Open magnetic structures - Coronal holes and fast solar wind

Transcription

1 Open magnetic structures - Coronal holes and fast solar wind The solar corona over the solar cycle Coronal and interplanetary temperatures Coronal holes and fast solar wind Origin of solar wind in magnetic network Multi-fluid modelling of the solar wind

2 Corona of the active sun 1998 Fe XIV 5303 Å EIT - LASCO C1/C2

3 Solar wind speed and density B outward Polar diagram V Ecliptic Density n R 2 B inward McComas et al., GRL, 25, 1, 1998

4 Electron density in the corona + Current sheet and streamer belt, closed Polar coronal hole, open magnetically Heliocentric distance / R s Guhathakurta and Sittler, 1999, Ap.J., 523, 812 Skylab coronagraph/ulysses in-situ

5 Electron temperature in the corona Streamer belt, closed Coronal hole, open magnetically David et al., A&A 336, L90, 1998 Heliocentric distance SUMER/CDS SOHO

6 Temperature profiles in the corona and fast solar wind SP SO ( Si 7+ ) T i ~ m i /m p T p ( He 2+ ) Corona Solar wind Cranmer et al., Ap.J., 2000; Marsch, 1991

7 Fast solar wind speed profile IPS Ulysses Lyman Doppler dimming mass flux continuity V (km s -1 ) Esser et al., ApJ, 1997 Radial distance / R s

8 Speed profile of the slow solar wind Speed profile as determined from plasma blobs in the wind Parker, 1963 Outflow starts at about 3 R S Radial distance / R S 60 Sheeley et al., Ap.J., 484, 472, 1998 Consistent with Helios data

9 Changing corona and solar wind SOHO/Ulysses North Heliolatitude / degree South McComas et al., 2000 Slow latitude scan (2-5 AU)

10 Solar wind fast and slow streams Helios 1976 Alfvén waves and small-scale structures Marsch, 1991

11 Solar wind stream structure and heliospheric current sheet Parker, 1963 Alfven, 1977

12 Rotation of the sun and corona Schwenn, 1998

13 Rotation of solar corona Fe XIV 5303 Å Time series: 1 image/day (24-hour averages) Rotation periods of coronal features 27.2 days LASCO /SOHO Stenborg et al., 1999 Long-lived coronal patterns exhibit uniform rotation at the equatorial rotation period!

14 Sun s loss of angular momentum carried by the solar wind Induction equation: x (V x B) = 0 --> r (V r B φ - B r V φ ) = - r 0 B 0 Ω 0 r 0 Momentum equation: ρv V φ = 1/4π B B φ --> r (ρ V r V φ - B r B φ ) = 0 L = Ω 0 r A 2 (specific angular momentum) V φ = Ω 0 r (M A 2 (r A /r) 2-1)/(M A 2-1) M A =V r (4πρ) 1/2 /B r Alfvén Machnumber Weber & Davis, ApJ, 148, 217, 1967 Helios: r A = R s

15 (Parker) spiral interplanetary magnetic field rot(e) = rot(vxb) = 0

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17 Solar wind types 1. Fast wind near activity minimum High speed kms -1 Low density 3 cm -3 Low particle flux 2 x 10 8 cm -2 s -1 Helium content 3.6%, stationary Source coronal holes Signatures stationary for long times (weeks!) 2. Slow wind near activity minimum Low speed km s -1 High density 10 cm -3 High particle flux 3.7 x 10 8 cm -2 s -1 Helium content below 2%, highly variable Source helmet streamers near current sheet Signatures sector boundaries embedded Schwenn, 1990

18 Solar wind types 3. Slow wind near activity maximum Similar characteristics as 2., except for Helium content Source Signatures 4%, highly variable active regions and small CHs shock waves, often imbedded 4. Solar ejecta (CMEs), often associated with shocks High speed kms -1 Helium content high, up to 30% Other heavy ions often Fe l6+ ions, in rare cases He + Signatures often magnetic clouds, about 30% of the cases related with erupting prominences Schwenn, 1990

19 Solar wind data from Ulysses Fast flow V n McComas et al., 2000 September 3, September 2, 2000 Latitude: - 65

20 Energetics of the fast solar wind Energy flux at 1 R S : F E = erg cm -2 s -1 Speed beyond 10 R S : V p = ( ) km s -1 Temperatures at 1.1 R s : T e T p K 1 AU: T p = K ; T α = 10 6 K ; T e = K Heavy ions: T i m i / m p T p ; V i - V p = V A γ/(γ-1) 2k B T S = 1/2m p (V 2 + V 2 ) γ=5/3, V =618 kms -1, T S =10 7 K for V p =700 kms -1 -> 5 kev

21 Solar wind models I Assume heat flux, Q e = - κ T e, is free of divergence and thermal equilibrium: T = T p =T e. Heat conduction: κ = κ o T 5/2 and κ o = erg/(cm s K); with T( ) = 0 and T(0) = 10 6 K and for spherical symmetry: 4πr 2 κ(t)dt/dr = const --> T = T 0 (R/r) 2/7 Density: ρ = n p m p +n e m e, quasi-neutrality: n=n p =n e, thermal pressure: p = n p k B T p + n e k B T e, then with hydrostatic equilibrium and p(0) = p 0 : dp/dr = - GMm p n/r 2 p = p 0 exp[ (7GMm p )/(5k B T 0 R) ( (R/r) 5/7-1) ] Problem: p( ) > 0, therefore corona must expand! Chapman, 1957

