Zhaohuan Zhu

TRANSITIONAL AND PRE-TRANSITIONAL DISKS: GAP OPENING BY MULTIPLE PLANETS?

We use two-dimensional hydrodynamic simulations of viscous disks to examine whether dynamically interacting multiple giant planets can explain the large gaps (spanning over one order of magnitude in radius) inferred for the transitional and pre-transitional disks around T Tauri stars. In the absence of inner disk dust depletion, we find that it requires three to four giant planets to open up large enough gaps to be consistent with inferences from spectral energy distributions, because the gap width is limited by the tendency of the planets to be driven together into 2:1 resonances. With very strong tidal torques and/or rapid planetary accretion, fewer planets can also generate a large cavity interior to the locally formed gap(s) by preventing outer disk material from moving in. In these cases, however, the reduction of surface density produces a corresponding reduction in the inner disk accretion rate onto the star; this makes it difficult to explain the observed accretion rates of the pre-transitional/transitional disks. We find that even with four planets in disks, additional substantial dust depletion is required to explain observed disk gaps/holes. Substantial dust settling and growth, with consequent significant reductions in optical depths, is inferred for typical T Tauri disks in any case, and an earlier history of dust growth is consistent with the hypothesis that pre-transitional/transitional disks are explained by the presence of giant planets. We conclude that the depths and widths of gaps and disk accretion rates in pre-transitional/transitional disks cannot be reproduced by a planet-induced gap opening scenario alone. Significant dust depletion is also required within the gaps/holes. Order-of-magnitude estimates suggest that the mass of small dust particles (1 μm) relative to the gas must be depleted to 10 −5 to 10 −2 of the interstellar medium value, implying a very efficient mechanism of small dust removal or dust growth.

Nonsteady accretion in protostars

Observations indicate that mass accretion rates onto low-mass protostars are generally lower than the rates of infall to their disks; this suggests that much of the protostellar mass must be accreted during rare, short outbursts of rapid accretion. We explore when protostellar disk accretion is likely to be highly variable. While constant α disks can in principle adjust their accretion rates to match infall rates, protostellar disks are unlikely to have constant α. In particular, we show that neither models with angular momentum transport due solely to the magnetorotational instability (MRI) nor gravitational instability (GI) are likely to transport disk mass at protostellar infall rates over the large range of radii needed to move infalling envelope material down to the central protostar. We show that the MRI and GI are likely to combine to produce outbursts of rapid accretion starting at a few AU. Our analysis is consistent with the time-dependent models of Armitage et al. and agrees with our observational study of the outbursting object FU Ori.

RINGED SUBSTRUCTURE AND A GAP AT 1 au IN THE NEAREST PROTOPLANETARY DISK

We present long-baseline Atacama Large Millimeter/submillimeter Array (ALMA) observations of the 870 micron continuum emission from the nearest gas-rich protoplanetary disk, around TW Hya, that trace millimeter-sized particles down to spatial scales as small as 1 AU (20 mas). These data reveal a series of concentric ring-shaped substructures in the form of bright zones and narrow dark annuli (1-6 AU) with modest contrasts (5-30%). We associate these features with concentrations of solids that have had their inward radial drift slowed or stopped, presumably at local gas pressure maxima. No significant non-axisymmetric structures are detected. Some of the observed features occur near temperatures that may be associated with the condensation fronts of major volatile species, but the relatively small brightness contrasts may also be a consequence of magnetized disk evolution (the so-called zonal flows). Other features, particularly a narrow dark annulus located only 1 AU from the star, could indicate interactions between the disk and young planets. These data signal that ordered substructures on ~AU scales can be common, fundamental factors in disk evolution, and that high resolution microwave imaging can help characterize them during the epoch of planet formation.

Two-dimensional Simulations of FU Orionis Disk Outbursts

We have developed time-dependent models of FU Ori accretion outbursts to explore the physical properties of protostellar disks. Our two-dimensional, axisymmetric models incorporate full vertical structure with a new treatment of the radiative boundary condition for the disk photosphere. We find that FU Ori-type outbursts can be explained by a slow accumulation of matter due to gravitational instability. Eventually, this triggers the magnetorotational instability, which leads to rapid accretion. The thermal instability is triggered in the inner disk, but this instability is not necessary for the outburst. An accurate disk vertical structure, including convection, is important for understanding the outburst behavior. Large convective eddies develop at the transition region between the thermal instability high-low states in the inner disk. The models are in agreement with Spitzer IRS spectra and also with peak accretion rates and decay timescales of observed outbursts, though some objects show faster rise timescale. We also propose that convection may account for the observed mild-supersonic turbulence and the short-timescale variations of FU Orionis objects.

