台灣清華大學， 物理系

Helioseismology (II)

Global and Local Helioseismology

(2010.08, 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

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 functions1

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 functions1

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)

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

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 EndThe End