1 Introduction

Extreme helium early-type stars are located in a region on the H-R diagram between 10 000 and 25 000  K  and with $\log L/\mbox{$L_{\odot}$ }\gtrsim3$. Although this locus coincides with that of massive main sequence stars, they are low mass stars ( ${\lesssim} 1.0 ~\mbox{$M_{\odot}$ }$) in an advanced stage of evolution. Their unusually low surface hydrogen abundance, less than 1% (Drilling et al. 1998; Jeffery et al. 2001) is a question not entirely solved by stellar evolution theory.

Several theories have been proposed to explain their origin. The most recent hypothesis, explain the evolution of a merged binary helium white dwarf to become a low-mass helium star (Saio & Jeffery 2000). But evolution models strongly depend on the stellar parameters, in particular, the stellar mass and metallicity have to be accurately known.

A few low-mass (early-type) helium stars show periodic light variations due to stellar pulsations (Kilkenny & Koen 1995; Lynas-Gray et al. 1984; Jeffery & Saio 1999; Kilkenny et al. 1999) which provide a direct way to measure their mass, metallicity and position within the H-R diagram. At present just two of these, V652 Her and BX Cir (BD + 13$^{\rm o}$3224 and LSS 3184) have been identified as purely radial pulsators.

The instability strip for extreme helium stars was first discovered, using OPAL opacities and linear analysis, by Saio (1995). He found that pulsation models become unstable due to the iron-group ionization opacity peak at around $2\times10^{5}$  K   (iron-group bump mechanism). For early-type helium stars the instability boundaries were approximately located between $\mbox{~\em$T_{\rm eff}$ }= 25~000$ and 16 000  K   and between L =300 and $1000~ \mbox{$L_{\odot}$ }$ with small variations depending on stellar mass and metallicity.

Non-linear analyses of V652 Her have been previously carried out by Fadeyev & Lynas Gray (1996), providing radial velocity and luminosity curves for 0.72 $M_{\odot }$  models in good agreement with observational data. They also studied the variations of velocity and luminosity amplitudes within the instability strip, finding that the boundaries are close to those proposed by Saio (1995).

Recent observations of V652 Her (Jeffery et al. 2001) using higher resolution have provided a lower value for its mass. Also a more accurate measurement of its abundances gives a higher nitrogen abundance than previous results, as well as a carbon abundance smaller than solar. New observations have also provided better estimates of the mass and effective temperature of BX Cir (Woolf & Jeffery 2000).

The goal of this paper is to constrain the stellar parameters and in particular, the mass, effective temperature and metal abundances of V652 Her and BX Cir, by comparing new non-linear models with the recent observational data, as well as to analyze the variations of the light and velocity curves for this range of masses and effective temperatures.