Astron. Astrophys. 363, 568-574 (2000)

1. Introduction

Using a nonlocal and time-dependent convective model of RR Lyrae star (K, , , and ), and taking a large enough number of mass zones to model the extended atmosphere, Bono et al. (1994b) predicted the presence of velocity gradients around the phases at minimum radius. In particular, they showed evidence of a phase shift between the base of the atmosphere and the "surface" (layer with the smallest optical depth). They concluded that the base of the photosphere, where weak metal-lines are formed, are affected by substantial variations in physical conditions, and in particular in both opacity and density. These are the physical quantities which cause a velocity gradient and/or which trigger the formation of a shock wave, and in turn the Van Hoof effect.

Recently Chadid & Gillet (1998, hereafter Paper I) detected for the first time the Van Hoof effect between some metallic lines (Fe II-Fe I, Fe II-Ti II, etc.) in the atmosphere of RR Lyrae itself. According to Van Hoof & Struve (1953), this means that the motion of the different photospheric layers is not synchronous. In other words, the pulsation motion of the deep atmosphere already has the form of a running wave. This effect is probably the consequence of the propagation of shock waves in this part of the atmosphere. The existence of prominent shocks at the photospheric level were first detected observationally by Chadid & Gillet (1996a, 1997) and then theoretically confirmed by nonlinear nonadiabatic pulsating models (Fokin & Gillet 1997).

In previous hydrodynamic studies (Hill 1972; Fokin 1992), two main shocks per pulsation period were observed. The first one, called early shock and discovered by Hill, was explained by a collision between the free-falling high atmospheric layers and the slower upwarding photospheric layers. It occurs during the bump in the light curve (around phase 0.7). The main shock appears near phase 0.9 and is the consequence of the mechanism which is at the origin of the pulsation. A detailed analysis of the physical origin of these shocks has been recently proposed by Fokin & Gillet (1997). In fact, it appears that several shocks are formed during each pulsation period. Their physical origin is of three types.

In classical Cepheids, Scuti and Cephei stars, the Van Hoof effect was detected between Balmer and metallic lines (Van Hoof et al. 1954; Mc Namara et al. 1955; Struve et al. 1955; Yang et al. 1982; Wallerstein et al. 1992; Butler 1993; Mathias & Gillet 1993; Mathias et al. 1997) and between metallic lines themselves (Wallerstein et al. 1992; Mathias & Gillet 1993; Mathias & Aerts 1996). In RR Lyrae stars, Mathias et al. (1995), for the first time, detected the Van Hoof effect between metallic lines and Balmer ones. They interpreted the absence of a Van Hoof effect between metallic lines themselves as the lack of strong shocks within the deep atmosphere. Thus, strong shock waves were thought to be present only in the high atmosphere where the hydrogen line cores are formed, while the metallic ones are created in the photospheric layers.

Today, pulsating atmospheric models of RR Lyrae stars, including shock waves, are starting to be proposed. If the spatial resolution in the atmospheric layers is high enough, the calculation of line profiles and their comparison with high resolution observations would provide the potential to understand the atmospheric motions, as well as to test the accuracy of the models. Fokin & Gillet (1997) presented two hydrodynamical models of this type, with slightly different parameters in temperature and luminosity. These models are purely radiative and based on a Lagrangean grid, which means that they cannot perfectly describe the hydrogen ionization zone (HIZ) due to a poor space resolution.

Although these models are elaborated enough to confirm the presence of the metallic line doubling in RR Lyrae (Fokin & Gillet 1997), the observational detection of the Van Hoof effect between metallic lines themselves enables us to perform an accurate test of these pulsating models, which we aim to do in this paper.

In Sect. 2 we briefly describe the nonlinear nonadiabatic pulsational models that we use to reproduce the Van Hoof effect observed by Chadid & Gillet (1998). In Sect. 3 the theoretical results concerning the Van Hoof effect between two metallic lines are discussed. The comparison with observations and some concluding remarks are given in Sect. 4.

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
helpdesk.link@springer.de