How Close Dark Matter Halos and MOND Are to Each Other: Three-Dimensional Tests Based on Gaia DR2

Yongda Zhu, Hai-Xia Ma, Xiao-Bo Dong, Yang Huang, Tobias Mistele, Bo Peng, Qian Long, Tianqi Wang, Liang Chang, Xi Jin

Submitted on 23 November 2022


Aiming at discriminating different gravitational potential models of the Milky Way, we perform tests based on the kinematic data powered by the Gaia DR2 astrometry, over a large range of (R,z) locations. Invoking the complete form of Jeans equations that admit three integrals of motion, we use the independent R- and z-directional equations as two discriminators (TR and Tz). We apply the formula for spatial distributions of radial and vertical velocity dispersions proposed by Binney et al., and successfully extend it to azimuthal components, σθ(R,z) and Vθ(R,z); the analytic form avoids the numerical artifacts caused by numerical differentiation in Jeans-equations calculation given the limited spatial resolutions of observations, and more importantly reduces the impact of kinematic substructures in the Galactic disk. It turns out that whereas the current kinematic data are able to reject Moffat's Modified Gravity (let alone the Newtonian baryon-only model), Milgrom's MOND is still not rejected. In fact, both the carefully calibrated fiducial model invoking a spherical dark matter (DM) halo and MOND are equally consistent with the data at almost all spatial locations (except that probably both have respective problems at low-|z| locations), no matter which a tracer population or which a meaningful density profile is used. Because there is no free parameter at all in the quasi-linear MOND model we use, and the baryonic parameters are actually fine-tuned in the DM context, such an effective equivalence is surprising, and might be calling forth a transcending synthesis of the two paradigms.


Comment: 20 pages, 13 figures; accepted for publication in MNRAS

Subject: Astrophysics - Astrophysics of Galaxies


Rotation curves of the Milky Way, with the predicted ones of the gravitational models compared with the observations. The cyan data points with error bars ($\pm 1\sigma$) are our averaged rotation curve over spatial bins with $\Delta R = 0.5$kpc (note that we increase the bin size at a few large-$R$ bins), based on the data of \citet[][]{eilers_circular_2019,mroz_rotation_2019,chrobakova_gaia-dr2_2020}. The baryonic mass parameters is from \citet{wangMilkyWayTotal2022}. The orange, blue, green, and red curves represent the Newtonian baryon-only, DM, QUMOND, and MOG models, respectively.