Two-Dimensional Inversion for Solar Internal Rotation
Abstract
The internal rotation of the sun is inferred by solving a fully two-dimensional inverse problem of the rotational splitting data of Libbrecht (1989, AAA 080.006). We solve a set of integral equations which relate the rotational splittings of the eigenfrequencies of the sun to the internal rotation rate of the sun, the latter being considered as a function of both the distance from the center and the latitude. For this purpose we suggest an inverse method and apply it to the present problem. The integral equations are descretized and reduced to a set of linear equations. First, we impose an error-weighted least-squares condition with some boundary constraints at the surface. Second, we impose a flatness condition: the average of the first derivatives of the rotation rate is required to be as small as possible under the first constraint. Inversions were carried out while fully utilizing singular-value decomposition. In order to stabilize the solution to observational and numeric errors, we discarded small singular values. The results of numerical experiments show that the best resolution is obtained within a depth range of 0.6 <~ r/R <~ 0.9 in the low-latitude region. By inverting the observed splittings, we found that the solar internal rotation in the low-latitude region is slightly faster than the surface rotation rate in the outer ten percent of the radius, and decreases to about five percent less than the surface rotation rate within the lower levels of the convection zone. In the region 0.7 <~ r/R <~ 0.8, the rotation rate within the low-latitude zone is as fast as the surface rate, but is slower than the surface rate at r/R <~ 0.7. The rotation rate within the mid-latitude region decreases with depth in the outer twenty percent of the radius, and gradually increases inward to be faster than the surface rate.
- Publication:
-
Publications of the Astronomical Society of Japan
- Pub Date:
- April 1991
- Bibcode:
- 1991PASJ...43..381S
- Keywords:
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- Inversions;
- Solar Oscillations;
- Solar Radiation;
- Solar Rotation;
- Integral Equations;
- Least Squares Method;
- Linear Equations;
- Two Dimensional Models;
- Solar Physics;
- SOLAR OSCILLATIONS;
- SOLAR ROTATION;
- SUN