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Yale University
Department of Astronomy
PHOEBE Undergraduate Manual
Farris Gillman
[email protected]
June 2013
Who is this manual written for?
This manual is meant to be written at an undergraduate level of understanding, for
undergraduates with some introductory knowledge of binary stars. This guide is written
specifically for the MAC version, but the same main features are in the GUI for all operating
systems, although they do look a little different.
What this manual will cover?
This manual will cover the use of the graphical user interface which utilizes the PHOEBE
library. Undergraduates should be able to use this manual to properly format their data before
inputting it into the program, work comfortably with the PHOEBE graphical user interface
(GUI), and troubleshoot many problems that they may encounter. Also included is a description
of several of the orbital parameters whose values PHOEBE can be used to determine. The use of
the PHOEBE scripter will not be covered in this manual.
What is PHOEBE?
PHOEBE ((PHysics Of Eclipsing BinariEs) is a free software package created by Andrej Prsa,
Gal Matijevic, Pieter Degroote, Steven Bloemen, Kelly Hambleton, and Joe Giammarco.
PHOEBE models observed data in order to determine the orbital elements and fundamental
properties of the stellar components in binary star systems. PHOEBE is based on the WilsonDevinney code which is also used in modeling binary star systems (Wilson, Devinney 1971).
There are three major components of the PHOEBE software package. The library contains all of
the algorithms and functions that are used to model eclipsing binary systems. The library can be
utilized through the GUI and the scripter (Prsa, Andrej, 2012). The GUI is an interface through
which the user can set parameter values, plot the light curves (LC) and radial velocity curves
(RV) and view the model results (Prsa, Andrej, 2012). The GUI is what this manual will largely
focus on, along with formatting data before use. The scripter is the final portion of the PHOEBE
package. It can be used for statistical tests for determining error, or the analysis of large data sets
(Prsa, Andrej, 2012). The use of the scripter will not be covered in this manual.
Before We Start:
Downloading: Before using PHOEBE it has to be downloaded onto the computer you will be
using. You will need to also download either the Van Hamme and Wilson limb darkening tables,
or the PHOEBE 2010 tables, and the information for the relevant filters used to create your LC
data. The filters used should be listed in the headers of the files. The following sections will
assume that you have all the necessary software and files downloaded and configured.
Formatting Data: Many of the problems that you may confront when using the GUI stem from
having improperly formatted data files. There are two main ways in which they may be
improperly formatted.
1) Julian Date: Researchers may subtract some constant from the Julian Date, so it is a smaller
number. For instance, they may subtract 2450000 or 2450000.5 or something similar. If they
subtract by some constant they may or may not say what constant they used in the header of the
file. This is why you must look at the dates in each of the files and determine if they used the
same constant. As shown previously, the difference may be off by just half of a day. If they
appear to be in the same format, that is either the same constant has been subtracted from all of
them, or no constant has been subtracted, then you can move on. If there was a difference and
you did not catch it, your solutions for the parameters later on will not converge, and the phase of
your RV data and LC data may be off by one half. If there is a difference in the format of the
Julian dates, and you have at least a guess of what it may be, you will need to alter the Julian
Dates to attempt to get them all in the same format. Some tips for doing this are
a. try and alter as few files as possible,
b. keep good notes (in the headers) of how you altered the dates,
c. save a copy of the original files in case you need to start over.
This applies to both LC files and RV files, so be sure to check and make sure the dates of all of
your files are formatted the same way.
2) Format of the files: First, let’s address the RV files. When you open the files there will be two or
three labeled columns. The first should be the date or phase, the second should be the radial
velocity of the stars (either the primary or secondary), and, if there is a third column, it should be
the standard deviation. If the columns are not in this order then rearrange them. The second note
about the RV files is that you can only input two (one with the radial velocities of the primary
star and one with those of the secondary) when you use PHOEBE. If you have multiple files, you
will need to combine them into only two files, one for the primary star and one for the secondary.
