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

Planet Shadows in Protoplanetary Disks. I: Temperature Perturbations

Planets embedded in optically thick passive accretion disks are expected to produce perturbations in the density and temperature structure of the disk. We calculate the magnitudes of these perturbations for a range of planet masses and distances. The model predicts the formation of a shadow at the position of the planet paired with a brightening just beyond the shadow. We improve on previous work on the subject by self-consistently calculating the temperature and density structures under the assumption of hydrostatic equilibrium and taking the full three-dimensional shape of the disk into account rather than assuming a plane-parallel disk. While the excursion in temperatures is less than in previous models, the spatial size of the perturbation is larger. We demonstrate that a self-consistent calculation of the density and temperature structure of the disk has a large effect on the disk model. In addition, the temperature structure in the disk is highly sensitive to the angle of incidence of stellar irradition at the surface, so accurately calculating the shape of the disk surface is crucial for modeling the thermal structure of the disk.Comment: 14 pages, 14 figures. To appear in Ap

Radiative Transfer on Perturbations in Protoplanetary Disks

We present a method for calculating the radiative tranfer on a protoplanetary disk perturbed by a protoplanet. We apply this method to determine the effect on the temperature structure within the photosphere of a passive circumstellar disk in the vicinity of a small protoplanet of up to 20 Earth masses. The gravitational potential of a protoplanet induces a compression of the disk material near it, resulting in a decrement in the density at the disk's surface. Thus, an isodensity contour at the height of the photosphere takes on the shape of a well. When such a well is illuminated by stellar irradiation at grazing incidence, it results in cooling in a shadowed region and heating in an exposed region. For typical stellar and disk parameters relevant to the epoch of planet formation, we find that the temperature variation due to a protoplanet at 1 AU separation from its parent star is about 4% (5 K) for a planet of 1 Earth mass, about 14% (19 K) for planet of 10 Earth masses, and about 18% (25 K) for planet of 20 Earth masses, We conclude that even such relatively small protoplanets can induce temperature variations in a passive disk. Therefore, many of the processes involved in planet formation should not be modeled with a locally isothermal equation of state.Comment: 23 pages, 8 figures (including 3 color figs). Submitted to Ap

Constraints on the Formation of the Planet Around HD188753A

The claimed discovery of a Jupiter-mass planet in the close triple star system HD 188753 poses a problem for planet formation theory. A circumstellar disk around the planet's parent star would be truncated close to the star, leaving little material available for planet formation. In this paper, we attempt to model a protoplanetary disk around HD 188753A using a fairly simple alpha-disk model, exploring a range of parameters constrained by observations of T Tauri-type stars. The disk is truncated to within 1.5 to 2.7 AU, depending on model parameters. We find that the in situ formation of the planet around HD 188753A is implausible.Comment: Accepted version, to appear in ApJ. 23 pages, 5 figures (3 in color

Disk Temperature Variations and Effects on the Snow Line in the Presence of Small Protoplanets

We revisit the computation of a "snow line" in a passive protoplanetary disk during the stage of planetesimal formation. We examine how shadowing and illumination in the vicinity of a planet affects where in the disk ice can form, making use of our method for calculating radiative transfer on disk perturbations with some improvements on the model. We adopt a model for the unperturbed disk structure that is more consistent with observations and use opacities for reprocessed dust instead of interstellar medium dust. We use the improved disk model to calculate the temperature variation for a range of planet masses and distances and find that planets at the gap-opening threshold can induce temperature variations of up to +/-30%. Temperature variations this significant may have ramifications for planetary accretion rates and migration rates. We discuss in particular the effect of temperature variations near the sublimation point of water, since the formation of ice can enhance the accretion rate of disk material onto a planet. Shadowing effects can cool the disk enough that ice will form closer to the star than previously expected, effectively moving the snow line inward.Comment: 28 pages, 14 figures, to appear in the Astrophysical Journa

Type I Migration in a Non-Isothermal Protoplanetary Disk

We calculate rates of Type I migration of protoplanets in a non-isothermal three-dimensional protoplanetary disk, building upon planet-disk models developed in previous work. We find that including the vertical thickness of the disk results in a decrease in the Type I migration rate by a factor of ~2 from a two-dimensional disk. The vertical temperature variation has only a modest effect on migration rates since the torques at the midplane are weighted heavily both because the density and the perturbing potential are maximized at the midplane. However, temperature perturbations resulting from shadowing and illumination at the disk's surface can decrease the migration rate by up to another factor of 2 for planets at the gap-opening threshold at distances where viscous heating is minimal. This would help to resolve the timescale mismatch between the standard core-accretion scenario for planet formation and the survival of planets, and could help explain some of the rich diversity of planetary systems already observed.Comment: 9 pages, 8 figures. Accepted to the Astrophysical Journa

Dust Rings and Cavities in the Protoplanetary Disks around HD 163296 and DoAr 44

We model substructure in the protoplanetary disks around DoAr 44 and HD 163296 in order to better understand the conditions under which planets may form. We match archival millimeter-wavelength thermal emission against models of the disks' structure that are in radiation balance with the starlight heating and in vertical hydrostatic equilibrium, and then compare to archival polarized scattered near-infrared images of the disks. The millimeter emission arises in the interior, while the scattered near-infrared radiation probes the disks' outer layers. Our best model of the HD 163296 disk has dust masses $81\pm 13$ $M_\oplus$ in the inner ring at 68 au and $82^{+26}_{-16}$ $M_\oplus$ in the outer ring at 102 au, both falling within the range of estimates from previous studies. Our DoAr 44 model has total dust mass $84^{+7.0}_{-3.5}$ $M_\oplus$. Unlike HD 163296, DoAr 44 as of yet has no detected planets. If the central cavity in the DoAr 44 disk is caused by a planet, the planet's mass must be at least 0.5 $M_J$ and is unlikely to be greater than 1.6 $M_J$. We demonstrate that the DoAr 44 disk's structure with a bright ring offset within a fainter skirt can be formed by dust particles drifting through a plausible distribution of gas.Comment: 18 pages, 19 figure

The 0.5 micrometer-2.2 micrometer Scattered Light Spectrum of the Disk Around TW Hya

We present a 0.5-2.2micron scattered light spectrum of the circumstellar disk around TW Hya from a combination of spatially resolved HST STIS spectroscopy and NICMOS coronagraphic images of the disk. \Ve investigate the morphology at the disk at distances> 40 AU over this wide range of wavelengths. We measure the surface brightness, azimuthal symmetry, and spectral character of the disk as a function of radius. We find that the scattering efficiency of the dust is largely neutral to blue over the observed wavelengths. We find a good fit to the data over a wide range of distances from the star if we use a model disk with a partial gap of 30% depth at 80 AU and with steep disk truncation exterior to 100 AU. If the gap is caused by a planetary companion in the process of accreting disk gas, it must be less than 20 Solar mass