1. Solar Modeling Sabatino Sofia Department of Astronomy Yale University New Haven, CT, USA

2. Solar variability group at Yale Astronomy Department Sabatino SofiaLinghuai Li Paolo VenturaFederico Spada

3. Most stars have an intrinsic variable brightness at some level They vary as a consequence of two mechanisms: 1)surface features (usually big starspots) rotating into and out of view on the stellar disk MAGNETIC STARS, LOW-MASS STARS 2)because of structural readjustments that affect the subphotospheric rate of energy output (luminosity) CEPHEIDS MIRA VARIABLES ETC.

4. THE SUN CAN VARY IN BOTH WAYS: ROTATION OF SURFACE FEATURES: e.g. ACTIVE REGIONS, NETWORK, etc. STRUCTURAL (INTERNAL)- ALL GLOBAL PARAMETERS CHANGE e.g. EVOLUTION WHICH TYPE OF VARIATION DOMINATES DEPENDS ON THE TIMESCALES INVOLVED.

5. SHORT TIMESCALE VARIABILITY

6. FOR VERY LONG TIMESCALES, VARIABILITY MUST BE DOMINATED BY INTERNAL CHANGES ---THEORY OF VARIATIONS ---ENERGY REQUIRED QUESTION: WHERE DO BOTH MECHANISMS CROSS OVER?

7. IT IS TO BE NOTED THAT MOST OF THE CONTROVERSY ABOUT THE ROLE OF SOLAR VARIABILITY ON CLIMATE CHANGE, AND THE RANGE OF THE SOLAR INPUT TO CLIMATE GIVEN IN THE IPCC REPORT ASSUMES THAT THE SOURCE OF ALL SOLAR VARIABILITY IS CONFINED TO SURFACE PHENOMENA WHY?

8. 1.A theoretical paper that indicated that the Sun could not change its structure on a timescale shorter than the thermal timescale at the base of the convective region, 10 5 years. 2. The slow secular changes of the TSI that would be most effective for climate change are difficult to detect with current instrumentation (radiometers).

9. WHY IS ITEM 1 NOT CORRECT?  NUMERICAL MODELS  OSCILLATION VARIATIONS WITH ACTIVITY CYCLE  MIRA-TYPE AND OTHER VARIABLE STARS  VARIATIONS OF THE PHOTOSPHERIC TEMPERATURE  DIFFERENCE OF TSI VALUE AT DIFFERENT ACTIVITY MINIMA

11. PROPERTIES OF STRUCTURAL CHANGES BECAUSE THEY INVOLVE THE ENTIRE CONVECTION ZONE (LOTS OF ENERGY), THEY CAN HAVE LONG TIMESCALE COMPONENTS FOR CLIMATE CHANGE LONG TIMESCALE COMPONENTS ARE DIFFICULT TO DIFFERENTIATE FROM INSTRUMENT DEGRADATION IN ENERGY FLUX-TYPE MEASUREMENTS SO, ALTHOUGH STRUCTURAL CHANGES MAY DOMINATE FOR CLIMATE, THEY ARE VERY DIFFICULT TO DETECT

12. All dynamo models involve seed magnetic fields, which grow because of differential rotation and/or turbulence. A variable magnetic field contributes to pressure, internal energy, and modifies energy transport both by convection and radiation, and internal dynamics (thus turbulence) IT AFFECTS THE STRUCTURE OF THE SOLAR INTERIOR PHYSICAL ORIGIN OF THE STRUCTURAL VARIATIONS: DYNAMO MAGNETIC FIELDS

13. WHEN THE STRUCTURE IS MODIFIED, ALL GLOBAL STELLAR PROPERTIES L R T eff Change. Also, the oscillations undergo changes THOSE CHANGES ARE INEVITABLE To predict the properties of those changes, we need to build models

14. CONVENTIONAL STELLAR MODELS ARE INADEQUATE 1.Sensitivity 2.Timescales 3.Inadequacy of standard mixing length theory of convection 4.Do not include magnetic fields, turbulence, rotation, etc.

15. EARLY MODELS 1D Include: Variable Magnetic Fields Turbulence Arbitrary Magnetic Field/Turbulence Interaction

16. NEW MODELS 2D Include: Rotation Realistic Variable Magnetic Fields Turbulence Modeled Magnetic field/turbulence Interaction

17. Results of 1D Models A dynamo type magnetic field does indeed affect the solar structure and dynamics, and as a consequence, all of the global parameters (R, Teff, L). The specific properties of the effects (the relationships between the variations of all the parameter pairs) depend on the currently unknown details of the magnetic field (magnitude, depth, shape, etc.), and of the interaction between the magnetic field and turbulence.

18. FOR EXAMPLE: A DEEPER MAGNETIC FIELD NEEDS TO BE LARGER TOPRODUCE A GIVEN LUMINOSITY CHANGE THE DEEPER FIELD CAUSES A LARGER RADIUS CHANGE A DEEPER FIELD HAS SMALLER EFEFCTS ON HIGH-l OSCILLATIONS, ETC. Hence, To verify the model of the solar variations it is necessary to observe, simultaneously, all of the global parameters, plus the oscillations.

19. PRIOR TO PICARD, THE REQUIRED DATA DID NOT EXIST

20. PICARD WILL MEASURE: - solar diameter, limb shape, asphericity in the photosphere -total solar irradiance -oscillation modes -Temperature variations in the photosphere AT A PHASE INTERVAL OF THE ACTIVITY CYCLE THAT MAXIMIZES THE VARIATIONS: ALL THE REQUIRED OBSERVATIONS

21. TESTS WITH 1D MODELS ASSUMPTIONS

22. We assume that the average TSI variation observed over the last 20 years is only due to structural changes

23. Radius Variations Radius is a powerful diagnostic of internal processes, BUT PAST MEASUREMENTS WERE VERY CONTROVERSIAL.

