Solar Wind Origin & Heating 2 Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Logistics 1. Background & history 2. In situ solar wind 3. Radio scintillations 4. Coronal remote-sensing (empirical connections between corona & solar wind) 5. Chromosphere & photosphere 6. Future instrumentation Part 1: ObservationsPart 2: Theory Everything is online at: 1. Photosphere: tip of the iceberg of the convection zone 2. Chromosphere: waves start to propagate and bump into the magnetic field 3. Corona: magnetic field is king; heating still a “problem” 4. “Other” wind acceleration ideas; evolution of waves & turbulence 5. Future directions for theory...? (discussions afterward?)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM The extended solar atmosphere... Heating is everywhere and everything is in motion

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Energy budget overview Photosphere: optical depth ~unity, with radiation dominating heating/cooling: Chromosphere: optically thin, radiation cools the plasma (all photons escape!) Heating is provided “mechanically,” by irreversible damping of kinetic motions Transition region & low corona: complicated balance of radiation, mechanical heating, downward conduction, and upward advection (enthalpy flux) Extended corona: direct heating balances upward advection (adiabatic cooling) Heliosphere: advection (adiabatic cooling) balances outward conduction What sets the temperature?

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Convection excites waves All cool stars with sub-photospheric convection undergo “p-mode” oscillations: Lighthill (1952) showed how turbulent motions generate acoustic power. These ideas have been more recently generalized to MHD... Cattaneo et al. (2003)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Convection excites waves All cool stars with sub-photospheric convection undergo “p-mode” oscillations: Lighthill (1952) showed how turbulent motions generate acoustic power. These ideas have been more recently generalized to MHD...

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Granules and Supergranules

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Inter-granular bright points (close-up) 100–200 km It’s widely believed that the G-band bright points are strong-field (1500 G) flux tubes surrounded by much weaker-field plasma.

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Waves in thin flux tubes splitting/merging torsion longitudinal flow/wave bending (kink-mode wave) Statistics of horizontal BP motions gives power spectrum of “kink-mode” waves. BPs undergo both random walks & intermittent (reconnection?) “jumps:”

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Waves in thin flux tubes splitting/merging torsion longitudinal flow/wave bending (kink-mode wave) Statistics of horizontal BP motions gives power spectrum of “kink-mode” waves. BPs undergo both random walks & intermittent (reconnection?) “jumps:” In reality, it’s not just the “pure” kink mode... (Hasan et al. 2005)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM “Traditional” chromospheric heating Vertically propagating acoustic waves conserve flux (in a static atmosphere): Amplitude eventually reaches V ph and wave-train steepens into a shock-train. Shock entropy losses go into heat; only works for periods < 1–2 minutes… New idea: “Spherical” acoustic wave fronts from discrete “sources” in the photosphere (e.g., enhanced turbulence or bright points in inter-granular lanes) may do the job with longer periods. Bird (1964) ~

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Time-dependent chromospheres? Carlsson & Stein (1992, 1994, 1997, 2002, etc.) produced 1D time-dependent radiation-hydrodynamics simulations of vertical shock propagation and transient chromospheric heating. Wedemeyer et al. (2004) continued to 3D...

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Runaway to the transition region (TR) Whatever the mechanisms for heating, they must be balanced by radiative losses to maintain chromospheric T. Why then isn’t the corona 10 9 K? Downward heat conduction smears out the “peaks,” and the solar wind also “carries” away some kinetic energy. Conduction also steepens the TR to be as thin as it is. When shock strengths “saturate,” heating depends on density only:

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM The coronal heating problem We still don’t understand the physical processes responsible for heating up the coronal plasma. A lot of the heating occurs in a narrow “shell.” Most suggested ideas involve 3 general steps: 1.Churning convective motions that tangle up magnetic fields on the surface. 2.Energy is stored in tiny twisted & braided “magnetic flux tubes.” 3.Collisions between ions and electrons (i.e., friction?) release energy as heat. Heating Solar wind acceleration!

