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Register a new userOn the diversity and statistical properties of protostellar discs
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Matthew R. Bate
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We present results from the first population synthesis study of protostellar discs. We analyse the evolution and properties of a large sample of protostellar discs formed in a radiation hydrodynamical simulation of star cluster formation. Due to the chaotic nature of the star formation process, we find an enormous diversity of young protostellar discs, including misaligned discs, and discs whose orientations vary with time. Star-disc interactions truncate discs and produce multiple systems. Discs may be destroyed in dynamical encounters and/or through ram-pressure stripping, but reform by later gas accretion. We quantify the distributions of disc mass and radii for protostellar ages up to $approx 10^5$ yrs. For low-mass protostars, disc masses tend to increase with both age and protostellar mass. Disc radii range from of order ten to a few hundred au, grow in size on timescales $le 10^4$ yr, and are smaller around lower-mass protostars. The radial surface density profiles of isolated protostellar discs are flatter than the minimum mass solar nebula model, typically scaling as $Sigma propto r^{-1}$. Disc to protostar mass ratios rarely exceed two, with a typical range of $M_{rm d}/M_* = 0.1-1$ to ages $le 10^4$ yrs and decreasing thereafter. We quantify the relative orientation angles of circumstellar discs and the orbit of bound pairs of protostars, finding a preference for alignment that strengths with decreasing separation. We also investigate how the orientations of the outer parts of discs differ from the protostellar and inner disc spins for isolated protostars and pairs.
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Using numerical hydrodynamic simulations, we study the gravitational fragmentation of an unstable protostellar disc formed during the collapse of a pre-stellar core with a mass of 1.2 M_sun. The forming fragments span a mass range from about a Jupiter mass to very-low-mass protostars and are located at distances from a few tens to a thousand AU, with a dearth of objects at < 100 AU. We explore the possibility of observational detection of the fragments in discs viewed through the outflow cavity at a distance of 250 pc. We demonstrate that one hour of integration time with the Atacama Large Millimeter/sub-millimeter Array (ALMA) is sufficient to detect the fragments with masses as low as 1.5 M_Jup at orbital distances up to 800 AU from the protostar. The ALMA resolution sets the limit on the minimum orbital distance of detectable fragments. For the adopted resolution of our simulated ALMA images of 0.1, the fragments can be detected at distances down to 50 AU. At smaller distances, the fragments usually merge with the central density peak. The likelihood for detecting the fragments reduces significantly for a lower resolution of 0.5. Some of the most massive fragments, regardless of their orbital distance, can produce characteristic peaks at approximately 5 micron and hence their presence can be indirectly inferred from the observed spectral energy distributions of protostars.
We investigate and discuss protostellar discs in terms of where the various non-ideal magnetohydrodynamics (MHD) processes are important. We find that the traditional picture of a magnetised disc (where Ohmic resistivity is dominant near the mid-plane, surrounded by a region dominated by the Hall effect, with the remainder of the disc dominated by ambipolar diffusion) is a great oversimplification. In simple parameterised discs, we find that the Hall effect is typically the dominant term throughout the majority of the disc. More importantly, we find that in much of our parameterised discs, at least two non-ideal processes have coefficients within a factor of 10 of one another, indicating that both are important and that naming a dominant term underplays the importance of the other terms. Discs that were self-consistently formed in our previous studies are also dominated by the Hall effect, and the ratio of ambipolar diffusion and Hall coefficients is typically less than 10, suggesting that both terms are equally important and listing a dominant term is misleading. These conclusions become more robust once the magnetic field geometry is taken into account. In agreement with the literature we review, we conclude that non-ideal MHD processes are important for the formation and evolution of protostellar discs. Ignoring any of the non-ideal processes, especially ambipolar diffusion and the Hall effect, yields an incorrect description of disc evolution.
