The Discovery of the Faintest Known Milky Way Satellite Using UNIONS

UMa3/U1 was discovered during an ongoing search for faint Local Group systems in the deep wide-field UNIONS. UNIONS is a consortium of Hawaii-based surveys working in conjunction to image a vast swath of the northern skies in the ugriz photometric bands. Four distinct surveys are contributing independent imaging: the Canada–France Imaging Survey (CFIS) at the Canada–France–Hawaii Telescope (CFHT) is targeting deep u and r photometry, Pan-STARRS is obtaining deep i and moderately deep z observations, the Wide Imaging with Subaru HSC of the Euclid Sky (WISHES) program is acquiring deep z at the Subaru Telescope, and the Waterloo–Hawaii IfA g-band Survey (WHIGS) is responsible for deep g imaging, also with Subaru. Together, these surveys are covering 5000 deg² at decl. of δ > 30° and Galactic latitudes of ∣b∣ > 30°. UNIONS was in part brought together to support the Euclid space mission, providing robust ground-based ugriz photometry necessary for photometric redshifts that would be the main pillar of Euclid's science operations. However, UNIONS is a separate survey whose aim is to maximize the science returns of this powerful, deep, wide-field photometric data set. UNIONS aims to deliver 5σ point-source depths of 24.3, 25.2, 24.9, 24.3, and 24.1 mag in ugriz, which are roughly equivalent to the first year of observations expected from the Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory, making UNIONS the benchmark photometric survey in the northern skies for the coming decade.

This work only utilizes the CFIS r-band and Pan-STARRS i-band catalogs. The median 5σ point-source depth in a 2'' aperture is 24.9 mag in r and 24.0 mag in i, although the Pan-STARRS i depth will increase over time owing to the scanning-type observing strategy employed. Currently, the area common to the two data sets spans more than 3500 deg² across both the north Galactic cap and south Galactic cap. These catalogs were cross-matched with a matching tolerance of 05, though sources typically matched to better than 013.

The median image quality of the CFIS r observations is an outstanding 069, allowing us to perform star–galaxy separation morphologically. We correct for galactic extinction using the E(B − V) values from Schlegel et al. (1998) assuming the conversion factors given by Schlafly & Finkbeiner (2011) for a reddening parameter of R_V = 3.1. The CFHT r-band filter is not present in the Schlafly & Finkbeiner (2011) list, so we adopt the conversion factor for the Dark Energy Camera (DECam) r-band filter (Flaugher et al. 2015) given that their full widths at half-maximum (FWHMs) are identical, and that the DECam r centroid is shifted redward from CFHT r by only 2 nm. For the remainder of the article, r will refer to CFIS r and i will refer to Pan-STARRS i unless otherwise specified.

UMa3/U1 was discovered as a spatially resolved overdensity of stars using a matched-filter approach. Variations on this general methodology have proven to be efficient and productive in discovering faint dwarf galaxies and faint star clusters in wide-field surveys (e.g., Koposov et al. 2007, 2015; Walsh et al. 2009; Bechtol et al. 2015; Drlica-Wagner et al. 2015; Homma et al. 2018).

Our particular implementation of the algorithm will be described here in brief, though we refer the reader to Smith et al. (2023) for a more detailed view of the search method. A matched filter seeks to isolate stars that belong to a particular stellar population, in order to create contrast in stellar density between the member stars of a putative satellite and the Milky Way stellar background. We start by selecting all stars in the UNIONS footprint that are consistent with a 12 Gyr, [Fe/H] = −2 PARSEC isochrone (Bressan et al. 2012), constructed from the CFHT r and Pan-STARRS i bands, with the isochrone shifted to a test distance. Stars are then tangent-plane-projected, binned into 05 × 05 pixels, and smoothed with Gaussian kernels with FWHMs of 12, 24, and 48. The broad-scale mean and variance are then subtracted and divided out from the smoothed maps, respectively, to find the significance of each pixel with respect to the Milky Way background. All peaks in the significance map are then recorded for future examination, and this process is repeated for a series of heliocentric distances spaced roughly logarithmically from 10 kpc to 1 Mpc.

Our matched-filter algorithm has been successful in detecting previously known dwarf galaxies. It should be noted that dwarf galaxy detections are the main focus of this search, but extragalactic star clusters are also typically old and metal-poor, so the matched filter ought to pick them up as well. We have used the known dwarf galaxy population to do a first-pass assessment of the algorithm's efficiency. Within 1 Mpc, we have recovered, with high statistical significance, all known Local Group dwarf galaxies (including M31 dwarfs) that were found in shallower surveys with matched-filter methods. We have also detected other galaxies in the local Universe out to 2 Mpc, and several Milky Way globular clusters.

UMa3/U1 is one of the most prominent candidates without a previous association produced from our search, on par with the detection significance of some known UFDs in the UNIONS sky. UMa3/U1 is most prominently detected in the significance map produced by the 12-smoothed, 10 kpc iteration at a statistical significance of 3.7σ above the background. For reference, Draco II is an ultrafaint satellite of the Milky Way whose true nature is unknown, but it has been estimated to be ∼20 kpc distant, and is detected at 2.8σ above the background in our own search. Figure 1 shows a color–magnitude diagram (CMD) using r, i photometry demonstrating the detection of stars about UMa3/U1 that meet the matched-filter selection criteria. We also show the equivalent CMD of a reference field, which is an equal-area elliptical annulus, to indicate the expected level of source contamination in the detection.

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We obtained spectroscopic data for 59 stars toward UMa3/U1 using the DEIMOS spectrograph (Faber et al. 2003) on the Keck II 10 m telescope. The data were taken on 2023 April 23 using a single mutlislit mask in excellent observing conditions. Ten targets were initially selected from membership analysis based on full astrometric data from Gaia (this selection is further explained in Section 3.3). The remaining 49 targets were selected from stars that were consistent with the observed stellar population of UMa3/U1 in r, i photometry that filled the slit mask around UMa3/U1.

