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The MHD equations

Part 1: From the Sun to the stars Paul Charbonneau, Université de Montréal Solar Botany Helioseismology: internal structure and flows Dynamos and magnetic fields Coronae and winds Eruptive events and radiative variability. The MHD equations. Magnetic cycles (1).

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The MHD equations

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  1. Part 1: From the Sun to the starsPaul Charbonneau, Université de Montréal Solar BotanyHelioseismology: internal structure and flowsDynamos and magnetic fieldsCoronae and windsEruptive events and radiative variability 2019 CRAQ Summer School From the sun to the stars

  2. The MHD equations 2019 CRAQ Summer School From the sun to the stars

  3. Magnetic cycles (1) 2019 CRAQ Summer School From the sun to the stars

  4. Simulated magnetic cycles[ Smolarkiewicz & Charbonneau, J. Comput. Phys. 236, 608-623 (2013) ] Large-scale organisation of the magnetic field takes place primarily at and immediately below the base of the convecting fluid layers. Magnetic field amplification through a dynamo mechanism: converting flow kinetic energy into (electro)magnetic energy. 2019 CRAQ Summer School From the sun to the stars

  5. Zonally-averaged Bphi at r/R =0.718 Magnetic cycles (1) Zonally-averaged Bphi at -58o latitude 2019 CRAQ Summer School From the sun to the stars

  6. The « millenium simulation »[ Passos & Charbonneau 2014, Astron. & Ap., 568, 113 ] Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record. 2019 CRAQ Summer School From the sun to the stars

  7. Characteristics of simulated cycles (1) Define a SSN proxy, measure cycle characteristics (period, amplitude…) and compare to observational record. 2019 CRAQ Summer School From the sun to the stars

  8. Characteristics of simulated cycles (2) r = 0.957/0.947 [ 0.763/0.841 ] r = -0.395/-0.147 [ -0.552/-0.320 ] r = 0.688/0.738 [ 0.322/0.451 ] r = -0.465/-0.143 [ 0.185/-0.117 ] 2019 CRAQ Summer School From the sun to the stars

  9. Dynamo saturation[ Racine et al., ApJ, 735 (2011) ] …then these two terms must mutually cancel out, or nearly so, in a statistically stationary state. If this is small… 2019 CRAQ Summer School From the sun to the stars

  10. Magnetic modulation of convective energy transport in EULAG-MHD simulation[ Cossette et al. 2013, ApJL, 777, L29 ] The simulation is more « luminous » at magnetic cycle maximum, by a solar-like 0.2% Lsol ! 2019 CRAQ Summer School From the sun to the stars

  11. Formation of magnetic flux strands (1)[ Nelson et al. 2013, Astrophys. J., 762: 73 ] Recent, very high resolution 3D MHD simulationsof 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. 2019 CRAQ Summer School From the sun to the stars

  12. 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 2019 CRAQ Summer School From the sun to the stars

  13. Starspots (1)  Large sunspots crossing the solar disk produce a significant dimming in luminosity, easily detected photometrically. The same can be expected to happen on solar type stars ! https://spot.colorado.edu/~koppg/TSI/ 2019 CRAQ Summer School From the sun to the stars

  14. Starspots (2)  Photometric variations attributed to starspots have been observed on a number of solar-type stars. Source: J. Drake, Harvard CfA Maps of starspot distribution can be produced; here for Zeta Andromeda; often these show huge « polar spots » 2019 CRAQ Summer School From the sun to the stars Source: Roettenbacher et al., Nature (2016)

  15. The Sun as a star Emission in the cores of the H and K spectral lines of Ca offers a good proxy of magnetic activity; and images taken through a narrow filter images its source S. Baliunas et al. 1995, ApJ, 438, 269. …but, the amplitude of Ca H+K emission is difficult to relate quantitatively to measures of « magnetic cycle amplitude »; the cycle period, in contrast, is (probably) unambiguous. 2019 CRAQ Summer School From the sun to the stars

