Thermal stresses in small meteoroids

II. Effects of an insulating surface layer

¹ Astronomical Institute of the Academy of Sciences, Fričova 298, 251 65 Ondřejov, Czech Republic
e-mail: capek@asu.cas.cz
² Institute of Astronomy, Charles University, V Holešovičkách 2, 180 00 Prague 8, Czech Republic
e-mail: vokrouhl@cesnet.cz

Received: 14 July 2011
Accepted: 2 November 2011

Abstract

Aims. We extend our previous analysis of thermal stresses in small, spherical and homogeneous meteoroids by taking into account the effects of a surface insulating layer.

Methods. Using analytical computations, we determine the temperature distribution in a spherical inhomogeneous body smaller than  ~10 cm with a high-conductivity core and a low-conductivity surface layer. Our main approximation consists in (i) linearization of the surface energy-conservation constraint and (ii) omission of the seasonal effects in the Fourier spectrum of the incident solar radiation flux. Using the temperature solution, we analytically compute the mechanical (thermal) stress field in the core, neglecting its effects in the particulate surface layer. Conditions for material failure in the whole volume of the body are analyzed. In particular, we pay attention to whether the surface layer depth evolves toward an equilibrium situation.

Results. As the meteoroid approaches the Sun, the thermal stress first exceeds the material strength at the surface of meteoroid. If the fractured material is able to stay on meteoroid, a particulate shell begins to form. After one revolution about the Sun, this process is roughly completed. We determine the dependence of its thickness on perihelion distance, spin axis orientation with respect to the Sun, and the size of meteoroid. We estimate the distribution of the final depths of the surface layer for eight major meteoroid showers with perihelion distances smaller than 1 AU.