Gravito-Turbulent Disks in 3D: Turbulent Velocities vs. Depth

Characterizing turbulence in protoplanetary disks is crucial for understanding how they accrete and spawn planets. Recent measurements of spectral line broadening promise to diagnose turbulence, with different lines probing different depths. We use 3D local hydrodynamic simulations of cooling, self-gravitating disks to resolve how motions driven by "gravito-turbulence" vary with height. We find that gravito-turbulence is practically as vigorous at altitude as at depth: even though gas at altitude is much too rarefied to be itself self-gravitating, it is strongly forced by self-gravitating overdensities at the midplane. The long-range nature of gravity means that turbulent velocities are nearly uniform vertically, increasing by just a factor of 2 from midplane to surface, even as the density ranges over nearly three orders of magnitude. The insensitivity of gravito-turbulence to height contrasts with the behavior of disks afflicted by the magnetorotational instability (MRI); in the latter case, non-circular velocities increase by at least a factor of 15 from midplane to surface, with various non-ideal effects only magnifying this factor. The distinct vertical profiles of gravito-turbulence vs. MRI turbulence may be used in conjunction with measurements of non-thermal linewidths at various depths to identify the source of transport in protoplanetary disks.Comment: Accepted to Ap

From Dust to Planetesimals: Criteria for Gravitational Instability of Small Particles in Gas

Dust particles sediment toward the midplanes of protoplanetary disks, forming dust-rich sublayers encased in gas. What densities must the particle sublayer attain before it can fragment by self-gravity? We describe various candidate threshold densities. One of these is the Roche density, which is that required for a strengthless satellite to resist tidal disruption by its primary. Another is the Toomre density, which is that required for de-stabilizing self-gravity to defeat the stabilizing influences of pressure and rotation. We show that for sublayers containing aerodynamically well-coupled dust, the Toomre density exceeds the Roche density by many (up to about 4) orders of magnitude. We present 3D shearing box simulations of self-gravitating, stratified, dust-gas mixtures to test which of the candidate thresholds is relevant for collapse. All our simulations indicate that the larger Toomre density is required for collapse. This result is sensible because sublayers are readily stabilized by pressure. Sound-crossing times for thin layers are easily shorter than free-fall times, and the effective sound speed in dust-gas suspensions decreases only weakly with the dust-to-gas ratio (as the inverse square root). Our findings assume that particles are small enough that their stopping times in gas are shorter than all other timescales. Relaxing this assumption may lower the threshold for gravitational collapse back down to the Roche criterion. In particular, if the particle stopping time becomes longer than the sound-crossing time, sublayers may lose pressure support and become gravitationally unstable.Comment: 19 pages, 13 figures, and 5 tables. ApJ accepte

Gravito-turbulence in irradiated protoplanetary discs

Using radiation hydrodynamics simulations in a local stratified shearing box with realistic equations of state and opacities, we explored the outcome of self-gravity at 50 AU in a protoplanetary disc irradiated by the central star. We found that gravito-turbulence is sustained for a finite range of the surface density, from $\sim 80$ to $\sim$ 250 gcm$^{-2}$. The disk is laminar below the range while fragments above it. In the range of gravito-turbulence, the Toomre parameter decreases monotonically from $\sim 1$ to $\sim 0.7$ as the surface density increases while an effective cooling time is almost constant at $\sim 4$ in terms of the inverse of the orbital frequency. The turbulent motions are supersonic at all heights, which dissipates through both shock waves and compressional heating. The compressional motions, occurring near the midplane, create upward flows, which not only contribute to supporting the disc but also to transporting the dissipated energy to the disc surfaces. The irradiation does not affect much the gravito-turbulence near the midplane unless the grazing angle is larger than 0.32. We also show that a simple cooling function with a constant cooling time does not approximate the realistic cooling.Comment: accepted for publication in MNRA

Nonlinear outcome of gravitational instability in an irradiated protoplanetary disc

Using local three dimensional radiation hydrodynamics simulations, the nonlinear outcome of gravitational instability in an irradiated protoplanetary disc is investigated in a parameter space of the surface density $\Sigma$ and the radius $r$. Starting from laminar flow, axisymmetric self-gravitating density waves grow first. Their self-gravitating degree becomes larger when $\Sigma$ is larger or the cooling time is shorter at larger radii. The density waves eventually collapse owing to non-axisymmetric instability, which results in either fragmentation or gravito-turbulence after a transient phase. The boundaries between the two are found at $r \sim 75$ AU as well as at the $\Sigma$ that corresponds to the initial Toomre's parameter of $\sim 0.2$. The former boundary corresponds to the radius where the cooling time becomes short, approximating unity. Even when gravito-turbulence is established around the boundary radius, such a short cooling time inevitably makes the fluctuation of $\Sigma$ large enough to trigger fragmentation. On the other hand, when $\Sigma$ is beyond the latter boundary (i.e. the initial Toomre's parameter is less than $\sim 0.2$), the initial laminar flow is so unstable against self-gravity that it evolves into fragmentation regardless of the radius or, equivalently, the cooling time. Runaway collapse follows fragmentation when the mass concentration at the centre of a bound object is high enough that the temperature exceeds the H$_2$ dissociation temperature.Comment: accepted for publication in MNRA

