Ursa Major III/UNIONS 1: The Darkest Galaxy Ever Discovered?

The recently discovered stellar system Ursa Major III/UNIONS 1 (UMa3/U1) is the faintest known Milky Way satellite to date. With a stellar mass of 16−5+6M⊙ and a half-light radius of 3 ± 1 pc, it is either the darkest galaxy ever discovered or the faintest self-gravitating star cluster known to orbit the Galaxy. Its line-of-sight velocity dispersion suggests the presence of dark matter, although current measurements are inconclusive because of the unknown contribution to the dispersion of potential binary stars. We use N-body simulations to show that, if self-gravitating, the system could not survive in the Milky Way tidal field for much longer than a single orbit (roughly 0.4 Gyr), which strongly suggests that the system is stabilized by the presence of large amounts of dark matter. If UMa3/U1 formed at the center of a ∼109 M ⊙ cuspy LCDM halo, its velocity dispersion would be predicted to be of order ∼1 km s−1. This is roughly consistent with the current estimate, which, neglecting binaries, places σ los in the range 1–4 km s−1. Because of its dense cusp, such a halo should be able to survive the Milky Way tidal field, keeping UMa3/U1 relatively unscathed until the present time. This implies that UMa3/U1 is plausibly the faintest and densest dwarf galaxy satellite of the Milky Way, with important implications for alternative dark matter models and for the minimum halo mass threshold for luminous galaxy formation in the LCDM cosmology. Our results call for multi-epoch high-resolution spectroscopic follow-up to confirm the dark matter content of this extraordinary system.


Introduction
Ultrafaint dwarf galaxies (UFDs) are stellar systems with  ★ < 10 5 M ⊙ , fainter than many globular clusters (GCs) but gravitationally bound by the presence of large amounts of dark matter.They constitute direct probes not only of the formation mechanisms that govern the extreme faint-end of the galaxy luminosity function, but also of the structure of low-mass dark matter halos and, indirectly, of the nature of dark matter (see, e.g., Bullock & Boylan-Kolchin 2017;Simon 2019;Sales et al. 2022, for recent reviews).
The overall abundance of UFDs reflects the number of low-mass dark matter halos able to harbor luminous galaxies, placing important constraints on models where the physical nature of dark matter leads to the suppression of low-mass halos, such as in "warm dark matter" (WDM; e.g.Bode et al. 2001;Lovell et al. 2014) or "fuzzy dark matter" (FDM; e.g.Hu et al. 2000) models.For cold dark matter (CDM) models, where the number of low-mass halos is expected to be overwhelmingly larger than the number of UFDs, the E-mail: errani@cmu.eduabundance of faint systems probes the mass threshold between halos that remain "dark" (starless) and those massive enough for luminous galaxy formation to proceed (Simon & Geha 2007;Ferrero et al. 2012;Peñarrubia et al. 2012;Fattahi et al. 2018).
This threshold is still being actively discussed, with some studies suggesting a relatively high virial1 halo mass threshold (∼10 9 M ⊙ ; Benitez-Llambay & Frenk 2020; Pereira-Wilson et al. 2023), determined primarily by the ability of hydrogen to cool in halos photoheated by the ambient UV background (Efstathiou 1992;Quinn et al. 1996;Gnedin 2000), and other studies arguing for a much lower mass threshold, in order to accommodate the sheer number of observed UFDs plus those still likely missing from our currently incomplete inventory of Milky Way satellites (e.g., Nadler et al. 2021, and references therein).
On the other hand, self-interacting dark matter (SIDM) or FDM models generally predict much lower dark matter densities, as a result of the inward energy transfer driven by self-interactions (SIDM - Colín et al. 2002;Zavala et al. 2013;Tulin & Yu 2018) or of the quantum pressure support arising from the uncertainty principle (FDM - Hu et al. 2000;Goodman 2000;Burkert 2020;Ferreira 2021).
Available data indicate that UFDs are, indeed, quite dense (see, e.g., Simon 2019;Battaglia & Nipoti 2022).This result has led recent SIDM modeling to consider much higher interaction cross sections than envisioned in earlier work (Silverman et al. 2023), in an attempt to reconcile observations with SIDM halos whose inner densities have been gravothermally enhanced by "core collapse" (Balberg et al. 2002;Nishikawa et al. 2020;Turner et al. 2021;Correa et al. 2022;Zeng et al. 2022Zeng et al. , 2023)).The same result places strong constraints on FDM models too, and suggests that earlier lower-mass bounds for ultra-light particles based on the "classical" dwarf spheroidal (dSphs) satellites of the Milky Way should be drastically revised (Safarzadeh & Spergel 2020).
Finally, UFDs are ideal laboratories for studying in unprecented detail the heavy element enrichment process driven by recurring episodes of star formation.Some of these galaxies are so faint and so metal poor that the abundance pattern of individual stars may well reveal the nucleosynthetic yields of individual Population III supernovae or other explosive stellar events in these chemically pristine systems (Frebel & Norris 2015;Hansen et al. 2017;Ji et al. 2019;Marshall et al. 2019).
These traits make UFDs highly valuable, and have given impetus to a number of specialized UFD searches using resolved stars in widefield photometric surveys.Because they are so faint, UFDs are elusive objects that barely stand out against the foreground of Galactic stars and the background of distant galaxies.
UFD candidates are typically identified by matched-filter techniques, which pinpoint clumps of old stars at a common distance (Koposov et al. 2008;Walsh et al. 2009;Martin et al. 2013;Drlica-Wagner et al. 2015).These clumps are then followed up with deeper photometry and spectroscopy to enable a full characterization of the system.When available, proper motions from the Gaia mission (Simon 2018;Pace & Li 2019;McConnachie & Venn 2020a,b;Li et al. 2021) can help to aid the discovery process, but at the expense of being applicable only to relatively nearby systems, given Gaia's relatively shallow depth compared to contemporary widefield, digital photometric surveys.
Distinguishing dark-matter-dominated UFDs from selfgravitating faint star clusters is the final, perhaps most difficult hurdle, one that can only be fully overcome by securing multiepoch line-of-sight velocities to test whether the system is a self-gravitating star cluster or a UFD bound by the presence of dark matter (Willman & Strader 2012).
For the faintest and most distant candidates, this is a most challenging task, given the few stars bright enough to obtain spectra for, the limited precision of the individual radial velocities, the uncertainties from low-number statistics (Laporte et al. 2019), and the possibility that binary stars may lead to inflated values of the velocity dispersion, confusing the interpretation (McConnachie & Côté 2010;Minor et al. 2010).
Although a few dozen candidate2 UFDs are currently known, with total luminosities in the range +1 >  V > −3 and sizes in the range 1 -20 pc (e.g.Muñoz et al. 2012;Balbinot et al. 2013;Torrealba et al. 2019;Mau et al. 2020;Cerny et al. 2023a,b), very few of those have been conclusively identified as dark-matter-dominated UFDs because of the difficulties listed above.
S+24 report a velocity dispersion for UMa3/U1 of  los = 3.7 + 1.4 −1.0 km s −1 on the basis of 11 likely member stars, which would imply a mass-to-light ratio of several thousands.The authors do, however, caution that the estimate of  los is very sensitive to the inclusion (or exclusion) of specific member stars: removing a single star (the largest outlier in velocity, perhaps a binary star) drops the estimate to  los = 1.9 + 1.4 −1.1 km s −1 .Removing a second outlier from the sample results in a formally unresolved velocity dispersion, consistent with the extremely small value expected if UMa3/U1 were a self-gravitating star cluster ( los ∼ 50 m/s).Should  los prove much higher than this value, it would imply that UMa3/U1 is the faintest, or "darkest", galaxy ever discovered.
Because of the sensitivity of the  los estimate to the two outliers, and because of the lack of repeat velocity measurements (needed to rule out the undue influence of binary stars), S+24 are unable to ascertain the true nature of UMa3/U1.It is clear, however, that regardless of its nature, this system is truly exceptional.
We present here a simple argument in favor of the interpretation of UMa3/U1 as a genuine dark-matter-dominated UFD.The argument relies on the fact that should UMa3/U1 be a self-gravitating star cluster lacking dark matter, its average density would be comparable to the mean density of the Galaxy at the pericenter of its orbit.As such, it could not survive long on its current orbit, which, given the short orbital time of UMa3/U1 around the Galaxy, seems extremely unlikely.
We elaborate on this idea in Sec. 2, where we use -body simulations to model the tidal evolution of UMa3/U1, under the assumption that it is a self-gravitating star cluster.In Sec. 3, we model UMa3/U1 as a dark-matter-dominated micro galaxy and show that its estimated velocity dispersion is consistent with that expected if UMa3/U1 inhabits a cuspy ∼10 9 M ⊙ CDM halo.Finally, we summarize and discuss our main conclusions in Sec. 4.