Recent observational progress has challenged the dust grain-alignment theories used to explain the polarized dust emission routinely observed in star-forming cores. In an effort to improve our understanding of the dust grain alignment mechanism(s), we have gathered a dozen ALMA maps of (sub)millimeter-wavelength polarized dust emission from Class 0 protostars, and carried out a comprehensive statistical analysis of dust polarization quantities. We analyze the statistical properties of the polarization fraction P_frac and dispersion of polarization position angles S. More specifically, we investigate the relationship between S and P_frac as well as the evolution of the product S*P_frac as a function of the column density of the gas in the protostellar envelopes. We find a significant correlation in the polarized dust emission from protostellar envelopes seen with ALMA; the power-law index differs significantly from the one observed by Planck in star-forming clouds. The product S*P_frac, which is sensitive to the dust grain alignment efficiency, is approximately constant across three orders of magnitude in envelope column density. This suggests that the grain alignment mechanism producing the bulk of the polarized dust emission in star-forming cores may not depend systematically on the local conditions such as local gas density. Ultimately, our results suggest dust alignment mechanism(s) are efficient at producing dust polarized emission in the various local conditions typical of Class 0 protostars. The grain alignment efficiency found in these objects seems to be higher than the efficiency produced by the standard RAT alignment of paramagnetic grains. Further study will be needed to understand how more efficient grain alignment via, e.g., different irradiation conditions, dust grain characteristics, or additional grain alignment mechanisms can reproduce the observations.
Truncated abstract: The formation of a protostellar disc is a natural outcome during the star formation process. As gas in a molecular cloud core collapses under self-gravity, the angular momentum of the gas will slow its collapse on small scales and promote the formation of a protostellar disc. Although the angular momenta of dense star-forming cores remain to be fully characterized observationally, existing data indicates that typical cores have enough angular momenta to form relatively large, rotationally supported discs. However, molecular clouds are observed to be permeated by magnetic fields, which can strongly affect the evolution of angular momentum through magnetic braking. Indeed, in the ideal MHD limit, magnetic braking has been shown to be so efficient as to remove essentially all of the angular momentum of the material close to the forming star such that disc formation is suppressed. This is known as the magnetic braking catastrophe. The catastrophe must be averted in order for the all-important rotationally supported discs to appear, but when and how this happens remains debated. We review the resolutions proposed to date, with emphasis on misalignment, turbulence and especially non-ideal effects. The dissipative non-ideal effects weaken the magnetic field, and the dispersive term redirects it to promote or hinder disc formation. When self-consistently applying non-ideal processes, rotationally supported discs of at least tens of au form, thus preventing the magnetic braking catastrophe. The non-ideal processes are sensitive to the magnetic field strength, cosmic ray ionization rate, and gas and dust grain properties, thus a complete understanding of the host molecular cloud is required. Therefore, the properties of the host molecular cloud -- and especially its magnetic field -- cannot be ignored when numerically modelling the formation and evolution of protostellar discs.
Using numerical hydrodynamics simulations we studied the gravitational collapse of pre-stellar cores of sub-solar mass embedded into a low-density external environment. Four models with different magnitude and direction of rotation of the external environment with respect to the central core were studied and compared with an isolated model. We found that the infall of matter from the external environment can significantly alter the disk properties as compared to those seen in the isolated model. Depending on the magnitude and direction of rotation of the external environment, a variety of disks can form including compact (<= 200 AU) ones shrinking in size due to infall of external matter with low angular momentum, as well as extended disks forming due to infall of external matter with high angular momentum. The former are usually stable against gravitational fragmentation, while the latter are prone to fragmentation and formation of stellar systems with sub-stellar/very-low-mass companions. In the case of counterrotating external environment, very compact (< 5 AU) and short-lived (<= a few * 10^5 yr) disks can form when infalling material has low angular momentum. The most interesting case is found for the infall of counterrotating external material with high angular momentum, leading to the formation of counterrotating inner and outer disks separated by a deep gap at a few tens AU. The gap migrates inward due to accretion of the inner disk onto the protostar, turns into a central hole, and finally disappears giving way to the outer strongly gravitationally unstable disk. This model may lead to the emergence of a transient stellar system with sub-stellar/very-low-mass components counterrotating with respect to that of the star.
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