2. Solar Irradiance, Diameter, Shape, and Activity J.R. Kuhn, Institute for Astronomy, University of Hawaii Rock Bush Marcelo Emilio Isabelle Scholl Phil Scherrer GONG10, June 2010

3. What can we learn about the solar cycle from precise “global” measurements?

4. …since 2002 A solar cycle of MDI; HMI debuts More than a solar cycle of helioseismic measurements COROT, “night-time solar physics”

5. Global solar properties Luminosity and irradiance Luminosity, radius, temp Frequency, magnetic field, temperature ‘Even’ m-dependent frequency splittings

6. Is solar the irradiance change primarily luminosity change?

7. Frequencies and F10.7 Broomhall et al. 2009

8. Even coefficient frequency splittings Splitting coefficient temporal variability qualitatively describes surface magnetism changes

9. Its hard to change the solar surface temperature by changing solar luminosity

10. The solar limb is largely fixed by rapid opacity decline “few km” thick transition from opaque to transparent

11. Solar radius, past results from under the atmosphere….

12. A fluctuating solar radius is seen from the ground 76 yr fluctuation with 0.2 arcsec half-amplitude 11 yr fluctuation, smallest sun at peak in sunspot number with 0.1 arcsec half- amplitude 76 yrs

13. Solar astrometry: Is the Sun shrinking? 0.05 – 0.2 arcsec/century Gilliland, 1981

14. Limb astrometry from Space dr Angle of arrival fluctuations define dr dI Photometric gain uncertainty (flatfielding) defines dr In practice limb isn’t knife edge, spacecraft pointing jitter is about 0.01 pixel (and correlated!), long term stability limitations are due to optics thermal drifts [(MDI) 1px=2”] NB: Telescope diffraction limit has very little to do with astrometric accuracy

15. Limb Astrometry Systematic Errors Spacecraft pointing jitter (not limiting) – “coherent” –MDI, 0.02 arcsec Optical errors (limiting) –Temporal stability Thermal changes, dimensional stability, index changes –Spatial changes Field focus variations –Two orders of magnitude larger than solar signals (MDI, 0.5arcsec) –“Roll” calibration essential MDI approach –Measure and calibrate all aspects of instrument –PROVEN: Shape measurements essentially achieved photometric precision (i.e. oblateness/hexadecapole uncertainty 0.5 mas in 12 images)

16. HMI Solar Limb Astrometry What Limb Astrometry from HMI? –The solar radius –The solar radius variations with time (and oscillations) –The solar radius variations with central angle (shape, and oscillations) Why Do This With HMI? –Can’t be done on the ground with HMI accuracy (in some cases by two orders of magnitude) –HMI will surpass MDI astrometric accuracy by at least one order of magnitude –These are difficult measurements, no other space experiment addresses the same technical issues and no other space experiment reproduces the HMI astrometric approach What are the pressing questions? –Does the solar radius change (at all) with solar cycle? Knowledge of radius changes and irradiance or luminosity changes constrains the solar cycle mechanisms… a long debated problem –What is the Sun’s shape and is this consistent with solar system limits on its gravitational potential and the internal rotation rate? –Limb Oscillations (p-modes, g-modes, r-modes) dispersion relation information has yet to be carefully measured and interpreted

17. Satellite limb profiles

18. MDI Raw Radius Data

19. Calibrated MDI astrometry systematics Front window: 6C gradient  1.5km focal length  0.84” Primary lens: 10C temperature focal shift  -0.2” OSS expansion: 10C temperature change expansion  0.75”

20. Instrument changes

21. The solar radius change…

22. The solar radius over time km

23. No solar cycle radius changes! W = dr/r / dL/L < 2 x 10 -2 –Solar cycle luminosity is much smaller than irradiance change –Solar asphericity and 2D atmosphere structure dominates dR and dL –Solar cycle frequency changes not due primarily to changing geometry (s) Some models can predict small W, c.f. Mullan et al. 2007 (although H- opacity effects on ‘radius’ ignored? )

24. Asphericity and solar shape Are solar cycle irradiance variations due to redistribution of emergent solar luminosity? –Latitudinal variation, dR(μ)/R –MDI and HMI solar shape measurements Modern ground-based solar shape measurements

25. Limb astrometry, MDI 6-50 pixel annulus 480pix MDI: 1.96” pixel HMI: 0.5” pix

26. HMI raw shape and limb photometry See GONG10 Bush et al. poster equator pole

27. Rolling HMI separates solar shape from optical distortion cos2θ cos3θ cos4θ cos5θ Satellite roll angle 

28. MDI and HMI sun during some rolls has no magnetic activity MDI: March 1997HMI: April 9 2010HMI: April 16 2010 MDI: Nov. 2009 MDI roll in 2001 available, but active sun HMI roll available every 6 months

29. Oblateness from 1997-2010 MDI and HMI observations without magnetic corrections 1997 MDI 2009 MDI 2010a HMI 2010b HMI

30. MDI Solar minimum (1997) and maximum (2001) roll data

31. MDI limb shape analysis, magnetic contamination – e.g. 2001 Magnetic contamination increases limb brightness, decreases limb radius Note scale: 40mas radius decrease, 0.01 intensity increase

32. After accounting for magnetic activity, the limb shape is still variable Active latitutes: If we missed magnetic contributions, oblateness would be even larger!

