The LMC tidal radius and mass

Star count maps of the outer LMC (e.g. Irwin 1991) show an extended distribution with a fairly sharp edge, typical of a tidally truncated system. To get an independent measurement using 2MASS star counts, we selected 12 subfields $0.5^\circ\times0.5^\circ$ in size which probe the LMC halo at the projected radii of $2^\circ - 5^\circ$ from the LMC center ( $l_{II}=280.5^\circ, b_{II}=-32.9^\circ$). The counts were fit to Gaussian and power-law spherical models, $\rho \propto e^{-{r^2 /2 a^2}}$ and $\rho \propto \left( 1 + r^2/a^2 \right)^{-\gamma}$, using a maximum likelihood procedure. The simple analytic forms for these profiles make the likelihood computation feasible. To estimate the mass of the LMC, we fit these analytic profiles by King models to estimate the tidal radius:

$$M_{LMC} = \left( r_t \over R_{LMC} \right)^3 2 M_{MW},$$ (6)

where R_LMC is the distance to the LMC and $M_{MW} = 5 \times 10^{11}\;M_\odot$ is the mass of the Milky Way. This is a total mass estimate, including both the halo and the disk mass.

This procedure will underestimate the mass for two reasons. First, simulations suggest that the observed r_t is 75%-80% of the dynamical critical point. Second, a tidally-limited object is likely to be elongated toward the Galactic center and therefore roughly along the line of sight. For a centrally-concentrated object, the axis ratio is a/c=1.5. The first correction yields a factor of $(10/8)^3\approx 2$. The second increases the enclosed volume by roughly 3/2 but whether or not this should be included depends on orientation. A reasonable correction factor is then between 2 and 3 and we conservatively choose the former. The parameters of the `best fit' models are a=2.6, 2.8 for the Gaussian and power-law model with $\gamma=2$, respectively. For both cases, the lower mass limit is $1\times10^{10}{\rm\,M_\odot}$ with a best estimate of $2\times10^{10}{\rm\,M_\odot}$. An in-depth presentation of these results is in preparation.

As an independent check, we made a naive estimate of the mass of the LMC from the analysis of the halo population using the star counts in our fields. Most of the sources observed by 2MASS are M-giants with the absolute magnitude in K-band K < -4^m (for the distance to the LMC of $50\,{\rm\,kpc}$ and 2MASS K_s-band SNR=10 flux limit of 14.3^m). Assuming that these M giants are representative of an intermediate age population with the extended distribution derived above, we may estimate the total stellar mass using an infrared luminosity function. For this purpose, we adopt the Galactic luminosity function in Wainscoat et al. (1992). Integrating over the luminosity function with a standard luminosity-mass relation results in stellar mass of $\approx 4 \times 10^9\;M_\odot$, which is consistent with these estimates.