Effect of Be Disk Evolution on Global One-Armed Oscillations

Effect of Be Disk Evolution on Global One-Armed Oscillations

Authors:

Oktariani et al

Abstract:

We study the effect of density distribution evolution on the global one-armed oscillation modes in low viscosity disks around isolated and binary Be stars. Observations show that some Be stars exhibit evidence of formation and dissipation of the equatorial disk. In this paper, we first calculate the density evolution in disks around isolated Be stars. To model the formation stage of the disk, we inject mass at a radius just outside the star at a constant rate for 30-50 years. As the disk develops, the density distribution approaches the form of the steady disk solution. Then, we turn off the mass injection to model the disk dissipation stage. The innermost part of the disk starts accretion, and a gap forms between the star and the disk. Next, we calculate the one-armed modes at several epochs. We neglect the effect of viscosity because the time-scale of oscillations is much shorter than the disk evolution time-scale for low viscosity. In the disk formation stage, the eigenfrequency increases with time toward the value for the steady state disk. On the other hand, one-armed eigenmodes in dissipating Be disks have significantly higher eigenfrequencies and narrower propagation regions. Observationally, such a change of mode characteristics can be taken as an evidence for gap opening around the star. In binary Be stars, the characteristics of the disk evolution and the eigenmodes are qualitatively the same as in isolated Be stars, but quantitatively they have shorter evolution time-scales and higher eigenfrequencies, which is in agreement with the observed trend.

Viscous Instability Triggered by Layered Accretion in Protoplanetary Disks

Viscous Instability Triggered by Layered Accretion in Protoplanetary Disks

Authors:

Hasegawa et al

Abstract:

Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate (M˙), while the disk midplane where MRIs are generally quenched ends up with a low value of M˙. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of α in 1D disk models. To this end, we obtain a new expression of α by utilizing an empirical formula that is derived from recent MHD simulations of stratified disks with Ohmic diffusion. It is interesting that this new formulation can be regarded as a general extension of the classical α. Armed with the new α, we perform a linear stability analysis of protoplanetary disks that undergo layered accretion, and find that a viscous instability can occur around the outer edge of dead zones. Disks become stable in using the classical α. We identify that the difference arises from Σ−dependence of M˙; whereas Σ is uniquely determined for a given value of M˙ in the classical approach, the new approach leads to M˙ that is a multi-valued function of Σ. We confirm our finding both by exploring a parameter space as well as by performing the 1D, viscous evolution of disks. We finally discuss other non-ideal MHD effects that are not included in our analysis, but may affect our results.

"Winds" in the Protoplanetary Disk can Suppress Exoplanet Migration

Suppression of type I migration by disk winds

Authors:

Ogihara et al

Abstract:

Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw < 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths.

Chondrule Transport in Protoplanetary Disks

Chondrule Transport in Protoplanetary Disks

Authors:

Goldberg et al

Abstract:

Chondrule formation remains one of the most elusive early Solar System events. Here, we take the novel approach of employing numerical simulations to investigate chondrule origin beyond purely cosmochemical methods. We model the transport of generically-produced chondrules and dust in a 1D viscous protoplanetary disk model, in order to constrain the chondrule formation events. For a single formation event we are able to match analytical predictions of the memory chondrule and dust populations retain of each other (complementarity), finding that a large mass accretion rate (≳10−7~M⊙~yr−1) allows for delays on the order of the disk's viscous timescale between chondrule formation and chondrite accretion. Further, we find older disks to be severely diminished of chondrules, with accretion rates ≲10−9~M⊙~yr−1 for nominal parameters. We then characterize the distribution of chondrule origins in both space and time, as functions of disk parameters and chondrule formation rates, in runs with continuous chondrule formation and both static and evolving disks. Our data suggest that these can account for the observed diversity between distinct chondrite classes, if some diversity in accretion time is allowed for.

The Role of the Snowline in Transporting Water to Habitable Zone Terrestrial Exoplanets

The snow line in viscous disks around low-mass stars: implications for water delivery to terrestrial planets in the habitable zone

Authors:

Mulders et al

Abstract:

The water ice or snow line is one of the key properties of protoplanetary disks that determines the water content of terrestrial planets in the habitable zone. Its location is determined by the properties of the star, the mass accretion rate through the disk, and the size distribution of dust suspended in the disk. We calculate the snow line location from recent observations of mass accretion rates and as a function of stellar mass. By taking the observed dispersion in mass accretion rates as a measure of the dispersion in initial disk mass, we find that stars of a given mass will exhibit a range of snow line locations. At a given age and stellar mass, the observed dispersion in mass accretion rates of 0.4 dex naturally leads to a dispersion in snow line locations of 0.2 dex. For ISM-like dust sizes, the one-sigma snow line location among solar mass stars of the same age ranges from 2 to 5 au. For more realistic dust opacities that include larger grains, the snow line is located up to two times closer to the star. We use these locations and the outcome of N-body simulations to predict the amount of water delivered to terrestrial planets that formed in situ in the habitable zone. We find that the dispersion in snow line locations leads to a large range in water content. For ISM-like dust sizes, a significant fraction of habitable-zone terrestrial planets around sun-like stars remain dry, and no water is delivered to the habitable zones of low-mass M stars (less than half a solar mass) as in previous works. The closer-in snow line in disks with larger grains enables water delivery to the habitable zone for a significant fraction of M stars and all FGK stars. Considering their larger numbers and higher planet occurrence, M stars may host most of the water-rich terrestrial planets in the galaxy if these planets are able to hold on to their water in their subsequent evolution.

The Evolution of Vicosity Over Time in Viscous Disks

EVOLUTION OF FINITE VISCOUS DISKS WITH TIME-INDEPENDENT VISCOSITY

Author:

Lipunova

Abstract:

We find Green functions for the accretion disk with fixed outer radius and time-independent viscosity. With the Green functions, a viscous evolution of the disk with any initial conditions can be described. Two types of inner boundary conditions are considered: the zero stress tensor and the zero accretion rate. The variable mass inflow at the outer radius can also be included. The well-known exponential decline of the accretion rate is a part of the solution with the inner zero stress tensor. The solution with the zero central accretion rate is applicable to disks around stars whose magnetosphere's boundary exceeds the corotation radius. Using the solution, the viscous evolution of disks in some binary systems can be studied. We apply the solution with zero inner stress tensor to outbursts of short-period X-ray transients during the time around the peak. It is found that for the Kramers' regime of opacity and the initial surface density proportional to the radius, the rise time to the peak is ${{t}_{{\rm rise}}}\approx 0.15\;r_{{\rm out}}^{2}/{{\nu }_{{\rm out}}}$ and the e-folding time of the decay is ${{t}_{{\rm exp} }}\approx 0.45\;r_{{\rm out}}^{2}/{{\nu }_{{\rm out}}}$. Comparison to non-stationary α-disks shows that both models with the same value of viscosity at the outer radius produce similar behavior on the viscous time-scale. For six bursts in X-ray novae, which exhibit fast-rise–exponential-decay and are fitted by the model, we find a way to restrict the turbulent parameter α.