[Paper Review] The rotation rates of massive stars: How slow are the slow ones?

J. O. Sundqvist, S. Simón‐Díaz+2 more|arXiv (Cornell University)|Oct 17, 2013

Stellar, planetary, and galactic studies37 references13 citations

TL;DR

This study evaluates the reliability of standard spectroscopic methods—Fourier transform (FT) and goodness-of-fit (GOF)—for measuring projected rotation speeds ($v\sin i$) in slowly rotating massive stars. Using two magnetic O-stars with known rotation periods ($P > 500$ days) and $v\sin i < 1\ \text{km}\,\text{s}^{-1}$, the authors find that both methods severely overestimate $v\sin i$ at $\approx 40-50\ \text{km}\,\text{s}^{-1}$, primarily due to inadequate treatment of microturbulence and macroturbulence, which confound rotational broadening signatures in spectral lines.

ABSTRACT

Context: Rotation plays a key role in the life cycles of stars with masses above 8 Msun. Hence, accurate knowledge of the rotation rates of such massive stars is critical for understanding their properties and for constraining models of their evolution. Aims: This paper investigates the reliability of current methods used to derive projected rotation speeds v sin i from line-broadening signatures in the photospheric spectra of massive stars, focusing on stars that are not rapidly rotating. Methods: We use slowly rotating magnetic O-stars with well-determined rotation periods to test the Fourier transform (FT) and goodness-of-fit (GOF) methods typically used to infer projected rotation rates of massive stars. Results: For our two magnetic test stars with measured rotation periods longer than one year, i.e., with v sin i &lt; 1 km/s, we derive v sin i ~ 40-50 km/s from both the FT and GOF methods. These severe overestimates are most likely caused by an insufficient treatment of the competing broadening mechanisms referred to as microturbulence and macroturbulence. Conclusions: These findings warn us not to rely uncritically on results from current standard techniques to derive projected rotation speeds of massive stars in the presence of significant additional line broadening, at least when v sin i

Motivation & Objective

• To assess the reliability of widely used spectroscopic techniques—Fourier transform (FT) and goodness-of-fit (GOF)—for measuring $v\sin i$ in massive stars.
• To investigate whether current methods can accurately retrieve $v\sin i$ in the slow-rotation regime ($v\sin i \lesssim 1\ \text{km}\,\text{s}^{-1}$) when competing broadening mechanisms are present.
• To evaluate the impact of microturbulence and macroturbulence on the accuracy of $v\sin i$ measurements in massive stars with known rotation periods.
• To address the long-standing observational puzzle of the apparent deficiency of O-stars with $v\sin i \approx 0\ \text{km}\,\text{s}^{-1}$.
• To improve the physical basis for interpreting $v\sin i$ measurements in massive stars, particularly for B-supergiants and magnetically braked stars.

Proposed method

• High-resolution spectroscopic data from the MiMeS database were used, specifically for two magnetic O-stars—HD 191612 and HD 108—with precisely measured rotation periods of 538 days and >1 year, respectively.
• The Fourier transform (FT) method was applied, using the first zero in the Fourier power spectrum to estimate $v\sin i$ from line-broadening signatures.
• The goodness-of-fit (GOF) method was employed, fitting observed line profiles with synthetic profiles that include rotational, microturbulent, and macroturbulent broadening components.
• The analysis compared results from both methods against the true $v\sin i$ values derived from the known rotation periods and stellar inclinations.
• Sensitivity tests were performed by varying the assumed macroturbulent profile (e.g., RT vs. isotropic), assessing the degeneracy in $v\sin i$ solutions.
• Synthetic profile tests were used to confirm that microturbulence of $\sim 20\ \text{km}\,\text{s}^{-1}$ can mimic rotational broadening at $\sim 30-40\ \text{km}\,\text{s}^{-1}$ in Fourier space.

Experimental results

Research questions

• RQ1 Can standard spectroscopic methods reliably measure $v\sin i$ in massive stars with $v\sin i \lesssim 1\ \text{km}\,\text{s}^{-1}$?
• RQ2 To what extent do microturbulence and macroturbulence distort the inferred $v\sin i$ values when using FT and GOF methods?
• RQ3 Why do observed populations of O- and B-stars show a deficiency of stars with $v\sin i \approx 0\ \text{km}\,\text{s}^{-1}$, despite theoretical expectations of slow rotators?
• RQ4 How does the assumed shape of macroturbulent velocity profiles affect the derived $v\sin i$ in GOF fitting?
• RQ5 Can the overestimation of $v\sin i$ in slow rotators be attributed to insufficient modeling of competing broadening mechanisms?

Key findings

• For the two magnetic O-stars HD 191612 and HD 108, both the FT and GOF methods yield $v\sin i \approx 40-50\ \text{km}\,\text{s}^{-1}$, despite their true $v\sin i$ being less than $1\ \text{km}\,\text{s}^{-1}$.
• The severe overestimation is primarily caused by the inadequate treatment of microturbulence and macroturbulence, which produce spectral line broadening that mimics rotational effects.
• Synthetic profile tests confirm that microturbulent velocities of $\sim 20\ \text{km}\,\text{s}^{-1}$ can generate Fourier-space minima at frequencies corresponding to $\sim 30-40\ \text{km}\,\text{s}^{-1}$, mimicking rotation.
• Assuming isotropic macroturbulence instead of the more physically motivated RT (radial-tangential) profile leads to degenerate GOF solutions across $v\sin i \approx 0-60\ \text{km}\,\text{s}^{-1}$, indicating high uncertainty.
• The results suggest that the observed deficiency of O-stars with $v\sin i \approx 0\ \text{km}\,\text{s}^{-1}$ may stem from systematic overestimation due to unmodeled broadening, not intrinsic lack of slow rotators.
• The findings imply that current $v\sin i$ measurements for slow-rotating massive stars—especially B-supergiants—may be systematically biased high, potentially reconciling observations with single-star evolution models that predict near-zero rotation.