  16. Olin C. Wilson nébulaire (1) 111 stars F2-M2 ! Emission in core of H+K lines of Calcium Note: a star can be magnetically active without exhibiting activity cycles !! 2019 CRAQ Summer School From the sun to the stars

  17. (1) Key parameterΩ: our Rossby Number: Measures the influence of rotation on convection; and thus quite possibly the efficiency of dynamo action Based on: mixing length theory of convection and mean-field dynamo models operating in « alpha-Omega » regime: Ro = U / Ω L = Prot / tc Pcyc~ Ro1.25 2019 CRAQ Summer School From the sun to the stars

  18. Conclusion (suite et fin) The two branches reflect two distinct modes of dynamo action …but, the Sun ends up sitting in the « no man’s land » between the two activity branches ; and it is of course the « best » data point (error bar < symbol size !) 2019 CRAQ Summer School From the sun to the stars

  19. Back to MHD numerical simulations (1)[ A. Strugarek et al., Science, 357, 185 (2017) ] MHD numerical simulations indicate a decreasing trend of cycle period with Ro The Sun now fits the stars ! 2019 CRAQ Summer School From the sun to the stars

  20. Back to MHD numerical simulations (1)[ A. Strugarek et al. ApJ XXX, YYY (2018) ] 2019 CRAQ Summer School From the sun to the stars

  21. Back to MHD numerical simulations (2)[ A. Strugarek et al., ApJ, 863, id35 (2018) ] Global cyclic behavior is sensitively dependent on the Rossby number; thus on both luminosity and rotation rate Around Ro~0.3 (solar), simulations can exhibit double cycles (observed in Sun!); one long-period and deep-seated, the other short-period and subsurface 2019 CRAQ Summer School From the sun to the stars

  22. Coronal emission Stellar X-ray emission increases with decreasing Rossby number up to Ro~0.1, then saturates; same trend independent of spectral type, from mid-F to M ! Pizzolato et al. A&A, 397, 147 (2003) This suggests universality In the mechanism of coronal X-ray emission 2019 CRAQ Summer School From the sun to the stars

  23. Minimum to remember from this data/simulation blitz Global, solar-like magnetic cycles materialize naturally In MHD simulations of solar/stellar convection ; Differential rotation and Coriolis forces are important agents effecting self-organisation of magnetic fields; MHD simulations suggest that characteristics of magnetic cycles are quite sensitive to stellar parameters, and that fairly abrupt transitions can occur in global cyclic behavior as the Rossby number is varied ; Magnetic cycles are common amongst solar-type stars, but a wide variety of behaviors is observed. We do not have a  concensus  model for the solar dynamo 2019 CRAQ Summer School From the sun to the stars

  24. Part 1: From the Sun to the starsPaul Charbonneau, Université de Montréal Solar BotanyHelioseismology: internal structure and flowsDynamos and magnetic fieldsCoronae and windsEruptive events and radiative variability 2019 CRAQ Summer School From the sun to the stars

  25. La couronne solaire 2019 CRAQ Summer School From the sun to the stars Source: High Altitude Observatory

  26. 1868: discovery of Helium Total eclipse of 18 August 1868: Lockyer and Janssen observe in the yellow portion of the spectrum of a prominence a spectral line which does not map onto any spectral line of any chemical element known on Earth. Conclusion: a new chemical element: Helium Helium was isolated in the lab only in 1895. Jules Janssen (1824-1907) J. Norman Lockyer (1836-1920) 2019 CRAQ Summer School From the sun to the stars

  27. 1869: the coronal green line Total eclipse of August 1869: Young and Harkness a spectral line in the green portion of the visible spectrum, which does not map onto any spectral line of any chemical element known on Earth.Conclusion: a new chemical element: Coronium Charles Young (1834-1908) 2019 CRAQ Summer School From the sun to the stars

