High-resolution measurements of the dark matter halo of NGC 2976: Evidence for a shallow density profile

We have obtained two-dimensional velocity fields of the dwarf spiral galaxy NGC 2976 in Halpha and CO. The high spatial (similar to 75 pc) and spectral (13 and 2 km s(-1), respectively) resolution of these observations, along with our multicolor optical and near-infrared imaging, allows us to measure the shape of the density pro. le of the dark matter halo with good precision. We find that the total (baryonic plus dark matter) mass distribution of NGC 2976 follows a rho(tot) proportional to r(-0.27 +/- 0.09) power law out to a radius of 1.8 kpc, assuming that the observed radial motions provide no support. The density pro. le attributed to the dark halo is even shallower, consistent with a nearly constant density of dark matter over the entire observed region. A maximal disk fit yields an upper limit to the K-band stellar mass-to-light ratio (M*/L-K) of 0.09(-0.08)(+0.15) M-./L-.K (including systematic uncertainties), with the caveat that for M*/L-K > 0.19 M-./L-.K the dark matter density increases with radius, which is unphysical. Assuming 0.10 M-./L-.K less than or similar to M-*/L-K less than or equal to 0.19 M-./L-.K, the dark matter density pro. le lies between rho(DM) proportional to r(-0.17) and rho(DM) proportional to r(-0.01). Therefore, independent of any assumptions about the stellar disk or the functional form of the density pro. le, NGC 2976 does not contain a cuspy dark matter halo. We also investigate some of the systematic effects that can hamper rotation curve studies and show that (1) long-slit rotation curves are far more vulnerable to systematic errors than two-dimensional velocity fields, ( 2) NGC 2976 contains radial motions that are as large as 90% of the rotational velocities at small radii, and (3) the Halpha and CO velocity fields of NGC 2976 agree within their uncertainties, with a typical scatter between the two velocities of 5.3 km s(-1) at any position in the galaxy.