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Abstract

Context. Standard spectroscopic analyses of variable stars are based on hydrostatic 1D model atmospheres. This quasi-static approach has not been theoretically validated. Aim. We aim at investigating the validity of the quasi-static approximation for Cepheid variables. We focus on the spectroscopic determination of the effective temperature T_eff, surface gravity log g, microturbulent velocity ξ_t, and a generic metal abundance log A, here taken as iron.
Methods: We calculated a grid of 1D hydrostatic plane-parallel models covering the ranges in effective temperature and gravity that are encountered during the evolution of a 2D time-dependent envelope model of a Cepheid computed with the radiation-hydrodynamics code CO5BOLD. We performed 1D spectral syntheses for artificial iron lines in local thermodynamic equilibrium by varying the microturbulent velocity and abundance. We fit the resulting equivalent widths to corresponding values obtained from our dynamical model for 150 instances in time, covering six pulsational cycles. In addition, we considered 99 instances during the initial non-pulsating stage of the temporal evolution of the 2D model. In the most general case, we treated T_eff, log g, ξ_t, and log A as free parameters, and in two more limited cases, we fixed T_eff and log g by independent constraints. We argue analytically that our approach of fitting equivalent widths is closely related to current standard procedures focusing on line-by-line abundances.
Results: For the four-parametric case, the stellar parameters are typically underestimated and exhibit a bias in the iron abundance of ≈-0.2 dex. To avoid biases of this type, it is favorable to restrict the spectroscopic analysis to photometric phases ϕ_ph ≈ 0.3…0.65 using additional information to fix the effective temperature and surface gravity.
Conclusions: Hydrostatic 1D model atmospheres can provide unbiased estimates of stellar parameters and abundances of Cepheid variables for particular phases of their pulsations. We identified convective inhomogeneities as the main driver behind potential biases. To obtain a complete view on the effects when determining stellar parameters with 1D models, multidimensional Cepheid atmosphere models are necessary for variables of longer period than investigated here.