Self-Gravitating (SG) Model
Assuming that UMa3/U1 is a self-gravitating star cluster, we adopt a simple model where its density profile is approximated by a spherical exponential distribution, with a scale radius  ★ and a total stellar mass  ★ = 8  0  3 ★ .The 3D and 2D half-mass radii are related to the scale radius through  h ≈ 2.67  ★ and  h ≈ 2.02  ★ , respectively.Under the assumption of dynamical equilibrium, the line-of-sight velocity dispersion may be computed from the projected virial theorem (Amorisco & Evans 2012;Errani et al. 2018), Using the parameters estimated by S+24,  ★ = 16 + 6 −5 M ⊙ and  h = (3 ± 1) pc, we estimate, for the self-gravitating case, a line-of-sight velocity dispersion of The uncertainties above are estimated from a Monte Carlo sample, taking into account the asymmetric measurement uncertainties on  ★ and  h .Note that a velocity dispersion this small is well below what S+24 could measure, given their observational setup.
Confirming that the (virial) velocity dispersion of UMa3/U1 is indeed of the order of a few km s −1 , as suggested from the dispersion estimate of S+24 from the 10-and 11-member samples (see Sec. 1), would rule out conclusively and convincingly the possibility that this system is a self-gravitating star cluster.

N-body Models
We use -body simulations to analyze the evolution of the self-gravitating UMa3/U1 model described above in the Milky Way gravitational potential.With a total stellar mass of  ★ = 16 + 6 −5 M ⊙ , UMa3/U1 likely contains only a few dozen stars (S+24 estimate  ★ ∼ 21 + 6 −5 stars brighter than 23.5 mag).The system is therefore intrinsically collisional, giving rise to a complex internal dynamical evolution that depends on the initial stellar mass function, the fraction of binary stars, the number of potential stellar remnants like neutron stars and black holes, and the exact stochastic realization of the underlying distribution function.None of these initial properties are well understood for faint stellar systems.A full exploration of this parameter space is hence, at the present day, impractical at best.With these caveats in mind, we model in this section UMa3/U1 as a collisionless system, which should be enough to broadly illustrate the dynamical evolution of UMa3/U1 in the Milky Way potential.
The progenitor of UMa3/U1 is modeled as an -body realization of an exponential sphere with 10 6 particles with isotropic velocity dispersion, generated using the code described in Errani & Peñarrubia (2020), available online3.We explore models with initial masses in the range 16 ≤  ★ /M ⊙ ≤ 160.All models have the same initial (2D) halflight radius of  h = 3 pc.
The integration is performed using the particle mesh code superbox (Fellhauer et al. 2000).This code employs two cubic grids of 128 3 cells comoving with the -body model with resolutions of 0.04 pc and 0.4 pc, respectively, as well as a fixed 128 3 cell grid containing the entire simulation volume, with a lower resolution of ≈ 1.6 kpc.

