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Solar and Solar-Terrestrial Physics Physics 363 Time: 3:15-4:45, Tuesday, Thursday Place: Hewlett , room 103 Instructor: Alexander Kosovichev e-mail: [email protected] Phone: 723-7667 Office: Physics and Astrophysics, room 128 URL: http://sun.stanford.edu/~sasha/PHYS363 Grades: bi- weekly assessments + presentations Lecture Plan 1. Jan. 8, Tuesday. Introduction: The Sun as a star. General properties, place in the Hertzsprung-Russell diagram. Distance, mass, radius, luminosity, composition, age, evolution, spectral energy distribution. "Big problems": solar neutrinos, rotation, dynamo, magnetic energy release, coronal heating. 2. Jan. 10, Thursday. Internal structure I. Stellar Scaling Laws. Standard model. Evolution. Nuclear reactions. Equation of state. Radiative transfer. 3. Jan. 15, Tuesday. Internal structure II. Stability. Convective transfer. Nonstandard models. Solar neutrinos, neutrino transitions, MSW effect. 4. Jan. 17, Thursday. Solar oscillations. Observations. Theory of p-, g-, and r-modes. Excitation mechanisms. 5. Jan. 22, Tuesday. Helioseismology I. Variational principle, perturbation theory. Inversions, sound speed and rotation inferences. 6. Jan. 24, Thursday. Helioseismology II. Local-area helioseismology, ringdiagrams, acoustic imaging, time-distance tomography. 7. Jan. 29, Tuesday. Convection. Granulation, supergranulation, giant cells. Blue shift, models. Energy balance. Superadiabatic layer. Rotational and magnetic effects. Numerical simulations. 8. Jan. 31, Thursday. Differential rotation. Observations. Heliographic coordinates. Oblateness, quadrupole moment, test of the general relativity. Rotational history. Models of differential rotation. 9. Feb. 5, Tuesday. Solar MHD. MHD equations, Alfven and magnetoacoustic waves. Instabilities. Shocks. 10. 11. 12. 13. 14. 15. 16. Feb. 7, Thursday. Dynamo The solar cycle, global magnetism. "Magnetic carpet". Mean-field electrodynamics, dynamo models. Feb. 12, Tuesday. Magnetic energy release. Reconnection. Particle acceleration. Observations. Theories of reconnection, current sheets, MHD and plasma instabilities. Acceleration mechanisms. Feb. 14, Thursday. Solar atmosphere. The structure of the solar atmosphere, photosphere, chromosphere, corona. Transition region. Chromospheric network, filaments, prominences, spicules. Feb. 19, Tuesday. Sunspots. Active regions. Flux tubes. Observations. Static models. Flows, Evershed effect. Formation and decay. Theories of emerging flux tubes, magnetic buoyancy. Feb. 21, Thursday. Flares. Observations. Radiation, radio-, X-, and gamma-rays. Energetic particles. Thin- and thick-target models, evaporation, heat conduction. Radiative and MHD shocks. Moreton waves, "sunquakes". Feb. 26, Tuesday. Corona. CME. Observations, eclipses. White light corona, Thompson scattering. Coronal heating, heat conduction. Largescale structure, change with the solar cycle. Coronal mass ejections, shocks. Feb. 28, Thursday. Solar wind. Observations. Expansion, Parker’s model, high- and low-speed wind. Composition, first-ionization potential effect. Sector structure, current sheet. Geomagnetic effects. Space weather. 17. 18. 19. 20. March 4, Tuesday. Space weather. Interaction of solar wind with the Earth's magnetosphere and planets. Geomagnetic effects. Space weather March 6, Thursday. Tools for solar observations I. Solar telescopes. Resolution, MTF, seeing. High resolution telescopes. Spectrographs. March 11, Tuesday. Tools for solar observations II. Measurements of the line shift. Magnetic fields and polarimetry. March 13, Thursday. Tools for solar observations III. Solar space missions: SOHO, TRACE, STEREO, Hinode, SDO. Neutrino telescopes. Books 1. 2. 3. 4. 5. 6. 7. 8. 9. Stix, M. 2002, The Sun: An Introduction, (Berlin: Springer) Cox, A.N., Lingston, W.C., Matthews, M.S., 1991, Solar Interior and Atmosphere (Tucson, University of Arizona) Zirin, H. 1988, Astrophysics of the Sun (Cambridge Univ. Press) Bahcall J.N. 1989, Neutrino Astrophysics (Cambridge Univ. Press) Foukal, P. 1990, Solar Astrophysics (New York: Wiley) Priest, E.R. 1982, Solar Magnetohydrodynamics (Dordrecht: Reidel) Golub, L., and Pasachoff, J.M. 1997, The Solar Corona (Cambridge Univ. Press) Sturrock, P. (ed.) 1986, Physics of the Sun, (Kluwer). Aschwanden, M. J., Physics of the Solar Corona, Springer, 2006 Essay Topics. