Bibcode
Kallinger, T.; Beck, P. G.; Stello, D.; Garcia, R. A.
Bibliographical reference
Astronomy and Astrophysics, Volume 616, id.A104, 18 pp.
Advertised on:
8
2018
Journal
Citations
40
Refereed citations
36
Description
Context. In recent years the global seismic scaling relations for the
frequency of maximum power, νmax ∝ g /
√Teff, and for the large frequency separation,
Δν ∝ √ρ¯, have drawn attention in
various fields of astrophysics. This is because these relations can be
used to estimate parameters, such as the mass and radius of stars that
show solar-like oscillations. With the exquisite photometry of Kepler,
the uncertainties in the seismic observables are small enough to
estimate masses and radii with a precision of only a few per cent. Even
though this seems to work quite well for main-sequence stars, there is
empirical evidence, mainly from studies of eclipsing binary systems,
that the seismic scaling relations systematically overestimate the mass
and radius of red giants by about 15% and 5%, respectively. Various
model-based corrections of the Δν-scaling reduce the problem
but do not solve it. Aims: Our goal is to define revised seismic
scaling relations that account for the known systematic mass and radius
discrepancies in a completely model-independent way. Methods: We
use probabilistic methods to analyse the seismic data and to derive
non-linear scaling relations based on a sample of six red giant branch
(RGB) stars that are members of eclipsing binary systems and about 60
red giants on the RGB as well as in the core-helium burning red clump
(RC) in the two open clusters NGC 6791 and NGC 6819. Results: We
re-examine the global oscillation parameters of the giants in the binary
systems in order to determine their seismic fundamental parameters and
we find them to agree with the dynamic parameters from the literature if
we adopt non-linear scalings. We note that a curvature and glitch
corrected Δνcor should be preferred over a local or
average value of Δν. We then compare the observed seismic
parameters of the cluster giants to those scaled from independent
measurements and find the same non-linear behaviour as for the eclipsing
binaries. Our final proposed scaling relations are based on both samples
and cover a broad range of evolutionary stages from RGB to RC stars: g /
√Teff = (νmax /
νmax,⊙)1.0075±0.0021 and
√ρ¯ = (Δνcor /
Δνcor,⊙)[η - (0.0085 ± 0.0025)
log2(Δνcor /
Δνcor,⊙)]-1, where g,
Teff, and ρ¯ are in solar units,
νmax,⊙ = 3140 ± 5 μHz and
Δνcor,⊙ = 135.08 ± 0.02 μHz, and η
is equal to one in the case of RGB stars and 1.04 ± 0.01 for RC
stars. Conclusions: A direct consequence of these new scaling
relations is that the average mass of stars on the ascending giant
branch reduces to 1.10 ± 0.03 M⊙ in NGC 6791 and
1.45 ± 0.06 M⊙ in NGC 6819, allowing us to revise
the clusters' distance modulus to 13.11 ± 0.03 and 11.91 ±
0.03 mag, respectively. We also find strong evidence that both clusters
are significantly older than concluded from previous seismic
investigations.
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