Making the hypervelocity-star tangential-velocity test of QUMOND self-consistent and feasible

Chakrabarty, Ostorero, Gallo, Ebagezio and Diaferio (2022) proposed a clean test of modified gravity at Galactic scales: hypervelocity stars (HVSs) ejected from the Galactic center with speeds above roughly 700–750 km/s should, in the quasi-linear formulation of modified Newtonian dynamics (QUMOND), have azimuthal velocity components $|v_\phi|$ below a small, predictable upper limit set by the Galaxy's non-axisymmetric baryonic mass distribution, whereas Newtonian gravity with a realistic dark-matter halo imposes no such bound. The authors explicitly left the programme unfinished: the test rests on a circular identification of HVS candidates, neglects the MOND external-field effect, the poorly constrained Milky Way hot gaseous halo, and perturbations from the Large Magellanic Cloud, and requires about tenfold better tangential-velocity precision than current astrometry delivers. The open problem is to build the quantitative, self-consistent framework — theory-by-theory HVS identification, external-field-effect and perturber quantification, halo-uncertainty marginalization, and observational-requirement forecasting — that establishes whether, and under what conditions, measured $|v_\phi|$ of high-speed HVSs can falsify QUMOND.

Background

Modified Newtonian dynamics (MOND) replaces Newtonian gravity at accelerations below the empirical scale $a_0 \approx 1.2 \times 10^{-10}\,\mathrm{m/s^2}$ with a nonlinear relation that makes galaxy dynamics depend only on the baryonic mass, thereby mimicking the effects usually attributed to dark matter (DM). In its quasi-linear formulation (QUMOND), the gravitational potential is obtained in two steps: an auxiliary 'phantom' density, computed from the baryonic mass through MOND's interpolating function — the function that bridges the Newtonian and deep-MOND acceleration regimes — sources a standard Poisson solve. A distinctive MOND prediction is the external-field effect (EFE): because the strong equivalence principle is violated, the internal dynamics of a self-gravitating system are altered by any ambient external field — for the Milky Way (MW), the pull of nearby structures — an effect with no Newtonian counterpart.

Hypervelocity stars (HVSs) offer a potentially sharp probe of this dichotomy. In the Hills mechanism, a binary star disrupted by the supermassive black hole at the Galactic center ejects one component at up to ~1000 km/s on a nearly radial trajectory, so the azimuthal component $v_\phi$ of its galactocentric velocity starts near zero and is generated only by non-axisymmetric parts of the Galactic potential. Chakrabarty et al. (2022) integrated HVS orbits in QUMOND and in Newtonian gravity with a triaxial or misaligned DM halo, showing that for 4 $M_\odot$ stars ejected faster than about 710–750 km/s (the threshold rises for lower masses, to about 800 and 830 km/s for 3 and 2.5 $M_\odot$ stars), the star never turns around in the inner Galaxy, and at galactocentric distances of roughly 15–60 kpc its QUMOND azimuthal speed is bounded by a small conservative upper limit $|v^{\max}_\phi(r)|$ — for example $|v_\phi| \lesssim 2$ km/s at $r \sim 20$ kpc when only the triaxial bulge breaks axial symmetry, and somewhat more when a nonspherical hot gaseous (HG) halo — the MW's X-ray-emitting circumgalactic gas corona — is included. In Newtonian gravity with a DM halo of axis ratio $q_y = 1.1$–$1.2$, $|v_\phi|$ can reach 6–10 km/s at the same distance. A single confirmed HVS with $|v_\phi|$ above the QUMOND limit would therefore falsify QUMOND.

