J/A+A/575/A36 BAGEMASS code (Maxted+, 2015)
Bayesian mass and age estimates for transiting exoplanet host stars.
Maxted P.F.L., Serenelli A.M., Southworth J.
<Astron. Astrophys. 575, A36 (2015)>
=2015A&A...575A..36M 2015A&A...575A..36M
ADC_Keywords: Models, evolutionary
Keywords: stars: solar-type - binaries: eclipsing - planetary systems
Abstract:
The mean density of a star transited by a planet, brown dwarf or
low mass star can be accurately measured from its light curve. This
measurement can be combined with other observations to estimate its
mass and age by comparison with stellar models.
Our aim is to calculate the posterior probability distributions for
the mass and age of a star given its density, effective temperature,
metallicity and luminosity.
We computed a large grid of stellar models that densely sample the
appropriate mass and metallicity range. The posterior probability
distributions are calculated using a Markov-chain Monte-Carlo method.
The method has been validated by comparison to the results of other
stellar models and by applying the method to stars in eclipsing binary
systems with accurately measured masses and radii. We have explored
the sensitivity of our results to the assumed values of the
mixing-length parameter, αMLT, and initial helium mass
fraction, Y.
Description:
BAGEMASS calculates the posterior distribution of a star's mass, age
and initial metallicity given observed values or priors on the star's
mean density, effective temperature, surface metallicity and
luminosity.
This software should compile without much trouble on any modern linux
system, the only package you may need to install is cfitsio:
http://heasarc.gsfc.nasa.gov/fitsio/fitsio.html
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
bagemass.tgz 512 3341462 Compressed tar file with all files required to
install the software
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Description of file:
INSTALLATION
------------
Commands entered on the command line are preceeded by "$". Output from
the program is preceeded by ">".
1. Download the compressed tar file bagemass.tgz from CDS.
2. Unpack the archive
$ tar xzvf bagemass.tgz
This will create a directory bagemass-A+A
3. Move to the directory created in the previous step.
$ cd bagemass-A+A
4. Use any text editor to edit the file Makefile, e.g.,
$ pico Makefile
Change the values of the variables INSTALL, LCFITSIO, F77 and
FFLAGS as needed.
5. Compile and install
$ make
You may see some warnings when src/herm2ev.f and src/herm3ev.f are
compiled - these can be ignored.
The following directories will be created in the installation
directory if they do not already exist.
bin/
share/
share/bagemass/
6. [Optional] Remove object files
$ make clean
7. If the "bin" sub-directory in the installation directory is not
already in the PATH system variable of your shell, add it now
(and "rehash" if needed).
RUNNING THE PROGRAM
-------------------
The program is run using the following command
$ bagemass
The version number of the program is printed and the user is
offered a choice of model grids, e.g.,
> Available alpha_MLT and He-enhancement values are ...
> 1 1.78 0.00
> 2 1.50 0.00
> 3 1.78 0.02
> Enter model grid number [1] >
The default grid number is shown in square brackets. Hit return to
accept the default or enter the grid number desired and then hit
return.
The full path to the model grid is displayed and the models are
loaded (this can take a few seconds).
The next set of prompts enable the user to enter the observed data
for the star to be studied. See Maxted et al. 2015 for a description
of these four observed quantities.
> Enter T_eff [K] [6000., 100., -100.] >
> Enter log L/Lsun [0.0, 5.0, -5.0] >
> Enter observed metallicity, [Fe/H]_s [0.0, 0.1, -0.1] >
> Enter observed density, rho/rho_Sun [1.00, 0.01, -0.01] >
Observations are entered in the format
value +error -error
This enables the user to use asymmetrical error bars if needed. If
the measurements has symmetrical error bars, simply enter this value
twice, once as a positive value and once as a negative value. All
three numbers must be entered on the same line, followed by return.
The next three prompts enable the user to enter priors on the age,
initial metallicity and mass of the star.
