Conservation of radial actions in time-dependent spherical potentials

ABSTRACT 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 $\propto \dot{\Phi }/\Phi \, P(E,L)$. 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 $\tilde {D}(J_r) \lt 0.01\, J_r^2$. 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 $\sigma /m_\chi = 1\, {\rm cm^2g^{-1}}$) have invariant radial actions during the formation of a cored density profile.

Spin effects in the effective field theory approach to Post-Minkowskian conservative dynamics

Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to $$ \mathcal{O}\left({G}^2\right) $$ O G 2 , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

Evolution of subhalo orbits in a smoothly growing host halo potential

ABSTRACT The orbital parameters of dark matter (DM) subhaloes play an essential role in determining their mass-loss rates and overall spatial distribution within a host halo. Haloes in cosmological simulations grow by a combination of relatively smooth accretion and more violent mergers, and both processes will modify subhalo orbits. To isolate the impact of the smooth growth of the host halo from other relevant mechanisms, we study subhalo orbital evolution using numerical calculations in which subhaloes are modelled as massless particles orbiting in a time-varying spherical potential. We find that the radial action of the subhalo orbit decreases over the first few orbits, indicating that the response to the growth of the host halo is not adiabatic during this phase. The subhalo orbits can shrink by a factor of ∼1.5 in this phase. Subsequently, the radial action is well conserved and orbital contraction slows down. We propose a model accurately describing the orbital evolution. Given these results, we consider the spatial distribution of the population of subhaloes identified in high-resolution cosmological simulations. We find that it is consistent with this population having been accreted at $z \lesssim 3$, indicating that any subhaloes accreted earlier are unresolved in the simulations. We also discuss tidal stripping as a formation scenario for NGC 1052-DF2, an ultra diffuse galaxy significantly lacking DM, and find that its expected DM mass could be consistent with observational constraints if its progenitor was accreted early enough, $z \gtrsim 1.5$, although it should still be a relatively rare object.

Energy map and effective metric in an effective-one-body theory based on the second-post-Minkowskian approximation

Effective-one-body (EOB) theory was originally proposed based on the post-Newtonian (PN) approximation and plays an important role in the analysis of gravitational wave signals. Recently, the post-Minkowskian (PM) approximation has been applied to the EOB theory. The energy map and the effective metric are the two key building blocks of the EOB theory, and in PN approximation radial action variable correspondence is employed to construct the energy map and the effective metric. In this paper, we employ the PM approximation up to the second order, and use the radial action variable correspondence and the precession angle correspondence to construct the energy map and the effective metric. We find that our results based on the radial action variable correspondence, are exactly the same with those obtained based on the precession angle correspondence. Furthermore, we compare the results obtained in this work to the previous existing ones.

Resonance sweeping by a decelerating Galactic bar

ABSTRACT We provide the first quantitative evidence for the deceleration of the Galactic bar from local stellar kinematics in agreement with dynamical friction by a typical dark matter halo. The kinematic response of the stellar disc to a decelerating bar is studied using secular perturbation theory and test particle simulations. We show that the velocity distribution at any point in the disc affected by a naturally slowing bar is qualitatively different from that perturbed by a steadily rotating bar with the same current pattern speed Ωp and amplitude. When the bar slows down, its resonances sweep through phase space, trapping, and dragging along a portion of previously free orbits. This enhances occupation on resonances, but also changes the distribution of stars within the resonance. Due to the accumulation of orbits near the boundary of the resonance, the decelerating bar model reproduces with its corotation resonance the offset and strength of the Hercules stream in the local vR-vφ plane and the double-peaked structure of mean vR in the Lz–φ plane. At resonances other than the corotation, resonant dragging by a slowing bar is associated with a continuing increase in radial action, leading to multiple resonance ridges in the action plane as identified in the Gaia data. This work shows models using a constant bar pattern speed likely lead to qualitatively wrong conclusions. Most importantly we provide a quantitative estimate of the current slowing rate of the bar $\dot{\Omega }_{\rm p}= (-4.5 \pm 1.4) \, {\rm km}\, {\rm s}^{-1}\, {\rm kpc}^{-1}\, {\rm Gyr}^{-1}$ with additional systematic uncertainty arising from unmodelled impacts of e.g. spiral arms.

