The Likely Thermal Evolution of the Irregularly Shaped S-Type Astraea Asteroid

The thermal evolution of asteroids provides information on the thermal processes of the protoplanetary disk. Since irregular bodies have a large surface subject to fast heat loss, we used the finite element method (FEM) to explore the likely thermal pathways of one of these bodies. To test our FEM approach, we compared the FEM to another algorithm, the finite difference method (FDM). The results show that the two methods calculated a similar temperature magnitude at the same evolutionary time, especially at the stage when the models had temperatures around 800 K. Furthermore, this investigation revealed a slight difference between the methods that commences with a declining temperature, particularly around the center of the model. The difference is associated with the tiny thickness of the boundary used in the FDM, whereas the FEM does not consider the thickness of the boundary due to its self-adapting grid. Using the shape data provided by DAMIT, we further explored the likely thermal evolution pathway of the S-type asteroid Astraea by considering the radionuclide 26Al. Since we only focused on the thermal pathways of conduction, we considered that the accretion lasts 2.5 Ma (1 Ma = 1,000,000 years) by assuming that Astraea has not experienced iron melting. The results show a high interior temperature area with a shape similar to the shape of Astraea, indicating the influence of the irregular shape on thermal evolution. The interior of Astraea achieved the highest temperature after 4.925 Ma from the accretion of planetesimals. After that time of high temperature, Astraea gradually cooled and existed more than 50 Ma before its heat balanced approximately to its external space. We did not find signs of apparent fast cooling along the shortest z-axis as in previous studies, which could be due to the hidden differences in the distances along the axes. The methodology developed in this paper performs effectively and can be applied to study the thermal pathways of other asteroids with irregular shapes.