Mutual sticking of dust aggregates is the first step toward planetesimal formation in protoplanetary disks. In spite that the electric charging of dust particles is well recognized in some contexts, ...it has been largely ignored in the current modeling of dust coagulation. In this study, we present a general analysis of the dust charge state in protoplanetary disks, and then demonstrate how the electric charging could dramatically change the currently accepted scenario of dust coagulation. First, we describe a new semianalytical method to calculate the dust charge state and gas ionization state self-consistently. This method is far more efficient than previous numerical methods, and provides a general and clear description of the charge state of a gas-dust mixture. Second, we apply this analysis to compute the collisional cross section of growing aggregates taking their charging into account. As an illustrative example, we focus on early evolutionary stages where the dust has been thought to grow into fractal (D ~ 2) aggregates with a quasi-monodisperse (i.e., narrow) size distribution. We find that, for a wide range of model parameters, the fractal growth is strongly inhibited by the electric repulsion between colliding aggregates and eventually 'freezes out' on its way to the subsequent growth stage involving collisional compression. Strong disk turbulence would help the aggregates to overcome this growth barrier, but then it would cause catastrophic collisional fragmentation in later growth stages. These facts suggest that the combination of electric repulsion and collisional fragmentation would impose a serious limitation on dust growth in protoplanetary disks. We propose a possible scenario of dust evolution after the freezeout. Finally, we point out that the fractal growth of dust aggregates tends to maintain a low ionization degree and, as a result, a large magnetorotationally stable region in the disk.
Recent (sub)millimeter polarimetric observations toward the young star HL Tau have successfully detected polarization emission from its circumstellar disk. The polarization pattern observed at 0.87 ...mm is uniform and parallel to the disk's minor axis, consistent with the self-scattering of thermal emission by dust particles whose maximum radius is 100 m. However, this maximum size is considerably smaller than anticipated from dust evolution models that assume a high sticking efficiency for icy particles. Here we show that the unexpectedly small particle size can be explained if CO2 ice covers the particles in the outer region of the HL Tau disk. CO2 ice is one of the most major interstellar ices, and laboratory experiments show that it is poorly sticky. Based on dust evolution models accounting for CO2 ice mantles, as well as aggregate sintering, we simulate the polarimetric observation of HL Tau at 0.87 mm. We find that the models with CO2 ice mantles better match the observation. These models also predict that only particles lying between the H2O and CO2 snow lines can grow to millimeter to centimeter sizes and that their rapid inward drift results in a local dust gap similar to the 10 au gap of the HL Tau disk. We also suggest that the millimeter spectral index for the outer part of the HL Tau disk is largely controlled by the optical thickness of this region and does not necessarily indicate dust growth to millimeter sizes.
ABSTRACT The latest observation of HL Tau by ALMA revealed spectacular concentric dust rings in its circumstellar disk. We attempt to explain the multiple ring structure as a consequence of aggregate ...sintering. Sintering is known to reduce the sticking efficiency of dust aggregates and occurs at temperatures slightly below the sublimation point of the constituent material. We present a dust growth model that incorporates sintering and use it to simulate global dust evolution due to sintering, coagulation, fragmentation, and radial inward drift in a modeled HL Tau disk. We show that aggregates consisting of multiple species of volatile ices experience sintering, collisionally disrupt, and pile up at multiple locations slightly outside the snow lines of the volatiles. At wavelengths of 0.87-1.3 mm, these sintering zones appear as bright, optically thick rings with a spectral slope of 2 , whereas the non-sintering zones appear as darker, optically thinner rings of a spectral slope of 2.3 -2.5. The observational features of the sintering and non-sintering zones are consistent with those of the major bright and dark rings found in the HL Tau disk, respectively. Radial pileup and vertical settling occur simultaneously if disk turbulence is weak and if monomers constituting the aggregates are ∼ 1 m in radius. For the radial gas temperature profile of T = 310 ( r / 1 au ) − 0.57 K , our model perfectly reproduces the brightness temperatures of the optically thick bright rings and reproduces their orbital distances to an accuracy of 30 % .
