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We present a new method to constrain the grain size in protoplanetary disks with polarization observations at millimeter wavelengths. If dust grains are grown to the size comparable to the wavelengths, the dust grains are expected to have a large scattering opacity and thus the continuum emission is expected to be polarized due to self-scattering. We perform 3D radiative transfer calculations to estimate the polarization degree for the protoplanetary disks having radial Gaussian-like dust surface density distributions, which have been recently discovered. The maximum grain size is set to be 100 µm and the observing wavelength to be 870 µm. We find that the polarization degree is as high as 2.5% with a subarcsec spatial resolution, which is likely to be detected with near-future ALMA observations. The emission is polarized due to scattering of anisotropic continuum emission. The map of the polarization degree shows a double peaked distribution and the polarization vectors are in the radial direction in the inner ring and in the azimuthal direction in the outer ring. We also find the wavelength dependence of the polarization degree: the polarization degree is the highest if dust grains have a maximum size of a max ∼ λ/2π, where λ is the observing wavelength. Hence, multi-wave and spatially resolved polarization observations toward protoplanetary disks enable us to put a constraint on the grain size. The constraint on the grain size from polarization observations is independent of or may be even stronger than that from the opacity index.

The fragmentation of molecular cloud cores a factor of 1.1 denser than the critical Bonnor-Ebert sphere is examined though three-dimensional numerical simulations. A nested grid is employed to resolve fine structure down to 1 AU while following the entire structure of the molecular cloud core of radius 0.14 pc. A barotropic equation of state is assumed to take account of the change in temperature during collapse, allowing simulation of the formation of the first core. A total of 225 models are shown to survey the effects of initial rotation speed, rotation law, and amplitude of bar mode perturbation. The simulations show that the cloud fragments whenever the cloud rotates sufficiently slowly to allow collapse but fast enough to form a disk before first-core formation. The latter condition is equivalent to 0 t ff e0:05, where 0 and t ff denote the initial central angular velocity and the freefall time measured from the central density, respectively. Fragmentation is classified into six types: disk-bar, ring-bar, satellite, bar, ring, and dumbbell types according to the morphology of collapse and fragmentation. When the outward decrease in initial angular velocity is more steep, the cloud deforms from spherical at an early stage. The cloud deforms into a ring only when the bar mode (m ¼ 2) perturbation is very minor. The ring fragments into two or three fragments via ring-bar type fragmentation and into at least three fragments via ring type fragmentation. When the bar mode is significant, the cloud fragments into two fragments via either bar or dumbbell type fragmentation. These fragments eventually merge because of their low angular momenta, after which several new fragments form around the merged fragment via satellite type fragmentation. This satellite type fragmentation may be responsible for the observed wide range of binary separation.

We report ALMA observations of dust continuum, 13 CO J = 3-2, and C 18 O J = 3-2 line emission toward a gapped protoplanetary disk around HD 142527. The outer horseshoe-shaped disk shows the strong azimuthal asymmetry in dust continuum with the contrast of about 30 at 336 GHz between the northern peak and the southwestern minimum. In addition, the maximum brightness temperature of 24 K at its northern area is exceptionally high at 160 AU from a star. To evaluate the surface density in this region, the grain temperature needs to be constrained and was estimated from the optically thick 13 CO J = 1 3-2 emission. The lower limit of the peak surface density was then calculated to be 28 g cm −2 by assuming a canonical gas-to-dust mass ratio of 100. This finding implies that the region is locally too massive to withstand self-gravity since Toomre's Q < ∼ 1-2, and thus, it may collapse into a gaseous protoplanet. Another possibility is that the gas mass is low enough to be gravitationally stable and only dust grains are accumulated. In this case, lower gas-to-dust ratio by at least 1 order of magnitude is required, implying possible formation of a rocky planetary core.

We studied the collapse of rotating molecular cloud cores with inclined magnetic fields, based on three-dimensional numerical simulations. The numerical simulations start from a rotating Bonnor-Ebert isothermal cloud in a uniform magnetic field. The magnetic field is initially taken to be inclined from the rotation axis. As the cloud collapses, the magnetic field and rotation axis change their directions. When the rotation is slow and the magnetic field is relatively strong, the direction of the rotation axis changes to align with the magnetic field, as shown earlier by Matsumoto & Tomisaka. When the magnetic field is weak and the rotation is relatively fast, the magnetic field inclines to become perpendicular to the rotation axis. In other words, the evolution of the magnetic field and rotation axis depends on the relative strength of the rotation and magnetic field. Magnetic braking acts to align the rotation axis and magnetic field, while the rotation causes the magnetic field to incline through dynamo action. The latter effect dominates the former when the ratio of the angular velocity to the magnetic field is larger than a critical value 0 /B 0 > 0:39G 1 / 2 c À1 s , where B 0 , 0 , G, and c s denote the initial magnetic field, initial angular velocity, gravitational constant, and sound speed, respectively. When the rotation is relatively strong, the collapsing cloud forms a disk perpendicular to the rotation axis and the magnetic field becomes nearly parallel to the disk surface in the high-density region. A spiral structure appears due to the rotation and the wound up magnetic field in the disk.