Searching for correlations in GAIA DR2 unbound star trajectories

• In the PBH cold dark matter scenario, close encounters could eject stars from dwarf galaxies at hundreds to thousands of km/s, with HVS trajectories pointing back to their source dwarf spheroidal galaxy.Some high-velocity stars in globular-cluster cores may also exceed escape velocity.Source: §1 · p. 1
• The study develops a Bayesian framework to search for close encounters by correlating Gaia DR2 stellar trajectories with those of dwarf and nearby galaxies and globular clusters.Source: §1 · p. 1
• The search focuses on likely recent events in Milky Way dwarf galaxies, where the authors expect the most massive dwarfs to be more likely sources, but Gaia’s accurate six-dimensional measurements are limited to stars relatively near the Sun, up to about 13 kpc.Source: §1 · p. 2
• The authors analyze candidate stars’ Hertzsprung–Russell diagram positions to check whether their evolutionary status is consistent with travel over large distances.Source: §1 · p. 2

2.1 Hyper-velocity stars

• The HVS selection is cleaned using a velocity threshold and removal of potentially spurious radial velocities, with additional astrometric-quality criteria.The velocity criterion is v − σv ≳ 500 km/s; the supplied selection also specifies astrometric cuts.Source: §2.1 · p. 2
• The final HVS selection contains 1,649 stars, with unbound-probability, color, magnitude, and astrometric-quality cuts applied to a larger Gaia DR2 selection.The initial catalog contains 7,183,262 stars; the final selection uses Pub > 0.5 and further quality cuts.Source: §2.1 · p. 2
• The study compares Marchetti et al. (2019) and Anders et al. (2019) distances because the former omit parallax systematic errors and can overestimate distant-star distances.For distant stars, Marchetti et al. estimates are about twice the Anders et al. estimates on average.Source: §2.1 · p. 2

2.2 Globular clusters and galaxies

• The comparison sample includes 52 globular clusters with full phase-space and radius measurements and 35 galaxies with matched positions, sizes, and motions.Source: §2.2 · p. 3
• The selected globular clusters and galaxies span varied Galactocentric positions and sizes, from globular-cluster radii of tens to hundreds of parsecs to Andromeda’s roughly 23 kpc major semi-axis.Most galaxies lie farther away than the HVS selection; Sagittarius is the largest object within the farthest-HVS distance.Source: §2.2 · p. 4, Figure 5 · p. 4

3.1 Trajectories

• Orbits are integrated in a four-component Milky Way potential, with trajectories traced back 100 Myr for globular clusters and 1 Gyr for galaxies.Large, distant objects use 100 kyr resolution and are integrated up to 5 Gyr; the adopted parameters match Marchetti et al. (2019).Source: §3.1 · p. 4, Table 1 · p. 5

3.2 Impact parameter

• A star is compatible with scattering when its impact parameter θ falls within the relevant range: θ ≲1 for globular clusters and θ ≲10 for galaxies.The broader galaxy threshold accounts for uncertain size proxies and dwarf-galaxy ellipticity.Source: §3.2 · p. 5

3.3 Likelihoods

• Trajectory likelihoods are sampled from the measured parameter distributions, using at least 1,000 draws per star–system pair to recover Bayes factors at the O(1%) level.The method neglects right-ascension and declination errors for computational convenience, and uses a log-normal radius distribution where appropriate.Source: §3.3 · p. 5

3.4 Hypothesis testing

• The hypothesis test compares trajectory intersection with no intersection by integrating the impact-parameter likelihood under a flat prior and varying its upper threshold θ∗.The lower threshold θ0 represents the smallest expected scattering distance; the authors note that conclusions depend on prior choice.Source: §3.4 · p. 6
• The analytical CDF approximation differs from empirical Bayes factors by about 10% for likelihoods peaked in the relevant θ range, and within 5% for objects with K ≳1.The likelihoods are fit with skew log-normal distributions for θ ≲10.Source: §3.3 · p. 5, §3.4 · p. 6

