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We present an ab initio approach to the solar coronal heating problem by modeling a small part of the solar corona in a computational box using a three-dimensional MHD code including realistic physics. The observed solar granular velocity pattern and its amplitude and vorticity power spectra, as reproduced by a weighted Voronoi tessellation method, are used as a boundary condition that generates a Poynting flux in the presence of a magnetic field. The initial magnetic field is a potential extrapolation of a SOHO/MDI high-resolution magnetogram, and a standard stratified atmosphere is used as a thermal initial condition. Except for the chromospheric temperature structure, which is kept nearly fixed, the initial conditions are quickly forgotten because the included Spitzer conductivity and radiative cooling function have typical timescales much shorter than the time span of the simulation. After a short initial start-up period, the magnetic field is able to dissipate (3-4) x 106 ergs cm-2 s-1 in a highly intermittent corona, maintaining an average temperature of ~106 K, at coronal density values for which simulated images of the TRACE 171 and 195 A passbands reproduce observed photon count rates.

Data from recent numerical simulations of the solar corona and transition region are analyzed, and the magnetic field connections between the low corona and the photosphere are found to be close to those of a potential field. The field line-to-field line displacements follow a power-law distribution with typical displacements of just a few Mm. Three loops visible in simulated TRACE filters are analyzed in detail and found to have significantly different heating rates and distributions thereof, one of them showing a small-scale heating event. The dynamical structure is complicated, even though all the loops are visible in a single filter along most of their lengths. The loops are nonstatic and are in the process of evolving into loops with very different characteristics. Differential emission measure (DEM) curves along one of the loops illustrate that DEM curves have to be treated carefully if physical characteristics are to be extracted.

The solar acoustic p-mode line profiles are asymmetric. Velocity spectra have more power on the low-frequency sides, whereas intensity profiles show the opposite sense of asymmetry. Numerical simulations of the upper convection zone have resonant p-modes with the same asymmetries and asymmetry reversal as the observed modes. The temperature and velocity power spectra at optical depth tcont = 1 have the opposite asymmetry, as is observed for the intensity and velocity spectra. At a fixed geometrical depth, corresponding toimg1.gif = 1, however, the temperature and velocity spectra have the same asymmetry. This indicates that the asymmetry reversal in the simulation is produced by radiative transfer effects and not by correlated noise. The cause of this reversal is the nonlinear amplitude of the displacements in the simulation and the nonlinear dependence of the H- opacity on temperature. Where the temperature is hotter the opacity is larger and photons escape from higher, cooler layers. This reduces the fluctuations in the radiation temperature compared to the gas temperature. The mode asymmetry reversal in the simulation is a small frequency-dependent differential effect within this overall reduction. Because individual solar modes have smaller amplitudes than the simulation modes, this effect will be smaller on the Sun.

In this work we use models of molecular clouds and non-LTE radiative transfer calculations to compare the column densities of molecular clouds with their LTE 13CO column densities. The cloud models consist of three-dimensional grids of density and velocity fields obtained as solutions of the compressible magnetohydrodynamic equations in a 1283 periodic grid in both the supersonic and super-Alfvenic regimes. Because of the random nature of the velocity field and the presence of shocks, the densities span a continuous range of values covering about 6 orders of magnitude (from ~0.1 to ~105 cm-3). As a result, the LTE column densities can be calculated over 3 orders of magnitude. We find that LTE column densities of molecular clouds typically underestimate the mean 13CO true column densities by factors ranging from 1.3 to 7. These results imply that the standard LTE methods for the derivation of column densities from CO data systematically underestimate the true values independent of other major sources of uncertainty such as the relative abundance of CO.

This work presents a new physical model of the star formation rate (SFR), which is verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, avir, the rms sonic Mach number, ${\cal M}_{\rm S,0}$, and the ratio of mean gas pressure to mean magnetic pressure, b0. The SFR is predicted to decrease with increasing avir (stronger turbulence relative to gravity), to increase with increasing ${\cal M}_{\rm S,0}$ (for constant values of avir), and to depend weakly on b0 for values typical of star forming regions (${\cal M}_{\rm S,0}\approx 4$-20 and b0 [?] 1-20). In the unrealistic limit of b0 - [?], that is, in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvenic turbulence). The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. The dependence of the SFR on the virial parameter is shown to agree very well with the theoretical predictions.