33. Solar oblateness isn’t constant But note: Fivian et al. 2007 from RHESSI claim 2006 oblateness is surface value MDI and HMI Solar shape data

34. RHESSI photometry technique Fivian, Hudson, Lin, 2007

35. Oblateness coefficient variability from RHESSI

36. Helioseismic splittings also sample solar shape These are tiny shape variations, 2001 to 2010 Req- Rpole change is about 2.5km, smaller than our limits on the solar cycle mean radius variation Helioseismic “oblateness” (the “even” frequency splitting coefficients) are anticorrelated with geometric oblateness Acoustic (interior) atmosphere non-homologously expanding with respect to “surface” (Kosovichev, Lefebvre 1995, 1996) Oblateness changes are too small to account for even coefficient variations (and opposite in sign)

37. The solar brightness, ground, MDI, HMI Ground Oblateness Measurements HMI MDI

38. Solar cycle acoustic changes Primarily NOT geometric effects (in mean frequencies or splittings) The solar atmosphere change with cycle is not well described by any 1-dimensional model (either magnetic or thermal) Diffuse, unresolved, magnetic flux and surface brightness is needed

39. “Superficial” vs. “seeing the tachocline” Tough problem: “everything” is correlated with possibly complex causal connections (cf. Basu et al. 2009 “hints of tachocline” visible in helioseismic time dependence) Magnetic vs. “thermal”

40. Deep origins of magnetized plasma must carry excess entropy to surface Convection Zone Radiative Zone Tachocline region Photosphere Over a solar cycle magnetized fluid over 11yr increases entropy by 0.1% at base of SCZ Radiative flux through magnetized fluid sees lower opacity and increased entropy relative to non-magnetized fluid Solar cycle magnetic fields Magnetized fluid is “hotter” Thermal “antishadows” Temperature gradient enhanced stable stratification becomes unstable

41. Alternatively, vertical surface B fields decrease vertical “irradiance” The integrated disk brightness change due to bright faculae is 38% of the faint faculae NB: cf. Ken Topka facular contrast results “Bright” faculae are dark, at any wavelength near disk center Data from the Precision Photometric Solar Telescope Continuum contrast vs. vertical orientation and CaK contrast

42. Magnetic fields and irradiance

43. Fast and slow B vs. irradiance Fast variations: B increases “I”Slow variations: B decreases I

44. Frequency variations are not determined simply by solar activity (from Broomhall et al. 2009)

45. Global photometric timeseries analysis Solar and stellar observations converge  studies of resolved stellar magnetic atmospheres are happening: Night-time solar physics

46. Spots and faculae may produce only a tiny luminosity pertubation (flux redistribution) dI time Use solar rotation to describe angular variation in active region or spot “irradiance” … luminosity T/4

47. Full-disk observations show flux redistribution (data high-pass filtered with 60d moving-mean) Regardless of phase of the solar cycle (min-to-max) the irradiance autocorrelation shows clear evidence that active regions (faculaea nd sunspots) redistribute flux. Low temporal frequency signal shows evidence of additional luminosity signal

48. CoRoT Photometry – stay tuned

49. Conclusions Very precise global solar measurements are important for understanding the solar cycle Solar cycle helioseismic effects are primarily thermal or magnetic sound speed effects (not geometry) One-dimensional models don’t convincingly account for cycle variations  heterogenous, unresolved (mixed) magnetic field effects are required

51. Magnetized plasma from RZ is hotter P 3E5cm B P 6MG, l P 3E5cm At the top of the radiative zone... Tachocline shear layer unresolved helioseismically, l O 0.018R (Schatzman et al. 2000) Tachocline region l

54. A useful solar cycle model must connect and explain all of these observations, none exists yet Surface brightness changes Helioseismic changes Irradiance changes

55. What was the question? Boundaries are great “Superficialist” problems Listening to the data Clocks

56. Driving the Solar Cycle

57. Irradiance changes This plot shows the residual from the 150d moving means. +0.1W/m^2/G -0.2W/m^2/G The slow variations using 30d averages are plotted here

58. Helioseismic asphericity (Vorontsov, 2002) (Antia et al. 2001) 26 nHz/G 140 nHz/K (1989)

59. Irradiance/luminosity change Suppose 4 DT/T = DI/I, so 0.1W/m^2/G implies 0.1 K/G solar cycle change If magnetic field causes thermal stratification change and frequency shifts then 26/140 K/G = 0.18 K/G

