Comparing Hertz and SHARP results for the central 20" of M82.

The Hertz result for M82 is 1.0 % at 80 degrees

This is for a position that is within a few arcsec (about 3" E, 2" N) of
the submillimeter centroid of M82.

This is a 3-sigma result (barely).

I was curious to see how this might compare with the SHARP result, so I
attempted to do my own crude average of John's recent results for M82.

I had to include the low-polarization parts of M82 in the average, not
only the 2-sigma detections, so I used his map from May 15th, that shows
all data points regardless of the significance.  Since most points are for
regions where the flux is much lower than the peak, I used only four
points in the average:

- the central point, for which I estimate 1.2% at 75 degrees

- the point just to the West, for which I estimate 0.6% at 110 degrees

- the point just to the East, for which I estimate 1.5% at 50 degrees

- the point one step to the East and one step to the North, for which I
get 2.0% at 75 degrees

The separation between the points is about 10 arcsec, so all these
positions contribute to the flux measured by Hertz.  Since the latter two
points have significantly lower flux, judging from the grey-scale map, I
gave them half the weight of the first two points.

The Stokes' parameters for the four points are, respectively (in percent):

  q     u
-1.04 +0.60
-0.46 -0.39
-0.26 +1.48
-0.35 +1.97

And the weighted average is:

-0.60 +0.65

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Comparision of the two instruments' results:

instrument:     Hertz    SHARP

P:              1.0      0.9
Phi:            80       67
q:              -0.94    -0.60
u:              +0.34    +0.65

The errors in q, u, and P are about 0.3% for Hertz

One could make an estimate of the errors in the SHARP result by 
propagating errors, but I have not tried this.

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