J. E. Bjorkman

TWO-DIMENSIONAL RADIATIVE TRANSFER IN PROTOSTELLAR ENVELOPES. I. EFFECTS OF GEOMETRY ON CLASS I SOURCES

We present two-dimensional radiation transfer models of class I protostars and show the effect of including more realistic geometries on the resulting spectral energy distributions and images. We begin with a rotationally flattened infalling envelope as our comparison model and add a flared disk and bipolar cavity. The disk affects the spectral energy distribution most strongly at edge-on inclinations, causing a broad dip at about 10 lm (independent of the silicate feature) due to high extinction and low scattering albedo in this wavelength region. The bipolar cavities allow more direct stellar+disk radiation to emerge into polar directions and more scattering radiation to emerge into all directions. The wavelength-integrated flux, often interpreted as luminosity, varies with viewing angle, with pole-on viewing angles seeing 2–4 times as much flux as edge-on, depending on geometry. Thus, observational estimates of luminosity should take into account the inclination of a source. The envelopes with cavities are significantly bluer in near-IR and mid-IR color-color plots than those without cavities. Using one-dimensional models to interpret Class I sources with bipolar cavities would lead to an underestimate of envelope mass and an overestimate of the implied evolutionary state. We compute images at near-, mid-, and far-IR wavelengths. We find that the mid-IR colors and images are sensitive to scattering albedo and that the flared disk shadows the midplane on large size scales at all wavelengths plotted. Finally, our models produce polarization spectra that can be used to diagnose dust properties, such as albedo variations due to grain growth. Our results of polarization across the 3.1 l mi ce feature agree well with observations for ice mantles covering 5% of the radius of the grains. Subject headings: circumstellar matter — dust, extinction — polarization — radiative transfer — stars: formation — stars: pre–main-sequence

TWO-DIMENSIONAL RADIATIVE TRANSFER IN PROTOSTELLAR ENVELOPES. II. AN EVOLUTIONARY SEQUENCE

We present model spectral energy distributions (SEDs), colors, polarization, and images for an evolutionary sequence of a low-mass protostar from the early collapse stage (Class 0) to the remnant disk stage (Class III). We find a substantial overlap in colors and SEDs between protostars embedded in envelopes (Class 0–I) and T Tauri disks (Class II), especially at mid-IR wavelengths. Edge-on Class I–II sources show double-peaked SEDs, with a short-wavelength hump due to scattered light and a long-wavelength hump due to thermal emission. These are the bluest sources in mid-IR color-color diagrams. Since Class 0 and I sources are diffuse, the size of the aperture over which fluxes are integrated has a substantial effect on the computed colors, with larger aperture results showing significantly bluer colors. Viewed through large apertures, the Class 0 colors fall in the same regions of mid-IR color-color diagrams as Class I sources and are even bluer than Class II–III sources in some colors. It is important to take this into account when comparing color-color diagrams of star formation regions at different distances or different sets of observations of the same region. However, the near-IR polarization of the Class 0 sources is much higher than the Class I–II sources, providing a means to separate these evolutionary states. We varied the grain properties in the circumstellar envelope, allowing for larger grains in the disk midplane and smaller grains in the envelope. In comparing with models with the same grain properties throughout, we find that the SED of the Class 0 source is sensitive to the grain properties of the envelope only—that is, grain growth in the disk in Class 0 sources cannot be detected from the SED. Grain growth in disks of Class I sources can be detected at wavelengths greater than 100 lm. Our image calculations predict that the diffuse emission from edge-on Class I and II sources should be detectable in the mid-IR with the Space Infrared Telescope Facility (SIRTF) in nearby star-forming regions (out to several hundred parsecs). Subject headings: circumstellar matter — dust, extinction — polarization — radiative transfer — stars: formation — stars: pre–main-sequence

RADIATIVE EQUILIBRIUM AND TEMPERATURE CORRECTION IN MONTE CARLO RADIATION TRANSFER

We describe a general radiative equilibrium and temperature correction procedure for use in Monte Carlo radiation transfer codes with sources of temperature-independent opacity, such as astrophysical dust. The technique utilizes the fact that Monte Carlo simulations track individual photon packets, so we may easily determine where their energy is absorbed. When a packet is absorbed, it heats a particular cell within the envelope, raising its temperature. To enforce radiative equilibrium, the absorbed packet is immediately reemitted. To correct the cell temperature, the frequency of the reemitted packet is chosen so that it corrects the temperature of the spectrum previously emitted by the cell. The reemitted packet then continues being scattered, absorbed, and reemitted until it finally escapes from the envelope. As the simulation runs, the envelope heats up, and the emergent spectral energy distribution (SED) relaxes to its equilibrium value without iteration. This implies that the equilibrium temperature calculation requires no more computation time than the SED calculation of an equivalent pure scattering model with fixed temperature. In addition to avoiding iteration, our method conserves energy exactly because all injected photon packets eventually escape. Furthermore, individual packets transport energy across the entire system because they are never destroyed. This long-range communication, coupled with the lack of iteration, implies that our method does not suffer the convergence problems commonly associated with Λ-iteration. To verify our temperature correction procedure, we compare our results with standard benchmark tests, and finally we present the results of simulations for two-dimensional axisymmetric density structures.

