High-resolution spectroscopy for Cepheids
distance determination. II. A period-projection factor relation
Nardetto, N., Mourard, D., Mathias,
Ph., Fokin, A., Gillet, D.
A&A, 471, pg.661-669 (2007)
Abstract
Context. The projection factor is a key quantity for the
interferometric Baade-Wesselink (hereafter IBW) and surface-brightness
(hereafter SB) methods of determining the distance of Cepheids. Indeed,
it allows a consistent combination of angular and linear
diameters of the star.
Aims.We aim to determine consistent projection factors that include the
dynamical structure of the Cepheids’ atmosphere.
Methods. Hydrodynamical models of δ Cep and ℓ Car have been used to
validate a spectroscopic method of determining the projection
factor. This method, based on the amplitude of the radial velocity
curve, is applied to eight stars observed with the HARPS
spectrometer. The projection factor is divided into three sub-concepts
: (1) a geometrical effect, (2) the velocity gradient within the
atmosphere,
and (3) the relative motion of the “optical” pulsating photosphere
compared to the corresponding mass elements (hereafter
fo−g). Both, (1) and (3) are deduced from geometrical and
hydrodynamical models, respectively, while (2) is derived directly from
observations.
Results.The Fe I 4896.439 Å line is found to be the best one to use in
the context of IBWand SB methods. A coherent and consistent
period-projection factor relation (hereafter Pp relation) is derived
for this specific spectral line: p = [−0.064 ± 0.020] log P + [1.376 ±
0.023]. This procedure is then extended to derive dynamic projection
factors for any spectral line of any Cepheid.
Conclusions. This Pp relation is an important tool for removing bias in
the calibration of the period-luminosity relation of Cepheids.
Moreover, it reveals a new physical quantity fo−g to
investigate in the
near future
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