Engineering topics

Zhu, Zhaohuan

Publications and source records attributed to Zhu, Zhaohuan.

At least 19 records

DOE OSTI2017

How Do Stars Gain Their Mass? A JCMT/SCUBA-2 Transient Survey of Protostars in Nearby Star-forming Regions

Most protostars have luminosities that are fainter than expected from steady accretion over the protostellar lifetime. The solution to this problem may lie in episodic mass accretion—prolonged periods of very low accretion punctuated by short bursts of rapid accretion. However, the timescale and amplitude for variability at the protostellar phase is almost entirely unconstrained. In A James Clerk Maxwell Telescope/SCUBA-2 Transient Survey of Protostars in Nearby Star-forming Regions, we are monitoring monthly with SCUBA-2 the submillimeter emission in eight fields within nearby (<500 pc) star-forming regions to measure the accretion variability of protostars. The total survey area of ∼1.6 deg{sup 2} includes ∼105 peaks with peaks brighter than 0.5 Jy/beam (43 associated with embedded protostars or disks) and 237 peaks of 0.125–0.5 Jy/beam (50 with embedded protostars or disks). Each field has enough bright peaks for flux calibration relative to other peaks in the same field, which improves upon the nominal flux calibration uncertainties of submillimeter observations to reach a precision of ∼2%–3% rms, and also provides quantified confidence in any measured variability. The timescales and amplitudes of any submillimeter variation will then be converted into variations in accretion rate and subsequently used to infer the physical causes of the variability. This survey is the first dedicated survey for submillimeter variability and complements other transient surveys at optical and near-IR wavelengths, which are not sensitive to accretion variability of deeply embedded protostars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Global MHD Simulations of Accretion Disks in Cataclysmic Variables (CVs). II. The Relative Importance of MRI and Spiral Shocks

We perform global three-dimensional MHD simulations of unstratified accretion disks in cataclysmic variables (CVs). By including mass inflow via an accretion stream, we are able to evolve the disk to a steady state. We investigate the relative importance of spiral shocks and the magnetorotational instability (MRI) in driving angular momentum transport and how each depend on the geometry and strength of the seed magnetic field and the Mach number of the disk (where Mach number is the ratio of the azimuthal velocity and the sound speed of gas). We use a locally isothermal equation of state and adopt temperature profiles that are consistent with CV disk observations. Our results indicate that the relative importance of spiral shocks and MRI in driving angular momentum transport is controlled by the gas Mach number and the seed magnetic field strength. MRI and spiral shocks provide comparable efficiency of angular momentum transport when the disk Mach number is around 10 and the seed magnetic field has plasma β=400 (where β is the ratio of gas pressure and magnetic pressure). The MRI dominates whenever the seed field strength, or the disk Mach number, is increased. Among all of our simulations, the effective viscosity parameter α{sub eff}∼0.016--0.1 after MRI saturates and the disk reaches steady state. Larger values of α{sub eff} are favored when the seed magnetic field has vertical components or the flow has stronger magnetization (1/β). Our models all indicate that the role of MRI in driving angular momentum transport thus mass accretion in CV disks is indispensable, especially in cool disks with weak spiral shocks.

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DOE OSTI2016

SHOCK-DRIVEN ACCRETION IN CIRCUMPLANETARY DISKS: OBSERVABLES AND SATELLITE FORMATION

Circumplanetary disks (CPDs) control the growth of planets, supply material for satellites to form, and provide observational signatures of young forming planets. We have carried out two-dimensional hydrodynamical simulations with radiative cooling to study CPDs and suggested a new mechanism to drive the disk accretion. Two spiral shocks are present in CPDs, excited by the central star. We find that spiral shocks can at least contribute to, if not dominate, the angular momentum transport and energy dissipation in CPDs. Meanwhile, dissipation and heating by spiral shocks have a positive feedback on shock-driven accretion itself. As the disk is heated up by spiral shocks, the shocks become more open, leading to more efficient angular momentum transport. This shock-driven accretion is, on the other hand, unsteady due to production and destruction of vortices in disks. After being averaged over time, a quasi-steady accretion is reached from the planet’s Hill radius all the way to the planet surface, and the disk α coefficient characterizing angular momentum transport is ∼0.001–0.02. The disk surface density ranges from 10 to 1000 g cm{sup −2} in our simulations, which is at least three orders of magnitude smaller than the “minimum-mass subnebula” model used to study satellite formation; instead it is more consistent with the “gas-starved” satellite formation model. Finally, we calculate the millimeter flux emitted by CPDs at ALMA and EVLA wavelength bands and predict the flux for several recently discovered CPD candidates, which suggests that ALMA is capable of discovering these accreting CPDs.

