1. Measuring the shape of the Sun H.S. Hudson, M.D. Fivian & H.J. Zahid Space Sciences Lab, UC Berkeley

2. HAO 9/26/06 Motivation Helioseismology lets us study the solar interior Other constraints on interior structure and dynamics exist, e.g. the irradiance and the visible shape We’re fortuitously re-doing the Dicke oblateness experiment from space with RHESSI

3. HAO 9/26/06 Historical background The properties L O, M O, and   (and X, Y, and Z) more or less characterize a star, but none of them are really constant The observed variations of L O, the “solar constant,” include ~ half a dozen known components The solar shape and the total irradiance are strongly linked: d(ln L O )/d(ln R O ) = w

4. HAO 9/26/06 Historical background The properties L O, M O, and   (and X, Y, and Z) more or less characterize a star, but none of them are really constant The observed variations of L O, the “solar constant,” include ~ half a dozen known terms The solar shape and the total irradiance are strongly linked: d(ln L O )/d(ln R O ) = w … but we are not sure about the magnitude, or sign, of w!

5. HAO 9/26/06 Total solar irradiance variations - highlights

6. HAO 9/26/06 ARAA 26, 473 (1988) Frohlich, 2005 * *

7. HAO 9/26/06 ARAA 26, 473 (1988) Frohlich, 2005 Flares Minutes 200 ppm at most Woods et al. 2004

8. HAO 9/26/06 Two recent-suggested possible additional components R.C. Willson & A. Mordvinov, “Secular total irradiance trend during solar cycles 21-23,” GRL (2003) G. Withbroe, “Quiet Sun contributions to the total solar irradiance,” Solar Phys. 235, 369 (2006)

9. HAO 9/26/06 Two recent-suggested possible additional components R.C. Willson & A. Mordvinov, “Secular total irradiance trend during solar cycles 21-23,” GRL 2003 (controversial) G. Withbroe, “Quiet Sun contributions to the total solar irradiance,” Solar Phys. 235, 369 (2006)

10. HAO 9/26/06 Two recent-suggested possible additional components R.C. Willson & A. Mordvinov, “Secular total irradiance trend during solar cycles 21-23,” GRL 2003 (controversial) G. Withbroe, “Quiet Sun contributions to the total solar irradiance,” Solar Phys. 235, 369 (2006) (identifiable with the “active network”?)

11. RHESSI measures the shape of the Sun

12. HAO 9/26/06 Reuven Ramaty High-Energy Solar Spectroscopic Imager

13. HAO 9/26/06

15. Operating principle of the RHESSI Solar Aspect Sensor (SAS) Sensor: 1024-pixel linear CCD, 1.73 arc sec/pixel Spectral band: 670 nm x 12 nm FWHM Readout: limbs ~100 sec -1, chords ~1 min -1 We get about 10 9 points per year @ <20 mas RMS

16. HAO 9/26/06 FWHM ≈ 4.5 arcsec ≈ 2.6 pixels

17. HAO 9/26/06 Data

18. HAO 9/26/06 The p-modes explain some of the “noise” August 2004: 57-orbit incoherent sum spectrum

19. HAO 9/26/06 August 2004: 57-orbit incoherent sum spectrum

20. HAO 9/26/06 Potentially observable limb features p-modes ! g-modes r-modes ? Granulation Other convective motions Sunspots ! Faculae ! Active network Flares Prominences Coronal holes Oblateness ! Higher-order shape terms Gravitational moments J2, J4… Global temperature variation Limb-darkening function Planetary tides

21. HAO 9/26/06 Very early oblateness measurements Auwers, 1891

22. HAO 9/26/06 Very early oblateness measurements Auwers, 1891 P - A > 0 => prolate!

23. HAO 9/26/06 SOHO/MDI Emilio et al., 2000

24. HAO 9/26/06 Solar Disk Sextant (1992, 1994, 1995, 1996 flights) Egidi et al., Solar Phys. 236, 407 (2006)

25. HAO 9/26/06 SOHO/MDI results: Emilio et al. 2007

26. HAO 9/26/06 RHESSI synoptic-chart representation

27. HAO 9/26/06 RHESSI Fourier components

28. HAO 9/26/06 SOHO/MDI results: Emilio et al. 2007

29. HAO 9/26/06 Oblateness time series

30. HAO 9/26/06 RHESSI time series

31. HAO 9/26/06 Oblateness results* SDS3.96 +- 0.93 mas MDI-19974.35 +- 1.40 mas MDI-20019.45 +- 0.95 mas RHESSI-20046.86 +- 0.22 mas *Amplitude of axisymmetric quadrupole term, ~half of equator-pole radius difference Dicke (1970) solid-body reference 4.05 mas Need estimates based on seismic results

32. HAO 9/26/06 Next step: masking out magnetic activity

33. HAO 9/26/06 SOHO EUV limb photometry

34. HAO 9/26/06 SOHO EUV and MDI comparisons

35. HAO 9/26/06 Simple masking

36. HAO 9/26/06 MDI limb photometry (Sheeley & Warren 2007)

37. HAO 9/26/06 MDI limb photometry (Sheeley & Warren 2007)

38. HAO 9/26/06

39. What about g-modes? Rogers & Glatzmaier 2005 Toner et al. 1999 RHESSI orbital period 96 min

40. HAO 9/26/06 Conclusions The RHESSI/SAS data provide (by far) the best measures of solar limb-shape variations, an independent window on the solar interior We can see oblateness and expect to measure higher-order shape terms Sunspots, faculae, and p-modes show clear signals We dare to think about g-modes, but the analysis will be very challenging