Solar Modeling

Sabatino SofiaDepartment of Astronomy

Yale UniversityNew Haven, CT, USA

Solar variability group at Yale Astronomy Department

Sabatino Sofia Linghuai Li

Paolo Ventura Federico Spada

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.

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.

SHORT TIMESCALE VARIABILITY

FOR VERY LONG TIMESCALES,

VARIABILITY MUST BE DOMINATED BY INTERNAL CHANGES

---THEORY OF VARIATIONS

---ENERGY REQUIRED

QUESTION:

WHERE DO BOTH MECHANISMS CROSS OVER?

IT IS TO BE NOTED THAT MOST OF THE CONTROVERSYABOUT THE ROLE OF SOLAR VARIABILITY ON CLIMATECHANGE,

AND

THE RANGE OF THE SOLAR INPUT TO CLIMATE GIVEN IN THE IPCC REPORT ASSUMES THAT

THE SOURCE OF ALL SOLAR VARIABILITY IS CONFINEDTO SURFACE PHENOMENA

WHY?

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, 105 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).

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

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 TODIFFERENTIATE FROM INSTRUMENT DEGRADATION

IN ENERGY FLUX-TYPE MEASUREMENTS

SO, ALTHOUGH STRUCTURAL CHANGES MAY DOMINATE FOR CLIMATE, THEY ARE VERY

DIFFICULT TO DETECT

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

WHEN THE STRUCTURE IS MODIFIED, ALL GLOBAL STELLAR PROPERTIES

LR

Teff

Change.

Also, the oscillations undergo changes

THOSE CHANGES ARE INEVITABLE

To predict the properties of those changes, we need to build models

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.

EARLY MODELS

1D

Include:

Variable Magnetic Fields

Turbulence

Arbitrary Magnetic Field/Turbulence Interaction

NEW MODELS

2D

Include:

Rotation

Realistic Variable Magnetic Fields

Turbulence

Modeled Magnetic field/turbulence Interaction

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.

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.

PRIOR TO PICARD,

THE REQUIRED DATA DID NOT EXIST

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 THATMAXIMIZES THE VARIATIONS:

ALL THE REQUIRED OBSERVATIONS

TESTS WITH 1D MODELS

ASSUMPTIONS

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

Radius Variations

Radius is a powerful diagnostic of internal processes,

BUT PAST MEASUREMENTS WERE VERY CONTROVERSIAL.

Ground-based measurements give results that are Incompatible with each other

Possible exception: duration of total solar eclipses

2 Space-based results

MDI/SOHOSDS

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

Observation: P-mode frequency

Observations: CZ base

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 RELATIONSHIPLINKING THEM.

Observational constraints

Magnetically –modulated turbulent models

HOWEVERHOWEVER

THE 1D TREATMENT IMPOSES UNREALISTIC RESTRICTIONS TO THE CONFIGURATION OF THEDYNAMO 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.

We have been developing a 2D code over nearly a decade, and testing it over the last 2 years:

OblatenessLimb darkening (limited by the Eddington approximation)Temperature as a function of latitudeRadius changes2D 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 inantiphase with the field strength.

I will not write down all the equations since they are:

Messy, complicated and unenlightening

Already published

INSTEAD, I WILL SHOW SOME RESULTS

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 differentIt can address evolution

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.

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.

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, SORCEAND OTHER SPACE MISSIONS WHICH ARE STILL OPERATIONAL WILL ASSIST

THEORETICALLY, WE NEED TO FINISH THE FOLLOWING TASKS:

1. INCLUDE SOPHISTICATED ATMOSPHERE2. DETERMINE VALUE OF W

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

INTERACT WITH CLIMATE SCIENTISTS TO HAVETHEM 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 CO2 IN THE ATMOSPHERE OF THE EARTH?

If there is a significant solar component to climate change, it will bedue 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