We used the 1200 G grating, which covers a wavelength range of 6400−9100 Å, with the OG550 blocking filter with the aim of measuring the Ca ii infrared triplet (CaT) absorption feature. Observations consisted of 3 × 20 minute exposures, or 3600 s of total exposure time. Data were reduced to 1D wavelength-calibrated spectra using the open-source Python-based data reduction code PypeIt (Prochaska et al. 2020). PypeIt reduces the eight individual DEIMOS detectors as four mosaic images, where each red/blue pair of detectors is reduced independently. When reducing data for this paper, PypeIt's default heliocentric and flexure corrections were turned off and a linear flexure term was determined as part of the 1D data reductions below.

Stellar radial velocities and calcium triplet equivalent widths (EWs) were measured using a preliminary version of the DMOST package (M. Geha et al. 2023, in preparation). In brief, DMOST forward-modeled the 1D stellar spectrum for each star from a given exposure with both a stellar template from the PHOENIX library and a telluric absorption spectrum from TelFit (Gullikson et al. 2014). The velocity was determined for each science exposure through a Markov Chain Monte Carlo (MCMC) procedure constraining both the radial velocity of the target star and the wavelength shift of the telluric spectrum needed to correct for slit miscentering (see, e.g., Sohn et al. 2007). The final radial velocity for each star was derived through an inverse-variance weighted average of the velocity measurements from each exposure. The systematic error reported by the pipeline, derived from the reproducibility of velocity measurements across masks and validated against spectroscopic surveys, is ∼ 1 km s⁻¹ (see M. Geha et al. 2023, in preparation). Lastly, DMOST measured the EW from the CaT by fitting a Gaussian-plus-Lorentzian model to the coadded spectrum (for stars at signal-to-noise ratios, S/Ns, > 15) or a Gaussian model (for stars at S/N < 15). We assumed a 0.2 Å systematic error on the total EW determined from independent repeat measurements. Thanks to excellent observing conditions, we measured velocities and combined CaT EWs for 31 of the 59 targets and achieved spectra with a median S/N per pixel ranging from 15 to 74 for the 10 suspected members.

The matched-filter detection algorithm only searches for stellar populations with an age of 12 Gyr and a metallicity of [Fe/H] = −2, and results of the search provide an initial estimate of the distance to UMa3/U1. We further refine these properties through visual inspection in an iterative process, where we make small systematic tweaks to the distance, metallicity, and age of the stellar population until a satisfactory model is settled on. We also point out that UMa3/U1 has an extraordinarily low stellar mass (which will be explored further in Section 3.6) so this by-eye analysis is based on only a handful of stars spanning ∼6.5 mag on a CMD.

We initially set the distance to 10 kpc and explore a grid of PARSEC isochrones spanning 5–13 Gyr in age (τ) in steps of 1 Gyr and −2.2 to −1.0 in metallicity ([Fe/H]) in steps of 0.1 dex by eye. [Fe/H] = −2.2 appears to be a good fit to the data. An age τ ≥ 11 Gyr is a good fit to the few stars at the main-sequence turnoff (MSTO). Changing the age by ∼1 Gyr results in minor changes in the shape of the isochrone, while changes in metallicity are negligible, so we adopt τ = 12 Gyr and [Fe/H] = −2.2 for all calculations and derivations going forward. We note, however, that [Fe/H] = −2.2 is the most metal-poor isochrone available in our set, so this isochrone may only be an upper limit on the true systemic metallicity.

For the distance estimate, we prioritize fitting the MSTO to the four brightest stars due to their small photometric uncertainties, though the fainter stars appear to be slightly bluer on average than our best-fit isochrone, the most metal-poor in the set. While this could be explained by the large photometric uncertainties at this magnitude, we have overlaid slightly more metal-poor MIST isochrones (Choi et al. 2016). We do not find a significantly better fit, and note that variance between isochrones from different databases is large enough that attempting to constrain the distance with greater accuracy may not be appropriate. We therefore adopt a 10% uncertainty on the distance estimate, giving 10 ± 1 kpc. Adjustments of 1 kpc are incrementally made to the distance of the isochrone, and this appears to be appropriate. Figure 2 shows CMDs with all matched-filter-selected stars brighter than i₀ ∼ 23 mag, where the PARSEC isochrones are overplotted with small variations in distance and age.

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Unfortunately, we are unable to use either tip of the red giant branch (TRGB) or horizontal branch (HB) stars to further constrain the distance to UMa3/U1 as this system is so sparsely populated that no stars currently exist in these more highly evolved, shorter-duration stages of the stellar lifecycle. Given the relative closeness of the system, along with the r saturation limits of r ∼ 17.5 mag, we also search through the Third Data Release (DR3) from Gaia (Gaia Collaboration et al. 2016, 2021), but a lack of bright stars in the direction of UMa3/U1 confirms that no TRGB or HB stars are present. Additionally, we search the PS1 RR Lyrae (Sesar et al. 2017) and Gaia variability (Gaia Collaboration 2022) catalogs, but cannot identify any RR Lyrae stars within a few arcminutes of UMa3/U1. We therefore cannot use the properties of these variable stars to further constrain the heliocentric distance.

