DATE: January 16, 2013    NOTES BY: Joan Burkepile   iguana@ucar.edu

Explanation of polarization brightness and Ne/cm^2  plots produced for Sept 15, 2009
The plots are produced using code that makes these assumptions about the composition and 3D structure of the corona:

1) assumes all material is in the plane-of-sky
2) assumes fully ionized hydrogen with a mix of 90% hydrogen and 10% helium (by number).

Assumption 1) produces a LOWER LIMIT to the derived mass and density estimates.

The code produces plots of electron number per area (Ne/cm^2) and assumes nothing about the integration path length.
In order to get the density the user must apply a LOS path length.
I have estimated a path length at a given coronal height based on the Thomson scattering function of
polarization brightness (see Hundhausen 1993 Appendix A, Fig A3). Most of the electrons that produce
the polarization brightness (via scattering of photospheric photons) lie within -/+ 25 degrees of the solar 
limb. Therefore I have chosen a 50 degree path length. I then simply compute:
Path length =   50./360. *  2*pi*(r+R) 
  where r = height above limb; R = radius of Sun (R = 6.96 x 10^10 cm)

Path Length   Height above limb
1.1x10^10 cm   1.15
1.2x10^10 cm   1.25
1.44x10^10 cm  1.50
1.67x10^10 cm  1.75
1.95x10^10 cm  2.00
2.22x10^10 cm  2.25
2.5x10^10 cm   2.5

YOU NEED TO DIVIDE THE NUMBER Ne/cm^2  BY THE PATH LENGTH TO GET DENSITY
You then get densities that range from close to 10^9 at 1.15 solar radii in the west limb helmet (brightest structure)
to 10^6 and lower (noise level) at large heights and over the poles.

REFERENCE:

Hundhausen, A.J., 1993, 'Sizes and locations of coronal mass ejections: SMM Observations from 1980 and 1984-1989, J. Geophys. Res.
V 98, pp 13177-13200