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Register a new userRadiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona
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We present a series of numerical simulations of the quiet Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Suns atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.
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We introduce two new methods that are designed to improve the realism and utility of large, active region-scale 3D MHD models of the solar atmosphere. We apply these methods to RADMHD, a code capable of modeling the Suns upper convection zone, photosphere, chromosphere, transition region, and corona within a single computational volume. We first present a way to approximate the physics of optically-thick radiative transfer without having to take the computationally expensive step of solving the radiative transfer equation in detail. We then briefly describe a rudimentary assimilative technique that allows a time series of vector magnetograms to be directly incorporated into the MHD system.
We present a comprehensive radiative magnetohydrodynamic simulation of the quiet Sun and large solar active regions. The 197 Mm wide simulation domain spans from the uppermost convection zone to over 100 Mm in the solar corona. Sophisticated treatments of radiative transfer and conduction transport provide the necessary realism for synthesizing observables to compare with remote sensing observations of the Sun. This model self-consistently reproduces observed features of the quiet Sun, emerging and developed active regions, and solar flares up to M class. Here, we report an overview on the first results. The surface magnetoconvection yields an upward Poynting flux that is dissipated in the corona and heats the plasma to over one million K. The quiescent corona also presents ubiquitous propagating waves, jets, and bright points with sizes down to 2 Mm. Magnetic flux bundles generated in a solar convective dynamo emerge into the photosphere and gives rise to strong and complex active regions with Over $10^{23}$ Mx magnetic flux. The coronal free magnetic energy, which is about 18% of the total magnetic energy, accumulates to about $10^{33}$ erg. The coronal magnetic field is not forcefree, as the Lorentz force needs to balance the pressure force and viscous stress as well as to drive magnetic field evolution. Emission measure from $log_{10}T = 4.5$ to $log_{10}T > 7$ provides a comprehensive view on structures and dynamics in the active region corona, such as coronal loops in various lengths and temperatures, mass circulation by evaporation and condensation, and eruptions from jets to large-scale mass ejections.
The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points. These points can be found directly in a potential field extrapolation or their density can be estimated from Fourier spectrum of the magnetogram. The spectral estimate, which assumes that the extrapolated field is random, homogeneous and has Gaussian statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHOs MDI. The majority of null points occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate for the modulation transfer function we find that a potential field extrapolation contains, on average, one magnetic null point, with altitude greater than 1.5 Mm, above every 322 square Mm patch of quiet Sun. Analysis of 562 quiet Sun magnetograms spanning the two latest solar minimum shows that the null point density is relatively constant with roughly 10% day-to-day variation. At heights above 1.5 Mm, the null point density decreases approximately as the inverse cube of height. The photospheric field in the quiet Sun is well approximated as that from discrete elements with mean flux 1.0e19 Mx distributed randomly with density n=0.007 per square Mm.
We investigate the fine structure of magnetic fields in the atmosphere of the quiet Sun. We use photospheric magnetic field measurements from {sc Sunrise}/IMaX with unprecedented spatial resolution to extrapolate the photospheric magnetic field into higher layers of the solar atmosphere with the help of potential and force-free extrapolation techniques. We find that most magnetic loops which reach into the chromosphere or higher have one foot point in relatively strong magnetic field regions in the photosphere. $91%$ of the magnetic energy in the mid chromosphere (at a height of 1 Mm) is in field lines, whose stronger foot point has a strength of more than 300 G, i.e. above the equipartition field strength with convection. The loops reaching into the chromosphere and corona are also found to be asymmetric in the sense that the weaker foot point has a strength $B < 300$ G and is located in the internetwork. Such loops are expected to be strongly dynamic and have short lifetimes, as dictated by the properties of the internetwork fields.
In the solar atmosphere, Alfven waves are believed to play an important role in the transfer of energy from the photosphere to the corona and solar wind, and in the heating of the chromosphere. We perform numerical computations to investigate energy transport and dissipation associated with torsional Alfven waves propagating in magnetic flux tubes that expand from the photosphere to the corona in quiet-Sun conditions. We place a broadband driver at the photosphere that injects a wave energy flux of $10^7$ erg cm$^{-2}$ s$^{-1}$ and consider Ohms magnetic diffusion and ion-neutral collisions as dissipation mechanisms. We find that only a small fraction of the driven flux, $sim 10^5$ erg cm$^{-2}$ s$^{-1}$, is able to reach coronal heights, but it may be sufficient to partly compensate the total coronal energy loss. The frequency of maximal transmittance is $sim 5$ mHz for a photospheric field strength of 1 kG and is shifted to smaller/larger frequencies for weaker/stronger fields. Lower frequencies are reflected at the transition region, while higher frequencies are dissipated producing enough heat to balance chromospheric radiative losses. Heating in the low and middle chromosphere is due to Ohmic dissipation, while ion-neutral friction dominates in the high chromosphere. Ohmic diffusion is enhanced by phase mixing because of the expansion of the magnetic field. This effect has the important consequence of increasing the chromospheric dissipation and, therefore, reducing the energy flux that reaches the corona. We provide empirical fits of the transmission coefficient that could be used as input for coronal models.
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