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. Solar diameter, oblateness and gravitational quadrupole moment Solar neutrino problem. Predictions of the solar cycle. Helioseismic inverse problem for structure. Helioseismic inverse problem for rotation Excitation of solar oscillations. Solar convection and turbulence. Mechanism of differential rotation. Solar tachocline. Magnetic reconnection. MHD shocks and Moreton waves. Dynamo models. Acceleration mechanisms in solar flares. Coronal mass ejections. Mechanisms of coronal heating. Coronal seismology. Acceleration of solar wind. Waves in magnetosphere General Properties of the Sun. Hertzsprung-Russel Diagram. Sun Hertzsprung-Russel Diagram. Numbers in the mainsequence band are stellar masses in units ofcatalog the solar mass. 22,000 stars from Hipparcos Dotted lines correspond to constant radius in units of the solar radius.RW - radiatively driven wind. •1911-13, Ejnar Hertzsprung and Henry Norris Russell independently developed H-R diagram •Horizontal axis - spectral type (or, equivalently, color index or surface temperature) •Vertical axis - absolute magnitude (or luminosity) •Data points define definite regions, suggesting common relationship exists for stars composing region. Each region represents stage in evolution of stars. •The place of a star on the H-R diagram also tells us about its radius, energy generation and transport, periods and growth rates of pulsations, rotation rate, stellar activity, X-ray coronas, etc. •Sun is G2 main-sequence star. Lies roughly in middle of diagram among what are referred to as yellow dwarfs. Overall properties Age 45 109 years 101065 years Mass ( M ) 199 1033 g 103330 g 696 1010 cm 101084 cm Radius ( R ) Mean density 1.4 g cm 3 10015 g cm 3 Mean distance from Earth (AU) 15 1013 cm 101384 cm 274 104 cm s 2 10444 cm s 2 Surface gravity ( g ) Escape velocity 617 107 cm s 1 10779 cm s 1 386 1033 erg s 1 103359 erg s 1 Luminosity ( L ) Equatorial rotation period 26 days 10635 s Angular momentum 17 1048 g cm 2 s 1 104823 g cm 2 s 1 Mass loss rate 1012 g s 1 5785 K Effective temperature ( Te ) 10376 K 1 arc sec 726 km 10786 cm Distance Until recently distances in the solar system were measured by triangulation. More accurate results are obtained by measuring radar echos. In principle, a single measurement of a linear distance between two bodies of the solar system is sufficient to derive all distances between the planets and the Sun. This is because of Kepler’s third law which relates semi-major axes ai and periods Ti for a body m : a 3 GM (1 mM ) 2 2 T 4 The ratios of the semi-major axes of two bodies is: 3 2 a1 T1 1 m1M a T 1 m M 2 2 2 Masses m1 and m2 are determined from the mutual perturbations of planetary orbits. The Sun is not used directly to determine the distance to the Sun, the astronomical unit (AU). Distance - II Kepler’s law Triangulation The light time for 1 AU is: A 499004782 0000006 s The speed of light by definition (since 1983) is c 299792458 m s 1 . 1AU 149597880 2 km Then, The major semi-axis for the Earth is a 1000000036 AU 1496 1013 cm. Linear distances on the Sun are measured in arc sec: 1 726 km at the disk center. The Sun's angular size varies from 31' 27.7" to 32' 31.9" during the course of a year. Sun’s rotation axis is inclined by 7.25 degrees to the ecliptic January 5 February 8 March 7 April 8 May 5 June 5 July 7 August 13 September 8 October 11 November 9 December 7 Figure : Due to the Earth revolution and axis inclination, the position angle of the Sun’s axis is varying all along the sidereal year. The value of this angle is near zero around Earth perihelion and aphelion. The distance of the Sun’s rotational poles from the limb has been exaggerated: at maximum the shift reaches 7°. We can only see the sunspots’ paths as straight lines in early June and