Calculation of mag errors

[Andrew Bennett <andrew.bennett@ns.sympatico.ca>]

Consider a star of MV=12.00 on HVRA2604797,
somewhere near the middle of the image.
It would have an integrated flux of 3321 digits.
Do aperture photometry using 30 pixels.
Properly chosen, these would capture 80.54%
of the flux or 2675 digits.
With a (reciprocal) Gain=2.9, the photon noise
is 2675/Gain = 922 digits^2

The median background level is 1884 digits.
The measured standard deviation of the background
is 28.56 digits
  (I misquoted this figure in a previous post: this value
does include the median sky background.)
                           or a variance of 816 digit^2
Of this, the sky brightness contributes 1884/Gain
= 650 digits^2; the balance of 166 digit^2 is everything
else: dark current noise, electronic noise etc.
The 30 points contribute 30x816 = 24470 digits^2.

If the background is estimated from 400 points, the
variance of the estimate is 816/400 =  2.04 digit^2
This error affects each of the 30 points by the same
amount so the total added variance is 30x30 = 900
times this or 1835 digits^2

Summing:
Star photon noise 922 digits^2
Sky noise 24470 digits^2
Background estimation 1835 digits^2
Total 27228 digits^2

Relative standard deviation 
root(27228)/2675 = 0.06169
Magnitude s.d. = this x 1.0857 = 0.06698 mags

You can move the numbers around by changing
the number of points in the aperture and the number
of points over which the background is estimated
but you can't move them very far!

The values 0.019 to 0.022 mags in the database are wrong.

Andrew Bennett, Avondale Vineyard, NS, Canada