The Binary Fraction of Stars in the Dwarf Galaxy Ursa Minor via Dark Energy Spectroscopic Instrument

TL;DR

This work measures the binary fraction in the Ursa Minor dwarf spheroidal galaxy using multi-epoch LOSV data from DESI's Milky Way Survey, employing forward-modeling of binary orbits with orbital-parameter distributions drawn from solar-neighborhood studies. A grid-informed systematic LOSV floor and an MCMC likelihood on a per-star variability statistic $\beta$ yield $f_b \approx 0.61$ (D model) or $0.69$ (M model), with metal-rich stars showing a modestly higher $f_b$ than metal-poor ones and central regions showing lower binary fractions. The analysis includes robustness tests against sampling biases and period-distribution systematics, concluding that the observed trends are not fully attributable to observational selection or model assumptions, though the one-year baseline limits sensitivity to long-period binaries. The results have implications for binary survival in metal-poor environments and for interpreting stellar dynamics in dwarf galaxies, and they motivate longer time-baseline surveys to sharpen constraints on longer-period binaries.

Abstract

We utilize multi-epoch line-of-sight velocity measurements from the Milky Way Survey of the Dark Energy Spectroscopic Instrument to estimate the binary fraction for member stars in the dwarf spheroidal galaxy Ursa Minor. Our dataset comprises 670 distinct member stars, with a total of more than 2,000 observations collected over approximately one year. We constrain the binary fraction for UMi to be $0.61^{+0.16}_{-0.20}$ and $0.69^{+0.19}_{-0.17}$, with the binary orbital parameter distributions based on solar neighborhood observation from Duquennoy \& Mayor (1991) and Moe \& Di Stefano (2017), respectively. Furthermore, by dividing our data into two subsamples at the median metallicity, we identify that the binary fraction for the metal-rich ([Fe/H]>-2.14) population is slightly higher than that of the metal-poor ([Fe/H]<-2.14) population. Based on the Moe \& Di Stefano model, the best-constrained binary fractions for metal-rich and metal-poor populations in UMi are $0.86^{+0.14}_{-0.24}$ and $0.48^{+0.26}_{-0.19}$, respectively. After a thorough examination, we find that this offset cannot be attributed to sample selection effects. We also divide our data into two subsamples according to their projected radius to the center of UMi, and find that the more centrally concentrated population in a denser environment has a lower binary fraction of $0.33^{+0.30}_{-0.20}$, compared with $1.00^{+0.00}_{-0.32}$ for the subsample in more outskirts.

Figures (14)

• Figure 1: Spatial distribution of stars observed by DESI tertiary programs in UMi, shown in a gnomonic projection. The footprints of Tertiary 28 and Tertiary 33 are illustrated by the red and orange regions, respectively. Black ellipses denote the 1, 5, and 10 elliptical half-light radii of UMi.
• Figure 2: The basic information of our selected member stars (670 in total) of UMi. Top: The histogram showing the MJD distribution for each epoch. Due to the observation strategy of the Tertiary Program, the MJD range for each star spans from several days to almost a year. Bottom: Cumulative histograms of the number of epochs per star. The lighter dashed histogram shows the distribution before stacking multiple spectra taken on the same night (see Step 4 in Section \ref{['sec:umimem']}), while the solid black histogram shows the distribution after merging those exposures into a single epoch.
• Figure 3: Top-left panel: Color–magnitude diagram for UMi member stars. The red dashed line marks the color–magnitude selection used to exclude horizontal branch stars. Top-right panel: LOSV distribution for all measurements of the member stars, derived from stacked spectra obtained each night. Bottom-left panel: Spatial distribution of UMi member stars in equatorial coordinates in a gnomonic projection. The red ellipse marks the division between the inner and outer subsamples based on projected radius from the galactic center (see Section \ref{['sec:discussion']}). The three black ellipses correspond to the 1, 5, and 10 elliptical half-light radii, identical to those shown in Figure \ref{['fig:footprint']}. Bottom-right panel: Metallicity distribution of UMi member stars, measured from stacked spectra combining all available exposures for each star.
• Figure 4: The distribution of LOSV variability, $\beta$, as constructed from our $10^5$ mock samples. The blue line represents the probability density profile derived from the non-binary samples, while the orange line corresponds to that from the binary samples. The black histogram shows the observed $\beta$ distribution of the real data.
• Figure 5: Relative maximum log-likelihood as a function of the assumed systematic error floor ($\sigma_{\rm sys}$). Each point represents the maximum log-likelihood obtained from the MCMC analysis for a given value of $\sigma_{\rm sys}$, normalized by subtracting the overall maximum log-likelihood. The peak occurs at $\sigma_{\rm sys} = 1.2\ {\rm km\ s}^{-1}$, indicating the most likely value of the systematic error floor under the observing conditions of our sample.