The energetics of the slow solar windThe energetics of the slow solar windLeon Ofman, Catholic University of America, NASA GSFC, Code 612.1,

Greenbelt, MD 20771, USA (Leon.Ofman@gsfc.nasa.gov)

Slow solar wind in streamers

Wave driven fast wind in coronal holes

Introduction

• The solar wind shapes the magnetized plasma environment in which solar magnetic disturbances and charged particles propagate.

• IPS and SOHO observations show that the acceleration of the slow and fast solar wind takes place close to the sun (<10Rs).

• Ulysses observation shows that the fast solar wind is relatively steady, while the slow wind is highly variable, dense (compared to fast wind) and associated with streamers (McComas et al 1997, 2000, 2003).

• Helios and Ulysses observations find Alfvénic fluctuations at 0.3 AU and >1 AU with f-1 spectrum in the range 10-6-10-4Hz and f-5/3 at higher frequencies (Goldstein et al 1995).

• Interplanetary scintillation (IPS) measurements show significant perpendicular velocity fluctuations in the extended corona, a signature of Alfvén waves (Klinglesmith 1997; Canals et al 2002), and rapid acceleration close to the sun (Grall et al 1996).

• SOHO/UVCS observations of minor ions in coronal holes find high temperature anisotropies (T/T||>10) and preferential acceleration of the heavy ions over protons (Kohl et al 1997; Cranmer et al 1998).

• Compositional variations in the solar wind are observed in-situ by Ulysses and ACE, and can be use to constrain the models.

• Low frequency MHD waves, high frequency ion-cyclotron waves, reconnection, particle beams and plasma instabilities were proposed as the sources of energy and momentum of the solar wind.

• Solar B will help to determine the heating by MHD waves and reconnection events that can drive the solar wind.

Abstract: Observations and numerical models show that the slow solar wind is associated with coronal streamers. However, the exact heating and acceleration mechanism of the slow wind is unknown. Moreover, the energization mechanism is likely to be different for electrons, protons, and heavy ions. Some of the main objectives of Solar B is to understand the opening of magnetic field and heating of the coronal plasma that forms the solar wind. Recent results of three-fluid numerical models of the slow solar wind heating and acceleration in coronal streamers are shown. The possible heating mechanisms of electrons, protons, and heavy ions in the slow wind, and the formation of open flux in streamers is discussed. The relation of the numerical results to past observations by SOHO, and Ulysses spacecraft, and future observations with Solar B is discussed.

Conclusions• The solar wind determines the background

magnetized plasma environment in which CME’s, and energetic charged particles propagate.

• Slow wind in streamers, and fast wave driven wind in coronal holes was modeled with the three-fluid code in a self-consistent model, and the different proton and heavy ions (He++, O5+) outflow, density, and temperature profiles are determined.

• The acceleration of the slow and fast solar wind plasma takes place close to the sun (<10Rs).

• The main heat deposition must occur below the sonic point (~2Rs) for the slow solar wind.

• Solar-B’s high spatial, temporal and velocity resolution will enable to determine the role of MHD wave heating and small scale reconnection events in the acceleration region of the slow solar wind.

References• Breen, A. R., A. Canals, R. A. Fallows, P. J. Moran, and M. Kojima: 2002,

`Large-scale structure of the solar wind from interplanetary scintillation measurements during the rising phase of cycle 23'. Advances in Space Research, 29, 379.

• Canals, A., A. R. Breen, L. Ofman, P. J. Moran, and R. A. Fallows: 2002, `Estimating random transverse velocities in the fast solar wind from EISCAT Interplanetary Scintillation measurements'. Annales Geophysicae 20, 1265.

• Cranmer, S.R., Field, G.B., and Kohl, J. L.: 1999, `Spectroscopic Constraints on Models of Ion Cyclotron Resonance Heating in the Polar Solar Corona and High-Speed Solar Wind’, ApJ, 518, 937

• Goldstein, B. E., et al.: 1995, `Properties of magnetohydrodynamic turbulence in the solar wind as observed by Ulysses at high heliographic latitudes'. Geophys. Res. Lett. 22, 3393.

• Grall, R. R., et al.: 1996, `Rapid acceleration of the polar solar wind'. Nature 379, 429.

• Klinglesmith, M.: 1997, `The polar solar wind from 2.5 to 40 solar radii: Results of intensity scintillation measurements'. Ph.D. Thesis, UCSD.

• Kohl, J. L., et al: 1997, `First Results from the SOHO Ultraviolet Coronagraph Spectrometer'. Solar Phys. 175, 613.

• Kojima, M., A. R. Breen, K. Fujiki, K. Hayashi, T. Ohmi, and M. Tokumaru: 2004, `Fast solar wind after the rapid acceleration'. J. Geophys. Res. 109, 4103.

• McComas, D. J., et al.: 2000, `Solar wind observations over Ulysses' first full polar orbit'. J. Geophys. Res. 105, 10419.

• McComas, D.J., et al.: 2003, 'The three-dimensional solar wind around solar maximum’, Geophys. Res. Lett., 30(10), 24-1.

