[Paper Review] Probing the mass-loss history of AGB and red supergiant stars from CO rotational line profiles - II. CO line survey of evolved stars: derivation of mass-loss rate formulae

E. De Beck, L. Decin+5 more|UvA-DARE (University of Amsterdam)|Aug 5, 2010

Stellar, planetary, and galactic studies88 references129 citations

TL;DR

This paper derives analytical formulae to estimate mass-loss rates in evolved stars—AGB, red supergiant, and yellow hypergiant stars—using CO rotational line profiles across eight transitions. By modeling non-local thermal equilibrium radiative transfer in circumstellar envelopes, the method accounts for line saturation and spatial resolution, enabling accurate estimation of high mass-loss rates, with CO(2–1) providing the most reliable single-line estimate.

ABSTRACT

We aim to (1) set up simple and general analytical expressions to estimate mass-loss rates of evolved stars, and (2) from those calculate estimates for the mass-loss rates of asymptotic giant branch (AGB), red supergiant (RSG), and yellow hypergiant stars in our galactic sample. Rotationally excited lines of CO are a very robust diagnostic in the study of circumstellar envelopes (CSEs). When sampling different layers of the CSE, observations of these molecular lines lead to detailed profiles of kinetic temperature, expansion velocity, and density. A state-of-the-art, nonlocal thermal equilibrium, and co-moving frame radiative transfer code that predicts CO line intensities in the CSEs of late-type stars is used in deriving relations between stellar and molecular-line parameters, on the one hand, and mass-loss rate, on the other. We present analytical expressions for estimating the mass-loss rates of evolved stellar objects for 8 rotational transitions of the CO molecule, apply them to our extensive CO data set covering 47 stars, and compare our results to those of previous studies. Our expressions account for line saturation and resolving of the envelope, thereby allowing accurate determination of very high mass-loss rates. We argue that, for estimates based on a single rotational line, the CO(2-1) transition provides the most reliable mass-loss rate. The mass-loss rates calculated for the AGB stars range from 4x10^-8 Msun/yr up to 8x10^-5 Msun/yr. For RSGs they reach values between 2x10^-7 Msun/yr and 3x10^-4 Msun/yr. The estimates for the set of CO transitions allow time variability to be identified in the mass-loss rate. Possible mass-loss-rate variability is traced for 7 of the sample stars. We find a clear relation between the pulsation periods of the AGB stars and their derived mass-loss rates, with a levelling off at approx. 3x10^-5 Msun/yr for periods exceeding 850 days.

Motivation & Objective

• To develop general, analytical expressions for estimating mass-loss rates in evolved stars using CO rotational line profiles.
• To account for line saturation and envelope resolving effects in deriving mass-loss rate formulae for high-precision estimates.
• To apply these formulae to a sample of 47 evolved stars to derive mass-loss rates and detect variability.
• To investigate the relationship between pulsation periods and mass-loss rates in AGB stars.
• To estimate the 12C/13C isotope ratio from CO line intensity ratios as a probe of stellar evolution.

Proposed method

• Utilizes a non-local thermal equilibrium (non-LTE) radiative transfer code in the co-moving frame to model CO line intensities in circumstellar envelopes.
• Derives analytical relations between stellar parameters (e.g., luminosity, temperature) and CO line observables (e.g., line width, optical depth, integrated flux) to estimate mass-loss rate.
• Applies the formalism to 47 evolved stars observed in 8 CO rotational transitions (J=1–0 to J=8–7), covering both low- and high-excitation lines.
• Corrects for interstellar and circumstellar reddening using (V–K)0 color indices and empirical temperature calibrations.
• Uses CO(2–1) line as the primary reference due to optimal balance between sensitivity and line saturation effects.
• Employs multi-line CO data to detect time variability in mass-loss rates and derive 12C/13C ratios from line intensity ratios.

Experimental results

Research questions

• RQ1 What analytical formulae can reliably estimate mass-loss rates in evolved stars using CO rotational line profiles, accounting for saturation and resolution?
• RQ2 Which CO transition provides the most accurate single-line estimate of mass-loss rate for evolved stars?
• RQ3 How do mass-loss rates in AGB and red supergiant stars correlate with their pulsation periods?
• RQ4 Can time variability in mass-loss rates be detected from multi-epoch CO line data?
• RQ5 What is the 12C/13C isotope ratio in evolved stars, and how does it relate to their evolutionary state?

Key findings

• The derived analytical formulae allow accurate estimation of mass-loss rates across 8 CO rotational transitions, with CO(2–1) providing the most reliable single-line estimate.
• Mass-loss rates for AGB stars range from 4×10⁻⁸ M⊙ yr⁻¹ to 8×10⁻⁵ M⊙ yr⁻¹, while red supergiants show rates between 2×10⁻⁷ M⊙ yr⁻¹ and 3×10⁻⁴ M⊙ yr⁻¹.
• Seven stars in the sample show evidence of time variability in their mass-loss rates, detectable through multi-line CO profile analysis.
• A clear correlation exists between pulsation period and mass-loss rate in AGB stars, with a plateau at ~3×10⁻⁵ M⊙ yr⁻¹ for periods exceeding 850 days.
• The 12C/13C isotope ratio is derived from CO line intensity ratios, providing a probe of chemical evolution and evolutionary state.
• The method successfully accounts for line saturation and spatial resolution, enabling robust estimation of high mass-loss rates up to ~10⁻⁴ M⊙ yr⁻¹.