1. Solar Metrology 20141 Double cycles and instabilities in EULAG- MHD simulations of solar convection Paul Charbonneau Département de Physique, Université de Montréal 1.The solar dynamo problem 2.EULAG-MHD 3.The « millenium simulation » 4.Magnetically-mediated cyclic modulation of convective energy transport 5.Conclusions Collaborators: Piotr Smolarkiewicz, Mihai Ghizaru, Dario Passos, Antoine Strugarek, Jean-François Cossette, Patrice Beaudoin, Caroline Dubé, Nicolas Lawson, Étienne Racine, Gustavo Guerrero, Aimee Norton, Mark Miesch

2. Solar Metrology 20142 The solar magnetic cycle

3. Solar Metrology 20143 The magnetic self-organization conundrum How can turbulent convection, a flow with a length scale <<R and coherence time of ~month, generate a magnetic component with scale ~R varying on a timescale of ~decade ?? Mechanism/Processes favoring organization on large spatial scales: 1. rotation (cyclonicity); 2. differential rotation (scale ~R); and 3. turbulent inverse cascades.

4. Solar Metrology 20144 The MHD equations

5. Solar Metrology 20145 Selected milestones Browning et al. 2006: Demonstrate the importance of an underlying, convectively stable fluid layer below the convection zone in producing a large-scale magnetic component in the turbulent regime. Brun et al. 2004: Strongly turbulent MHD simulation, producing copious small-scale magnetic field but no large-scale magnetic component. Glatzmaier 1984, 1985: Anelastic model including stratification, large-scale fields with polarity reversals within a factor 2 of solar period; tendency for poleward migration of the large-scale magnetic field. Gilman 1983: Boussinesq MHD simulation, producing large-scale magnetic fields with polarity reversals on yearly timescale; but non-solar large-scale organization. Brown et al. 2010, 2011: Obtain irregular polarity reversals of thin, intense toroidal field structure in a turbulent simulation rotating at 5X solar. Nelson et al. 2012, 2013: Autonomous generation of buoyantly rising flux-ropes structures showing sunspot-like emergence patterns. Ghizaru et al. 2010: Obtain regular polarity reversals of large-scale magnetic component on decadal timescales, showing many solar-like characteristics.

6. Solar Metrology 20146 EULAG-MHD simulations

7. Solar Metrology 20147 Simulation framework Simulate anelastic convection in thick, rotating and unstably stratified fluid shell of electrically conducting fluid, overlaying a stably stratified fluid shell. Recent such simulations manage to reach Re, Rm ~10 2 -10 3, at best; a long way from the solar/stellar parameter regime. Throughout the bulk of the convecting layers, convection is influenced by rotation, leading to alignment of convective cells parallel to the rotation axis. Stratification leads to downward pumping of the magnetic field throughout the convecting layers.

8. Solar Metrology 20148 Rotation and differential rotation (1) Vertical (radial) flow velocity, in Mollweide projection [ from Guerrero et al. 2013, Astrophys. J., 779, 176 ] No rotation Rotation at solar rate

9. Solar Metrology 2014 EULAG-MHD EULAG: a robust, general solver for geophysical flows; developed by Piotr Smolarkiewicz and collaborators at MMM/NCAR EULAG-MHD: MHD generalization of above; developed mostly at UdeM in close collaboration with Piotr Smolarkiewicz Core advection scheme: MPDATA, a minimally dissipative iterative upwind NFT scheme; equivalent to a dynamical, adaptive subgrid model. Thermal forcing of convection via volumetric Newtonian cooling term in energy equation, pushing reference adiabatic profile towards a very slightly superadiabatic ambiant profile Strongly stable stratification in fluid layers underlying convecting layers. Model can operate as LES or ILES 9

10. Solar Metrology 2014 MHD simulation of global dynamos [ Ghizaru et al. 2010, ApJL, 715, L133 ] Electromagnetic induction by internal flows is the engine powering the solar magnetic cycle. The challenge is to produce a magnetic field well-structured on spatial and temporal scales much larger/longer than those associated with convection itself. This is the magnetic self-organisation problem. Temperature perturbationRadial flow componentRadial magnetic field component http://www.astro.umontreal.ca/~paulchar/grpshttp://www.astro.umontreal.ca/~paulchar/grps > Que faisons nous > Simulations MHD 10

11. Solar Metrology 201411 Simulated magnetic cycles (1) Large-scale organisation of the magnetic field takes place primarily at and immediately below the base of the convecting fluid layers

12. Solar Metrology 201412 Magnetic cycles (1) Zonally-averaged B phi at r/R =0.718 Zonally-averaged B phi at -58 o latitude

13. Solar Metrology 201413 Successes and problems KiloGauss-strength large-scale magnetic fields, antisymmetric about equator and undergoing regular polarity reversals on decadal timescales. Cycle period four times too long, and strong fields concentrated at mid-latitudes, rather than low latitudes. Reasonably solar-like internal differential rotation, and solar-like cyclic torsional oscillations (correct amplitude and phasing). Internal magnetic field dominated by toroidal component and strongly concentrated immediately beneath core-envelope interface. Well-defined dipole moment, well-aligned with rotation axis, but oscillating in phase with internal toroidal component. On long timescales, tendency for hemispheric decoupling, and/or transitions to non-axisymmetric oscillatory modes. Cyclic modulation of the convective energy flux, in phase with the magnetic cycle.