24. Ground-based measurements give results that are Incompatible with each other Possible exception: duration of total solar eclipses 2 Space-based results MDI/SOHO SDS

29. In our simulations we only assumed that the radius variations are in antiphase with the activity cycle, but of unknown amplitude.

30. Observation: P-mode frequency

31. Observations: CZ base

32. BECAUSE IN 1D A MAGNETIC FIELD CAN ONLY PRODUCE A POSITIVE PRESSURE, IT ALONE CANNOT LEAD TO RADIUS CHANGES IN ANTIPHASE WITH THE ACTIVITY CYCLE THIS LED US TO INCLUDE THE EFFECT OF A MAGNETICALLY MODULATED TURBULENCE IN THE SIMULATIONS IN THE ABSENCE OF A THEORY ON THE MODULATION OF TURBULENCE BY A MAGNETIC FIELD, WE POSTULATED A SIMPLE ARBITRARY RELATIONSHIP LINKING THEM.

34. Observational constraints

35. Magnetically –modulated turbulent models

36. HOWEVER THE 1D TREATMENT IMPOSES UNREALISTIC RESTRICTIONS TO THE CONFIGURATION OF THE DYNAMO FIELD AND TO THE INTERNAL SOLAR DYNAMICS. THE REAL SUN IS MULTIDIMENSIONAL. IN ORDER TO PROVIDE A ROBUST INTERPRETATION OF THE DATA, WE NEED AT LEAST A 2D TREATMENT.

37. We have been developing a 2D code over nearly a decade, and testing it over the last 2 years: Oblateness Limb darkening (limited by the Eddington approximation) Temperature as a function of latitude Radius changes 2D oscillation diagnostics, etc. A poloidal field causes a change of R in phase with the field strength, whereas a toroidal field causes a radius change in antiphase with the field strength.

38. I will not write down all the equations since they are: Messy, complicated and unenlightening Already published INSTEAD, I WILL SHOW SOME RESULTS

44. We use the global parameters to determine unique models vs. time, and then test the models with helioseismology. However, our helioseismic technique is direct: We derive properties from our models-These will be compared with observations. If they do not agree, our models are not good. Conventional helioseismology uses inverse approach Our approach is interesting because: Source of errors are different It can address evolution

45. The PICARD data will be able to separate internal variations (determined from photospheric temperature and diameter) from surface magnetic effects. The limb profile will test the model atmosphere, and separate the effects of possible profile variations (both in latitude and time) from diameter changes. In combination with SDO measurements, maybe changes of oscillation spectrum as a function of latitude and phase of the cycle.

46. POTENTIAL OF RADIUS MEASUREMENTS 1.ANGULAR CALIBRATION DOES NOT DEGRADE 2. WE CANNOT MEASURE PAST SOLAR IRRADIANCE, BUT WE CAN INFER PAST RADIUS CHANGES 3. DETERMINE FROM PICARD DATA W= dlnR/dlnL 4. DETERMINE PAST VALUES FOR L (THUS TSI) TO BE USED IN CLIMATE STUDIES.

47. IT IS OBVIOUS THAT WE ARE AT THE THRESHOLD OF SOLVING THE PROBLEM OF THE ORIGIN OF SOLAR VARIABILITY ON TIMESCALES OF DECADES TO MILLENNIA. OBSERVATIONALLY, THE MOST CRITICAL DATA WILL BE PROVIDED BY PICARD, ALTHOUGH SOHO, MDI, SORCE AND OTHER SPACE MISSIONS WHICH ARE STILL OPERATIONAL WILL ASSIST THEORETICALLY, WE NEED TO FINISH THE FOLLOWING TASKS: 1.INCLUDE SOPHISTICATED ATMOSPHERE 2.DETERMINE VALUE OF W

48. STRATEGY COMPLETE DEVELOPMENT OF INTERNAL MODELS DEVELOP OPTIMAL ANALYSIS TOOLS FOR PICARD DATA, WHICH USED IN CONTEXT OF REFINED INTERNAL MODEL, UNCOVERS THE PHYSICAL PROPERTIES OF THE ENGINE OF SOLAR VARIABILITY. DETERMINE FROM OBSERVATIONS, AND CONFIRM WITH THEORY, THE VALUE OF W = dlnR/dlnL FOR ALL TIMESCALES. CARRY OUT EXHAUSTIVE SEARCH FOR OLD ECLIPSE DATA. USING W, DETERMINE L FOR AS MANY ECLIPSES, AS WELL DISTRIBUTED IN TIME, AS POSSIBLE

49. INTERACT WITH CLIMATE SCIENTISTS TO HAVE THEM INCLUDE SOLAR VARIATIONS IN THE MODELS THAT ARE USED TO DETERMINE THE CLIMATE SENSITIVITY TO GLOBAL WARMING, NAMELY: WHAT IS THE CHANGE IN TEMPERATURE TO BE EXPECTED ONLY FROM A DOUBLING OF THE CONCENTRATION OF CO 2 IN THE ATMOSPHERE OF THE EARTH?

50. If there is a significant solar component to climate change, it will be due to INTERNAL VARIABILITY This variability can be physically understood (maybe PREDICTABLE), and determined for at least after 1715 The required observational data will be obtained by several satellites, but primarily PICARD We are near completion of the development of the theoretical infrastructure required to optimally interpret the PICARD results, and to extract the climate implications SUMMARY