December. Mass Once distances are known the Sun’s mass is determined from Kepler’s law. Only the product, GM , is determined with high precision: GM (132712438 000000005) 1026 cm3s2 The gravitation constant is determined in laboratory measurements: G (6672 0004) 108 cm3g 1s2 Therefore, M (19891 00012) 1033 g Mass loss due to the energy radiated into space: 1 dM dt L c2 4 1012 g s Mass loss due to the solar wind: 1012 g s 1 . The total loss during the Sun’s life of 15 1017 s: 75 1029 g (0.04%). Radius The angular diameter is defined as the angular distance between the inflection points of the intensity profile at two opposite limbs. It is measured photoelectrically. Results for the solar radius: apparent angular apparent linear photospheric( 1 ) 1 960"01 0"1 6960 1010 cm (6.9626 0.0007) 1010 cm 2 959"68 0"01 (6.9602 0.00007) 1010 cm 6955 1010 cm 1 Wittman, A. 1977, Astron. Astrophys., 61, 255 2 Brown, T.M. & Christensen-Dalsgaard, J. 1998, ApJ, 500, L195. The current reference 69599 007 Mm. value is: (69599 00007) 1010 cm = Helioseismic estimate of the solar radius from f-mode frequencies: (69568 00003) 1010 cm (Schou, J. et al., 1997, ApJ, 489, L197). The frequencies of the f mode (surface gravity wave) depend only on the horizontal wavenumber k l (l 1)R ( l is the mode angular degree) and surface gravity g GM R 2 : gk GM [l (l 1)]1 2 R3 This allows us to estimate R from the wave dispersion relation, (l ) , and GM . The discrepancies may be related to the poor understanding the upper convective boundary layer of the Sun. The evolutionary change of the solar radius: dR dt 24 cm/year. There is controversial evidence that the solar radius changes with the solar activity cycle. The Sun’s mean density: 1408 g/cm 3 . The gravitational acceleration: g GM R 2 274 104 cm/s 2 . Oblateness Oblateness is defined as ( Requator Rpole ) R RR Origin: rotation + magnetic fields (?). Measurements: even n Rsurf ( ) R 1 rn Pn (cos ) n 2 where Pn are Legendre polynomials. r2 Solar Disk Sextant 1 SOHO/MDI 2 1 2 ( 5810 0400) 106 (5329 0452) 106 r4 ( 417 459) 107 ( 553 040) 107 (1996) ( 141 055) 107 (1997) Lydon, T.J. & Sofia, S. 1996, Phys.Rev.Lett., 76, 177. Kuhn, J. et al. 1998, Nature, 392, 155. Quadrupole moment The gravitational potential: 2 GM R ( r ) P2 ( ) 1 J 2 r r where J 2 is the quadrupole moment. From the equation of hydrostatic equilibrium: 2 R J2 r2 3g where is the Sun’s angular velocity. The first term is almost equal to r2 : 2 R 3g 5625 10 6 . 7 Therefore, J 2 (184 40) 10 . If general relativity describes the advance of perihelion of Mercury, then 4298 004 acrsec/century corresponds to a quadrupole moment (23 31) 107 . Composition The approximate fraction of the mass of the plasma near the surface of the Sun: Element abundance H (hydrogen) He (helium) Li (lithium) Be (beryllium) B (boron) C (carbon) N (nitrogen) O (oxygen) 0735 075 0248 025 155 109 141 1011 200 1010 372 10 4 115 104 676 10 4 Luminosity The solar luminosity, L , is the the total output of electromagnetic energy per unit time. It is measured from space because the Earth’s atmosphere attenuates the solar radiation. L (3845 0006) 1033 erg s The absolute magnitude of the Sun is M 474 (at 10 parsec distance). The Sun’s luminosity increased by 28% over the Sun’s life of about 46 109 years. The total irradiance at 1 AU ("solar constant"): S L 4 A2 1367 2 W/m 2 . Absorption in the Earth’s atmosphere. The edge of the shaded area marks the height where the radiation is reduced to 1/2 of its original strength. UV - ultraviolet; V- visible; IR infrared. Irradiance The total irradiance at 1 AU ("solar constant"): S L 4 A2 1367 2 W/m 2 . The composite total irradiance from 1977 to 1999. Note the variation with the solar activity cycle of order 0.1% Effective temperature The effective temperature is determined by: L 4 R T 2 4 eff where 567032 1011 erg/cm 2 K 4 is the Stefan-Boltzmann constant. Teff 5777 25 K Spectral energy distribution The energy flux, F ( ) , is the emitted energy per unit area, time and wavelength interval. The spectral irradiance: S ( ) F ( ) R 2 (1 AU) 2 Intensity, I ( ) , is the energy