ar X iv : a st ro - p h / 93 12 01 1 v 1 6 D ec 1 99 3 Dark matter annihilations in the Large Magellanic Cloud

The study of the kinematics of globular clusters in the outer regions of the Large Magellanic Cloud by Schommer et al. [1] suggested a flat rotation curve, perhaps out to 15 kpc: the LMC might have a dark matter halo. Here, from a composite H i and star cluster rotation curve (fig. 1), I want to estimate the parameters of an isothermal halo added to a ‘maximum disk.’ Luks and Rohlfs [2], in the analysis of their extended 21-cm line survey of the LMC, showed that the H i kinematics can be modeled by that of a flat disk in differential rotation. The rotation curve they obtained considering data within a ±5 sector of the major axis is shown by crosses in fig. 1. The geometrical and kinematical parameters they assumed for the LMC are as follows: distance 50 kpc; inclination 33; position angle of the major axis 162; H i kinematic center (α0, δ0) = (5 1248,−6903.6); heliocentric velocity of the H i kinematic center 282.4 km/s radially and 483 km/s tangentially towards 87 position angle. Using for consistency the same geometrical and kinematical parameters as in ref. [2], I have redetermined the star cluster rotation curve in Schommer et al. [1], reading the heliocentric velocities and the positions of the 83 star clusters from their tables 1 and 2. To render the cluster rotation curve symmetric, the radial systemic velocity was adjusted by 6.9 km/s. The points shown as circles in fig. 1 were obtained using the clusters lying within ±30 of the major axis and beyond 3 kpc of the center. The velocities have been binned in 1 kpc bins. The error bars represent the standard deviation of the mean of velocities, while circles without error bars are single objects. The rotation curve cannot be firmly determined from these data points. Nevertheless let us try to compare models with and without a dark matter halo. The most recent surface photometry of the LMC is provided by the CCD observations of Bothun and Thompson [3] with a camera set up in a parking lot. An exponential disk with central brightness μ0 = 21.17 mag/arcsec and scale length 1.677 (1.46 kpc) fits the surface-brightness profile well in the innermost 3 (2.6 kpc). (Values in parentheses are for the assumed LMC distance of 50 kpc.) I use the parameters of this fit plus a constant mass-to-luminosity ratio to derive the rotation curve due to the exponential disk. Since signs of truncation are present beyond 2.6 kpc, this choice somewhat overestimates the disk contribution in the outer regions. The dashed curve in fig. 1 corresponds to a disk M/L = 3.3 in solar units. Higher mass-to-luminosity ratios would give curves overshooting the radio data points. I now add a halo with canonical density profile ρ(r) = ρ0a /(r + a), where a is the core radius and ρ0 is the central dark matter density. Imposing that the disk+halo rotation curve passes close to the outermost points, the combination ρ0a , which corresponds to the asymptotic rotation velocity, is constrained to be ≈ 5 10 g/cm · kpc. Unfortunately, a determination of the two halo parameters separately cannot be achieved with the present data. The core radius is presumably ≪ 10 kpc and will be kept as a parameter. For sake of illustration, a rotation curve with a = 1 kpc and ρ0 = 5 10 −24 g/cm is plotted as a solid line in fig. 1.