Tidal Disruption Timescales
We begin by simply evolving the SG UMa3/U1 model forward from its observed present-day position and proper motions, as listed by S+24.Using the Schönrich et al. ( 2010) solar velocity with respect to the local standard of rest results in an orbit with a pericenter of  peri ≈ 13 kpc, and apocenter of  apo ≈ 30 kpc.The total bound mass is shown, as a function of time, in Figure 1, where the blue diamond symbol (along the vertical dotted line labeled "now") represents the present-day configuration of UMa3/U1.As is clear from this figure, the system fully disrupts in less than two radial orbital times (with  orb = 0.4 Gyr in the EP20 potential).This result holds for all orbits compatible with the observed position and velocity of UMa3/U1; see Appendix A. Note that all models, independently of their initial mass, fully disrupt within ∼0.6 Gyr from now, suggesting that if UMa3/U1 is a self-gravitating object, then we observe it at a very special point in time in its evolution.
The short survival time of the SG UMa3/U1 model is not surprising, for its mean density is comparable to the mean density of the Milky Way inside the pericenter of the orbit: where  peri ≈ 240 km s −1 (Huang et al. 2016;Eilers et al. 2019) is the circular velocity of the Milky Way at  peri .For comparison, the mean density of the SG UMa3/U1 model within its 3D half-light radius is where the quoted uncertainty takes into account the asymmetric measurement uncertainties on stellar mass  ★ and half-light radius.
To complete the analysis, we modify the initial mass of the SG UMa3/U1 model to ensure that it survives for a longer period of time on the same orbit, and adjust it to match, at present, the observed properties of UMa3/U1.The initial conditions are generated by first integrating the orbit backward in time.For the model to match today's properties after evolving for, say, 12 Gyr (i.e., ∼27 full orbits), it must have been substantially more massive/denser, as indicated by the red diamond symbol in Fig. 1.Tidal mass loss little affects the size of the bound remnant, so a model with a similar half-mass radius but an initial mass of ∼136 M ⊙ could, in principle, have been the progenitor of today's UMa3/U1.The evolution of this progenitor in the mass-radius plane is shown in Fig. 2.
The colored curves in Fig. 2 are fitted to disruption times measured in the simulations.As shown in Errani et al. (2023), on a given orbit, the disruption times depend mainly on the initial density contrast between progenitor and host, measured Still, all of these models disrupt fully in less than ∼0.6 Gyr from now.Given that stars in UMa3/U1 are likely ≳ 11 Gyr old (S+24), it would require quite the coincidence to discover UMa3/U1 just as we witness its final orbit around the Milky Way.

Tidal Debris
However unlikely the SG UMa3/U1 model might be, a robust prediction that may be scrutinized observationally is the presence of tidal debris along the orbit.Given the extremely low velocity dispersion of the progenitor, the debris should align along a thin stream, as depicted by the red dots in the top panel of Fig. 3.The particular realization shown in this figure corresponds to the 12 Gyr old progenitor identified by the red diamond in Fig. 1, but the configuration would be similar for other massive progenitors.Note that the -body model used here approximates UMa3/U1 as a collisionless system.The detailed stream properties will be affected by internal collisional processes, which in turn depend on the initial mass function, the fraction of binary stars, and the presence of dark stellar remnants (see, e.g.Spurzem & Kamlah 2023).
The bottom panel of Fig. 3 shows a close-up view of the present-day configuration of the simulated UMa3/U1 system, in Galactic coordinates.Because of the intrinsic faintness of the system, only a few individual stars are expected to trace the tidal tails outside the inner couple of arcminutes from the center of the system (the half-mass radius spans roughly 1 ′ at 10 kpc, the assumed distance of UMa3/U1; see S+24).
We may use those stars to test the possibility that the velocity dispersion estimate of UMa3/U1 might be artificially enhanced by the presence of stars in the process of being stripped from the system.We find that the line-of-sight velocity dispersion using all stars within 1, 2, 3, and 5 half-mass radii varies by less than ∼20 m s −1 from its average value of ∼60 m s −1 .In addition, the total line-of-sight velocity gradient across the galaxy is less than 25 m s −1 /arcmin, so that stars 6 ′ ahead or behind the main body of the remnant differ by less than 300 m s −1 on average, a value too small to be detectable with the line-of-sight velocities of S+24.These results are not unexpected, given the extremely low escape velocity of the SG UMa3/U1 model, which (assuming the exponential profile of Eq. 1) is only For comparison, all of the likely UMa3/U1 members with available velocity estimates identified by S+24 lie within 4  h from the center of UMa3/U1.
The velocity dispersion estimate in the SG model thus seems to depend only weakly on the radial extent over which stars are collected, and certainly does not approach in any case the few km/s estimated by S+24 using 10 or 11 likely members (and neglecting binaries).We conclude that the inclusion of weakly bound stars, or of stars stirred by the Galactic tidal field, cannot explain such a high velocity dispersion estimate.

