# Finding the Phase of an Exoplanet using the ephemeries

So I'm currently researching Star-planet Interactions for HD 156279, I'm taking the flux of the Ca II H&K lines and trying to plot them against the phase of the planet, looking for evidence of magnetic or tidal interactions.

Now I have my flux as show below: And I know the Phase=(time-ephem)/period. Now my professor said I can find the ephemeris from this site: http://exoplanet.eu/ephemeris/hd_156279_b/ The problem I'm having is figuring out what the ephemeris is? I know the Period is 131.05, I assume the Time parameter is 2455525.59 as given by the webpage although I'm not sure about that either. I understand that phase should be between 0.0-1.0 and if I use 2455525.59 for time and using a converter for JD for my first flux in the table above (2009-07-06 12:41:11 = 2455019.0285995 and I assume this is the ephem I'm looking for) if I plug those into my equation I get 3.865...so I'm guessing that's not what I'm looking for. Any help would be greatly appreciated. I would ask my advisor but he's out sick with covid...so I'm trying to figure this out on my own.

Thanks!

An ephemeris (plural ephemerides) is a collection of predictions of the positions of one or more celestial objects. An epoch is a reference point from which time is measured. The phase represents the fraction of the period of a periodic phenomenon that has passed, omitting whole periods. Phase is often represented as an angle (between 0 and 360 degrees or $$2\pi$$ radians), or as a number between 0 and 1. Your question is based on that latter convention. So the phase $$\phi$$ is

$$\begin{equation} \phi = \dfrac{t - t_\text{epoch}}{P} \bmod 1 \end{equation}$$

where $$t$$ is the time of interest, $$t_\text{epoch}$$ is the epoch, $$P$$ is the period, and $$\text{mod}$$ is the modulo operator.

You can take the MJD (Modified Julian Date) from your flux table as $$t$$; it represents time since the epoch of MJD in units of a day. You can choose any epoch that is convenient. If you use the epoch of MJD as your epoch then $$t_\text{epoch} = 0$$, so then the phase formula becomes

$$\begin{equation} \phi = \dfrac{t}{131.05} \bmod 1 \end{equation}$$

The phase of the first observation from your flux table is then

$$\begin{equation} \phi = \dfrac{55018.52594}{131.05} \bmod 1 = 419.8285077 \bmod 1 = 0.8285077 \end{equation}$$

As an aside: Do not confuse the phase described above with the phase angle that is mentioned in your bottom graph. The phase angle describes the distribution of light and dark across the celestial object as seen by the observer, not the location of the celestial object in its orbit independent of any observer. The (orbital) phase increases at a fixed rate (between the sudden drops from 1 to 0) but the rate of increase of the phase angle usually varies, especially when the orbit is not a perfectly circular one.

If the phase varies from 0 to $$F$$ then the phase formula is
$$\begin{equation} \phi = \left( F \dfrac{t - t_\text{epoch}}{P} \right) \bmod F \end{equation}$$
If you plot your flux as a function of phase then changing $$F$$ doesn't change the graph but only changes the range of numbers along the x axis.