We follow a procedure that is based on the methodology laid out in Martin et al. (2008, 2016a) to estimate the structural parameters of UMa3/U1 assuming the distribution of member stars is well described by an elliptical, exponential radial surface density profile and a constant field contamination. The profile, ρ_dwarf(r), is parameterized by the centroid of the profile (x₀, y₀), the ellipticity (defined as = 1 − b/a, where b/a is the minor-to-major-axis ratio of the model), the position angle of the major axis θ (defined east of north), the half-light radius (which is the length of the semimajor axis r_h), and the number of stars N* in the system. The model is written as

$$\begin{eqnarray}&&{\rho }_{\mathrm{dwarf}}(r)=\displaystyle \frac{{1.68}^{2}}{2\pi {r}_{{\rm{h}}}^{2}(1-\epsilon )}{N}^{* }\exp \left(\displaystyle \frac{-1.68r}{{r}_{{\rm{h}}}}\right),\end{eqnarray} \tag{ 1 }$$

where r, the elliptical radius, is related to the projected sky coordinates (x, y) by

$$\begin{eqnarray}\begin{array}{rcl}r & = & \left\{{\left[\displaystyle \frac{1}{1-\epsilon }\left((x-{x}_{0})\cos \theta -(y-{y}_{0})\sin \theta \right)\right]}^{2}\right.\\ & & +{\left.{\left[{\left((x-{x}_{0})\sin \theta -(y-{y}_{0})\cos \theta \right)}^{2}\right]}^{2}\right\}}^{\tfrac{1}{2}}.\end{array}\end{eqnarray} \tag{ 2 }$$

We assume that the background stellar density is uniform, which is reasonable on the scale of arcminutes up to a degree or so. The background, Σ_b, is calculated as follows:

$$\begin{eqnarray}&&{{\rm{\Sigma }}}_{{\rm{b}}}=\displaystyle \frac{n-{N}^{* }}{A},\end{eqnarray} \tag{ 3 }$$

where n is the total number of stars in the field of view and A is the total area, normalizing the background density with respect to the selected region. We combine the elliptical, exponential surface density model with the uniform background term to construct our posterior distribution function,

$$\begin{eqnarray}&&{\rho }_{\mathrm{model}}(r)={\rho }_{\mathrm{dwarf}}(r)+{{\rm{\Sigma }}}_{{\rm{b}}},\end{eqnarray} \tag{ 4 }$$

which we sample with the afine-invariant MCMC sampler emcee (Foreman-Mackey et al. 2013) to estimate the most likely structural parameters to describe UMa3/U1. We apply flat priors to all parameters, the bounds of which are given in Table 1.

Table 1. Flat Priors for Each Parameter in the MCMC Analysis

Parameter	Prior
x0	−6' ≤ Δx0 ≤ +6'
y0	−6' ≤ Δy0 ≤ +6'
rh	0' < rh < 9'
	0 ≤ < 1
θ	−90° ≤ θ < +90°
N*	0 ≤ N* ≤ 100

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Prior to invoking this method, we select only those stars that are selected by the matched filter, this time using the 12 Gyr, [Fe/H] = −2.2 isochrone that was determined in Section 3.1. We apply an additional magnitude cut, retaining stars with i ≤ 23.5 mag to ensure incompleteness effects do not skew the parameter estimation.

The emcee routines are initialized with 64 walkers, each running for 10,000 iterations with the first 2000 iterations thrown out to account for burn-in. The program shows good convergence and the median value for each parameter, along with the 16th and 84th percentiles taken as uncertainties, is provided in Table 2 along with all other measured and derived properties. UMa3/U1 is compact, with a physical half-light radius (r_h, the semimajor axis of the elliptical distribution) derived to be $0\buildrel{\,\prime}\over{.} \,{9}_{-0\buildrel{\,\prime}\over{.} 3}^{+0\buildrel{\,\prime}\over{.} 4^{\prime} }$, or 3 ± 1 pc in physical units.

Table 2. Measured and Derived Properties for UMa3/U1

Property	Description	Value
αJ2000	R.A.	11h38m498
δJ2000	Decl.	+31°4'42''
rh,ang	Angular Half-light Radius	$0\buildrel{\,\prime}\over{.} {9}_{-0\buildrel{\,\prime}\over{.} 3}^{+0\buildrel{\,\prime}\over{.} 4^{\prime} }$
rh,phys	Physical Half-light Radius	3 ± 1 pc
	Ellipticity	${0.5}_{-0.3}^{+0.2}$
θ	Position Angle	$169{^\circ }_{-{12}^{^\circ }}^{+{18}^{^\circ }}$
N*	Number of Stars (down to i = 23.5 mag)	${21}_{-5}^{+6}$
D⊙	Heliocentric Distance	10 ± 1 kpc
(m − M)0	Distance Modulus	15.0 ± 0.2 mag
τ	Age (Isochrone)	12 Gyr a
[Fe/H]	Metallicity (Isochrone)	−2.2 dex b
Mtot	Total Stellar Mass	${16}_{-5}^{+6}$ M⊙
MV	Absolute V-band Magnitude	+2.2${}_{-0.3}^{+0.4}$ mag
Ntot	Total Number of Stars	${57}_{-19}^{+21}$
μeff	Effective Surface Brightness	27 ± 1 mag arcsec−2
μα cos δ	Proper Motion in R.A.	−0.75 ± 0.09 (stat) ± 0.033 (sys) mas yr−1 c
μδ	Proper Motion in Decl.	1.15 ± 0.14 (stat) ± 0.033 (sys) mas yr−1 c
〈v⊙〉	Mean Heliocentric Velocity	88.6 ± 1.3 km s−1
σv	Intrinsic Velocity Dispersion	${3.7}_{-1.0}^{+1.4}$ km s−1 d
M/L1/2	Dynamical Mass-to-light Ratio (<rh)	${6500}_{-4300}^{+9100}$ M⊙/L⊙ d
rperi	Pericenter	${12.9}_{-0.7}^{+0.7}$ kpc
rapo	Apocenter	${26}_{-3}^{+2}$ kpc
${z}_{\max }$	Maximum Height above Milky Way Disk	${17}_{-2}^{+2}$ kpc
orb	Orbital Eccentricity	${0.34}_{-0.03}^{+0.02}$
Δtperi	Time between Pericenters	${373}_{-34}^{+32}$ Myr
tsince	Time since Last Pericenter	${31}_{-2}^{+2}$ Myr

Notes.