Evaporation Timescales
In addition to external tidal forces, internal collisional processes may alter the structure and bound mass of a stellar system.This is especially true for a system with as few stars as UMa3/U1, which may "evaporate" due to collisions between stars in less than a Hubble time.Assuming, for simplicity, that all stars have the same mass of ∼0.25 M ⊙ , we find that UMa3/U1 has approximately  h ≈ 2  ★ /M ⊙ ≈ 32 stars within the half-light radius.For an isolated cluster, the relaxation time is related to the half-mass crossing time by (see e.g.Equation (2-62) in Spitzer 1987 and Equation (8-1) in Binney & Tremaine 1987): where  cross ≈ (  ★ /2 3 h ) −1/2 = (42 ± 22) Myr for  ★ = 16 M ⊙ and  h = 4 pc.The uncertainties quoted here are estimated by linear propagation of the measurement uncertainties.
A rough estimate of the evaporation time scale is then given by (see p. 491 in Binney & Tremaine 1987): evap ≈ 136  rel = (6.5 ± 3.4) Gyr . (7) This time scale is substantially longer than the time scale for full tidal disruption.Evaporation time estimates are shown as the dashed colored curves in Fig. 2. Collisional evaporation is thus unlikely to alter our main conclusion above: the short time to full tidal disruption clearly disfavors the suggestion that UMa3/U1 is a self-gravitating star cluster.

Dark-matter-dominated Model
The simplest alternative to explain the long-term survival of UMa3/U1 in the Galactic tidal field is that UMa3/U1 is embedded in a dark matter subhalo, which protects the stellar component from tidal forces.The presence of dark matter would lead to a much increased velocity dispersion compared with the self-gravitating case studied in the previous section.
As a definite example, we shall adopt below the 10-member dispersion estimate of  los = 1.9 + 1.4 −1.1 km s −1 reported by S+24, although we note again that this value may be revised once future observations enable a proper accounting of the effect of potential binary stars.We note as well that even a lower value of the velocity dispersion would qualify UMa3/U1 as a UFD, provided that it is substantially above the ∼50 m/s expected from the SG model.

Dynamical Mass Estimate
The velocity dispersion adopted above would imply a dynamical-to-stellar mass ratio comparable to the most heavily dark-matter-dominated dwarfs known to date.We show this los  −1 , vs. stellar mass,  ★ , for Local Group dwarf galaxies (squares) and GCs (circles).The dashed diagonal lines indicate dynamical-to-stellar mass ratios of Υ dyn = 1 and 1000, respectively (see Eq. 8 for the definition).GCs are distributed with little scatter around the Υ dyn = 1 line.Dwarf galaxies, whose dynamics are dominated by dark matter, lie well above that line.Taking its measured velocity dispersion at face value, UMa-3 is located well within the LCDM prediction (the purple rectangle, see Sec. 3.2), whereas the SG model explored in Sec. 2, by construction, falls exactly on the Υ dyn = 1 line.References for the data shown are listed in footnote 4. in Fig. 4, where we contrast UMa3/U1 with a compilation4 of dynamical and stellar masses of Local Group dwarf galaxies (squares) and GCs (circles) with measured kinematics.The diagonal dashed curves correspond to constant dynamical-tostellar mass ratios, approximated by In the above equation, we estimate the dynamical mass  dyn (<  h ) enclosed within the 3D half-light radius  h from the combined measurement of the line-of-sight velocity dispersion  los and 2D half-light radius  h , with the coefficient5 as in

r e m n a n t i n i t i a l
Figure 5. Mean density, ρh , enclosed within the 3D half-light radius,  h , for Local Group dwarf galaxies (squares) and GCs (filled circles), compared with UMa3/U1.The diamond labeled "U1" shows the mean density expected if UMa3/U1 is a fully self-gravitating stellar system without dark matter.
The upper diamond labelled "UMa3"' corresponds to adopting the measured velocity dispersion of 1.9 km s −1 .A gray band shows the mean enclosed densities as a function of radius for LCDM (NFW) halos considered sufficiently massive to allow stars to form, taking into account the expected scatter in concentration (see the text for details).An example halo (labeled "initial") with a virial mass of  =2 cr ≈ 9.5 × 10 8  ⊙ , corresponding to the  = 2 hydrogen-cooling critical mass with average concentration, is shown in black.The dashed curve illustrates the "tidal track" tracing the evolution of the characteristic density ρmx = ρ(<  mx ) and size  mx of an NFW halo as it is stripped by tides, with the black circles highlighting the initial and asymptotic values.The lower black curve corresponds to the asymptotic remnant of the "initial" model placed on the UMa3/U1 orbit.mass  ★ is approximated assuming a stellar mass-to-light ratio of  ★ / V ≈ 1.6 (as in Woo et al. 2008 for galaxies with old stellar populations).Self-gravitating star clusters follow closely a line with constant dynamical-to-stellar mass ratio labeled Υ dyn = 1, whereas dwarfs are clearly offset to much higher values of the dynamical-to-stellar mass ratio.
The blue diamond at the bottom left corner shows where UMa3/U1 would be located if it was a faint GC akin to the SG model explored earlier (in which case it would be called "UNIONS 1", or U1, for short).The other blue diamond labeled "UMa3" corresponds to adopting the 10-star dispersion  los = 1.9 + 1.4 −1.1 km s −1 , resulting in a dynamical-to-stellar mass ratio of Υ dyn = 1.2 + 2.8 −1.0 × 10 3 .In this case, UMa3 sits comfortably close to the dwarf galaxy trend, extrapolated to extremely low stellar masses (i.e., extremely faint luminosities).
Assuming hereafter that UMa3/U1 is a dwarf galaxy (in which case it would simply be called "Ursa Major III" or UMa3, for short), we examine next whether it would be expected to survive the strong Galactic tidal field.We begin by comparing in Fig. 5 the mean density of the system within its half-mass radius, ρh , with ρperi , the mean density of the Galaxy at the pericenter of the orbit, shown by a horizontal dotted line segment.As discussed earlier, the "U1" symbol indicates that UMa3/U1's density would be comparable to ρperi (and thus doomed to rapid tidal disruption) if it was a self-gravitating cluster.
We estimate the density of UMa3 by computing the dynamical mass enclosed within its 3D half-light radius using (see footnote 5) and dividing by the volume of a sphere of radius  h = (4/3)  h .
If  los = 1.9 which is roughly ∼1000 times higher than the density of the SG model, and thus safe from tidal disruption.As shown by the blue diamond labeled "UMa3" in Fig. 5, the mean density of UMa3 would in that case be comparable to that of some GCs, many of which are known to orbit the Galaxy on orbits with pericenters as small as or smaller than 13 kpc.
The mean density computed above would make UMa3 not only the faintest and smallest, but also the densest UFD ever detected, with important implications for both the mass of the CDM halo inhabited by UMa3 and for alternative models of dark matter.We address these issues next.

