Gaps in Protoplanetary Disks as Signatures of Planets: I. Methodology and Validation

We examine the observational consequences of partial gaps being opened by planets in protoplanetary disks. We model the disk using a static alpha-disk model with detailed radiative transfer, parametrizing the shape and size of the partially cleared gaps based on the results of hydrodynamic simulations. Shadowing and illumination by stellar irradiation at the surface of the gap leads to increased contrast as the gap trough is deepened by shadowing and cooling and the far gap wall is puffed up by illumination and heating. In calculating observables, we find that multiple scattering is important and derive an approximation to include these effects. A gap produced by a 200 M_Earth (70 M_Earth) planet at 10 AU can lower/raise the midplane temperature of the disk by up to ~-25/+29% (~-11/+19%) by shadowing in the gap trough and illumination on the far shoulder of the gap. At the distance of Taurus, this gap would be resolvable with ~0.01" angular resolution. The gap contrast is most significant in scattered light and at thermal continuum wavelengths characteristic of the surface temperature, reducing or raising the surface brightness by up to order of magnitude. Since gaps sizes are correlated to planet mass, this is a promising way of finding and determining the masses of planets embedded in protoplanetary disks.Comment: 11 pages, 9 figures. Accepted to Ap

Radiative Transfer Models of a Possible Planet in the AB Aurigae Disk

Recent coronagraphic imaging of the AB Aurigae disk has revealed a region of low polarized scattered light suggestive of perturbations from a planet at a radius of ~100 AU. We model this darkened region using our fully non-plane-parallel radiative-transfer code combined with a simple hydrostatic equilibirum approximation to self-consistently solve for the structure of the disk surface as seen in scattered light. By comparing the observations to our models, we find that the observations are consistent with the absence of a planet, with an upper limit of 1 Jupiter mass.Comment: Accepted to ApJ Letter

Circle actions on almost complex manifolds with 4 fixed points

Let the circle act on a compact almost complex manifold $M$. In this paper, we classify the fixed point data of the action if there are 4 fixed points and the dimension of the manifold is at most 6. First, if $\dim M=2$, then $M$ is a disjoint union of rotations on two 2-spheres. Second, if $\dim M=4$, we prove that the action alikes a circle action on a Hirzebruch surface. Finally, if $\dim M=6$, we prove that six types occur for the fixed point data; $\mathbb{CP}^3$ type, complex quadric in $\mathbb{CP}^4$ type, Fano 3-fold type, $S^6 \cup S^6$ type, and two unknown types that might possibly be realized as blow ups of a manifold like $S^6$. When $\dim M=6$, we recover the result by Ahara in which the fixed point data is determined if furthermore $\mathrm{Todd}(M)=1$ and $c_1^3(M)[M] \neq 0$, and the result by Tolman in which the fixed point data is determined if furthermore the base manifold admits a symplectic structure and the action is Hamiltonian

Symplectic circle actions with isolated fixed points

Consider a symplectic circle action on a closed symplectic manifold with non-empty isolated fixed points. Associated to each fixed point, there are well-defined non-zero integers, called weights. We prove that the action is Hamiltonian if the sum of an odd number of weights is never equal to zero (the weights may be taken at different fixed points). Moreover, we show that if $\dim M=6$, or if $\dim M=2n \leq 10$ and each fixed point has weights $\{\pm a_1, \cdots, \pm a_n\}$ for some positive integers $a_i$, it is enough to consider the sum of three weights. As applications, we recover the results for semi-free actions, and for certain circle actions on six-dimensional manifolds