1. Intrinsic variability induced by dynamo magnetic fields in solar-like stars Federico Spada 1, Rainer Arlt 1, Manfred Küker 1, and Sabatino Sofia 2 1 Leibniz-Institut für Astrophysik Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam, Germany 2 Department of Astronomy, Yale University, 260 Whitney Avenue, New Haven, CT 06511, USA 06/08/2015Federico Spada - XXIX IAU GA, FM 131 XXIX IAU General Assembly – Focus Meeting 13 Brightness Variations of the Sun and Sun-like Stars

2. Structural variations due to dynamo magnetic fields 06/08/2015Federico Spada - XXIX IAU GA, FM 132

3. The variability we wish to model Due to dynamo magnetic fields (variable extra pressure/energy contributions, effect on energy transport, …) Intrinsic (e.g., luminosity, as opposed to irradiance, variation) On time scales of decades to millennia (i.e., longer than the 11-year cycle, shorter than evolutionary) 06/08/2015Federico Spada - XXIX IAU GA, FM 133

4. In solar-like stars: radius inflation in active binaries 06/08/2015Federico Spada - XXIX IAU GA, FM 134 Feiden & Chaboyer (2012, 2013, 2014); Spada et al. (2013) δR/R(observed − modeled) up to 5% in eclipsing binaries possibly due to strong surface magnetic (≈ kG) magnetic fields

5. In the Sun: towards a theory of solar magnetic variability Difficult measurements small effects, calibration issues TSI modeling usually ignores intrinsic variations Potentially relevant for climate (t. s. of decades to millennia) 06/08/2015Federico Spada - XXIX IAU GA, FM 135 Frölich (2013)

6. Constraints on L and R variations 06/08/2015Federico Spada - XXIX IAU GA, FM 136 δL/L < 10 -3 Solar Disk Sextant (SDS) Sofia, S., et al. 2013, MNRAS, 436, 2151 δR/R ~ 2  10 -4 Frölich (2013)

7. Stellar structure perturbation due to magnetic fields The magnetic perturbation affects: 1.The hydrostatic equilibrium equation 2.The convective stability and temperature gradient 3.The equation of state (EOS) 06/08/2015Federico Spada - XXIX IAU GA, FM 137 (Lydon & Sofia, 1995)

8. We model the equilibrium response to the perturbation 06/08/2015Federico Spada - XXIX IAU GA, FM 138 non-magnetic model (B 0 =0) increasing B 0

9. Results do not depend on the perturbation age 06/08/2015Federico Spada - XXIX IAU GA, FM 139 δR non-magnetic model (B 0 =0) different onset of the perturbation

10. Two magnetic field configuration Gaussian profileDynamo profile 06/08/2015Federico Spada - XXIX IAU GA, FM 1310 CoreSurface CZ bottom

11. Maximum field strength Gaussian profile: helioseismology Dynamo profile: equipartition 06/08/2015Federico Spada - XXIX IAU GA, FM 1311 (1)Goode & Dziembowski (1993); (2)Chou & Serebryanskiy (2002); (3)Baldner et al. (2009); (4)Antia et al. (2000). B 0 ≤ 6. kG

12. Results: δR, δL insensitive to Gaussian vs. Dynamo profiles Radius variationLuminosity variation 06/08/2015Federico Spada - XXIX IAU GA, FM 1312 −δL/L δR/R Field depth controls P mag /P gas, which is the most important parameter in 1D!

13. Results: for shallow fields, large radius variations are possible! 06/08/2015Federico Spada - XXIX IAU GA, FM 1313 Maximum B 0

14. Results: for shallow fields, large radius variations are possible! 06/08/2015Federico Spada - XXIX IAU GA, FM 1314 B 0 tuned to have δR = 2  10 -4

15. Conclusions Stellar equilibrium response to magnetic perturbation δR and δL almost insensitive to radial profile (in 1D!) δR and δL very sensitive to peak location (P mag /P gas ) δR ≈ 2  10 -4 are theoretically plausible for shallow fields 06/08/2015Federico Spada - XXIX IAU GA, FM 1315

16. Magnetic field configuration 1) Gaussian profile, subject to helioseismic constraints 2) Radial profile from the output of a 2D dynamo model 06/08/2015Federico Spada - XXIX IAU GA, FM 1316 (1)Goode & Dziembowski (1993); (2)Chou & Serebryanskiy (2002); (3)Baldner et al. (2009); (4)Antia et al. (2000). α effect (contours: “Top”, “Bottom”) Rotation and meridional circulation

17. Convective stability criterion modified by the magnetic field 06/08/2015Federico Spada - XXIX IAU GA, FM 1317 Schatten & Sofia (1981) B P tot /P gas f Modified Schwarzschild criterion for stability:

18. The Solar Disk Sextant (SDS) Balloon-borne telescope, measuring solar diameter Angular measurement, not subject to degradation Seven flights between 1992 and 2011 06/08/2015Federico Spada - XXIX IAU GA, FM 1318 Sofia et al. (2013)

19. Convective structure of a perturbed 1 M  model 06/08/2015Federico Spada - XXIX IAU GA, FM 1319 surfacecenterCZ base deep shallow

20. Convective structure of a perturbed 0.6 M  model 06/08/2015Federico Spada - XXIX IAU GA, FM 1320 surfaceCZ basecenter shallow deep