^a All isochrones with τ > 11 Gyr fit the data well, but we adopt τ = 12 Gyr for computations. ^b [Fe/H] = −2.2 is the most metal-poor isochrone available in our set. ^c Systematic uncertainties were investigated by Lindegren et al. (2021). ^d The removal of a single star (#2 in Table 3) drops the velocity dispersion to ${1.9}_{-1.1}^{+1.4}$ km s⁻¹, decreasing the inferred M/L_1/2 to ${1900}_{-1600}^{+4400}$ M_⊙/L_⊙.

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Despite its extreme dearth of giant stars, UMa3/U1 lies close enough that several stars are brighter than the approximate limiting magnitude (G ∼ 21 mag) of Gaia DR3. Using stars with full astrometric data (Lindegren et al. 2021), we estimate the systemic proper motion of UMa3/U1 and assign likelihoods for individual stars to be members of this faint stellar system.

We follow the methodology of Jensen et al. (2024), which builds on McConnachie & Venn (2020a, 2020b), and we refer the reader to those papers for more details regarding the algorithm. Briefly, the method uses spatial, photometric, and astrometric information about each star, in conjunction with the structural parameters derived for some stellar system, to compute the likelihood that a given star is a member of a putative stellar system rather than a member of the Milky Way foreground stellar population. The Milky Way foreground prior distributions for each parameter are calculated empirically using a subset of stars detected by Gaia in a 2° circle about the location of the system, where the Gaia photometry was extinction-corrected following Gaia Collaboration et al.(2018).

In this application to UMa3/U1, we use the structural parameters derived from UNIONS data in Section 3.2 and the stellar population estimates of τ = 12 Gyr and [Fe/H] = −2.2. The systemic proper motion of UMa3/U1 is estimated by the membership algorithm to be (μ_α cos δ, μ_δ ) = (−0.75 ± 0.09 (stat) ± 0.033 (sys), 1.15 ± 0.14 (stat) ± 0.033 (sys)) mas yr⁻¹. This process also identifies seven stars with P_sat > 0.99 (where P_sat is the membership likelihood) and an additional star with P_sat = 0.75. Jensen et al. (2024) have investigated the workings of this code, finding that P_sat ∼ 0.2 actually corresponds to a ∼50% probability of being a member (based on known members identified via radial velocities), so we find eight high-likelihood member stars in total based on Gaia measurements. Two additional stars with marginal membership likelihoods (0.01 < P_sat < 0.10) near to the centroid of UMa3/U1 are also targeted in our spectroscopic follow-up for further investigation.

As discussed in Section 2.3, 31 of the 59 target spectra are successfully measured following M. Geha et al. (2023, in preparation), producing heliocentric radial velocities (v_⊙) and combined CaT EWs (the sum of all three CaT absorption features, Σ_EW). Traditionally, methods of inferring metallicity ([Fe/H]) from CaT EWs have been calibrated using red giant branch (RGB) stars (Starkenburg et al. 2010; Carrera et al. 2013). Due to its extraordinarily low stellar mass, U1 only has a single post-main-sequence star visible on its CMD, with this one star lying at the inflection point of the best-fitting isochrone where the subgiant branch transitions to the RGB. We estimate this star to have log(g) = 3.51 using the best-fit isochrone, so while it has evolved off the main sequence, it is outside the range of log(g) for which [Fe/H] estimators have been calibrated. The calibration from Starkenburg et al. (2010) considered model spectra computed for RGB stars with 0.5 ≤ log(g) ≤ 2.5 while Carrera et al. (2013) calibrated the [Fe/H]–CaT Σ_EW relationship using RGB stars that lay in the range 0.7 ≤ log(g) ≤ 3.0, where log(g) was derived from high-resolution spectroscopy. However, we still are able to use the measured Σ_EW to help with membership identification.

Using a combination of v_⊙, Σ_EW, and membership likelihoods assigned from the algorithm described in Section 3.3, we isolate member stars. In Figure 3, we plot all potential member stars on-sky and on a CMD of extinction-corrected r, i photometry. The four brightest members are all in good agreement with the best-fit isochrone. In the range 20 ≤ G₀ ≤ 21 mag, there are several stars that are all roughly consistent with the isochrone, though there is some scatter. The eight sources marked with blue circles are those with high membership likelihoods (P_sat ≥ 0.75) and the orange squares are three additional stars that are consistent with Gaia-identified members both spatially and in v_⊙, but do not have full astrometric data, and could therefore not be identified by the membership algorithm. The red "X" represents one of the marginal members (P_sat = 0.02) noted in Section 3.3 and its formal membership will be discussed below (Section 3.4.1). All eight member stars are seen to cluster in proper-motion space (bottom left panel of Figure 3), and we note that five of these members are tightly clustered at the systemic proper motion (see Table 2). The three other members have large uncertainties, as they are the faintest of the members with measured proper motions, but they are still consistent with the systemic proper motion (within 2σ–3σ). Additionally, the bottom right panel of Figure 3 shows the Σ_EW–v_⊙ plane of all stars observed with Keck/DEIMOS. The suspected members cluster at v_⊙ ∼ 90 km s⁻¹ and Σ_EW ∼ 1.5 Å, neatly separated from all other measured stars. Photometric and dynamical properties are listed for all likely members and the two confirmed nonmembers in Table 3.

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3.4.1. Marginal Members

Here, we offer evidence to suggest that the two marginal members identified in Section 3.3 (0.01 < P_sat < 0.10) are in truth not members of UMa3/U1. First, star #5 in Table 3 has very unusual measurements in both velocity and Σ_EW, so we examine its spectrum and find it to lack any CaT absorption features while featuring a broad-emission-like bump around 7200 Å. Paired with a proper motion close to zero, we suspect that this source may be a background quasar and consequently exclude it from our analysis.