For the age and metallicity, the default values are a flat distribution
over the valid model range. Priors values are entered in the format
loerr lolim hilim hierr
For chain values between lolim and hilim, the prior has a value
of 1. If hierr is >0 and the chain value is >hilim, then the prior has
a value exp(-0.5*(value-hilim)2/hierr2), and similarly for lolim and
loerr. For example, you can add a prior constraint that the age of star
must be less than the age of the Galactic disc (10 ± 1 Gyr) using the
following input.
$ Enter prior on age [Gyr] [0.0, 0.0, 17.5, 0.0] > 0 0 10 1
If hilim=0 then all trial chain points greater than hilim are rejected,
and similarly for lolim.
The prior on the mass is given by
log(Likelihood) = alpha*Mass
The default is to use a flat prior prior for mass, i.e.,alpha=0. For a
Salpeter distribution use alpha=-2.35.
The following prompts control the behaviour of Markov Chain calculation.
First there are 2 scaling factors that can be adjusted.
> Enter initial step size scale [0.500] >
> Enter MCMC step size scaling factor [1.00] >
These can generally be left at their default values, but you can
experiment with these values if you are having trouble getting your
Markov chain to converge. The first value scales the step size
calculated by perturbing each of the parameters in-turn prior to the
first Markov chain. The second value sets the step size in the two
Markov chains as a factor of the standard deviation of each jump
parameter.
The last two prompts set the lengths of the two Markov chains.
> Number of steps for MCMC burn-in [1000] >
> Number of MCMC steps [10000] >
The default values are ok for test runs, but for proper analysis
you will probably want to use values of 50-100,000 for both chains.
The calculation starts as soon as the last prompt is completed.
The output to screen summarizes the progress of the calculation. This
is self-explanatory once you have read and understood the description
of the method in Maxted et al. (2015) and the description of the
various output variables in the following section.
One value of interest is the mean acceptance rate for the 2nd MCMC
chain. This will generally have a value of 0.5±0.1 for a well-mixed
chain, perhaps slightly lower for complex cases. Values of the
acceptance rate lower than about 0.2 may suggest that the MCMC chain
has not converged.
OUTPUT FILES
------------
The following output files will also be created every time bagemass is
run.
chain.dat - Second Markov chain.
zams.dat - zero-age main sequence at best-fit [Fe/H]
track.dat - evolution file for best-fit mass and [Fe/H]
track_mlo.dat - evolution track for best-fit mass - error, and
best-fit [Fe/H]
track_mhi.dat - evolution track for best-fit mass + error, and
best-fit [Fe/H]
isochrone.dat - isochrone for best-fit age and [Fe/H]
isochrone_alo.dat - isochrone for best-fit age - error, and
best-fit [Fe/H]
isochrone_ahi.dat - isochrone for best-fit age + error, and
best-fit [Fe/H]
These are ascii files with comments in the headers preceeded with '#'
that describe the content of the file and give the variable names for
each column.
The variables in chain.dat are as follows.
Step - Markov chain step number
Age - Age in Gyr
Mass - Stellar mass in solar units
[Fe/H]_i - Initial metallicity
DeltaR - Undocumented/disabled feature (should always by 0.0)
Teff - Effective temperature in Kelvin
LogL - Logarithm of the luminosity in solar units
[Fe/H]_s - Surface metallicity
rho - Stellar density in solar units.
Xc - Central hydrogen abundance per unit mass
loglike - Logarithm of the likelihood
Chisq - chi-squared.
The content of the files zams.dat, etc. is similar, but it addition
the following variables are provided.
Radius - Radius in solar units
logg - Logarithm of the surface gravity in units of cm.s-2
Some variables appear twice in these files under column headings
Radius_0, Teff_0, etc.
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Acknowledgements:
Pierre Maxted, p.maxted(at)keele.ac.uk
(End) Patricia Vannier [CDS] 13-Jan-2015