# Exploring the influence of different velocity fields on Wolf-Rayet star spectra

## TL;DR

This study systematically investigates how different velocity field models affect Wolf-Rayet star spectra, highlighting the importance of velocity law choice in spectral analysis and stellar parameter determination.

## Contribution

It provides a comprehensive analysis of the impact of $eta$-type velocity laws on WR spectra, comparing models with hydrodynamic atmospheres and emphasizing the need for diverse velocity law considerations.

## Key findings

- $eta$-exponent significantly influences spectral features.
- Values of $eta extgreater 8$ are unlikely in nature.
- UV spectroscopy is essential to accurately determine terminal velocities.

## Abstract

Given their strong stellar winds, Wolf-Rayet (WR) stars exhibit emission line spectra that are predominantly formed in expanding atmospheric layers. The description of the wind velocity field $v(r)$ is therefore a crucial ingredient in the spectral analysis of WR stars, possibly influencing the determination of stellar parameters. In view of this, we perform a systematic study by simulating a sequence of WR-star spectra for different temperatures and mass-loss rates using $\beta$-type laws with $0.5\leq\beta\leq 20$. We quantify the impact of varying $v(r)$ by analysing diagnostic lines and spectral classifications of emergent model spectra computed with the Potsdam Wolf-Rayet (PoWR) code. We additionally cross-check these models with hydrodynamically consistent -- hydro -- model atmospheres. Our analysis confirms that the choice of the $\beta$-exponent has a strong impact on WR-star spectra, affecting line widths, line strengths and line profiles. In some parameter regimes, the entire range of WR subtypes could be covered. Comparison with observed WR stars and hydro models revealed that values of $\beta \gtrsim 8$ are unlikely to be realized in nature, but a range of $\beta$-values needs to be considered in spectral analysis. UV spectroscopy is crucial here to avoid an underestimation of the terminal velocity $v_\infty$. Neither single- nor double-$\beta$ descriptions yield an acceptable approximation of the inner wind when compared to hydro models. Instead, we find temperature shifts to lower $T_{2/3}$ when employing a hydro model. Additionally, there are further hints that round-lined profiles seen in several early WN stars are an effect from non-$\beta$ velocity laws.