Seismic Probing of the Dynamics of the Solar Interior Michael Thompson University of Sheffield

Thanks to … Rachel Howe Alexander Kosovichev Matthias Rempel Juri Toomre for results and presentation material used in this talk

Outline 1.Introduction 2.Temporally varying flows Global results and meridional circulation Flows around active regions 3.Search for structural variations Frequency variations with time Global results Variations associated with active regions

Uncertainties Microphysics Opacities Equation of state Nuclear reaction rates Diffusion of elements Macrophysics Rotation Magnetic fields Macroscopic mixing Stellar convection

Sunspot cycles Latitude 2000 Sunspot number 1870

Sound waves propagating in sun Refraction of waves provides lower boundary of resonant cavity Resonant cavities are of differing extent

l=6,m=0 Resonant modes the sun l=6,m=3l=6,m=6 Schematic of a resonant mode of the sun l=3,m=2 Spherical harmonic degree l, order m Examples of spherical harmonics

The inverse problem Observed frequencies  Sun’s internal structure & dynamics

Data from space – in particular from three instruments on the SOHO satelite SOI-MDI GOLF VIRGO Data from ground-based networks, in particular BiSON, GONG, LOWL GONG network sites

Global-mode seismology Measure mode properties ω; A, Γ; line-shapes Eigenfunctions / spherical harmonics Frequencies ω nlm (t) depend on conditions in solar interior determining wave propagation ω nlm – degeneracy lifted by rotation and by structural asphericities and magnetic fields Inversion provides maps such as of c and ρ and rotation and wave-speed asphericities North-south averages Snapshots at successive times: typically 2-month averages Spherical harmonics

Introduction: History ACRIM observations 1980, Birmingham/Tenerife: sun-as-a-star observations going back to 1975 (BiSON) IRIS: sun-as-a-star Big Bear Solar Observatory (Libbrecht and co-workers): resolved-sun observations Mount Wilson: high-degree observations since LOWL/ECHO medium degree, 1994-present GONG (1995-present), MDI (1996-present); continuous resolved-sun observations.

History (schematic)

Rotation Inversion Results

The continuous medium-degree observations covering an 11-year solar cycle (GONG, MDI) have revealed the deep-penetrating structure of the migrating zonal flow pattern known as the torsional oscillation, as well as giving hints of possible other periodicities in the rotation rate close to the tachocline. Temporal changes in the structure of the solar interior are more challenging to measure, as the obvious solar-cycle effects are dominated by the surface.

Rotation Inversion Results Contours at approx. 25 o to axis Surface Shear Tachocline

Rotation Inversion Results

Rotation of the deeper solar interior from BiSON and LOWL data

Convection-Zone Dynamics So-called ‘torsional oscillation’ is a pattern of weak slower and faster zonal flows migrating from mid- latitudes to the equator and poles over the solar cycle. First observed by Howard and Labonte (1980) in surface observations Surface Doppler measurements from Mt Wilson go back to (Ulrich 2001).

Helioseismic Detections of the Torsional Oscillation Woodard and Libbrecht (1993) saw hints in BBSO data. Seen in early MDI f- mode data by Kosovichev & Schou (1997)

Helioseismic Detection of the Torsional Oscillation Seen in 4 years of GONG and 3 years of MDI data by Toomre et al. (2000), Howe, Komm & Hill (2000), Howe et al. (2000) Penetration depth at least 0.92R.

Torsional Oscillation Antia and Basu (2001) drew attention to high- latitude, poleward-moving part of phenomenon.

Torsional oscillations of whole convection zone Differencing rotation inversions relative to solar minimum (1996) at successive 72-day epochs reveals the torsional oscillations at low and high latitudes through much of the convection zone.

It is also revealing to stack fewer results, so the evolution of the whole convection zone can be seen. Here we difference rotation inversions relative to solar minimum at successive 1-year epochs.

Torsional Oscillation Vorontsov et al 2002 Extrapolation using 11-yr sinusoid

Zonal Flow Pattern

Zonal Flow Patterns (Time-Radius) MDI OLA MDI RLS GONG RLS Howe et al 2005

Phase and amplitude (MDI OLA) at different latitudes

Torsional Oscillation: Latest We now have a full 11yr cycle of observations! Animation based on 11+11/2 year sinusoids.