emitted per unit area, time, wavelength interval, and sterad. It depends on angular distance from the normal to the surface. F ( ) 2 I ( )cos sin d 0 (check this). The limb-darkening function is I ( ) I (0 ) Solar irradiance spectrum 1 Angstrom = 10-10 m = 10-8 cm = 0.1 nm 1 nm = 10 A 3 million K 1 million K 60,000 K 6,000 K Temperature (K) 10 7 Corona nH 10 6 T 10 5 10 10 14 Transition Region Chromosphere 104 1012 10 10 10 8 3 10 10 16 2 Total Hydrogen Density (cm-3) Temperature & Density Structure of the “Solar Atmosphere” 10 3 10 4 10 5 Height Above Photosphere (km) Visible spectrum The visible spectrum. The upper curve - I (0 ) ; the lower curve F ( ) (intensity averaged over the disk); The smooth curve is a black-body spectrum at T Teff 5557 K. Note the hydrogen H absorption line at 6563 nm. Infrared spectrum About 44% of the energy is emitted above 08 m. The spectrum is approximated by the Reileigh-Jeans relation: S ( ) 2ckT 2 ( R 1 AU) 2 The brightness temperature, TB , is defined by I B (TB ) , where I is the observed absolute intensity, 2h 3 1 B (T ) 2 c exp(hkT ) 1 is the Kirchhoff-Plank function. TB 5000 K at 10 m. The infrared spectral irradiance. Radio spectrum The radio spectrum begins at 1 nm. The energy is often given per unit frequency rather than per unit wavelength. For quiet Sun it continues smoothly from the infrared. Discovered in 1942. Solar radio emission. Dots and solid curve - quiet Sun; dashed - slowly varying component ( s component ); dotted curves - rapid events ( bursts ). Note the transition between 1 cm and 1 m. There is a transition in TB from 104 K to 106 K - transition from the solar chromosphere to corona. UV spectrum UV irradiance. The solid and dashed smooth curves are black-body spectra. Note the sharp decrease at 210 nm due to the ionization of Al I. Absorption lines are mostly above 200 nm. Below 150 nm emission lines dominate the spectrum. The most prominent is the Lyman line at 121.57 nm. The spectrum is highly variable. EUV and X-ray spectrum EUV is below 120 nm. It is highly variable, and characterized by a large number of emission lines from highly ionized atom, e.g. Fe XVI. The range of TB is 6 from 8000 K to 4 10 K. The main source of EUV radiation is the transition region between the chromosphere and corona. Soft X-ray emission is between 0.1 nm and 10 nm. Hard X-rays are below 1 nm. Soft X-ray from GOES satellite Black body radiation Black body spectrum depends only on temperature 3 million K 1 million K 60,000 K 6,000 K Temperature (K) 10 7 Corona nH 10 6 T 10 5 10 10 14 Transition Region Chromosphere 104 1012 10 10 10 8 3 10 10 16 2 Total Hydrogen Density (cm-3) Temperature & Density Structure of the “Solar Atmosphere” 10 3 10 4 10 5 Height Above Photosphere (km) Visible solar spectrum with absorption (Fraunhofer) lines Color indices Color indices are rough characteristics of the spectral energy distribution. 0 0 U B 25 log S ( ) EU ( )d log S ( ) EB ( )d CUB 0 0 B V 25 log S ( ) EB ( )d log S ( ) EV ( )d CBV where EU EV EB are ultraviolet, blue and visible filter functions about 100 nm wide, centered at 365, 440, and 548 nm respectively. Constants CUB and CBV are chosen that both U B and B V are zero for A0-type stars. The Sun has U B 020 and B V 066 . Real-time solar images http://sohowww.nascom.nasa.gov/ http://www.bbso.njit.edu/cgi-bin/LatestImages http://www.raben.com/maps/ White-light Image SOHO/MDI Continuum 6768 A Magnetogram magnetogram H-alpha H-alpha 6563 A Ca II K line Chromosphere Ca II K 3933 A EUV He II 304 Å SOHO EIT He II 304A EUV Fe IX/X 171 Å SOHO EIT Fe IX/X 171 A Fe XII 195 A Fe XV 284 A “Big” problems in solar physics • • • • • • Solar neutrino problem Solar cycle and dynamo Magnetic energy storage and release Particle acceleration Coronal heating Source of solar wind Solar Neutrino Problem Solar cycle and dynamo Magnetic energy storage and release Particle acceleration RHESSI observations of July 23, 2002, flare 00:20-00:40 UT (RED: 12-20 keV, BLUE: 100-150 keV) Coronal heating Source of solar wind "The sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do“ Galileo Galilei