The escape velocity curve of the Milky Way in modified Newtonian dynamics

Abstract

We determine the escape velocity from the Milky Way (MW) at a range of Galactocentric radii in the context of Modified Newtonian Dynamics (MOND). Due to its non-linear nature, escape is possible if the MW is considered embedded in a constant external gravitational field (EF) from distant objects. We model this situation using a fully self-consistent method based on a direct solution of the governing equations out to several thousand disk scale lengths. We try out a range of EF strengths and mass models for the MW in an attempt to match the escape velocity measurements of Williams et al. (2017).A reasonable match is found if the EF on the MW is ∼ 0.03a 0 , towards the higher end of the range considered. Our models include a hot gas corona surrounding the MW, but our results suggest that this should have a very low mass of ∼ 2 × 10 10 M to avoid pushing the escape velocity too high. Our analysis favours a slightly lower baryonic disk mass than the ∼ 7 × 10 10 M required to explain its rotation curve in MOND. However, given the uncertainties, MOND is consistent with both the locally measured amplitude of the MW rotation curve and its escape velocity over Galactocentric distances of 8−50 kpc.

Numerical Solutions of the External Field Effect on the Radial Acceleration in Disk Galaxies

“…The QUMOND numerical median relation agrees well with the approximate analytic expression for the RAR proposed by Zonoozi et al (2021) based on Banik & Zhao (2018):…”

A plane of high-velocity galaxies across the Local Group

“…This was recently confirmed by observations, which are in tension with a naive application of the RAR but not a more rigorous treatment of MOND (Caldwell et al 2017). This external field effect hardly matters for calculating the rotation curve of the MW but is crucial to its escape velocity, measurements of which can be fit reasonably well in MOND (Banik & Zhao 2017b).…”

“…A similar halo is thought to be necessary around the MW to explain the truncation of the Large Magellanic Cloud's gas disk (Salem et al 2015). These gas halos seem to contain perhaps 3 × 10 10 M each, with much larger amounts being very unlikely given constraints from the MW escape velocity curve (Banik & Zhao 2017b). Considering that the MW rotation curve flatlines at ∼ 180 km/s (Kafle et al 2012) while that of M31 flattens at ∼ 225 km/s (Carignan et al 2006), MOND suggests their total baryonic mass is 2.3 × 10 11 M .…”

Origin of the Local Group satellite planes

“…To account for this, we integrate the assumed surface density law (Table 3) to obtain the mass represented by each particle, later using these masses as statistical weights when analysing our simulations (Section 4). We treat M31 as an exponential disk but use a double exponential model for the MW, whose adopted mass distribution is the same as that used in Banik & Zhao (2018a) to calculate its rotation and escape velocity curves in MOND.…”