Plasma Unbound:New Insights into Heating the Solar Corona and Accelerating the Solar Wind Steven R. CranmerHarvard-Smithsonian Center for Astrophysics
Outline: 1. Brief historical background 2. Solar wind acceleration: waves vs. reconnection? 3. Successes of wave/turbulence models (1D → 3D) 4. The Young Sun: an accretion-powered stellar wind! Plasma Unbound:New Insights into Heating the Solar Corona and Accelerating the Solar Wind Steven R. CranmerHarvard-Smithsonian Center for Astrophysics
Motivations Solar corona & solar wind: • Space weather can affect satellites, power grids, and astronaut safety. • The Sun’s mass-loss & X-ray history impacted planetary formation and atmospheric erosion. • The Sun is a “laboratory without walls” for many basic processes in physics, at regimes (T, P) inaccessible on Earth! • plasma physics • nuclear physics • non-equilibrium thermodynamics • electromagnetic theory
The extended solar atmosphere Everywhere one looks, the plasma is “out of equilibrium!”
1860–1950: Evidence slowly builds for outflowing magnetized plasma in the solar system: • solar flares aurora, telegraph snafus, geomagnetic “storms” • comet ion tails point anti-sunward (no matter comet’s motion) • 1958: Eugene Parker proposed that the hot corona provides enough gas pressure to counteract gravity and accelerate a “solar wind.” Too-brief history • Total eclipses let us see the vibrant outer solar corona: but what is it? • 1870s: spectrographs pointed at corona: • 1930s: Lines identified as highly ionized ions: Ca+12 , Fe+9 to Fe+13 it’s hot! • Fraunhofer lines (not moon-related) • unknown bright lines
The solar corona • Plasma at 106 K emits most of its spectrum in the UV and X-ray . . . Coronal hole (open) “Quiet” regions Active regions
The coronal heating problem • We still do not 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.Something releases this energy as heat. Particle-particle collisions? Wave-particle interactions? “I think you should be more explicit here in step two.”
A small fraction of magnetic flux is OPEN Peter (2001) Fisk (2005) Tu et al. (2005)
In situ solar wind: properties • Mariner 2 (1962): first direct confirmation of continuous fast & slow solar wind. • Uncertainties about which type is “ambient” persisted because measurements were limited to the ecliptic plane … • 1990s: Ulysses left the ecliptic; provided first 3D view of the wind’s source regions. • 1970s: Helios (0.3–1 AU). 2007: Voyagers @ term. shock. fast slow 300–500 high chaotic all ~equal more low-FIP speed (km/s) density variability temperatures abundances 600–800 low smooth + waves Tion >> Tp > Te photospheric
What processes drive solar wind acceleration? Two broad paradigms have emerged . . . • Wave/Turbulence-Driven (WTD) models, in which flux tubes “stay open” • Reconnection/Loop-Opening (RLO) models, in which mass & energy are injected from closed-field regions. vs. • There’s a natural appeal to the RLO idea, since only a small fraction of the Sun’s magnetic flux is open. Open flux tubes are always near closed loops! • The “magnetic carpet” is continuously evolving and making new connections. • Open-field regions show frequent coronal jets (SOHO, Hinode/XRT).
Waves & turbulence in the photosphere • Helioseismology: direct probe of wave oscillations below the photosphere (via modulations in intensity & Doppler velocity) • How much of that wave energy “leaks” up into the corona & solar wind? Still a topic of vigorous debate! • Measuring horizontal motions of magnetic flux tubes is more difficult . . . but may be more important? splitting/merging torsion 0.1″ longitudinal flow/wave bending (kink-mode wave)
Waves in the corona • Remote sensing provides several direct (and indirect) detection techniques: • Intensity modulations . . . • Motion tracking in images . . . • Doppler shifts . . . • Doppler broadening . . . • Radio sounding . . . SOHO/LASCO (Stenborg & Cobelli 2003)
Waves in the corona • Remote sensing provides several direct (and indirect) detection techniques: • Intensity modulations . . . • Motion tracking in images . . . • Doppler shifts . . . • Doppler broadening . . . • Radio sounding . . . Tomczyk et al. (2007)
Waves in the corona • Remote sensing provides several direct (and indirect) detection techniques: • The Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO has measured plasma properties of protons, ions, and electrons in low-density collisionless regions of the corona (1.5 to 10 solar radii). • Ion cyclotron waves (10–10,000 Hz) have been suggested as a “natural” energy source that can be tapped to preferentially heat & accelerate the heavy ions, as observed.
