Estimating the dynamical masses of dwarf galaxies in the presence of binary-star contamination

Abstract

Ultra-faint dwarf galaxies (UFDs) show extreme dynamical mass-to-light ratios of approximately 100-5000 in solar units within the half-light radius, making them critical tests for cosmological models. However, it is a concern whether the line-of-sight (l.o.s.) velocity component of the orbital motion of undetected binary stars is significantly inflating the observed l.o.s. velocity dispersions and, consequently, UFDs dynamical mass estimates. We correct the current estimates of these quantities for UFDs to account for the presence of undetected binaries with single-epoch data. We use the latest binary population models in the solar neighborhood to compute the expected velocity distribution of binary stars. We then convolve this distribution with a Gaussian to model the l.o.s. velocity distribution of UFDs in a mixture model, in which the binary fraction is a free parameter. We apply this methodology to observed UFDs whose dynamical masses are potentially inflated by binaries. In order to generalize to the multi-epoch data case, we compute the velocity distribution of undetected binaries by applying the same cuts to the models as one would apply to the observed data to remove binaries. We find that estimated dynamical masses of UFDs decrease by a factor of 1.5 to 3 once undetected binaries are accounted for. These corrections significantly affect considerations about DM models based on these systems, even challenging the classification of Leo IV, Unions I and Sagittarius II as galaxies. We find that a dedicated multi-epoch campaign spanning one year could substantially mitigate the impact of binaries. Finally, we find that the expected level of binary-star contamination in DM halo density profile inferences from dynamical models of classical dwarf spheroidal galaxies is negligible.

Figures (5)

• Figure 1: Observed $\sigma_{los}$ and estimated masses of UFDs. Upper panel: Observed $\sigma_{los}$ for the UFDs analyzed in this work sorted by $\sigma_{los, f\text{=0}}$. Lower panel: Mass estimated with Eq. \ref{['eq:wolf']} versus the luminosity, both in log-scale. The diagonal gray dashed lines indicate regions of constant M/L (= $M_{dyn}(<r_{1/2})/(L/2)$) in solar units indicated by the numbers. The horizontal black lines show the 1$\sigma$ ranges for $L$. The red, blue, and green vertical lines indicate the median and 1-$\sigma$ ranges for the values uncorrected by binaries, corrected assuming a uniform prior on $f$ and corrected assuming $f$ = 0.7, respectively. The shaded lines in the upper panel indicate the 3-$\sigma$ range.
• Figure 2: Observed velocity dispersion as a function of the underlying binary fraction for mock datasets of 10 stars with intrinsic $\sigma_{los}$ values of 0.5 km s$^{-1}$, 1 km s$^{-1}$, and 3 km s$^{-1}$. The red solid curves correspond to single-epoch observations without correction for the presence of binary stars, while the blue dashed curves refer to a dataset with three epochs and a one-year time baseline after excluding stars exhibiting velocity variability $>3 \times$$\Delta v_{los}$. The lines indicate the median recovered values, and the shaded regions denote the 1$\sigma$ confidence intervals.
• Figure 3: Inference on $\sigma_{los}$, $v_{sys}$ and $f$ for all the UFDs considered in this work, as indicated in the titles. The results of the analysis when not including the impact of undetected binaries are shown in red uncorrected by binaries, while those including the correction and assuming a uniform prior in f are illustrated in black, as indicated in the legend.
• Figure 4: Observed velocity dispersion as a function of the underlying binary fraction for mock datasets of 10 stars with intrinsic $\sigma_{los}$ values of 0.5 km s$^{-1}$, 1 km s$^{-1}$, and 3 km s$^{-1}$. The red solid curves correspond to single-epoch observations without correction for the presence of binary stars, while the blue dashed curves refer to a dataset with three epochs and a one-year time baseline after excluding stars exhibiting velocity variability $>3 \times$$\Delta v_{los}$. The lines indicate the median recovered values, and the shaded regions denote the 1$\sigma$ confidence intervals.
• Figure 5: DM enclosed mass profiles for the three mock galaxies. From top to bottom they have $\gamma$ = 0, 0.5, and 1. The black line shows the true DM density profile used to generate the mock; the blue line and band show the median and 1-$\sigma$ range for the output parameters of the modeling of the underlying mock; the orange line shows the same for the modeling of the mock contaminated by binaries. The symbols indicate the value estimated by mass estimators, applied to both populations, with the same color-coding.