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Slides and bibliography

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. Slides and bibliography.

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Slides and bibliography

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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. Slides and bibliography pdf copies of these powerpoint slides will be made available at: http://www.astro.umontreal.ca/~paulchar/craq2019/craq2019-1.pdf http://www.astro.umontreal.ca/~paulchar/craq2019/craq2019-2.pdf I will also place in the same directory a 3-page pdf document providing a reading list and links to web sites particularly relevant to the topics covered in these (currently not there! Will appear before the end of the week!) 2019 CRAQ Summer School From the sun to the stars

  3. 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

  4. Solar/stellar magnetism « If the sun did not have a magnetic field, it would be as boring a star as most astronomers believe it to be » (Attributed to R.B. Leighton) 2019 CRAQ Summer School From the sun to the stars

  5. Harriot, Fabricius, Galileo, Scheiner… 2019 CRAQ Summer School From the sun to the stars

  6. Sunspots = magnetic fields Regions of strong (~kG) concentrated magnetic fields in the solar photosphere; the concept: emerging magnetic flux rope George E. Hale (1868-1938) Zeeman splitting ! G.E. Hale et al. ApJ, 49,153-178, (1919) 2019 CRAQ Summer School From the sun to the stars Graphics by D. Passos

  7. The sunspot cycle (1) Heinrich Schwabe Discovered in 1843 by an amateur astronomer, after 17 years of nearly continuous sunspot observations. The sunspot cycle has a period of approximately 11 years, and its amplitude shows large cycle-to-cycle fluctuations, as well as extended episodes of apparent halt.. Rudolf Wolf 2019 CRAQ Summer School From the sun to the stars

  8. The sunspot cycle (2) 2001, cycle peak Magnetogram 2019 CRAQ Summer School From the sun to the stars

  9. The sunspot cycle (3) Magnetogram 15 sept. 2018 2019 CRAQ Summer School From the sun to the stars

  10. Hale’s polarity Laws Source: solarcyclescience.com Ordering of magnetic polarity of sunspot pair is opposite in each solar hemisphere, and reverses from one sunspot cycle to the next. Indicative of an equatorially antisymmetric internal toroidal magnetic field component undergoing cyclic polarity reversals 2019 CRAQ Summer School From the sun to the stars

  11. Le cycle magnétique (3) Data animation courtesy D. Hathaway, NASA/MSFC Animation by D. Hathaway, NASA/Ames 2019 CRAQ Summer School From the sun to the stars

  12. The solar magnetic cycle Zonal average of surface radial magnetic component Magnetic polarity reversal every ~11 yr, full magnetic cycle period ~22 yr 2019 CRAQ Summer School From the sun to the stars

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

  14. La couronne solaire Source: NASA/SDO 2019 CRAQ Summer School From the sun to the stars

  15. Solar activity: eruptive events 2019 CRAQ Summer School From the sun to the stars

  16. Coronal mass ejections Solar activity SoHO/LASCO C-3 2019 CRAQ Summer School From the sun to the stars

  17. UV emission and flares Solar ac SoHO/LASCO C-3 tivity 2019 CRAQ Summer School From the sun to the stars SoHO/EIT 19.5 nm

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

  19. The « solar constant » Definition: Wavelength-integrated electromagnetic energy illuminating one square meter of Earth’s upper atmosphere, at a Sun-Earth distance of one astronomical unit (149598500 km). Now called Total Solar Irradiance (TSI), amd measured from space since 1978 TSI = 1362 +/- 4 Watt / m2 The +/- 4 W/m2 is not a measurement error… 2019 CRAQ Summer School From the sun to the stars

  20. The total solar irradiance http://spot.colorado.edu/~koppg/TSI/ 2019 CRAQ Summer School From the sun to the stars

  21. The solar spectral irradiance Plot by J. Lean, NRL, courtesy NASA From UV to X-Rays, variability increases a lot with decreasing wavelength; However, the bulk of electromagnetic energy at these wavelengths is absorbed very high in the Earth’s atmosphere (stratosphere and higher). The UV (120-400nm) accounts for 1% of the TSI, but 14% of its variability. 2019 CRAQ Summer School From the sun to the stars

