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Should transforming magnitudes reduce error?

woodblock
Affiliation
American Association of Variable Star Observers (AAVSO)
Wed, 04/14/2021 - 15:39

In an attempt to check my methods I picked 5 reference stars from the chart for V0398 uma. Then I picked one of those stars as a test star and calculated it's magnitude against each of the remaining reference stars to give me 4 x V magnitudes. The untransformed magnitudes came out roughly right with a SD of 0.05. Not very good I know. I was expecting that when I added in the transform values it would be better but actually it came out a lot worse SD = 0.3

Would you expect that transforming the magnitudes to improve the accuracy?

The catalogue V magnitude of the test star is 11.601. The average of my untransformed magnitudes was 11.572 with an SD of 0.05. The average transformed magnitude came out at 11.806 with a SD of 0.3

 Steve

 

Wed, 04/14/2021 - 20:10
Transformed magnitudes improve accuracy

The short answer is yes. For non-transformed magnitudes, the closer the colour of your comp and target stars, the more accurate the result, other things being equal, and assuming low airmass (in my case, probably less than 1.05).

I quantified this with my DSLR camera a while ago, by plotting B-V difference (between comp and target) on the x axis and the difference between measured and catalogue magnitudes on the y axis, for a series of photometric standard stars with a wide range of B-V.

The slopes for B, V and R plots were 0.48, 0.12 and 0.29 respectively. Those slopes mean that for a B-V comp/target difference of 1.0 the B, V and R measured mags will be incorrect by 0.48, 0.12 and 0.29 mags respectively. The relationship is linear, so simple math tells you the errors for smaller B-V differences.

Bear in mind that the slopes of such plots for cameras other than mine may well be different.

Roy