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DOE OSTI2016

THE ERUPTION OF THE CANDIDATE YOUNG STAR ASASSN-15QI

Outbursts on young stars are usually interpreted as accretion bursts caused by instabilities in the disk or the star–disk connection. However, some protostellar outbursts may not fit into this framework. In this paper, we analyze optical and near-infrared spectra and photometry to characterize the 2015 outburst of the probable young star ASASSN-15qi. The ∼3.5 mag brightening in the V band was sudden, with an unresolved rise time of less than one day. The outburst decayed exponentially by 1 mag for 6 days and then gradually back to the pre-outburst level after 200 days. The outburst is dominated by emission from ∼10,000 K gas. An explosive release of energy accelerated matter from the star in all directions, seen in a spectacular cool, spherical wind with a maximum velocity of 1000 km s{sup −1}. The wind and hot gas both disappeared as the outburst faded and the source returned to its quiescent F-star spectrum. Nebulosity near the star brightened with a delay of 10–20 days. Fluorescent excitation of H{sub 2} is detected in emission from vibrational levels as high as v = 11, also with a possible time delay in flux increase. The mid-infrared spectral energy distribution does not indicate the presence of warm dust emission, though the optical photospheric absorption and CO overtone emission could be related to a gaseous disk. Archival photometry reveals a prior outburst in 1976. Although we speculate about possible causes for this outburst, none of the explanations are compelling.

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DOE OSTI2016

A DWARF TRANSITIONAL PROTOPLANETARY DISK AROUND XZ TAU B

We report the discovery of a dwarf protoplanetary disk around the star XZ Tau B that shows all the features of a classical transitional disk but on a much smaller scale. The disk has been imaged with the Atacama Large Millimeter/submillimeter Array (ALMA), revealing that its dust emission has a quite small radius of ∼3.4 au and presents a central cavity of ∼1.3 au in radius that we attribute to clearing by a compact system of orbiting (proto)planets. Given the very small radii involved, evolution is expected to be much faster in this disk (observable changes in a few months) than in classical disks (observable changes requiring decades) and easy to monitor with observations in the near future. From our modeling we estimate that the mass of the disk is large enough to form a compact planetary system.

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DOE OSTI2016

Global MHD simulations of accretion disks in cataclysmic variables. I. The importance of spiral shocks

We present results from the first global 3D MHD simulations of accretion disks in cataclysmic variable (CV) systems in order to investigate the relative importance of angular momentum transport via turbulence driven by the magnetorotational instability (MRI) compared with that driven by spiral shock waves. Remarkably, we find that even with vigorous MRI turbulence, spiral shocks are an important component of the overall angular momentum budget, at least when temperatures in the disk are high (so that Mach numbers are low). In order to understand the excitation, propagation, and damping of spiral density waves in our simulations more carefully, we perform a series of 2D global hydrodynamical simulations with various equation of states, both with and without mass inflow via the Lagrangian point (L1). Compared with previous similar studies, we find the following new results. (1) The linear wave dispersion relation fits the pitch angles of spiral density waves very well. (2) We demonstrate explicitly that mass accretion is driven by the deposition of negative angular momentum carried by the waves when they dissipate in shocks. (3) Using Reynolds stress scaled by gas pressure to represent the effective angular momentum transport rate α{sub eff} is not accurate when mass accretion is driven by non-axisymmetric shocks. (4) Using the mass accretion rate measured in our simulations to directly measure α defined in standard thin-disk theory, we find 0.02≲α{sub eff}≲0.05 for CV disks, consistent with observed values in quiescent states of dwarf novae. In this regime, the disk may be too cool and neutral for the MRI to operate and spiral shocks are a possible accretion mechanism. However, we caution that our simulations use unrealistically low Mach numbers in this regime and, therefore, future models with more realistic thermodynamics and non-ideal MHD are warranted.