LONG-TERM EVOLUTION OF PROTOSTELLAR AND PROTOPLANETARY DISKS. I. OUTBURSTS

As an initial investigation into the long-term evolution of protostellar disks, we explore the conditions required to explain the large outbursts of disk accretion seen in some young stellar objects. We use one-dimensional time-dependent disk models with a phenomenological treatment of the magnetorotational instability (MRI) and gravitational torques to follow disk evolution over long timescales. Comparison with our previous two-dimensional disk model calculations indicates that the neglect of radial effects and two-dimensional disk structure in the one-dimensional case makes only modest differences in the results; this allows us to use the simpler models to explore parameter space efficiently. We find that the mass infall rates typically estimated for low-mass protostars generally result in AU-scale disk accretion outbursts, as predicted by our previous analysis. We also confirm quasi-steady accretion behavior for high mass infall rates if the values of α-parameter for the MRI are small, while at this high accretion rate convection from the thermal instability may lead to some variations. We further constrain the combinations of the α-parameter and the MRI critical temperature, which can reproduce observed outburst behavior. Our results suggest that dust sublimation may be connected with full activation of the MRI. This is consistent with the idea that small dust captures ions and electrons to suppress the MRI. In a companion paper, we will explore both long-term outburst and disk evolution with this model, allowing for infall from protostellar envelopes with differing angular momenta

OBSERVATIONAL SIGNATURES OF PLANETS IN PROTOPLANETARY DISKS. I. GAPS OPENED BY SINGLE AND MULTIPLE YOUNG PLANETS IN DISKS

It has been suggested that the gaps and cavities recently discovered in transitional disks are opened by planets. To explore this scenario, we combine two-dimensional two fluid (gas + particle) hydrodynamical calculations with three-dimensional Monte Carlo Radiative Transfer simulations, and study the observational signatures of gaps opened by one or several planets, making qualitative comparisons with observations. We find that a single planet as small as 0.2 MJ can produce a deep gap at millimeter (mm) wavelengths and almost no features at near-infrared (NIR) wavelengths, while multiple planets can open up a few *10 AU wide common gap at both wavelengths. Both the contrast ratio of the gaps and the wavelength dependence of the gap sizes are broadly consistent with data. We also confirm previous results that NIR gap sizes may be smaller than mm gap sizes due to dust-gas coupling and radiative transfer effects. When viewed at a moderate inclination angle, a physically circular on-centered gap could appear to be off-centered from the star due to shadowing. Planet-induced spiral arms are more apparent at NIR than at mm wavelengths. Overall, our results suggest that the planet-opening-gap scenario is a promising way to explain the origin of the transitional disks. Finally, inspired by the recent ALMA release of the image of the HL Tau disk, we show that multiple narrow gaps, well separated by bright rings, can be opened by 0.2 MJ planets soon after their formation in a relatively massive disk.

The Missing Cavities in the SEEDS Polarized Scattered Light Images of Transitional Protoplanetary Disks: A Generic Disk Model

Transitional circumstellar disks around young stellar objects have a distinctive infrared deficit around 10 μm in their spectral energy distributions, recently measured by the Spitzer Infrared Spectrograph (IRS), suggesting dust depletion in the inner regions. These disks have been confirmed to have giant central cavities by imaging of the submillimeter continuum emission using the Submillimeter Array (SMA). However, the polarized near-infrared scattered light images for most objects in a systematic IRS/SMA cross sample, obtained by HiCIAO on the Subaru telescope, show no evidence for the cavity, in clear contrast with SMA and Spitzer observations. Radiative transfer modeling indicates that many of these scattered light images are consistent with a smooth spatial distribution for μm-sized grains, with little discontinuity in the surface density of the μm-sized grains at the cavity edge. Here we present a generic disk model that can simultaneously account for the general features in IRS, SMA, and Subaru observations. Particularly, the scattered light images for this model are computed, which agree with the general trend seen in Subaru data. Decoupling between the spatial distributions of the μm-sized dust and mm-sized dust inside the cavity is suggested by the model, which, if confirmed, necessitates a mechanism, such as dust filtration, for differentiating the small and big dust in the cavity clearing process. Our model also suggests an inwardly increasing gas-to-dust ratio in the inner disk, and different spatial distributions for the small dust inside and outside the cavity, echoing the predictions in grain coagulation and growth models.

