Schou, J., 1991, in Gough, D. O. & Toomre, J., eds, Challenges to Theories of the

Structure of Moderate-Mass Stars, Springer-Heidelberg, p. 93.

Schou, J. 2003, in this volume.

Schou, J. et al., 1998, ApJ, 505, 390.

Sekii, T., 1990, in Osaki, Y. & Shibahashi, H., eds, Progress of Seismology of the

Sun and Stars, Springer-Verlag, Berlin, p. 337.

Sekii, T., 1991, PASJ, 43, 381.

Sekii, T., 1993, MNRAS, 264, 1018.

Sekii, T., 1995, in Ulrich, R. K., ed., GONG 1994: Helio- and Astero-Seismology

from Earth and Space, the Astronomical Society of the Paci¬c, San Francisco,

p. 74.

Sekii, T., 1997, in Provost, J. & Schmider, F.-X., eds, IAU Symp. 181: Sounding

Solar and Steller Interiors, Kluwer Academic, Dordrecht, p. 189.

Sekii, T., Gough D. O. & Kosovichev A. G., 1995, in Ulrich, R. K., ed., GONG

1994: Helio- and Astero-Seismology from Earth and Space, the Astronomical

Society of the Paci¬c, San Francisco, p. 59.

Spiegel, E. A. & Zahn, J.-P., 1992, A&A, 265, 106.

Toomre, J. 2003, in this volume.

Toutain, T. & Fr¨hlich, C., 1992, A&A, 257, 287.

o

Toutain, T. & Kosovichev, A. G., 1994, A&A, 284, 265.

Unno, W., Osaki, Y, Ando, H., Saio, H. & Shibahashi, H., 1989, Nonradial

Oscillations of Stars (second edition), University of Tokyo Press.

Weber, M. A., Acton, L. W., Alexander, D. & Kubo, S., 1999, Solar Phys., 189,

271.

19

Telechronohelioseismology

ALEXANDER KOSOVICHEV

W. W. Hansen Experimental Physics Laboratory, Stanford University,

HEPL Annex A201, Stanford, CA 94305-4085, USA

Telechronohelioseismology (or time-distance helioseismology) is a new diag-

nostic tool for three-dimensional structures and ¬‚ows in the solar interior.

Along with the other methods of local-area helioseismology, the ring diagram

analysis, acoustic holography and acoustic imaging, it provides unique data

for understanding turbulent dynamics of magnetized solar plasma. The tech-

nique is based on measurements of travel time delays or wave-form perturba-

tions of wave packets extracted from the stochastic ¬eld of solar oscillations.

It is complementary to the standard normal mode approach which is lim-

ited to diagnostics of two-dimensional axisymmetrical structures and ¬‚ows.

I discuss theoretical and observational principles of the new method, and

present some current results on large-scale ¬‚ows around active regions, the

internal structure of sunspots and the dynamics of emerging magnetic ¬‚ux.

19.1 Introduction

Telechronohelioseismology (or telechronoseismology) is de¬ned as a sub-

discipline of helioseismology by Gough (1996) in his reply to criticism of

the term ˜asteroseismology™ (Trimble 1995). Gough argued that, being de-

rived from all classical Greek words, ˜thoroughbred™ telechronohelioseismol-

ogy should be preferred to ˜oedipal combinations™ of Greek and Latin words.

Telechronohelioseismology belongs to a new class of helioseismic measure-

ments, broadly de¬ned as epichorioseismology† (also called local-area helio-

seismology), which provides three-dimensional diagnostics of the solar inte-

rior.

Helioseismology is originally based on interpretation of the frequencies of

† The main root comes from χωριoν, meaning a particular place. The pre¬x epi-, from the

preposition πι (with smooth breathing), has a host of meanings, but denotes direction (Gough,

private communication).

279

Kosovichev

280

normal modes of solar oscillation. This approach allows us to estimate global

axisymmetrical components of the Sun™s properties such as the sound speed

(e.g. Christensen-Dalsgaard et al. 1985), the density (Kosovichev, 1990),

the adiabatic exponent (Elliott & Kosovichev 1998), the element abundances

(Gough & Kosovichev 1988), and the rotation rate (Duvall et al. 1984).

