Applications of MHD Turbulence: from SUMER to Ulysses! Steven R. Cranmer, Harvard-Smithsonian CfA

1. O+5 O+6 protons electrons Polar coronal hole Applications of MHD Turbulence: from SUMER to Ulysses!Steven R. Cranmer, Harvard-Smithsonian CfA

2. (1) Theoretical MHD turbulence models as “illustrative context” for SUMER measurements

3. New SUMER constraints • Landi & Cranmer (2009, arXiv:0810.0018) analyzed a set of SUMER line widths that suggest preferential ion heating at r≈ 1.05 to 1.2 Rs in coronal holes. • We produced and compared two independent models: r = 1.07 Rs Te • Solve a semi-empirical ion heating equation with an arbitrary normalization for ion cyclotron wave power. Each ion is modeled independently of others. Normalization varied till agrees w/ data. (CvB2005 used for: up, ρ, VA, B0) • Use the Cranmer & van Ballegooijen (2003, 2005) models to predict the ion cyclotron wave power spectrum at a given height.

4. Example heating model for O VI • How well do we really know the proton temperature? Vary as free parameter... UVCS constraints SUMER constraints • The yellow/green curves seem to do the best... they imply strong Coulomb collisional coupling at the SUMER heights!

5. Compare all ions at r = 1.069 Rs • Colors: different choices for proton temperature. Black curves: theoretical resonant spectra from Cranmer & van Ballegooijen (2003) advection-diffusion model. y-axis: wave power needed to produce ion heating r = 1.07 Rs

6. Black curves: anisotropic MHD cascade • Can MHD turbulence generate ion cyclotron waves? Many models say no! • 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.

7. Black curves: anisotropic MHD cascade • Can MHD turbulence generate ion cyclotron waves? Many models say no! • 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 preferentially! • Cranmer & van Ballegooijen (2003) modeled the anisotropic cascade with advection & diffusion in k-space and found somek “leakage” . . .

8. An advection-diffusion cascade model • The Cranmer & van Ballegooijen (2003) advection-diffusion equation: • “Critical balance” (Higdon/Goldreich/Sridhar/others) was built into the eqns . . . • Rapid decay to higher k║ is contained in f(x). Cho et al. (2002) examined various functional forms as fits to numerical simulations (not enough dynamic range?). • CvB2003 solved an approximate version of the advection-diffusion eqn to get: • Key parameter: β/γ. van Ballegooijen (1986) argued for β/γ ≈ 1 (random walk)

9. Advection-diffusion cascade results • Taking the anisotropic spectrum and using linear Maxwell-Vlasov dissipation rates, the ratio of proton vs. electron heating can be derived as a function of position in the fast solar wind (using the Cranmer & van Ballegooijen 2005 model):

10. Compare all ions at r = 1.069 Rs • Colors: different choices for proton temperature. Black curves: theoretical resonant spectra from Cranmer & van Ballegooijen (2003) advection-diffusion model. y-axis: wave power needed to produce ion heating r = 1.07 Rs

11. Power increase at large Z/A ? • This is not predicted by simple turbulent cascade models. • If it is real, it might be: • Increased wave power from plasma instabilities that are centered around either the alpha (Z/A = 0.5) or proton (Z/A = 1) resonances (Markovskii 2001; Zhang 2003; Laming 2004; Markovskii et al. 2006) ? • Predicted “spectral flattening” due to oblique propagation and/or compressibility effects in dispersion relation? Harmon & Coles (2005) invoked these effects to model the observed IPS density fluctuation spectra. • A kind of “bottleneck effect” wherein the power piles up near the dissipation scale, due to nonlocal interactions between disparate scales in k-space (Falkovich 1994; Biskamp et al. 1998) ???

12. (2) Proton-electron heat partitioning in the inner solar wind (0.3 to 5 AU)

13. Self-consistent corona/wind models • Cranmer, van Ballegooijen, & Edgar (2007) computed solutions for the waves & background one-fluid plasma state along various flux tubes... going from the photosphere to the heliosphere. • The only free parameters: radial magnetic field & photospheric wave properties. (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!)

14. Cranmer et al. (2007) results T (K) Ulysses SWOOPS Goldstein et al. (1996) reflection coefficient

15. Problem: too hot at Ulysses ? standard (n=1) model rapid-quenching (n=2) model Ulysses Tp

16. Electron heat conduction • At ~1 AU, the modeled T(r) is a balance between adiabatic cooling & collisionless conduction. • We’ve used Hollweg (1974):

17. Empirical energy balance • If these regions really are collisionless, we know (nearly) every term in the proton and electron energy conservation equations . . . • If the radial derivatives can be taken (without the uncertainty being compounded too much!), it is possible to solve for the heating rates Qp and Qe.

18. In situ temperatures (high-speed wind only)

19. Solve for the heating rates!

20. Proton / electron partitioning Very preliminary result: • Inner heliosphere (Helios): well understood with proton-electron equipartition?! • Do protons really gobble up more energy at r > 1 AU ? • Plasma β goes up as r goes up. This gives a similar trend as found by, e.g., Quataert & Gruzinov (1999) for purely linear damping of MHD waves.

21. What to do next? • Qp vs. Qe: Also put limits on partitioning in corona from UVCS & SUMER. • Many of the proposed ion heating mechanisms haven’t really been tested with realistic coronal plasma conditions! (i.e., plasma beta, driving wave amplitudes & frequencies, etc.) • The mechanisms of “parallel cascade” in low-beta plasmas need to be more fully worked out! (the tail that wags the dog?) The CvB (2003) “advection-diffusion” model is a crass local approximation to a truly nonlocal effect. • What about Len Fisk and Nathan Schwadron? Explore relationships between turbulence and reconnection theory! • Better measurements are needed: • both remote and in situ! • (CPEX Phase-A study will be done in • early 2009... Solar Probe Plus • development gearing up soon, too...)

22. Conclusions • UV coronagraph 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 global models of coronal heating and the solar wind. • The extreme plasma conditions in coronal holes (Tion>> 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 conclusive “constraints.” For more information: http://www.cfa.harvard.edu/~scranmer/