Diffusion of radial action in a galactic disc

Context. The stellar migration of the galactic disc stars has been invoked to explain the dispersion of stellar metallicity observed in the solar neighbourhood. Aims. We seek to identify the dynamical mechanisms underlying stellar migration in an isolated galaxy disc under the influence of a bar. Our approach is to analyse the diffusion of dynamical quantities. Methods. We extend our previous work by exploring Chirikov’s diffusion rate (and derived timescale) of the radial action JR in an idealised N-body simulation of an isolated disc galaxy. We limit our study to the evolution of the disc region well after the formation of the bar, in a regime of adiabatic evolution. Results. The JR diffusion timescale TD(JR) is less than 3 Gyr for roughly half the galaxy mass. It is always much shorter than the angular momentum diffusion timescale TD(Lz) outside the stellar bar. In the disc, ⟨TD(JR)⟩ ∼ 1 Gyr. All non-axisymmetric morphological structures that are characteristic of resonances and waves in the disc are associated to particles with TD(JR) < 3 Gyr and TD(Lz) > 10 Gyr. Short TD(JR) can be explained by the gradual de-circularisation of initially circular orbits (JR = 0) under the effect of intermittent. Inner Linblad resonance scattering by wave trains propagating in the disc, well beyond the outer Lindblad resonance of the bar (OLR). This leads to a moderate secular heating of the disc beyond the bar’s OLR for 7 Gyr, which is comparable to solar neighbourhood observations. The complex multi-wave structure, mixing permanent and intermittent modes, allows for multiple resonance overlaps.

The orbital phase space of contracted dark matter haloes

ABSTRACT We study the orbital phase space of dark matter (DM) haloes in the auriga suite of cosmological hydrodynamics simulations of Milky Way (MW) analogues. We characterize haloes by their spherical action distribution, $F\left(J_{{r}},L\right)$, a function of the specific angular momentum, L, and the radial action, Jr, of the DM particles. By comparing DM-only and hydrodynamical simulations of the same haloes, we investigate the contraction of DM haloes caused by the accumulation of baryons at the centre. We find a small systematic suppression of the radial action in the DM haloes of the hydrodynamical simulations, suggesting that the commonly used adiabatic contraction approximation can result in an underestimate of the density by $\sim 8{{ \rm {per\ cent}}}$. We apply an iterative algorithm to contract the auriga DM haloes given a baryon density profile and halo mass, recovering the true contracted DM profiles with an accuracy of $\sim 15{{ \rm {per\ cent}}}$, that reflects halo-to-halo variation. Using this algorithm, we infer the total mass profile of the MW’s contracted DM halo. We derive updated values for the key astrophysical inputs to DM direct detection experiments: the DM density and velocity distribution in the Solar neighbourhood.

Radial migration and vertical action in N-body simulations

ABSTRACT We study the radial migration of stars as a function of orbital action as well as the structural properties of a large suite of N-body simulations of isolated disc galaxies. Our goal is to establish a relationship between the radial migration efficiency of stars and their vertical action. We aim to describe how that relationship depends on the relative gravitational dominance between the disc and the dark matter halo. By changing the mass ratio of our disc and dark matter halo, we find a relationship between disc dominance, number, and strength of spiral arms, and the ensuing radial migration as a function of the vertical action. We conclude that the importance of migration at large vertical action depends on the strength of the spiral arms and therefore the dominance of the disc. Populations with more radial action undergo less radial migration, independently of disc dominance. Our results are important for the future of analytical modelling of radial migration in galaxies and further the understanding of radial migration that is a key component of the restructuring of galaxies, including the Milky Way.

THE INFLUENCE OF DARK MATTER HALO ONTO EVOLUTION OF SUPERMASSIVE BLACK HOLE

The influence of dark matter (DM) on the growth of supermassive black holes (SMBHs) is studied. It is shown that gravitational scattering of DM particles on bulge stars leads to diffusion of DM in phase space {m, mz, I} (m denotes the angular momentum and I is the radial action). Appropriate diffusion coefficients are calculated for different bulge models, and it is argued that the diffusion along m axis is the most important effect. It is shown that this process leads to noticeable flow of DM into the black hole (BH), resulting in its power-law growth: M bh ∝ t9/16. Comparison with observational data shows that, in principle, this effect may explain observed masses of SMBHs. Special attention is paid to the corrections related to the innermost region of BH gravitational influence and the diffusion along I axis. Their influence on the BH growth law is shown to be negligible.