Again, it is a good idea to save the original files before proceeding.
Next, let’s address LC files. When you open your LC files there should be several columns, the
first should be the date or phase, the second the magnitude or flux, and the third, if it is there,
should be the standard deviation or standard weight. If the columns are not in this order,
rearrange them so that they are. Unlike RV files, PHOEBE can work with multiple LC files at a
time, so there should be no need to combine them.
Modeling with PHOEBE:
Now that you have the necessary elements downloaded and your data is properly configured, you
can begin modeling with PHOEBE. This will be broken into the following sections: a quick tour,
inputting data, using the graphs, adding parameters, and finding converging solutions.
A Quick Tour:
When you first open the PHOEBE GUI, you will see several tabs and controls. This quick guide
will help you familiarize yourself with the ones you will be using most often. The buttons at the
top are short cuts, and the tabs organize the elements of the rest of PHOEBE’s functions.
The “Open” and “Save” buttons can be used to save your current session in PHOEBE, or to open
a previous session. The “LC Plot” and “RV Plot” buttons are short cuts to your LC and RV plots,
which can also be accessed using the plotting tab. Under the “Data” tab you are able to name the
binary you are using, say what kind of binary it is, define your normal Magnitude, and input your
files. The “Parameters” tab will take you to all of your stellar parameters which are divided into
“Ephemeris,” “System,” “Orbit,” “Component,” “Surface,” “Luminosity,” “Limb Darkening,”
and “Spots.” The fitting tab will take you to where you can calculate new values for your
parameters, compare them to their previous values and update them. Finally the “Plotting” tab
will take you to your RV and LC plots which can be made into new windows for easier access
using the small button in the top right corner of the “LC Plot” and “RV Plot” tabs, under the
“Plotting” tab.
Inputting Data:
Now that you have explored a little, it is time to begin. The first step is to input your data files.
Let’s start with the LC files. Under the “Data” tab, in the section for “LC data” click add. Then
click the bar next to where it says “Filename” and select your first file. Then label the first
second and third columns appropriately using the drop down tabs. If there is no third column,
select “Unavailable.” Then select the appropriate filter, which should be listed in the header of
your file. If the filter is not listed in the drop down menu either PHOEBE was not configured
properly, or all of the necessary files were not downloaded.
You can add several LC files. If you are having trouble with the formatting please refer to part 2
of “Formatting Data” above.
The RV files can be added in a similar manner to the LC files, with just a few differences. First,
there is no filter for the RV files, and second, PHEOBE will only work if only two RV files are
uploaded; one for the primary star and one for the secondary star. For more information, refer to
part 2 of “Formatting Data” above.
Once this is done, you need to account for the effects of limb darkening on the magnitude or flux
from the stars. So, go to the “Parameters” tab, then the “Limb Darkening” tab. Select the table
you will be using (either Van Hamme, or PHOEBE). Next, under “Model” select the
Logarithmic Law, and click “Interpolate.” When the window pops up for the interpolation, select
one of your files in the drop down menu next to interpolate, then click interpolate at the bottom
of this window.
If this works, click “Update” and continue to do this for the remaining LC files and the
Bolometric filter. If it does not work, it is likely that you have not downloaded the table that you
are trying to use.
Using the Graphs:
For the next step it is necessary for you to use the RV and LC plots. So, click on the “Plotting”
tab and start with the LC plots. Next, click the boxes next to each of your LC files for both the
observed and synthetic curves (listed at the bottom) and click “Plot.” It will look something like
this:
The next step is to get the y-axis to be more or less within the range of -1 to 1. To do this, go
back to the “Data” tab and find where it says “Zero magnitude.”
You can then adjust this value until you find the desired range on the y-axis. Refer back to your
LC plot between each change and re-plot it until you reach the desired result. Ideally, the
observed curve should fill the space, and the range of the y-axis should be around -1 to 1. The
example below has a range from 0 to 2 which will work as well.
