Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

Outline: 1. Background: basic ideas about heating & acceleration 2. Corona and solar wind: 3. Chromosphere: acoustic waves & discrete sources? Alfvénic turbulence Ion-cyclotron resonance Steven R. Cranmer Harvard-Smithsonian Center for Astrophysics

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Thanks George CollinsStan OwockiJohn Kohl Colleagues and collaborators: 1990 to present (including Prize Committee!) Experimental physicists who design, build, operate, and calibrate the telescopes and instruments on which we depend.

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 The solar atmosphere Heating is everywhere!

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 The solar wind 1958: Gene Parker proposed that the hot corona provides enough gas pressure to counteract gravity and accelerate a “solar wind.” 1962: Mariner 2 confirmed it! Momentum conservation: To sustain a wind,  /  t = 0, and RHS must be naturally “tuned:” Lambert W function (see Cranmer 2004)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Heating mechanisms A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Heating mechanisms A surplus of proposed ideas? (Mandrini et al. 2000; Aschwanden et al. 2001) Where does the mechanical energy come from? How 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

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 AC versus DC heating? Are they really so very different? Waves cascade into MHD turbulence (eddies), which tends to: Onofri et al. (2006) e.g., Dmitruk et al. (2004) » break up into thin reconnecting sheets on its smallest scales. » accelerate electrons along the field and generate currents. Coronal current sheets are unstable in a variety of ways to growth of turbulent motions which may dominate the energy loss & particle acceleration.

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Outline: 1. Background: basic ideas about heating & acceleration 2. Corona and solar wind: 3. Chromosphere: acoustic waves & discrete sources? Alfvénic turbulence Ion-cyclotron resonance

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 UVCS / SOHO slit field of view: Mirror motions select height Instrument rolls indep. of spacecraft 2 UV channels: LYA & OVI 1 white-light polarimetry channel SOHO (the Solar and Heliospheric Observatory) was launched in Dec with 12 instruments probing solar interior to outer heliosphere. The Ultraviolet Coronagraph Spectrometer (UVCS) measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii. (Kohl et al. 1995) Combines occultation with spectroscopy to reveal the solar wind acceleration region.

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 UVCS results: solar minimum ( ) On-disk profiles: T = 1–3 million K Off-limb profiles: T > 200 million K ! The fastest solar wind flow is expected to come from dim “coronal holes.” In June 1996, the first measurements of heavy ion (e.g., O +5 ) line emission in the extended corona revealed surprisingly wide line profiles...

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 The impact of UVCS UVCS has led to new views of the collisionless nature of solar wind acceleration. Key results include: The fast solar wind becomes supersonic much closer to the Sun (~2 R s ) than previously believed. In coronal holes, heavy ions (e.g., O +5 ) both flow faster and are heated hundreds of times more strongly than protons and electrons, and have anisotropic temperatures. (e.g., Kohl et al. 1997,1998)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 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 to 10,000 Hz) suggested as a natural energy source that can be tapped to preferentially heat & accelerate heavy ions. Dissipation of these waves produces diffusion in velocity space along contours of ~constant energy in the frame moving with wave phase speed: Ion cyclotron waves in the corona lower Z/A faster diffusion

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Where do cyclotron waves come from? (1) Base generation by, e.g., “microflare” reconnection in the lanes that border convection cells (e.g., Axford & McKenzie 1997). Both scenarios have problems... (2) Secondary generation: low-frequency Alfven waves may be converted into cyclotron waves gradually in the corona.

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 “Opaque” cyclotron damping (1) If high-frequency waves originate only at the base of the corona, extended heating “sweeps” across the spectrum. For proton cyclotron resonance (Tu & Marsch 1997):

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 “Opaque” cyclotron damping (2) However, minor ions can damp the waves as well: Something very similar happens to resonance-line photons in winds of O, B, Wolf-Rayet 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.

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 MHD turbulence It is highly likely that somewhere in the outer solar atmosphere the fluctuations become turbulent and cascade from large to small scales: 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., Dmitruk et al. 2002)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 But does turbulence generate cyclotron waves? Preliminary models say “probably not” in the extended corona. (At least not in a straightforward way!) In the corona, “kinetic Alfven waves” with high k heat electrons (T >> T ) when they damp linearly. Nonlinear instabilities that locally generate high-freq. waves (Markovskii 2004)? Coupling with fast-mode waves that do cascade to high-freq. (Chandran 2006)? 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? freq. horiz. wavenumber MHD turbulence cyclotron resonance- like phenomena something else?