Quantum phase transition and entanglement in Li atom system

In this paper we study the quantum phase transition and entanglement in s1=1/2 and s2=1 spin pair system by the exact diagonalization method. We show that, for this exactly solvable quantum bi-spin system, entanglement appears before quantum phase transition and disappears after it. Moreover, we show that the von Neumann entropy, as a measure of entanglement, can reveal quantum phase transition in this system.Comment: 5 pages, 2 figure

Charmonium dissociation in collision with phi meson in hadronic matter

The phi-charmonium dissociation reactions in hadronic matter are studied. Unpolarised cross sections for 12 reactions are calculated in the Born approximation, in the quark-interchange mechanism and with a temperature-dependent quark potential. The potential leads to remarkable temperature dependence of the cross sections. With the cross sections and the phi distribution function we calculate the dissociation rates of the charmonia in the interactions with the phi meson in hadronic matter. The dependence of the rates on temperature and charmonium momentum is meaningful to the influence of phi mesons on charmonium suppression.Comment: 21 pages, 12 figure

Three Dimensional MHD Simulation of Circumbinary Accretion Disks -2. Net Accretion Rate

When an accretion disk surrounds a binary rotating in the same sense, the binary exerts strong torques on the gas. Analytic work in the 1D approximation indicated that these torques sharply diminish or even eliminate accretion from the disk onto the binary. However, recent 2D and 3D simulational work has shown at most modest diminution. We present new MHD simulations demonstrating that for binaries with mass ratios of 1 and 0.1 there is essentially no difference between the accretion rate at large radius in the disk and the accretion rate onto the binary. To resolve the discrepancy with earlier analytic estimates, we identify the small subset of gas trajectories traveling from the inner edge of the disk to the binary and show how the full accretion rate is concentrated onto them.Comment: updated to ApJ accepted versio

How Empty are Disk Gaps Opened by Giant Planets?

Gap clearing by giant planets has been proposed to explain the optically thin cavities observed in many protoplanetary disks. How much material remains in the gap determines not only how detectable young planets are in their birth environments, but also how strong corotation torques are, which impacts how planets can survive fast orbital migration. We determine numerically how the average surface density inside the gap, sigma_gap, depends on planet-to-star mass ratio q, Shakura-Sunyaev viscosity parameter alpha, and disk height-to-radius aspect ratio h/r. Our results are derived from our new GPU-accelerated Lagrangian hydrodynamical code PEnGUIn, and are verified by independent simulations with ZEUS90. For Jupiter-like planets, we find sigma_gap \propto q^-2.2 alpha^1.4 (h/r)^6.6, and for near brown dwarf masses, sigma_gap \propto q^-1 alpha^1.3 (h/r)^6.1. Surface density contrasts inside and outside gaps can be as large as 10^4, even when the planet does not accrete. We derive a simple analytic scaling, sigma_gap \propto q^-2 alpha^1 (h/r)^5, that compares reasonably well to empirical results, especially at low Neptune-like masses, and use discrepancies to highlight areas for progress.Comment: Accepted to Ap

Optimal Throughput--Outage Analysis of Cache-Aided Wireless Multi-Hop D2D Networks -- Derivations of Scaling Laws

Cache-aided wireless device-to-device (D2D) networks have demonstrated promising performance improvement for video distribution compared to conventional distribution methods. Understanding the fundamental scaling behavior of such networks is thus of paramount importance. However, existing scaling laws for multi-hop networks have not been found to be optimal even for the case of Zipf popularity distributions (gaps between upper and lower bounds are not constants); furthermore, there are no scaling law results for such networks for the more practical case of a Mandelbrot-Zipf (MZipf) popularity distribution. We thus in this work investigate the throughput-outage performance for cache-aided wireless D2D networks adopting multi-hop communications, with the MZipf popularity distribution for file requests and users distributed according to Poisson point process. We propose an achievable content caching and delivery scheme and analyze its performance. By showing that the achievable performance is tight to the proposed outer bound, the optimal scaling law is obtained. Furthermore, since the Zipf distribution is a special case of the MZipf distribution, the optimal scaling law for the networks considering Zipf popularity distribution is also obtained, which closes the gap in the literature.Comment: A condensed version of this paper will be submitted to IEEE Transactions on Communication

Series expansion in fractional calculus and fractional differential equations

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functions and derive corresponding differential equations. For finitely fractionally-differentiable functions, we observe that the non-infinitely fractionally-differentiability is due to more than one fractional indices. We expand functions with two fractional indices and display how this kind of series expansion can help to solve fractional differential equations.Comment: 15 pages, no figur