Date of Award

Spring 1-1-2014

Document Type


Degree Name

Doctor of Philosophy (PhD)


Astrophysical & Planetary Sciences

First Advisor

Mark Rast

Second Advisor

Matthias Rempel

Third Advisor

Phil Armitage

Fourth Advisor

Benjamin Brown

Fifth Advisor

Juri Toomre


We examine the effect of deep convection and magnetic fields on solar supergranulation. While supergranulation was originally identified as a convective flow from relatively great depth below the solar surface, recent work suggests that supergranules may originate near the surface. We use the MURaM code to simulate solar-like surface convection with a realistic photosphere and domain size up to 197 x 197 x 49 Mm3. This yields nearly five orders of magnitude of density contrast between the bottom of the domain and the photosphere which is the most stratified solar-like convection simulations that we are aware of.

Magnetic fields were thought to be a passive tracer in the photosphere, but recent work suggests that magnetism could provide a mechanism that enhances the supergranular scale flows at the surface. In particular, the enhanced radiative losses through long lived magnetic network elements may increase the lifetime of photospheric downflows and help organize low wavenumber flows. Since our simulation does not have sufficient resolution to resolve increased cooling by magnetic bright points, we artificially increase the radiative cooling in elements with strong magnetic ux. These simulations increase the cooling by 10% for magnetic field strength greater than 100 G. We find no statistically significant difference in the velocity or magnetic field spectrum by enhancing the radiative cooling. We also find no differences in the time scale of the flows or the length scales of the magnetic energy spectrum. This suggests that the magnetic field is determined by the flows and is largely a passive tracer. We use these simulations to construct a two-component model of the flows: for scales smaller than the driving (integral) scale (which is four times the local density scale height) the flows follow a Kolmogorov (k-5/3) spectrum, while larger scale modes decay with height from their driving depth (i.e. the depth where the wavelength of the mode is equal to the driving (integral) scale). This model reproduces the MURaM results well and suggests that the low wavenumber power in the photosphere imprints from below. In particular, the amplitude of the driving (integral) scale mode at each depth determines how much power imprints on the surface flows. This is validated by MURaM simulations of varying depth that show that increasing depths contribute power at a particular scale (or range of scales) that is always at lower wavenumbers than shallower flows. The mechanism for this imprinting remains unclear but, given the importance of the balances in the continuity equation to determining the spectrum of the flows, we suggest that pressure perturbations in the convective upflows are the imprinting mechanism.

By comparing the MURaM simulations to SDO/HMI observations (using the coherent structure tracking code to compute the inferred horizontal velocities on both data sets), we find that the simulations have significant excess power for scales larger than supergranulation. The only way to match observations is by using an artificial energy flux to transport the solar luminosity for all depths greater than 10 Mm below the photosphere (down to the bottom of the domain at 49 Mm depth). While magnetic fields from small-scale dynamo simulations help reduce the rms velocity required to transport the solar luminosity below the surface, this provides only a small reduction in low wavenumber power in the photosphere.

The convective energy transport in the Sun is constrained by theoretical models and the solar radiative luminosity. The amplitude or scale of the convective flows that transport the energy, however, are not constrained. The strong low wavenumber flows found in these local simulations are also present in current generation global simulations. While local or global dynamo magnetic fields may help suppress these large-scale flows, the magnetic fields must be substantially stronger throughout the convection domains for these simulations to match observations. The significant decrease in low wavenumber flow amplitude in the artificial energy flux simulation that matches the observed photospheric horizontal velocity spectrum suggests that convection in the Sun transports the solar luminosity with much weaker large-scale flows. This suggests that we do not understand how convective transport works in the Sun for depths greater than 10 Mm below the photosphere.