TY - JOUR

T1 - Conservation of radial actions in time-dependent spherical potentials

AU - Burger, Jan D.

AU - Peñarrubia, Jorge

AU - Zavala, Jesús

N1 - Publisher Copyright:
© 2021 The Author(s).

PY - 2021/11/1

Y1 - 2021/11/1

N2 - In slowly evolving spherical potentials, φ(r, t), radial actions are typically assumed to remain constant. Here, we construct dynamical invariants that allow us to derive the evolution of radial actions in spherical central potentials with an arbitrary time dependence. We show that to linear order, radial actions oscillate around a constant value with an amplitude ∝ φ /φP(E,L). Using this result, we develop a diffusion theory that describes the evolution of the radial action distributions of ensembles of tracer particles orbiting in generic time-dependent spherical potentials. Tests against restricted N-body simulations in a varying Kepler potential indicate that our linear theory is accurate in regions of phase-space in which the diffusion coefficient ˜D (Jr ) < 0.01 J 2r. For illustration, we apply our theory to two astrophysical processes. We show that the median mass accretion rate of a Milky Way (MW) dark matter (DM) halo leads to slow global time-variation of the gravitational potential, in which the evolution of radial actions is linear (i.e. either adiabatic or diffusive) for ∼84 per cent of the DM halo at redshift z = 0. This fraction grows considerably with look-back time, suggesting that diffusion may be relevant to the modelling of several Gyr old tidal streams in action-angle space. As a second application, we show that dynamical tracers in a dwarf-size self-interacting DM halo (with σ/mχ = 1 cm2g−1) have invariant radial actions during the formation of a cored density profile.

AB - In slowly evolving spherical potentials, φ(r, t), radial actions are typically assumed to remain constant. Here, we construct dynamical invariants that allow us to derive the evolution of radial actions in spherical central potentials with an arbitrary time dependence. We show that to linear order, radial actions oscillate around a constant value with an amplitude ∝ φ /φP(E,L). Using this result, we develop a diffusion theory that describes the evolution of the radial action distributions of ensembles of tracer particles orbiting in generic time-dependent spherical potentials. Tests against restricted N-body simulations in a varying Kepler potential indicate that our linear theory is accurate in regions of phase-space in which the diffusion coefficient ˜D (Jr ) < 0.01 J 2r. For illustration, we apply our theory to two astrophysical processes. We show that the median mass accretion rate of a Milky Way (MW) dark matter (DM) halo leads to slow global time-variation of the gravitational potential, in which the evolution of radial actions is linear (i.e. either adiabatic or diffusive) for ∼84 per cent of the DM halo at redshift z = 0. This fraction grows considerably with look-back time, suggesting that diffusion may be relevant to the modelling of several Gyr old tidal streams in action-angle space. As a second application, we show that dynamical tracers in a dwarf-size self-interacting DM halo (with σ/mχ = 1 cm2g−1) have invariant radial actions during the formation of a cored density profile.

KW - Dark matter

KW - Diffusion

KW - Galaxies: Kinematics and dynamics; galaxies: Statistics

KW - Stars: Kinematics and dynamics

UR - http://www.scopus.com/inward/record.url?scp=85118107585&partnerID=8YFLogxK

U2 - 10.1093/mnras/stab2568

DO - 10.1093/mnras/stab2568

M3 - Article

AN - SCOPUS:85118107585

VL - 508

SP - 1404

EP - 1430

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 1

ER -