Theoretical astrophysics and plasma physics at RPC

Abstract:

We study the gravitational dynamics of quasi-hierarchical triple systems, where the outer orbital period is significantly longer than the inner one, but the outer orbit is extremely eccentric, rendering the time at pericentre comparable to the inner period. Such systems are not amenable to the standard techniques of perturbation theory and orbit-averaging. Modelling the evolution of these triples as a sequence of impulses at the outer pericentre, we show, by comparing with direct three-body integrations, that such triples lend themselves to a description as an analytical map between subsequent outer pericentre passages. This map exhibits secular oscillations, going beyond the von Zeipel–Lidov–Kozai mechanism. We show that the time to coalescence due to gravitational waves in such systems is modified. We then study the long-term evolution under this map, which lead to a random-walk-like behaviour of the inner eccentricity. While this behaviour is probably absent from isolated triples, it could exist in triples where the outer orbit is weakly coupled to a system with which it can exchange angular momentum, and we describe some properties of this random walk.

Abstract:

ABSTRACT The challenge presented by computing actions for eccentric orbits in axisymmetric potentials is discussed. In the limit of vanishing angular momentum about the potential’s symmetry axis, there is a clean distinction between box and loop orbits. We show that this distinction persists into the regime of non-zero angular momentum. In the case of a Stäckel potential, there is a critical value $I_{3\rm crit}(E)$ of the third integral $I_3$ below which $I_3$ does not contribute to the centrifugal barrier. An orbit is of box or loop type according as its value of $I_3$ is smaller or greater than $I_{3\rm crit}$. We give algorithms for determining $I_{3\rm crit}(E)$ and the critical action $J_{z\rm crit}$ below which orbits in any given potential are boxes. It is hard to compute the actions and especially the frequencies of orbits that have $J_z\simeq J_{z\rm crit}$ using the Stäckel Fudge. A modification of the Fudge that alleviates the problem is described.

Abstract:

We present three-dimensional Dedalus simulations of Rayleigh–Bénard convection with a blackbody-radiating free upper surface, subject to a low-amplitude oscillatory forcing that mimics tidal perturbations in convective envelopes of stars and planets. The forcing period is 10–100 times shorter than the convective time-scale, . Using a Reynolds decomposition of the velocity field averaged over one oscillation period, in which the tidal oscillations naturally constitute the fluctuating field and convection the mean flow, we elucidate the kinetic energy exchange between the two. Provided the oscillatory Reynolds number exceeds a modest threshold, we find that the oscillations systematically transfer kinetic energy to the mean flow at a volume-averaged rate , where is the rms fluctuation velocity. This reflects strong, order-unity correlations between the fluctuation velocities and the mean flow. These arise because the oscillatory forcing displaces fluid elements that are then redirected by buoyancy and incompressibility in the same manner as the mean flow. The transfer is dominated by correlations involving vertical velocity fluctuations and vertical gradients of the mean flow. The resulting energy transfer rate is consistent, within the equilibrium-tide framework, with the observed tidal circularization of solar-type binaries and with the orbital evolution of moons of Jupiter and Saturn. This validates the formalism proposed by C. Terquem (2021) for the dissipation of fast tides, a long-standing problem. Replacing the free surface with a rigid upper boundary significantly and artificially modifies the correlations.