Takashi Sekii

The modified truncated SVD method for regularization in general form

The truncated singular value decomposition (SVD) method is useful for solving the standard-form regularization problem:

Asteroseismic measurement of surface-to-core rotation in a main-sequence A star, KIC 11145123

\min ||{\bf x}||_2

Asteroseismic measurement of slow, nearly-uniform surface-to-core rotation in the main sequence F star KIC 9244992

subject to

High Resolution Helioseismic Imaging of Subsurface Structures and Flows of A Solar Active Region Observed by Hinode

\min ||A{\bf x} - {\bf b}||_2

Observations of Sunspot Oscillations in G Band and Ca II H Line with Solar Optical Telescope on Hinode

. This paper presents a modification of the truncated SVD method, which solves the more general problem:

Initial Helioseismic Observations by Hinode/SOT

\min ||L{\bf x}||_2

A Statistical Study of Coronal Active Events in the North Polar Region

subject to

DETECTION OF SUPERGRANULATION ALIGNMENT IN POLAR REGIONS OF THE SUN BY HELIOSEISMOLOGY

\min ||A{\bf x} - {\bf b}||_2

Helioseismic Signature of Chromospheric Downflows in Acoustic Travel-Time Measurements from Hinode

, where L is a general matrix with full row rank. The extra work, associated with the introduction of the matrix L, is dominated by a QR-factorization of a matrix with dimensions smaller than those of L. In order to determine the optimal solution, it is often necessary to compute a sequence of regularized solutions, and it is shown how this can be accomplished with little extra computational effort. Finally, the new method is illustrated with an example from helioseismology.

Shape of a slowly rotating star measured by asteroseismology

We have discovered rotationally split core g-mode triplets and surface p-mode triplets and quintuplets in a terminal age main-sequence A star, KIC 11145123, that shows both δ Sct pmode pulsations and γ Dor g-mode pulsations. This gives the first robust determination of the rotation of the deep core and surface of a main-sequence star, essentially model independently. We find its rotation to be nearly uniform with a period near 100 d, but we show with high confidence that the surface rotates slightly faster than the core. A strong angular momentum transfer mechanism must be operating to produce the nearly rigid rotation, and a mechanism other than viscosity must be operating to produce a more rapidly rotating surface than core. Our asteroseismic result, along with previous asteroseismic constraints on internal rotation in some B stars, and measurements of internal rotation in some subgiant, giant and white dwarf stars, has made angular momentum transport in stars throughout their lifetimes an observational science.