I have some astronomical light curves for which I'm trying to recover some periodicities. One of them (from TESS) has many thousand samples across ~23 days, with a ~1-day gap in the middle. The resulting Lomb-Scargle periodogram looks something like this, where the y-axis is power and the x-axis is period, up to a periods of ~14 days. The black dotted line is the assumed rotation period, ignore that.
Intuitively, I want to say the broad signal signal from 7-12 days isn't real. Not only does it not feel real (given it's breadth and qualitative inconsistency with what I see in the light curve), but I've been told before to be careful with signals longer than ~1/3 the timespan of your light curve. The peak of the broad feature is ~8.7 days, which is longer than 1/3 the light curve baseline (~7.7 days). I've been ignoring this signal up to this point, but... should I?
I've been reading a bit and I've yet to find anything concrete about the reliably longest period one should expect to recover from a light curve. This paper (https://iopscience.iop.org/article/10.3847/1538-4365/aab766/pdf) suggests that one can recover up to the baseline of the light curve (~23 days in this case). Plus, the 0.1% False Alarm Probability (calculated via bootstrap) is the miniscule grey bar at the bottom of the plot, suggesting that a, 8.7-day period isn't a product of the sampling rate.
I tried calculating the periodogram via phase dispersion minimization, but I get a bunch of garbage for the TESS light curve, so I figured I'd come here before spending more time on that or reading about Lomb-Scargle some more. And for reference I am using AstroPy's Lomb-Scargle function for these calculations. Any pointers anyone can provide would be helpful! Thanks.