  22. The solar cycle in soft X-Rays Source:YOHKOH Legacy Archive/Montana State U. Solar activity 2019 CRAQ Summer School From the sun to the stars

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

  24. Space Weather Solar eruptive events impact near-Earth’s space environment as well as the upper atmosphere ( > 50 km) Source: SOHO http://sohowww.nascom.nasa.gov 2019 CRAQ Summer School From the sun to the stars

  25. Magnetic fields do it all ! The Sun’s magnetic field is the dynamical driver and energy source of all eruptive events, as well as radiative variability Source: SOHO/EIT/MDI; seehttp://sohowww.nascom.nasa.gov 2019 CRAQ Summer School From the sun to the stars

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

  27. Minimum to remember from your brief tour of the solar zoo The Sun is a magnetized, variable star ; Solar variability unfolds over a vast range of spatial and temporal scales ; The solar magnetic field is the driver and energy source for all eruptive phenomena, as well as radiative variability ; The solar magnetic cycle is the pulse modulating every manifestation of solar activity ; Understand solar activity demands understanding the origin and evolution of the Sun’s magnetic field. 2019 CRAQ Summer School From the sun to the stars

  28. 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

  29. Helioseismology: sounding the Sun (1) Discovered in 1962 by R. Leighton, understood a decade later by J. Leibacher and R. Stein Resonant acoustic waves excited by convection; « p-modes » (pressure is the restoring force) Because sound speed increases with depth, p-modes are refracted back up as they propagate into the interior p-modes are reflected by the quasi-discontinuity in density at the photosphere: induces vertical displacement (~a few m s-1) 2019 CRAQ Summer School From the sun to the stars

  30. Helioseismology: sounding the Sun (2) The MHD induction equation: The Lorentz force in MHD: The surface Doppler signal can be decomposed into spherical harmonics Source: GONG web site https://gong.nso.edu/gallery 2019 CRAQ Summer School From the sun to the stars

  31. Helioseismology: sounding the Sun (3) Then for each mode, get frequency from amplitude time series The Lorentz force in MHD: Each « ridge » in frequency-wavenumber diagram is a radial overtone; millions of modes are measured ! Source: GONG web site https://gong.nso.edu/gallery 2019 CRAQ Summer School From the sun to the stars

  32. Helioseismology: internal structure The frequency of a p-mode measures the average sound speed over the acoustic ray path; combining this info for many modes yields a very tight constraint on T(r), and thus on solar internal structure Source: C.P. Garay, ResearchGate The Sun’s p-mode frequencies are known to a much, much better accuracy than its mass, radius, temperature, luminosity 2019 CRAQ Summer School From the sun to the stars

  33. Asteroseismology (1) p-modes are now detected photometrically in many solar-type stars (e.g. 16CygA a.k.a. HD 186408 a.k.a. KIC12069424) Internal structure can be constrained quite tightly, and provide ages even for field stars ! And there is more… W.J. Chaplin et al., ARA&A51, 353 (2013) 2019 CRAQ Summer School From the sun to the stars

  34. Main sequence Asteroseismology (2) Main sequence Subgiant W.J. Chaplin et al., ARA&A51, 353 (2013) Subgiant Base of RGB [ All ~ 1 M☉ ] 2019 CRAQ Summer School From the sun to the stars

  35. Helioseismology: internal rotation (1) For a non-rotating star, the prograde/retrograde acoustic modes are degenerate in frequency; no longer the case in a rotating star ! The frequency splitting of a given mode pair (+/- m) is a measure of the mean rotation in its acoustic cavity ! With million of such mode pairs measured, the solar internal (differential) rotation can be mapped in depth and latitude 2019 CRAQ Summer School From the sun to the stars

  36. Helioseismology: internal rotation (2) • Noteworthy features: • Near-surface radial shear layer • Latitudinal gradient within convection zone: « equatorial acceleration » • Radial shear at base of convection zone: « tachocline » • Outer radiative core rotating quasi-rigidly Source: NASA MSFC https://solarscience.msfc.nasa.gov/Helioseismology.shtml 2019 CRAQ Summer School From the sun to the stars

