台灣清華大學， 物理系 Helioseismology (II) Global and Local Helioseismology ( , 北京 ) 周定一 Dean-Yi Chou

Helioseismolgy Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior.

Basic Principle to probe Solar Interiors Different modes penetrate into different depths.

Observations in Helioseismology Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior. Observations set r = R But it still gives the same dispersion relation:

Local Helioseismolgy Using solar p modes measured on the solar surface to probe the local properties of the solar interior. Global Helioseismolgy Using solar p modes measured on the solar surface to probe the global properties of the solar interior. The life time of p modes used in global helioseismology needs to be long enough to go around the Sun. This gives a criterion: l < 150 It needs higher l (shorter wavelength).

Examples of Important Achievements in Global Helioseismology Confirm and refine the standard model Depth dependence of sound speed Differential rotation pattern Wave excitation mechanism Solar-cycle variations of rotation and sound speed near the base of the convection zone ???

Observations in Helioseismology Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior. Observations set r = R But it still gives the same dispersion relation:

k-ω Diagram

Sound Speed and Density Profile

Internal Differential Rotation

(comparison of different methods)

Local Helioseismolgy Using solar p-mode oscillations measured on the solar surface to probe the local properties of the solar interior. Local properties (local inhomegeneity): 1.magnetic fields 2.flows 3.thermal perturbation 4.other local properties

> Fourier-Hankel decomposition (Braun et al. 1987) > Ring-diagram Analysis (Hill 1988) > Time-Distance Analysis (Duvall et al. 1993) > Acoustic Imaging (Chang et al. 1997) > Holography ? (Chou et al. 2007) > Direction Filter (Chou et al. 2009) Techniques in Local Helioseismology

Examples of Important Achievements in Local Helioseismology Flows around sunspots Flows in the convection zone (near surface) Sound-speed perturbation around sunspots Meridional flows in the convection zone (distribution and solar-cycle variations) Acoustic power in sunspots

Ring-diagram Analysis (Hill 1988) Basic principle: 1.Flows affect p-mode frequencies. 2.2-d flow patterns can be derived from frequency shifts.

The average velocity over the region, (Ux, Uy), is determined by fitting power spectra to It needs inversion to obtain depth distribution.

Flow pattern from ring-diagram analysis d = 7.1 Mm

Time-Distance Analysis (Duvall et al. 1993) Measuring changes in travel time due to inhomogeneity Cross-correlation functions 1 2

Fit cross-correlation functions to a Gabor wavelet

Information from travel time flow velocity wave speed perturbation Through inversion, the distributions of flow velocity and wave speed perturbation below the surface can be obtained.

Time-Distance Analysis (Duvall et al. 1993) Measuring changes in travel time due to inhomogeneity Cross-correlation functions 1 2

Kosovichev et al. (2000) (MDI data) flow velocity and wave-speed perturbation in an active region from time-distance analysis 16 Mm

wave-speed perturbation for an active region Kosovichev et al. (2000) (MDI data)

wave-speed perturbation for an emerging flux region 8 hour interval 1 2 3

Acoustic Imaging (Chang et al., 1997) Is it possible to image the solar interior with acoustic waves measured on the surface?

imaging = adding signals in phase Principle of imaging  There is no such a lens for the solar interior.  One needs a computational lens.

Constructed Images from Acoustic Imaging

 Although the computation lens is focused on the target point, information along the ray path is contained in the signals used in reconstruction.  The phase and intensity information at a target point include information along the ray path.  One needs to do inversion to obtain more precise distribution of inhomogeneity.

Sound-speed perturbation from inversion of travel-time perturbation in acoustic imaging vertical cut measured inversion (Sun & Chou, 2001) 54Mm 169 Mm

Acoustic imaging technique has been used to map the far side of the Sun. Application:

Limits of local helioseimology > Modes of longer wavelength penetrate deeper. > β increases with depth rapidly. 1.Limit on spatial resolution 2.Limit on depth

The End