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DOE OSTI2016

THE VLA VIEW OF THE HL TAU DISK: DISK MASS, GRAIN EVOLUTION, AND EARLY PLANET FORMATION

The first long-baseline ALMA campaign resolved the disk around the young star HL Tau into a number of axisymmetric bright and dark rings. Despite the very young age of HL Tau, these structures have been interpreted as signatures for the presence of (proto)planets. The ALMA images triggered numerous theoretical studies based on disk–planet interactions, magnetically driven disk structures, and grain evolution. Of special interest are the inner parts of disks, where terrestrial planets are expected to form. However, the emission from these regions in HL Tau turned out to be optically thick at all ALMA wavelengths, preventing the derivation of surface density profiles and grain-size distributions. Here, we present the most sensitive images of HL Tau obtained to date with the Karl G. Jansky Very Large Array at 7.0 mm wavelength with a spatial resolution comparable to the ALMA images. At this long wavelength, the dust emission from HL Tau is optically thin, allowing a comprehensive study of the inner disk. We obtain a total disk dust mass of (1–3) × 10{sup −3} M {sub ⊙}, depending on the assumed opacity and disk temperature. Our optically thin data also indicate fast grain growth, fragmentation, and formation of dense clumps in the inner densest parts of the disk. Our results suggest that the HL Tau disk may be actually in a very early stage of planetary formation, with planets not already formed in the gaps but in the process of future formation in the bright rings.

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DOE OSTI2016

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 μm 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.

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DOE OSTI2016

Planetary signatures in the SAO 206462 (HD 135344B) disk: A spiral arm passing through vortex?

The disk surrounding SAO 206462, an 8 Myr old Herbig Ae star, has recently been reported to exhibit spiral arms, an asymmetric dust continuum, and a dust-depleted inner cavity. By carrying out two-dimensional, two-fluid hydrodynamic calculations, we find that a planetary-mass companion located at the outer disk could be responsible for these observed structures. In this model, the planet excites primary and secondary arms interior to its orbit. It also carves a gap and generates a local pressure bump at the inner gap edge where a vortex forms through Rossby wave instability. The vortex traps radially drifting dust particles, forming a dust-depleted cavity in the inner disk. We propose that the vortex is responsible for the brightest southwestern peak seen in infrared scattered light and sub-millimeter dust continuum emission. In particular, it is possible that the scattered light is boosted as one of the spiral arms passes through the high density vortex region, although the vortex alone may be able to explain the peak. We suggest that a planetary companion with a mass of 10–15 M{sub J} is orbiting SAO 206462 at 100–120 au. Monitoring of the brightest peak over the next few years will help reveal its origin because the spiral arms and vortex will show distinguishable displacement.

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DOE OSTI2016

INSIDE-OUT PLANET FORMATION. III. PLANET–DISK INTERACTION AT THE DEAD ZONE INNER BOUNDARY

The Kepler mission has discovered more than 4000 exoplanet candidates. Many of them are in systems with tightly packed inner planets. Inside-out planet formation (IOPF) has been proposed as a scenario to explain these systems. It involves sequential in situ planet formation at the local pressure maximum of a retreating dead zone inner boundary (DZIB). Pebbles accumulate at this pressure trap, which builds up a pebble ring and then a planet. The planet is expected to grow in mass until it opens a gap, which helps to both truncate pebble accretion and also induce DZIB retreat that sets the location of formation of the next planet. This simple scenario may be modified if the planet undergoes significant migration from its formation location. Thus, planet–disk interactions play a crucial role in the IOPF scenario. Here we present numerical simulations that first assess the degree of migration for planets of various masses that are forming at the DZIB of an active accretion disk, where the effective viscosity is undergoing a rapid increase in the radially inward direction. We find that torques exerted on the planet by the disk tend to trap the planet at a location very close to the initial pressure maximum where it formed. We then study gap opening by these planets to assess at what mass a significant gap is created. Finally, we present a simple model for DZIB retreat due to penetration of X-rays from the star to the disk midplane. Overall, these simulations help to quantify both the mass scale of first (“Vulcan”) planet formation and the orbital separation to the location of second planet formation.

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DOE OSTI2016

AN M DWARF COMPANION AND ITS INDUCED SPIRAL ARMS IN THE HD 100453 PROTOPLANETARY DISK

Recent VLT/SPHERE near-infrared imaging observations revealed two spiral arms with a near m = 2 rotational symmetry in the protoplanetary disk around the ∼1.7 M{sub ⊙} Herbig star HD 100453. A ∼0.3 M{sub ⊙} M dwarf companion, HD 100453 B, was also identified at a projected separation of 120 AU from the primary. In this Letter, we carry out hydrodynamic and radiative transfer simulations to examine the scattered light morphology of the HD 100453 disk as perturbed by the companion on a circular and coplanar orbit. We find that the companion truncates the disk at ∼45 AU in scattered light images, and excites two spiral arms in the remaining (circumprimary) disk with a near m = 2 rotational symmetry. Both the truncated disk size and the morphology of the spirals are in excellent agreement with the SPHERE observations at Y, J, H, and K1-bands, suggesting that the M dwarf companion is indeed responsible for the observed double-spiral-arm pattern. Our model suggests that the disk is close to face on (inclination angle ∼5°), and that the entire disk-companion system rotates counterclockwise on the sky. The HD 100453 observations, along with our modeling work, demonstrate that double spiral arm patterns in near-infrared scattered light images can be generically produced by companions, and support future observations to identify the companions responsible for the arms observed in the MWC 758 and SAO 206462 systems.

