Empirical Testing of Solar Coronal

and Solar Wind Models

Lauren WoolseyUniversity of Maryland - College Park (2011)

Mentor: Dr. Leonard Strachan

IntroductionWhat 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 theprocesses used in the model correctlydescribe 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 modelsb) 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.gifRIGHT: 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 αBelow: O VI lines

MAS: Modeling the Corona

* 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

T0 = 20,000 K

From the B-field

NSO at Kitt Peak

SOLAR WINDPARAMETERS:1 – 20 solar radii

Relaxation to Steady State

and radiation loss term Hch= Hexp+ HQS+

HAR

Q(t) from Athay (1986)

Temperature

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

* 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.

* 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.

Case 1: Sample Lyα profiles

Streamer at 2.5 Rsun

Coronal Hole at 2.5 Rsun

Case 2: Assume Tmodel = Tavg

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

Table: Best α value where Imod = Iobs

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 RsunLandi & 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

* 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.

Recommendations

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!

UVCS Instrument Parameters

* Ly-α channelRuling frequency: 2400 l/mmAngle of incidence α: 12.85°Angle of diffraction β: 3.98°Main radius of curvature: 750 mmMinor radius of curvature: 729.5 mmReciprocal 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

* 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

DATE LONGITUDE

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 = (mc2/2kλ0

2)*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

UVCS Data

{n,v,T,B}

{ I(λ) }

CORPRO

DAS v40

Data Map

{ I(rows,col) }

“Observed”{ Itot, Δλ1/e }

“Modeled”{ Itot, Δλ1/e }

Goal is to search for consistency between the MAS model and the UVCS Data by usingForward Modeling.