Spectroscopic properties of a two-dimensional time-dependent Cepheid model II. Determination of stellar parameters and abundances

TL;DR

This study evaluates the accuracy of using static 1D models to determine stellar parameters of Cepheid variables by comparing them with dynamic models, highlighting phase-dependent biases and the need for multi-dimensional modeling.

Contribution

It demonstrates that hydrostatic 1D models can yield unbiased stellar parameters for Cepheids during specific pulsation phases, and identifies convective inhomogeneities as a key bias source.

Findings

1D models underestimate parameters by ~0.2 dex in iron abundance.

Biases are minimized when analyzing phases 0.3 to 0.65.

Multi-dimensional models are needed for longer-period Cepheids.

Abstract

Standard spectroscopic analyses of variable stars are based on hydrostatic one-dimensional model atmospheres. This quasi-static approach has theoretically not been validated. We aim at investigating the validity of the quasi-static approximation for Cepheid variables. We focus on the spectroscopic determination of the effective temperature $T_\mathrm{eff}$, surface gravity $\log \,g$, microturbulent velocity $\xi_\mathrm{t}$, and a generic metal abundance $\log\,A$ -- here taken as iron. We calculate a grid of 1D hydrostatic plane-parallel models covering the ranges in effective temperature and gravity encountered during the evolution of a two-dimensional time-dependent envelope model of a Cepheid computed with the radiation-hydrodynamics code CO5BOLD. We perform 1D spectral syntheses for artificial iron lines in local thermodynamic equilibrium varying the microturbulent velocity and abundance. We fit the resulting equivalent widths to corresponding values obtained from our dynamical model. For the four-parametric case, the stellar parameters are typically underestimated exhibiting a bias in the iron abundance of $\approx-0.2\,\mbox{dex}$. To avoid biases of this kind it is favourable to restrict the spectroscopic analysis to photometric phases $\phi_\mathrm{ph}\approx0.3\ldots 0.65$ using additional information to fix effective temperature and surface gravity. 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. For obtaining a complete view on the effects when determining stellar parameters with 1D models, multi-dimensional Cepheid atmosphere models are necessary for variables of longer period than investigated here.