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Helioseismology and the Sun's Interior

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Helioseismology and the Sun's Interior Solar interior Helioseismology and the Sun’s interior Michael J Thompson gets under the skin of the Sun using waves on its surface. Abstract 1: Doppler image of the Sun taken by the MDI instrument on board the Helioseismology is the study of the solar SOHO satellite, ranging from interior using observations of waves on the roughly –2 km s–1 (dark Sun’s surface. It has done much to improve tones) to +2 km s–1 (light our understanding of the interior of the tones). The dominant Sun, testing the physical inputs used to grading is due to the model stellar interiors and providing a Sun’s rotation; but the residual when detailed map of the Sun’s structure and this and other internal rotation. This in turn has greatly large-scale influenced theories of the solar magnetic motions are dynamo. These interior studies thus make corrected for a valuable bridge between solar physics reveals the and studies of the structure and evolution Sun’s resonant- mode of other stars. Recent developments oscillations. include new local techniques for (Courtesy SOHO/ unprecedented studies of subsurface MDI research group structures and flows in emerging active at Stanford regions, under sunspots, and even of active University.) regions on the far side of the Sun. These developments hold the possibility of a real understanding of how the interior links to solar magnetic activity in the corona and heliosphere. Finally, studies such as those of the deep solar interior are on the verge of becoming possible for other stars –2500 –2000 –1500 –1000 –500 0 500 1000 1500 2000 exhibiting similar multimode oscillations. velocity (m/s) here are many reasons to study the Sun. Sun. The Sun can support various wave motions, much progress has been made in helioseismology It is the only star that can be observed in notably acoustic waves and gravity waves: these through analysis of the Sun’s global modes of Tgreat detail, so it provides an important set up global resonant modes. The modes in oscillation. Some results on the Sun’s internal input to our understanding of stellar structure which the Sun is observed to oscillate are pre- structure and its rotation are reviewed here. In and evolution. The Sun greatly influences the dominantly acoustic modes, though the acoustic the past decade global-mode studies of the Sun Earth and near-Earth environment, particularly wave propagation is modified by gravity and the have been complemented by so-called local helio- through its outputs of radiation and particles, so Sun’s internal stratification, and by bulk motions seismic techniques such as tomography, which studying it is important for understanding and magnetic fields. The frequencies and other have been used to study flows in the near-surface solar–terrestrial relations. And the Sun also pro- observed properties of the oscillations can be layers and flows and structures under sunspots vides a unique laboratory for studying some fun- used to make inferences about the physical state and active regions of sunspot complexes. damental physical processes in conditions that of the solar interior. The excitation mechanism cannot be realized on Earth. It was discovered is generally believed to be turbulent convective Solar oscillations in the 1960s (Leighton et al. 1962) that patches motions in the subsurface layers of the Sun, The Sun’s oscillations are observed in line-of- of the Sun’s surface were oscillating with a which generate acoustic noise. This is a broad- sight Doppler velocity measurements over the period of about five minutes. Initially these were band source, but only those waves that satisfy visible solar disk, and also in measurements of thought to be a manifestation of local convec- the appropriate resonance conditions construc- variations of its continuum intensity of radiation tive motions, but by the 1970s it was understood tively interfere to give rise to resonant modes. caused by compression of the radiating gas by from theoretical work (Ulrich 1970, Leibacher One of the first deductions from helio- the waves. Wave motions with the largest hori- and Stein 1971) and from further observational seismology (Gough 1977, Ulrich and Rhodes zontal scales are detectable in observations of work (Deubner 1975, Claverie et al. 1979) that 1977) was that the Sun’s convection zone was sub- the Sun as a star, in which light from the whole the observed motions are the superposition of stantially deeper than in the contemporaneous visible disk is collected and analysed as a single many global resonant modes of oscillation of the solar models. From then up to the present day, time series. Motions on smaller horizontal August 2004 Vol 45 4.21 Solar interior scales require spatially resolved measurements 2: The power in the