Why do we need a Fourier Coefficient database?
Well, to be perfectly honest, we don't really need anything. However, if you are a researcher
in the area of regularly pulsating, intrinsic variables, you have probably run across Fourier coefficients at
some time in your life. As can be seen in the many papers about Fourier
coefficients, they are quite useful.
Since the introduction of the modern form of finding coefficients, there have been many publications
concerning them. Sometimes, a different form of the original formula is used - this can make
comparisons difficult or introduce unexpected errors if these differences are not noted. Sometimes
different photometric systems are used - that has to be noted as well. This website is an effort
to provide researchers with a comprehensive listing of coefficients - or as comprehensive
as I can make it.
A few things to note -
- Only Intrinsic variables are included. Fourier analysis of eclipsing variables has been done, but is
not included here.
- Magnitude and color data is based upon a cos function while
velocity terms are based upon a sin function.
- Every effort has been made to include the original data - only minor changes have been made to
provide a uniform set of terms. In some cases this involved transforming phase terms from degrees
to radians, or something similar. If a sin function was used to derive
the variables, that difference is accounted for in the datasets so that
you don't have to later change the values.
- For graphical and searching purposes, the phase terms,
ij, are defined by a cosine function.
Also, they are presented in the form seen in the graphical displays.
This means that some values are greater than 2 , but
that can be easily fixed using most spreadsheet/database format programs.
- Names of variables are according to the General Catalog of Variable Stars listings (for galactic
variables), or the Helen Sawyer Hogg Catalog scheme (for cluster variables).
Stars found in large scale surveys have their original survey
name, when it isn't included in either of the other previously
mentioned naming schemes. This is mainly seen in extragalactic
variables and some in the galactic bulge (towards Sagittarius).
- Variable types are debatable for some stars, particularly the very short period ones. At this time only
the following types are distinguished - Cepheids, RR Lyrae AB-types, RR Lyrae C-types, Delta Scuti, and SX Phe stars.
This means that all types of Cepheids are lumped together into the "Cepheid" catagory.
Type is usually determined by the GCVS listing or
Christine Clement's on-line database for
- Data is provided as completely as possible. In some cases, authors derive
15 terms for the Fourier function, which can amount to quite a lot of
data. In cases where data is missing or excluded (such for error terms)
a value of 99.99 is inserted into the dataset so that the data
remains in uniform columns when used for spreadsheets or graphing
At the present time there is data for over 1000 galactic variables,
as well as more than 1100 cluster variables (in 35
different clusters), and nearly 6500 extragalactic variables in 6 different
If you would like to make a suggestion or if you have data to provide to the database, just
contact me, Siobahn Morgan.
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