Empirical Testing
of Solar Coronal and
Solar Wind Models
Lauren Woolsey
University of Maryland - College Park (2011)
Mentor: Dr. Leonard Strachan
Introduction
What is the Solar Wind?
* Outflow of particles discovered theoretically in 1958 and experimentally in 1962.
* Two regimes of solar wind  Coronal Holes and Streamer belts?
* Coronal Holes have open field lines, source of fast solar wind.
* Non-thermal heating may be significant factor in wind generation.
Models can help determine mechanisms.
Research Goal:
* Use the thermodynamic MAS model
output to compare synthesized
emission line profiles to those from
UVCS observations.
* In this way, we hope to verify if the
processes used in the model correctly
describe the corona and solar wind.
Image: http://www.mreclipse.com/SEphoto/
TSE1991/image/TSE91-4cmp1w.JPG
Introduction (continued)
Experimental Approach
* Two main types of science activity: theory and experiment
* By comparing models with observations, we can:
a) help to constrain parameters used in theoretical models
b) propose new observations to verify model predictions
* Forward modeling allows for comparison of model with observation. Model
parameters are converted into observables.
* Role of UV spectroscopic observations: Line-of-sight profiles provide estimates
for plasma parameters such as densities, temperatures, and outflow speeds,
which allow energetics to be constrained.
Self-consistent coronal/solar wind models
* The model only takes inputs at the base of the corona
* A change in the magnetic field will alter the plasma
parameters, which then change the field.
SOHO: Our Data Source
* UVCS (Ultraviolet Coronagraph Spectrometer)
~Instrument on SOlar and Heliospheric Observatory
~Spectral lines include H Lyα and O VI 1032 & 1037 Å
LEFT: https://www.cfa.harvard.edu/~scranmer/SSU/soho_inlab_large.gif
RIGHT: http://celebrating200years.noaa.gov/breakthroughs/coronagraph/soho_650.jpg
SOHO: UVCS Synoptic Data
* Exposures at different heights for Lyα and OVI channels
Slit has 360 rows of 7” pixels,
which provides 42’ length.
For Lyα (1216 Å) Observations:
 Spectral Resolution is 0.23 Å
 Spatial Resolution range is
12” x 15” – 24” x 24”
 Hard stop at 270°
At low heights, synoptic fields of
view overlap for full coverage;
higher, there are gaps in the data.
For model comparisons, UVCS
data were interpolated to make a
denser grid.
SOHO: Data Analysis
* Data Analysis Software (DAS) v.40 calibrates raw UVCS
data into physical units
* Gaussian fits to the data determine total intensities and
1/e widths  DATA MAP
At left, Quick Look
image from DAS40.
At Right: H Ly α
Below: O VI lines
MAS: Modeling the Corona
Image: http://www.predsci.com/corona/
jul10eclipse/fl_ec1012_007_terrestrial.jpg
* The model tested is an MHD model of the Corona named
Magnetohydrodynamics Around a Sphere (MAS).
* Developers: J. Linker, Z. Mikić, R. Lionello, P. Riley, N.
Arge, and D. Odstrcil
* One of the more complex
solar wind models
available, but it is only
a one-fluid model (not
physical for a plasma)
* Solves MHD equations for
steady state or
dynamical solutions
n0 = 2 x 1012 cm-3
Relaxation to Steady State
T0 = 20,000 K
From the B-field
Temperature
NSO at Kitt Peak
and radiation loss term
Hch= Hexp+ HQS+ HAR
Q(t) from Athay (1986)
SOLAR WIND
PARAMETERS:
1 – 20 solar radii
MAS: 3D Grid to 1D Line
* For each solar rotation, the model returns 3D arrays
of data for V (shown), Ne, Te, and B, which we
plot at different radii, latitudes, and longitudes.
* UVCS integrates along a specified line
of sight (LOS), model must match.
* Defining a LOS: Polar Angle, Height,
Endpoints
* Once the model data is
defined along a line of
sight, spectral profiles produced with the model
plasma parameters can be compared with the
UVCS observed profiles.
Compare: CORPRO
* CORPRO computes a LOS-integrated spectral profile I(λ)
 At each LOS point, calculate emissivity (ne, v, Te, Tp):
 The total intensity is a sum of these emissivities
 1/e width is fitted directly from integrated profile
* Profiles can be plotted to
get visual comparison
* Model provides a single
value for T, we must
determine its components
Case 1: Assume Tmodel = Te
* Solve Tp by matching Imodel = Iobs
* Electron temperature controls ionization
fraction  N(P) term in total intensity
* Proton Temperature is a “kinetic temperature.”
It controls the 1/e width. However, Tp can
also affect total intensity through Doppler
dimming.
* Tp is determined by adjusting the parameter
until the modeled intensity matches
observed intensity (within data uncertainty)
* 1σ observational error bars may be smaller than
symbols. No model error was provided.
Case 1: Sample Lyα profiles
Streamer at 2.5 Rsun 
 Coronal Hole at 2.5 Rsun
* Tp is reasonable in a streamer
* Tp is unphysical in coronal hole and provides a poor
match to the observations.
*Need a better way to include T in the CORPRO model
for a coronal hole.
