J/A+A/587/A31 Statistical test on binary stars non-coevality (Valle+, 2016)
A statistical test on the reliability of the non-coevality of stars in binary
systems.
Valle G., Dell'Omodarme M., Valle G., Prada Moroni P.G., Degl'Innocenti S.
<Astron. Astrophys. 587, A31 (2016)>
=2016A&A...587A..31V 2016A&A...587A..31V (SIMBAD/NED BibCode)
ADC_Keywords: Binaries, eclipsing; Models, evolutionary ; Stars, ages
Keywords: binaries: eclipsing - methods: statistical - stars: evolution -
stars: low-mass
Abstract:
We develop a statistical test on the expected difference in age
estimates of two coeval stars in detached double-lined eclipsing
binary systems that are only caused by observational uncertainties. We
focus on stars in the mass range [0.8; 1.6] Msun, with an initial
metallicity [Fe/H] from -0.55 to 0.55dex, and on stars in the
main-sequence phase. The ages were obtained by means of the SCEPtER
technique, a maximum-likelihood procedure relying on a pre-computed
grid of stellar models. The observational constraints used in the
recovery procedure are stellar mass, radius, effective temperature,
and metallicity [Fe/H]. To check the effect of the uncertainties
affecting observations on the (non-)coevality assessment, the chosen
observational constraints were subjected to a Gaussian perturbation
before applying the SCEPtER code. We defined the statistic W computed
as the ratio of the absolute difference of estimated ages for the two
stars over the age of the older one. We determined the critical values
of this statistics above which coevality can be rejected in dependence
on the mass of the two stars, on the initial metallicity [Fe/H], and
on the evolutionary stage of the primary star. The median expected
difference in the reconstructed age between the coeval stars of a
binary system - caused alone by the observational uncertainties -
shows a strong dependence on the evolutionary stage. This ranges from
about 20% for an evolved primary star to about 75% for a near ZAMS
primary. The median difference also shows an increase with the mass of
the primary star from 20% for 0.8M☉ stars to about 50% for
1.6M☉ stars. The reliability of these results was checked by
repeating the process with a grid of stellar models computed by a
different evolutionary code; the median difference in the critical
values was only 0.01. We show that the W test is much more sensible to
age differences in the binary system components than the alternative
approach of comparing the confidence interval of the age of the two
stars. We also found that the distribution of W is, for almost all the
examined cases, well approximated by beta distributions.
The proposed method improves upon the techniques that are commonly
adopted for judging the coevality of an observed system. It also
provides a result founded on reliable statistics that simultaneously
accounts for all the observational uncertainties.
Description:
The table contains the W0.95 critical values, for the 1087 binary
systems considered in the paper. Tha table also lists the parameters
of the beta distributions approximating the empirical W distributions.
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
table2.dat 54 1087 Critical values for the W statistics
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See also:
http://astro.df.unipi.it/stellar-models : Stellar models Home Page
Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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1- 3 F3.1 Msun M1 Mass of the primary star
5- 7 F3.1 Msun M2 Mass of the secondary star
9- 13 F5.2 --- [Fe/H] Metallicity [Fe/H]
17- 19 F3.1 --- r Relative age of the primary star
21- 26 F6.4 --- W095 Critical value at level 0.05
30- 35 F6.4 --- e_W095 Statistical error on the critical value
37- 44 F8.6 --- a Paramater a of the beta distribution
46- 54 F9.6 --- b Paramater b of the beta distribution
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Acknowledgements:
Giada Valle, valle(at)df.unipi.it
(End) Giada Valle [Pisa University], Patricia Vannier [CDS] 12-Jan-2016