Recovering Solar Toroidal Field Dynamics From Sunspot Location Patterns

We analyze both Kitt Peak magnetogram data and MDI continuum intensity sunspot data to search for the following solar toroidal band properties: width in latitude and the existence of a tipping instability (longitudinal m=1 mode) for any time during the solar cycle. To determine the extent which we can recover the toroidal field dynamics, we forward model artificially generated sunspot distributions from subsurface toroidal fields we assigned certain properties. We analyzed two sunspot distribution parameters using MDI and model data: the average latitudinal separation of sunspot pairs as a function of longitudinal separation, and the number of sunspot pairs creating a given angle with respect to the E-W direction. A toroidal band of 10 degrees width with a constant tipping of 5 degrees best fits MDI data early in the solar cycle. A toroidal band of 20 degrees width with a tipping amplitude decreasing in time from 5 to 0 degrees best fits MDI data late in the solar cycle. Model data generated by untipped toroidal bands cannot fit MDI high latitude data and can fit only one parameter at low latitudes. Tipped toroidal bands satisfy chi squared criteria at both high and low latitudes. We conclude this is evidence to reject the null hypothesis - that toroidal bands in the solar tachocline do not experience a tipping instability - in favor of the hypothesis that the toroidal band experiences an m=1 tipping instability. Our finding that the band widens from ~10 degrees early in the solar cycle to ~20 degrees late in the solar cycle may be explained in theory by magnetic drag spreading the toroidal band due to altered flow along the tipped field lines.Comment: This paper is accepted to Astrophysical Journal, September 2005 issu

Concentration of toroidal magnetic field in the solar tachocline by eta-quenching

We show that if the turbulent magnetic diffusivity used in solar dynamos is assumed to be 'quenched' by increasing toroidal fields, much larger amplitude and more concentrated toroidal fields can be induced by differential rotation from an assumed poloidal field than if there is no quenching. This amplification and concentration mechanism is weakened and bounded by j x B feedbacks on the differential rotation. Nevertheless, it is strong enough to contribute to the creation of ~100 kG toroidal fields near the base of the convection zone, perhaps in conjunction with the 'exploding flux tube' process. Such high fields are necessary for sunspots to occur in low solar latitudes.Comment: 8 pages, 6 figures, added references, corrected typos, accepted by Ap

Indirect measurement of the mean meridional circulation in the southern hemisphere

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Meteorology, 1964.Includes bibliographical references (leaves 48-49).by Peter Augustus Gilman.M.S

Physical Origin of Differences among various Measures of Solar Meridional Circulation

We show that systematic differences between surface Doppler and magnetic element tracking measures of solar meridional flow can be explained by the effects of surface turbulent magnetic diffusion. Feature-tracking speeds are lower than plasma speeds in low and mid-latitudes, because magnetic diffusion opposes poleward plasma flow in low-latitudes whereas it adds to plasma flow at high latitudes. Flux transport dynamo models must input plasma flow; the model-outputs yield estimates of the surface magnetic feature tracking speed. We demonstrate that the differences between plasma speed and magnetic pattern speed in a flux-transport dynamo are consistent with the observed difference between these speeds.Comment: To appear in Ap

Hydromagnetic model for the solar general circulation.

Massachusetts Institute of Technology. Dept. of Meteorology. Thesis. 1966. Ph.D.Bibliography: p. 197-202.Ph.D

Solar Multi-Scale Convection and Rotation Gradients Studied in Shallow Spherical Shells

The differential rotation of the sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and mid-latitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients, and may influence dynamics on a global scale in ways that are not yet understood. To investigate such dynamics, we have constructed a series of three-dimensional numerical simulations of turbulent compressible convection within spherical shells, dealing with shallow domains to make such modeling computationally tractable. These simulations are the first models of solar convection in a spherical geometry that can explicitly resolve both the largest dynamical scales of the system (of order the solar radius) as well as smaller-scale convective overturning motions comparable in size to solar supergranulation (20--40 Mm). We find that convection within these simulations spans a large range of horizontal scales, and that the radial angular velocity gradient in these models is typically negative, especially in low- and mid-latitude regions. Analyses of the angular momentum transport indicates that such gradients are maintained by Reynolds stresses associated with the convection, transporting angular momentum inward to balance the outward transport achieved by viscous diffusion and large-scale flows in the meridional plane. We suggest that similar mechanisms associated with smaller-scale convection in the sun may contribute to the maintenance of the observed radial shear layer located immediately below the solar photosphere.Comment: 45 pages, 17 figures, ApJ in press. A preprint of paper with hi-res figures can be found at http://www-lcd.colorado.edu/~derosa/modelling/modelling.htm

Theory of Solar Meridional Circulation at High Latitudes

We build a hydrodynamical model for computing and understanding the Sun's large-scale high latitude flows, including Coriolis forces, turbulent diffusion of momentum and gyroscopic pumping. Side boundaries of the spherical 'polar cap', our computational domain, are located at latitudes $\geq 60^{\circ}$. Implementing observed low latitude flows as side boundary conditions, we solve the flow equations for a cartesian analog of the polar cap. The key parameter that determines whether there are nodes in the high latitude meridional flow is $\epsilon=2 \Omega n \pi H^2/\nu$, in which $\Omega$ is the interior rotation rate, n the radial wavenumber of the meridional flow, $H$ the depth of the convection zone and $\nu$ the turbulent viscosity. The smaller the $\epsilon$ (larger turbulent viscosity), the fewer the number of nodes in high latitudes. For all latitudes within the polar cap, we find three nodes for $\nu=10^{12}{\rm cm}^2{\rm s}^{-1}$, two for $10^{13}$, and one or none for $10^{15}$ or higher. For $\nu$ near $10^{14}$ our model exhibits 'node merging': as the meridional flow speed is increased, two nodes cancel each other, leaving no nodes. On the other hand, for fixed flow speed at the boundary, as $\nu$ is increased the poleward most node migrates to the pole and disappears, ultimately for high enough $\nu$ leaving no nodes. These results suggest that primary poleward surface meridional flow can extend from $60^{\circ}$ to the pole either by node-merging or by node migration and disappearance.Comment: Accepted in Ap

The Solar Benchmark: Rotational Modulation of the Sun Reconstructed from Archival Sunspot Records

We use archival daily spot coverage measurements from Howard et al. (1984) to study the rotational modulation of the Sun as though it were a distant star. A quasi-periodic Gaussian process measures the solar rotation period $P_\mathrm{rot} = 26.3 \pm 0.1$ days, and activity cycle period $P_\mathrm{cyc} = 10.7 \pm 0.3$ years. We attempt to search for evidence of differential rotation in variations of the apparent rotation period throughout the activity cycle and do not detect a clear signal of differential rotation, consistent with the null results of the hare-and-hounds exercise of Aigrain et al. (2015). The full reconstructed solar light curve is available online.Comment: Accepted for publication in MNRA