Observation of Alfvén Waves
in the Solar Corona
Steven Tomczyk (HAO/NCAR)
In collaboration with
Scott McIntosh (HAO/NCAR)
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.
Solar Variability
SOHO/LASCO
Steven Tomczyk
Peiking University
7 June 2011
Coronal Magnetism
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
Steven Tomczyk
Peiking University
7 June 2011
Coronal Seismology
TRACE July 14, 1998
Steven Tomczyk
Oscillation Amplitude ~100 km/s
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)
Tunable Filter / Polarimeter
Coronal Magnetograph
Calibration Polarizer Stage
Light Trap
Occulting Disk
Collimating Lens
Pre-Filter Wheel
Filter/Polarimeter
Re-Imaging Lens
Detector
Deployed to 20 cm OneShot
Coronagraph at NSO Sac Peak
Steven Tomczyk
Peiking University
7 June 2011
CoMP Instrument
2.8 Rsun Full FOV Images
Stokes I, Q, U, V
FeXIII 1074.7 and 1079.8 nm,
HeI 1083.0 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
Steven Tomczyk
Peiking University
7 June 2011
Sample CoMP Measurements
a) Intensity, b) LOS velocity, c) Field Azimuth, d) LOS Field
Strength, obtained on Oct 31, 2005, 2.5 hour average
Steven Tomczyk
Peiking University
7 June 2011
Wave Observation Details

Date: 30 Oct. 2005

Duration: 8 hours

Spatial Scale: 4.5 arcsec/pixel

Cadence: 28.5 s

FeXIII 1074.7 Emission Line

3 Wavelengths Across Line

Stokes I, Q, U only

2.8 Rsun 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
Power Spectrum
f-1.49
f-1.54
observed p-mode envelope
f-7.5
Power Law Slope of -1.5 for Isotropic MHD Turbulence (e.g. Kraichnan, 1965)
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
Van Vleck Effect
90° Ambiguity in
B Field Direction
Waves Propagate Along Magnetic Field Lines
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
Top
Bottom
Inward and Outward Wave Propagation is Evident
as Upward and Downward Slanted Lines
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 0.3-2 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
In
Pout
Pin
Disparity between inward and outward
wave power implies strong wave damping
Steven Tomczyk
Peiking University
Out
Pout  Pin
Pout  Pin
7 June 2011
Wave Damping
Pout / Pin
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
The energy flux can be estimated by:
FW = ρ v2 cph
where ρ is the density and cph is the wave phase
speed. Assuming ρ=2x10-16 g and using the measured
values of v (~0.3 km/s) and cA gives a flux of the energy
propagating in the observed waves of:
FW ~ 0.01 Wm-2
Need ~100 Wm-2 to balance the radiative
losses of the quiet solar corona.
Steven Tomczyk
Peiking University
7 June 2011
Summary
 Perturbations seen in velocity, not intensity
 Wave propagation is aligned with magnetic field
 Phase speeds 0.3-2 Mm/s
These are Alfvén waves – kink mode variety
 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
Steven Tomczyk
Peiking University
7 June 2011
Noise Estimate
 B   ne
B

  9 3 
vA 
 1210 
4
 20 G   10 cm 
Then,
1/2
(km/s) (Aschwanden, 2004)
1/2
 σ v A   ne

  9 3  (G)
σ B  
 60 km/s   10 cm 
An uncertainty in the phase speed of 60 km/s, and an electron
density of 109 cm-3 results in a 1 G magnetic field uncertainty
Need ne/σne > ~3; CoMP measurements: σvphase < 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 1074.7/1079.8 ratio for density diagnostic.
Steven Tomczyk
Peiking University
7 June 2011