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Coronal heating mechanisms So many ideas, taxonomy is needed! (Mandrini et al. 2000; Aschwanden et al. 2001) Where does the mechanical energy come from? vs.

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Coronal heating mechanisms So many ideas, taxonomy is needed! (Mandrini et al. 2000; Aschwanden et al. 2001) Where does the mechanical energy come from? How rapidly is this energy coupled to the coronal plasma? waves shocks eddies (“AC”) vs. twisting braiding shear (“DC”) vs.

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Coronal heating mechanisms So many ideas, taxonomy is needed! (Mandrini et al. 2000; Aschwanden et al. 2001) Where does the mechanical energy come from? How rapidly is this energy coupled to the coronal plasma? How is the energy dissipated and converted to heat? waves shocks eddies (“AC”) vs. twisting braiding shear (“DC”) vs. reconnectionturbulence interact with inhomog./nonlin. collisions (visc, cond, resist, friction) or collisionless

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Coronal heating mechanisms So many ideas, taxonomy is needed! (Mandrini et al. 2000; Aschwanden et al. 2001) Where does the mechanical energy come from? How rapidly is this energy coupled to the coronal plasma? How is the energy dissipated and converted to heat? waves shocks eddies (“AC”) vs. twisting braiding shear (“DC”) vs. reconnectionturbulence interact with inhomog./nonlin. collisions (visc, cond, resist, friction) or collisionless

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Reconnection in closed loops Models of how coronal heating (F X ) scales with magnetic flux (Φ) are growing more sophisticated... Closed loops: Magnetic reconnection e.g., Longcope & Kankelborg 1999 Gudiksen & Nordlund (2005)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Properties of MHD waves In the absence of a magnetic field, acoustic waves propagate at the sound speed (restoring force is gas pressure)… B-field exerts “magnetic pressure” as well as “magnetic tension” transverse to the field. The characteristic speed of MHD fluctuations is the Alfvén speed… Plasma β = (gas pressure / magnetic pressure) ~ (c s /V A ) 2 “high beta:” fluid motions push the field lines around “low beta:” fluid flows along “frozen in” field lines

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Properties of MHD waves Phase speeds: Alfven, fast, slow mode; ● = sound speed, ● = Alfven speed β = 12β = 2.4β = 0.6β = 1.2β = 0.12 F/S modes damp collisionally in low corona; Alfven modes are least damped. Standard MHD dispersion applies only for frequencies << particle Larmor freq’s. For high freq & low β, Alfven mode → “ion cyclotron;” fast mode → “whistler.”

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Alfvén wave evolution Energy density & flux: Static medium: A(r)A(r)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Alfvén wave evolution Energy density & flux: Static medium: Non-zero wind speed (“wave action conservation”): Alfvén waves also reflect & refract as the background properties change… A(r)A(r)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Ion cyclotron waves in the corona? UVCS observations have rekindled theoretical efforts to understand heating and acceleration of the plasma in the (collisionless?) acceleration region of the wind. Alfven wave’s oscillating E and B fields ion’s Larmor motion around radial B-field Ion cyclotron waves (10–10,000 Hz) suggested as a “natural” energy source that can be tapped to preferentially heat & accelerate heavy ions.

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Ion cyclotron waves in the corona Dissipation of ion cyclotron waves produces diffusion in velocity space along contours of ~constant energy in the frame moving with wave phase speed: lower Z/A faster diffusion

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Where do cyclotron waves come from? Alfvén waves with frequencies > 10 Hz have not yet been observed in the corona or solar wind, but ideas for their origin abound.... (1) Base generation by, e.g., “microflare” reconnection in the lanes that border convection cells (e.g., Axford & McKenzie 1997). Problem: “minor” ions consume base-generated wave energy before it can be absorbed by ions seen by UVCS. (2) Secondary generation: low-frequency Alfvén waves may be converted into cyclotron waves gradually in the corona. Problem: Turbulence produces mainly small-scale eddies in the direction transverse to the field; these don’t have high frequencies!

