Extended Coronal Heating and Solar Wind Acceleration over the Solar Cycle S. R. Cranmer, J. L. Kohl, M. P. Miralles, & A. A. van Ballegooijen Harvard-Smithsonian Center for Astrophysics
Extended Coronal Heating and Outline: Solar Wind Acceleration over 1. What (and where) can we measure? 2. How do measurements constrain theories? S. R. Cranmer, J. L. Kohl, M. P. Miralles, & A. A. van Ballegooijen the Solar Cycle 3. Ongoing modeling: Waves & the peculiar solar minimum Harvard-Smithsonian Center for Astrophysics
Measurement smörgåsbord Telescopes ( remote sensing ) Solar disk (1 1.5 R s ) vs. coronagraph occultation (~1.? 10 R s ) & eclipses Visible-light continuum: electron density, electron temperature, kinematic motions UV/EUV emission lines: density, charge states, bulk speeds, temperatures, departures from Maxwellian velocity distributions, wave motions EUV/X-ray imaging: emission measure (density, temperature), kinematic speeds, magnetic fields (via coronal seismology) Radio sounding Density fluctuations (scintillations), magnetic field fluctuations (Faraday rotation) In situ detection Magnetic & electric fields: coronal connectivity, reconnection, waves/turbulence Particles (p, e, α, heavy ions): density, charge states, bulk speeds, temperatures, departures from Maxwellian velocity distributions, kinetic instabilities
Solar wind speeds UVCS/SOHO LASCO/SOHO
Temperatures (fast wind) SUMER UVCS wave sloshing removed (model dependent!) in situ
Corona Current minimum vs. 1996 minimum Polar coronal holes: smaller in area ( 15%; Kirk et al. 2009), lower mean polar magnetic field ( 42%; wso.stanford.edu), and more XBPs (Gabriel et al.) UVCS H I Lyα intensities higher, but O VI intensities lower (both possibly consistent with lower T e & n e?); preferential ion heating appears to be relatively unchanged (Gardner et al.; Miralles et al.) More small equatorial coronal holes now; less transverse B-pressure from poles. 1996 2008 Streamer belt: latitude spread is wider. In situ (Tokumaru et al. 2009) Polar fast wind has lower magnetic field ( 18%), lower density ( 17%), lower temperature ( 14%), but is just as fast. (Smith & Balogh 2008; McComas et al. 2008) Heliospheric current sheet is less equatorially confined, but band of slow wind hugs the HCS more tightly now (±8 o ) than before (±20 o ) (Zhao & Fisk)
How do measurements constrain theories? Optimal situation: Observations provide unambiguous measurement X. Theoretical model contains no free parameters, and produces prediction Y. If X=Y (inside error bars), we have new evidence that the theory holds. If X Y (outside error bars), the theory is falsified. The real world is never this simple, but we keep our eyes on the prize. Things to avoid: Inserting theoretical assumptions into primary presentation of observations. Overdetermining theoretical models with too many observationally derived inputs, then claiming victory by comparing with observations. For all examples that I recall, this was completely unintentional!
However, observations can certainly point the way to new theoretical investigations...
Pointing the way (1): coronal connectivity Luhmann et al. (2002) applied the Wang & Sheeley (1990) speed/flux-expansion relation to several solar cycles of PFSS reconstructions. v > 550 km/s 350 < v < 550 km/s v < 350 km/s (see also Nolte et al. 1976; Hick et al. 1995; Liewer et al. 2004; Sakao et al. 2007) MIN MAX Is the physics of coronal heating and (slow) wind acceleration different depending on the source region? hole/streamer boundary (streamer edge ) streamer plasma sheet ( cusp/stalk ) smallest coronal holes active regions
Pointing the way (2): ion cyclotron resonance UVCS/SOHO observations rekindled theoretical efforts to understand heating and acceleration of the plasma in the (collisionless!) acceleration region of the wind. ~ Ion cyclotron waves (10 10,000 Hz) were suggested as a natural energy source that can be tapped to preferentially heat & accelerate heavy ions. How & where are these waves generated? In picoflares at the surface? (inconsistent with radio IPS & damping physics) Gradually over several solar radii? Turbulent cascade: convert low-freq. Alfvén waves into high-freq. waves? Should make waves that want to heat the wrong way? Leakage of power to ion cyclotron modes? Current sheets?
Working from the other direction... What can ab initio theoretical models tell us about why this solar minimum is so different?
An ongoing debate Two broad classes of models have evolved that attempt to self-consistently answer the question: How are fast and slow wind streams accelerated? Wave/Turbulence-Driven (WTD) models Reconnection/Loop-Opening (RLO) models My ramblings: arxiv: 0909.2847 See previous & next talks...
Waves & turbulence in open flux tubes Photospheric flux tubes are shaken by an observed spectrum of horizontal motions. Alfvén waves propagate along the field, and partly reflect back down (non-wkb). Nonlinear couplings allow a (mainly perpendicular) cascade, terminated by damping. Cranmer, van Ballegooijen, & Edgar (2007) computed self-consistent solutions of waves & background one-fluid plasma state along various flux tubes. Only free parameters: waves at photosphere & magnetic field along flux tube.
Results: turbulent heating & acceleration For realistic lower boundary values of turbulence amplitudes & correlation lengths, the resulting coronal heating gives T max ~ 1 2 MK. Varying radial dependence of field strength (B r ~ A 1 ) changes location of the Parker (1958) critical point. Crit. pt. low: most heating occurs above it kinetic energy fast wind! Ulysses SWOOPS Goldstein et al. (1996) Crit. pt. high: most heating occurs below it thermal energy denser and slower wind! (for details, see Cranmer et al. 2007)
The peculiar solar minimum We know the polar magnetic field is lower during the present minimum than it was in 1996. Let s postulate that the photospheric field strength in individual (100 km width, 1.5 kg) flux tubes is unchanged. 1996 1997 WSO polar field strength (low corona) is ~40% lower (http://wso.stanford.edu/polar.html) 2007 2009 Ulysses in situ polar field strength is ~18% lower (Smith & Balogh 2008).
Results: peculiar fast solar wind How do the plasma properties in interplanetary space vary from the 1996 1997 minimum to the present minimum? Fractions given as (new old)/old New magnetic field model was run with same parameters as old model. speed density Temp. Ulysses polar data 03 % 17 % 14 % WTD model output +01 % 22 % 08% v, n, T (output) P gas P dyn 28 % 22 % 21 % 27 % B field (input) (McComas et al. 2008)
Progress towards a module for 3D codes? The problem: To truly test these ideas, it would be nice to insert the coronal heating physics into global 3D simulations! In this model, calculating heating rates requires knowing the degree of non-wkb Alfvén wave reflection along each flux tube. Reflection is nonlocal: Requires CPU-intensive solutions of wave transport equations; one for each wave freq., each flux tube, & each time step. A possible solution? (teaser) It is possible to estimate the reflection, using only local plasma parameters, in various limiting cases (zero freq., infinite freq.) and bridge these limits together. New paper on this (with a FORTRAN heating-rate subroutine included as online-only material) will be submitted to ApJ next week....
SOHO continues to give us a unique perspective on coronal heating and the collisionless acceleration regions of the solar wind. Iterative testing and refininement of theoretical models is ongoing. Conclusions Advances in MHD turbulence feed back into solar wind models, as well as into other areas of plasma physics & astrophysics. For more information: http://www.cfa.harvard.edu/~scranmer/