# What Dynamic Changes in the Sun Drive the

• Slides: 25

What Dynamic Changes in the Sun Drive the Evolution of Oscillation Frequencies through the Activity Cycle? Philip R. Goode Big Bear Solar Observatory New Jersey Institute of Technology Big Bear Solar Observatory 11 March 2002

The Sun’s Irradiance Variations are Small, but Hard to Explain Big Bear Solar Observatory 11 March 2002

The Solar Cycle Changes in the Sun § Naively, luminosity varies like irradiance and the Sun is a blackbody. Then, allowed size of the changes in the Sun’s output -In truth, we have cast the Sun’s changing magnetic field, thermal structure and turbulent velocity as temperature changes. Further, is there a role for a changing solar radius? § Principal Collaborator: -Wojtek Dziembowski, University of Warsaw Big Bear Solar Observatory 11 March 2002

Variations in the Solar Radius § Brown & Christensen-Dalsgaard (1998): 1981 -1987 annual average Rs each year the same within measurement errors (± 37 km) --comparable to those of Wittman (1997) for same time interval --much smaller than annual changes reported by Ulrich & Bertello (1995) -- sun grows with growing activity -- and Laclare et al. (1996) – sun shrinks with growing activity -- for the same interval ( 200 Km from maximum to minimum) Big Bear Solar Observatory 11 March 2002

Variations in the Solar Radius from Space § Emilio et al. (2000) MDI limb observations: annual radius increase with increasing activity of 5. 9± 0. 7 Km/year Big Bear Solar Observatory 11 March 2002

Normal Modes of the Sun ( ) Big Bear Solar Observatory 11 March 2002

Helioseismic Radius Using MDI f-modes § l 2 l(l+1)GMs/Rl 3 : Asymptotically surface waves, but f-modes see different effective gravities – depending on l § l / l=-3/2 Rs/Rs : means model value minus true value § From this, Schou et al. (1997) determined Rs= 695. 68± 0. 03 Mm Big Bear Solar Observatory 11 March 2002

The Surface Radius of the Sun § Auwers (1891): Rs=Ds/2=695. 99± 0. 04 Mm --standard value for 100 years § Schou et al. (1997): Rs= 695. 68± 0. 03 Mm --MDI f-modes § Brown & Christensen-Dalsgaard (1998): Rs=Ds/2=695. 508± 0. 026 Mm --HAO Solar Diameter Monitor Big Bear Solar Observatory 11 March 2002

Solar Cycle Variations in the f-mode Radius § Must look more carefully at this form of the equation because there are problems with using it to determine the considerably smaller changes the (fmode) radius from year to year: § Even though Rl Rs , cannot expect Rl Rs. The problem is we must contemplate changes beyond a simple radius change because near surface effects also contribute to frequency changes — turbulence (Brown 1984) and/or magnetic fields (Evans & Roberts 1990). Big Bear Solar Observatory 11 March 2002

Rate of Shrinking from f-modes § To account for near-surface contribution to the frequency change we add a second term — Il 0, as l , l weak function of l Big Bear Solar Observatory 11 March 2002

Evolution of f-mode Radius § With : d. Rf/dt = -1. 51± 0. 31 km/y § Without : d. Rf/dt = -1. 82± 0. 64 km/y § Results imply at a depth of 610 Mm, the sun shrank by some 5 km during the rising phase of this activity cycle § d f/dt= 0. 180± 0. 051 Hz/y, noisy with some cross-talk § As small as it is, a shrinking sun is not easy to explain Big Bear Solar Observatory 11 March 2002

Near-Surface Terms from pmodes § Note that rise of cycle starts early 1997, so fits for d. R/dt start then § Note 0 systematically rises, but behavior is much more muted than anisotropic terms — this is a clue to the shrinking of outermost layers of the sun Big Bear Solar Observatory 11 March 2002

f-mode Radius Changes -Entropy and Random R. M. S. Field, Goldreich et al. (1991) Big Bear Solar Observatory 11 March 2002

Big Bear Solar Observatory 11 March 2002

How Big Can the Shrinking Be? Big Bear Solar Observatory 11 March 2002

More Acceptable: Variation in the R. M. S. Magnetic Field § For a purely radial random field ( =-1), an increasing field implies contraction. § For an isotropic random field ( =1/3), an increasing field implies expansion! A nontrivial constraint! Big Bear Solar Observatory 11 March 2002

What about the Radius? § Need to have accurate information about the outer ~4 Mm to combine with the shrinking beneath § This outermost region is where one expects the largest activity induced changes — because of rapid decline of gas pressure — thermal structure most susceptible to field induced changes in convective energy transport efficiency Big Bear Solar Observatory 11 March 2002

p-mode ’s for the Last 4 Mm § p-mode spectrum is >10 x richer than that for fmodes — reminder can’t use p-modes for radius ( R-1. 5 valid only if changes homologous throughout whole sun) § For f-modes: d f/dt= 0. 180± 0. 051 Hz/y § For p-modes: d p, 0/dt= 0. 149± 0. 008 Hz/y — A much more precise value to describe the last 4 Mm Big Bear Solar Observatory 11 March 2002

Consider Radial R. M. S. Random Field Growth ( =-1), then T/T as Source § Solid lines and dotted lines fit , other forms possible § <Bph> < 100 G § <B> < 300 G at 4 Mm § T/T too large at surface § cannot exclude T/T at 10 -3 level in subphotospheric layers. Big Bear Solar Observatory 11 March 2002

Isotropic Random R. M. S. Field in Outermost Layers? § =1/3 is precluded in f-mode layer because that layer shrinks how can it be present above when field above wants to be radial? Radial random field is the most economical to account for frequency changes. § For =-1, the splitting kernels ( k>0) are much larger than those for the isotropic part. This is consistent with the anisotropic ’s (like 3) being much larger than for isotropic ’s ( 0). Big Bear Solar Observatory 11 March 2002

Is the Sun Hotter or Cooler at Activity Maximum? § Required changes in turbulent flows are probably too large to account for frequency changes § Limiting problem to magnetic field and temperature alone, for aspherical part can use condition of mechanical equilibrium to pose problem for field or temperature change § Spherical part goes through thermal equilibrium condition – much harder to treat Big Bear Solar Observatory 11 March 2002

Small-scale Aspherical Random R. M. S. Field Each component, k, gives rise to P 2 k distortion of sun’s shape and for k>0 temperature pert. Big Bear Solar Observatory 11 March 2002

For k>0, Eliminate T/T, and Big Bear Solar Observatory 11 March 2002

Is the Sun Hotter at Activity Minimum? Big Bear Solar Observatory 11 March 2002

What Next ? § Treat condition of thermal equilibrium to constrain surface averaged temperature change because of the sharper minimum in c 2 for k=0 § More thorough analysis of MDI and GONG data – more years, etc. § Use BBSO Ca II K and Disk Photometer data to constrain the field to link irradiance and luminosity § Three color photometry from Disk Photometer § Use formalism to probe for buried magnetic field Big Bear Solar Observatory 11 March 2002