The ¬rst idea that helioseismology can measure local properties of the

solar interior was suggested by Gough & Toomre (1983). They estimated the

in¬‚uence of large-scale convective eddies on the wave patterns of ¬ve-minute

oscillations of high degree and showed that the distortion to the local k ’ ω

relation has two constituents: one depends on the horizontal component of

the convective velocity and has a sign which depends on the sign of ω/k; the

other depends on temperature ¬‚uctuations and is independent of the sign of

ω/k. They concluded that by studying the distortions it would be possible

to reveal some aspects of the large-scale ¬‚ow in the solar convection zone.

This idea is developed now in a sophisticated measurement procedure called

ring-diagram analysis (Hill 1988; Gonz´lez Hern´ndez et al. 2000; Haber

a a

et al. 2000).

Further developments of epichorioseismology led to the idea to perform

the measurements of local wave distortions in the time-distance space in-

stead of the traditional Fourier space (Duvall et al. 1993). In this case the

wave distortions can be measured as perturbations of wave travel times.

However, because of the stochastic nature of solar waves it is impossible

to track individual wave fronts. Instead, it was suggested to use a cross-

covariance time-distance function that provides a statistical measure of the

wave distortion. Indeed, by calculating a cross-covariance of solar oscil-

lation signals at two points one may hope that the main contribution to

this cross-covariance will be from waves propagating between these points.

However, the interpretation of these measurements is extremely challenging,

and various approximations are used to relate the observed perturbations

of travel times to internal properties such as sound-speed perturbations and

¬‚ow velocities.

In this brief review, I discuss basic principles and procedures of telechrono-

seismology and some initial results.

19.2 Observational and Theoretical Principles

The basic idea of telechronohelioseismology is to measure the acoustic travel

time between di¬erent points on the solar surface, and then to use the mea-

surement for inferring perturbations of the sound speed and ¬‚ow velocities in

the interior along the wave paths connecting the surface points (Fig. 19.1a).

Telechronohelioseismology 281

Fig. 19.1. (a) A sample of ray paths of acoustic waves propagating through the Sun™s

interior from surface point A. (b) The cross-covariance as a function of the travel

distance and lag time. The lowest ridge corresponds to wave packets propagating

between two points on the solar surface directly, e.g. along ray path AB (solid

curve). The second ridge from below corresponds to acoustic waves that have an

additional re¬‚ection at the surface (˜second bounce™), e.g. along ray path ACB. This

ridge appears re¬‚ected at the distance of 180—¦ , because the propagation distance is

measured in the interval from 0—¦ to 180—¦ .

This idea is similar to seismology of the Earth. However, unlike in the

Earth, the solar waves are generated stochastically by numerous acoustic

sources in the subsurface layer of turbulent convection. Therefore, the wave

travel time and other wave propagation properties are determined from the

cross-covariance function, Ψ(„, ∆), of the oscillation signal, f (t, dr), between

di¬erent points on the solar surface (Duvall et al. 1993):

T

1

f (t, dr1 )f — (t + „, dr 2 )dt,

Ψ(„, ∆) = (19.1)

T 0

where ∆ is the angular distance between the points with coordinates dr1 and

dr2 , „ is the delay time, and T is the total time of the observations. Because

of the stochastic nature of excitation of the oscillations, function Ψ must be

averaged over some areas on the solar surface to achieve a signal-to-noise

ratio su¬cient for measuring travel times „ . The oscillation signal, f (t, dr),

is usually the Doppler velocity or intensity. A typical cross-covariance func-

tion averaged over the whole disk is shown in Figure 19.1b. It displays a

set of ridges. The lowest ridge corresponds to wave propagating directly be-

tween two surface points, (the lowest ridge). The second ridge from below

Kosovichev

282

is formed by waves which experience one additional re¬‚ection at the surface