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DOE OSTI2015

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 (3D) 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 nonlinear 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 3D hydrodynamical models than images based on two-dimensional models assuming vertical hydrostatic equilibrium, indicating the need to model observations with full 3D hydrodynamics. Overall, companion-induced spiral arms not only pinpoint the companion’s position but also provide three independent ways (pitch angle, separation between two arms, and contrast of arms) to constrain the companion’s mass.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

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 M{sub J} can produce a deep gap at millimeter 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 millimeter 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 millimeter 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 Atacama Large Millimeter Array release of the image of the HL Tau disk, we show that multiple narrow gaps, well separated by bright rings, can be opened by 0.2M{sub J} planets soon after their formation in a relatively massive disk.

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DOE OSTI2015

ARE PROTOPLANETARY DISKS BORN WITH VORTICES? ROSSBY WAVE INSTABILITY DRIVEN BY PROTOSTELLAR INFALL

We carry out two-fluid, two-dimensional global hydrodynamic simulations to test whether protostellar infall can trigger the Rossby wave instability (RWI) in protoplanetry disks. Our results show that infall can trigger the RWI and generate vortices near the outer edge of the mass landing on the disk (i.e., centrifugal radius). We find that the RWI is triggered under a variety of conditions, although the details depend on the disk parameters and the infall pattern. The common key feature of triggering the RWI is the steep radial gradient of the azimuthal velocity induced by the local increase in density at the outer edge of the infall region. Vortices form when the instability enters the nonlinear regime. In our standard model where self-gravity is neglected, vortices merge together to a single vortex within ∼20 local orbital times, and the merged vortex survives for the remaining duration of the calculation (>170 local orbital times). The vortex takes part in outward angular momentum transport, with a Reynolds stress of ≲10{sup −2}. Our two-fluid calculations show that vortices efficiently trap dust particles with stopping times of the order of the orbital time, locally enhancing the dust to gas ratio for particles of the appropriate size by a factor of ∼40 in our standard model. When self-gravity is considered, however, vortices tend to be impeded from merging and may eventually dissipate. We conclude it may well be that protoplanetary disks have favorable conditions for vortex formation during the protostellar infall phase, which might enhance early planetary core formation.

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DOE OSTI2015

Dust transport in MRI turbulent disks: Ideal and non-ideal MHD with ambipolar diffusion

We study dust transport in turbulent protoplanetary disks using three-dimensional global unstratified MHD simulations including Lagrangian dust particles. The turbulence is driven by the magnetorotational instability (MRI) with either ideal or non-ideal MHD that includes ambipolar diffusion (AD). In ideal MHD simulations, the surface density evolution (except for dust that drifts fastest), turbulent diffusion, and vertical scale height of dust can all be reproduced by simple one-dimensoinal and/or analytical models. However, in AD dominated simulations which simulate protoplanetary disks beyond 10s of AU, the vertical scale height of dust is larger than previously predicted. To understand this anomaly in more detail, we carry out both unstratified and stratified local shearing box simulations with Lagrangian particles, and find that turbulence in AD dominated disks has very different properties (e.g., temporal autocorrelation functions and power spectra) than turbulence in ideal MHD disks, which leads to quite different particle diffusion efficiency. For example, MRI turbulence with AD has a longer correlation time for the vertical velocity, which causes significant vertical particle diffusion and large dust scale height. In ideal MHD the Schmidt numbers (Sc) for radial and vertical turbulent diffusion are Sc{sub r}∼1 and Sc{sub z}≳3, but in the AD dominated regime both Sc{sub r} and Sc{sub z} are ≲1. Particle concentration in pressure bumps induced by MRI turbulence has also been studied. Since non-ideal MHD effects dominate most regions in protoplanetary disks, our study suggests that modeling dust transport in turbulence driven by MRI with non-ideal MHD effects is important for understanding dust transport in realistic protoplanetary disks.

