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Magnetohydrodynamic simulations of stellar differential rotation and meridional circulation

Magnetohydrodynamic simulations of stellar differential rotation and meridional circulation (submitted to A&A, arXiv:1407.0984). Bidya Binay Karak (Nordita fellow) In collaboration with Petri J. Kapyla, Maarit J. Kapyla, and Axel Brandenburg. Internal solar rotation from helioseismology.

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Magnetohydrodynamic simulations of stellar differential rotation and meridional circulation

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  1. Magnetohydrodynamic simulations of stellar differential rotation and meridional circulation (submitted to A&A, arXiv:1407.0984) Bidya Binay Karak (Nordita fellow) In collaboration with Petri J. Kapyla, Maarit J. Kapyla, and Axel Brandenburg

  2. Internal solar rotation from helioseismology =>Solar-like differential rotation observed in rapidly rotating dwarfs (e.g. Collier Cameron 2002) Gilman & Howe (2003) When polar regions rotate faster than equator regions is called anti-solar differential rotation. -observed in slowly rotating stars (e.g., K giant star HD 31993; Strassmeier et al. 2003; Weber et al. 2005).

  3. Transition from solar-like to anti-solar differential rotation in simulations (Gilman 1978; Brun & Palacios 2009; Chan 2010; Kapyla et al. 2011; Guerrero et al. 2013; Gastine et al. 2014) Independent of model setup. (Gilman 1977) Solar-like Solar-like Anti-solar Anti-solar Guerrero et al. (2013) Gastine et al. (2014)

  4. Bistability of differential rotation Observed in many HD simulations Gastine et al. (2014) from Boussinesq convection. Kapyla et al. (2014) in fully compressible simulations

  5. Model equations We carry out a set of full MHD simulations

  6. Computations are performed in spherical wedge geometry: We performed several simulations by varying the rotational influence on the convection. We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection

  7. MHD Co = 1.34, 1.35, 1.44, 1.67, 1.75 Rotational effect on the convection is increased

  8. MHD HD Co = 1.34, 1.35, 1.44, 1.67, 1.75 Rotational effect on the convection is increased 939 430 263 443 430 325 503 430 315 980 430 265 918 430 261

  9. Identifying the transition of differential rotation No evidence of bistability! Gastine et al. (2014) Kapyla et al. (2014) Magnetic field helps to produce more solar-like differential rotation

  10. A-S diff. rot.S-L diff. rot. Meridional circulation

  11. Azimuthally averaged toroidal field near the bottom of SCZ Runs produce solar-like differential rotation Runs produce anti-solar differential rotation

  12. From Run A (AS Diff.Rot) Variation: ~ 50% ~ 6% ~ 75% Temporal variations from Run A

  13. How the variation in large-scale flow comes?

  14. Variation of Lorentz forces over magnetic cycle Maximum Minimum

  15. Angular momentum fluxes(e.g., Brun et al. 2004; Beaudoin et al. 2013) Coriolis force Reynolds stress Maxwell stress (Rudiger 980, 1989)

  16. Run A (produces anti-solar differential rotation) cm2/s Reynolds Viscosity Lambda effect Run E(produces solar-like differential rotation) cm2/s

  17. Run A (produces anti-solar differential rotation) Meridonal circulation Maxwell stress Mean-magnetic part Run E (produces solar-like differential rotation)

  18. Temporal variation: From Run A (solar-like diff. rot.) Max Min Reynolds stress Meridional Maxwell stress Mean-magnetic circulation part

  19. Thanks for your attention! BTW, my NORDITA fellowship will end next year mid, so looking for next post doc position. 19

  20. Drivers of the meridional circulation (Ruediger 1989; Kitchatinov & Ruediger 1995; Miesch & Hindman 2011)

  21. Identifying the transition of differential rotation

  22. Boundary conditions For velocity field: Radial and latitudinal boundaries are impenetrable and stress-free For magnetic field:Perfect conductor at latitudinal boundaries and lower radial boundary. Radial field condition at the outer boundary On the latitudinal boundaries we assume that the density and entropy have vanishing first derivatives. On the upper radial boundary we apply a black body condition: We add a small-scale low amplitude Gaussian noise as initial condition for velocity and magnetic field Initial state isoentropic

  23. Computations are performed in spherical wedge geometry: We use pencil-code. Boundary conditions For velocity field: Radial and latitudinal boundaries are impenetrable and stress-free For magnetic field:Perfect conductor at latitudinal boundaries and lower radial boundary. Radial field condition at the outer boundary On the latitudinal boundaries we assume that the density and entropy have vanishing first derivatives. On the upper radial boundary we apply a black body condition:

  24. From Run E (SL Diff Rot) Variation: ~ 40% ~ 4% ~ 50% ~ 60%

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