Formation of a disc gap induced by a planet: Effect of the deviation from Keplerian disc rotation

The gap formation induced by a giant planet is important in the evolution of the planet and the protoplanetary disc. We examine the gap formation by a planet with a new formulation of one-dimensional viscous discs which takes into account the deviation from Keplerian disc rotation due to the steep gradient of the surface density. This formulation enables us to naturally include the Rayleigh stable condition for the disc rotation. It is found that the derivation from Keplerian disc rotation promotes the radial angular momentum transfer and makes the gap shallower than in the Keplerian case. For deep gaps, this shallowing effect becomes significant due to the Rayleigh condition. In our model, we also take into account the propagation of the density waves excited by the planet, which widens the range of the angular momentum deposition to the disc. The effect of the wave propagation makes the gap wider and shallower than the case with instantaneous wave damping. With these shallowing effects, our one-dimensional gap model is consistent with the recent hydrodynamic simulations.Comment: 15 pages, 13 figures, accepted for publication in MNRA

Enhanced resonant force between two entangled identical atoms in a photonic crystal

We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation of their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms is close to the edge of a photonic gap. Differences between the two models considered of photonic crystal are discussed in detail, as well as comparison with the analogous system of two impurity atoms in a quantum semiconductor wire. A numerical estimate of the effect in a realistic situation is also discussed.Comment: 8 page

Mass Estimates of a Giant Planet in a Protoplanetary Disk from the Gap Structures

A giant planet embedded in a protoplanetary disk forms a gap. An analytic relationship among the gap depth, planet mass $M_{p}$, disk aspect ratio $h_p$, and viscosity $\alpha$ has been found recently, and the gap depth can be written in terms of a single parameter $K= (M_{p}/M_{\ast})^2 h_p^{-5} \alpha^{-1}$. We discuss how observed gap features can be used to constrain the disk and/or planet parameters based on the analytic formula for the gap depth. The constraint on the disk aspect ratio is critical in determining the planet mass so the combination of the observations of the temperature and the image can provide a constraint on the planet mass. We apply the formula for the gap depth to observations of HL~Tau and HD~169142. In the case of HL~Tau, we propose that a planet with $\gtrsim 0.3$ is responsible for the observed gap at $30$~AU from the central star based on the estimate that the gap depth is $\lesssim 1/3$. In the case of HD~169142, the planet mass that causes the gap structure recently found by VLA is $\gtrsim 0.4 M_J$. We also argue that the spiral structure, if observed, can be used to estimate the lower limit of the disk aspect ratio and the planet mass.Comment: 16 pages, 5 figures, accepted for publication in The Astrophysical Journal Letter

Easy-to-Use InDel Markers for Genetic Mapping between Col-0 and Ler-0 Accessions of Arabidopsis thaliana

Map-based gene cloning has played a key role in many genetic studies using the model plant,Arabidopsis thaliana. In the post-next generation sequencing era, identification of point mutations and their corresponding genes is increasingly becoming a powerful and important approach to define plant gene function. To perform initial mapping experiments efficiently on Arabidopsis mutants, enrichment of easy-to-use and reliable polymorphic DNA markers would be desirable. We present here a list of InDel polymorphic markers between Col-0 and Ler-0 accessions that can be detected in standard agarose gel electrophoresis

On the Interaction between a Protoplanetary Disk and a Planet in an Eccentric Orbit: Application of Dynamical Friction

We present a new analytic approach to the disk-planet interaction that is especially useful for planets with eccentricity larger than the disk aspect ratio. We make use of the dynamical friction formula to calculate the force exerted on the planet by the disk, and the force is averaged over the period of the planet. The resulting migration and eccentricity damping timescale agrees very well with the previous works in which the planet eccentricity is moderately larger than the disk aspect ratio. The advantage of this approach is that it is possible to apply this formulation to arbitrary large eccentricity. We have found that the timescale of the orbital evolution depends largely on the adopted disk model in the case of highly eccentric planets. We discuss the possible implication of our results to the theory of planet formation.Comment: 27 pages, 11 figures, 2 tables, ApJ accepte

Online Neural Path Guiding with Normalized Anisotropic Spherical Gaussians

The variance reduction speed of physically-based rendering is heavily affected by the adopted importance sampling technique. In this paper we propose a novel online framework to learn the spatial-varying density model with a single small neural network using stochastic ray samples. To achieve this task, we propose a novel closed-form density model called the normalized anisotropic spherical gaussian mixture, that can express complex irradiance fields with a small number of parameters. Our framework learns the distribution in a progressive manner and does not need any warm-up phases. Due to the compact and expressive representation of our density model, our framework can be implemented entirely on the GPU, allowing it produce high quality images with limited computational resources