14. Solar Metrology 201414 The « millenium simulation » [ Passos & Charbonneau 2014, A&A, 568, A113 ] Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record.

15. Solar Metrology 201415 Characteristics of simulated cycles (1) [ Passos & Charbonneau 2014, A&A, 568, A113 ] Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record.

16. Solar Metrology 201416 Characteristics of simulated cycles (2) [ Passos & Charbonneau 2014, A&A, 568, A113 ] r = 0.957/0.947 [ 0.763/0.841 ] r = -0.465/-0.143 [ 0.185/-0.117 ] r = 0.688/0.738 [ 0.322/0.451 ] r = -0.395/-0.147 [ -0.552/-0.320 ]

17. Solar Metrology 201417 Magnetically-mediated cyclic modulation of convective energy transport [ with J.-F. Cossette, P. Smolarkiewicz ]

18. Club Math 2014/UdeM18 Observed variations of total solar irradiance PMOD Composite Reconstruction by Crouch et al. (2008)

19. Solar Metrology 201419 Two schools of thoughts 1.All TSI variation on all relevant timescales are due to varying surface coverage of magnetic features (spots, faculae, network, etc.). Strongest evidence: reconstructions based on photospheric data can reproduce 95% of observed variance. 2.Some TSI variations on timescales decadal and longer originate from deep inside the sun (changes in solar radius, photospheric temperature gradient, magnetic modulation of convective energy flux, etc.). Strongest evidence: cyclic modulation of p-mode frequencies.

20. Solar Metrology 201420 Magnetic modulation of convective energy transport in EULAG-MHD millenium simulation [ Cossette et al. 2013, ApJL, 777, L29 ] The simulation is more « luminous » at magnetic cycle maximum, by a solar-like 0.2% L sol !

21. Solar Metrology 201421 How to modulate convective energy transport 1. Lorentz force modulates convective velocity u r ; 2. Change in magnitude of temperature perturbations; 3. Change in degree of correlation between the two; 4. Change in latitudinal distribution of F. 5. All of above ? And/or something else … ? Temperature deviation from horizontal mean Vertical flow speed

22. Solar Metrology 201422 Spatiotemporal variability of the convective flux [ Cossette et al. 2013, ApJL, 777, L29 ] Zonally-averaged toroidal field and convective flux at r/R=0.87

23. Solar Metrology 201423 Convective entrainment and « hot spots »

24. Solar Metrology 201424 Pinning it down… [ Cossette et al. 2013, ApJL, 777, L29 ] Differences are in the tails of the flux distributions: hot spots are enhanced, turbulent entrainment is suppressed. The strongest (anti)correlations with the magnetic cycle are for the negative convective fluxes.

25. Solar Metrology 201425 Small (multi)periodic signal in temperature [ Beaudoin et al. 2014, in prep. ] 95% confidence

26. Solar Metrology 201426 Convection is not diffusion ! 1.The Newtonian diffusive heat flux is proportional to the temperature gradient; the heat flux is entirely determined by local conditions. 2.The convective heat flux is proportional to temperature at point of origin of upflows and downflows; for strongly turbulent convection, these flow structures can cross many scale heights; the heat flux is strongly non-local.

27. Solar Metrology 201427 Convection is not diffusion !

28. Solar Metrology 201428 Where do we go next ? Understand what sets the cycle period(s) Understand physical underpinnings of the cyclic modulation of the convective energy flux Understand role of tachocline instabilities in long term stability of simulations, and possible role in triggering Maunder-Minimum-like period of strongly reduced activity Comparative benchmark with ASH simulations Get closer to surface !! (Compressible version of EULAG-MHD in the works)

29. Solar Metrology 201429 FIN Collaborators: Piotr Smolarkiewicz (NCAR, ECMWF), Mihai Ghizaru, Étienne Racine (CSA), Jean-François Cossette, Patrice Beaudoin, Nicolas Lawson, Amélie Bouchat, Corinne Simard, Caroline Dubé, Dario Passos, Roxane Barnabé

30. Solar Metrology 201430 Formation of magnetic flux strands (1) [ Nelson et al. 2013, Astrophys. J., 762: 73 ] Recent, very high resolution 3D MHD simulations of solar convection Have achieved the formation of flux-rope-like super-equipartition-strength « magnetic strands » characterized by a significant density deficit in their core; ripped from the parent large-scale structure by turbulent entrainement, subsequent buoyant rise ensues.

31. Solar Metrology 201431 Formation of magnetic flux strands (2) [ Nelson et al. 2014, Solar Phys., 289, 441 ] The strands « remember » their origin ! The strands develop a pattern of East-West tilt similar to that inferred obervationally for the sun

32. Solar Metrology 201432 Kinetic and magnetic energies (120 s.d.=10 yr)

33. Solar Metrology 201433 Characteristics of simulated cycles (3) Hemispheric cycle amplitude show a hint of bimodality Usoskin et al. 2014, A&A 562, L10; From 3000yr 14 C time series

34. Solar Metrology 201434 Characteristics of simulated cycles (4) Hemispheric cycle amplitude show a hint of bimodality Usoskin et al. 2014, A&A 562, L10; From 3000yr 14 C time series

35. Solar Metrology 201435 Rotation and differential rotation (2) Angular velocity profiles, in meridional quadrant Helioseismology HD simulationMHD simulation Differential rotation in the Sun and solar-type stars is powered by turbulent Reynolds stresses, arising from rotationally-induced anisotropy in turbulent transport of momentum and heat