<p>INT refers to the <a href="https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" rel="nofollow">floor function</a>. So $\mathrm{INT}(x)$ is the largest integer not exceeding $x$. </p>

<p>In this case, the function is used to get the fractional part of $\frac{\mathrm{HJD}-T_0}{P}$, i.e. the part after the decimal point. So if for example $\frac{\mathrm{HJD}-T_0}{P}=3.4$, then $\frac{\mathrm{HJD}-T_0}{P}-\mathrm{INT}\left(\frac{\mathrm{HJD}-T_0}{P}\right)=0.4$.</p>

CC BY-SA 3.0
2016-08-09T19:59:03.890Z
2016-08-09T19:59:03.890Z
wythagoras
<p>You are free to pick your reference point any way you want.  You could pick a $\text{HJD}$ at which the star is brightest, or dimmest, or exactly average, or you could pick the $\text{HJD}$ of the first observation, or you could even set $T_0 = 0$.  If two people pick different $T_0$, then the phases they find differ by a constant value (<a href="https://en.wikipedia.org/wiki/Modular_arithmetic" rel="nofollow noreferrer">modulo</a> 1).</p>

<p>It is convenient to set $T_0$ at or before the smallest $\text{HJD}$ in your observations, so that all $\text{HJD} - \text{T_0}$ are nonnegative, because the $\text{INT}$-like functions provided by calculators, computer languages, and software libraries don't all round negative numbers in the same direction.  Many round all numbers towards zero, so that $+3.4$ yields $+3$ (as we want) and $-3.4$ yields $-3$, but here we want $-3.4$ to yield $-4$, otherwise you get negative phases before $T_0$ and positive phases after $T_0$.</p>

<p>If your observations of brightness are evenly spaced in time, then you can use a <a href="https://en.wikipedia.org/wiki/Fast_Fourier_transform" rel="nofollow noreferrer">Fast Fourier Transform</a> to find the approximate period and phase.</p>

CC BY-SA 3.0
2017-09-06T06:46:29.677Z
2017-09-06T06:46:29.677Z
Louis Strous
<p>I want to convert the list of Julian date values of observing brightness of a Cepheid variable into its phase.<br />
The equation I found in the Internet is the following:</p>

<p>$$\mathrm{Phase}= \frac{\mathrm{HJD}-T_0}{P} - \mathrm{INT}\left[\frac{\mathrm{HJD}-T_0}{P}\right]$$
What is the $\mathrm{INT}$ in this equation? I only know that $T_0$ is the one reference point among the list of Julian date values and $P$ is the period. </p>

<p>Also, what kind of criteria exist in determining the reference point?</p>

<star><time><luminosity><cepheids>
Deriving phase of a pulsating star from list of Julian date values of observing brightness
7_G.S.N
# Deriving phase of a pulsating star from list of Julian date values of observing brightness

(Asked by: username_0 on 2016-08-09)

I want to convert the list of Julian date values of observing brightness of a Cepheid variable into its phase.  
The equation I found in the Internet is the following:

$$\mathrm{Phase}= \frac{\mathrm{HJD}-T\_0}{P} - \mathrm{INT}\left[\frac{\mathrm{HJD}-T\_0}{P}\right]$$
What is the $\mathrm{INT}$ in this equation? I only know that $T\_0$ is the one reference point among the list of Julian date values and $P$ is the period.

Also, what kind of criteria exist in determining the reference point?

**Tags:** star, time, luminosity, cepheids

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## 2 answers

### Answer by username_1 on 2016-08-09. Score: 3 | Accepted answer

INT refers to the [floor function](https://en.wikipedia.org/wiki/Floor_and_ceiling_functions). So $\mathrm{INT}(x)$ is the largest integer not exceeding $x$.

In this case, the function is used to get the fractional part of $\frac{\mathrm{HJD}-T\_0}{P}$, i.e. the part after the decimal point. So if for example $\frac{\mathrm{HJD}-T\_0}{P}=3.4$, then $\frac{\mathrm{HJD}-T\_0}{P}-\mathrm{INT}\left(\frac{\mathrm{HJD}-T\_0}{P}\right)=0.4$.


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### Answer by username_2 on 2017-09-06. Score: 0

You are free to pick your reference point any way you want. You could pick a $\text{HJD}$ at which the star is brightest, or dimmest, or exactly average, or you could pick the $\text{HJD}$ of the first observation, or you could even set $T\_0 = 0$. If two people pick different $T\_0$, then the phases they find differ by a constant value ([modulo](https://en.wikipedia.org/wiki/Modular_arithmetic) 1).

It is convenient to set $T\_0$ at or before the smallest $\text{HJD}$ in your observations, so that all $\text{HJD} - \text{T\_0}$ are nonnegative, because the $\text{INT}$-like functions provided by calculators, computer languages, and software libraries don't all round negative numbers in the same direction. Many round all numbers towards zero, so that $+3.4$ yields $+3$ (as we want) and $-3.4$ yields $-3$, but here we want $-3.4$ to yield $-4$, otherwise you get negative phases before $T\_0$ and positive phases after $T\_0$.

If your observations of brightness are evenly spaced in time, then you can use a [Fast Fourier Transform](https://en.wikipedia.org/wiki/Fast_Fourier_transform) to find the approximate period and phase.


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