# MonteCarlo simulations to test light curve variability

I have an average orbital light curve for a source, that is, binned count rate vs orbital phase, where the count rate are averaged over a number of orbit.

I want to run MonteCarlo simulations to find the probability of obtaining a "very different" light curve profile (defined by certain criteria) by chance.

The criteria is that at a certain phase, the simulated profile must have a count rate that is less than $30\%$ than the real one.

My approach was to draw $10^5$ (or so) values for each phase bin, giving to the distributions a Poisson statistics.

However, it seems that, over $10^5$ simulations, none of the fake profiles, are significantly different from the average one, that is the condition established in the criteria is never met.

I have absolutely no experience with MonteCarlo simulations, therefore I am afraid I am doing something wrong. It seems to me reasonable that the condition is never met by chance, but I would like to know more on possible sources of error in my reasoning.

Is the mine a good approach? Is it enough to give a Poissonian distribution to the simulated values to ensure statistical variability? Should I increase the number of simulations?

EDIT: a Light curve is the behavior of the light (photon count rate) emitted by a source (e.g., a star) as a function of the time. An orbital light curve, is the same in the case of a binary system, that is the light curve is roughly periodical over the orbital period (in this case, the photon count rate is plotted versus the orbital phase, e.g., $\phi=t/P$, with $t$ time of the observed events and $P$ orbital period of the source). An averaged orbital light curve is an orbital light curve whose photon count rate has been averaged over a number of period. Here is a typical light curve: The profiles are shown two times for clarity, but they are exactly the same.

• In order to conduct a simulation, you must specify the probability model for an "orbital light curve" (whatever that might be!), which is not adequately done in the question. If you would edit it to provide enough information in that regard, it might be answerable.
– whuber
Jan 20 '15 at 15:19
• @whuber So, I do not know what a probability model is, and from a quick look on the web does not seem easy to understand. Can you address me for this particular case? Also, is it not possible that my average profile is the probability model? Jan 20 '15 at 15:32
• I have no idea how to address it because I don't know what an "orbital light curve" is, nor what kind of data you have collected (or will simulate) about one. I suspect most of your readers will be in the same position. A probability model is two things: (1) a mathematical description of expected relationships among the data (such as a typical formula for a curve) and (2) a mathematical description of how, and how much, actual data might vary from the expectation. You don't have to do the math, but you have to supply enough information for others to be able to do it.
– whuber
Jan 20 '15 at 15:42
• Thanks again. (1) Do you mean a 'function'? (2) Is not this given by the statistical distribution? I will add a figure of a typical light curve in the original thread. Jan 20 '15 at 15:50
• @whuber, I found this (pag. $6$), where MonteCarlo simulations, at least in Astronomy, are said to be not constrained to probabilistic models. Do you agree? Jan 21 '15 at 10:24