• Ofman, L.: 2000, ‘Source Regions of the Slow Solar Wind in Coronal Streamers’, Geophys. Res. Lett., 27, 2885, 2000.

• Ofman, L.: 2004, `Three-fluid model of the heating and acceleration of the fast solar wind'. J. Geophys. Res. 109, 10.1029/2003JA010221.

• Sheeley, et al.: 1997, ‘Measurements of flow speeds in the corona between 2 and 30Rs’, ApJ, 484, 472.

•The wind is driven self-consistently by the 1/f spectrum of Alfvén waves at 1Rs. The waves dissipate through phase-mixing with viscous, and resistive dissipation.

The slow solar wind is modeled by adding outflowing multi-ion plasma to an initial multipole (potential) field. The model is evolved to steady state, and the streamer with the current-sheet is formed self-consistently.

Figure 8: Three fluid model of the solar wind in streamers with polytropic energy equation (=1.05). The left panels show the radial outflow speed and the right panels show the He++ (top) and protons densities.

Figure 2: The solar wind acceleration and perpendicular fluctuations determined by LASCO and IPS measurements.

Figure 6: The proton velocity and the electron temperature in the solar wind obtained with the three-fluid model (e, p, O5+). The velocity fluctuations due to the Alfvén waves are evident in V, and the compressive fluctuation are evident in Vr. The electron heating is in plume-like structures.

where Zk is the charge number; Ak is the atomic mass number of species k, Euk is the Euler number, Fr is the Froude number, Fk,coul is the Coulomb friction term, Fv is the viscous term, Ckji is the thermal coupling term, Hk and Sk are loss and heating terms, and k=5/3.

The normalized three fluid equations for V<<c, with gravity, resistivity, viscosity, and Coulomb friction, neglecting electron inertia, assuming quasi-neutrality are:

Three-fluid solar wind model

(1)

(4)

(3)

(2)

(5)

Figure 12: The results of thermally conductive three-fluid (e, p, He++) solar wind model in a coronal streamer driven by an empirical heating function.

Figure 5: The driving Alfvén wave spectrum at 1Rs.

Figure 4: Polar plots of solar wind speed as a function of latitude for Ulysses’ first two orbits. Sunspot number (bottom panel) shows that the first orbit occurred through the solar cycle declining phase and minimum while the second orbit spanned solar maximum (McComas et al 2003).

Figure1: The velocity of the slow solar wind (right panel) determined from LASCO observations of ‘blobs’ of coronal material as markers for the slow wind outflow (Sheeley et al 1997).

p

He++O5+

p

p

p

He++

He++

H0p=0.5H0i=12Vd=0.034

H0p=0H0i=12Vd=0.05

H0p=0.5H0i=0.5Vd=0.034

H0p=0.5H0i=10Vd=0.034

Figure 7: Results of 2.5D three fluid model of the fast solar wind in coronal holes. The outflow speed of protons (solid lines) and ions (dashed lines) in the model coronal hole averaged over are shown: (a) preferential (compared to protons) heating of He++; (b) same as (a), but with O5+ as the heavy ions; (c) equal heat input per particle for protons and He++ ions; (d) wave-driven wind accelerated and heated by Alfvén waves with empirical heating for He++ ions only (Ofman 2004).

Self consistent heating

,2

j

Se

,3

4)(

22

21

2

0

ppp

rpr

p

VV

rr

V

r

VrS

,)1( /,0 krkk erS

S

,2

2/5 BB

BTTH kc

Heating Terms

Ohmic heating:

Viscous heating:

Empirical heating:

Heat conduction along field lines:

Typical value of n~10-4.

(6)

(9)

(8)

(7)

Radiative cooling: )(,0 TTHH r (10)

pO5+

r=5Rs

r=1.8Rs

Co-latitude (deg)

r=2.33Rs

180 90135

V (

km/s

)

3f model (Ofman 2000)

UVCS (Strachan et al 2002)

Figure 3: The comparison of 3-fluid model to UVCS observations. The acceleration profile of the O5+ ions across a streamer. UVCS observations are shown on the right, and three-fluid model on the left.

UVCS

(Ofman 2000)

O VI

Ly

Figure 9: The field lines (left panel) and the stream lines for protons and He++ ions

Figure 11: The propagation of the Alfvén wave injected into the streamer at the base of the corona (two left panel), and regions of the currents associated with the wave (right panel).

Figure 10: The cross section of the streamer at 1.49Rs showing the proton and He++ outflow speed (left panel and density variation (right panel)

Discussion•The three fluid models show that the slow wind emerges from streamers, with the outflow along the edges of streamers and the stalk of the streamer.•The heavy ions settle in the core of the streamer. In open field regions the ions are dragged out by the proton flow due to Coulomb friction. This leads to abundance variation of heavy ions across the streamer, as observed by UVCS.•Similar to fast wind, MHD waves are good candidates for heating the slow solar wind protons, and ion-cyclotron waves are likely to heat the heavy ions.•Injection of Alfvén waves into the streamer shows that the core of the open field region can be heated by waves. However, only small fraction of waves reach the stalk of the streamer. These waves may be detected by Solar B.•The heating of heat conductive streamer by waves and with various forms of empirical heating function is currently under study.