The Hot Inner Disk of FU Orionis

We have constructed a detailed radiative transfer disk model which reproduces the main features of the spectrum of the outbursting young stellar object FU Orionis from ~4000 A to ~8 μm. Using an estimated visual extinction AV ~ 1.5, a steady disk model with a central star mass ~0.3 M☉, and a mass accretion rate ~2 × 10-4 M☉ yr-1, we can reproduce the SED of FU Ori quite well. Higher values of extinction used in previous analysis (AV ~ 2.1) result in SEDs which are less well fitted by a steady disk model, but might be explained by extra energy dissipation of the boundary layer in the inner disk. With the mid-infrared spectrum obtained by the IRS on board the Spitzer Space Telescope, we estimate that the outer radius of the hot, rapidly accreting inner disk is ~1 AU, using disk models truncated at this outer radius. Inclusion of radiation from a cooler irradiated outer disk might reduce the outer limit of the hot inner disk to ~0.5 AU. In either case, the radius is inconsistent with a pure thermal instability model for the outburst. Our radiative transfer model implies that the central disk temperature Tc ≥ 1000 K out to ~0.5-1 AU, suggesting that the magnetorotational instability can be supported out to that distance. Assuming that the ~100 yr decay timescale in brightness of FU Ori represents the viscous timescale of the hot inner disk, we estimate the viscosity parameter to be α ~ 0.2-0.02 in the outburst state, consistent with numerical simulations of the magnetorotational instability in disks. The radial extent of the high- region is inconsistent with the model of Bell & Lin, but may be consistent with theories incorporating both gravitational and magnetorotational instabilities.

THE STRUCTURE OF SPIRAL SHOCKS EXCITED BY PLANETARY-MASS COMPANIONS

Direct imaging observations have revealed spiral structures in protoplanetary disks. Previous studies have suggested that planet-induced spiral arms cannot explain some of these spiral patterns, due to the large pitch angle and high contrast of the spiral arms in observations. We have carried out three dimensional (3-D) hydrodynamical simulations to study spiral wakes/shocks excited by young planets. We find that, in contrast with linear theory, the pitch angle of spiral arms does depend on the planet mass, which can be explained by the non-linear density wave theory. A secondary (or even a tertiary) spiral arm, especially for inner arms, is also excited by a massive planet. With a more massive planet in the disk, the excited spiral arms have larger pitch angle and the separation between the primary and secondary arms in the azimuthal direction is also larger. We also find that although the arms in the outer disk do not exhibit much vertical motion, the inner arms have significant vertical motion, which boosts the density perturbation at the disk atmosphere. Combining hydrodynamical models with Monte-Carlo radiative transfer calculations, we find that the inner spiral arms are considerably more prominent in synthetic near-IR images using full 3-D hydrodynamical models than images based on 2-D models assuming vertical hydrostatic equilibrium, indicating the need to model observations with full 3-D hydrodynamics. Overall, companion-induced spiral arms not only pinpoint the companions position but also provide three independent ways (pitch angle, separation between two arms, and contrast of arms) to constrain the companions mass.

THE STRUCTURE OF PRE-TRANSITIONAL PROTOPLANETARY DISKS. I. RADIATIVE TRANSFER MODELING OF THE DISK+CAVITY IN THE PDS 70 SYSTEM

Through detailed radiative transfer modeling, we present a disk+cavity model to simultaneously explain both the spectral energy distribution (SED) and Subaru H-band polarized light imaging for the pre-transitional protoplanetary disk PDS 70. In particular, we are able to match not only the radial dependence but also the absolute scale of the surface brightness of the scattered light. Our disk model has a cavity 65 AU in radius, which is heavily depleted of sub-micron-sized dust grains, and a small residual inner disk that produces a weak but still optically thick near-IR excess in the SED. To explain the contrast of the cavitys edge in the Subaru image, a factor of ~1000 depletion for the sub-micron-sized dust inside the cavity is required. The total dust mass of the disk may be on the order of 10?4 M ?, only weakly constrained due to the lack of long-wavelength observations and the uncertainties in the dust model. The scale height of the sub-micron-sized dust is ~6 AU at the cavity edge, and the cavity wall is optically thick in the vertical direction at H-band. PDS 70 is not a member of the class of (pre-)transitional disks identified by Dong et?al., whose members only show evidence of the cavity in the millimeter-size dust but not the sub-micron-sized dust in resolved images. The two classes of (pre-)transitional disks may form through different mechanisms, or they may simply be at different evolution stages in the disk-clearing process.