[Paper Review] Modeling Massive Stars with Rotation: the Case of Nitrogen Enrichments

A. Maeder, G. Meynet+2 more|ArXiv.org|Oct 3, 2008

Astro and Planetary Science3 citations

TL;DR

This paper argues that nitrogen enrichment in massive stars is a multivariate function of mass, age, rotation velocity (v sin i), metallicity, and binarity, and that apparent contradictions in observational data arise from uncontrolled parameter variations. When mass and age are constrained, rotational mixing is strongly supported by observations, especially in low-metallicity environments like the SMC and LMC.

ABSTRACT

Recently, the concept of rotational mixing has been challenged by some authors (e.g. Hunter et al. 2008). We show that the excess N/H is a multivariate function f(M, age, v, sin i, multiplicity,Z). To find a correlation of a multivariate function with some parameter, it is evidently necessary to limit as much as possible the range of the other involved parameters. When this is done, the concept of rotational mixing is supported by the observations. We also show that the sample data are not free from several biases. A fraction of about 20% of the stars may escape to the relation as a result of binary evolution.

Motivation & Objective

• To resolve the controversy over rotational mixing in massive stars by analyzing the multivariate nature of nitrogen enrichment.
• To identify and correct for observational biases in v sin i and abundance measurements that distort observed correlations.
• To demonstrate that when mass and age are controlled, observed N/H excesses correlate strongly with rotation velocity.
• To quantify the impact of binary evolution on nitrogen enrichment, estimating ~20% of stars may escape the rotational mixing relation due to tidal mixing or mass transfer.
• To validate theoretical models of rotational mixing against observed N/H abundances in Galactic, LMC, and SMC stellar populations.

Proposed method

• Analyzes observed N/H excesses in massive stars across different galaxies (Galaxy, LMC, SMC) with varying metallicities (Z).
• Uses theoretical models to predict log(N/H) evolution during the main sequence as a function of initial mass, rotation velocity, and metallicity.
• Applies multivariate analysis to isolate the dependence of N/H on v sin i by constraining mass and age ranges in observational samples.
• Evaluates biases in the Hunter et al. (2008) dataset: lack of Be stars, neglect of gravity darkening, and incorrect mass estimates from non-rotating models.
• Compares observed v sin i vs. N/H relations in NGC 2004 and N11 clusters with theoretical predictions from Meynet & Maeder (2000).
• Reassesses mass estimates for fast-rotating stars using log g vs. log T_eff diagrams to correct for rotational effects on gravity.

Experimental results

Research questions

• RQ1 Is the observed lack of correlation between v sin i and N/H in massive stars due to uncontrolled variations in mass, age, or metallicity?
• RQ2 To what extent do observational biases—such as missing Be stars or incorrect gravity corrections—distort the observed relation between rotation and nitrogen enrichment?
• RQ3 How does the multivariate dependence of N/H on mass, age, v sin i, metallicity, and binarity affect the interpretation of observational data?
• RQ4 What fraction of massive stars may appear to deviate from the rotational mixing relation due to binary evolution processes?
• RQ5 Can the observed N/H excesses in low-metallicity environments (e.g., SMC) be explained by rotational mixing alone, or are other processes required?

Key findings

• The N/H excess in massive stars is a multivariate function f(M, age, v sin i, multiplicity, Z), and correlations with v sin i only emerge when mass and age are tightly constrained.
• In low-metallicity environments (Z ≈ 0.004 in SMC), observed N/H excesses reach up to 1.9 dex, consistent with strong rotational mixing predictions.
• The sample from Hunter et al. (2008) is biased toward slow rotators: the ratio of high- to low-velocity stars is only 0.14, compared to 0.40 in unbiased clusters.
• A significant fraction (~20%) of stars may escape the rotational mixing relation due to binary evolution, including tidal mixing and mass transfer.
• Star nb. 100 in NGC 2004, with v sin i = 323 km s⁻¹, may be misclassified due to rotational effects—its mass may be overestimated, and it could be a younger or binary star.
• Gravity darkening and rotational effects on surface gravity lead to systematic errors in mass estimation; correcting for these improves agreement with theoretical models.