# Astronomical detection significance from magnitude error

At this website:

The passage at the bottom states that a V-band magnitude of 17.62, with an error $\pm$0.02 is a 49.4-$\sigma$ detection significance.

How is this value calculated? Could you provide the working? I have a similar problem, with a set of magnitudes and errors, and would like to know at what magnitude limit I can claim a statistically significant (6-sigma) detection.

Thanks

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I don't know the answer, but I'm pretty sure that it's not derivable from just the above information. At a quick glance through that Web page I don't think that the required information to derive that significance is there either. In general, to assess the significance of a detection like this, I think you'd need to know something like the background sky brightness. – Ted Bunn Feb 19 '11 at 20:32

If you want the detection significance, it is calculated as $\frac {N_{p} - N_{b}}{\sigma_{b}}$ where
• $N_{p}$ is the number of raw counts at the peak of the star's point spread function,
• $N_{b}$ is the average number of raw counts in the background near the star, and
• $\sigma_{b}$ is the standard deviation in the raw counts of the background near the star.