In situ fluctuations & turbulence • Fourier transform of B(t), v(t), etc., into frequency: f -1 “energy containing range” f -5/3 “inertial range” The inertial range is a “pipeline” for transporting magnetic energy from the large scales to the small scales, where dissipation can occur. Magnetic Power f -3“dissipation range” few hours 0.5 Hz
Waves & turbulence: the big picture • Various observations can be “stitched together” to form a reasonably consistent picture of Alfvénic fluctuations from photosphere to heliosphere . . . • Some kind of damping is needed (e.g., Cranmer & van Ballegooijen 2005)
Turbulent dissipation = coronal heating? • In hydrodynamics, von Kármán, Howarth, & Kolmogorov worked out cascade energy flux via dimensional analysis: • In MHD, cascade is possible only if there are counter-propagating Alfvén waves… (“cascade efficiency”) Z– Z+ • n = 1: an approximate “golden rule” from theory • Caution: this is an order-of-magnitude scaling! (e.g., Pouquet et al. 1976; Dobrowolny et al. 1980; Zhou & Matthaeus 1990; Hossain et al. 1995; Dmitruk et al. 2002; Oughton et al. 2006) Z–
Self-consistent models along a flux tube • 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)
Magnetic flux tubes & expansion factors A(r) ~ B(r)–1 ~ r2 f(r) (Banaszkiewicz et al. 1998) Wang & Sheeley (1990) defined the expansion factor between “coronal base” and the source-surface radius ~2.5 Rs. TR polar coronal holes f ≈ 4 quiescent equ. streamers f ≈ 9 “active regions” f ≈ 25
Results of wave/turbulence models • Cranmer et al. (2007) computed self-consistent solutions for waves & background plasma along flux tubes going from the photosphere to the heliosphere. • Only free parameters:superradial flux tube expansion & photospheric wave properties. (No arbitrary “coronal heating functions” were used.) • Self-consistent coronal heating comes from gradual Alfvén wave reflection & turbulent dissipation. • Mass flux determined by allowing transition region to “float” until energy balance is stable. • Flux-tube geometry determines where Parker’s “critical point” occurs. • Low rcrit: supersonic heating → fast wind • High rcrit: subsonic heating → slow wind (Leer & Holzer 1980; Pneuman 1980)
Cranmer et al. (2007): other results Wang & Sheeley (1990) ACE/SWEPAM ACE/SWEPAM Ulysses SWICS Ulysses SWICS Helios (0.3-0.5 AU)
Where do we go from here? 3D global MHD models Real-time “space weather” predictions? Self-consistent WTD models Z– Z+ Z–
How is wave reflection treated? • At photosphere:empirically-determined frequency spectrum of incompressible transverse motions (from statistics of tracking G-band bright points) • At all larger heights:self-consistent distribution of outward (z–) and inward (z+) Alfvenic wave power, determined by linear non-WKB transport equation: 3e–5 1e –4 3e –4 0.001 0.003 0.01 0.03 0.1 0.3 0.9 “refl. coef” = |z+|/|z–| TR
Reflection in simple limiting cases . . . • Many earlier studies solved these equations numerically (e.g., Heinemann & Olbert 1980; Velli et al. 1989, 1991; Barkhudarov 1991; Cranmer & van Ballegooijen 2005). • As wave frequency ω→ 0, the superposition of inward & outward waves looks like a standing wave pattern: phase shift → 0 • As wave frequency ω→∞, reflection becomes weak . . . phase shift → – π/2 • Cranmer (2010) presented approximate “bridging” relations between these limits to estimate the non-WKB reflection without the need to integrate along flux tubes. • See also Chandran & Hollweg (2009); Verdini et al. (2010) for other approaches!
