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

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

The [FORMULA] 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 [FORMULA] (Spitzer 1987), where [FORMULA] 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 [FORMULA] = 3.2 E(B-V) (DaCosta & Armandroff 1990), and [FORMULA] to compute total cluster V -band luminosities. The corresponding values for [FORMULA] are given in column 10 and 11 of Table 2.

The [FORMULA] 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 [FORMULA]. It is entirely possible that these estimates of [FORMULA] suffer from incomplete removal of the effects of seeing and are consequently too high. The largest source of uncertainty in [FORMULA] is generally in the estimation of [FORMULA], 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 [FORMULA] 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 [FORMULA] are [FORMULA] for those clusters observed with HST, and probably closer to 50% for those clusters imaged only from the ground.

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

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998