Challenges in modeling the dark matter halo of NGC 1052-DF2: Cored versus cuspy halo models

The discovery of NGC 1052-DF2 and subsequent modeling have shown that NGC 1052-DF2 is deficient in dark matter and is in conflict with the standard stellar-to-halo mass ratio. In this work, we aim to resolve the degeneracy between the dynamical models on the mass estimate of the NGC 1052-DF2.We constructed mass models of NGC 1052-DF2 using an anisotropic distribution function with a radially varying anisotropy parameter and studied the effect of the various model parameters on the dark matter estimates. We used the observed stellar photometry as an input parameter to construct the distribution function and employed a Markov Chain Monte Carlo (MCMC) method to estimate the dark matter model parameters.We find that mass models with a cuspy dark matter halo have comparable $\chi^{2}$ to models with zero dark matter. Moreover, the cuspy dark matter halo fails to consistently account for the observed velocity dispersion in the inner and outer regions of the galaxy. Consequently, we rule out the possibility of a cuspy dark matter halo for describing the mass models of NGC 1052 - DF2. Our study shows that the cored dark matter halo model with a total mass of $\log(M_{DM}/M_{\odot})=10.5$ explains the observed kinematics but requires an extraordinarily large scale length (20kpc) and an outer cutoff radius (26kpc). While the cored mass model provides a comparatively better fit, our findings emphasize that the mass models are largely unconstrained by the available kinematic data. Our results suggest that NGC 1052 - DF2 may not only have an ultra-diffuse stellar distribution but that it can, within uncertainties in the available kinematic data, potentially host an ultra-diffuse dark matter distribution compatible with the standard stellar-to-halo mass relation (SHMR) predicted by galaxy formation and evolution models