  37. Rotation and differential rotation (1) No rotation Rotation at solar rate This is stratified, rotating turbulence ! Vertical (radial) flow velocity, in Mollweide projection [ from Guerrero et al. 2013, Astrophys. J., 779, 176 ] 2019 CRAQ Summer School From the sun to the stars

  38. Convection + rotation = differential rotation Separate flow u into a slowly-varying, large-scale component U, and rapidly varying, small-scale component u’ (turbulent convection): Average fluid equations over an intermediate length scale such that <u’>=0 ; averaged momentum equation becomes: A new force term appears on the RHS: Reynolds stresses, arising when correlations exists between small-scale flow components (due, e.g., to Coriolis force). This is what drives differential rotation in the Sun/stars ! 2019 CRAQ Summer School From the sun to the stars

  39. The Rossby number We need to quantify impact of rotation on convection; consider fluid momentum equation written in rotating frame: Fluid inertia Coriolis force Form dimensionless ratio of these two terms: This is the Rossby number ; if Ro <1 , rotation strongly influences flow dynamics ; like it does for tropical cyclones on Earth (Ro~0.1) ; but definitely not in your bathtub (Ro~102) 2019 CRAQ Summer School From the sun to the stars

  40. « Solar » vs « Anti-solar » differential rotation Ro~1.2 Ro~0.3 The « tipping point » is at Ro ~ 0.5; very close to solar value ! 2019 CRAQ Summer School From the sun to the stars

  41. Solar differential rotation The Sun http://gong.nso.edu/gallery/disk2k10/data/resource/torsional/torsional.html EULAG-HD (simulation) 2019 CRAQ Summer School From the sun to the stars

  42. Minimum to remember from your brief tour of stellar hydrodynamics Helioseismology allows to measure the internal structure and rotation of the Sun; Asteroseismology is starting to do the same thing; Rotational influences on convective dynamics generate turbulent stresses driving internal differential rotation; The key parameter measuring the influence of rotation on convection is the Rossby number ; At its present convective luminosity and rotation rate, the Sun is a fast rotator (Ro~0.3); but is close to the transition point to the regime of low rotational influence. 2019 CRAQ Summer School From the sun to the stars

  43. 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

  44. The homopolar generator (1) Consider an electrical charge in the disk; its velocity due to the disk’s rotation is: If a vertical magnetic field threads the disk: Then the charge will feel a magnetic force oriented in the radial direction: 2019 CRAQ Summer School From the sun to the stars

  45. The homopolar generator (2) Consider now the circuit formed by connecting the edge of the disk to the axle by frictionless sliding contacts. The electromotive force in the circuit operates only in the disk, so we can write: As a consequence of this emf, a current will flow through the resistor 2019 CRAQ Summer School From the sun to the stars

  46. The homopolar dynamo (1) Relate current to magnetic flux: Write Ohm’s Law, including now counter-electromotive force: Substituting in mechanical emf: Wrap the wire about the axle prior to connection The current (and field) will grow initially if: 2019 CRAQ Summer School From the sun to the stars

  47. The homopolar dynamo (2) If the field grows, we can wait long enough to reach a time when it exceeds the applied field, which can then be « disconnected »: This ODE has solutions of the form: The current (and magnetic field) will grow exponentially provided that: 2019 CRAQ Summer School From the sun to the stars

  48. The homopolar dynamo (3) Fundamentally, astrophysical dynamos work like this !! 2019 CRAQ Summer School From the sun to the stars

  49. Maxwell’s equations 2019 CRAQ Summer School From the sun to the stars

  50. From Maxwell to MHD (1) Step 1: Drop displacement current to revert to the original form of Ampère’s Law: Step 2: Write down Ohm’s Law in a frame co-moving with the fluid: Step 3: Non-relativistic transformation back to the laboratory frame of reference: 2019 CRAQ Summer School From the sun to the stars

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