Star #8 in Table 3 is featured in both Figures 3 and 4 as a red "X," where measurements show evidence that it is not a member. While this star does lie close to the systemic proper motion of UMa3/U1, it also has a proper motion near zero. In Figure 3, the gray contours show the empirical distribution of all stars measured by Gaia within 2° of UMa3/U1 and there is an overdensity near the origin, giving this star a high likelihood of being part of the proper-motion background. Additionally, this star is more than 7 × r_h from the centroid of the stellar overdensity. Figure 4 shows that this star is offset from the mean velocity by 3.8σ, where the dispersion of the distribution is calculated in Section 3.5. The final piece of evidence comes from the Σ_EW relative to other likely member stars. Despite not being able to calculate [Fe/H], we can see on the Gaia CMD in Figure 3 that there are seven suspected members, as well as the marginal member being discussed here, in the range 20 ≤ G₀ ≤ 21 mag. Therefore, if all these stars are true members, they are all similar types of dwarf stars and thus should have similar values of log(g), T_eff, and [Fe/H]. Additionally, the isochrone fitting implies that this is a metal-poor population ([Fe/H] ∼ −2.2). The seven suspected members are all clustered around ∼1.5 Å while star #8 has Σ_EW = 4.42 ± 0.44 Å. If this star in question really is a main-sequence dwarf star in UMa3/U1 (and is therefore at the same distance of 10 kpc), it must be far more metal-rich than than the other suspected member stars, which would be extremely anomalous. All told, we feel this accumulation of evidence implies that star #8 is very unlikely to be a member of UMa3/U1, so we exclude it from the member list for the following analysis of the velocity distribution.

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We follow Walker et al. (2006) to measure the mean and intrinsic dispersion in heliocentric velocity. We construct the following log-likelihood function:

$$\begin{eqnarray}\begin{array}{lll}\mathrm{ln}L & = & -\displaystyle \frac{1}{2}\displaystyle \sum _{i=1}^{N}\mathrm{ln}({\sigma }_{i}^{2}+{\sigma }_{v}^{2})-\displaystyle \frac{1}{2}\displaystyle \sum _{i=1}^{N}\displaystyle \frac{{\left({v}_{i}-\langle {v}_{\odot }\rangle \right)}^{2}}{{\sigma }_{i}^{2}+{\sigma }_{v}^{2}}\\ & & -\displaystyle \frac{N}{2}\mathrm{ln}(2\pi ),\end{array}\end{eqnarray} \tag{ 5 }$$

where v_i and σ_i are the measured velocity and uncertainty for each individual star, 〈v_⊙〉 is the mean heliocentric radial velocity of UMa3/U1, and σ_v is the intrinsic velocity dispersion, which are the model parameters and quantities of physical interest. The log-likelihood function is maximized with respect to 〈v_⊙〉 and σ_v using emcee. The final estimates are 〈v_⊙〉 = 88.6 ± 1.3 km s⁻¹ and ${\sigma }_{v}={3.7}_{-1.0}^{+1.4}$ km s⁻¹, where the uncertainties are the 16th and 84th percentiles of the distributions produced by the MCMC. This result is shown in the leftmost panels of Figure 5.

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We investigate the robustness of this result to understand how the selection of UMa3/U1 member stars might change the measured intrinsic velocity dispersion. We systematically exclude individual stars from the velocity dispersion estimation, one by one, and find that star #2 (denoted in Table 3), the largest velocity outlier, causes the largest change by reducing the velocity dispersion to ${\sigma }_{v}={1.9}_{-1.1}^{+1.4}$ km s⁻¹. Continuing in this direction, we keep star #2 out of the member list and systematically exclude individual stars to find the next most impactful source. Removing star #4, a high-S/N measurement at the high-velocity end of the distribution, produces an unresolved velocity dispersion. This systematic analysis of the velocity distribution is relevant because the presence of binary stars in dwarf galaxies can inflate the measured dispersion by several kilometers per second relative to the true intrinsic dispersion (McConnachie & Côté 2010; Minor et al. 2010), and binary fractions in "classical" dwarf spheroidals have been found to vary broadly, ranging from 14% to 78% (Minor 2013; Spencer et al. 2017, 2018; Arroyo-Polonio et al. 2023).

Our spectroscopic measurements indicate that the intrinsic velocity dispersion of UMa3/U1 is resolved, but we note that repeat observations are critical for this to be confirmed. Results from the MCMC calculations for the systematic removal of stars #2 and #4 are shown in the central and rightmost panels of Figure 5 and identify which sources require particularly careful spectroscopic follow-up observations.

We now aim to derive the total stellar mass by creating a sample of mock stellar populations that emulate the characteristics of UMa3/U1. We follow a similar methodology to that of Martin et al. (2016a) in creating the mock populations.

We assume the underlying stellar population of UMa3/U1 is described by a canonical two-part Kroupa initial mass function (IMF; Kroupa 2001) and a stellar population of τ = 12 Gyr, [Fe/H] = −2.2. We create a single mock stellar population by first drawing a distance from a normal distribution with a mean of 10 kpc and a standard deviation of 1 kpc, and shifting the theoretical isochrone to that distance. We then similarly draw a number of stars (N*) from a normal distribution with a mean of 21 and a standard deviation of 5.5 (average of 16th and 84th percentiles reported in Table 2), which will act as the target number of stars above the adopted completeness limit, i = 23.5 mag. Randomly sampling D_⊙ and N* propagates previously derived uncertainties through to the final stellar mass estimation. We then sample individual stellar masses from the IMF, converting each to the i band and checking if i_star ≥ 23.5 mag. We sample the IMF until N* stars above the completeness limit have been accrued, at which point we sum the stellar masses of all stars (including those below the completeness limit). We repeat this process to create 100,000 mock stellar populations of UMa3/U1 and find the median total stellar mass to be ${M}_{\mathrm{tot}}={16}_{-5}^{+6}$ M_⊙, where the uncertainty spans the 16th and 84th percentiles of the total stellar mass distribution. This can be recast in terms of the frequentist p-value; we reject that the total stellar mass is greater than 38 M_⊙ at the 99.9% confidence level. The distribution of total stellar masses for all mock stellar populations is shown in Figure 6.