The test is nevertheless not yet applicable, for five interlocking reasons stated by the source authors. First, deciding that an observed high-velocity star really was ejected from the Galactic center requires integrating its orbit backward in time, but the potential in which one integrates is precisely what is being tested: the procedure is circular unless the identification is redone independently within each candidate theory, including the EFE in QUMOND. Second, the EFE itself perturbs the trajectories of the most distant HVSs, and its quantitative impact is unknown. Third, the QUMOND upper limit depends on the mass, radial extent, and three-dimensional shape of the HG halo, which observations constrain only poorly. Fourth, external perturbers — above all the Large Magellanic Cloud (LMC), whose Newtonian perturbations of HVS trajectories were quantified already by Kenyon et al. (2018) — can inject tangential motion, and their effect has not been computed in MOND. Fifth, current proper-motion measurements — proper motion is a star's angular motion on the sky, from which tangential velocity is derived — come from Gaia Early Data Release 3 (EDR3), the early third data release of ESA's Gaia astrometry satellite, and leave relative uncertainties on $v_\phi$ of ~50–340% for the known HVS sample; roughly tenfold better precision, of the microarcsecond class proposed for dedicated space-astrometry missions like Theia, is needed for a decisive test.

Problem Statement

The problem, as posed by the concluding discussion of Chakrabarty et al. (2022), is to convert their theoretical QUMOND-versus-Newtonian discrimination criterion into a practicable, self-consistent empirical test by resolving five linked open issues:

1. Self-consistent HVS identification. Develop a non-circular procedure that, within each candidate gravity theory separately — QUMOND, including its external-field effect, and Newtonian gravity with a dark-matter halo — integrates candidate high-velocity-star orbits backward in time and determines whether the star is consistent with Galactic-center ejection in that theory, so that a star enters the test only if its HVS status survives every model under consideration.

2. Quantify the external-field effect. Compute the quantitative impact of the MOND external-field effect on HVS trajectories at large galactocentric distances, where it is expected to matter most, and determine how it modifies the QUMOND upper limit $|v^{\max}_\phi(r)|$.

3. Propagate hot-halo uncertainty. Marginalize (or observationally narrow) the QUMOND $|v_\phi|$ upper limits over the poorly constrained mass, radial extent, and oblateness of the Milky Way's hot gaseous halo, so that the falsification threshold carries explicit error bars.

4. Quantify external perturbers. Determine which stars and sky directions are safe to use by quantifying, in each theory, the tangential-velocity perturbations induced by external perturbers — the Large Magellanic Cloud in particular, whose MOND-specific treatment (including the external-field effect) has no existing calculation.

5. Establish the observational requirement. Determine the astrometric precision, sample size, stellar masses, and sky coverage under which measured $|v_\phi|$ of high-speed HVSs beyond the mass-dependent minimum radius (roughly 15/30/50 kpc for 4/3/2.5 $M_\odot$ stars) could decisively distinguish QUMOND from Newtonian gravity with dark matter, given foreseeable instruments.

These components serve one common objective: a quantitative feasibility verdict on the HVS tangential-velocity test — either a demonstrated, self-consistent discriminating protocol with specified observational requirements, or a demonstration that the test cannot discriminate between the theories. The feasibility verdict depends on all five components jointly rather than on any subset of them. The two outcomes carry the same evidentiary burden: a demonstration that the test cannot discriminate must show that the QUMOND and Newtonian $|v_\phi|$ predictions, together with the uncertainties propagated from the hot-halo marginalization and the external perturbers, overlap across the accessible stellar masses, galactocentric distances, and sky coverage, so that no measured $|v_\phi|$ could separate the two theories.