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 An Alfvén wave heating model Cranmer & van Ballegooijen (2005) built a model of the global properties of incompressible non-WKB Alfvenic turbulence along an open flux tube. Background plasma properties (density, flow speed, B-field strength) were fixed empirically; wave properties were modeled with virtually no “free” parameters. Lower boundary condition: observed horizontal motions of G-band bright points.

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Inter-granular bright points For the movie, see:

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Inter-granular bright points (close-up) 100–200 km

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Thin tubes merge into supergranular funnels Peter (2001) Tu et al. (2005)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Turbulent heating models Cranmer & van Ballegooijen (2005) solved the wave equations & derived heating rates for a fixed background state. New models: (preliminary!) self-consistent solution of waves & background one- fluid plasma state along a flux tube: photosphere to heliosphere Ingredients: Alfven waves: non-WKB reflection, turbulent damping, wave-pressure acceleration Acoustic waves: shock steepening, TdS & conductive damping, full spectrum, wave-pressure acceleration Rad. losses: transition from optically thick (LTE) to optically thin ( CHIANTI + PANDORA ) Heat conduction: transition from collisional (electron & neutral H) to collisionless “streaming”

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Turbulent heating models For a polar coronal hole flux-tube: Basal acoustic flux: 10 8 erg/cm 2 /s (equiv. “piston” v = 0.3 km/s) Basal Alfvenic perpendicular amplitude: 0.4 km/s Basal turbulent scale: 120 km (G-band bright point size!) T (K) reflection coefficient Transition region is too high (8 Mm instead of 2 Mm), but otherwise not bad...

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Why is the fast/slow wind fast/slow? Several ideas exist; one powerful one relates flux tube expansion to wind speed (Wang & Sheeley 1990). Physically, the geometry determines location of Parker critical point, which determines how the “available” heating affects the plasma: vs. SUBSONIC coronal heating: “puffs up” scale height, draws more particles into wind: M u SUPERSONIC coronal heating: subsonic region is unaffected. Energy flux has nowhere else to go: M same, u Banaszkiewicz et al. (1998)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Why is the fast/slow wind fast/slow? Compare multiple 1D models in solar-minimum flux tubes with Ulysses 1st polar pass (Goldstein et al. 1996):

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Outline: 1. Background: basic ideas about heating & acceleration 2. Corona and solar wind: 3. Chromosphere: acoustic waves & discrete sources? Alfvénic turbulence Ion-cyclotron resonance

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 The “classical” chromosphere Vernazza, Avrett, & Loeser (1981)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Solar convection & surface waves Cool stars with sub-photospheric convection undergo p-mode oscillations: Lighthill (1952) showed how turbulent motions generate acoustic power; more recently generalized to MHD.... The atmosphere is dynamic! Cattaneo et al. (2003) For the movie, see:

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Solar convection & surface waves Cool stars with sub-photospheric convection undergo p-mode oscillations: Lighthill (1952) showed how turbulent motions generate acoustic power; more recently generalized to MHD.... The atmosphere is dynamic!

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Time-dependent models 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...

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Problems with existing models... The time-steady models (both semi-empirical and with “weak-shock theory”) don’t reproduce the observed dynamics. 1D “CS” time-dependent models are too intermittent (too-strong shocks alternate with regions of no heating at all). Obs: Liu (1974) Imax/Icont ~ 0.2 Imax/Imin ~ 4 CS model: Uitenbroek (2002) Imax/Icont ~ 0.8 Imax/Imin ~ 100

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Ingredients of a “better” solution? Acoustic waves from small discrete “sources” in the photosphere (from, e.g., enhanced turbulence in intergranular lanes) High frequencies that are difficult to detect observationally (especially if they belong to ~horizontally propagating waves) Musielak et al. (1994)

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Exploratory study of discrete sources vertical “slab”expanding “cone” f = 10%f = 100% vertical flux energy-balance temperature Cranmer et al. (2006) evolved a simple set of wave/shock energy balance equations in various “non-magnetic” geometries:

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Exploratory study of discrete sources Simulate thermodynamics of cylindrical slabs / discrete sources (all at z=1800 km) Base: v=0.3 km/s Base: v = km/s “CS-like” 1D model “weak-shock” models Base: v each = 0.06 km/s filling = 1% v eff = km/s

Turbulence and Wave Dissipation in the Chromosphere, Corona, and Solar Wind Steven R. Cranmer SPD Annual Meeting, June 27, 2006 Conclusions For more information: Ultraviolet coronagraph spectroscopy has led to fundamentally new views of the acceleration regions of the solar wind. The surprisingly extreme plasma conditions in solar coronal holes (T ion >> T p > T e ) have guided theorists to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics. Future observational programs are needed: More plasma diagnostics Better understanding! next-generation UVCS... with imaging? high-resolution chromospheric T(x,y,z,t)