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Additionally, we convert this mass to luminosity and absolute V-band magnitude (M_V ). We calculate the empirical baryonic M/L to be ∼1.4 for a 12 Gyr, [Fe/H] = −2.2 stellar population, so a stellar mass of ${16}_{-5}^{+6}$ M_⊙ implies a total luminosity of 11.4 ± 3.6 L_⊙, which is equivalent to a total absolute V-band magnitude of +2.2${}_{-0.3}^{+0.4}$ mag. We also compute the effective surface brightness by dividing half the total flux by the area enclosed by one elliptical half-light radius and converting to mag arcsec⁻². This comes to 27 ± 1 mag arcsec⁻². All properties derived here can be found in Table 2.

Several assumptions are used in this methodology, so we perform several modified analyses to assess the robustness of this result with respect to these choices. Given a 5σ point-source depth of 24.0 mag in i, we choose a magnitude cut of i = 23.5 mag to mitigate issues with stellar completeness when deriving stellar parameters, notably the total number of stars in the system. We do not perform a detailed stellar completeness investigation, but we do repeat the same stellar mass analysis using more restrictive magnitude cuts of 23.2 mag (10σ depth) and 22.4 mag (20σ depth). These produce total stellar mass estimates of ${21}_{-6}^{+7}$ M_⊙ and ${22}_{-8}^{+9}$ M_⊙, respectively, which are consistent with the initial estimate within uncertainties. We also repeat the analysis using a Chabrier IMF (Chabrier 2003), which produces a nearly identical result of ${17}_{-5}^{+6}$ M_⊙. Finally, we investigate the impact of varying age and metallicity as these parameters are constrained by eye alone. We run the same analysis for isochrones of ages 11 and 13 Gyr (holding [Fe/H] fixed at −2.2), which gives total stellar masses of 17 and 16 M_⊙ and absolute V-band magnitudes of +2.0 and +2.2 mag, respectively. Similarly, we use isochrones of metallicities −2.1 and −2.0 (holding age fixed at 12 Gyr), producing total stellar masses of 17 and 18 M_⊙ and absolute V-band magnitudes of +2.2 and +2.1 mag, respectively. For all isochrone changes, we recalculate the empirical baryonic M/L. This analysis appears to be very robust to small variations in age and metallicity.

We note that a common approach to calculating absolute magnitude is to add up the luminosity contribution of every star and obtain an absolute magnitude for each individual mock stellar population (e.g., Martin et al. 2016a; Collins et al. 2022, 2023; Martínez-Delgado et al. 2022; McQuinn et al. 2023a, 2023b). This is in contrast to simply counting up the luminosity contribution of each individually observed star on the CMD, which gives the present-day luminosity of the system. Direct counting can be challenging due to difficulties in effectively accounting for background/foreground contamination in the member star sample. UMa3/U1 has a median of 57 total stars (down to 0.1 M_⊙, over the 100,000 mock populations) meaning that small number statistics play a huge role. Based on the isochrones used to model UMa3/U1, the most massive star is 0.8 M_⊙ while the MSTO is at ∼0.77 M_⊙. Late-stage stars (RGB, HB) have a massive contribution to the total luminosity of such a tiny system, so mock populations that happen to sample a single star in the mass range 0.77–0.8 M_⊙ have a dramatically boosted total absolute magnitude, skewing the distribution. For this reason, we consider the total stellar mass to be a more stable tracer of the stellar content of UMa3/U1, thus providing an estimate of absolute magnitude whose variance is less heavily affected by the occasional sampling of a single late-stage star.

In Smith et al. (2023), we developed a similar method to estimate the absolute magnitude of the Boötes V UFD. This methodology was found to produce an excess in the number of bright, late-stage stars (RGB, HB), which resulted in an overestimation of the total absolute magnitude. We rederive the total stellar mass and absolute magnitude of Boötes V following the methodology described in this section by producing 1000 realizations using the stellar population and structural parameters found in Smith et al. (2023). We measure the stellar mass of Boötes V to be ${1044}_{-485}^{+775}$ M_⊙, which, when converted to absolute V-band magnitude, gives ${M}_{V}=-{2.4}_{-0.6}^{+0.7}$ mag. This is consistent with the V-band magnitude found by Cerny et al. (2023a) using deeper, targeted follow-up observations from GMOS on Gemini North, measured to be $-{3.2}_{-0.3}^{+0.3}$ mag.

With estimates for all six phase space parameters available, we now use a simple dynamical model to investigate the orbit of UMa3/U1 and its interaction history with the Milky Way. We approximate UMa3/U1 as a point mass in a Milky Way potential, implemented with the Python-wrapped package gala (Price-Whelan 2017). The Milky Way potential used for this analysis is comprised of three components: (1) a Miyamoto & Nagai (1975) disk, (2) a Hernquist (1990) bulge, and (3) a spherical Navarro–Frenk–White (NFW) dark matter halo (Navarro et al. 1996). The parameters used for the bulge and disk are taken from the listed citations whereas the NFW dark matter halo parameters (${M}_{200,\mathrm{MW}}^{\mathrm{DM}}$, R₂₀₀) are adopted from estimates in Cautun et al. (2020), where a concentration parameter of 12 was chosen. This potential produces a circular velocity at the radius of the Sun similar to a recent estimate (v_circ(R_⊙) = 229 km s⁻¹; Eilers et al. 2019). We use a right-handed Galactocentric coordinate system such that the Sun is located at (X, Y, Z) = (8.122, 0.0, 0.0) kpc, with local-standard-of-rest velocities of [U, V, W] = [10.79, 11.06, 7.66] km s⁻¹ (Robin et al. 2022).