References

1. Chakrabarty, S. S., Ostorero, L., Gallo, A., Ebagezio, S., & Diaferio, A. (2022). Probing modified Newtonian dynamics with hypervelocity stars. Astronomy & Astrophysics, 657, A115. DOI: 10.1051/0004-6361/202141136. https://doi.org/10.1051/0004-6361/202141136 (preprint: arXiv:2104.10174)
2. Gallo, A., Ostorero, L., Chakrabarty, S. S., Ebagezio, S., & Diaferio, A. (2022). Probing the shape of the Milky Way dark matter halo with hypervelocity stars: A new method. Astronomy & Astrophysics, 663, A72. DOI: 10.1051/0004-6361/202142679. https://doi.org/10.1051/0004-6361/202142679 (preprint: arXiv:2111.09657)
3. Marchetti, T., Evans, F. A., & Rossi, E. M. (2022). Gaia DR3 in 6D: the search for fast hypervelocity stars and constraints on the Galactic Centre environment. Monthly Notices of the Royal Astronomical Society, 515, 767–774. DOI: 10.1093/mnras/stac1777. https://doi.org/10.1093/mnras/stac1777 (preprint: arXiv:2206.06962)
4. Liao, J., Du, C., Li, H., Ma, J., & Shi, J. (2023). Hypervelocity Stars Track Back to the Galactic Center in Gaia DR3. The Astrophysical Journal Letters, 944, L39. DOI: 10.3847/2041-8213/acb7d9. https://doi.org/10.3847/2041-8213/acb7d9
5. Liao, J., Du, C., Deng, M., Ye, D., Li, H., Huang, Y., Shi, J., & Ma, J. (2024). The Origin of High-velocity Stars Considering the Impact of the Large Magellanic Cloud. The Astronomical Journal, 167, 76. DOI: 10.3847/1538-3881/ad18c4. https://doi.org/10.3847/1538-3881/ad18c4 (preprint: arXiv:2401.02017)
6. Kenyon, S. J., Bromley, B. C., Brown, W. R., & Geller, M. J. (2018). Impact of the Galactic Disk and Large Magellanic Cloud on the Trajectories of Hypervelocity Stars Ejected from the Galactic Center. The Astrophysical Journal, 864, 130. DOI: 10.3847/1538-4357/aada04. https://doi.org/10.3847/1538-4357/aada04
7. Koop, O., & Helmi, A. (2024). Testing MOND using the dynamics of nearby stellar streams. Astronomy & Astrophysics, 689, A57. DOI: 10.1051/0004-6361/202348211. https://doi.org/10.1051/0004-6361/202348211 (preprint: arXiv:2406.08872)
8. Ma, L., Zhang, Z., Wang, H., & Wu, X. (2025). Measuring Mass of Gas in Central Galaxies Using Weak Lensing and Satellite Kinematics in MOND. The Astrophysical Journal, 984(2), 101. DOI: 10.3847/1538-4357/adc728. https://doi.org/10.3847/1538-4357/adc728 (preprint: arXiv:2409.13329)
9. De Martino, I. (2023). Dynamics of dwarf galaxies in scalar-tensor-vector gravity. Physical Review D, 108, 044074. DOI: 10.1103/PhysRevD.108.044074. https://doi.org/10.1103/PhysRevD.108.044074 (preprint: arXiv:2308.15908)
10. Banik, I., Pittordis, C., Sutherland, W., Famaey, B., Ibata, R., Mieske, S., & Zhao, H. (2024). Strong constraints on the gravitational law from Gaia DR3 wide binaries. Monthly Notices of the Royal Astronomical Society, 527(3), 4573–4615. DOI: 10.1093/mnras/stad3393. https://doi.org/10.1093/mnras/stad3393 (preprint: arXiv:2311.03436)
11. Cavieres, M., Koposov, S. E., Rossi, E. M., Penoyre, Z., & Verberne, S. (2026). Discovery of Galactic-centre-ejected star in DESI DR1. Astronomy & Astrophysics, 709, A117. DOI: 10.1051/0004-6361/202659104. https://doi.org/10.1051/0004-6361/202659104
12. Malbet, F., Boehm, C., Krone-Martins, A., Amorim, A., Anglada-Escudé, G., Brandeker, A., et al. (2021). Faint objects in motion: the new frontier of high precision astrometry. Experimental Astronomy, 51, 845–886. DOI: 10.1007/s10686-021-09781-1. https://doi.org/10.1007/s10686-021-09781-1 (86 authors; preprint: arXiv:2111.08709)