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Where do cyclotron waves come from? Impulsive plasma micro-instabilities that locally generate high-freq. waves (Markovskii 2004)? Non-linear/non-adiabatic KAW-particle effects (Voitenko & Goossens 2004)? Coupling with fast-mode waves that do cascade to high-freq. (Chandran 2006)? If the corona is filled with thin collisionless shocks, ions can pass through them and aquire gyromotion when the background field changes direction (Lee & Wu 2000)? Collisionless velocity filtration from intrinsically suprathermal velocity distributions (Pierrard et al. 2004)? Larmor “spinup” in dissipation-scale current sheets (Dmitruk et al. 2004)? KAW damping leads to electron beams, further (Langmuir) turbulence, and Debye-scale electron phase space holes, which heat ions perpendicularly via “collisions” (Ergun et al. 1999; Cranmer & van Ballegooijen 2003)? How then are the ions heated & accelerated? MHD turbulence cyclotron resonance- like phenomena something else? We can compute a net heating rate from the cascade, even if we don’t know how the energy gets “partitioned” to the different particle species.

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Turbulence It is highly likely that somewhere in the outer solar atmosphere the fluctuations become turbulent and cascade from large to small scales. The original Kolmogorov (1941) theory of incompressible fluid turbulence describes a constant energy flux from the largest “stirring” scales to the smallest “dissipation” scales. Largest eddies have kinetic energy ~ v 2 and a “turnover” time-scale  =l/v, so the rate of transfer of energy goes as v 2 /  ~ v 3 /l. Dimensional analysis can give the spectrum of energy vs. eddy-wavenumber k: E k ~ k –5/3

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM MHD turbulence: 2 kinds of “anisotropy” With a strong background field, it is easier to mix field lines (perp. to B) than it is to bend them (parallel to B). Also, the energy transport along the field is far from isotropic: Z+Z+ Z–Z– Z–Z– (e.g., Hossain et al. 1995; Matthaeus et al. 1999; Dmitruk et al. 2002)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Open flux tubes: global model 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. (Heinemann & Olbert 1980; Hollweg 1981, 1986; Velli 1993; Matthaeus et al. 1999; Dmitruk et al. 2001, 2002; Cranmer & van Ballegooijen 2003, 2005; Verdini et al. 2005; Oughton et al. 2006; many others!)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Alfvén wave amplitudes: Sun to 1 AU Pure wave-action conservation produces either too much power at 1 AU, or too little in the corona. Turbulence seems to damp and heat at just the right level… Cranmer & van Ballegooijen (2005)

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Solving the Parker solar wind equation Parker (1958) noticed that the equation of motion exhibits a “singular point…” Solution depends on knowing T(r); all equations should be solved simultaneously. Key issue: Is the heating “deposited” above or below the critical point? time-steady; isothermal

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Alfvén wave pressure (“pummeling”) Contours: wind speed at 1 AU (km/s) Just as E/M waves carry momentum and exert pressure on matter, acoustic and MHD waves do work on the gas via similar net stress terms: This works only for an inhomogeneous (radially varying) background plasma. Wave pressure & gas pressure work together to produce high-speed solar wind; each point in this grid represents a solution to the Parker critical pt. eqn. PCHPCH

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM “The kitchen sink” Cranmer, van Ballegooijen, & Edgar (2007) computed self-consistent solutions of waves & background one-fluid plasma state along various flux tubes... going from the photosphere to the heliosphere. (astro-ph/ ) Ingredients: Alfvén waves: non-WKB reflection with full spectrum, turbulent damping, wave-pressure acceleration Acoustic waves: shock steepening, TdS & conductive damping, full spectrum, wave-pressure acceleration Radiative losses: transition from optically thick (LTE) to optically thin ( CHIANTI + PANDORA ) Heat conduction: transition from collisional (electron & neutral H) to collisionless “streaming”

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Polar coronal hole model: it works! Grids of exploratory models led to the optimal choice for lower boundary parameters: Basal acoustic flux: 10 8 erg/cm 2 /s (equivalent “piston” v = 0.3 km/s) Basal Alfvenic perpendicular amplitude: km/s Basal turbulent scale: 75 km (G-band bright point size?) T (K) reflection coefficient Transition region is too high (7 Mm instead of 2 Mm), but otherwise not bad...