LCDM Expectations
In LCDM, galaxies form deep within the potential wells of dark matter halos (White & Rees 1978).The ability of hydrogen gas to cool efficiently in the presence of the cosmic UV background is expected to impose a minimum critical halo mass below which LCDM halos are not expected to be able to host luminous galaxies.
Benitez-Llambay & Frenk (2020) argue that, after reionization, the critical virial mass needed to enable star formation to proceed evolves with redshift  roughly as using a virial temperature of  = 2 × 10 4 K.At redshift  = 0, the resulting critical mass equals  =0 cr ≈ 4.9 × 10 9 M ⊙ .At earlier redshifts, the critical mass was somewhat lower.The best-fitting isochrone for U1/UMa3 corresponds to a stellar age of ≳ 11 Gyr (S+24).Assuming Planck Collaboration et al. (2020) cosmological parameters, this corresponds roughly to a redshift of  ∼ 2, which we shall adopt in what follows.
The cosmological simulations analyzed by Pereira-Wilson et al. (2023) confirm that stars first form in halos exceeding the critical mass given by Eq. 11.We use their Figure 7 to estimate a range of halo masses for the potential progenitor halo of UMa3 (up to 0.5 dex above  cr ) .Combining this with the  = 2 average NFW concentration (±0.15 dex scatter) from Ludlow et al. (2016), we obtain a range of mass profiles for UMa3, which we show as a gray band in Fig. 5.The mean density profile of a halo with virial mass  =2 cr ≈ 9.5×10 8 M ⊙ is shown as a solid black curve within the gray band.
Fig. 5 shows that UMa3's mass density is (for the assumed  los ) comfortably within the range expected for a galaxy inhabiting a cuspy NFW halo with mass close to critical.Less massive NFW halos are less dense at all radii, and would therefore have difficulty matching UMa3's estimated density.For example, an LCDM "minihalo" with virial mass 106 M ⊙ at  = 0 would have a mean density of ≈ 1.2 × 10 9 M ⊙ kpc −3 at  ∼ 4 pc, well below UMa3.
The high dark matter density estimated for UMa3 thus disfavors the possibility that it may have formed at the center of a minihalo and supports the view that luminous galaxies, no matter how faint, only form in halos near or above the critical virial mass of Benitez-Llambay & Frenk (2020).
If UMa3 is indeed a "micro galaxy" (EP20) at the center of a cuspy NFW halo, we may use the results of EN21 and Errani et al. (2022) to predict its evolution under the influence of the Galactic tidal field6.The main result of their study is that tides gradually strip a halo, approaching an asymptotic state where the characteristic density of the bound remnant equals roughly 16 × ρperi .The subhalo characteristic density evolves following a well-defined "tidal track" (Peñarrubia et al. 2008) until the asymptotic characteristic density has been reached.The bound remnant is well approximated by an "exponentially truncated" NFW profile (see Errani & Navarro 2021, for details).
The initial density profile of a halo of critical mass  =2 cr , is shown by the solid black curve in Fig. 5, labeled "initial".This halo has a circular velocity that peaks at  mx = 23 km s −1 at a radius  mx = 3.0 kpc.Its characteristic mean density at  mx equals ρmx = 3.3 × 10 6 M ⊙ kpc −3 , shown as a black circle in Fig. 5.The tidal track is shown by the dashed black curve, which stops once the asymptotic remnant density of ρmx ≈ 16 × ρperi has been reached.An exponentially truncated NFW profile (the black curve labeled "asy.remnant") illustrates the final density profile of that halo on this orbit.
We emphasize that the asymptotic remnant properties depend on those of the initial NFW halo adopted.Choosing an initial halo with a higher characteristic initial density would lead to an asymptotic remnant whose mean density, at  = 4 pc, is higher.It is clear from Fig. 5 that although Galactic tides are expected to reduce the central dark matter density of a cuspy halo, a well-characterized bound remnant is predicted to survive, whose density at radii as small as 4 pc may be as high as ∼10 10 M ⊙ /kpc 3 .
The full range of dynamical masses and densities expected at that radius in LCDM (varying halo mass and concentration) is shown by the purple curves labeled "LCDM" in Fig. 4 and Fig. 5, respectively.The corresponding range of velocity dispersions is 0.16 ≲  los /km s −1 ≲ 1.5, which is compatible with the current 10-member dispersion estimate of  los = 1.9 + 1.4 −1.1 km s −1 (S+24).We conclude that UMa3's properties are consistent with those expected from a micro galaxy deeply embedded at the center of a fairly massive, cuspy LCDM halo.

