On the Self‐consistent Response of Stellar Systems to Gravitational Shocks

Abstract

We study the reaction of a globular star cluster to a time-varying tidal perturbation (gravitational shock) using self-consistent N-body simulations and address two questions.First, to what extent is the cluster interior protected by adiabatic invariants. Second, how much further energy change does the postshock evolution of the cluster potential produce and how much does it affect the dispersion of stellar energies. We introduce the adiabatic correction as ratio of the energy change, ∆E , to its value in the impulse approximation. When the potential is kept fixed, the numerical results for the adiabatic correction for stars with orbital frequency ω can be approximated as (1 + ω 2 τ 2 ) −γ . For shocks with the characteristic duration of the order the half-mass dynamical time of the cluster, τ ∼ < t dyn,h , the exponent γ = 5/2. For more prolonged shocks, τ ∼ > 4 t dyn,h , the adiabatic correction is shallower, γ = 3/2. When we allow for self-gravity and potential oscillations which follow the shock, the energy of stars in the core changes significantly, while the total energy of the system is conserved. Paradoxically, the postshock potential fluctuations reduce the total amount of energy dispersion, ∆E 2 . The effect is small but real and is due to the postshock energy change being statistically anti-correlated with the shock induced heating. These results are to be applied to Fokker-Planck models of the evolution of globular clusters.

The Effects of Ram-pressure Stripping and Supernova Winds on the Tidal Stirring of Disky Dwarfs: Enhanced Transformation into Dwarf Spheroidals

“…Owing to ram-pressure stripping, at a given distance R from the center of our dwarfs, increasing gas fractions correspond to smaller M, and thus to larger ΔE/E; thus, the gas-rich dwarfs suffer more effective tidal shocks, which explains both their enhanced mass loss and augmented morphological transformation into dSph-like systems. Taking into account adiabatic corrections (e.g., Gnedin & Ostriker 1999) strengthens this conclusion. Indeed, for less concentrated mass distributions, adiabatic corrections result in even larger ΔE/E compared to those predicted by the impulse approximation.…”

Response of Dark Matter Halos to Condensation of Baryons: Cosmological Simulations and Improved Adiabatic Contraction Model

“…For noncrossing spherical shells, the radial velocity can be expressed using the first integrals of motion C (e.g., Ryden & Gunn 1987;Gnedin & Ostriker 1999) as…”

The dynamics of satellite disruption in cold dark matter haloes

“…The quantity A ( x ), the adiabatic correction, reduces the heating if the internal orbital time is significantly shorter than the impulsive time‐scale. We explore both the Spitzer correction and the Weinberg correction (Weinberg 1994a,b; Gnedin & Ostriker 1999), where x =ωπ R p / V p and ω is the azimuthal frequency of an orbit at r . Equations determine the energy change for each mass shell and for each shock event.…”

“…As shown in , determining resonant orbits requires detailed calculations. Using equation (24) of Weinberg (1994b), Gnedin & Ostriker (1999) show that the number of stars at the peak amplitude scales as 1/τ, where τ is the characteristic duration of the shock. The resonant shock and the resonant torque are based on the same physics with a different coupling and frequency.…”