FFT, How to decide if there is a signal among noise? I have sets of data of different deep sky objects. My job is to check for any periodicity.

I use IDL to run an FFT and wavelet methods to check for a signal. To test my code I ran the IDL built in FFT operation on a sine wave, my code works. 

I then add noise to the sine wave and increase the noise until I cant distinguish the frequency peak in the FFT output.

My question is what mathematical method can I use to say 'yes there is a signal and this is its frequency' or 'no there is no signal' ? Can or should I get a percent of certainty ? 

This post is very close to what I'm asking, but I only have one data set for an object so how could I make a ROC curve?: What statistic is used to determine presence of a signal in noise?

Also I think I dont want a ROC curve.
I will respond to any question you may have about my question. Thank you very much for your help. I am currently do research at UC Santa Cruz as an undergraduate.
As a fellow astrophysicist, I suggest you use the standard 3 sigma above noise for detection, and 5 sigma above noise if you want to do analysis on what you find.

If your noise does not have a flat background, you need to subtract a "Flat", an estimation of that the background might be. If you know what the noise should look like, such as exponential, gaussian, etc., try subtracting such a curve. If not, try a first order polynomial. If not good enough, then go with a second order.

Beyond that, it becomes interpretation... What if that tendency you notice in the noise is actually a signal, spread over many frequencies?

Try computing the FFT of a pure white noise image, to get an idea of what your noise is supposed to look like. (Off course, remember that FFTs assumes your signal is periodic beyond its edges. Don't forget to zero-pad your data, and use a correct apodization, or limit your analysis to something smaller than half the size of your image.)