[Paper Review] Models of circumstellar molecular radio line emission: Mass loss rates for a sample of bright carbon stars

F. L. Schoeier, H. Olofsson|ArXiv.org|Jan 26, 2001

Astrophysics and Star Formation StudiesPhysics and Astronomy35 references133 citations

TL;DR

This study models circumstellar CO radio line emission from 69 bright carbon stars using radiative transfer and energy balance calculations to derive mass loss rates, expansion velocities, and temperature structures. It finds mass loss rates span 5×10⁻⁹ to 2×10⁻⁵ M☉ yr⁻¹, with a median of 2.8×10⁻⁷ M☉ yr⁻¹, and reveals strong correlations between mass loss rate, pulsational period, and luminosity, supporting dust-driven wind models with pulsation playing a key role.

ABSTRACT

Using a detailed radiative transfer analysis, combined with an energy balance equation for the gas, we have performed extensive modelling of circumstellar CO radio line emission from a large sample of optically bright carbon stars. We determine some of the basic parameters that characterize circumstellar envelopes (CSEs), e.g., the stellar mass loss rate, the gas expansion velocity, and the kinetic temperature structure of the gas. The derived mass loss rates span almost four orders of magnitude, from 5E-9 up to 2E-5 solar masses per year, with the median mass loss rate being 3E-7 solar masses per year. We estimate that the estimated mass loss rates are typically accurate to 50% within the adopted circumstellar model. The physical conditions prevailing in the CSEs vary considerably over such a large range of mass loss rates. Among other things, it appears that the dust-to-gas mass ratio and/or the dust properties change with the mass loss rate. We find that the mass loss rate and the gas expansion velocity are well correlated, and that both of them clearly depend on the pulsational period and (with larger scatter) the stellar luminosity. Moreover, the mass loss rate correlates weakly with the stellar effective temperature, in the sense that the cooler stars tend to have higher mass loss rates, but there seems to be no correlation with the stellar C/O-ratio. We conclude that the mass loss rate increases with increased regular pulsation and/or luminosity, and that the expansion velocity increases as an effect of increasing mass loss rate (for low mass loss rates) and luminosity.

Motivation & Objective

• To determine mass loss rates, gas expansion velocities, and kinetic temperature structures in circumstellar envelopes (CSEs) of bright carbon stars using detailed radiative transfer and energy balance modeling.
• To assess the reliability of mass loss rate determinations by testing the sensitivity of results to model assumptions and observational constraints.
• To investigate the physical drivers of mass loss by analyzing correlations with pulsational period, luminosity, effective temperature, and C/O ratio.
• To identify and characterize deviations from spherical symmetry and smooth mass loss, particularly in stars with detached CO shells.
• To estimate the contribution of carbon stars to the interstellar medium's gas budget and assess their role in galactic chemical evolution.

Proposed method

• Employed a spherically symmetric, smooth, constant-velocity outflow model for circumstellar envelopes with continuous mass loss.
• Applied radiative transfer calculations to multi-transition CO line emission data from the Swedish-ESO submillimeter telescope, Onsala 20 m telescope, and NRAO 12 m telescope.
• Incorporated the photodissociation model of Mamon et al. (1988) to account for CO destruction by UV radiation in the outer envelope.
• Used radial brightness profiles from CO(1→0) observations to constrain envelope size and density structure, testing the r⁻² density law.
• Combined observational constraints (multi-line data, radial profiles) with theoretical modeling to derive mass loss rates and gas temperature profiles.
• Evaluated dust-to-gas mass ratios and dust properties by comparing model results with observed temperature structures and mass loss trends.

Experimental results

Research questions

• RQ1 What are the derived mass loss rates, expansion velocities, and temperature structures for a sample of bright carbon stars based on CO radio line emission modeling?
• RQ2 How do mass loss rates correlate with pulsational period, luminosity, effective temperature, and C/O ratio in carbon stars?
• RQ3 To what extent do observed radial brightness profiles deviate from the r⁻² density law, indicating time-variable mass loss or non-spherical symmetry?
• RQ4 What is the contribution of carbon stars to the interstellar medium’s gas return, and how do extreme sources compare?
• RQ5 Why do some stars (e.g., those with detached CO shells) fail to be well-fit by the standard smooth wind model?

Key findings

• Mass loss rates for the sample span from ∼5×10⁻⁹ M☉ yr⁻¹ to ∼2×10⁻⁵ M☉ yr⁻¹, with a median of 2.8×10⁻⁷ M☉ yr⁻¹, indicating a narrow peak in the distribution around 3×10⁻⁷ M☉ yr⁻¹.
• The mass loss rate is strongly correlated with pulsational period and stellar luminosity, and shows a weak trend with effective temperature, where cooler stars tend to have higher mass loss rates.
• Gas expansion velocity increases with both mass loss rate (at low rates) and luminosity, supporting a dust-driven wind mechanism with pulsation as a key driver.
• No significant correlation was found between mass loss rate and the stellar C/O ratio, suggesting that C/O abundance does not directly control mass loss in these stars.
• Five stars exhibit detached CO shells, indicating past episodes of enhanced mass loss; their current mass loss rates are lower, and shell masses appear to increase with age, suggesting a recurrence timescale of ∼10⁵ years.
• The model fits are typically accurate to within ∼50% under the adopted assumptions, and deviations in radial brightness profiles suggest time-variable mass loss or non-spherical geometry in a few cases.