Effects on vsini determinations of O stars from 3D model atmospheres with high turbulent velocities

Technical Summary: Effects on $v \sin i$ Determinations of O Stars from 3D Model Atmospheres with High Turbulent Velocities

Problem Statement
Determining the projected rotational velocity ($v \sin i$) of massive O stars is fundamental to understanding their life cycles and constraining evolutionary models. However, this determination faces a primary challenge: the degeneracy between rotational line broadening and other broadening mechanisms, specifically macroturbulence. Observations of O-star absorption lines reveal velocity dispersions ($\sigma_V \sim 50$ km/s) far exceeding thermal motions, which cannot be explained by rotation alone. While empirical techniques like the Fourier Transform (FT) method and Goodness-of-Fit (GOF) method are standard for separating these components, previous work (e.g., Sundqvist et al. 2013b) suggests these methods become unreliable when $v \sin i \lesssim 50$ km/s due to the overlap of broadening components. Recent 3D radiation-hydrodynamics (RHD) simulations have shown that high turbulent velocities naturally reproduce this "extra broadening," but these models previously lacked rotation, leaving the separation problem unaddressed in a realistic 3D context.

Methodology
The authors introduce rotation into existing 3D RHD model atmospheres of O stars to generate synthetic line profiles that include both rotation and intrinsic turbulent velocities.

• Model Setup: Using a 3D model (Delbroek et al. 2025) with a fixed inner boundary rotation ($v_{\text{rot,in}}$), the authors conserve azimuthal angular momentum to simulate rotation. They focus on the O III 5594 Å absorption line.
• Mock Observations: The authors generate synthetic line profiles for various observer inclination angles ($i$). These profiles serve as "mock observations" where the true $v \sin i$ and macroturbulent velocity ($v_{\text{macro}}$) are known from the simulation.
• Retrieval Analysis: The authors apply standard empirical 1D methods to these 3D mock data to test their reliability:
  1. Fourier Transform (FT): Searching for the first zero in the Fourier power spectrum to determine $v \sin i$.
  2. Goodness-of-Fit (GOF): Fitting the line profile using a convolution of rotational and isotropic Gaussian macroturbulent broadening to find best-fit parameters.
• Constraints: The study assumes the 3D models have no noise (unlike real observations) and acknowledges that 3D profiles may lack the symmetry of 1D models, potentially affecting the fit.

Key Results
The analysis reveals significant limitations in standard methods when turbulent velocities are high and unknown:

• FT Method Reliability: The FT method yields reasonable results only when $v \sin i > v_{\text{macro}}$. When $v \sin i < v_{\text{macro}}$, the method becomes highly unreliable, often overestimating $v \sin i$ by factors of 3 to 10. Crucially, the FT method always produces a non-zero result due to fiducial minima created by high turbulent velocities, even for pole-on views ($i=0^\circ$) where rotation should be undetectable.
• GOF Method Degeneracy: The GOF method exhibits a strong degeneracy between $v \sin i$ and $v_{\text{macro}}$. When neither parameter significantly dominates the other, the best-fit values are not unique but are distributed across a large region of the parameter space.
• The "Howarth Curve" Degeneracy: The region of degenerate best-fit values in the GOF analysis closely follows the empirical formula derived by Howarth et al. (2007):
  $$C = \sqrt{\frac{v_{\text{macro}}^2}{2} + \frac{(v \sin i)^2}{4}}$$
  The inferred value ($C_i$) is consistently greater than or equal to the expected value ($C_e$). This implies that standard fitting can only constrain the sum of these terms, not the individual components, unless one clearly dominates.
• Parameter Constraints:
  • If $v \sin i \gg v_{\text{macro}}$, $v \sin i$ is well-constrained, but $v_{\text{macro}}$ is not.
  • If $v_{\text{macro}} \gg v \sin i$, $v_{\text{macro}}$ is well-constrained, but $v \sin i$ is overestimated.
  • If $v \sin i \approx v_{\text{macro}}$, neither parameter can be reliably determined individually.

Significance and Claims
The paper concludes that standard spectroscopic methods (FT and GOF) generally cannot independently determine $v \sin i$ and $v_{\text{macro}}$ in the presence of high turbulent velocities found in 3D O-star atmospheres. Instead, these methods primarily approximate the combined quantity $\sqrt{v_{\text{macro}}^2/2 + (v \sin i)^2/4}$.

The authors assert that this finding necessitates a re-analysis and re-interpretation of previously established empirical correlations between $v \sin i$ and $v_{\text{macro}}$ (e.g., Simón-Díaz et al. 2017) and the statistical distributions of observed rotation rates in O-star populations (e.g., Ramírez-Agudelo et al. 2013). The study suggests that previous determinations of rotation rates may be significantly altered if the macroturbulent velocity was not independently calibrated (e.g., via 3D simulations) or if it did not clearly dominate the broadening. The paper does not propose new observational techniques but highlights the need to reinterpret existing data in light of these 3D atmospheric effects.