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Register a new userGravitational collapse of magnetized clouds II. The role of Ohmic dissipation
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We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free-fall along radial field lines. This so-called ``kinematic approximation ignores the back reaction of the Lorentz force on the accretion flow. In quasi steady-state, and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendres polynomials and confluent hypergeometric functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius), where the magnetic field becomes asymptotically straight and uniform. In our solution, the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by several orders of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.
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We study the self-similar collapse of an isothermal magnetized rotating cloud in the ideal magnetohydrodynamic (MHD) regime. In the limit of small distance from the accreting protostar we find an analytic solution that corresponds to free-fall onto a central mass point. The density distribution is not spherically symmetric but depends on the mass loading of magnetic field lines, which can be obtained by matching our inner solution to an outer collapse solution previously computed by Allen, Shu & Li. The concentration of magnetic field trapped by the central mass point under field-freezing, independent on the details of the starting state, creates a split monopole configuration where the magnetic field strength increases as the inverse square of the distance from the center. Under such conditions, the inflow eventually becomes subalfvenic and the outward transfer of angular momentum by magnetic braking very efficient, thus preventing the formation of a centrifugally supported disk. Instead, the azimuthal velocity of the infalling gas decreases to zero at the center, and the gas spirals into the star. Therefore, the dissipation of dynamically important levels of magnetic field is a fundamental requisite for the formation of protoplanetary disks around young stars.
Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional MHD nested-grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the center of the cloud. When the isothermal gas is stable for fragmentation in a contracting disk, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentations are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disk is supported by centrifugal force, the disk fragments through a ring configuration (ring fragmentation). This is realized in a fast rotating adiabatic core as Omega >0.2 tau_ff^-1, where Omega and tau_ff represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disk is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2 - 4 fragments (bar fragmentation). Even if a disk is thin, the disk dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows are ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.
We analyse column density and temperature maps derived from Herschel dust continuum observations of a sample of massive infrared dark clouds (G11.11-0.12, G18.82-0.28, G28.37+0.07, G28.53-0.25). We disentangle the velocity structure of the clouds using 13CO 1-0 and 12CO 3-2 data, showing that these IRDCs are the densest regions in massive giant molecular clouds and not isolated features. The probability distribution function (PDF) of column densities for all clouds have a power-law distribution over all (high) column densities, regardless of the evolutionary stage of the cloud: G11.11-0.12, G18.82-0.28, and G28.37+0.07 contain (proto)-stars, while G28.53-0.25 shows no signs of star formation. This is in contrast to the purely log-normal PDFs reported for near/mid-IR extinction maps. We only find a log-normal distribution for lower column densities, if we perform PDFs of the column density maps of the whole GMC in which the IRDCs are embedded. By comparing the PDF slope and the radial column density profile, we attribute the power law to the effect of large-scale gravitational collapse and to local free-fall collapse of pre- and protostellar cores. Independent from the PDF analysis, we find infall signatures in the spectral profiles of 12CO for G28.37+0.07 and G11.11-0.12, supporting the scenario of gravitational collapse. IRDCs are the densest regions within GMCs, which may be the progenitors of massive stars or clusters. At least some of the IRDCs are probably the same features as ridges (high column density regions with N>1e23 cm-2 over small areas), which were defined for nearby IR-bright GMCs. Because IRDCs are only confined to the densest (gravity dominated) cloud regions, the PDF constructed from this kind of a clipped image does not represent the (turbulence dominated) low column density regime of the cloud.
In arXiv:gr-qc/9504004 it was shown that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. More recently, in the attempt to extend the same approach to the case of $f(R)$ theories of gravity, it was found that a non-equilibrium setting is indeed required in order to fully describe both this theory as well as classical GR (arXiv:gr-qc/0602001). Here, elaborating on this point, we show that the dissipative character leading to a non-equilibrium spacetime thermodynamics is actually related -- both in GR as well as in $f(R)$ gravity -- to non-local heat fluxes associated with the purely gravitational/internal degrees of freedom of the theory. In particular, in the case of GR we show that the internal entropy production term is identical to the so called tidal heating term of Hartle-Hawking. Similarly, for the case of $f(R)$ gravity, we show that dissipative effects can be associated with the generalization of this term plus a scalar contribution whose presence is clearly justified within the scalar-tensor representation of the theory. Finally, we show that the allowed gravitational degrees of freedom can be fixed by the kinematics of the local spacetime causal structure, through the specific Equivalence Principle formulation. In this sense, the thermodynamical description seems to go beyond Einsteins theory as an intrinsic property of gravitation.
Hot Jupiter atmospheres exhibit fast, weakly-ionized winds. The interaction of these winds with the planetary magnetic field generates drag on the winds and leads to ohmic dissipation of the induced electric currents. We study the magnitude of ohmic dissipation in representative, three-dimensional atmospheric circulation models of the hot Jupiter HD 209458b. We find that ohmic dissipation can reach or exceed 1% of the stellar insolation power in the deepest atmospheric layers, in models with and without dragged winds. Such power, dissipated in the deep atmosphere, appears sufficient to slow down planetary contraction and explain the typically inflated radii of hot Jupiters. This atmospheric scenario does not require a top insulating layer or radial currents that penetrate deep in the planetary interior. Circulation in the deepest atmospheric layers may actually be driven by spatially non-uniform ohmic dissipation. A consistent treatment of magnetic drag and ohmic dissipation is required to further elucidate the consequences of magnetic effects for the atmospheres and the contracting interiors of hot Jupiters.
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