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*Astron. Astrophys. 333, L35-L38 (1998)*
## 1. Introduction
The longer period Cepheids are particularly important in the
context of the primary distance scale because they are bright enough
to be visibile at a great distance. However, due to their low number,
they have been poorly studied both observationally and theoretically.
Simon & Kanbur (1995) considered 50 Cepheids in Galaxy and IC 4182
with period *P* less than 70 d, compared them with hydrodynamical
pulsation models and concluded that a detailed comparison between
theory and observations must await a more extensive and accurate
sample of observed stars. Antonello & Morelli (1996) analyzed all
the available photometric *V* data of galactic Cepheids with
period less than 70 d looking for possible resonance effects; they
noted some small features in the Fourier parameters-period diagrams
which were ascribed tentatively to expected resonances. Aikawa &
Antonello (1997) tried to reproduce these observations with nonlinear
models, but their conclusion was that the increasing nonadiabaticity
of the pulsation with period probably reduces the effectiveness of
resonance mechanisms. Finally, Simon & Young (1997) studied long
period Cepheids in the period range d in
Magellanic Clouds looking for galaxy-to-galaxy differences in the
Cepheid distributions. Resonances between pulsation modes, which were
studied essentially in Cepheids with *P* less than about 30 d,
represent a powerful comparison tool between observations and
theoretical model predictions, because they affect the shape of the
curves of pulsating stars in specific period ranges. The comparison of
the Fourier parameters of observed and theoretical light and radial
velocity curves allows to probe the stellar interior and to put
constraints on the stellar physical parameters. After the work of
Simon & Lee (1981) on the resonance at
d between the fundamental and second overtone
mode in classical bump Cepheids, several papers by various authors
were devoted to this topic, from both the observational and
theoretical point of view. For example, Buchler & Kovacs (1986)
and Moskalik & Buchler (1989) studied the general effects of 2:1
and 3:1 resonances in radial stellar pulsations and discussed the
possible astrophysical implications, Petersen (1989) discussed the
possible two- and three-mode resonances in Cepheids, and Antonello
(1994) looked for the expected effects in short period Cepheids.
Recent reviews on galactic and Magellanic Cloud Cepheids pulsating in
fundamental and first overtone mode and on the problems raised by the
comparison with the pulsational models are those by Buchler (1996) and
Beaulieu & Sasselov (1996). The resonance effects in Magellanic
Cloud Cepheids cannot be reproduced by models constructed using
current input physics and reasonable mass-luminosity relations; in
particular the case of first overtone Cepheids characterized by
(Antonello et al. 1990) has proven to be rather
difficult for theorists. We mention in passing also the recent
resonance , studied in the models of hypothetical
second overtone mode Cepheids (Antonello & Kanbur 1997).
In the present work we have considered the long-period Cepheids in
Magellanic Clouds, with available photometric and radial velocity data
which were suitable for Fourier decomposition. The initial purpose of
the work was simply to extend the comparison between theory and
observations to Cepheids with the longest known periods, but the
probable discovery of a new resonance effect suggested to publish the
present Letter in advance of the comparison with the hydrodynamical
models (Antonello & Aikawa, in preparation).
© European Southern Observatory (ESO) 1998
Online publication: April 20, 1998
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