Consequences for Alternative Dark Matter Models
Although consistent with LCDM, the extreme properties of UMa3 inferred assuming that the 10-member velocity dispersion measurement holds ( los = 1.9 + 1.4 −1.1 km s −1 ) would be difficult to reconcile with alternative dark matter models that predict lower dark matter densities.
We begin by discussing UFDs in FDM models, where the density of a dark-matter-dominated UFD is thought to reflect the central density of the "solitonic core" that forms at the center of a halo made up of ultralight particles (Schive et al. 2014a,b;Safarzadeh & Spergel 2020).Cosmological simulations of FDM halo formation find that the central density of the core, at redshift  = 0, is given by (using Equation 3 and Equation 7in Schive et al. 2014b) where   is the mass of the ultralight particle, and  halo is a measure of the halo virial mass7.
Attempts to fit the density profile of the "classical" dwarf spheroidal satellites of the Milky Way (like Fornax or Sculptor) with a solitonic core yield upper limits for   of order 10 −22 eV/c 2 (Marsh & Pop 2015;González-Morales et al. 2017).This is mainly because the mean densities of Fornax and Sculptor are of order 107 -10 8 M ⊙ kpc −3 , consistent with Eq. 12 for  halo ∼ 10 10 M ⊙ and   ∼ 10 −22 eV/c 2 .
Achieving a density as high as that estimated for UMa3 (i.e., ∼4 × 10 10 M ⊙ kpc −3 , see Eq. 10) would require the ultralight particle mass to be as large as   ∼ 3 × 10 −21 eV/c 2 (or a halo mass as large as  halo ∼ 10 12 M ⊙ , which seems rather unlikely).This choice, however, would deny the main motivation for FDM: that the presumed kpc-scale cores in dwarf galaxies suggested by some studies reflect the de Broglie wavelength of the ultralight particle (Goodman 2000;Hu et al. 2000;Hui et al. 2017;Ferreira 2021).Reconciling FDM with the high densities of observed UFDs has already been recognized as a difficult challenge to traditional FDM models (Burkert 2020;Safarzadeh & Spergel 2020), a challenge that would become much more severe if the high density of UMa3 is confirmed by future velocity dispersion measurements.
Finally, the estimated high density of UMa3 is also difficult to accommodate with the kpc-size cores expected in self-interacting dark matter models, at least for interaction cross sections of order 1 cm 2 g −1 (see; e.g., Tulin & Yu 2018, and references therein).For this choice, collisions between particles erase the central cusp of a dark matter halo, creating a core with constant density that, on the scale of dwarf galaxies, does not exceed a few times 10 8 M ⊙ kpc −3 (Zavala et al. 2013;Vogelsberger et al. 2014).Matching the high density of UMa3 (and, indeed, of other UFDs) would require gravothermal "core collapse" to occur, raising the innermost dark matter densities to values as large as those predicted for cuspy LCDM halos, and observed in UFDs (see, e.g.Hayashi et al. 2021;Silverman et al. 2023).
The timescale for core collapse, however, likely exceeds the age of the Universe for SIDM models with velocityindependent interaction cross sections (Zeng et al. 2022; though some authors argue that the core collapse timescales may be shortened considerably by tidal effects, see Nishikawa et al. 2020).Further work is clearly needed to reconcile SIDM models with the high densities of UFDs in general, and of UMa3 in particular, should the current density estimate prove robust to binary stars.

Annihilation Signals
The remarkably high density of ρh ∼ 4 × 10 10 M ⊙ kpc −3 (Eq.10) combined with the heliocentric distance of only (10 ± 1) kpc (S+24) render UMa3/U1 an interesting target for the study of potential signals of dark matter self-annihilation.The astrophysical component to the annihilation signal for velocity-independent annihiliation may be expressed through the -factor (see, e.g.Walker et al. 2011), which for stellar tracers embedded in an NFW subhalo can be estimated from (see Equation 13in Evans et al. 2016) In the above equation, the integral is performed along the line of sight  over a solid angle ΔΩ, and ,  h , and  los are the heliocentric distance, projected half-light radius, and line-ofsight velocity dispersion of UMa3/U1, respectively.The angle  limits the solid angle over which the integral is computed, and is chosen here to match the Fermi Large Area Telescope resolution at GeV scales,  = 0 • .5 (Ackermann et al. 2014).
The -factor of ∼10 21 GeV 2 /c 4 /cm 5 computed in Eq. 13 takes the measured properties of UMa3/U1 at face value.Monte-Carlo sampling of measurement uncertainties yields a 16 th -84 th percentile range of 10 19 ≲ /(GeV 2 /c 4 /cm 5 ) ≲ 10 22 for the underlying distribution.Even when taking these large uncertainties into account, UMa3/U1 would be one of the "brightest" satellites of the Milky Way for potential annihilation signals, matching or exceeding the expected signal of all other known Milky Way dwarf spheroidal and ultrafaint satellites (see Table A2 in Pace & Strigari 2019).

