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A Bayesian Exploration of the Mass of Ursa Major III: Kinematics, Rotation and their influence on the Mass to Light Ratio

T. R. Adams, B. J. Brewer, G. F. Lewis

TL;DR

This study probes whether UMa III/U1 exhibits intrinsic rotation and how such rotation would affect its inferred mass-to-light ratio, a key discriminator between a dark-matter-dominated ultra-faint dwarf and a star cluster. Using a Bayesian framework and nested sampling, it compares a non-rotating model to a one-component rotational model with velocities of 11 member stars; the non-rotating description is decisively favored, yielding Bayes factors around 12 for the full sample and about 5 for a reduced sample. The inferred velocity dispersion remains of order a few km/s, and rotation contributes little to the dynamical support, producing a high lower bound on M/L when assuming modest inclination (e.g., ≈734 M_⊙/L_⊙ at 30°). The results, although favoring a non-rotating, pressure-supported interpretation, keep UMa III/U1 ambiguous between a UFD and a self-gravitating star cluster due to data sensitivity to member selection and model assumptions, underscoring the need for additional velocity measurements.

Abstract

We investigate the kinematics of the potential ultra-faint dwarf galaxy (UFD) UMa III/U1 using Bayesian inference to search for the signal of any potential intrinsic rotation. The magnitude of rotation is relevant to estimating the total mass of UMa III/U1, which is critical in determining whether or not UMa III/U1 is in fact a UFD, or possibly a star cluster home to a significant binary fraction. A non-rotating model and a rotational model are fitted for the current total population of member stars of UMa III/U1, finding that a non-rotating model was preferred by a factor of $\sim 5-12 \times$. This was repeated on a reduced population of UMa III/U1, where potential contaminant stars were removed. A similar preference for non-rotation was found for these reduced populations. We calculate a lower-bound rotational mass estimate for UMa III/U1 and a corresponding lower bound mass-to-light ratio of $ 734.4^{+339.0}_{-176.2} \mathrm{M_\odot} / \mathrm{L_\odot} $ for the total population. We conclude that UMa III/U1 still remains an ambiguous object with viable arguments for both the UFD and self-gravitating star cluster scenarios, however under both, UMa III/U1 is unlikely to be supported by rotational pressure.

A Bayesian Exploration of the Mass of Ursa Major III: Kinematics, Rotation and their influence on the Mass to Light Ratio

TL;DR

This study probes whether UMa III/U1 exhibits intrinsic rotation and how such rotation would affect its inferred mass-to-light ratio, a key discriminator between a dark-matter-dominated ultra-faint dwarf and a star cluster. Using a Bayesian framework and nested sampling, it compares a non-rotating model to a one-component rotational model with velocities of 11 member stars; the non-rotating description is decisively favored, yielding Bayes factors around 12 for the full sample and about 5 for a reduced sample. The inferred velocity dispersion remains of order a few km/s, and rotation contributes little to the dynamical support, producing a high lower bound on M/L when assuming modest inclination (e.g., ≈734 M_⊙/L_⊙ at 30°). The results, although favoring a non-rotating, pressure-supported interpretation, keep UMa III/U1 ambiguous between a UFD and a self-gravitating star cluster due to data sensitivity to member selection and model assumptions, underscoring the need for additional velocity measurements.

Abstract

We investigate the kinematics of the potential ultra-faint dwarf galaxy (UFD) UMa III/U1 using Bayesian inference to search for the signal of any potential intrinsic rotation. The magnitude of rotation is relevant to estimating the total mass of UMa III/U1, which is critical in determining whether or not UMa III/U1 is in fact a UFD, or possibly a star cluster home to a significant binary fraction. A non-rotating model and a rotational model are fitted for the current total population of member stars of UMa III/U1, finding that a non-rotating model was preferred by a factor of . This was repeated on a reduced population of UMa III/U1, where potential contaminant stars were removed. A similar preference for non-rotation was found for these reduced populations. We calculate a lower-bound rotational mass estimate for UMa III/U1 and a corresponding lower bound mass-to-light ratio of for the total population. We conclude that UMa III/U1 still remains an ambiguous object with viable arguments for both the UFD and self-gravitating star cluster scenarios, however under both, UMa III/U1 is unlikely to be supported by rotational pressure.
Paper Structure (12 sections, 8 equations, 4 figures, 4 tables)

This paper contains 12 sections, 8 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background/Literature Review
  3. Approach
  4. Data
  5. Bayesian Inference
  6. Kinematic Analysis
  7. Priors
  8. Results
  9. Total Population
  10. Reduced Population
  11. Mass Estimates
  12. Discussion/Conclusions

Figures (4)

  • Figure 1: Positions and relative velocities of the $11$ radial velocity members of UMa III/U1. The size of each marker corresponds to the member velocity.
  • Figure 2: Posterior distributions of model parameters for the total population
  • Figure 3: Posterior distributions of model parameters for the reduced population.
  • Figure 4: Posterior distribution of the estimated mass of UMa III/U1 at inclination angles of $30^{\circ}$, $45^{\circ}$ and $90^{\circ}$. The non-rotating posterior distribution for an inclination of $90^{\circ}$ is also shown.