# How to determine the time of periastron passage (T) of a single lined spectroscopic binary?

I am working on finding spectroscopic elements of a single lined spectroscopic binary. All I have is irregularly spaced radial velocity data which needs to be phase folded to plot a velocity curve (RV vs Time from T). For phase folding I need orbital period P and time of periastron passage T. I have determined the period by plotting a Lomb-Scargle periodogram but I'm unable to find a method to determine T. I can use already published value of T for that spectroscopic binary, but I want to learn how to determine T myself. Is there any method to determine T from RV data?

• You need to fit the RV curve. One of the free parameters can be time of periastron. NB. You can only get this if there's significant eccentricity! Commented Mar 20, 2022 at 23:18
• @ProfRob Thanks for the help! This was very easy but I completely missed it ðŸ¥². Basically one can fit the equation $$V = V_{com} + K\left[e \cos(\omega) \pm \sin\left(2\pi\frac{(t - T)}{P}\right)\right]$$ to the RV data, where the $\pm$ sign refers to the primary or secondary component and $t$ is the time of observation. Since $P$ is known, the parameters $V_{com}$, $K$, $e$, $\omega$ and $T$ can be determined via the fit. Commented Mar 21, 2022 at 18:05
• Yes, that is how it is done AFAIK. Commented Mar 21, 2022 at 19:05