The Proper Motion of Draco II with HST using Multiple Reference Frames and Methodologies

TL;DR

The study addresses the challenge of measuring Draco II’s proper motion, a critical yet difficult task for ultra-faint dwarfs due to tiny angular motions. It combines two epochs of HST/ACS imaging (~7-year baseline) with three reference-frame methodologies: HubPUG using Gaia DR3 stars, HubPUG using background galaxies, and BP3M combining Gaia priors with HST data and background galaxies. The key findings show that background galaxies as a reference frame yield the most precise systemic PM, with $(\mu_\alpha^*, \mu_\delta) = (1.043 \pm 0.029, 0.879 \pm 0.028)$ mas/yr, while Gaia-only HubPUG and BP3M results are consistent within uncertainties; tangential velocities are on the order of $\sim100$ km s$^{-1}$. This work demonstrates that including background galaxies and Bayesian joint-frame methods can achieve sub-0.03 mas/yr precision in the low-source-count regime, enhancing orbit modeling of Milky Way satellites and enabling robust cross-instrument astrometry for future facilities such as JWST, Euclid, and Roman.

Abstract

We present proper motion (PM) measurements for Draco II, an ultra-faint dwarf satellite of the Milky Way. These PMs are measured using two epochs of Hubble Space Telescope Advanced Camera for Surveys (HST/ACS) imaging separated by a 7 year time baseline. Measuring PMs of low-luminosity systems is difficult due to the low number of member stars, requiring a precise inertial reference frame. We construct reference frames using three different sets of external sources: 1) stars with Gaia DR3 data, 2) stationary background galaxies, and 3) a combination of the two. We show that all three reference frames give consistent PM results. We find that for this sparse, low-luminosity regime including background galaxies into the reference frame improves our measurement by up to $\sim2\times$ versus using only Gaia astrometric data. Using 301 background galaxies as a reference frame, we find that Draco II's systemic PM is $(μ_α^*, μ_δ) = (1.043\pm0.029, 0.879\pm0.028)$ mas/yr, which is the most precise measurement of the three we present in this paper.

Figures (6)

• Figure 1: Summary of the results for the PM measurement of Draco II from HubPUG utilizing the Gaia frame-of-reference. The left-hand and right-hand panels show the results for $\mu_\alpha^*$ and $\mu_\delta$, respectively. The orange points below the dashed orange line represent each of the PM estimates of Draco II that come from individual Gaia stars, sorted by magnitude (brightest at the top). The red points (third and fourth from the top) are the inverse-variance weighted mean of the individual PMs, with the dotted line tracing the median throughout the entire plot, and showing the unmodified weighted mean uncertainties as well as the uncertainties rescaled by the $\chi^2_\nu$. The top two blue points are the PM for Draco II as reported by Battaglia+2021 and pace+2022, both calculated using only data from Gaia eDR3.
• Figure 2: Three examples of background galaxies in the Draco II field, with each row being a distinct galaxy. Left column: the 11$\times$11 pixel stamp of the galaxy in the second-epoch image jf9q02tvq. Middle column: the convolved galaxy profile template built from the first-epoch image stack. Right column: difference image of the first column minus the second column.
• Figure 3: Left: Average first-epoch flc$(x,y)$ positions of Draco II member stars used in the local and chip corrections, colored by the excess PM of each star along the right ascension axis. Middle: Average first-epoch flc$(x,y)$ positions of Draco II member stars used in the the local correction, colored by the excess PM of each star along the declination axis. Right: CMD of the Draco II member stars used in the the local correction, colored by the total excess PM of each star. This is the same set of stars used as the initial input for the transformation to the comoving frame. Additionally, in gray, we plot all objects in our DOLPHOT stellar catalog.
• Figure 4: Summary of the results for the PM measurement of Draco II from HubPUG utilizing background galaxies as a frame-of-reference. The left-hand and right-hand panels show the results for $\mu_\alpha^*$ and $\mu_\delta$, respectively. The orange points below the dashed orange line represent each of the PM estimates of Draco II that come from individual background galaxies, sorted by magnitude (brightest at the top). In order to maintain plot legibility, we only plot the 118 of the 301 background galaxies used in the calculation with total PM uncertainties $<1.0$ mas/yr. The red points (fourth and fifth from the top) are the inverse-variance weighted mean of the individual PMs, with the dotted line tracing the median throughout the entire plot, and showing the unmodified weighted mean uncertainties as well as the uncertainties rescaled by the $\chi^2_\nu$. The top two blue points are the PM for Draco II as reported by Battaglia+2021 and pace+2022, both calculated using only data from Gaia eDR3, and the third point is our HubPUG weighted-mean value presented in §\ref{['sec:method1']}.
• Figure 5: Summary of the results for the PM measurement of Draco II from BP3M utilizing a combination of Gaia stars and background galaxies. The left-hand and right-hand panels show the results for $\mu_\alpha^*$ and $\mu_\delta$, respectively. The orange points below the dashed orange line represent each of the PM estimates of Draco II that come from individual stars that are members of Draco II, sorted by magnitude (brightest at the top). The red point (fifth from the top) is the mean systemic motion of Draco II taking into account the values from individual stars and the correlations between their PMs, with the dotted line tracing the median throughout the entire plot. The top two blue points are the PM for Draco II as reported by Battaglia+2021 and pace+2022, both calculated using only data from Gaia eDR3, and the third and fourth points are our HubPUG weighted-mean values presented in §\ref{['sec:method1']} and §\ref{['ssec:gals']}.