As a ``normal'' SSP we define a coeval stellar population of a single metallicity and characterised by either a Salpeter (1955) or a Kroupa (2001)-type stellar initial mass function (IMF), i.e., a two-part power law covering the stellar mass range from $0.1 ~M_\odot$ to $\sim$ $125~ M_\odot$ , depending on metallicity.

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Assuming that light traces mass, the observed half-light radii must be corrected for projection onto the sky by applying a correction factor of 3/4 (e.g., Fleck et al. 2006).

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... stars

Although, strictly speaking, Eq. (1) is valid for line-of-sight velocity dispersions instead of the equivalent dispersions based on proper-motion studies, the effect of ignoring this will be mass overestimates by a factor of 2 (or $\Delta \log L/M = +0.3$ ) if the clusters' kinematics are isotropic. This does not affect our conclusions.

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... only

Despite the extent of the error bar associated with the age estimate of the Pleiades, Kroupa et al. (2001) showed this cluster to have re-virialised by an age of 50 Myr, so that it is unlikely affected by the aftermath of the gas-expulsion phase.

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... clusters

For a quantitative estimate of this effect, let us assume that our clusters are well represented by Plummer models. However, we note that this is an unproven assumption; younger clusters are likely more extended (e.g. Elson et al. 1987), whereas older clusters (particularly lower-mass objects) may be significantly depleted in their outer regions and hence could be much more compact. A back-of-the-envelope calculation shows then that the following relations apply (from Heggie & Hut 2003): $R_{\rm c,intr} = R_{\rm hm,proj} /\!\sqrt{2}$ , $R_{\rm virial} = R_{\rm hm,proj} \times 16 / 3 \pi$ , and $R_{\rm hm,intr} \simeq 1.305 R_{\rm hm,proj}$ . This leads, approximately, to $R_{\rm c,intr} \simeq 1.035 R_{\rm c,proj}$ , and therefore $R_{\rm hm,proj} \simeq 1.464 R_{\rm c,proj}$ . Here, the subscripts ``c'', ``hm'', ``intr'', and ``proj'' stand for core, half mass, intrinsic, and projected. This result only holds approximately for a Plummer model; it gives us a rough idea of the errors involved in our analysis, leading to $\Delta(L_V/M_{\rm dyn}) \sim -0.165$ (in solar units).

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... lines

However, we need an unbiased sample to explore this option statistically and in more detail.

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... Tacconi-Garman

Although these authors published a mass determination of $M_{\rm cl} = 6.3^{+5.3}_{-3.7} \times 10^4~ M_\odot$ for Westerlund 1, they recently redetermined its velocity dispersion and hence its mass, at $M_{\rm cl} \sim 1.25 \times 10^5~ M_\odot$ (Mengel & Tacconi-Garman 2007b).

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...2001)

NGC 3532 is also strongly flattened (Gieseking 1981), roughly orthogonal to the Galactic plane. Both theory and N-body simulations suggest that the effects of the Galactic tidal field give rise to a flattening of cluster outskirts in the direction towards the Galactic Centre and perpendicular to the Galactic plane (see Mathieu 1985).

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