1. The Standard Solar Model and Its Evolution Marc Pinsonneault Ohio State University Collaborators: Larry Capuder Scott Gaudi

2. Summary The Sun is predicted to become brighter as it ages for fundamental stellar structure reasons This 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

3. Standard Solar Model Initial Conditions: Mass, Composition, Evolutionary State Equations of Stellar Structure –Conservation Laws The Solar Calibration –Reproduce current solar properties, adjust model uncertainties

4. In the Beginning… There are interesting problems around the formation of the Sun –Rotation: Hydrodynamic assembly phase Protostar-disk interaction –Mixing and Light Element Depletion –However, subsequent solar evolution is insensitive to the initial conditions (Vogt- Russell theorem)

5. Standard Model Assumptions and Ingredients Equation of State: OPAL; close to ideal gas Energy Generation: Adelberger et al. 2010; primarily pp Opacities: OP or OPAL; radiative core Convection Theory: MLT; convective envelope Gravitational settling included Rotation, rotational mixing, mass loss not included

6. Standard Luminosity Evolution Early transient phase (~30 Myr) when the Sun contracts and heats up Steady core H burning phase where the Sun steadily brightens

7. Why does the Sun brighten as it ages? Pressure gradient balances gravity Sun remains hot through H fusion 4 1 H => 1 4 He 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

8. Hotter More Luminous

9. Structural and Luminosity Changes Bahcall, Pinsonneault & Basu 2001

10. 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

11. Good Agreement! Solar neutrinos Helioseismology implies a high O abundance –Disagreement with some recent models claiming a lower solar O, but only at ~ 2  –Sound speed agreement to 0.1 – 1% in any case

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

13. Net Result: Almost a Perfect Invariant! Solar L(t) is within 0.5% or better at all points during MS evolution

14. What About Mass Loss? Any change to solar evolution would require a drastic alteration… The current solar mass loss rate ~1.3 x 10 12 g/s is far too small to impact evolution What properties of the ancient Sun could have been very different? –Look at rotation

15. Young Stars Can Be Rapid Rotators Denissenkov, Pinsonneault & Terndrup 2010

16. 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

17. Lx is a strong function of mass and rotation rate Pizzolato et al. 2003 Rossby numberRotation Period

18. Angular Momentum Evolution Protostellar initial state Star-disk coupling Core-envelope coupling Epstein & Pinsonneault 2012 Denissenkov, Pinsonneault & Terndrup 2010

19. Simple Extension of the Standard Model with Mass Loss Evolve assuming…. –dM/dt = (  /  sun )^a *(dM/dt) sun –  evolution from standard assumptions –Observed saturation in X-ray flux

20. Solar Evolution With Mass Loss Some Early Changes Possible However…. Rapid spin down  Solar wind rapidly converges to present-day value

21. 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

22. 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 physics Improved Wind Models