Adding Parameters:
The next step is for you to begin actually fitting the parameters to your data. We will begin by
solving for the parameters that can be determined using just the LC files. First, unselect the RV
files.
A good place to start is with the period. The period is one of a few parameters that can be
determined using either the RV data or the LC data. By looking at either the LC files or RV files
you can guess a value close to the period. Once you have an approximate value for the period, go
to the “Parameters” tab. Under the “Ephemeris” tab you will see the period. Input your
approximate value, then plot the LC plots and adjust the period manually, consulting the plots
each time you change it, until the period of the synthetic curves matches the period of the
observed plots.
Once the modeled line appears reasonably close to the line formed by the observed data points,
click the box associated with that parameter, and then move on to the next parameter.
You will use this process again for each of the parameters, so in more general terms it can be
outlined by the following steps:
1. Adjust the parameter to see the effect on the synthetic curve.
2. Continue adjusting the parameter while consulting the plots until it best matches the curves.
3. Once you have the parameter fairly close to matching the curve, check the box next to it to signal
to PHOEBE that it should fit the parameter when you have it calculated the parameters later on.
While you have just the LC files selected, repeat these three steps for the inclination and surface
potentials of both stars. The goal is to have the synthetic curve match the data points as best as
possible.
The left panel shows how the LC synthetic curves should fit the data. The right panel shows how the RV synthetic
curves should fit the data.
After getting your values fairly close manually, you can proceed to the section “Finding
Converging Solutions.” After completing the steps outlined there for the LC data parameters you
will need to return to this section to manually fit the parameters generated by the RV data, or
both types of data.
To finish fitting the data, reselect the RV files under the “Data” tab, and unselect the LC files and
the parameters you found while using them, without changing their values. Once that is done,
repeat the three steps listed on the previous page for manually fitting the parameters. Start with
the phase shift and then move onto the center-of-mass velocity (VGA), the length of the semimajor axis (SMA), and the mass ratio (RM). Finally, reselect the LC data and the parameters and
continue onto the next section.
Finding Converging Solutions:
Before you go any further save your session in PHOEBE so you can go back to your manually
fitted values and adjust them later if you have problems with the calculating step. Finally, you
are ready to use Phoebe to refine the fit of the parameters that the user selected. To do this, go to
the fitting tab, and prompts the program to calculate the best fit. Once the program has finished
running, compare the initial value and the new value. If they are fairly close update the initial
values, and plots the fit curve against the data to check it. The user can then continue calculating,
checking the values, updating, and then checking the plots so long as the values; a) stay fairly
close to those found by the user manually, b) appear to be approaching a constant value, and c)
make the fit better with each iteration of this process. If they are not fairly close, try changing
some of your parameters manually for a closer fit before calculating.
Troubleshooting
The following are a few problems you may come across, and some steps you can take to try and
solve them.
Problems with the RV Curve (the primary and secondary are out of phase by more/less than
one half, there are random points that don’t belong etc.)
Most problems with the RV curves will likely stem from human error if you are combining
multiple files, so if you combined files double check your work. Be sure that all of the dates are
in the same format and that simple formatting things like leading zeros are all in the same format.
If they are out of phase, it is likely that the dates are in different formats.
Problems with the LC Curve (the LC curves are all at very different magnitudes, there is no
definition in some of them, some of the LC curves are off by different phases etc.)
If you are having trouble with the LC curves being at different phases, adjust your period. If they
are at very different luminosities or some looked flattened, make sure that you made your limb
darkening corrections, as forgetting to do so will often result in this issue.
Problems Calculating Values (The values won’t converge, I am getting unreasonable answers)
This can be caused by a multitude of problems. The first step is to adjust the parameters
manually which are the least stable so that the synthetic curve more closely fits the data points.