The Spectral Energy Distribution of HH 30 IRS: Constraining the Circumstellar Dust Size Distribution

We present spectral energy distribution (SED) models for the edge-on classical T Tauri star HH 30 IRS that indicate that dust grains have grown to larger than 50 μm within its circumstellar disk. The disk geometry and inclination are known from previous modeling of multiwavelength Hubble Space Telescope images, and we use the SED (0.5 μm ≤ λ ≤ 3 mm) to constrain the dust size distribution. Model spectra are shown for different circumstellar dust models: a standard interstellar medium (ISM) mixture and larger grain models. As compared to ISM grains, the larger dust grain models have a shallower wavelength-dependent opacity: smaller at short wavelengths and larger at long wavelengths. Models with the larger dust grains provide a good match to the observed SED of HH 30 IRS. Although the currently available SED is poorly sampled, we estimate L* ≈ 0.2 L☉, Mdisk ≈ 1.5 × 10-3 M☉, and a power law with exponential cutoff dust grain size distribution. This model provides a good fit to the currently available data, but mid- and far-IR observations are required to more tightly constrain the size distribution. The accretion luminosity in our models is Lacc 0.2L*, corresponding to an accretion rate 4 × 10-9 M☉ yr-1. Dust size distributions that are simple power-law extensions (i.e., no exponential cutoff) yield acceptable fits to the optical/near-IR but too much emission at millimeter wavelengths, and require larger disk masses up to Mdisk ~ 0.5 M☉. Such a simple size distribution would not be expected in an environment such as the disk of HH 30 IRS (i.e., where coagulation and accretion processes are occurring in addition to grain shattering), particularly over such a large range in grain sizes. Its ability to adequately characterize the grain populations, however, may be determined from more complete observational sampling of the SED in the mid- to far-IR.

Constraints on a planetary origin for the gap in the protoplanetary disc of GM Aurigae

The unusual spectral energy distribution (SED) of the classical T Tauri star GM Aurigae provides evidence for the presence of an inner disc hole extending to several au. Using a combination of hydrodynamical simulations and Monte Carlo radiative transport, we investigate whether the observed SED is consistent with the inner hole being created and maintained by an orbiting planet. We show that an ∼ 2M J planet, orbiting at 2.5 au in a disc with mass

Non-LTE Monte Carlo Radiative Transfer. I. The Thermal Properties of Keplerian Disks around Classical Be Stars

We present a three-dimensional non-LTE Monte Carlo radiative transfer code that we use to study the temperature and ionization structure of Keplerian disks around classical Be stars. The method we employ is largely similar to the Monte Carlo transition probability method developed by Lucy. Here we present a simplification of his method that avoids the use of the macroatom concept. Our investigations of the temperature structure of Be star disks show that the disk temperature behavior is a hybrid between the behavior of young stellar object (YSO) disks and hot star winds. The optically thick inner parts of Be star disks have temperatures that are similar to YSO disks, while the optically thin outer parts are like stellar winds. Thus, the temperature at the disk midplane initially drops, reaching a minimum at 3-5 stellar radii, after which it rises back to the optically thin radiative equilibrium temperature at large distances. On the other hand, the optically thin upper layers of the disk are approximately isothermal—a behavior that is analogous to the hot upper layers of YSO disks. Interestingly, unlike the case of YSO disks, we find that disk flaring has little effect on the temperature structure of Be star disks. We also find that the disks are fully ionized, as expected, but that there is an ionization minimum in the vicinity of the temperature minimum. The deficit of photoionization at this location makes it the most likely site for the low ionization state lines (e.g., Fe II) that produce the shell features observed in Be stars. Finally, we find that despite the complex temperature structure, the infrared excess is well approximated by an equivalent isothermal disk model whose temperature is about 60% of the stellar temperature. This is largely because at long wavelengths, the effective photosphere of the disk is located in its isothermal regions.

Observations and modeling of the inner disk region of T tauri stars

We present observations of four T Tauri stars using long baseline infrared interferometry from the Palomar Testbed Interferometer. The target sources, T Tau N, SU Aur, RY Tau, and DR Tau, are all known to be surrounded by dusty circumstellar disks. The observations directly trace the inner regions (<1 AU) of the disk and can be used to constrain the physical properties of this material. For three of the sources observed, the infrared emission is clearly resolved. We first use geometric models to characterize the emission region size, which ranges from 0.04 to 0.3 AU in radius. We then use Monte Carlo radiation transfer models of accretion disks to jointly model the spectral energy distribution and the interferometric observations with disk models including accretion and scattering. With these models, we are able to reproduce the data set with extended emission arising from structures larger than 10 mas contributing less than 6% of the K-band emission, consistent with little or no envelope remaining for these class II sources [d log(λFλ)/d log λ ≈ -2-0 in the infrared]. The radiation transfer models have inner radii for the dust similar to the geometric models; however, for RY Tau, emission from gas within the inner dust radius contributes significantly to the model flux and visibility at infrared wavelengths. The main conclusion of our modeling is that emission from inner gas disks (between the magnetic truncation radius and the dust destruction radius) can be a significant component in the inner disk flux for sources with large inner dust radii.