Summary and Conclusions
Ursa Major III/UNIONS 1 (UMa3/U1) is a recently discovered satellite of the Milky Way whose extreme properties offer unique insights into the formation process of some of the faintest objects in the Universe.It is by far the faintest satellite ever discovered: at  V ≈ +2.2, it is ∼10 times fainter than the faintest confirmed ultrafaint dwarfs, and ∼10 times fainter than the least luminous globular cluster.It is also as small as some of the most compact GCs, with a projected half-mass radius of only ∼3 pc.
Taken at face value, the line-of-sight velocity dispersion computed from the radial velocities of 10 or 11 likely members suggests the presence of dark matter (which would confirm that UMa3/U1 is indeed a dwarf galaxy).However, the lack of repeat velocity measurements and the strong dependence of the measured dispersion on the inclusion of two specific member stars leave open the possibility that UMa3/U1 is actually a self-gravitating faint cluster of stars.
The main conclusions of our work are summarized below.
(1) The orbit of the system around the Milky Way is well characterized, with a pericentric distance of only ≈ 13 kpc, an apocentric distance of ≈ 30 kpc, and a radial orbital time of ≈ 0.4 Gyr.We use N-body simulations to show that, taken its observed size and stellar mass at face value, UMa3/U1 cannot survive for much longer than a single orbit if self-gravitating.Either UMa3/U1 is a GC remnant observed at a remarkably fine-tuned point in time, or it is indeed a galaxy that has survived tidal disruption because of the stabilizing effect of dark matter.
(2) The simulations do rule out the possibility that "tidal stirring" may have enhanced the observed  los to values as high as a few km/s.The models predict that, if self-gravitating, UMa3/U1 should be surrounded by a stream of tidally stripped stars, that should be searched for with high priority.
We conclude that (1) and ( 2) strongly support the view that UMa3/U1 is a dark matter-dominated "micro galaxy", indeed the faintest, or "darkest", galaxy ever discovered.
(3) If the  los = 1.9 + 1.4 −1.1 km s −1 estimated using the 10 mostlikely member stars is correct, then the mean dark matter density for UMa3/U1 would be ≈ 4 × 10 10 M ⊙ kpc −3 within its 3D half-light radius of ∼4 pc.This makes UMa3/U1 the densest ultra-faint galaxy known, a result that suggests that UMa3/U1 formed at the very center of a fairly massive (∼10 9 -10 10 M ⊙ ) cuspy cold dark matter halo, whose innermost regions should be able to survive the strong tidal field of the Galaxy for a Hubble time.This in turn implies a relatively high halo mass threshold for luminous galaxy formation in LCDM, as advocated by the "critical" mass model of Benitez-Llambay & Frenk (2020).
(4) If confirmed, the high dark matter density estimated for UMa3/U1 would have strong implications for alternative dark matter models.In the case of "fuzzy dark matter" (FDM), identifying it with the central density of the "solitonic core" yields an estimate for the mass of the ultra-light particle of ∼3 × 10 −21 eV, more than one order of magnitude higher than the 10 −22 eV upper limits inferred in previous work (Marsh & Pop 2015;González-Morales et al. 2017).This inconsistency casts doubt on the ground motivation for FDM models, which, if confirmed, would require a re-evaluation of the model.
(5) Such a high dark matter density would also place strong constraints on SIDM models, where the dense halo cusps are eroded by collisional effects, leading to a substantial reduction of the dark matter central densities compared to LCDM.In the context of SIDM, UMa3/U1's central density can only be reproduced in systems that have undergone gravothermal "core collapse", placing stringent constraints on the allowed values of the collisional cross section.
Our models show that accurate and extremely precise dispersion estimates are crucial to differentiating between UMa3/U1 being a dark-matter-dominated "micro galaxy", or an extremely faint self-gravitating star cluster.If the current estimate of UMa3's dynamical density is confirmed by future observations, it would not only confirm UMa3 as the "darkest" galaxy discovered to date, but it would also highlight that the predictions of LCDM seem to hold down to the faintest end of the galaxy luminosity function.position and velocity of UMa3/U1 at face value, while the dotted and dashed curves show orbits representative for the 16 th and 84 th percentile of the underlying distribution.
For each of the orbits shown in the top panel of Fig. 6, we evolve an -body model of UMa3/U1 forward in time, using the same setup as in Sec. 2. The initial stellar mass and half-light radius are chosen to match the currently observed values of  ★ = 16 M ⊙ and  h = 3 pc.We show the evolution of the bound mass for each of these -body models in the bottom panel of Figure 6.All models disrupt within the next few pericenter passages, showing that the results of Sec. 2 are fairly insensitive to the choice of the Milky Way potential, and fairly robust within the estimated uncertainties of the observed position and velocity of UMa3/U1.

