Rotation of the Globular Cluster Population of the Dark Matter Deficient Galaxy NGC 1052-DF4: Implication for the Total Mass

TL;DR

The paper investigates whether the globular cluster system of the dark matter-deficient galaxy NGC 1052-DF4 hosts a rotating component that could bias dynamical mass inferences. It applies Bayesian inference to seven confirmed globular clusters, comparing rotating and non-rotating kinematic models (including an alternative-prior Rotational Model) using marginal likelihoods and Bayes factors derived from nested sampling, with the rotation form given by $v_r(\theta)=A\sin(\theta-\phi)$. The results show a weak preference for a non-rotational model (Bayes factor $\approx 2.46$) and rotation amplitudes consistent with zero, implying the GC system’s rotation does not significantly affect the mass estimate. Consequently, the inferred mass within $7.5$ kpc remains low, dominated by velocity dispersion $\sigma$, which supports the conclusion that NGC 1052-DF4 is truly dark matter deficient and consistent with tidal-disruption scenarios. The findings are robust to rotation-model choices and align with related work on NGC 1052-DF2 and recent tidal-disruption interpretations, reinforcing the DM-deficient interpretation of NGC 1052-DF4.

Abstract

We explore the globular cluster population of NGC 1052-DF4, a dark matter deficient galaxy, using Bayesian inference to search for the presence of rotation. The existence of such a rotating component is relevant to the estimation of the mass of the galaxy, and therefore the question of whether NGC 1052-DF4 is truly deficient of dark matter, similar to NGC 1052-DF2 another galaxy in the same group. The rotational characteristics of seven globular clusters in NGC 1052-DF4 were investigated, finding that a non-rotating kinematic model has a higher Bayesian evidence than a rotating model, by a factor of approximately 2.5. In addition, we find that under the assumption of rotation, its amplitude must be small. This distinct lack of rotation strengthens the case that, based on its intrinsic velocity dispersion, NGC 1052-DF4 is a truly dark matter deficient galaxy.

Figures (6)

• Figure 1: Positions of the NGC 1051-DF4 globular clusters relative to the center of the galaxy. The size and colour of the circle represent each globular cluster's velocity along the line of sight; the larger the circle, the higher the absolute value of the velocity.
• Figure 2: Corner plot of the parameters' posterior distribution for the Non-Rotational Model.
• Figure 3: Corner plot of the parameters' posterior distribution for the Rotational Model.
• Figure 4: Corner plot of the parameters' posterior distribution for the Rotational Model with Alternative Priors.
• Figure 5: Posterior distribution of the estimated mass of NGC 1052-DF4 with the different rotational inclination. The red curve represents a $90^o$ inclination, the blue dash curve has a $45^o$ inclination, and the green dot curve has a $30^o$ inclination.