Towards a higher mass for NGC1052-DF2: an analysis based on full distribution functions

It is demonstrated that the kinematics of the 10 star clusters in NGC2052-DF2 is compatible with a high dynamical mass close to those implied by the standard stellar-to-halo-mass ratio (SHMR). The analysis relies on a convenient form for the distribution function (DF) of projected phase space data, capturing non-gaussian features in the spread of true velocities of the mass tracers. A key ingredient is tidal stripping by the gravity of the apparently nearby larger galaxy, NGC 1052. Tidal stripping decreases the range of velocities of mass tracers, while only mildly lowering the total mass inside the trimming radius $r_{tr}$. The analysis is performed assuming halo profiles consistent with simulations of the $\Lambda$CDM model. For the fiducial value $r_{tr}=10$ kpc, we find that the virial mass of the pre-trimmed halo is $M<1.6\times 10^{10}M_\odot$ at $2\sigma$ ($95\%$) and $M<8.6\times 10^{9}M_\odot$ at $1.64\sigma$ ($90\%$). For the mass within 10 kpc we obtain, $M_\mathrm{10kpc}<3.9\times 10^{9}M_\odot$ and $<2.9\times 10^{9}M_\odot$ at $2\sigma$ and $1.64\sigma$, respectively. The $2\sigma$ upper limit on the virial mass is roughly a factor of 3-5 below the mean SHMR relation.Taking $r_{tr}=20$ kpc, lowers the $2\sigma$ virial mass limits by a factor of $\sim 4$, bringing our results closer to those of Wasserman et al. (2018) without their SHMR prior.