Astrophysical dust formation under the influence of temperature fluctuations

A general stochastic approach and its application to AGB winds

Zentrum für Astronomie und Astrophysik (ZAA), TU Berlin, Hardenbergstr. 36, 10623 Berlin, Germany e-mail: schirrmacher@astro.physik.tu-berlin.de

Received: 13 December 2007
Accepted: 9 July 2008

Abstract

Context. Dust formation, i.e. the condensation of solid particles from a gas phase, occurs in astrophysical environments that are sufficiently cool and offer a sufficiently high density of condensable species. Since many astrophysical systems in which dust forms have turbulent features and the dust formation rates depend significantly on temperature, we investigate the influence of temperature fluctuations on dust condensation in dust-driven AGB winds.

Aims. We present an approach for the time-dependent stochastic description of astrophysical dust formation and apply this in developing a fast algorithm, which is well suited for implementation into numerical models of dynamical AGB winds. The influence of the fluctuations on the dynamical structure is then investigated for a large sample of wind parameters.

Methods. We employ a mathematical method, which describes the dust formation under the influence of random temperature fluctuations as a stochastic process. A system of Fokker-Planck equations for the one-point distribution function of the conjoint temporal development of temperature and dust results. Gas-box studies of this system have led us to a simplified microturbulent description for the implementation into time-dependent numerical wind models.

Results. A method for the investigation of temperature fluctuations on dust formation is presented, which can be adapted to a variety of astrophysical situations. For dust-driven AGB winds, a microturbulent description turns out to be admissible. In AGB winds, rms-temperature fluctuations of 20–60 K can result in increased mass loss rates of 10–30% depending on the details of the physical model assumptions.

Conclusions. The presented method for the treatment of temperature fluctuations with respect to dust formation has been succesfully applied to dynamical AGB winds. We suggest how to apply the method to other astrophysical systems. The influence of the fluctuations on the dynamics of dust-driven AGB winds is remarkable, but not overwhelming.