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

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

Front representation of set partitions

Let $\pi$ be a set partition of $[n]=\{1,2,...,n\}$. The standard representation of $\pi$ is the graph on the vertex set $[n]$ whose edges are the pairs $(i,j)$ of integers with $i<j$ in the same block which does not contain any integer between $i$ and $j$. The front representation of $\pi$ is the graph on the vertex set $[n]$ whose edges are the pairs $(i,j)$ of integers with $i<j$ in the same block whose smallest integer is $i$. Using the front representation, we find a recurrence relation for the number of $12... k12$-avoiding partitions for $k\geq2$. Similarly, we find a recurrence relation for the number of $k$-distant noncrossing partitions for $k=2,3$. We also prove that the front representation has several joint symmetric distributions for crossings and nestings as the standard representation does.Comment: 16 pages, 7 figures, final versio