B. Supplementary Dark-matter-only N-body Simulations
In Sec. 3, we discuss the observable consequences for a scenario where UMa3/U1 is embedded in a dark matter subhalo.Our analysis makes use of the empirical findings of EN21, which suggest that tidally stripped NFW halos converge towards a stable asymptotic remnant state, where the A black solid curve shows the evolution computed using the EN21 model, while the blue and red curves correspond to  -body models evolved in an axisymmetric and a spherical host potential, respectively.The gray shaded area shows the parameter space where the  -body models are likely affected by insufficient particle numbers (  mx ≤ 3000) and/or spatial resolution ( mx ≤ 8Δ).Both  -body models disrupt artificially after ≈ 5 Gyr, whereas the EN21 model predicts an evolution toward a stable remnant state.
characteristic density of the subhalo is determined by the mean density of the host at pericenter.The model of EN21 assumes a spherical, isothermal host potential.The combined mass distribution of the halo, the bulge and the disk in the inner regions of the Milky Way is not spherical, however, but more appropriately approximated by an axisymmetric model.Using -body simulations, we now aim to test to what extent the tidal evolution of a dark matter subhalo on the orbit of UMa3/U1 depends on the geometry of the underlying potential.We place two NFW -body subhalo models on orbits with pericenter and apocenter matching those of UMa3/U1, and evolve these models in (1) the axisymmetric EP20 potential and (2) a spherical isothermal potential with a constant circular velocity of  c = 240 km s −1 .The -body subhalo models are chosen to have initial properties identical to those of the  = 2 hydrogen cooling limit (HCL) halo of Fig. 5, and  = 10 7 particles.We generate the models using the same code as in Sec. 2 (see footnote 3), and evolve the models using the particle mesh code superbox (Fellhauer et al. 2000), adopting a spatial resolution of Δ ≈ 20 pc for the highest-resolving grid.
The results of the experiment are shown in Fig. 7, where we confront the time evolution of the subhalo structural parameters  mx ,  mx measured in the two -body models against those computed using the EN21 model.For the first ∼2 Gyr of tidal evolution, both -body models are in good agreement with EN21.The gray shaded area in Fig. 7 shows the region of parameter space where the number of -body particles ( mx ≤ 3000) and/or the spatial resolution of the simulation ( mx ≤ 8Δ) are insufficient to reliably model the tidal evolution of the subhalo (see Appendix A in EN21 for a convergence study).Indeed, in the gray shaded region, the evolution of the body models diverges from the EN21 track, and both models artificially disrupt after ∼5 Gyr of evolution.The EN21 model instead predicts an evolution toward a stable remnant state.The filled circles along the evolutionary track are spaced by 1 Gyr, and show that the remnant state is approached asymptotically, with tidal evolution gradually slowing down as the remnant state is approached.
Remarkably, the tidal evolution of the -body model evolved in the axisymmetric potential is near identical to the one evolved in the spherical potential.For the orbit of UMa3/U1, the detailed shape of the potential hence seems to have negligible impact on the tidal evolution of a dark matter subhalo.

Figure 1 .
Figure1.Mass evolution of self-gravitating (SG)  -body models for the UMa3/U1 stellar system.All models have an initial (2D) half-light radius of  h = 3 pc.A blue band shows the 1- measurement uncertainty around the current mass of UMa3/U1.The evolution of an example model with initial mass  ★ = 136 M ⊙ (the red diamond symbol) is highlighted in black.Note that all models, independently of their initial mass, fully disrupt within ∼0.6 Gyr from now, suggesting that if UMa3/U1 is a self-gravitating object, then we observe it at a very special point in time in its evolution.

Figure 2 .
Figure 2. The same as Fig. 1, but for the tidal evolution in the mass-size plane.Numerical estimates of the tidal disruption ( dis ) and evaporation ( eva , Eq. 7) timescales are shown by the solid and dashed colored curves, respectively.The present-day mass and size of UMa3/U1 are shown as the blue diamond with 1  error bars.A gray curve shows the evolution of the example model highlighted in Fig. 1.

Figure 3 .
Figure 3. Top panel: orbit of UMa3/U1 in Galactic coordinates.The red points show a Monte Carlo sample of stripped stars drawn from the  -body model highlighted in Fig. 1.Bottom panel: surface density map of the self-gravitating (SG) model (grayscale).The orbit is shown using a dotted curve, with an arrow indicating the direction of motion along the orbit.

Figure 4 .
Figure 4. Dynamical mass,  h  2los  −1 , vs. stellar mass,  ★ , for Local Group dwarf galaxies (squares) and GCs (circles).The dashed diagonal lines indicate dynamical-to-stellar mass ratios of Υ dyn = 1 and 1000, respectively (see Eq. 8 for the definition).GCs are distributed with little scatter around the Υ dyn = 1 line.Dwarf galaxies, whose dynamics are dominated by dark matter, lie well above that line.Taking its measured velocity dispersion at face value, UMa-3 is located well within the LCDM prediction (the purple rectangle, see Sec. 3.2), whereas the SG model explored in Sec. 2, by construction, falls exactly on the Υ dyn = 1 line.References for the data shown are listed in footnote 4.

Figure 6 .
Figure6.Top panel: galactocentric distance of UMa3/U1 as a function of time, obtained by forward integrating orbits in the EP20 (black curves) and (Bovy 2015, red curves) potentials.The solid curves take the current position and velocity of UMa3/U1 at face value.The dotted and dashed lines correspond to orbits representative of the 16 th and 84 th percentiles of the underlying distribution of measurement uncertainties.Bottom panel: the evolution of the bound mass of self-gravitating (SG)  -body models evolved on the orbits shown above.In all cases, the SG models disrupt within a few pericenter passages.

Figure 7 .
Figure 7. Tidal evolution of characteristic size  mx and velocity  mx for an NFW subhalo on the orbit of UMa3/U1.The initial values ( mx0 = 3 kpc,  mx0 = 23 km s −1 ) are identical to the subhalo model discussed in Sec.3.A black solid curve shows the evolution computed using the EN21 model, while the blue and red curves correspond to  -body models evolved in an axisymmetric and a spherical host potential, respectively.The gray shaded area shows the parameter space where the  -body models are likely affected by insufficient particle numbers (  mx ≤ 3000) and/or spatial resolution ( mx ≤ 8Δ).Both  -body models disrupt artificially after ≈ 5 Gyr, whereas the EN21 model predicts an evolution toward a stable remnant state.