3.7 Thermal asphericity and subsurface magnetic fields

Latitudinal variations (asphericity) in the sound speed may be caused by temperature perturbations induced by convection or magnetism or they may be caused by the direct influence of the Lorentz force on the propagation speed of acoustic waves. The two effects are difficult to disentangle in helioseismic inversions.

Latitudinal sound speed variations inferred by global helioseismology are found to be very weak (about one part in $104$ ) and appear to be dominated by small-scale magnetic activity near the solar surface (Gough, 1996 ; Dziembowski et al., 2000 ; Antia et al., 2001 , 2003 ). In particular, enhancements in the sound speed are found to correlate well with latitudinal bands of magnetic activity in the photosphere which migrate toward the equator during the course of the solar activity cycle. However, weak latitudinal variations have also been detected deeper in the interior. Time-averaged inversions reveal a significant sound speed enhancement throughout the convection zone, peaking at a latitude of $~ 60o$ and radius of $~ 0.92R o .$ (Dziembowski et al., 2000 ; Antia et al., 2001 , 2003 ). This feature appears to be present at least over the time interval from 1995 to 2002 and its magnitude is consistent with a fractional sound speed variation of about $10-4$ , a magnetic field of strength $~ 60 kG$ , or some combination of the two.

Probing magnetic fields near the base of the convection zone is of particular importance to solar dynamo theory since the tachocline and overshoot region are believed to play a key role in generating and storing toroidal magnetic flux which eventually rises to the surface to form active regions (see Section 4.5). Such fields have not yet been unambiguously detected but helioseismic measurements have suggested an upper limit of about $300 kG$ (Basu, 1997 ; Antia et al., 2000 , 2003 ).

Thermal asphericity induced by convective motions may also give rise to latitudinal irradiance variations in the photosphere which can in principle be measured. However, in practice, such variations are dominated by magnetic features such as sunspots and faculae, making it difficult to distinguish purely thermal effects (Hudson, 1988 ). Early estimates of the pole-equator temperature difference (reviewed by Altrock and Canfield, 1972 ) were only able to set upper limits of a few K. After removing the facular contribution, Kuhn et al. (1988 ) report residual irradiance variations which they interpret as latitudinal temperature variations. The temperature peaks at low latitudes in warm bands which correlate well with the magnetic activity belts, propagating toward the equator as the cycle progresses. A second component is also present, consisting of warm poles which exhibit little variation over the course of the activity cycle. The amplitudes of the low and high-latitude maxima are about $3 K$ and $1 K$ , respectively, relative to the temperature minimum at mid-latitudes. However, further analysis has called this interpretation into question and suggests that the irradiance variations may instead be attributed to emission from diffuse magnetic elements (Woodard and Libbrecht, 2003 ).

Asphericity in the density field appears to be even weaker than that in the sound speed (fractional variation $< 10- 4$ ) and has not yet been reliably detected (Antia et al., 2001 ).