Milky Way dark matter distribution or MOND test from vertical stellar kinematics with Gaia DR3

Vertical stellar kinematics+density can be used to trace the dark matter distribution [or the equivalent phantom mass in a Modified Newtonian Dynamics (MOND) scenario] through Jeans equations. In this paper, we want to improve this type of analysis by making use of the recent data of the 6D information from the Gaia-DR3 survey in the anticenter and the Galactic poles to obtain the dynamical mass distribution near plane regions, including extended kinematics over a wide region of 8 kpc$<R<$22 kpc, $|z|<3$ kpc. Our conclusions are as follows: (i) the model of the spherical dark matter halos and the MOND model are compatible with the data; (ii) the model of the disky dark matter (with density proportional to the gas density) is excluded; (iii) the total lack of dark matter (there is only visible matter) within Newtonian gravity is compatible with the data; for instance, at solar Galactocentric radius, we obtained $\Sigma=39\pm 18$ M$_\odot$ pc$^{-2}$ for $z=1.05$ kpc, compatible with the expected value for visible matter alone of 44 M$_\odot$ pc$^{-2}$, thus allowing zero dark matter. Similarly, for $R>R_\odot$, $z=1.05$ kpc: $\Sigma=28.7\pm 9.6$, $23.0\pm 5.7$, $16.9\pm 5.8$, $11.4\pm 6.6$ M$_\odot$ pc$^{-2}$, respectively, for $R=10,13,16,19$ kpc, compatible with visible matter alone. Larger error bars in comparison with previous works are not due to worse data or a more awkward technique but to a stricter modeling of the stellar distribution.