Applying Noether’s Theorem to Matter in the Milky Way: Evidence for External Perturbations and Non-steady-state Effects from Gaia Data Release 2

Abstract

We apply Noether's theorem to observations of main-sequence stars from the Gaia Data Release 2 archive to probe the matter distribution function of the Galaxy. That is, we examine the axial symmetry of stars at vertical heights z, 0.2 ≤ |z| ≤ 3 kpc, to probe the quality of the angular momentum L z as an integral of motion. The failure of this symmetry test would speak to a Milky Way, in both its visible and dark matter, that is not isolated and/or not in steady state. The left-right symmetry-breaking pattern we have observed, north and south, reveals both effects, with a measured deviation from symmetry of typically 0.5%. We show that a prolate form of the gravitational distortion of the Milky Way by the Large Magellanic Cloud, determined from fits to the Orphan stream by Erkal et al. (2019), is compatible with the size and sign of the axial-symmetry-breaking effects we have discovered in our sample of up to 14.4 million main-sequence stars, speaking to a distortion of an emergent, rather than static, nature.

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“…Thus if L z is an integral of motion, then the associated matter distribution is axially symmetric; also if L is an integral of motion, then the associated matter distribution is spherically symmetric. Thus a failure of axial symmetry speaks to failure of L z as an integral of motion [44]. Along related lines, we note that, as an extension of Lichtenstein's theorem [45] in fluid mechanics, an isolated, static, self-gravitating, ergodic 3 stellar systems has been shown to be spherically symmetric [38], though this can also be shown without reference to fluid mechanics, where we refer to [46] for an extended discussion and further references.…”

“…This is seen in both gas, via radio observations, and in the visible motion of stars. As discussed below, this is indicative of a non-static potential [44], which may be caused by recent interactions of our MW, in particular within the last Gyr, and ongoing. The primary culprits behind these perturbations are the LMC/SMC system as well as the massive Sagittarius dwarf system and its associated DM overdensities.…”

“…Determining the predicted kinematic signature in the Galaxy's disk or halo resulting from a close interaction with a massive satellite such as Sagittarius [183,184] is a subject of ongoing theoretical study, even if Sagittarius is less massive [185] than once suggested [186]. Moreover, the LMC [187,44,188], with or without Sagittarius [189], can influence the Milky Way, and studying their impacts remains an active area of research. Also see Section 6.4 below.…”

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“…Substantive observational evidence of vertical oscillations of the stellar disc has been found from photometrical and kinematical studies with different surveys (e.g. Widrow et al 2012;Williams et al 2013;Xu et al 2015;Carrillo et al 2018;Wang et al 2018;Bennett & Bovy 2019;Wang et al 2019;Gardner, Hinkel & Yanny 2020). The Galaxy seems to have a ringing, wobbling, flaring and warped disc, which would cause deviations from mirror symmetry with respect to its mid-plane.…”

“…From different surveys, there is substantive observational evidence of vertical oscillations of the stellar disc, causing it to act as a ringing, wobbling or flaring disc (e.g. Widrow et al 2012;Williams et al 2013;Xu et al 2015;Carrillo et al 2018;Wang et al 2018;Bennett & Bovy 2019;Wang et al 2019;Gardner, Hinkel & Yanny 2020). These may have been caused by the recent passage of a massive satellite such as the Sagittarius dwarf galaxy (e.g.…”