  28. 1941: the VERY hot corona In 1931 Lyot designs and builds the first coronograph allowing in-depth study of the coronal spectrum. The width of coronal spectral line leads Lyot to suggest that the temperature of the coronal plasma stands around 600000K In 1941, laboratory spectroscopic studies by Grotrian et Edlén demonstrate that the coronal spectral lines assigned to « coronium » are due to highly ionized Fe and Ni, indicating temperatures of 1-2 million K !! Walter Grotrian (1890-1954) Bernard Lyot (1897-1952) Bengt Edlén (1906-1993) 2019 CRAQ Summer School From the sun to the stars

  29. Coronal heating To offset conductive, radiative and mechanical energy losses in the corona requires some 1 kW m-2 ; this adds up to 10-5 of the solar luminosity : not so much, right … ? Parker solar probe (NASA) But, heat flows from hot to cold; a 6000K photosphere cannot provide heat to a 106K coronal plasma through purely thermodynamical processes at or near equilibrium Currently favored candidate non-equilibrium mechanism include dissipation of magnetoacoustic waves excited by photospheric convection, and in situ dissipation of electrical current sheets; in both cases, the coronal magnetic field is a primary player. Coronal heating is arguably the greatest unsolved mystery of solar physics !! 2019 CRAQ Summer School From the sun to the stars

  30. Hydrostatic coronae (1) Spherically-symmetric, unmagnetized and very hot plasma in hydrostatic equilibrium in the Sun’s gravity; Use perfect gas law and replace energy equation by polytropic relationship, with fixed base temperature, pressure and density: Easy to obtain an analytic solution: With the base sound speed given by: 2019 CRAQ Summer School From the sun to the stars

  31. Hydrostatic coronae (2) The pressure and density asymptote to constant values at large distances ! The interstellar medium cannot equilibrate that pressure Consequently: the hydrostatic corona cannot remain hydrostatic !! 2019 CRAQ Summer School From the sun to the stars

  32. 1683-1730: the non-vacuum of interplanetary space Zodiacal light (ecliptic plane) Gegenschein (antisolar point) Giovanni Domenico Cassini (1625-1712) 2019 CRAQ Summer School From the sun to the stars

  33. 1899: particules from the Sun Aurorae in the lab ! Kristian Birkeland (1867-1917) 2019 CRAQ Summer School From the sun to the stars

  34. 1951: A solar wind ? The hint: misalignment of the neutral and ionized components of comet tails. NASA STEREO-A, 01 Oct 2007 Ludwig Biermann (1906-1993) 2019 CRAQ Summer School From the sun to the stars

  35. The Parker wind solution (1)[ E.N. Parker, ApJ, 128, 664 (1958) ] Spherically-symmetric stationary unmagnetized radial wind outflow; use again polytropic relationship with fixed base temperature. Mass conservation requires: E.N. Parker (1927-) The r-component of the momentum equation yields: Regularity of the solution requires the wind to become supersonic at a sonic point rs : The solar wind should be supersonic (ur~500 km s-1) at Earth’s orbit ! Measured in situ by Lunik 2 (1960), Explorer 10 (1961), Mariner 2 (1962) 2019 CRAQ Summer School From the sun to the stars

  36. The Parker wind solution (2) Hard to distinguish from hydrostatic corona close in; but now the the pressure, density and temperature all vanish at large distances 2019 CRAQ Summer School From the sun to the stars

  37. Solar activity 2019 CRAQ Summer School From the sun to the stars

  38. The Parker spiral (1) Flux freezing + high plasma beta: the wind drags the coronal magnetic field outwards; even though flow is radial, rotation of the sun leads to an azimuthal bending of what would otherwise be a radial fieldline 2019 CRAQ Summer School From the sun to the stars

  39. The Parker spiral (2) At Earth’s orbit, the interplanetary magnetic field makes an angle of 55o with respect to the sun-Earth line. This angle, predicted by the Parker wind solution, is measured at the predicted value! By Jupiter’s orbit, the fieldlines are almost purely azimuthal (90o) Stellar winds drag into interstellar space magnetic fields generated by dynamo action within their interior 2019 CRAQ Summer School From the sun to the stars