Also, you can unselect some values and continue calculating the others for a while. Also, double
check that all of the formatting for the dates is correct. A final adjustment that you can make if
the stars are very close in size is the switch the primary and secondary radial velocity curves.
Parameters and How They are calculated:
Origin of HJD Time: Also known as the time of periastron, this is the value of T0. As such its
value is 0.0 for this study.
Orbital Period: This can be determined from analysis of either the light curve, or the RV curve.
In the light curve, it is the time between dips in the light curve caused by the primary star moving
in front of the secondary star. From the RV curve, the period is the time it takes for one of the
stars to go from redshift to blue shift and back to redshift.
This image shows how the period of a
binary star system is defined, as well as
what behavior the dips in the LC reveal.
(Imagine.gsfc.nasa.gov)
Semi-major Axis (in Solar Radii): This can be determined using Kepler’s 3rd law. Once the user
solves for the sum of the masses (see equation under mass ratio) the user can use the following
equation to solve for a, the semi-major axis. P is the orbital period.
𝑎3
(𝑚1 + 𝑚2 ) = 2
𝑃
Objects 1 and 2, in the figure to the left, represent the primary and
secondary stars in a binary system. The semi-major axis is one half the
distance between the two stars at the point in their orbit when they are the
farthest apart.
Mass Ratio: This is the value of the mass of the secondary (or less massive) star over the primary
(or more massive) star. This is found using Newton’s third law and the RV curves. The ratio of
the velocities of the star is equal to the ratio of their masses, as seen in the equation below.
𝑀1 𝐾2
=
𝑀2 𝐾1
Inclination in Degrees: The inclination is the angle between the plane of the binary stars’ orbits
and the line of sight of the observer. The inclination can only be determined in eclipsing binaries
using the shape of the dips in the light curve. When used in conjunction with other parameters,
the shape and duration of the light curve will yield the inclination. Once it is determined, the user
can use the following equation to solve for the sum of the masses. Velocities are determined by
RV curve, period by the RV curve or light curve, and G and π are both constants.
(𝑚1 + 𝑚2 ) =
𝑃 (𝑣1,𝑟 + 𝑣2,𝑟 )3
2𝜋𝐺
𝑠𝑖𝑛3 (𝑖)
Argument of the Periastron: This is the angle between the periapsis (the point in the orbit where
the star is closest to the focus where the center of mass is located) and the point where the star
crosses the plane defined by the observers line of sight. This angle (ω) is located within the
orbital plane of the star.
This is an illustration of the argument of periastron, also known as the
argument of periapsis. It also shows the orbital plane, and reference
direction (line of sight). (http://en.wikipedia.org/wiki/File:Orbit1.svg)
Orbital Eccentricity: This is a measure about how circular or elliptical the star’s orbits are. Given
the periastron and the apastron (the greatest distance between the stars) the eccentricity can be
determined using the equation below where rp is the periastron, and ra is the greatest distance
between them. This can only be determined for spectroscopic binaries.
𝑟𝑎 − 𝑟𝑝
𝑒=
𝑟𝑎 + 𝑟𝑝
Effective Temperature of the Primary/Secondary Star: The light curve of eclipsing binaries
yields a temperature ratio between the two stars, and the classification of the stars (based on their
spectra, will yield their classification. From this information we can determine the temperature of
both stars. The temperatures of the stars are, in turn, used to calculate the limb darkening, which
must be taken into account when determining the inclination of the systems orbit from the dips in
the light curve.
Primary/Secondary Star Surface Potential: Inversely proportional to the radius of the star. This
parameter is a measurement of the relative force of the gravitational pressure, and that of the
pressure caused by heat radiation for each of the stars.
References:
Prsa, Andrej. PHOEBE - PHysics Of Eclipsing BinariEs. Tech. Villanova University, June 2012.
Web. 10 May 2013.
Wilson, R., Devinney, E., APJ, 166, 605 (1971)