We perform simulations of the dust and gas disk evolution to investigate the observational features of a dust pileup at the dead-zone inner edge. We show that the total mass of accumulated dust ...particles is sensitive to the turbulence strength in the dead zone, dead, because of the combined effect of turbulence-induced particle fragmentation (which suppresses particle radial drift) and turbulent diffusion. For a typical critical fragmentation velocity of silicate dust particles of 1 m s−1, the stress-to-pressure ratio dead needs to be lower than 3 × 10−4 for dust trapping to operate. The obtained dust distribution is postprocessed using the radiative transfer code RADMC-3D to simulate infrared scattered-light images of the inner part of protoplanetary disks with a dust pileup. We find that a dust pileup at the dead-zone inner edge, if present, casts a shadow extending out to ∼10 au. In the shadowed region the temperature significantly drops, which in some cases yields even multiple water snow lines. We also find that even without a dust pileup at the dead-zone inner edge, the disk surface can become thermally unstable, and the excited waves can naturally produce shadows and ring-like structures in observed images. This mechanism might account for the ring-like structures seen in the scattered-light images of some disks, such as the TW Hya disk.
The gas temperature in protoplanetary disks (PPDs) is determined by a combination of irradiation heating and accretion heating, with the latter conventionally attributed to turbulent dissipation. ...However, recent studies have suggested that the inner disk (a few au) is largely laminar, with accretion primarily driven by magnetized disk winds, as a result of nonideal magnetohydrodynamic (MHD) effects from weakly ionized gas, suggesting an alternative heating mechanism by Joule dissipation. We perform local stratified MHD simulations including all three nonideal MHD effects (ohmic, Hall, and ambipolar diffusion) and investigate the role of Joule heating and the resulting disk vertical temperature profiles. We find that in the inner disk, as ohmic and ambipolar diffusion strongly suppress electrical current around the midplane, Joule heating primarily occurs at several scale heights above the midplane, making the midplane temperature much lower than that with the conventional viscous heating model. Including the Hall effect, Joule heating is enhanced/reduced when the magnetic fields threading the disks are aligned/anti-aligned with the disk rotation, but it is overall ineffective. Our results further suggest that the midplane temperature in the inner PPDs is almost entirely determined by irradiation heating, unless viscous heating can trigger thermal ionization in the disk innermost region to self-sustain magnetorotational instability turbulence.
Context. The ocean mass of the Earth is only 2.3 × 10−4 of the whole planet mass. Even including water in the interior, the water fraction would be at most 10−3−10−2. Ancient Mars may have had a ...similar or slightly smaller water fraction. What controlled the amount of water in these planets has not been clear, although several models have been proposed. It is important to clarify the control mechanism to discuss water delivery to rocky planets in habitable zones in exoplanetary systems, as well as that to Earth and Mars in our solar system. Aims. We consider water delivery to planets by icy pebbles after the snowline inwardly passes planetary orbits. We derive the water mass fraction (fwater) of the final planet as a function of disk parameters and discuss the parameters that reproduce a small value of fwater comparable to that inferred for the Earth and ancient Mars. Methods. We calculated the growth of icy dust grains to pebbles and the pebble radial drift with a 1D model, by simultaneously solving the snowline migration and dissipation of a gas disk. With the obtained pebble mass flux, we calculated accretion of icy pebbles onto planets after the snowline passage to evaluate fwater of the planets. Results. We find that fwater is regulated by the total mass (Mres) of icy dust materials preserved in the outer disk regions at the timing (t = tsnow) of the snowline passage of the planetary orbit. Because Mres decays rapidly after the pebble formation front reaches the disk outer edge (at t = tpff), fwater is sensitive to the ratio tsnow∕tpff, which is determined by the disk parameters. We find tsnow∕tpff < 10 or > 10 is important. By evaluating Mres analytically, we derive an analytical formula of fwater that reproduces the numerical results. Conclusions. Using the analytical formula, we find that fwater of a rocky planet near 1 au is similar to the Earth, i.e., ~10−4−10−2, in disks with an initial disk size of 30–50 au and an initial disk mass accretion rate of ~(10−8−10−7) M⊙ yr−1 for disk depletion timescale of approximately a few M yr. Because these disks may be median or slightly compact/massive disks, our results suggest that the water fraction of rocky planets in habitable zones may often be similar to that of the Earth if icy pebble accretion is responsible for water delivery.
ABSTRACT The transport of angular momentum by magnetic fields is a crucial physical process in the formation and evolution of stars and disks. Because the ionization degree in star-forming clouds is ...extremely low, nonideal magnetohydrodynamic (MHD) effects such as ambipolar diffusion and ohmic dissipation work strongly during protostellar collapse. These effects have significant impacts in the early phase of star formation as they redistribute magnetic flux and suppress angular momentum transport by magnetic fields. We perform three-dimensional nested-grid radiation magnetohydrodynamic simulations including ohmic dissipation and ambipolar diffusion. Without these effects, magnetic fields transport angular momentum so efficiently that no rotationally supported disk is formed even after the second collapse. Ohmic dissipation works only in a relatively high density region within the first core and suppresses angular momentum transport, enabling formation of a very small rotationally supported disk after the second collapse. With both ohmic dissipation and ambipolar diffusion, these effects work effectively in almost the entire region within the first core and significant magnetic flux loss occurs. As a result, a rotationally supported disk is formed even before a protostellar core forms. The size of the disk is still small, about 5 AU at the end of the first core phase, but this disk will grow later as gas accretion continues. Thus, the nonideal MHD effects can resolve the so-called magnetic braking catastrophe while keeping the disk size small in the early phase, which is implied from recent interferometric observations.
