A Statistical Framework to Identify Kinematically Outlying LMC Globular Clusters and Implications for the LMC's Dark Matter Profile

Abstract

The LMC's Globular Clusters (GCs) bring a novel opportunity to understand the LMC's assembly history and dark matter (DM) properties, provided the kinematically outlying GCs can be reliably identified. However, traditional diagnostics like the Energy-Angular Momentum space fail because of large uncertainties on the GC velocities. In this work, we develop a new, robust statistical framework for identifying kinematically outlying LMC GCs, by using their Gaia-DR3 Proper Motions (PMs) combined with previous Line-of-Sight (LoS) velocity measurements. We use the difference between a GC's velocity vector and the average velocity vector of the surrounding red clump stars as a metric for quantifying a GC's kinematic peculiarity. We account for both the velocity measurement uncertainties and the LMC's intrinsic velocity dispersion. We find 5 LMC GCs to be kinematically outlying based on PM differences alone, and additional 6 GCs if LoS velocity information is also used. Majority of the GCs with outlying PMs are clustered at a distance of 3-4 kpc from the LMC center. The inclusion of outlying LMC GCs introduces a bias of upto 30% in the LMC's enclosed mass estimates derived using GCs as dynamical tracers; caution must be exercised in choosing the GC sample for precisely determining the LMC's DM content. We discuss the possibility that the kinematically outlying LMC GCs may have been accreted from external galaxies, and motivate future spectroscopic follow-up of the GC population to better understand the assembly history of massive satellite galaxies of Milky Way like hosts.

Figures (5)

• Figure 1: The sample of LMC GCs used in our work is plotted in the specific energy (E, x-axis) v/s specific angular momentum ($L_z$, y-axis) space, with their $1\sigma$ errorbars. The coordinate frame is described at the start of section \ref{['sec:E-Lz']}. Given the large errorbars on most of the GCs, it is challenging to identify kinematic outliers with traditional diagnostics like the E-$L_z$ space, and a new framework is needed. The grey dashed vertical line marks $E = 0$, and GCs that reside to the right of it (NGC 2210, NGC 2159) are likely unbound to the LMC, making them obvious kinematic outliers.
• Figure 2: Left panel: PM difference vectors (in grey) between the GC (in blue) and their surrounding RC stars (in magenta). Only the 6 GCs having a statistically significant difference with their surrounding stars under both Gaia DR3 data ($M_\mathrm{data}$) and the RC kinematic model ($M_\mathrm{2Dmodel}$) are shown (see Table \ref{['table:Mmodel']}). These GCs are overlayed on a background of LMC stars obtained from Gaia DR3. The surrounding field PMs clearly show the expected rotational pattern. While the directions of the velocity differences do not show any trend, 5 of the 6 GCs are located at similar distances ($\sim 3-4$ kpc) from the LMC photometric center (marked with a green cross). Right panel: Distribution of the GCs in the $r$-$z$ space of the LMC-centric coordinate system. Green squares are all the non-outlier GCs. Outlying GCs under $M_\mathrm{3Dmodel}$ , $M_\mathrm{2Dmodel}$ , and $M_\mathrm{data}$ , are marked with yellow circles, pink hexagons and blue crosses respectively. Grey errorbars denote the $1-\sigma$ uncertainty in $z$. Uncertainties in $r$ are negligible compared to the uncertainty in $z$. Consistent with the finding in the left panel, the high difference GCs under all three scenarios (marked with yellow, pink and blue) are clustered in the $r$ - $z$ space. The 2D Kolmogorov-Smirnov test returns a $p$-value $\approx 0.01$ for the hypothesis that both the set of outlier GCs and the set of remaining GCs were drawn from the same underlying distribution, indicating that their clustering is statistically significant.
• Figure 3: GC velocity differences are compared with the velocity dispersion of the surrounding stars, as a function of the radial coordinate (R). The velocity dispersions are obtained in two ways - using Gaia DR3 data (green solid line) and using the RGB model of Vasiliev_2018 (orange dashed line). The 6 high difference GCs identified in Table \ref{['table:Mmodel']} are marked in pink and the remaining GCs are marked in blue. $1-\sigma$ errorbars on the velocity differences are also shown. The green band denotes the standard deviation of the velocity dispersion values in each distance bin (1--2 kpc, 2--3 kpc and so on), with the average velocity dispersion for that distance bin marked with the solid green line.
• Figure 4: Dependence of the kinematic differences between the LMC GC population and their surrounding stars on the GC ages. The red points correspond to the entire GC sample analyzed in this work, categorized into young GCs (age $< 0.5$ Gyr, 4 in number), intermediate age GCs (0.5 Gyr $\leq$ age $\leq$ 4 Gyr, 16 in number) and old GCs (age $\gtrsim$ 10 Gyr, 10 in number). The blue squares denote the 6 outliers in the $M_\mathrm{2Dmodel}$ scenario. Left panel shows the PM difference between the GC and surrounding stars as a function of GC age. When the entire GC sample is considerd, there is a slight mean trend of older GCs having higher kinematic differences. However, given the standard deviation of the PM difference in each age group, this trend is not statistically significant. Further, no correlation is evident between the PM difference and age of the 6 outlying GCs. There is no evidence of the statistical metrics $Q_{err}$ and $Q_{disp}$ having a statistically significant dependence on GC age ( middle panel and right panel respectively).
• Figure 5: The GC based LMC tracer mass estimate (TME) with the full GC sample (solid blue line) v/s the estimate obtained by removing the outlier GCs flagged by $M_\mathrm{data}$, $M_\mathrm{2Dmodel}$ and $M_\mathrm{3Dmodel}$ (solid red line in the left, middle and right panel respectively). The turquoise histogram depicts the TME distribution of the bootstrapped realizations obtained by randomly removing the same number of GCs as the oulying GCs and using only the remaining sample. The mean of the bootstrapped realizations (dashed blue line) is close to the full sample estimate as expected. We find that the kinematically outlying LMC GCs can bias the TME by as large as 30%.