A two-step gravitational cascade for the fragmentation of self-gravitating disks

Self-gravitating disks are believed to play an important role in astrophysics in particular regarding the star and planet formation process. In this context, disks subject to an idealized cooling process, characterized by a cooling timescale β expressed in unit of orbital timescale, have been extensively studied. We take advantage of the Riemann solver and the 3D Godunov scheme implemented in the code Ramses to perform high resolution simulations, complementing previous studies that have used Smoothed Particle Hydrodynamics (SPH) or 2D grid codes. We observe that the critical value of β for which the disk fragments is consistent with most previous results, and is not well converged with resolution. By studying the probability density function of the fluctuations of the column density (∑-PDF), we argue that there is no strict separation between the fragmented and the unfragmented regimes but rather a smooth transition with the probability of apparition of fragments steadily diminishing as the cooling becames less effective. We find that the high column density part of the ∑-PDF follows a simple power law whose slope turns out to be proportional to β and we propose an explanation based on the balance between cooling and heating through gravitational stress. Our explanation suggests that a more efficient cooling requires more heating implying a larger fraction of dense material which, in the absence of characteristic scales, results in a shallower scale-free power law. We propose that the gravitational cascade proceeds in two steps, first the formation of a dense filamentary spiral pattern through a sequence of quasi-static equilibrium triggered by the viscous transport of angular momentum, and second the collapse alongside these filaments that eventually results in the formation of bounded fragments.

Effects of photoevaporation on protoplanetary disc ‘isochrones’

ABSTRACT Protoplanetary discs are the site of star and planet formation, and their evolution and consequent dispersal deeply affect the formation of planetary systems. In the standard scenario they evolve on time-scales ∼Myr due to the viscous transport of angular momentum. The analytical self-similar solution for their evolution predicts specific disc isochrones in the accretion rate–disc mass plane. However, photoevaporation by radiation emitted by the central star is likely to dominate the gas disc dispersal of the innermost region, introducing another (shorter) time-scale for this process. In this paper, we include the effect of internal (X and EUV) photoevaporation on the disc evolution, finding numerical solutions for a population of protoplanetary discs. Our models naturally reproduce the expected quick dispersal of the inner region of discs when their accretion rates match the rate of photoevaporative mass loss, in line with previous studies. We find that photoevaporation preferentially removes the lightest discs in the sample. The net result is that, counter-intuitively, photoevaporation increases the average disc mass in the sample, by dispersing the lightest discs. At the same time, photoevaporation also reduces the mass accretion rate by cutting the supply of material from the outer to the inner disc. In a purely viscous framework, this would be interpreted as the result of a longer viscous evolution, leading to an overestimate of the disc age. Our results thus show that photoevaporation is a necessary ingredient to include when interpreting observations of large disc samples with measured mass accretion rates and disc masses. Photoevaporation leaves a characteristic imprint on the shape of the isochrone. Accurate data of the accretion rate–disc mass plane in the low disc mass region therefore give clues on the typical photoevaporation rate.

The turbulence boundary of a temporal jet

We examine the structure of the turbulence boundary of a temporal plane jet at$\mathit{Re}= 5000$using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity${v}_{n} $based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate of entrainment so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude$2{v}_{n} $and$- {v}_{n} $, respectively. We further identify a turbulent core region (TC) and a buffer region (BR) connecting the VSL and the TC. The BR grows in time and inviscid enstrophy production is important in this region. The BR shows many similarities with the turbulent–non-turbulent interface (TNTI), although the TNTI seems to extend into the TC. The average distance between the TC and the VSL, i.e. the BR thickness is about 10 Kolmogorov length scales or half a Taylor length scale, indicating that intense turbulent flow regions and viscosity-dominated regions are in close proximity.