论文标题
在时间依赖的球形电位中保存径向作用
Conservation of radial actions in time-dependent spherical potentials
论文作者
论文摘要
在缓慢发展的球形电位中，$φ（r，t）$通常假定径向动作保持恒定。在这里，我们构建了动态不变性，使我们能够以任意时间依赖性来得出球形中心电势中径向作用的演变。我们表明，对于线性顺序，径向动作围绕一个恒定值振荡，振幅$Δj_r\ propto \dotφ/φ\，p（e，l）$。使用此结果，我们开发了一种扩散理论，该理论描述了在通用时间依赖性的球形电位中绕的示踪剂颗粒集合的径向作用分布的演变。针对不同开普勒电位中有限的$ n $体体模拟的测试表明，我们的线性理论在相位区域中是准确的，其中扩散系数$ \ tilde {d}（j_r）<0.01 \，j_r^2 $。为了说明，我们将理论应用于两个天体物理过程。我们表明，银河系（MW）暗物质（DM）光环的中值质量增生率导致重力潜力的全球时间变化慢，其中径向动作的演变为$ \ sim的线性（即绝热或扩散性）的$ \ sim 84 $ 84 $ halo的dm halo halo in Redshift $ z = 0 $ z = 0 $ 84 $。随着回避时间的增长，这一比例大大生长，这表明扩散可能与动作角度空间中几个Gyr-Old潮汐流的建模有关。作为第二个应用程序，我们表明，在自我相互作用的DM（SIDM）矮晕中的动态示踪剂（带有$σ/m_χ= 1 \，{\ rm cm^2g^{ - 1}} $）具有不变的辐射动作，在芯密度谱的形成过程中。
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 $ΔJ_r \propto \dotΦ/Φ\,P(E,L)$. Using this result, we develop a diffusion theory that describes the evolution of the radial action distribution 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 $\tilde{D}(J_r) < 0.01\,J_r^2$. 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 $\sim 84$ per cent of the DM halo at redshift $z=0$. This fraction grows considerably with lookback 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 self-interacting DM (SIDM) dwarf halo (with $σ/m_χ= 1\,{\rm cm^2g^{-1}}$) have invariant radial actions during the formation of a cored density profile.