The ubiquity of clouds in the atmospheres of exoplanets, especially of super-Earths, is one of the outstanding issues for the transmission spectra survey. Understanding the formation process of ...clouds in super-Earths is necessary to interpret the observed spectra correctly. In this study, we investigate the vertical distributions of particle size and mass density of mineral clouds in super-Earths using a microphysical model that takes into account the vertical transport and growth of cloud particles in a self-consistent manner. We demonstrate that the vertical profiles of mineral clouds significantly vary with the concentration of cloud condensation nuclei and atmospheric metallicity. We find that the height of the cloud top increases with increasing metallicity as long as the metallicity is lower than the threshold. If the metallicity is larger than the threshold, the cloud-top height no longer increases appreciably with metallicity because coalescence yields larger particles of higher settling velocities. We apply our cloud model to GJ1214 b and GJ436 b, for which recent transmission observations suggest the presence of high-altitude opaque clouds. For GJ436 b, we show that KCl particles can ascend high enough to explain the observation. For GJ1214 b, by contrast, the height of KCl clouds predicted from our model is too low to explain its flat transmission spectrum. Clouds made of highly porous KCl particles could explain the observations if the atmosphere is highly metal-rich, and hence the particle microstructure might be a key to interpret the flat spectrum of GJ1214 b.
Standard accretion disk models suggest that the snow line in the solar nebula migrated interior to the Earth’s orbit in a late stage of nebula evolution. In this late stage, a significant amount of ...ice could have been delivered to 1 AU from outer regions in the form of mm to dm-sized pebbles. This raises the question why the present Earth is so depleted of water (with the ocean mass being as small as 0.023% of the Earth mass). Here we quantify the amount of icy pebbles accreted by terrestrial embryos after the migration of the snow line assuming that no mechanism halts the pebble flow in outer disk regions. We use a simplified version of the coagulation equation to calculate the formation and radial inward drift of icy pebbles in a protoplanetary disk. The pebble accretion cross section of an embryo is calculated using analytic expressions presented by recent studies. We find that the final mass and water content of terrestrial embryos strongly depends on the radial extent of the gas disk, the strength of disk turbulence, and the time at which the snow lines arrives at 1 AU. The disk’s radial extent sets the lifetime of the pebble flow, while turbulence determines the density of pebbles at the midplane where the embryos reside. We find that the final water content of the embryos falls below 0.023 wt% only if the disk is compact (<100 AU), turbulence is strong at 1 AU, and the snow line arrives at 1 AU later than 2–4 Myr after disk formation. If the solar nebula extended to 300 AU, initially rocky embryos would have evolved into icy planets of 1–10 Earth masses unless the snow-line migration was slow. If the proto-Earth contained water of ~1 wt% as might be suggested by the density deficit of the Earth’s outer core, the formation of the proto-Earth was possible with weaker turbulence and with earlier (>0.5–2 Myr) snow-line migration.
Dust grains emit intrinsic polarized emission if they are elongated and aligned in the same direction. The direction of the grain alignment is determined by external forces, such as magnetic fields, ...radiation, and gas flow against the dust grains. In this Letter, we apply the concept of the grain alignment by gas flow, which is called mechanical alignment, to the situation of a protoplanetary disk. We assume that grains have a certain helicity, which results in the alignment with the minor axis parallel to the grain velocity against the ambient disk gas and discuss the morphology of polarization vectors in a protoplanetary disk. We find that the direction of the polarization vectors depends on the Stokes number, which denotes how well grains are coupled to the gas. If the Stokes number is less than unity, the orientation of polarization is in the azimuthal direction because the dust velocity against the gas is in the radial direction. If the Stokes number is as large as unity, the polarization vectors show a leading spiral pattern because the radial and azimuthal components of the gas velocity against the dust grains are comparable. This suggests that if the observed polarization vectors show a leading spiral pattern, it would indicate that the Stokes number of dust grains is around unity, which is presumably radially drifting.
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