Astron. Astrophys. 321, 379-388 (1997)

5. Mass-to-light ratios

If we assume that the clusters are reasonably well represented by King models then, following Queloz et al.  (1995), we can compute the total mass using

Values of , and p have been tabulated for a range of concentration parameters by King (1966) and Peterson & King (1975).

The in Eq.  3 refers to the central velocity dispersion of the cluster. Given the small angular size of the clusters and our use of 1.5 and 2.0 arcsecond-wide slits, it is clear that our dispersion measurements will have been influenced by light from moderately large radii. We tested the effect of our slit-widths on the measured velocity dispersions by integrating luminosity-weighted, King model velocity dispersion profiles over the area subtended by our slit. We found that, over a large range in c, and for both slit-widths used, the measured velocity dispersion would be lower than the central velocity dispersion by about 5%. Hence, for the purposes of computing masses, we increased the measured dispersions in Table 1 accordingly. The resulting cluster masses we obtain using Eq.  3 are listed in column 7 of Table 2.

An alternative to the somewhat model-specific method used above is a straightforward application of the Virial theorem:

where we have assumed an isotropic velocity distribution and (Spitzer 1987), where is the half-mass radius. The masses computed using this equation are given in column 8 of Table 2.

Owing to M 31's low Galactic latitude, obscuration of the globular clusters by foreground Galactic dust varies significantly from one side of M 31 to the other. Using the extinction maps of Burstein & Heiles (1982), E(B-V) was estimated for each cluster and is given in column 9 of Table 2. Using the V -magnitudes given by Battistini et al.  (1987), we adopt = 3.2 E(B-V) (DaCosta & Armandroff 1990), and to compute total cluster V -band luminosities. The corresponding values for are given in column 10 and 11 of Table 2.

The ratios given in Table 2 are remarkably similar to those typically found in Galactic globulars (Pryor & Meylan 1993). Bo158 and 225 might seem a trifle high, but we note that both these clusters have only ground-based measurements of . It is entirely possible that these estimates of suffer from incomplete removal of the effects of seeing and are consequently too high. The largest source of uncertainty in is generally in the estimation of , being of the order of 15% even for the HST-imaged clusters. Uncertainties in the magnitude estimates of Battistini et al., in our estimates of the local extinction, and in the velocity dispersion measurements contribute each to the final uncertainty. Bo343 and 358 are exceptions to this general rule, having reasonably well-measured core radii, but rather less well-determined velocity dispersions. The formally estimated uncertainties in are for those clusters observed with HST, and probably closer to 50% for those clusters imaged only from the ground.

Table 2 shows that the ratios derived with Eq.  4(column 11) are systematically 50% larger than those obtained with Eq.  3 (column 10). This gives a rough idea on how model dependent are our estimates.

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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