No self-shadowing instability in 2D radiation-hydrodynamical models of irradiated protoplanetary disks

Theoretical models of protoplanetary disks including stellar irradiation often show a spontaneous amplification of scale height perturbations, produced by the enhanced absorption of starlight in enlarged regions. In turn, such regions cast shadows on adjacent zones that consequently cool down and shrink, eventually leading to an alternating pattern of overheated and shadowed regions. Previous investigations have proposed this to be a real self-sustained process, the so-called self-shadowing or thermal wave instability, which could naturally form frequently observed disk structures such as rings and gaps, and even potentially enhance the formation of planetesimals. All of these, however, have assumed in one way or another vertical hydrostatic equilibrium and instantaneous radiative diffusion throughout the disk. In this work we present the first study of the stability of accretion disks to self-shadowing that relaxes these assumptions, relying instead on radiation-hydrodynamical simulations. We first construct hydrostatic disk configurations by means of an iterative procedure and show that the formation of a pattern of enlarged and shadowed regions is a direct consequence of assuming instantaneous radiative diffusion. We then let these solutions evolve in time, which leads to a fast damping of the initial shadowing features in layers close to the disk surface. These thermally relaxed layers grow towards the midplane until all temperature extrema in the radial direction are erased in the entire disk. Our results suggest that radiative cooling and gas advection at the disk surface prevent a self-shadowing instability from forming, by damping temperature perturbations before these reach lower, optically thick regions.Comment: 26 pages, 19 figures. Accepted for publication in ApJ. Complementary videos can be found in https://youtu.be/RT8IFe8W13

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks II. Secondary instabilities and stability regions

The vertical shear instability (VSI) is a hydrodynamical instability likely to produce turbulence in the dead zones of protoplanetary disks. Various aspects of this instability remain to be understood, including the disk regions where it can operate and the physical phenomena leading to its saturation. In this work, we studied the growth and evolution of secondary instabilities parasitic to the VSI, examining their relation with its saturation in axisymmetric radiation-hydrodynamical simulations of protoplanetary disks. We also constructed stability maps for our disk models, considering temperature stratifications enforced by stellar irradiation and radiative cooling and incorporating the effects of dust-gas collisions and molecular line emission. We found that the flow pattern produced by the interplay of the axisymmetric VSI modes and the baroclinic torque forms bands of nearly uniform specific angular momentum. In the high-shear regions in between these bands, the Kelvin-Helmholtz instability (KHI) is triggered. The significant transfer of kinetic energy to small-scale eddies produced by the KHI and possibly even the baroclinic acceleration of eddies limit the maximum energy of the VSI modes, likely leading to the saturation of the VSI. A third instability mechanism, consisting of an amplification of eddies by baroclinic torques, forms meridional vortices with Mach numbers up to $\sim 0.4$. Our stability analysis suggests that protoplanetary disks can be VSI-unstable in surface layers up to tens of au for reasonably high gas emissivities, even in regions where the midplane is stable. This picture is consistent with current observations of disks showing thin midplane millimeter-sized dust layers while appearing vertically extended in optical and near-infrared wavelengths.Comment: Accepted for publication in Astronomy & Astrophysic

Vertical shear instability in two-moment radiation-hydrodynamical simulations of irradiated protoplanetary disks I. Angular momentum transport and turbulent heating

We studied the linear and nonlinear evolution of the Vertical Shear Instability (VSI) in axisymmetric models of protoplanetary disks, focusing on the transport of angular momentum, the produced temperature perturbations, and the applicability of local stability conditions. We modeled the gas-dust mixture via high-resolution two-moment (M1) radiation-hydrodynamical simulations including stellar irradiation with frequency-dependent opacities. We found that, given sufficient depletion of small grains (with a dust-to-gas mass ratio of $10\%$ of our nominal value of $10^{-3}$ for $<0.25$ $\mu$m grains), the VSI can operate in surface disk layers while being inactive close to the midplane, resulting in a suppression of the VSI body modes. The VSI reduces the initial vertical shear in bands of approximately uniform specific angular momentum, whose formation is likely favored by the enforced axisymmetry. Similarities with Reynolds stresses and angular momentum distributions in 3D simulations suggest that the VSI-induced angular momentum mixing in the radial direction may be predominantly axisymmetric. The stability regions in our models are well explained by local stability criteria, while the employment of global criteria is still justifiable up to a few scale heights above the midplane, at least as long as VSI modes are radially optically thin. Turbulent heating produces only marginal temperature increases of at most $0.1\%$ and $0.01\%$ in the nominal and dust-depleted models, respectively, peaking at a few (approximately three) scale heights above the midplane. We conclude that it is unlikely that the VSI can, in general, lead to any significant temperature increase since that would either require it to efficiently operate in largely optically thick disk regions or to produce larger levels of turbulence than predicted by models of passive irradiated disks.Comment: Accepted for publication in Astronomy & Astrophysic

Effect of diet, age and sex on the renal response to immune injury in the rat

Effect of diet, age and sex on the glomerular response to immune injury in the rat. We investigated the effect of three factors, namely dietary protein intake, age and sex, on the susceptibility of the renal glomerulus to the binding of antiglomerular basement membrane antibody (anti-GBM) in the early (heterologous) phase of anti-GBM nephritis, and the consequent reduction in glomerular filtration rate (GFR) as measured by inulin clearance (CIn). The effect of diet was examined in ≈ 8 week-old female Munich-Wistar rats fed a 40% high (HP) or a 6% low (LP) protein diet, and that of sex and age in male and female rats, 6 week or 10 month old. Following an intravenous dose (3 to 20 µg/g body wt) of radiolabeled nephritogenic anti-GBM, assessment of glomerular function was followed by quantitation of anti-GBM binding (values corrected for GBM surface area) in isolated glomeruli. At a given plasma level of antibody, the degree of binding of anti-GBM was slightly but significantly higher in HP than LP-fed rats; the decrease in GFR was significantly more pronounced in HP than LP-fed animals. The amount of anti-GBM binding was significantly greater in adult than young animals; however, the consequent decrease in GFR was more pronounced in the young than adult animals. Sex dependency was not discernible in anti-GBM binding or reduction in GFR. In all of the above experimental groups, the degree of anti-GBM binding was closely correlated with the plasma level of anti-GBM, but not with effective renal plasma flow rate, measured by PAH clearance. Separate groups of rats were subjected to experimental manipulation of single nephron GFR, glomerular capillary hydraulic pressure and glomerular plasma flow rate, by partial aortic constriction and saralasin administration. This set of experiments, using a tracer amount of non-nephritogenic anti-GBM, revealed that glomerular anti-GBM binding is independent of any of the above parameters. The studies indicate that dietary protein intake and age, but not sex, are among the factors determining the susceptibility of the glomerulus to acute immune injury. Since the binding of anti-GBM is determined by the affinity property of the glomerulus per se, and not by the prevailing hemodynamic pattern, the observed dependence of susceptibility to functional impairment on age and protein intake appears to also reflect a property of the glomerulus, which is influenced by age and the degree of dietary protein intake