VLTI observations of the Orion Belt stars: I. eps Orionis

TL;DR

This work tackles how to constrain the current state and structure of the nearest massive OB stars by combining high-angular-resolution interferometry with spectroscopy and SEDs. The authors develop and apply a modified PHOEBE2 framework with new interferometric and spectroscopic modules to model non-spherical, rotating stars via triangular meshes and grids of synthetic spectra, using a simplex/chi-squared approach for fitting. They present a detailed single-star model for the B0 Ia supergiant $\varepsilon$ Ori, finding it to be near-critically rotating and non-spherical with $d\approx384$ pc, $m\approx28$ M⊙, $R_{equiv}\approx27$–$34$ R⊙, and $T_{eff}\approx25{,}000$ K, though tensions remain between interferometric and spectroscopic constraints and closure-phase signatures suggest circumstellar material or possible disk features. The results illustrate the power and challenges of joint interferometric-spectroscopic modeling for massive stars and lay the groundwork for the planned follow-up study of the Orion Belt multiple systems, with broad implications for massive-star evolution and end states.

Abstract

Massive stars play a decisive role in the evolution of the Universe. In order to constrain their current state and structure, we need sufficiently complex models, constrained by astrometric, interferometric, and spectroscopic observations. However, they are not available for distant stars. Instead, we focused on the nearest massive stars in the Orion Belt. We obtained VLTI interferometric observations of Orion Belt stars and calibrated visibility data from the GRAVITY and PIONIER instruments. Additionally, we obtained spectroscopic data from the CFHT and CTIO observatories. For modelling, we used a modified version of PHOEBE2, extended with new interferometric and spectroscopic modules. To describe non-spherical, rotating, or Roche-like stars, integrals over triangular meshes have to be computed, using extensive grids of synthetic spectra. For fitting, we used the simplex algorithm and chi2 mapping of the parameter space. In this paper, we present single-star models of the B0Ia supergiant eps Ori. Interferometric visibilities indicate that the star is not spherical but rotating close to its critical velocity. The preferred distance, d=(384+-8)pc, corresponds to the median of distances for the Orion OB1b association. We obtained the following parameters: m=(28.4+-2.0)Msol, R=(27.6+-1.5)Rsol, Teff=25000 K, i=45deg, longitude of the ascending node, Omega=300deg, and Prot=4.3+1.0d. This compromise model provides a reasonable fit to wind-free Balmer line profiles, but there is still some tension between interferometric and spectroscopic datasets, corresponding to a faster- vs. slower-rotating star. Our fast-rotating model implies that circumstellar matter should be naturally present, in the form of wind or disk, and contribute to continuum radiation. The fast rotation of eps Ori is compatible with a merger, formed from a multiple system of comparable mass, like del, zet or sig Ori.

Figures (21)

• Figure 1: Coverage for interferometric measurements showing the squared visibility $V^2$ vs baselines $(u,v) \equiv \vec{B}/\lambda$ in cycles per baseline. Individual panels show four stars in Orion's Belt ($\zeta$, $\sigma$, $\varepsilon$, and $\delta$ Ori). For each star, all nights are plotted. Colours correspond to visibility values.
• Figure 2: Examples of reduced squared visibilities, $V^2$, of the science targets, $\varepsilon$, $\delta$, $\zeta$, and $\sigma$ Ori. Measurements are from nights: 20 November 2023, 22 November 2023, 8 January 2024, and 23 November 2023, respectively. Science targets are with obvious signals from companions. For the single star $\varepsilon$ Ori, the signal suggests an elongated or non-spherical shape, unlike the calibrator $\zeta$ Lep, which exhibits a perfectly spherical shape. Colours correspond to individual baselines. The squared visibilities of calibrators are in Fig. \ref{['reduced_visibility_cal']}.
• Figure 3: Comparison of DIBs' intensities for $\varepsilon$ Ori and stars which are close on the sky (HD 37140 and HD 36628). The most distant star has the deepest DIBs, while the star with the lowest distance has very weak DIBs. The spectrum of $\varepsilon$ Ori also shows weak DIBs, which suggests its distance is lower than 420 pc. The spectra were taken from public archives of CFHT and ESO.
• Figure 4: Grids of synthetic spectra BSTAR and OSTAR Lanz_2003ApJS..146..417LLanz_2007ApJS..169...83L used in our spectroscopic models. Each spectrum is parametrised by $\log g$ and $T$. To describe also critically rotating stars (cf. green points), it was necessary to compute additional ATLAS spectra Castelli2003IAUS..210P.A20C for low values of $\log g$ and $T$.
• Figure 5: Almost spherical model of $\varepsilon$ Ori based on PIONIER observations in H-band with fixed $v\sin i$Puebla2016. Left: Squared visibility vs projected baseline $B/\lambda$. Right: Corresponding triangular mesh with the passband intensities (greyscale). The model was converged starting with the parameters from Table \ref{['vsini_fixed_table']} (bold line). The best-fit was with $\chi^2_{\mathrm{VIS}} = 11.23$. The free parameters were $i = 13.6$ deg, $m = 20.3$ _⊙ M$_{\odot}$, $\Omega = 293.7$ deg, $P_\mathrm{rot} = 4.01$ d. The fixed parameters were $v\sin i = 70\,{\rm km}\,{\rm s}^{-1}$, $T = 25\,000$ K, $\gamma = 25.9$ km s$^{-1}$ and the derived parameters were $v = 298\,{\rm km}\,{\rm s}^{-1}$, $R_\mathrm{equiv} = 22.43$ _⊙ R$_{\odot}$ (derived), $R_{\mathrm{pole}} = 22.29$ _⊙ R$_{\odot}$ (derived), $R_{\mathrm{equ}} = 22.46$ _⊙ R$_{\odot}$ (derived), $\theta_\mathrm{equiv} = 0.543$ mas. The star is close to critical rotation and has an almost pole-on orientation in order to decrease projected rotation (cf. $v\sin i$).