Multiple Disk Gaps and Rings Generated by a Single Super-Earth: II. Spacings, Depths, and Number of Gaps, with Application to Real Systems

ALMA has found multiple dust gaps and rings in a number of protoplanetary disks in continuum emission at millimeter wavelengths. The origin of such structures is in debate. Recently, we documented how one super-Earth planet can open multiple (up to five) dust gaps in a disk with low viscosity ($\alpha\lesssim10^{-4}$). In this paper, we examine how the positions, depths, and total number of gaps opened by one planet depend on input parameters, and apply our results to real systems. Gap locations (equivalently, spacings) are the easiest metric to use when making comparisons between theory and observations, as positions can be robustly measured. We fit the locations of gaps empirically as functions of planet mass and disk aspect ratio. We find that the locations of the double gaps in HL Tau and TW Hya, and of all three gaps in HD 163296, are consistent with being opened by a sub-Saturn mass planet. This scenario predicts the locations of other gaps in HL Tau and TW Hya, some of which appear consistent with current observations. We also show how the Rossby wave instability may develop at the edges of several gaps and result in multiple dusty vortices, all caused by one planet. A planet as low in mass as Mars may produce multiple dust gaps in the terrestrial planet forming region.Comment: 16 pages; ApJ accepte

Multiple Disk Gaps and Rings Generated by a Single Super-Earth

We investigate the observational signatures of super-Earths (i.e., Earth-to-Neptune mass planets) in their natal disks of gas and dust. Combining two-fluid global hydrodynamics simulations with a radiative transfer code, we calculate the distributions of gas and of sub-mm-sized dust in a disk perturbed by a super-Earth, synthesizing images in near-infrared scattered light and the mm-wave thermal continuum for direct comparison with observations. In low viscosity gas ($\alpha\lesssim10^{-4}$), a super-Earth opens two annular gaps to either side of its orbit by the action of Lindblad torques. This double gap and its associated gas pressure gradients cause dust particles to be dragged by gas into three rings: one ring sandwiched between the two gaps, and two rings located at the gap edges farthest from the planet. Depending on system parameters, additional rings may manifest for a single planet. A double gap located at tens of AUs from a host star in Taurus can be detected in the dust continuum by the Atacama Large Millimeter Array (ALMA) at an angular resolution of ~0".03 after two hours of integration. Ring and gap features persist in a variety of background disk profiles, last for thousands of orbits, and change their relative positions and dimensions depending on the speed and direction of planet migration. Candidate double gaps have been observed by ALMA in systems like HL Tau (D5 and D6) and TW Hya (at 37 and 43 AU); we submit that each double gap is carved by one super-Earth in nearly inviscid gas.Comment: 23 pages, 1 table, 14 figures, ApJ accepte

Standing sausage modes in coronal loops with plasma flow

Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops.We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated, its solutions used to construct standing modes. Two transverse profiles are distinguished, one being the generalized Epstein distribution (profile E) and the other (N) proposed recently in Nakariakov et al.(2012). A parameter study is performed on the dependence of the maximum period $P_\mathrm{max}$ and cutoff length-to-radius ratio $(L/a)_{\mathrm{cutoff}}$ in the trapped regime on the density parameters ($\rho_0/\rho_\infty$ and profile steepness $p$) and flow parameters (magnitude $U_0$ and profile steepness $u$). For either profile, introducing a flow reduces $P_\mathrm{max}$ relative to the static case. $P_\mathrm{max}$ depends sensitively on $p$ for profile N but is insensitive to $p$ for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: $(L/a)_{\mathrm{cutoff}}$ may be substantially reduced in the case with flow relative to the static one. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E better describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfv\'en speed can make coronal loops considerably less likely to support trapped standing sausage modes.Comment: 11 pages, 9 figures, to appear in Astronomy & Astrophysic