1. Yao Chen School of Earth and Space Sciences Univ. of Sci. and Tech. of China Theoretical studies on heavy ions in the slow wind from quiescent-streamer edges

2. Outline 1.Basic elements in modeling the slow wind from quiescent streamer edges coronal source geometry heating mechanism observational constraint 2. Numerical results 3. summary/discussions

3. (1) coronal sources/origins of the slow wind? associated with the bright streamer belt around solar minimum (e.g., Feldman et al., 1981; Gosling 1981; Habbal et al. 1997; Raymond et al. 1997 ……) during active phases: small coronal holes & active regions (e.g. Nolte et al. 1995; Neugebauer et al., 1998; Hick et al., 1995 ……) From McComas et al., 2003 GRL Ulysses + LASCO C2+ HAO Mauna Loa +EIT

4. slow wind sources/origins at solar min.? Wang et al., JGR, 2000 Noci et al., 1997 Footpoint diffusion model Fisk et al., 1998, SSR somehow associated with the bright streamer belt from the open lines surrounding the streamer released from the closed lines after reconnections with approaching open lines at the streamer-hole boundary from the open lines in between a few isolated sub-streamers

5. Simple streamer diagram with labeled structures (Uzzo et al., ApJ, 2006): current sheet, streamer cusp, streamer core (closed), stalk, edges (legs), (2) Geometry of the slow wind from streamer edges (edges)

6. (2.1) Observational indication on the tube geometry of the slow wind: Anticorrelation between the solar wind speed at 1AU and the expansion rate at the source surface (2.5 solar radii) (Levine et al., 1977; Wang and Sheeley, 1990)  the slow wind undergoes the most dramatic expansion/divergence near the source surface  in line with 2d sw models for self-consistent calculations of the tube geometry

7. (2.2) Self-consistent calculations of wind geometries Heliocentric distance Fast wind Slow wind Fast wind: monotonic expansion rate Slow wind from streamer edges: non-monotonic expansion rate with the most dramatic expansion near the cusp point Two-d MHD model for the solar wind (Hu et al., JGR 2003) Magnetic topology Expansion factors

8. (2.3)Mathematical description of the 1d slow wind geometry f 1 : Kopp & Holzer, 1976 f : Chen & Li, 2004, ApJL r c : altitude of the cusp ω  f max : distance to the current sheet r 2 : width of fast divergence & convergence region Two-d calcul. Fast wind Slow wind Expansion factor r (Solar radii) fmax (w) rcrc

9.  T O >T p, T perp >T para (Strachan et al., 02; Frazin et al.,03, ApJ) Latitudinal distribution at 2.33 Solar Radii (Strachan et al., 02)  the dominant processes that heat the ions in the coronal holes and fast wind may also be important in the slow wind from streamers (cyc. resonance?) In coronal holes and fast wind  ion cyclotron resonance (Kohl et al., 98; Tu et al., 98; Marsch, 81; Hollweg & Isenberg,02 … ) (3) Heating mechanism slow wind from str. edges fast wind from polar holes

10. Ion-cyclotron resonance as a driving mechanism (Hollweg & Isenberg, 2002, a review paper) Alfvenic turbulence cascade  cyclotron waves (Hollweg, 1986; Isenberg,1990 … ) This study is an extension of previous fast wind models (Hu et al., 1999; Li et al., 2002...) To determine the resonant heating and acceleration rates, the Kolmogorov turbulence cascade Quasi-linear theory of the wave-particle interaction Cold plasma approx. of the wave dispersion relation The power-law index of the cyclotron-wave spectra: -2, turbulence level < 30 km/s (25 km/s) at the coronal base (3) Heating mechanism

11. Basic elements: (1) observational constraints mainly from UVCS (2) geometry: non-monotonic expansion rate (3) Boundary conditions at the coronal base: Dense (n ~ 2 - 3 X10 8 cm -3 ) hot ( T~ 1.2 – 1.3 MK) (4) Heating mechanism: UVCS observations on O 5+ ions  ion cyclotron resonance Theoretical studies on heavy ions in the slow wind from quiescent-streamer edges

12. Quiescent Streamer: Red crosses: Uzzo, 2006 (April 2003) Equatorial streamer around sol. min. Error bars: Strachan, 2002 Blue squares (velocity): Frazin 2003 Blue diamonds: Kohl et al., 1997 Proton effective temperature: Red triangles: Uzzo et al., 2006 Black pluses: Strachan et al., 2002 Density (cm -3 )Velocity (km s -1 ) protons O 5+ protons O 5+ Effective Temp. (K) protons O 5+ electrons (thermal T) Velocity dip Results