To characterize the orbit, we perform a Monte Carlo (MC) randomization, where we generate 1000 samples of the initial orbital conditions (i.e., input parameters {α_J2000, δ_J2000, D_⊙, μ_α cos δ, μ_δ , v_r }), which are previously measured in this analysis. Each parameter, aside from the sky positions (α_J2000, δ_J2000) as their uncertainties are negligible, is modeled by a Gaussian distribution with the standard deviation given by the errors indicated in Table 2. The orbit of each point mass is integrated 0.5 Gyr both forward and backward in time in steps of 10⁻³ Gyr. Figure 7 displays the orbits of all 1000 realizations, with the blue tracks tracing backward in time and the red tracks tracing forward in time. The coordinate system is arranged such that Milky Way rotation proceeds clockwise on the XY-plane depicted in the left panel of Figure 7, meaning that the orbit of UMa3/U1 is prograde. The mean orbit is shown in black and the distribution of all 1000 realizations shows that the orbit is quite stable to uncertainties on the input parameters. Several key parameters, namely the pericenter (r_peri, the closest approach to the Milky Way), apocenter (r_apo, the furthest point from the Milky Way), ${z}_{\max }$ (the maximum height above the disk), time between pericenters (orbital time), time since the last pericenter, and orbital eccentricity, are calculated for each orbit, and the median along with the 16th and 84th percentiles for each parameter is presented in Table 2.

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The potential that we use does not include the Large Magellanic Cloud (LMC). We note that Pace et al. (2022) computed the change in orbital parameters of all known UFDs (at the time) given the inclusion and exclusion of the LMC. With r_peri and r_apo of 12.9 and 26 kpc, respectively, UMa3/U1 has a smaller apocenter than all the UFDs considered by Pace et al. (2022), and a smaller pericenter than all but one UFD in the Pace et al. (2022) list when integrated in a Milky Way–only potential. To find the best sample to compare to UMa3/U1, we select all UFDs in Pace et al. (2022) with r_peri < 30 kpc and r_apo < 50 kpc. This group comprises Tucana III, SEGUE 1, SEGUE 2, and Willman 1. Of these, Tucana III is on a nearly radial orbit and is thought to be tidally disrupting. SEGUE 1, SEGUE 2, and Willman 1 are all relatively unaffected by the inclusion of the LMC in the gravitational potential in Pace et al. (2022). Given that UMa3/U1 orbits more closely to the Milky Way than any of these UFDs, we conclude that its orbit is unlikely to be strongly affected by the LMC.

Broadly speaking, there are two possible origins for UMa3/U1: either it formed in situ or it was accreted into the Milky Way. Based on the orbit derived in Section 3.7 UMa3/U1 does not appear to be a on a disklike or bulgelike orbit. Massari et al. (2019) describe bulge globular clusters as having r_apo < 3.5 kpc and disk globular clusters as having ${z}_{\max }\lt 5\,\mathrm{kpc}$. UMa3/U1 does not satisfy the criterion for either category, with an apocenter of 25.2 kpc and ${z}_{\max }=16.7\,\mathrm{kpc}$. The findings of Leaman et al. (2013) show that in situ, disklike globular clusters rarely have a mean metallicity less than −2 and while Di Matteo et al. (2019) argue that a significant portion of the inner Milky Way halo may be comprised of metal-poor ([Fe /H] < −1), heated thick-disk stars, they likely extend only to a metallicity of −2. The metallicity of UMa3/U1 is not strongly constrained, as the PARSEC isochrone database does not extend lower than a metallicity of [Fe/H] = −2.2, but it appears metal-poor nonetheless. UMa3/U1 is on a prograde orbit with a clear, but not too drastic, inclination with respect to the Milky Way plane and therefore could have formed in situ, though it would be fairly anomalous in its orbit, and somewhat anomalous in its metallicity with respect to the known properties of disk globular clusters.

The alternative is that UMa3/U1 could have been accreted onto the Milky Way halo. With an orbital period of ${373}_{-34}^{+32}$ Myr, UMa3/U1 has likely had time to complete many pericentric passages of the Milky Way, which may have led to tidal stripping. There is no stellar stream in the galstreams (Mateu 2023) catalog that matches the position or kinematics of UMa3/U1, but it could be fruitful to search for a faint stream along the orbital path given that this satellite has likely been interacting with the outer disk for many orbits.

UMa3/U1 may have been accreted on its own or as a companion to some larger system, so we compute the orbital properties of all Milky Way satellites with measured velocities and proper motions. At the total orbital energy of UMa3/U1, the orbits of globular clusters M68 and Ruprecht 106 are found to have the most similar X, Y, and Z angular momenta, with M68 being a particularly close match in apocenter and the maximum height above/below the disk when examining other orbital parameters. M68 is previously thought to have been accreted onto the Milky Way from a satellite galaxy (Yoon & Lee 2002), so this orbital similarity could indicate that UMa3/U1 and M68 were accreted as part of the same system. If UMa3/U1 is the tidally stripped remains of a dwarf galaxy then it could have hosted M68 prior to accretion, whereas if UMa3/U1 is a star cluster, perhaps it and M68 formed in the same environment. We present the orbital parameters of all Milky Way satellites in Figure 8, where the Milky Way dwarf galaxies are all dwarfs within 420 kpc (roughly the distance to Leo T) from McConnachie (2012), ¹⁴ the classical globular cluster measurements are taken from Harris (1996, 2010 edition), and the most similar systems, globular clusters M68 and Ruprecht 106, are highlighted.

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Although the low metallicity of UMa3/U1 does not exclude it from an in situ formation in the heated thick disk, the orbital parameters are inconsistent with the criteria used to define disk and bulge globular cluster populations. We favor a scenario where UMa3/U1 was accreted onto the Milky Way halo.

