High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer. Observation of Alfvén Waves in the Solar Corona Steven Tomczyk (HAO/NCAR) In collaboration with Scott McIntosh (HAO/NCAR)

Steven Tomczyk Peiking University 7 June 2011 Solar Variability SOHO/LASCO

Steven Tomczyk Peiking University 7 June 2011 The Corona is a Magnetically Dominated System Magnetic Fields are Responsible for: Solar Variability Space Weather Coronal Heating Solar Wind Acceleration Particle Acceleration Understanding and Prediction Requires Measurement of Coronal Magnetic Fields - Which are Currently Lacking Coronal Magnetism

Steven Tomczyk Peiking University 7 June 2011 TRACE July 14, 1998 Oscillation Amplitude ~100 km/s Coronal Seismology

Steven Tomczyk Peiking University 7 June 2011 Coronal Seismology Impulsively excited, strongly damped oscillations Seen in intensity images from e.g. Trace Standing kink mode waves Application is limited

Steven Tomczyk Peiking University 7 June 2011 Coronal Multi-channel Polarimeter (CoMP) Light Trap Collimating Lens Pre-Filter Wheel Filter/Polarimeter Detector Occulting Disk Re-Imaging Lens Calibration Polarizer Stage Deployed to 20 cm OneShot Coronagraph at NSO Sac Peak Tunable Filter / Polarimeter Coronal Magnetograph

Steven Tomczyk Peiking University 7 June R sun Full FOV Images Stokes I, Q, U, V FeXIII and nm, HeI nm 0.14 nm bandpass 4.5 arcsec/pixel Linear Polarization (Hanle) → POS Magnetic Field Direction (Not Strength) Circular Polarization (Zeeman) → LOS Magnetic Field Strength Doppler Shift → Velocity CoMP Instrument

Steven Tomczyk Peiking University 7 June 2011 a) Intensity, b) LOS velocity, c) Field Azimuth, d) LOS Field Strength, obtained on Oct 31, 2005, 2.5 hour average Sample CoMP Measurements

Steven Tomczyk Peiking University 7 June 2011 Wave Observation Details  Date: 30 Oct  Duration: 8 hours  Spatial Scale: 4.5 arcsec/pixel  Cadence: 28.5 s  FeXIII Emission Line  3 Wavelengths Across Line  Stokes I, Q, U only  2.8 R sun Full Field-of-View EIT 195 FeXII

Steven Tomczyk Peiking University 7 June 2011 Intensity and Velocity Time Series Velocity Amplitude ~0.3 km/s rms

Steven Tomczyk Peiking University 7 June 2011 Power Spectrum

Steven Tomczyk Peiking University 7 June 2011 f f observed p-mode envelope f -7.5 Power Law Slope of -1.5 for Isotropic MHD Turbulence (e.g. Kraichnan, 1965) Power Spectrum

Steven Tomczyk Peiking University 7 June 2011 Wave Propagation Direction Adapted from photospheric/chromospheric phase travel time analysis (e.g. Jefferies, Finsterle, McIntosh). Cross correlate reference pixel with surrounding pixels, Island of correlation gives direction of wave propagation.

Steven Tomczyk Peiking University 7 June 2011 Wave Propagation Direction Subject to 180° and 90° ambiguity

Steven Tomczyk Peiking University 7 June 2011 Correlation with Magnetic Field Direction Waves Propagate Along Magnetic Field Lines Van Vleck Effect 90° Ambiguity in B Field Direction

Steven Tomczyk Peiking University 7 June 2011 Tracing Wave Propagation

Steven Tomczyk Peiking University 7 June 2011 Space-Time Diagram Interpolate Doppler Velocity onto Wave Propagation Track Inward and Outward Wave Propagation is Evident as Upward and Downward Slanted Lines Bottom Top

Steven Tomczyk Peiking University 7 June 2011 Spatio-Temporal Frequency (k-ω) Diagram Phase Speed 650 km/s 2 x More Outward Power Outward and Inward Phase Speeds Same No Dispersion

Steven Tomczyk Peiking University 7 June 2011 Filtered Time Distance Plots

Steven Tomczyk Peiking University 7 June 2011 Phase Speed Determination

Steven Tomczyk Peiking University 7 June 2011 Phase Speed Map Phase Speeds Mm/s Potential for Coronal Seismology

Steven Tomczyk Peiking University 7 June 2011 Phase Speed Map Inward Phase Speeds are more uncertain Seismology is more sensitive than circular polarization

Steven Tomczyk Peiking University 7 June 2011 Inward/Outward Wave Power P out P in Disparity between inward and outward wave power implies strong wave damping OutIn

Steven Tomczyk Peiking University 7 June 2011 Wave Damping Verth, Goosens and Terradas (2010) modeled the variation of CoMP power ratio with frequency and found it to be consistent with Resonant Damping mechanism

Steven Tomczyk Peiking University 7 June 2011 Wave Energy Content F W = ρ  v 2  c ph where ρ is the density and c ph is the wave phase speed. Assuming ρ=2x g and using the measured values of v (~0.3 km/s) and c A gives a flux of the energy propagating in the observed waves of: F W ~ 0.01 Wm -2 Need ~100 Wm -2 to balance the radiative losses of the quiet solar corona. The energy flux can be estimated by:

Steven Tomczyk Peiking University 7 June 2011 Summary  Perturbations seen in velocity, not intensity  Wave propagation is aligned with magnetic field  Phase speeds Mm/s  Power spectrum shows likely origin is photospheric 5-minute oscillations, background consistent with MHD turbulence  The resolved waves do not have enough energy to heat the corona, but unresolved waves may have enough These are Alfvén waves – kink mode variety

Steven Tomczyk Peiking University 7 June 2011 Noise Estimate (Aschwanden, 2004) Then, An uncertainty in the phase speed of 60 km/s, and an electron density of 10 9 cm -3 results in a 1 G magnetic field uncertainty Need n e /σ ne > ~3; CoMP measurements: σ vphase < 50 km/s (3 hours)

Steven Tomczyk Peiking University 7 June 2011 Future Prospects  Doppler imaging with CoMP provides us with an opportunity to greatly widen the application of coronal seismology.  All MHD wave interpretations require knowledge of plasma density. Need to obtain measurements of density to exploit seismology.  Circular polarization (Zeeman) yields LOS B field, waves yield transverse component of B field - Polarization and coronal seismology will provide a powerful constraint on vector coronal magnetic fields.  CoMP now at MLSO obtaining routine coronal wave observations. FeXIII / ratio for density diagnostic.