Variable gravitational potential of Milky Way analogues in HESTIA suite

Investigations of trajectories of various objects orbiting the Milky Way (MW) halo with modern precision, achievable in observations by Gaia, requires sophisticated, non-stationary models of the Galactic potential. In this paper we analyze the evolution of the spherical harmonics expansion of MW analogues potential in constrained simulations of the Local Group (LG) from the HESTIA suite. We find that at distances $r\ge 100$~kpc the non-spherical part of the potential demonstrates a significant impact of the environment: ignoring the mass distribution outside the virial radius of the MW results in $>$20\% errors in the potential quadrupole at these distances. {Account of the environment results in a noticeable change of the angular momenta of objects orbiting MW analogues}. Spherical harmonics vary significantly during the last 6 Gyr. We attribute variations of the potential at $r\ge 30$~kpc to the motions of MW satellites and LG galaxies. We also predict that the non-sphericity of the real MW potential should grow with distance in the range $r_\mathrm{vir}<r<500$~kpc, since all realizations of simulated MW-like objects demonstrate such a trend.