Spectroscopic properties of a two-dimensional time-dependent Cepheid model

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 Teff, surface gravity log g, microturbulent velocity ξt, 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 Teff, log g, ξt, and log A as free parameters, and in two more limited cases, we fixed Teff 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 ϕph ≈ 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.

Atmospheric parameters of Cepheids from flux ratios with ATHOS: I. The temperature scale

“…The excitation equilibrium of Fe i and Fe ii lines is commonly used to derive the effective temperature of FGK stars, including in our own analyses of Cepheids (e.g., Lemasle et al 2007Lemasle et al , 2008Lemasle et al , 2017, under the assumptions of hydrostatic and local thermodynamic equilibrium (LTE). The first hypothesis obviously does not hold for pulsating variables and biases the results as recently verified for Cepheids by Vasilyev et al (2017Vasilyev et al ( , 2018. The LTE hypothesis does not hold either (e.g.…”

Atmospheric parameters of Cepheids from flux ratios with ATHOS

“…The excitation equilibrium of Fe I and Fe II lines is commonly used to derive the effective temperature of FGK stars, including in our own analyses of Cepheids (e.g., Lemasle et al 2007Lemasle et al , 2008Lemasle et al , 2017, under the assumptions of hydrostatic and local thermodynamic equilibrium (LTE). The first hypothesis obviously does not hold for pulsating variables and biases the results as recently verified for Cepheids by Vasilyev et al (2017Vasilyev et al ( , 2018. The LTE hypothesis does not hold either (e.g., Fuhrmann 1998;Thévenin & Idiart 1999) and this is also true for Cepheids (e.g., Vasilyev et al 2019).…”

Two-dimensional non-LTE O I 777 nm line formation in radiation hydrodynamics simulations of Cepheid atmospheres

“…2 which also shows the parameters for the model M3 and M9. 5200 5300 5400 5500 5600 5700 5800 5900 6000 Technical details concerning 1D hydrostatic models can also be found in Vasilyev et al (2018).…”

“…As in the case of observations, Fe i and Fe ii lines were used for the diagnostic of the microturbulent velocity. The line list, which was given in Vasilyev et al (2018), contains artificial neutral and singly ionised iron lines with excitation potentials 1, 3, and 5 eV. Oscillator strengths were chosen to cover the linear and non-linear parts of the curve of growth.…”

“…Secondly, the surface gravity of our 1D models is based on the effective acceleration g eff of an Lagrangian mass element located near optical depth unity in the 2D models. This differs from a g eff adopting the condition of ionisation balance, which is traditionally used in classical 1D analyses to measure the surface gravity (Vasilyev et al 2018).…”