Linear ephemeris

Question

What is the T in the formula for the linear ephemeris T_max = T + P*E, please? P stands for the period; E, for ephemeris. How to determine T? I have T_max and P. Or is it a referent epoch? Many thanks

Answer 1

This is a fairly standard ephemeris for e.g. times of maximum light of a variable star but you are getting some of the symbols mixed up. The ephemeris is normally written as: $$ T_{event} = T_0 + P\times E $$ where $T_{event}$ is the time of the given event (time maximum or minimum light, maximum positive radial velocity etc), $T_0$ is a reference time when the particular event occurred in the past, $P$ is the period and $E$ is an integer "cycle count" of how many times the particular event has recurred.

In this specific example, your 'event' is a time of maximum light, $T_0=2454767.4648$, $P=0.4737$. If you wanting to calculate the next time of maximum light, you need to:

1. calculate the HJD for the time of interest ($T_{now}$),
2. obtain an estimate of the cycle count $E=\textrm{int}(\frac{T_{now}-T_0}{P})$
3. Add 1 to $E$ to obtain the next time of maximum light
4. Plug the new $E$ into your ephemeris which will give the HJD of the new/next $T_{max}$

As a worked example, for "now":

T_now = 2459359.4269246464
E = (2459359.4269246464-2454767.4648)/0.4737 = 9693.81913583739
int(E)+1 = 9694
Next T_max = 2454767.4648 + 0.4737 * 9694
           = 2459359.5126