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DOE OSTI2015

ACCRETING CIRCUMPLANETARY DISKS: OBSERVATIONAL SIGNATURES

I calculate the spectral energy distributions of accreting circumplanetary disks using atmospheric radiative transfer models. Circumplanetary disks only accreting at 10{sup –10} M {sub ☉} yr{sup –1} around a 1 M{sub J} planet can be brighter than the planet itself. A moderately accreting circumplanetary disk ( M-dot ∼10{sup −8} M{sub ⊙} yr{sup −1}; enough to form a 10 M{sub J} planet within 1 Myr) around a 1 M{sub J} planet has a maximum temperature of ∼2000 K, and at near-infrared wavelengths (J, H, K bands), this disk is as bright as a late-M-type brown dwarf or a 10 M{sub J} planet with a ''hot start''. To use direct imaging to find the accretion disks around low-mass planets (e.g., 1 M{sub J} ) and distinguish them from brown dwarfs or hot high-mass planets, it is crucial to obtain photometry at mid-infrared bands (L', M, N bands) because the emission from circumplanetary disks falls off more slowly toward longer wavelengths than those of brown dwarfs or planets. If young planets have strong magnetic fields (≳100 G), fields may truncate slowly accreting circumplanetary disks ( M-dot ≲10{sup −9} M{sub ⊙} yr{sup −1}) and lead to magnetospheric accretion, which can provide additional accretion signatures, such as UV/optical excess from the accretion shock and line emission.

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DOE OSTI2014

Dust trapping by vortices in transitional disks: evidence for non-ideal magnetohydrodynamic effects in protoplanetary disks

We study particle trapping at the edge of a gap opened by a planet in a protoplanetary disk. In particular, we explore the effects of turbulence driven by the magnetorotational instability on particle trapping, using global three-dimensional magnetohydrodynamic (MHD) simulations including Lagrangian dust particles. We study disks either in the ideal MHD limit or dominated by ambipolar diffusion (AD) which plays an essential role at the outer regions of a protoplanetary disk. With ideal MHD, strong turbulence (the equivalent viscosity parameter α ∼ 10{sup –2}) in disks prevents vortex formation at the edge of the gap opened by a 9 M{sub J} planet, and most particles (except the particles that drift fastest) pile up at the outer gap edge almost axisymmetrically. When AD is considered, turbulence is significantly suppressed (α ≲ 10{sup –3}), and a large vortex forms at the edge of the planet induced gap, which survives ∼1000 orbits. The vortex can efficiently trap dust particles that span 3 orders of magnitude in size within 100 planetary orbits. We have also carried out two-dimensional hydrodynamical (HD) simulations using viscosity as an approximation to MHD turbulence. These HD simulations can reproduce vortex generation at the gap edge as seen in MHD simulations. Finally, we use our simulation results to generate synthetic images for ALMA dust continuum observations on Oph IRS 48 and HD 142527, which show good agreement with existing observations. Predictions for future ALMA cycle 2 observations have been made. We conclude that the asymmetry in ALMA observations can be explained by dust trapping vortices and the existence of vortices could be the evidence that the outer protoplanetary disks are dominated by AD with α < 10{sup –3} at the disk midplane.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Accretion outbursts in self-gravitating protoplanetary disks

We improve on our previous treatments of the long-term evolution of protostellar disks by explicitly solving disk self-gravity in two dimensions. The current model is an extension of the one-dimensional layered accretion disk model of Bae et al. We find that gravitational instability (GI)-induced spiral density waves heat disks via compressional heating (i.e., PdV work), and can trigger accretion outbursts by activating the magnetorotational instability (MRI) in the magnetically inert disk dead zone. The GI-induced spiral waves propagate well inside of the gravitationally unstable region before they trigger outbursts at R ≲ 1 AU where GI cannot be sustained. This long-range propagation of waves cannot be reproduced with the previously used local α treatments for GI. In our standard model where zero dead-zone residual viscosity (α{sub rd}) is assumed, the GI-induced stress measured at the onset of outbursts is locally as large as 0.01 in terms of the generic α parameter. However, as suggested in our previous one-dimensional calculations, we confirm that the presence of a small but finite α{sub rd} triggers thermally driven bursts of accretion instead of the GI + MRI-driven outbursts that are observed when α{sub rd} = 0. The inclusion of non-zero residual viscosity in the dead zone decreases the importance of GI soon after mass feeding from the envelope cloud ceases. During the infall phase while the central protostar is still embedded, our models stay in a 'quiescent' accretion phase with M-dot {sub acc}∼10{sup −8}--10{sup −7} M{sub ⊙} yr{sup −1} over 60% of the time and spend less than 15% of the infall phase in accretion outbursts. While our models indicate that episodic mass accretion during protostellar evolution can qualitatively help explain the low accretion luminosities seen in most low-mass protostars, detailed tests of the mechanism will require model calculations for a range of protostellar masses with some constraint on the initial core angular momentum, which affects the length of time spent in a quasi-steady disk accretion phase.

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