Case 2: Assume Tmodel = Tavg
* Goal is to improve the coronal hole (CH)
comparison
* Include non-thermal term in proton temperature:
Tp is a kinetic temperature: ½mv2 = kT
* Most likely source of non-thermal velocity is from
Alfvén waves, which are included in MAS model
Table: Best α value where Imod = Iobs
Tavg = ½(Te + Tp)
Te = α Tavg
Tp = (2 – α) Tavg
Height (Rsun)
Value for α
1.7
1.24 +/- 0.04
2.0
1.98 +/- 0.02
2.25
(2.0) +/- 0.01
Case 2: Results for CH
* For a fixed α, vnt can be determined
using the model for vnt vs. r at right
and B, n, and v parameters from MAS
model to match line widths.
* Non-thermal velocities:
89.8 km/s at 1.7 Rsun
90.3 km/s at 2.0 Rsun
Landi & Cranmer (2009)
Left: Coronal Hole @ 1.7 Rsun; Right: @ 2.0 Rsun
Summary of Results
* STREAMER
★ Generally, the equatorial region (the slow-wind
regime) is well-described by the MAS model when
using case 1 (Tmod = Te).
* CORONAL HOLE
★ Te is increasing at 2 Rsun with no sign of a
turnover below 2.25 Rsun.
★ Non-thermal velocities are roughly 90 km/s for
protons (most UVCS studies focus on OVI ions)
★ With the set of values determined for α and vnt
there is excellent agreement between MAS model
and observations.
* While agreement is good, it is not unique.
Future Work
* Examine the MAS model and other MHD models for
other periods in the solar cycle
* Incorporate the data from O VI to add further
constraints to the model parameters
* Study an active region in the corona to see how
shaped empirical heating function compares to
observations
Recommendations
* MAS model should incorporate separate Te and Tp
parameters (two-fluid physics) in order to be more
physically accurate, or provide a better definition of
which single temperature is calculated.
References
Akinari, N. (2007). Broadening of resonantly scattered ultraviolet emission lines by coronal hole
outflows. ApJ, 660: 1660-1673.
Cranmer et al. (1999). An empirical model of a polar coronal hole at solar minimum. ApJ, 511: 481.
Jacques, S.A. (1977). Momentum and energy transport by waves in the solar atmosphere and solar
wind. ApJ, 215: 942-951.
Kohl et al. (1995). The Ultraviolet Coronagraph Spectrometer for the Solar and Heliospheric
Observatory. Solar Physics, 162(1-2): 313-356.
Landi, E. and Cranmer, S.R. (2009). Ion temperatures in the low solar corona: Polar coronal holes at
solar minimum. ApJ, 691: 794-805.
Lionello, R., J.A. Linker, and Z. Mikić (2009). Multispectral emission of the Sun during the first whole
Sun month: Magnetohydrodynamics simulations. ApJ, 690: 902-912.
Ong et al. (1997). Self-consistent and time-dependent solar wind models. ApJ, 474: L143-L145.
Withbroe, G.L., J.L. Kohl, and H. Weiser (1982). Probing the solar wind acceleration region using
spectroscopic techniques. Space Science Reviews, 33: 17-52.
THANK YOU!
Image: http://map.gsfc.nasa.gov/media/990529/index.html
UVCS Instrument Parameters
* Ly-α channel
Ruling frequency: 2400 l/mm
Angle of incidence α: 12.85°
Angle of diffraction β: 3.98°
Main radius of curvature: 750 mm
Minor radius of curvature: 729.5 mm
Reciprocal Dispersion: 5.54 Å/mm (1st order)
Spectral Bandwidth of pixel: 0.14 Å (1st order)
Spatial width of pixel: 0.025 mm
Image: http://www.chrismadden.co.uk/moon/micro.html
Carrington Rotations
 DATE
LONGITUDE 
* Model takes a base synoptic magnetogram from a full
Carrington Rotation (e.g. from NSO at Kitt Peak)
* One CR represents a full solar rotation from a point
when 0° longitude faces Earth to the next.
Image from http://people.hao.ucar.edu/sgibson/wholesun/DATA/AGU_CORONAL/wsm_195_merid_150_lab.gif
Parameters from Line Width
If absence of non-thermal velocities (e.g. Alfvén waves):
V1/e = c*Δλ1/e/λ0
V1/e = sqrt(2kT/m)
T = (m/2k)*V1/e2 = (mc2/2kλ02)*Δλ1/e2
Lyα 1216 Å from H (m = proton mass)
V1/e = 246.6*Δλ1/e
V1/e = sqrt( T/60.5 )
T = ( 3.68 x 106 ) Δλ1/e2
1032 Å from OVI (m = 16*proton mass)
V1/e = 291*Δλ1/e
V1/e = sqrt( T/965 )
T = ( 81.7 x 106 ) Δλ1/e2
MAS
Model
{n,v,T,B}
CORPRO
Goal is to search for
consistency between
the MAS model and the
UVCS Data by using
Forward Modeling.
UVCS
Data
{ I(rows,col) }
DAS v40
“Modeled”
{ Itot, Δλ1/e }
“Observed”
{ Itot, Δλ1/e }
Data Map
{ I(λ) }