Tools for Predicting the Rates of Turbulent Heating for Protons, Electrons, & Heavy Ions in the Solar Wind S. R. Cranmer 1, B. D. G. Chandran 2, and A. A. van Ballegooijen 1 (1) Harvard-Smithsonian CfA, (2) UNH

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 The Sun-heliosphere plasma system

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 The Sun-heliosphere plasma system B O +5 O +6 electrons protons UV spectroscopy: In situ:

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Anisotropic MHD turbulence Can MHD turbulence explain the presence of perpendicular ion heating? Maybe not! k k ? Energy input

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Anisotropic MHD turbulence Can MHD turbulence explain the presence of perpendicular ion heating? Maybe not! Alfvén waves propagate ~freely in the parallel direction (and don’t interact easily with one another), but field lines can “shuffle” in the perpendicular direction. Thus, when the background field is strong, cascade proceeds mainly in the plane perpendicular to field (Strauss 1976; Montgomery 1982). k k Energy input

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Anisotropic MHD turbulence Can MHD turbulence explain the presence of perpendicular ion heating? Maybe not! k k Energy input ion cyclotron waves kinetic Alfvén waves Ω p /V A Ω p /c s In a low-β plasma, cyclotron waves heat ions & protons when they damp, but kinetic Alfvén waves are Landau- damped, heating electrons. Alfvén waves propagate ~freely in the parallel direction (and don’t interact easily with one another), but field lines can “shuffle” in the perpendicular direction. Thus, when the background field is strong, cascade proceeds mainly in the plane perpendicular to field (Strauss 1976; Montgomery 1982).

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 We model the wave transport → cascade → coupling → heating, in fast solar wind. Multi-mode coupling? Fast-mode waves propagate – and cascade – more isotropically than Alfvén waves. Chandran (2005) suggested that Alfvén and fast-mode waves may share energy via nonlinear couplings (AAF, AFF). If coupling is strong enough, some high-frequency fast-mode wave energy may feed back to the Alfvén modes → ion cyclotron! (Jacques 1977) For the Alfvén waves, Q m depends on: Wave reflection: Z + ≠ Z – (Chandran & Hollweg 2009) Turb. correlation length L (obeys its own transport eqn.) Damping rate: turb. cascade visc/cond/Ohm First, we solve radial transport equations for the energy densities (U m ) of the individual Alfvén, fast, and slow mode fluctuations.

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Alfvén, fast, & slow mode waves in fast wind We compute how the A, F, S modes perturb velocity, magnetic field, & density: Free parameters: lower boundary conditions on U m & normalization for corr. length.

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Alfvén, fast, & slow mode waves in fast wind Caveat: changing correlation length (L ~ 1/k outer ) changes collisional damping a lot: 300 km 200 km 130 km L at r = R s : 100 km 50 km 30 km Earlier estimates: 75 km (CvB07) 300 km (CvB05) It’s unlikely for Sun-generated slow-mode waves to survive to large heights, so we ignore them for remainder of this work (see, however, Howes et al. 2011). Our standard model for fast-mode waves is a representative example, not a definitive prediction!

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Model cascade + Alfvén/fast-mode coupling Turbulent cascade modeled as time-steady advection/diffusion in wavenumber space. Dissipation from KAW Landau damping (A) and transit-time damping (F) included. Coupling between A & F modes treated with Chandran (2005) weak turb. timescale. Pure Alfvén mode:Alfvén mode with AAF/AFF coupling:

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Preliminary coupling results We computed heating rates for protons & electrons from Vlasov-Maxwell dispersion. Fast-mode wave power varied up & down from the standard model... Helios & Ulysses

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Preferential heavy ion heating UV spectroscopy provides constraints on Q ion for O +5 ions in the corona... SUMER (Landi & Cranmer 2009); UVCS (Cranmer et al. 1999)

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Conclusions For more information: Advances in MHD turbulence theory continue to help improve our understanding about kinetic particle heating in the corona and solar wind. Our coupling mechanism is only one possibility: see SH43C-1974 (stochastic KAWs), SH43C-1967 (EMIC instability), SH53B-2036 (transit time damping), etc. However, we still do not have complete enough observational constraints to be able to choose between competing theories.

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Extra slides...

CPI is a large-aperture ultraviolet coronagraph spectrometer that has been proposed to be deployed on the International Space Station (ISS). The primary goal of CPI is to identify and characterize the physical processes that heat and accelerate the plasma in the fast and slow solar wind. CPI follows on from the discoveries of UVCS/SOHO, and has unprecedented sensitivity, a wavelength range extending from 25.7 to 126 nm, higher temporal resolution, and the capability to measure line profiles of He II, N V, Ne VII, Ne VIII, Si VIII, S IX, Ar VIII, Ca IX, and Fe X, never before seen in coronal holes above 1.3 solar radii. See white paper at: September 29: NASA selected CPI as an Explorer Mission of Opportunity project to undergo an 11-month Phase A concept study.

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 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 + 2 nd 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:

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 UVCS results: solar minimum ( ) 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... On-disk profiles: T = 1–3 million K Off-limb profiles: T > 200 million K !

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Parameters in the solar wind What wavenumber angles are “filled” by anisotropic Alfvén-wave turbulence in the solar wind? (gray) What is the angle that separates ion/proton heating from electron heating? (purple curve) k k θ Goldreich &Sridhar (1995) electron heating proton & ion heating

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Nonlinear mode coupling? Can Alfvén waves couple with fast-mode waves enough to feed back energy into the high-freq Alfvén waves? Chandran (2005) said maybe... There is observational evidence for compressive (non-Alfvén) waves, too... (e.g., Krishna Prasad et al. 2011)

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Alfvén waves: from photosphere to heliosphere Hinode/SOT G-band bright points SUMER/SOHO Helios & Ulysses UVCS/SOHO Undamped (WKB) waves Damped (non-WKB) waves Cranmer & van Ballegooijen (2005) assembled together much of the existing data on Alfvénic fluctuations:

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 A turbulence-driven solar wind? The measured wave dissipation is consistent with the required coronal heating! A likely scenario is that the Sun produces MHD waves that propagate up open flux tubes, partially reflect back down, and undergo a turbulent cascade until they are damped at small scales, causing heating. Cranmer et al. (2007) explored the wave/turbulence paradigm with self-consistent 1D models, and found a wide range of agreement with observations. Z+Z+ Z–Z– Z–Z– (e.g., Matthaeus et al. 1999) Ulysses

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Cranmer et al. (2007): other results Ulysses SWICS Helios ( AU) Ulysses SWICS ACE/SWEPAM Wang & Sheeley (1990)

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Proton & ion energization (in situ) 0.3–1 AU (Marsch 1991) 1 AU (Collier et al. 1996) B 1 AU (Berger et al. 2011)

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 Wave-particle interactions Alfven wave’s oscillating E and B fields ion’s Larmor motion around radial B-field Parallel-propagating ion cyclotron waves (10–10,000 Hz in the corona) have been suggested as a natural energy source... instabilities dissipation lower q i /m i faster diffusion (e.g., Cranmer 2001)

SH41C-04: Proton, Electron, & Ion HeatingCranmer, Chandran, & van Ballegooijen, Dec. 8, 2011 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 turbulence cascades to small perpendicular scales, the tight 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; Lehe et al. 2009). 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; Cranmer et al. 2012). 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 stochastic wave-particle interactions and heat ions (Voitenko & Goossens 2006; Wu & Yang 2007; Chandran 2010).