Cyclic variability of the circumstellar disk of the Be star zeta Tauri II. Testing the 2D global disk oscillation model

Context. About 2/3 of the Be stars present the so-called V/R variations, a phenomenon characterized by the quasi-cyclic variation in the ratio between the violet and red emission peaks of the H i emission lines. These variations are generally explained by global oscillations in the circumstellar disk forming a one-armed spiral density pattern that precesses around the star with a period of a few years. Aims. This paper presents self-consistent models of polarimetric, photometric, spectrophotometric, and interferometric observations of the classical Be star ζ Tauri. The primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. Detailed three-dimensional, NLTE radiative transfer calculations were carried out using the radiative transfer code HDUST. The most up-to-date research on Be stars was used as input for the code in order to include a physically realistic description for the central star and the circumstellar disk. The model adopts a rotationally deformed, gravity darkened central star, surrounded by a disk whose unperturbed state is given by a steady-state viscous decretion disk model. It is further assumed that this disk is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disk model for ζ Tauri and a rigorous solution of the radiative transfer, a very good fit of the time-average properties of the disk was obtained. This provides strong theoretical evidence that the viscous decretion disk model is the mechanism responsible for disk formation. The global oscillation model successfully fitted spatially resolved VLTI/AMBER observations and the temporal V/R variations in the Hα and Brγ lines. This result convincingly demonstrates that the oscillation pattern in the disk is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

Infrared Signatures of Protoplanetary Disk Evolution

We investigate the observational signatures of a straightforward evolutionary scenario for protoplanetary disks, in which the disk mass of small km) particles decreases homologously with time, but ([50 the disk structure and stellar parameters do not change. Our goal is to identify optimal infrared spectral indicators of the existence of disks, their structure, and mass evolution that may be tested with the upcoming SIRT F mission. We present simulated spectral energy distributions (SEDs) and colors over a wide range of masses, 10~8 Our Monte Carlo radiative equilibrium techniques M _ „ M disk „ 10~1 M _ . enable us to explore the wide range of optical depths of these disks and incorporate multiple, anisotropic dust scattering. The SED is most sensitive to disk mass in the far-IR and longer wavelengths, as is already known from millimeter and radio observations. As the disk mass decreases, the excess emission of the disk over the stellar photosphere diminishes more rapidly at the longest than at short wavelengths. At near-infrared wavelengths, the disk remains optically thick to stellar radiation over a wide range of disk masses, resulting in a slower decline in the SED in this spectral regime. Therefore, near-IR excesses (K[L ) provide a robust means of detecting disks in star clusters down to M disk D 10~7 M _ , while the far-IR excess probes the disk mass, the caveat being that large inner-disk holes can decrease the near-IR disk emission. Various other disk parameters (outer radius, —aring, and dust size distribution) alter the SED quantitatively, but do not change our general conclusions on the evolution of SEDs and colors with the mass of small particles in the disk. Reducing the disk mass results in a clear progression in color-color diagrams, with low-mass disks displaying the bluest colors. We interpret color-color diagrams for TaurusAuriga sources in the context of decreasing disk mass. DiUerent viewing angles yield degeneracies in the color-mass relationship, but highly inclined disks are very faint and red and are readily identi—ed in color-magnitude diagrams.

CHARA Array K'-Band Measurements of the Angular Dimensions of Be Star Disks

We present the firstK 0 -band,long-baseline interferometric observations of the northern Be starsCas,� Per,� Tau, andDra. The measurements were made with multiple telescope pairs of the CHARA Array interferometer and in every case the observations indicate that the circumstellar disks of the targets are resolved. We fit the interferometric visibilities with predictions from a simple disk model that assumes an isothermal gas in Keplerian rotation. We derive fitsof thefourmodelparameters(diskbasedensity,radialdensityexponent,disknormalinclination,andpositionangle) for each of the targets. The resulting densities are in broad agreement with prior studies of the IR excess flux, and the resultingorientationsgenerallyagreewiththosefrominterferometricHandcontinuumpolarimetricobservations.We find that the angular size of the K 0 diskemissionis smaller thanthatdeterminedfor the Hemission, and weargue that thedifferenceisthe resultof a larger Hopacityandtherelativelylarger neutral hydrogenfractionwithincreasingdisk radius. All the targets are known binaries with faint companions, and we find that companions appear to influence the interferometric visibilities in the cases ofPer andDra. We also present contemporaneous observations of the H� , H� ,andBremissionlines.Syntheticmodelprofilesoftheselinesthatarebasedonthesamediskinclinationandradial densityexponentasderivedfromtheCHARA Arrayobservationsmatchtheobservedemissionlinestrengthif thedisk base density is reduced by � 1.7 dex.