Results: numerical integration vs. approx. 3e–5 1e –4 3e –4 0.001 0.003 0.01 0.03 0.1 0.3 0.9 “refl. coef” = |z+|/|z–| TR 3e–5 1e –4 3e –4 0.001 0.003 0.01 0.03 0.1 0.3 0.9 ω0
Results: coronal heating rates • Each “row” of the contour plot contributes differently to the total, depending on the power spectrum of Alfven waves . . . Tomczyk & McIntosh (2009) f –5/3 Cranmer & van Ballegooijen (2005) observational constraints on heating rates
How did we get here? • The Young Sun: • Kelvin-Helmholz contraction: An ISMcloud fragment becomes a “protostar;” gravitational energy is converted to heat. • Hayashi track: protostar reaches approx. hydrostatic equilibrium, but slower gravitational contraction continues. Observed as the T Tauri phase. • Henyey track: Tcore reaches ~107 K and hydrogen burning begins to dominate → ZAMS.
T Tauri stars: active accretion & outflows • T Tauri stars exhibit signatures of disk accretion (outer parts), “magnetospheric accretion streams” & X-ray corona (inner parts), and dense(polar?)outflows. • Nearly every observational diagnostic varies in time, sometimes with stellar rotation, but often more irregularly. (Romanova et al. 2007) (Matt & Pudritz 2005, 2008)
Accretion-driven T Tauri winds • Cranmer (2008, 2009) extended the solar wave/turbulence models to the outer atmospheres of young, solar-type stars. • The impact of inhomogeneous “clumps” on the stellar surface generates MHD waves that propagate horizontally (like solar Moreton & EIT waves!). • These “extra” waves input orders of magnitude more energy into a turbulent MHD cascade, and can give rise to stellar winds with dM/dt up to 106 times solar!
Accretion-driven T Tauri winds • Results: wind mass loss rate increases ~similarly with the accretion rate. • For high enough densities, radiative cooling “kills” the coronal heating!
Conclusions • Theoretical advances in MHD turbulence are helping improve our understanding about coronal heating, solar wind acceleration, and other astrophysical environments. • It is becoming easier to include “real physics” in 1D → 2D → 3D models of the complex Sun-heliosphere system. • We still do not have complete enough observational constraintsto be able to choose between competing theories… • but progress on all fronts is being made. vs. For more information: http://www.cfa.harvard.edu/~scranmer/
Results: turbulent heating & acceleration T (K) Ulysses SWOOPS Goldstein et al. (1996) reflection coefficient
Results: flux tubes & critical points • Wind speed is ~anticorrelated with flux-tube expansion & height of critical point. Cascade efficiency: n=1 n=2 rcrit rmax (where T=Tmax)
Results: heavy ion properties • Frozen-in charge states • FIP effect (using Laming’s 2004 theory) Ulysses SWICS Cranmer et al. (2007)
Results: in situ turbulence • To compare modeled wave amplitudes with in-situ fluctuations, knowledge about the spectrum is needed . . . • “e+”: (in km2 s–2 Hz–1 ) defined as the Z– energy density at 0.4 AU, between 10–4 and 2 x 10–4 Hz, using measured spectra to compute fraction in this band. Helios (0.3–0.5 AU) Tu et al. (1992) Cranmer et al. (2007)
B ≈ 1500 G (universal?) f ≈ 0.002–0.1 B ≈ f B , . . . . . . • Thus, . . . and since Q/Q ≈ B/B , the turbulent heating in the low corona scales directly with the mean magnetic flux density there (e.g., Pevtsov et al. 2003; Schwadron et al. 2006; Kojima et al. 2007; Schwadron & McComas 2008). Results: scaling with magnetic flux density • Mean field strength in low corona: • If the regions below the merging height can be treated with approximations from “thin flux tube theory,” then: B ~ ρ1/2 Z± ~ ρ–1/4 L┴ ~ B–1/2
Results: solar wind “entropy” • Pagel et al. (2004) found ln(T/nγ–1) (at 1 AU) to be strongly correlated with both wind speed and the O7+/O6+ charge state ratio. (empirical γ = 1.5) • The Cranmer et al. (2007) models (black points) do a reasonably good job of reproducing ACE/SWEPAM entropy data (blue). • Because entropy should be conserved in the absence of significant heating, the quantity measured at 1 AU may be a long-distance “proxy” for the near-Sun locations of strong coronal heating.