60. The tachocline: Where luminosity perturbations come from? Convection Zone Radiative Zone Tachocline region Photosphere Over a solar cycle magnetized fluid over 11yr increases entropy by 0.1% at base of SCZ Radiative flux through magnetized fluid sees lower opacity and increased entropy relative to non-magnetized fluid Solar cycle magnetic fields Magnetized fluid is “hotter” Thermal “antishadows” Temperature gradient enhanced stable stratification becomes unstable

61. Magnetized plasma from RZ is hotter P 3E5cm B P 6MG, l P 3E5cm At the top of the radiative zone... Tachocline shear layer unresolved helioseismically, l O 0.018R (Schatzman et al. 2000) Tachocline region l

62. More numbers...

63. During the solar cycle a thin layer of magnetized plasma at the top of the radiative zone is eroded away from above by convective penetration, brought on by this radiative instability. This “relaxation oscillator” could be characterized by the condition on B that leads to instability and the higher enthalpy per magnetic energy density. Observable: Flux which originates from the RZ must have a higher enthalpy/magnetic energy density than magnetized fluid generated by CZ or photospheric mechanisms.

64. Superficial two component (faculae+spots) irradiance models Models based on resolved CaK images or B flux have been used to “explain” irradiance Observed time-variable irradiance Observed time and latitudinal facular/spot dist. (determined by proxy) Facular/spot irradiance contrast function.m is cosine central angle Models which use a statistical fit to determine the coefficients b and k can account for 70-90% of the irradiance variability (c.f. Solanki, Lean and collaborators)

65. Superficial, two component faculae + spot models are empirical and imcomplete The integrated disk brightness change due to bright faculae is 38% of the faint faculae NB: Ken Topka substantially made this point 8 years ago! “Bright” faculae are dark, at any wavelength near disk center Data from the Precision Photometric Solar Telescope

66. How does the convection zone transport heat? mixing-length diffusion conflicts

67. MLT convection fails to estimate SCZ conductivity Non-mixing length theory (realistic) solar convection has highly correlated vertical flows. The effective conductivity of the solar convection zone is far from mixing length theory approximations (images from Georgobiani Stein, and Kuhn) small perturbations are diffusive but anisotropic and with conductivity much smaller than mixing length predictions

68. Transport properties of the perturbed convection zone aren’t analogous to a “high conductivity silver slab.” Correlated flows over many density scale heights make the CZ anisotropic and not as well mixed as mixing length models predict.

69. Superficial models miss time dependence of irradiance componets Spot and facular signals peak about 1 year before luminosity signal F = 0.08 E 0.005 B -0.09 E 0.01 dB/dt sunspot peak Total irradiance

70. Spots and faculae may produce only a tiny luminosity pertubation (flux redistribution) dI time We use solar rotation to describe angular variation in active region or spot “irradiance” … luminosity T/4 If irradianceis due to flux redistribution, its autocorelation must yield a negative “dip” at T/4=7d due to opposite sign flux enhancements between normal and near-tangent viewing angles

71. Full-disk observations show flux redistribution (data high-pass filtered with 60d moving-mean) Regardless of phase of the solar cycle (min-to-max) the irradiance autocorrelation shows clear evidence that active regions (faculae and sunspots) redistribute flux. Low temporal frequency signal shows evidence of additional luminosity signal. NB Frolich finds more complex behavior in VIRGO data...

72. Superficial models miss irradiance and luminosity distinction Immediate effect of B flux appearing at low latitudes is to decrease irradiance (flux directed away from normal direction) -- this is dB/dt term of regression for I(t) Long term effect is from higher entropy magnetized plasma to increase solar luminosity in proportion to B flux

73. Superficial models miss diffuse irradiance component

74. Solar cycle changes Photometry from Mt. Wilson, previous cycle implied this limb temperature Most of a solar cycle was obtained from Mt. Wilson oblateness expt. MDI Roll data photometry imply this limb temperature distribution

75. Phase properties

76. Delayed Oscillator RZ CZ BfBf F(t) G(t) Flux storage and “heating” in RZ, G[ a,e] Flux diffusion and winding in CZ, F[ b,d]

77. Delayed Oscillator Output

78. Solar Cycle Effects Delayed oscillator - correlated driving amplitude and phase delay in RZ. Higher amplitudes imply shorter periods (8%)...

79. Solar cycle phase regulation Solar cycle coherence and amplitude variability hint at a stable storage or steady flux transport process, i.e. Babcock- Leighton stochastic flux transport, not intrinsically non-linearity mechanisms

80. To do... find the complete luminosity budget of surface magnetic fields find B (and dB/dt) at tachocline determine dQ/dB from first principles build a relaxation delayed oscillator model for the full CZ

82. Convection Zone Radiative Zone Tachocline region Photosphere Over a solar cycle magnetized fluid over 11yr increases entropy by 0.1% at base of SCZ Radiative flux through magnetized fluid sees lower opacity and increased entropy relative to non-magnetized fluid Solar cycle magnetic fields Magnetized fluid is “hotter” Thermal “antishadows” Temperature gradient enhanced stable stratification becomes unstable