CzeV343: discovery of a double eclipsing binary with periods near a 3:2 ratio
P. Cagas1 & O. Pejcha2
1 BSO, Zlin, Czech Republic
In our paper, we suggest that CzeV343 is a quadruple system composed of two eclipsing binaries. If the two binaries are indeed physically connected, the parameters of the mutual orbit can be obtained by precision timing of minima over time through light travel time effect, apsidal motion or orbital precession. However, such goal requires joint analysis of data from different sources obtained through various techniques and with insufficiently quantified uncertainties. In particular, photometric uncertainties are often underestimated, which yields too small uncertainties in minima timings if determined through analysis of a χ2 surface. The task is even more difficult for double eclipsing binaries, especially those with periods close to a resonance such as CzeV344, where minima get often blended with each other.
In addition to CzeV343, two double eclipsing binaries are known: V994 Her and KIC 4247791 and more will likely be discovered in the near future. In order to aid the analysis of systems such as CzeV343, we make publicly available our code that solves the double binary parameters simultaneously and then uses these parameters to determine minima timings (or more specifically O-C values) for individual datasets. In both cases, the uncertainties (or more precisely confidence intervals) are determined through bootstrap resampling of the original data. This procedure to a large extent alleviates the common problem with underestimated photometric uncertainties and provides a check on possible degeneracies in the parameters and the stability of the results. While there are shortcomings to this method as well when compared to Markov Chain Monte Carlo methods, the ease of the implementation of bootstrapping is a significant advantage.
Additionally, the code has a number of functions to read data and pass parameters between the minimizing routine and the binary light curve code. In fact, these routines are the only original part of the code: we use the great minimization routine cmpfit and the excellent binary light curve code JKTEBOP by John Southworth.
The code is designed to work under linux because of the easiness to combine C and Fortran. But it runs exactly the same under Windows in Cygwin. The code has a capability of multithreading through OpenMP. To make use of this capability, you need a recent compiler. The code works without modification with no multithreading support, but (especially) the bootstrapping gets very slow.
This code is based on external minimization routine and eclipsing binary light curve code. You need to get them separately.
Go to http://www.physics.wisc.edu/~craigm/idl/cmpfit.html and download cmpfit-1.2. Unzip the file in the directory with our code - this should do the trick. Just check the main Makefile that the paths are correct.
This is a bit more difficult as it requires editing the JKTEBOP source code to link it with the rest of the C code.
When you successfuly compile the code, then it should be set up so that you get results just by running ./hierarchy.exe followed by ./bootstrap.exe output.dat or ./oc.exe. There are some comments in the source files - if you want to do something with the code then you'd have to go through the sources anyway so it's better to start early.
The output of hierarchy and bootstrap is essentially Table 2 of our paper, while oc gives you Table 1.