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Magnetic flux tubes T (K) reflection coefficient Vary the magnetic field, but keep lower-boundary parameters fixed. “active region” fields

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Fast vs. slow wind emerges naturally The wind speed & density at 1 AU behave mainly as observed. Goldstein et al. (1996) Ulysses SWOOPS Cascade efficiency: n=1 n=2

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Progress toward better understanding Because of the need to determine non-WKB (nonlocal!) reflection coefficients, it may not be easy to insert into global/3D MHD models. Doesn’t specify proton vs. electron heating (they conduct differently!) Does turbulence generate enough ion-cyclotron waves to heat the minor ions? Are there additional (non-photospheric) sources of waves / turbulence / heating for open-field regions? (e.g., flux cancellation events) (B. Welsch et al. 2004) Existing models are not too bad, but...

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Plumes and jets: more reconnection? (Fisk et al. 1999) How much do plumes and jets contribute to the “mean” solar wind? Still debated… Wang (1994, 1998) suggested that small-scale magnetic reconnection events at the coronal base gives rise to plumes. Is this what Hinode/XRT sees? These events may be hotter than mean plasma at the base, but cooler higher up!

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Future directions for theory Generation and nonlinear evolution of the solar wind fluctuation spectra must be understood. Self-consistent kinetic models (from corona to wind) of protons, electrons, & ions are needed. Because these processes interact with one another on a wide range of scales, their impact can only be evaluated when all are included together. There’s a need for “phenomenological” terms that encapsulate what we learn from micro-scale simulations, so that macro-scale modeling can proceed!

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Conclusions More plasma diagnostics Better understanding For more information: The past decade, SOHO (especially UVCS) has led to fundamentally new views of the collisionless acceleration regions of the solar wind. Theoretical advances in MHD turbulence are “feeding back” into global solar wind models. The extreme plasma conditions in coronal holes (T ion >> T p > T e ) have guided us to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics. There’s a lot to do (theory & observation)!

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Extra slides...

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM “Opaque” cyclotron damping (1) If high-frequency waves originate only at the base of the corona, extended heating must “sweep” across the frequency spectrum. For proton cyclotron resonance only (Tu & Marsch 1997):

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM “Opaque” cyclotron damping (2) However, minor ions can damp the waves as well: Something very similar happens to resonance-line photons in winds of super-luminous massive stars! Cranmer (2000, 2001) computed “tau” for >2500 ion species. If cyclotron resonance is indeed the process that energizes high-Z/A ions, the wave power must be replenished continually throughout the extended corona.

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Charge/mass dependence Assuming enough “replenishment” (via, e.g., turbulent cascade?) to counteract local damping, the degree of preferential ion heating depends on the assumed distribution of wave power vs. frequency (or parallel wavenumber): O VI (O +5 ) measurement used to normalize heating rate. Mg X (Mg +9 ) showed a much narrower line profile (despite being so close to O +5 in its charge- to-mass ratio)!

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Future diagnostics: additional ions? For one specific choice of the power-law index, we can also include either: enough “local” damping (depending on “tau”) or enough Coulomb collisions to produce the narrower Mg +9 profile widths... (Cranmer 2002, astro-ph/ )

Solar Wind Origin and Heating 2 Steven Cranmer, June 13, Solar Physics Summer School, Sunspot, NM Aside: two other (non-cyclotron) ideas... Kinetic Alfven waves with nonlinear amplitudes generate E fields that can scatter ions non-adiabatically and heat them perpendicularly (Voitenko & Goossens 2004). If the corona is filled with “thin” MHD shocks, an ion’s upstream v becomes oblique to the downstream field. Some gyro-motion arises before the ion “knows” it! (Lee & Wu 2000).