The M_V –r_h plane helps us visualize the traits typical of dwarf galaxies, globular clusters, and faint satellites whose nature remains ambiguous. We have reconstructed this space in Figure 9, where the classical globular clusters and Milky Way dwarf galaxies are taken from the same references as those for Figure 8, and the faint satellite measurements are compiled from literature. A full list of references can be found in the Appendix. UMa3/U1 is far fainter and smaller than any confirmed Milky Way dwarf galaxies, and lies in a size range occupied by faint, ambiguous satellites and globular clusters.

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As suggested by Willman & Strader (2012), taken in the context of the ΛCDM framework, dwarf galaxies reside in their own dark matter halos while globular clusters do not. Dynamical mass estimators (e.g., Wolf et al. 2010; Errani et al. 2018) rely on the intrinsic stellar velocity dispersion within a system, which can then be compared with the total stellar luminosity to yield a dynamical M/L. The faintest dwarf galaxies have been measured to have M/L in excess of 10³ M_⊙/L_⊙ (Simon 2019, and references therein) while globular clusters typically have M/L ∼2 (Baumgardt et al. 2020), consistent with strictly baryonic mass being present.

If UMa3/U1 is a star cluster, and is therefore composed solely of baryonic matter, then we can use the measured properties of total stellar mass and half-light radius to predict the line-of-sight velocity dispersion of its constituent stars using the mass estimator of Wolf et al. (2010):

$$\begin{eqnarray}&&{M}_{1/2}=930\cdot {\sigma }_{v}^{2}\cdot {r}_{{\rm{h}}}\,{M}_{\odot },\end{eqnarray} \tag{ 6 }$$

where σ_v is given in kilometers per second, r_h is given in parsecs, and M_1/2 is the mass enclosed within r_h. Solving for σ_v , we estimate σ_v ∼ 50 m s⁻¹.

However, in Section 3.5, we measured the intrinsic velocity dispersion to be 3.7 km s⁻¹ from 11 member stars. Now, given σ_v , we compute the dynamical M/L of UMa3/U1 by dividing Equation (6) by the luminosity enclosed within r_h, L_1/2, which is found by converting M_tot to L_tot using a baryonic M/L ∼1.4 and taking half the result. We carry out the calculation using a 10⁶-realization MC procedure to propagate measurement uncertainties, where each input quantity is modeled as a Gaussian distribution with a mean and standard deviation given by the values listed in Table 2. For quantities with uneven uncertainties, we adopt the larger of the two bounds. The dynamical M/L is measured to be ${6500}_{-4300}^{+9100}$ M_⊙/L_⊙, implying the presence of a massive dark matter halo, and that UMa3/U1 is a dwarf galaxy with astonishingly little stellar mass.

In Section 3.5, we already discussed how the presence of binary stars can inflate the measured dispersion, and we identified the member stars whose velocities and uncertainties appear to contribute most significantly to the estimated value of 3.7 km s⁻¹. The removal of star #2 from the membership list led to ${\sigma }_{v}={1.9}_{-1.1}^{+1.4}$ km s⁻¹, which translates to a dynamical M/L of ${1900}_{-1600}^{+4400}$ M_⊙/L_⊙. The volatility of the velocity dispersion with respect to the inclusion of certain candidate member stars makes it unclear as to whether it accurately represents the underlying gravitational potential of UMa3/U1.

Additionally, the use of the Wolf et al. (2010) mass estimator assumes that the system being assessed is in dynamical equilibrium. The orbit of UMa3/U1 has a pericenter of ${12.8}_{-0.8}^{+0.7}$ kpc and passes through the disk around 16 kpc from the Galactic center, where the stellar mass density is ∼1/50 of that at the solar neighborhood (Lian et al. 2022). It may be the case that repeated interactions with the outer Milky Way disk have led to tidal stripping, which could mean that some of the stars identified as members are in the midst of being stripped and have become unbound. If some of the stars that are actively becoming unbound have been observed as part of our spectroscopic follow-ups, their velocities would not be indicative of the gravitational potential underlying UMa3/U1. This could lead to an inflation of the measured velocity dispersion and a subsequent overestimation of the dynamical M/L. We investigate the Keck/DEIMOS velocity data by searching for a velocity gradient along the major axis of UMa3/U1, but no clear gradient is visible. We also might expect that stars in the outskirts would be unbound if there is active stripping, which could give them higher velocities relative to the mean. We rerun the velocity dispersion MCMC estimation algorithm, where we remove the three member stars that are most distant from the centroid (stars #1, #4, and #7). However, this leads to a slight increase in the intrinsic velocity dispersion, giving ${\sigma }_{v}={4.4}_{-1.3}^{+1.9}$ km s⁻¹, implying that outer stars are not wholly responsible for the well-resolved velocity dispersion. Using these probes of a velocity gradient and outer stars, we do not find clear signs of unbound stars.

While the measured velocity dispersion of ${\sigma }_{v}={3.7}_{-1.0}^{+1.4}$ km s⁻¹ may be tracing a massive dark matter halo, we emphasize that the presence of binary stars and unbound stars could impact the interpretation of σ_v as a direct indicator of dark matter. Multi-epoch spectroscopic data taken over a sufficiently long time baseline will be particularly crucial for identifying binary stars and assessing the dark matter content of UMa3/U1.

Focused dynamical modeling of the evolution of UMa3/U1 in the Milky Way halo may provide further clues as to whether this faint, tiny system is a dwarf galaxy or a star cluster. "Microgalaxies" and dwarf galaxies embedded in cuspy dark matter halos are predicted to be rather resilient to tidal disruption (Errani & Peñarrubia 2020; Errani et al. 2022) and the very existence of UMa3/U1 may place constraints on various dark matter models (Errani et al. 2023a). We refer the reader to work by Errani et al. (2023b) for a detailed analysis of UMa3/U1 and the implications of its survival in the Milky Way halo.