<p>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?</p>

CC BY-SA 4.0
2022-03-20T23:18:05.427Z
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!
ProfRob
CC BY-SA 4.0
2022-03-21T18:05:04.037Z
@ProfRob Thanks for the help! This was very easy but I completely missed it . 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.
ShaunakP
CC BY-SA 4.0
2022-03-21T19:05:06.940Z
Yes, that is how it is done AFAIK.
ProfRob
<binary-star><orbital-elements><radial-velocity>
How to determine the time of periastron passage (T) of a single lined spectroscopic binary?
ShaunakP
# How to determine the time of periastron passage (T) of a single lined spectroscopic binary?

(Asked by: username_0 on 2022-03-20)

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?

**Tags:** binary-star, orbital-elements, radial-velocity

> **Comments:**
> **username_1**: 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!  
> **username_0**: @username_1 Thanks for the help! This was very easy but I completely missed it . 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.  
> **username_1**: Yes, that is how it is done AFAIK.  

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