Applied Interdisciplinary Mathematics (AIM) Seminar

Stars are opaque, which makes it difficult to study their interiors. Recent space-based telescopes have led to the new field of asteroseismology: by measuring global oscillation modes of a star, you can infer its interior properties. Massive stars have convection in their cores which can generate waves, which might be detectable at the surface. In the first part of this talk, I will describe a heuristic way of estimating wave generation by convection, and compare it to high-resolution numerical simulations in Cartesian geometry. To make quantitative predictions to compare with observations, one must run simulations in spherical geometry. In the second part of my talk, I will present a new spectral algorithm for solving nearly arbitrary, tensorial PDEs in spherical coordinates. The challenge is to devise bases which respect regularity conditions at r=0, which depend on the rank of the tensor. The algorithm can be easily applied to the problem of wave generation by convection in stars, as well as a wide range of other problems in stellar astrophysics, core geophysics, and planetary sciences. Speaker(s): Daniel Lecoanet (Princeton University)