  We present new constraints on the density profiles of dark matter (DM) halos
in seven nearby dwarf galaxies from measurements of their integrated stellar
light and gas kinematics. The gas kinematics of low mass galaxies frequently
suggest that they contain constant density DM cores, while N-body simulations
instead predict a cuspy profile. We present a data set of high resolution
integral field spectroscopy on seven galaxies and measure the stellar and gas
kinematics simultaneously. Using Jeans modeling on our full sample, we examine
whether gas kinematics in general produce shallower density profiles than are
derived from the stars. Although 2/7 galaxies show some localized differences
in their rotation curves between the two tracers, estimates of the central
logarithmic slope of the DM density profile, gamma, are generally robust. The
mean and standard deviation of the logarithmic slope for the population are
gamma=0.67+/-0.10 when measured in the stars and gamma=0.58+/-0.24 when
measured in the gas. We also find that the halos are not under concentrated at
the radii of half their maximum velocities. Finally, we search for correlations
of the DM density profile with stellar velocity anisotropy and other baryonic
properties. Two popular mechanisms to explain cored DM halos are an exotic DM
component or feedback models that strongly couple the energy of supernovae into
repeatedly driving out gas and dynamically heating the DM halos. We investigate
correlations that may eventually be used to test models. We do not find a
secondary parameter that strongly correlates with the central DM density slope,
but we do find some weak correlations. Determining the importance of these
correlations will require further model developments and larger observational
samples. (Abridged)
