The Sub-Surface Structure of a Large Sample of Active Regions

We employ ring-diagram analysis to study the sub-surface thermal structure of active regions. We present results using a large number of active regions over the course of Solar Cycle 23. We present both traditional inversions of ring-diagram frequency differences, with a total sample size of 264, and a statistical study using Principal Component Analysis. We confirm earlier results on smaller samples that sound speed and adiabatic index are changed below regions of strong magnetic field. We find that sound speed is decreased in the region between approximately r=0.99R_sun and r=0.995R_sun (depths of 3Mm to 7Mm), and increased in the region between r=0.97R_sun and r=0.985R_sun (depths of 11Mm to 21Mm). The adiabatic index is enhanced in the same deeper layers that sound-speed enhancement is seen. A weak decrease in adiabatic index is seen in the shallower layers in many active regions. We find that the magnitudes of these perturbations depend on the strength of the surface magnetic field, but we find a great deal of scatter in this relation, implying other factors may be relevant.Comment: 16 pages, 11 figures, accepted for publication in Solar Physic

Stellar Inversion Techniques

Stellar seismic inversions have proved to be a powerful technique for probing the internal structure of stars, and paving the way for a better understanding of the underlying physics by revealing some of the shortcomings in current stellar models. In this lecture, we provide an introduction to this topic by explaining kernel-based inversion techniques. Specifically, we explain how various kernels are obtained from the pulsation equations, and describe inversion techniques such as the Regularised Least-Squares (RLS) and Optimally Localised Averages (OLA) methods.Comment: 20 pages, 8 figures. Lecture presented at the IVth Azores International Advanced School in Space Sciences on "Asteroseismology and Exoplanets: Listening to the Stars and Searching for New Worlds" (arXiv:1709.00645), which took place in Horta, Azores Islands, Portugal in July 201

Interpreting Helioseismic Structure Inversion Results of Solar Active Regions

Helioseismic techniques such as ring-diagram analysis have often been used to determine the subsurface structural differences between solar active and quiet regions. Results obtained by inverting the frequency differences between the regions are usually interpreted as the sound-speed differences between them. These in turn are used as a measure of temperature and magnetic-field strength differences between the two regions. In this paper we first show that the "sound-speed" difference obtained from inversions is actually a combination of sound-speed difference and a magnetic component. Hence, the inversion result is not directly related to the thermal structure. Next, using solar models that include magnetic fields, we develop a formulation to use the inversion results to infer the differences in the magnetic and thermal structures between active and quiet regions. We then apply our technique to existing structure inversion results for different pairs of active and quiet regions. We find that the effect of magnetic fields is strongest in a shallow region above 0.985R_sun and that the strengths of magnetic-field effects at the surface and in the deeper (r < 0.98R_sun) layers are inversely related, i.e., the stronger the surface magnetic field the smaller the magnetic effects in the deeper layers, and vice versa. We also find that the magnetic effects in the deeper layers are the strongest in the quiet regions, consistent with the fact that these are basically regions with weakest magnetic fields at the surface. Because the quiet regions were selected to precede or follow their companion active regions, the results could have implications about the evolution of magnetic fields under active regions.Comment: Accepted for publication in Solar Physic