13. Proton velocity (km s -1 ) Wang et al., 2000, JGR Comparison with the LASCO measurements of the velocities of the plasma blobs emitted from streamer cusps (  the bulk speed of the slow wind from streamer edges) Sonic point: 4 - 5Rs

14. Ion abundance (n i / n p ) Time to flight (hours) protons O 5+ Local abundance enhancement of O5+ ions 3 – 4 X10 -5  0.6X10 -5 Abundance at the base: 10 -5 Steady-state slow wind?: Necessary condition for steady slow wind from streamer edges: long-lived quiescent streamer (lasting for days)

15. Even the ratio of heating rates is much larger than the mass proportionality, Coulomb collisions are frequent enough to sustain a lower temperature ratio  declining trend of the ratio  in line with the in-situ measurements. Ratio of heating rates per partile Temperature ratio Mass proportionality

16. Dynamics of O5+ ions: 1–2 Rs: accelerated by protons 2–4 Rs: stagnated outflow r >4 Rs: accelerated by the thermal pressure  observed velocity jump Forces (10 -20 dyn) Gravitational force Collisional force -▽p-▽p Velocity (km s -1 ) protons O 5+ Dynamical cause for the formation Of the velocity dip of O5+ ions: gravitational settling (1)Collisional force decreases faster than the gravity (2)Heating in the slow wind is not fast enough (compared with collisions)  lower temperature  weaker driving force

17. Ions with the lowest charge-mass ratio : O 5+ Ion cyclotron resonance heating  the lower the q/m  the higher the temperature, the larger the eventual speed of the ions Solutions for ions with different charge (left) and mass (right) Velocity (km s -1 ) Thermal Temp. (K) Velocity (km s -1 )

18. Local enhancement of the Helium abundance, (e.g. Burgi 92; Hansteen et al., 97) Abundance at the base: 6%, max.: 9%, at 10 Rs: ~ 3% Helium abundance Ratio of heating rates per particle Temperature ratio Velocity (km s -1 ) protons He 2+ Effective Temp. (K) protons He 2+ electrons (thermal T) Solution for alpha particles

19. r c : altitude of the cusp, w: distance to the neutral sheet  a lower cusp or closer to the current sheet  smaller velocity minimum, larger abundance maximum Solutions to check the effect of geometry on the wind r c =3 v.s. r c =2 w=3 w=3 v.s. w=1 r c =3 Lower cusp Closer to the c.s. Ion abundance (n i / n p ) Velocity (km s -1 )

20. Summary/Discussions: 3-fluid model for the slow wind from streamer edges driven by Alfvenic turbulence and cyclotron resonance: (References: Chen et al., 2004 ApJ; Chen & Li, ApJL; Chen, ASR, 2005) (1) Elemental abundances vary significantly with altitudes:  keep in mind when making connections between the suspected coronal source & in-situ sw observ. with abundance measurements O 5+ ions

21. (2) velocity dip < than the observ. resolution (30 km s -1 ). Necessary conditions for a steady slow wind: long- lived quiescent streamer (>several days) (3) lower cusp.or. closer to the current sheet  more apparent velocity dips and local abundance enhancements. Velocity (km s -1 ) protons O 5+

22. Thanks!

23. (4) The expansion rate varies dramatically in the slow wind region  contribute to the large variation of the slow wind observed in-situ. Heliocentric distance Fast wind Slow wind Expansion factors

24. (5) Bifurcated streamer morphology? HI Lya OVI 1032/1038A Attributed to projection effect? (Vasquez et al., 2003) Replenishing mechanism of O5+ ions in the core? Ion transition across the field lines by non-ideal MHD processes (Ofman, 2000) Heating inside? Non-steady effect Multipolar nature of the large scale streamer field? (e.g., Noci et al., 1997) Raymond et al., 1997

25. Solutions with different exponential heating functions

26. Alfven speed and sound speed

28. Temperature (K) Heating rates per particle (ergs s -1 ) protons O 5+ protons O 5+ Time scales Collisional Heating Adiabatic cooling Ratio of Heating rates >m i /m p Ratio of Temperatures<m i /m p

29. Heating rates per particle (ergs s -1 ) protons O 5+