obtained by separately observing different por- Sun’s acoustic 8 tions of the disk. To measure the frequencies p-mode oscillations, very precisely, long, uninterrupted series of as observed by the observations are desirable. Hence observations MDI instrument on are made from networks of dedicated small board the SOHO 7 solar telescopes distributed in longitude around satellite, as a function of frequency the Earth (these include the Global Oscillation and angular degree l. Network Group GONG making 1024 ×1024- The power lies on 6 pixel resolved observations and the Birmingham ridges that Solar Oscillation Network, BiSON, making Sun- correspond to as-a-star observations) or from space (for branches of the dispersion relation instance, the Solar and Heliospheric Orbiter 5 for p-modes, each SOHO satellite has three helioseismology branch correspond- instruments on board; in decreasing order of res- ing to a different ency (mHz) ency olution: MDI, VIRGO and GOLF). In Doppler value of the order n. u velocity the amplitudes of individual modes are (Courtesy SOHO/MDI freq 4 of order 10 cm s–1 or smaller, their superposition research group at Stanford University.) giving a total oscillatory signal of the order of –1 1kms . The largest-amplitude modes have fre- 3 quencies of around 3 mHz. A snapshot of the Doppler velocity as measured by MDI is shown in figure 1. The large-scale gradient across the image due to the Sun’s rotation, and slowly vary- 2 ing signals due to convection, can be removed by subtracting a running average of such Doppler images, to leave the signal of the Sun’s 1 global oscillations. The outer 30% of the Sun comprises the con- vectively unstable convection zone. Solar oscil- 0 50 100 150 200 250 300 angular degree (l) lations are stochastically excited by turbulent convection in the upper part of the convection zone: the modes are both excited and damped depth, because the temperature and hence sound different m but with the same values of n and l by their interactions with the convection. speed increase with depth. Near the surface, out- are called a multiplet: it is convenient also to ω Although large excitation events such as solar wards-propagating waves also get deflected, by introduce the mean multiplet frequency nl. flares may occasionally contribute, the dominant the sharply changing stratification in the near- High-frequency modes, with positive values of excitation is probably much smaller scale and surface layers. Hence the acoustic waves are the order n, are essentially acoustic modes probably takes place in downwards plumes trapped in a resonant cavity and form modes, (p-modes): for them the dominant restoring where material previously brought to the surface with discrete frequencies ω. The horizontal force is pressure. Low-frequency modes, with by convection has cooled and flows back into structure of the eigenfunctions of the modes is negative values of n, are essentially gravity m the solar interior. These form a very frequent and given by spherical harmonics Yl , where integers modes (g-modes) set up by gravity waves that widespread set of small-scale excitation sources. l (l ≥ 0) and m (–l ≤ m ≤ l) are respectively called can propagate where there is a stable stratifica- On the timescales of the observed solar oscil- the “degree” and “azimuthal order” of the tion. There is an intermediate mode with n =0: lations, the bulk of the solar interior can be con- mode. The structure of the eigenfunction in the this is the fundamental or f-mode. For large val- sidered to be in thermal equilibrium and to radial direction into the Sun is described by a ues of l, the f-mode has the physical character provide a mean static large-scale equilibrium third quantum number n, called the “order” of of a surface gravity mode. The observed global background state in which the waves propagate. the mode: the absolute value of n is essentially modes of the Sun are p-modes and f-modes. Moreover, the timescales are sufficiently short the number of nodes between the centre and the Modes of low degree (mostly l = 0,1,2,3) are that the perturbations of pressure (p) and den- surface of the Sun in, for example, the pressure detectable in observations of the Sun as a star: sity (ρ) in the interior are related by an adiabatic perturbation eigenfunction. Hence each reso- low-degree p-modes are sensitive to conditions relation. At high frequencies, pressure forces nant frequency can be labelled with three quan- throughout the Sun, including the energy- ω provide the dominant restoring force for the tum numbers thus: nlm. The labelling is such generating core. Spatially resolved observations ω small perturbative motions about equilibrium, that at fixed l and m, the frequency nlm is a have detected p- and f- modes up to degrees of giving rise to acoustic waves. A key quantity for monotonic increasing function of n.
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