Dynamo Simulations in Solar Convection Zone

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1 Dynamo Simulations in Solar Convection Zone Bidya Binay Karak (Nordita fellow & Visitor at MPS) Collaborators: Axel Brandenburg (Nordita), Petri Käpylä and Maarit Käpylä (Aalto University) Thanks to organisers for the financial support! APSPM 2015, Seoul

2 Magnetic fields and dynamo process Large-scale/global dynamo: Produces organized, coherent large-scale magnetic field. Rotation, stratification and nonuniform rotation play crucial role! Rotation: Makes the convective motion helical à α effect. Non-uniform rotation: Stretch the magnetic field à Ω effect. See a recent review: Karak et al. (2014), Space Sci. Rev.

3 Small-scale magnetic field of Sun MDI magnetogram: Solar maximum Jin et al. (2011) Solar minimum

4 Small-scale magnetic field of Sun Jin et al. (2011) Interestingly, even the internetwork field the weakest component of solar magnetism having an unsigned flux of Mx, contributes at least four orders of magnitude larger flux than that of the bipolar-active regions during solar maximum.

5 Origin of the small-scale magnetic field 1. Result of a large-scale dynamo: the shredding of large-scale magnetic field and the decay of active regions. Then this small-scale field should be correlated with the sunspot cycle! Small-scale magnetic field does not have solar cycle dependence, and it does not have any latitudinal dependence (Hagenaar et al. 2003; Sanchez Almeida 2003; Lites et al. 2008; Lites 2011; Buehler et al. 2013). Jin et al. (2011) Jin & Wang (2012, 2015)

6 Origin of the small-scale magnetic field 2. Small-scale dynamo (do not call local dynamo/fluctuation dynamo/turbulent dynamo): Three-dimensional velocity fields sufficiently random in space and/or time can amplify small-scale magnetic fluctuations via random stretching of the field lines (Batchelor 1950; Zel'dovich et al. 1984; Childress & Gilbert 1995). No net helicity is required! Produces magnetic field at smaller scale than the velocity scale!

7 Dynamo simulations in solar convection zone =>Very challenging! (because of large spatial and temporal scale and much smaller values of fluid and magnetic diffusivity in the solar convection zone.) =>At small magnetic Prandtl number, the critical magnetic Reynolds number, R m C needed to excite the small-scale dynamo increases which makes the small-scale dynamo difficult. Early MHD simulations of small-scale dynamo Cattaneo (1999); Emonet & Cattaneo (2001); Cattaneo et al. (2003); Voegler et al. (2005); Voegler & Schuessler (2007); Rempel (2014); Hotta, Rempel & Yokoyama (2015) à Small-scale dynamo! Racine et al. Kaepylae et al., Warneck et al., Masada et al. Miesch & Brun, Karak et al. à Large-scale dynamo in the solar convection zone! However, in Sun both dynamos are operating in the same plasma!

8 Dynamo simulations in solar convection zone =>Very challenging! (because of large spatial and temporal scale and smaller values of fluid and magnetic diffusivity in the solar convection zone.) =>At small magnetic Prandtl number, the critical magnetic Reynolds number, R m C needed to excite the small-scale dynamo increases which makes the small-scale dynamo difficult. Early MHD simulations of small-scale dynamo Cattaneo (1999); Emonet & Cattaneo (2001); Cattaneo et al. (2003); Voegler et al. (2005); Voegler & Schuessler (2007); Rempel (2014); But I am a very simple man! Hotta, Rempel & Yokoyama (2015) à Small-scale dynamo! Karak et al. (2015) à Large-scale dynamo in solar convection zone! However, in Sun both dynamos are operating in the same plasma!

9 A simple setup for dynamo simulations (excites both large-scale and small-scale dynamos) Isothermal & compressible gas. Periodic box, imposed large-scale shear, turbulence is generated by helically forced flow.

10 Results from: only large-scale dynamo and, no small-scale dynamo B x B y B 2 b 2 The small-scale field is produced from the tangling of the large-scale field!

11 Results from: only large-scale dynamo and, no small-scale dynamo B x B y Small-scale field B 2 Large-scale field b 2 The small-scale field is produced from the tangling of the large-scale field! From a different simulation!

12 Results from a simulation when both dynamos are operating B x B y B 2 b 2

13 Results from a simulation when both dynamos are operating (Large R m, large D) From smallscale dynamo + tangling From small-scale dynamo See Karak & Brandenburg (2015) for more details.

14 Results from a simulation when both dynamos are operating Why this anti-correlation? Quenching of small-scale dynamo!

15 Results from a simulation when both dynamos are operating Same as earlier but here large-scale dynamo is weaker. Karak & Brandenburg (2015)

16 We carry out a set of full MHD simulations 0.72R r 0.97R 15 θ π 0 ϕ 2

17 Convection simulations in spherical geometry We performed several simulations by varying the rotational influence on the convection. Karak et al. (2015) We use much higher viscosity and diffusivity than in Sun and 10 6 times solar luminosity! Small-scale low amplitude Gaussian noise as initial condition.

18 Azimuthally averaged toroidal field near the bottom of SCZ They produce correct differential rotation. Karak et al. (2015) 5 times rotating than Sun Kapyla et al. (2012, 2013, 2015), Warnecke et al. (2014)

19 Equatorward migration in other simulations??? Toroidal field near surface Solar-like rotation Fan & Fang (2014) Masada et al. (2013,2014) Mabuchi et al. (2015) Racine et al. (2011) 3 times solar rotation--auguston et al. (2015 ) Guerrero et al. (2015)

20 Conclusion: ü Cartesian box simulations, although they are not solar-like, provide lots of insights which can be used in mean-field and global convection models. ü In recent years, we have seen some progress in global convection simulations. However, still they are struggling to resolve some fundamental issues. ü Until convection simulations become realistic we can work on hybrid mean-field models -- by putting more and more constrains from observations and convection simulations. Thank you!

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22 Dynamo number: R m (Large R m, small D) (Large R m, large D) small-scale dynamo! Both dynamos! D (Small R m, small D) No dynamo! (Small R m, large D) large-scale dynamo!

23 Results from a simulation when both dynamos are operating (Large R m, large D) Why this anti-correlation? Quenching of small-scale dynamo! Energy spectrum

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25 Identifying the transition of differential rotation

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

32 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) Guerrero et al. (2013) Gastine et al. (2014) Independent of model setup. Solar-like (Gilman 1977) Solar-like Anti-solar Anti-solar

33 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:

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