Unveiling stellar spin: Determining inclination angles in Be stars

¹ Instituto de Física y Astronomía, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111, Valparaíso, Chile
² Departamento de Física, Universidade Federal de São Paulo, Rua Prof. Artur Riedel, 275, 09972-270, Diadema, SP, Brazil
³ Centro Multidisciplinario de Física, Vicerrectoría de Investigación, Universidad Mayor, 8580745 Santiago, Chile
⁴ Instituto de Estadística, Facultad de Ciencias, Universidad de Valparaíso, Av. Gran Bretaña 1111, Valparaíso, Chile

^★ Corresponding author; daniela.turis@postgrado.uv.cl

Received: 30 October 2024
Accepted: 10 February 2025

Abstract

Context. The physical properties of stellar atmospheres in rapidly rotating massive stars, such as Be stars, are critical to understanding their evolution and their role as progenitors of supernovae. These stars, which often have near-critical rotation, exhibit equatorial stretching and gravity darkening, which significantly complicates the determination of parameters such as the inclination angle. Be stars, characterized by their extreme rotational velocities, serve as excellent candidates for exploring these phenomena. However, fundamental quantities such as polar and equatorial radii and inclination angles are typically derived from interferometry, which applies only to a limited number of stars.

Aims. This study aims to enhance the determination of inclination angles for Be stars using the ZPEKTR spectral synthesis code. By incorporating advanced models of gravity darkening and stellar deformation, we evaluated the effectiveness of this method with a sample of ten Be stars from the BeSOS database, comparing results with established interferometric data.

Methods. We used the ZPEKTR code to model the effects of stellar oblateness and gravity darkening on spectral lines, focusing on the HeI 4471 Å line. We applied a χ²-test minimization approach to identify the best-fitting models, and we evaluated the inclination angles derived against interferometric measurements.

Results. Our analysis reveals a robust linear correlation (slope: 0.952 ± 0.033; R² = 0.989) between the inclination angles derived from ZPEKTR and using interferometric techniques, which demonstrates an excellent agreement. The ZPEKTR code effectively models high rotational velocity effects, providing precise stellar parameter determinations.

Conclusions. The ZPEKTR code is a powerful tool for estimating inclination angles in Be stars. The results underscore the potential of advanced spectroscopic techniques to yield inclination measurements comparable to interferometry, which offers a pathway to studying distant massive stars for which interferometric observations are not feasible.