1 Introduction

Pulsating stars are among the principal tools to explore the adequacy of stellar structure and stellar evolution models. Classical Cepheids are the best studied of all pulsating stars, due to their key role as extragalactic distance estimators. The shape of their light or velocity curves in particular, can constrain structure and pulsation models. Hertzsprung (1926) noticed that the shape of Cepheid light curves varies along with the pulsation period: the curves exhibit a secondary "bump" that crosses the main sinusoidal signal at a period of about 10 days. This so-called "Hertzsprung progression" is related to the 2:1 resonance between the fundamental eigenmode P₀ and the second overtone P₂ (Buchler et al. 1990). It can therefore be used to derive information on the pulsation mechanism, the structure and the mass of a Cepheid, leading for instance to pulsational mass estimations ("bump mass"), that can be compared to the masses derived from evolution models (Cox 1980; Moskalik et al. 1992).

However, the light curve is less suitable than the radial velocity curve for precise constraints on resonances and on the pulsation mechanism. Since resonance is a dynamical phenomenon, it is better traced by a dynamical quantity such as the radial velocity than by photometry which, especially in the visual, is more affected by temperature changes than by actual pulsating motions. A dramatic illustration of this fact is given by Kienzle et al. (1999) and Feuchtinger et al. (2000) in their study of overtone Cepheids. In that case, while the light curve parameters were suggestive of a resonance near P=3 days, the velocity curves unambiguously indicated that the resonance is at P=4.2 days. For this reason, the analysis of radial velocity data is essential to refine the indications derived from the more abundant photometric data.

Light or velocity curve morphologies can be quantified by Fourier series fitting, the resulting amplitudes and phase being combined into Fourier parameters (Simon & Lee 1981). The most important parameter describing the Hertzsprung progression is $\phi _{21}$, the phase shift between the first and second order (see Sect. 3 for a precise definition). It constrains the position of the P₂/P₀ resonance, the feature that dominates the variation of Cepheid pulsation curve shape with period. Two other parameters are also very informative: A₁, the semi-amplitude of the first order, and R₂₁, the amplitude ratio of the second and first orders.

The P₂/P₀ resonance for Galactic Cepheids of solar metallicity is well studied and its position has been accurately measured by Moskalik et al. (1999) from the $\phi _{21}$ progression using radial velocity data for 82 Cepheids. However, the effect of metallicity on the location of this resonance is an open question. The precise position of the resonance, and its evolution with the metallicity, is important to constrain the new generation of pulsation models taking into account evolution (Alibert et al. 1999) and convection (Bono et al. 2000b; Feuchtinger et al. 2000). An accurate determination of the effect of metal-deficiency on Fourier parameters can lead to improvements in the models themselves, to a better understanding of the effect of metallicity, and ultimately to more confident predictions about the metallicity effects on the Cepheid distance scale - presently a very debated question (Tanvir 1999; Caputo et al. 2000). The radiative pulsation models (with frozen convection approximation) of Buchler (1997) predict a significant metallicity dependence on the shape of the $\phi _{21}$ progression, mainly in the form of a reduced variation of $\phi _{21}$ around the resonance period, while observational results from the extensive photometric data of the LMC and SMC microlensing experiments indicate roughly unchanged Fourier parameters around the resonance - although Antonello et al. (2000) recently suggested that the $\phi _{21}$ feature may be very weak in the metal-poor irregular galaxy IC 1613. As for radial velocity data, there is at present no quantitative estimate of curve morphology evolution for metal-deficient Cepheids.

Cepheids in the Galaxy follow a radial metallicity gradient of the order of -0.07 dex/kpc (Harris 1981). Consequently, Cepheids located near the edge of the Galactic disc, at galactocentric distances in the range 12-14 kpc, have an abundance similar to LMC Cepheids, [Fe/H $]\sim -0.3$ dex.

As a first step towards the determination of the properties of the P₂/P₀ resonance at low metallicities, we present new radial velocity data for outer disc metal-poor Cepheids, and analyse their Fourier decomposition parameters. These objects are studied in the context of a programme of distance determination by the surface brightness technique, in order to determine the effect of metallicity on Cepheid absolute magnitudes (Gieren et al. 1997; Fouqué & Gieren 1997). The present study is an initial by-product of that programme.