The thickness of H i in galactic discs under MOdified Newtonian Dynamics: theory and application to the Galaxy

The outskirts of galaxies are a very good laboratory for testing the nature of the gravitational field at low accelerations. By assuming that the neutral hydrogen gas is in hydrostatic equilibrium in the gravitational potential of the host galaxy, the observed flaring of the gas layer can be used to test modified gravities. For the first time, we construct a simple framework to derive the scaleheight of the neutral hydrogen gas disc in the MOdified Newtonian Dynamics (MOND) scenario and apply this to the MilkyWay. It is shown that using a constant gas velocity dispersion of $\sim 9 km s^{-1}$, MOND is able to give a very good fit to the observed HI flaring beyond a galactocentric distance of 17 kpc up to the last measured point $(\sim 40 kpc)$. Between 10 and 16 kpc, however, the observed scaleheight is about 40 per cent more than what MOND predicts for the standard interpolating function and 70 per cent for the form suggested by Famaey & Binney. Given the uncertainties in the non-thermal pressure support by cosmic rays and magnetic fields, MOND seems to be a plausible alternative to dark matter in explaining the Milky Way flaring. Studying the flaring of extended H I discs in external edge-on galaxies may be a promising approach to assess the viability of MOND.