Ion Heating in the Solar Corona & Solar Wind

Ion Heating in theSolar Corona & Solar Wind Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics

Outline: • Overview: coronal heating & the solar wind • Ion heating in the wind’s “acceleration region” • Ion heating in the lower corona • Proton vs. electron heating in the heliosphere Ion Heating in theSolar Corona & Solar Wind Steven R. CranmerHarvard-SmithsonianCenter for Astrophysics

Heating is everywhere . . . . . . and everything is in motion Solar plasma: bird’s eye view

Coronal heating • Plasma at 106 K emits most of its photons in the UV and X-ray . . . Coronal hole (open) “Quiet” regions Active regions

waves shocks eddies (“AC”) twisting braiding shear (“DC”) vs. The coronal heating problem • We still do not understand the physical processes responsible for “re-energizing” the coronal plasma. Much of it occurs in a narrow shell above the photosphere. Most suggested ideas involve 3 general steps: β << 1 • Churning convective motions tangle up magnetic fields on the surface. • Energy is stored in the magnetic field (small-scale flux tubes). Timescale?? • Energy is released (irreversibly) as heat, either via collisions or collisionless wave-particle interactions. β ~ 1 β > 1

Wang et al. (2000) Solar wind: connectivity to the corona • 1958:Eugene Parkerproposed that the hot corona provides enough gas pressure to counteract gravity and accelerate a “solar wind.” 1962:Mariner 2 saw it! • High-speed wind (600–800 km/s): strong connections to largest coronal holes. • Low-speed wind (300-500 km/s): no agreement on full range of source regions in the corona: “helmet streamers,” small coronal holes, active regions . . .

Multi-fluid collisionless effects?

Multi-fluid collisionless effects? O+5 O+6 protons electrons

Particles are not in “thermal equilibrium” …especially in the high-speed wind. VA mag. field uα–up Helios at 0.3 AU (e.g., Marsch et al. 1982) Ulysses at 2–4 AU (Reisenfeld et al. 2001) WIND at 1 AU (Collier et al. 1996)

On-disk vs. off-limb observations • On-disk measurements help reveal basal coronal heating & lower boundary conditions for solar wind. • Off-limb measurements (in the solar wind “acceleration region” ) allow dynamic non-equilibrium plasma states to be followed as the asymptotic conditions at 1 AU are gradually established. Occultation is required because extended corona is 5 to 10 orders of magnitude less bright than the disk! Spectroscopy provides detailed plasma diagnostics that imaging alone cannot.

Emission line diagnostics • Off-limb photons can be formed by both collisional excitation/de-excitation and resonant scattering of solar-disk photons. • Net Doppler shifts (from the known “rest wavelength”) indicate the bulk flow speed alongthe line-of-sight. • The widths of profiles tell us about random motions along the line-of-sight (i.e., temperature) • The total intensity (i.e., number of photons) tells us mainly about the density of atoms, but for resonant scattering there’s also another “hidden” Doppler effect that tells us about motions perpendicular to the line-of-sight. “Doppler dimming”

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 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. • 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: lower Z/A faster diffusion

Anisotropic MHD cascade • Where could ion cyclotron waves come from? Possibly a turbulent cascade . . . • Simulations & analytic models predict cascade from small to large k ,leaving k ~unchanged.“Kinetic Alfven waves” with large k do not necessarily have high frequencies.

Anisotropic MHD cascade • Where could ion cyclotron waves come from? Possibly a turbulent cascade . . . • Simulations & analytic models predict cascade from small to large k ,leaving k ~unchanged.“Kinetic Alfven waves” with large k do not necessarily have high frequencies. • In a low-beta plasma, KAWs are Landau-damped, heating electrons, notprotons! • Cranmer & van Ballegooijen (2003) modeled the anisotropic cascade with advection & diffusion in k-space and found somek “leakage.”

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).

r = 1.07 Rs Te Ion temperatures in the low corona • The SUMER spectrometer on the SOHO spacecraft looks directly at the Sun in the UV. • Landi & Cranmer (2009) analyzed SUMER line widths for >20 ions that suggest preferential ion heating at r≈ 1.05 to 1.2 Rs in coronal holes. • We produced & compared 2 independent models: • A semi-empirical ion heating equation with arbitrary normalization for the ion cyclotron wave power. (Each ion is modeled independently of the others.) Normalization varied till agrees with data. • Use the Cranmer & van Ballegooijen (2003, 2005) models of anisotropic turbulence to predict the ion cyclotron wave power at a given height.

Ion temperatures in the low corona • Landi & Cranmer (2009) results for inferred wave power at r= 1.07 Rs • Points correspond to individual ions (color=mass), with wave power for each ion determined from semi-empirical heating model. • Black curves show predictions of wave power vs. frequency from the anisotropic turbulence models of Cranmer & van Ballegooijen (2003, 2005). • Upturn at high frequencies: possibly due to plasma instabilities centered around either alpha (Z/A = 0.5) or proton (Z/A = 1) resonances? (Zhang 2003; Laming 2004; Markovskii 2001; Markovskii et al. 2006)

Proton vs. electron heating: 60 to 1000 Rsun • Helios (0.3–1 AU) and Ulysses (1.5–5 AU) measured Tp, Te, and heat conduction:

B Proton vs. electron heating: 60 to 1000 Rsun • Breech et al. (2009) & Cranmer et al. (2009) took 2 complementary approaches to constraining how the heating is partitioned between the two major species. • If we know temperature gradients, heat conduction fluxes, and Coulomb collision rates, we can solve for empiricalrates of heat input for protons and electrons. • Inner heliosphere: roughly equal heat input for the two species. • Outer heliosphere: ~80% of the heat goes to protons! • Compare with a simple theory for linear damping of Alfvénic wave spectra . . .

Future missions • Solar Probe (going in to ~10 Rs) is finally moving forward after decades of study. • CPEX (Coronal Physics Explorer) currently in Phase A concept study: next-generation UVCS & LASCO, capable of probing dozens of ions in coronal holes at UVCS heights! • More traditional “solar physics” missions (SDO) will put new constraints on physics of reconnection & turbulent heating.

Conclusions • Solar UV spectroscopy has led to fundamentally new views of the collisionless acceleration regions of the solar wind. • Theoretical advances in MHD turbulence continue to “feed back” into models of coronal heating and the solar wind. • The extreme plasma conditions in coronal holes (T ion>> Tp > Te ) have guided us to discard some candidate processes, further investigate others, and have cross-fertilized other areas of plasma physics & astrophysics. • Next-generation observational programs are needed for more conclusive “constraints.” For more information: http://www.cfa.harvard.edu/~scranmer/

Ion Heating in the Solar Corona & Solar Wind