The Standard Solar Modeland Its Evolution

Marc PinsonneaultOhio State University

Collaborators: Larry CapuderScott Gaudi

Summary

The Sun is predicted to become brighter as it ages for fundamental stellar structure reasonsThis luminosity evolution is extremely insensitive to assumptions about the input physics, except mass loss……and the rotation of the Sun, and by extension mass loss, was very similar to the current values for the last 4 Gyr

Standard Solar Model

Initial Conditions: Mass, Composition, Evolutionary StateEquations of Stellar Structure– Conservation Laws

The Solar Calibration– Reproduce current solar properties, adjust

model uncertainties

In the Beginning…

There are interesting problems around the formation of the Sun– Rotation:

Hydrodynamic assembly phaseProtostar-disk interaction

– Mixing and Light Element Depletion– However, subsequent solar evolution is

insensitive to the initial conditions (Vogt-Russell theorem)

Standard Model Assumptions and Ingredients

Equation of State: OPAL; close to ideal gasEnergy Generation: Adelberger et al. 2010; primarily ppOpacities: OP or OPAL; radiative coreConvection Theory: MLT; convective envelopeGravitational settling includedRotation, rotational mixing, mass loss not included

Standard Luminosity Evolution

Early transient phase (~30 Myr) when the Sun contracts and heats upSteady core H burning phase where the Sun steadily brightens

Why does the Sun brighten as it ages?

Pressure gradient balances gravitySun remains hot through H fusion4 1H => 1 4He has a necessary implication:– 8 particles -> 3 particles– To balance gravity fewer particles must

move faster and the density must rise– These factors drive higher energy

generation rates and luminosities in stars

Hotter

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e Lu

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Structural and Luminosity Changes

Bahcall, Pinsonneault & Basu 2001

What Tools Do We Have to Test the Sun?

Current Solar Properties: M, L, age, composition, solar wind…NeutrinosHelioseismology– Sound speed profile– Core helium profile– Scalar constraints: convection zone depth,

surface helium

GoodAgreement!

Solar neutrinosHelioseismology implies a high O abundance– Disagreement with

some recent models claiming a lower solar O, but only at ~ 2 s

– Sound speed agreement to 0.1 – 1% in any case

How Reliable is Solar Evolution?Vary input ingredients within error rangesVary sources of input physics (opacities, equation of state, heavy element mixture) to test systematic errors

Net Result: Almost a Perfect Invariant!

Solar L(t) is within0.5% orbetter at all points during MS evolution

What About Mass Loss?

Any change to solar evolution would require a drastic alteration…The current solar mass loss rate ~1.3 x 1012 g/s is far too small to impact evolutionWhat properties of the ancient Sun could have been very different?– Look at rotation

Young Stars Can Be Rapid Rotators

Denissenkov, Pinsonneault & Terndrup 2010

Link With Mass Loss

More rapid rotation is linked with higher coronal X-ray luminosities and mass loss rates (Wood et al. 2005)– dM/dt ~ Lx– Lx measures coronal heating, and is observed

to up to 1000x larger than solar for young stars

– Higher past mass loss is reasonable

Lx is a strong function of mass and rotation rate

Pizzolato et al. 2003

Rossby number Rotation Period

Angular Momentum EvolutionProtostellar initial stateStar-disk couplingCore-envelope coupling

Epstein & Pinsonneault 2012

Denissenkov, Pinsonneault & Terndrup 2010

Simple Extension of the Standard Model with Mass Loss

Evolve assuming….– dM/dt = (w/wsun)^a

*(dM/dt)sun

– w evolution from standard assumptions

– Observed saturation in X-ray flux

Solar Evolution

With Mass Loss

Some Early Changes PossibleHowever….

Rapid spin downÞSolar wind rapidly convergesto present-day value

What About More Severe Mass Loss?

Basic issue:– Enhanced solar mass loss

is most naturally driven by more rapid rotation in the younger Sun

– Solar analogs are observed to reach a few times solar rotation in a few hundred Myr

– Implies mass loss rates of order 10x solar or less for 90% of the solar age

Sackmann & Boothroyd 2003

Tests and Future Directions

Important tests of rotational history from Kepler and CoRoT will be arriving soon– Crucial check on old field stars

Experimental tests of solar interiors physicsImproved Wind Models