  40. Planetary magnetospheres (1) Solar wind The magnetized solar wind interacts with planetary magnetic fields and create an equilibrium structure: the magnetosphere 2019 CRAQ Summer School From the sun to the stars

  41. Planetary magnetospheres (2) Magnetospheres shield planetary atmospheres from the deleterious effects of wind outflows and solar/stellar activity; BUT: • The shield is incomplete: only charged particle are deflected; radiation goes straight through. • The shield is soft: mechanical deformation of the magnetosphere by impacting ejecta can induce currents and accelerate charged particles in situ • The shield has two holes, one over each magnetic pole • The shield is only there is the planet has a significant magnetic field • Without magnetospheres, planetary atmospheres can be eroded by stellar winds 2019 CRAQ Summer School From the sun to the stars

  42. Radiative impacts on Earth’s atmosphere Earth’s upper atmospheric layers absorp the bulk of short-wavelength (ionizing) radiation (UV, EUV, X-rays), with very little making it to ground level; just enough for sunburns ! « Space » begins here Ozone absorbs UV here We are here 2019 CRAQ Summer School From the sun to the stars

  43. Stellar Rotation: the Kraft relationship [ Kraft, ApJ 150, 551 (1967) ] Angular momentum content of intermediate and early-type stars: This relationship breaks down below 1.25 solar masses or so; two possibilities: Formation effect Angular momentum loss 2019 CRAQ Summer School From the sun to the stars

  44. Activity-rotation relationship (1) [ Skumanich, ApJ, 171, 565 (1972) ] Rotation and chromospheric activity both decrease in step as stars age; in both cases, decreasing as ~ t -1/2 ; since known as Skumanich’s Law 2019 CRAQ Summer School From the sun to the stars

  45. Activity-rotation relationship (2)[ Noyes et al., ApJ, 279, 763 (1984) ] A clean activity-rotation relationship materializes if CaK emission is first normalized to the bolometric luminosity: To first order, this «scales out» the convective flow speed dependence of the Rossby number, leaving only the dependence on rotation Activity increases with rotation !! F’HK=sigma T4 R’HK 2019 CRAQ Summer School From the sun to the stars

  46. The Weber-Davis wind solution (1)[ Weber & Davis, ApJ, 148, 217 (1967) ] Spherically-symmetric stationary wind outflow, computed in equatorial plane with radial B at surface; polytropic with fixed base temperature. The phi-momentum equation reduces to: Conservation of radial magnetic flux and mass in a spherically symmetric outflow implies that THIS QUANTITY is a constant; therefore, Introduce now Alfvén speed components: 2019 CRAQ Summer School From the sun to the stars

  47. The Weber-Davis wind solution (2)[ Weber & Davis, ApJ, 148, 217 (1967) ] From phi-component of MHD induction equation: Substituting for A_phi in our previous expression leads to This will blow up at the Alfvén radius, unless we set: This is the angular momentum content of a circular ring of radius rA rotating at angular velocity Omega; generalizing to a spherical shell: 2019 CRAQ Summer School From the sun to the stars

  48. The Weber-Davis wind solution (3) The wind solution must now cross 3 critical points ! Solar But, a WD solution for solar parameters hardly differs from the Parker purely hydrodynamical transsonic solution ! This is because magnetic and centrifugal forces contribute very little to the force balance in the wind: acceleration is primarily thermal 2019 CRAQ Summer School From the sun to the stars

  49. The Weber-Davis wind solution (4) For rapidly rotating, strongly magnetized stars, the wind dynamics becomes dominated by Magnetic and centrifugal forces beyond the sonic point, leading to very high asymptotic flow speeds 25X solar However: the mass loss rate is very nearly the same in all 3 wind solutions: 2019 CRAQ Summer School From the sun to the stars

  50. The Weber-Davis wind solution (5) 2019 CRAQ Summer School From the sun to the stars

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