4 RESULTS

• The search varies the lower prior threshold θ0 and upper threshold θ*; K > 1 indicates compatibility with an interaction with the object.The θ0 choices encode the assumption that scattering is unlikely in an object’s innermost region.Source: §4 · pp. 6–7
• Figure 7 shows likelihood-weighted sampled orbits with markers for present-day positions; distance uncertainty spreads trajectories radially, and paths after the encounter are unreliable.The authors state that post-encounter trajectories are not needed for their analysis.Source: Figure 7 · p. 7, §4 · p. 7
• With Marchetti et al. (2019) distances and θ0=0.36, two Sagittarius dSph stars are scattering candidates from 20–40 Myr ago, with the Bayes factor peaking near θ*=1.At θ0=0, no candidate events are found.Source: §4 · p. 7
• The candidate stars’ HR-diagram positions imply an age lower bound of about 100 Myr, compatible with the proposed scattering times.The analysis derives effective temperatures and bolometric luminosities and compares them with theoretical isochrones and evolutionary tracks.Source: §4 · p. 7
• Positive evidence is not confirmed when using Anders et al. (2019) distances.The authors note that a prior based on Sagittarius dSph’s three-dimensional dark-matter distribution is difficult to model given its strong tidal disruption.Source: §4 · p. 7

5 CONCLUSIONS

• Two stars are candidate Sagittarius dSph scattering events 20–40 Myr ago with Marchetti et al. (2019) distances; their ages are compatible with the events, with a lower bound of about 100 Myr.The result is not confirmed using Anders et al. (2019) distances.Source: §5 · p. 7
• The reported events may reflect PBH dark-matter scattering, but the small sample and uncertain PBH mass distribution prevent meaningful limits.Source: §5 · p. 7
• A follow-up focused on Sagittarius should model its actual shape, dark-matter distribution, and time evolution rather than use a spherical proxy.The current impact parameter uses radius as a proxy for object shape and dark-matter distribution.Source: §5 · p. 7
• Results depend strongly on distance methodology; Marchetti et al. (2019) distances are often larger, while parallax systematics call for confirmation with more accurate estimates.Source: §5 · pp. 7–8
• Future Gaia releases can improve phase-space coverage and systematic-error control; extending the search can test whether other large galaxies, such as the LMC, show comparable candidate interactions.Source: §5 · p. 8
• HVS trajectories compatible with extragalactic origins may also guide searches for faint, low-surface-brightness dwarf galaxies.Source: §5 · p. 8

APPENDIX A: ALTERNATIVE STELLAR SELECTION

• The alternative selection contains 1,747 stars meeting velocity and radial-velocity cuts but uses an unbound-probability threshold above 0.9 without further photometric or astrometric cuts.Most have negative parallaxes, indicating poor data quality.Source: Appendix A · pp. 9–10
• At θ0 = 0, two stars are compatible with Sagittarius dSph encounters 10–30 Myr ago; at θ0 = 0.36, three have positive evidence, with maximum Bayes factors K ∼ 2 and 10 for two stars.All candidate stars are compatible with being at least about 80 Myr old.Source: Figure A1 · p. 10, Appendix A · p. 10
• The candidate scattering evidence is not confirmed with Anders et al. (2019) distances, which flag the stars as possibly affected by spurious astrometry due to large RUWE.Source: Appendix A · p. 10

APPENDIX B: GALACTOCENTRIC COORDINATES

• Galactocentric coordinates use a right-handed Cartesian frame, with x toward the Galactic center, y roughly toward Galactic longitude ℓ = 90°, and z roughly toward the North Galactic Pole.Source: Appendix B · p. 10
• The frame adopts a Sun–Galactic Center distance of 8.33 ± 0.35 kpc, a Galactic Center height of 27 ± 4 pc, and a circular velocity of 220 km/s at the solar radius.Source: Appendix B · p. 10
• Table C1 lists the identifiers of the globular clusters used in the analysis.Source: Table C1 · p. 10

APPENDIX C: ORBITS DATA

• Tables C1 and C2 list identifiers for globular clusters and nearby galaxies, with Table C2 also giving detailed references for galaxy measurements.The galaxy list identifies dwarf galaxies and notes several excluded or ambiguous systems.Source: Appendix C · p. 10, Table C2 · p. 11
• The globular-cluster, galaxy, and star catalogs are available as ancillary files.Source: Appendix C · p. 10
• Table C3 reports Sagittarius dSph phase-space and size measurements, while Table C4 gives the properties of HVS compatible with scattering there under Marchetti et al. (2019) distances.Source: Appendix C · p. 10, Table C3 · p. 12, Table C4 · p. 13