22 Solar wind models II Density: ρ = n p m p +n e m e, quasi-neutrality: n=n p =n e, ideal-gas thermal pressure: p = n p k B T p + n e k B T e, thermal equilibrium: T = T p =T e, then with hydrodynamic equilibrium: mn p V dv/dr = - dp/dr - GMm p n/r 2 Mass continuity equation: mn p V r 2 = J Assume an isothermal corona, with sound speed c 0 =(k B T 0 /m p ) 1/2, then one has to integrate the DE: [(V/c 0 ) 2-1] dv/v = 2 (1-r c /r) dr/r With the critical radius, r c = GMm p /(2k B T 0 ) = (V /2c 0 ) 2 R, and the escape speed, V = 618 km/s, from the Sun s surface. Parker, 1958

23 Solar wind models III Introduce the sonic Mach number as, M s = V/c 0, then the integral of the DE (C is an integration constant) reads: (M s ) 2 - ln(m s ) 2 = 4 ( ln(r/r c ) + r c /r ) + C For large distances, M s >> 1; and V (ln r) 1/2, and n r -2 /V, reflecting spherical symmetry. Only the wind solution IV, with C=-3, goes through the critical point r c and yields: n -> 0 and thus p -> 0 for r ->. This is Parker s famous solution: the solar wind. Parker, 1958 V, solar breeze; III accretion flow

24 Funnels merging in coronal hole Cranmer and van Ballegoijen, ApJS, 2005 Field lines in (c) are plotted at 2.1 intervals at the solar surface, and thus each pair encompasses 1 2 funnels. Byhring et al., ApJ, 2008

25 On the source regions of the fast solar wind in coronal holes Image: EIT Corona in Fe XII 195 Å at 1.5 M K Hassler et al., Science 283, , 1999 Insert: SUMER Ne VIII 770 Å at K Chromospheric network Doppler shifts Red: down Blue: up Outflow at lanes and junctions

26 Detailed source region polar hole funnel Tu, Zhou, Marsch, et al., SW11, 2005

27 Loops and funnels in equatorial CH Field lines: brown open, and yellow closed Correlation: Field topology and plasma outflow (blue in open field) Wiegelmann, Xia, and Marsch, A&A, 432, L1, 2005

28 Flows and funnels in coronal hole Tu, Zhou, Marsch, et al., Science, 308, 519, 2005

29 Height profiles in funnel flows T / K V / km s Height / M m Height / M m Heating by wave sweeping Steep temperature gradients Critical point at 1 R S Hackenberg, Marsch, Mann, A&A, 360, 1139, 2000

30 Lateral mass and energy supply Sketch to illustrate the scenario of the solar wind origin and mass supply through reconnection. The supergranular convection is the driver of solar wind outflow in coronal funnels. Sizes and shapes of funnels and loops shown are drawn to scale. He, Tu and Marsch, Solar Phys., 2008

31 Modelling of coronal funnel up flow down heat flux He, Tu and Marsch, Solar Phys., 2008 Location of mass and energy supply

32 Fast solar wind acceleration by magnetic flux emergence Fisk et al., JGR 104, 19765, 1999

33 Fluid equations Mass flux: F M = ρ V A ρ = n p m p +n i m i Magnetic flux: F B = B A Total momentum equation: V d/dr V = - 1/ρ d/dr (p + p w ) - GM S /r 2 +a w Thermal pressure: p = n p k B T p + n e k B T e + n i k B T i MHD wave pressure: p w = (δb) 2 /(8π) Kinetic wave acceleration: a w = (ρ p a p + ρ i a i )/ρ Stream/flux-tube cross section: A(r)

34 Magnetic flux tube expansion factor (Banaszkiewicz et al. 1998) TR A(r) ~ B(r) 1 ~ r 2 f(r) Wang & Sheeley (1990) defined the expansion factor f(r) between coronal base and the sourcesurface radius ~2.5 R s. polar coronal holes f 4 equatorial streamers f 9 active regions f 25

35 Model of the fast solar wind N /cm -3 Low density, n 10 8 cm -3, consistent with coronagraph measurements T / K Fast acceleration hot protons, T max 5 M K V (V A ) / km s Radial distance / R S cold electrons small wave temperature, T w McKenzie et al., Geophys. Res. Lett., 24, 2877, 1997

36 Four-fluid model for turbulence driven heating of coronal ions Four-fluid 1-D corona/wind model Quasi-linear heating and acceleration by dispersive ioncyclotron waves Rigid power-law spectra with index: -2 γ -1 No wave absorption Turbulence spectra not self-consistent Preferential heating of heavy ions by waves Hu, Esser & Habbal, JGR, 105, 5093, 2000

37 Coronal line broadenings Limits on Alfvén wave amplitude δv: km/s in solar transition region Wilhelm, Marsch, Dwivedi, Feldman, Space Sci. Rev., 2008

38 Wave-turbulence driven model Cranmer and van Ballegooijen (2005) solved the transport equations for a grid of monochromatic periods (3 s to 3 days), then renormalized using a photospheric power spectrum. One free parameter: base jump amplitude (0 to 5 km/s allowed; ~3 km/s is best) Cranmer 2010

39 Coronal ion temperature profiles He H Wave-driven wind Three-fluid model Ofman, JGR, 2004

40 MHD equations for the 3-D solar wind The dependent variables are ρ, v, B, P, and Є, which is the plasma density, flow velocity in the frame rotating with the Sun, magnetic field, thermal pressure, and the Alfvén wave energy density, respectively. M is the solar mass, Ω the solar angular velocity vector, γ the polytropic index, the time, and r the radial distance. We use P n -γ. L is the wave damping length, and V A the Alfvén velocity. Usmanov et al., JGR 105, 12675, 2000

41 Acceleration of the solar wind Ulysses SWOOPS Goldstein et al. (1996)