission from ellipticals carried out by Trinchieri, Fabbiano, and Canizares (1986). These authors obtained binding masses for five ellipticals, but concluded that uncertainties in the temperature profile and the assumption that the gas was in hydrostatic equilibrium produced an uncertainty of a factor of 10 in these masses.

In an attempt to obtain mass estimates from X-ray data that were less dependent on a knowledge of the temperature profile, Fabian et al. (1986) derived an expression for the minimum mass of dark halos around ellipticals. They assumed that the gas within the dark halo was confined by a hydrostatic outer atmosphere. This is not unreasonable since there is hot intracluster gas surrounding many ellipticals. It was further assumed that the gas was convectively stable and extended to a radius r where the pressure reached P. These assumptions lead to a lower limit to the gravitational binding mass of a galaxy:

(7.3)

Here T₀ is the temperature of the hot gas at a pressure P₀ observed at a radius r₀ in the galaxy. A measurement of typical or mean values for a given galaxy therefore yields the minimum binding mass. A knowledge of the temperature profile is less important, although steep temperature gradients can affect the results to some extent. The limit in equation (7.3) is equivalent to the mass required to prevent a gas at a temperature T₀ from escaping the gravitational potential of the galaxy.

Fabian et al. (1986) applied this expression to the sample of Forman et al. (1985) and found masses that were somewhat higher, thereby requiring even larger amounts of DM. They found a mean value of (M/L_B) for these galaxies of 74, with some halos having masses in excess of 10¹³ M. However, Fabbiano (1989) considered the effects of temperature gradients and found that much lower masses could be obtained using the expression in equation (7.3). Nevertheless, DM halos were still required in 3 of the 5 cases studied. Despite the uncertainties, this method does provide relatively persuasive evidence for substantial DM halos around at least some ellipticals.

Loewenstein (1992) derives constraints on the total mass distribution of NGC 4472 from both X-ray and optical data. He combines observed projected velocity dispersions for the stars and globular clusters of this galaxy with an X-ray temperature based on Ginga data. Curiously, the X-ray temperature is higher than expected from the velocity dispersions. It is possible that discrete X-ray sources in the galaxy are leading to an overestimate of the gas temperature. Loewenstein (1992) concludes that marginally consistent models can be constructed which require a dark-to-luminous mass ratio around 10. Further, he finds it impossible to reconcile the data with models with no dark halos. These conclusions are disputed by Bertin, Pignatelli and Saglia (1992) who claim that models with and without DM can give similar X-ray temperature profiles.

Loewenstein (DMW) has applied the same technique to NGC 1399 using observations made with BBXRT. Again, the models require a substantial dark halo with a mass around an order of magnitude greater than the stellar component of the galaxy. Loewenstein (DMW) points out that these two galaxies are the only ellipticals that can be studied in this way at present, since X-ray spectra are not of sufficient quality to provide the required temperature information for other galaxies.