Poisson stats: signal to noise

AI Thread Summary
The discussion centers on calculating the uncertainty in the measurement of a star's apparent magnitude with a given signal-to-noise ratio (S/N). The user derives the flux (fA) from the magnitude equation and finds it to be approximately 3.98 e-7 J/s. They initially express uncertainty as 6.3 e-4 but realize there may be an error in their approach. The conversation also touches on the concept of RMS noise and its implications for error propagation in measurements. Ultimately, the user gains clarity on the calculations after further discussion.
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A star was measured to have an apparent magnitude m=16 with S/N=10 integrated over a minute. What is the uncertainty in the measurement?
signal=flux*area*time
noise=sqrt(signal)=sqrt(fAt)
So, S/N=sqrt(fAt)
How can I find fA?
m=-2.5logfAt+K
16=-2.5log(fAt)+K
Hoping that K is arbitrary (please verify this), I choose K=0
Then 16=-2.5log(fAt)
So fA=3.98 e-7 J/s (units inconsequential)
So, uncertainty =6.3 e-4
??
HELP!
edit:
Or, I can get N=uncertainty=sqrt(S/10)=sqrtS <--- something VERY wrong here
 
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I think this is an exercise in error propagation.
m=-2.5logfAt+K

You could also write m=-2.5log(I)+K
You have m, and I/dI=10. You want to find dm. (d means differential).

m + dm = -2.5log(I + dI) + K.
You could now substitute dI = I/10, and solve for m. That will work, since I will cancel.

However, I suspect they talk about RMS noise.
Which makes things a bit more complicated.
 


Originally posted by arcnets

However, I suspect they talk about RMS noise.
Which makes things a bit more complicated.
No, actually. You're answer if perfect. We went over this today in class. It didn't make sense then, but I think it's finally making sense. I was trying to hard to find S.
 

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