X The need for extended heating • The basal coronal heating problem is not yet solved, but the field seems to be “homing in on” the interplay between emerging flux, reconnection, turbulence, and helicity (shear/twist). • Above ~2 Rs, some other kind of energy deposition is needed in order to . . . • accelerate the fast solar wind (without artificially boosting mass loss and peak Te), • produce the proton/electron temperatures seen in situ (also magnetic moment!), • produce the strong preferential heating and temperature anisotropy of ions (in the wind’s acceleration region) seen with UV spectroscopy.
Multi-fluid collisionless effects! O+5 O+6 protons electrons coronal holes / fast wind (effects also present in slow wind)
Mirror motions select height • UVCS “rolls” independently of spacecraft • 2 UV channels: • 1 white-light polarimetry channel LYA (120–135 nm) OVI (95–120 nm + 2nd ord.) The UVCS instrument on SOHO • 1979–1995: Rocket flights and Shuttle-deployed Spartan 201 laid groundwork. • 1996–present: The Ultraviolet Coronagraph Spectrometer (UVCS) measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii. • Combines “occultation” with spectroscopy to reveal the solar wind acceleration region! slit field of view:
On-disk profiles: T = 1–3 million K Off-limb profiles: T > 200 million K ! UVCS results: solar minimum (1996-1997) • The Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO measures plasma properties of coronal protons, ions, and electrons between 1.5 and 10 solar radii. • In June 1996, the first measurements of heavy ion (e.g., O+5) line emission in the extended corona revealed surprisingly wide line profiles . . .
Coronal holes: the impact of UVCS UVCS/SOHO has led to new views of the acceleration regions of the solar wind. Key results include: • The fast solar wind becomes supersonic much closer to the Sun (~2 Rs) 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. 1998, 2006)
Alfven wave’s oscillating E and B fields ion’s Larmor motion around radial B-field Preferential ion heating & acceleration • UVCS observations have 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) suggested as a “natural” energy source that can be tapped to preferentially heat & accelerate heavy ions. lower Z/A faster diffusion
Evidence for ion cyclotron resonance Indirect: • UVCS (and SUMER) remote-sensing data • Helios (0.3–1 AU) proton velocity distributions (Tu & Marsch 2002) • Wind (1 AU): more-than-mass-proportional heating (Collier et al. 1996) (more) Direct: • Leamon et al. (1998): at ω≈Ωp, magnetic helicity shows deficit of proton-resonant waves in “diffusion range,” indicative of cyclotron absorption. • Jian, Russell, et al. (2009) : STEREO shows isolated bursts of ~monochromatic waves with ω≈ 0.1–1 Ωp
Can turbulence preferentially heat ions? If turbulent cascade doesn’t generate the “right” kinds of waves directly, the question remains:How are the ions heated and accelerated? • When MHD turbulence cascades to small perpendicular scales, the small-scale shearing motions may be able to generate ion cyclotron waves (Markovskii et al. 2006). • Dissipation-scale current sheets may preferentially spin up ions (Dmitruk et al. 2004). • If MHD turbulence exists for both Alfvén and fast-mode waves, the two types of waves can nonlinearly couple with one another to produce high-frequency ion cyclotron waves (Chandran 2005). • If nanoflare-like reconnection events in the low corona are frequent enough, they may fill the extended corona with electron beams that would become unstable and produce ion cyclotron waves (Markovskii 2007). • If kinetic Alfvén waves reach large enough amplitudes, they can damp via wave-particle interactions and heat ions (Voitenko & Goossens 2006; Wu & Yang 2007). • Kinetic Alfvén wave damping in the extended corona could lead to electron beams, Langmuir turbulence, and Debye-scale electron phase space holes which could heat ions perpendicularly (Matthaeus et al. 2003; Cranmer & van Ballegooijen 2003).