Comparison with modelling Courtesy M. Rempel

Variations in Ω ( r, θ ; t ) Variability in and near tachocline 1.3-yr variations in inferred rotation rate at low latitudes above and beneath tachocline Signature of dynamo field evolution? Radiative interior also involved in solar cycle? Link between tachocline and 1.3/1.4-yr variations in solar wind, aurorae, solar mean magnetic field ?

Variations at the Tachocline

Tachocline oscillations See Howe et al. (2000; Science 287, 2456) Basu & Antia (2001; MNRAS 324, 498)

The ‘1.3 year oscillation’ A.0.71R, equator residuals B.Power spectrum C.Power in max. power frequency bin, vs latitude D.Power in max. power frequency bin, vs radius.

Boberg et al Solar mean magnetic field Wavelet analysis of the Sun’s mean photospheric magnetic field: prominent periods are the rotation period and its 2 nd harmonic, and the 1.3/1.4-yr period

Jets in the tachocline as diagnostics of MHD processes there Christensen- Dalsgaard et al. 2004

The inferred jet has a steady amplitude and near-stationary location

Ring-Diagram Analysis Analyze acoustic wave fields over mosaic of tracked localized regions (each 15° square) Measure anisotropic frequency splittings of local f and p modes in power spectra Invert splittings to deduce flows with depth INVERSION KERNELS KERNELS

Solar Subsurface Weather 7 Mm 16 Mm Courtesy J. Toomre

Varying Pattern of Meridional Circulation Cells NORTH:DOUBLECELL NORTHSOUTH 2001 SOUTH:SINGLECELL POLEWARD FLOW NEAR SURFACE REVERSEDFLOW AT DEPTH MULTI-ROTATIONAVERAGES Courtesy J. Toomre

Flows near and beneath active region Apr 2001 Courtesy J. Toomre

Frequency Shifts of Acoustic Modes Mode frequencies are shifted by global magnetic flux. Shift depends on both frequency and degree. Diagrams from Howe, Komm & Hill 1999; Libbrecht and Woodard 1991.

Antia et al k=2k=4k=6 k=8 k=10k= Date Date (nHz) Solar results

k=2 k=4k=6 k=8 k=10k=12 4 (nHz) B k flux (G) where Antia et al. 2001

The Search for Subsurface Structural Changes Pattern of frequency shifts consistent with near- surface effects; surface layers poorly resolved, modeled.

Search for Structural Change Antia et al 2001 – sound speed change is all in ‘surface term’, but near- surface layers not resolved.

Time-distance helioseismology Measures travel times of acoustic or surface gravity waves propagating between different surface points through the interior. The travel times depend on conditions, flow velocity and sound speed along the ray path: Analysis proceeds by calculating cross-correlation of signal at different points on the surface:

Sound-speed map and magnetogram of AR on October 25, 2003, 4:00 UT (depth of the lower panel: 45 Mm) AR Courtesy A. Kosovichev

Sound-speed map and magnetogram of AR on October 26, 2003, 12:00 UT AR is emerging AR AR Courtesy A. Kosovichev

Emergence of AR 10488, October 26, 2003, 20:00 UT AR Courtesy A. Kosovichev

Emergence of AR 10488, October 27, 2003, 4:00 UT AR Courtesy A. Kosovichev

Growth and formation of sunspots of AR 10488, October 29, 2003, 4:00 UT AR Courtesy A. Kosovichev

Growth and formation of sunspots of AR 10488, October 31, 2003, 12:00 UT AR Courtesy A. Kosovichev

Cut in East-West direction through both magnetic polarities, showing a loop-like structure beneath AR 10488, October 30, 2003, 20:00 UT AR Courtesy A. Kosovichev

Conclusions Helioseismology has measured the differential rotation through much of the solar interior. The solar interior Is observed to be highly dynamic, at least to the bottom of the convection zone The whole convection zone is involved in the “torsional oscillation” over the solar cycle Zonal flows at the base of the convection zone – and possibly deeper – exhibited a transient 1.3-yr quasi-periodic oscillation in the rising phase of the solar cycle Observations can now make contact with theoretical predictions of dynamical variations in the solar interior

Conclusions Measured flows associated with active regions should likewise confront modelling of AR formation and evolution The variation of the even component of the frequencies is well correlated with surface magnetic field variation There is some latitudinal variation of sound speed, but any detected global temporal variation appears to be confined to the surface layers Local variations of “sound speed” under active regions are present under active regions and must give clues to AR formation and evolution