I have data consisting of radial velocities and times (covering about 10 000 days). The radial velocity changes with a period. I tried to find out the period using Stellingwerf's method (it was successful), and then I applied the bootstrap method to determine the uncertainty. I obtained a histogram that is very different from the Gaussian curve. What could be the cause?
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4$\begingroup$ Hi Anna-Kat, I really appreciate that you are asking all these questions, but I beg you to provide some more context. What are you working on? I can only guess from your previous questions that this is about some kind of light curve. Unless you explain exactly what you have done and how it has gone wrong (maybe a picture of the histogram :) I'm afraid that it might be difficult to help you. Thank you $\endgroup$– PrallaxAug 30, 2021 at 15:57
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2$\begingroup$ I edited the question $\endgroup$– Anna-KatAug 30, 2021 at 16:03
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$\begingroup$ For how many days does your light curve cover? Ten days? Ten thousand? "I have data consisting of radial velocities and times" is not really saying anything. $\endgroup$– uhohAug 30, 2021 at 16:58
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1$\begingroup$ About 10 000 days $\endgroup$– Anna-KatAug 30, 2021 at 17:02
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1$\begingroup$ I'm not an expert, but are you sure it should come out gaussian? Why do you believe it should? Sorry if this is a stupid question $\endgroup$– PrallaxAug 30, 2021 at 17:05
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1 Answer
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I hope that someone more knowledgeable than me will answer this question, but this is what I understand it is happening.
The bootstrap method gives an estimate of the probability distribution of the period, given the data. If the probability distribution were a Gaussian centered on the true period, you would probably see a Gaussian.
But when estimating the period of a radial velocity signal, this is often not the case. By looking at a peridogram, you see that there are many peaks, corresponding to the true period, to its harmonics and to other artifacts. In some cases it may even happen that a spurious peak is higher than the true period peak.
This is exactly what happens with the bootstrap method. You sample your data differently and as a result you may get one of the spurious peaks as the higher one and incorrectly select it as the period. This explains the look of your histogram. In your case, the bootstrap samples are most likely to select 1.372094d as the period, but also have a good chance to select 1.372105d. The values in between instead have a very low probability of being selected as the period.
