Is the Landau Theory Important for Stellar Dynamics?

From considerations of the Vlasov equation, Lau and Binney [1] have recently advocated the use of Case-Van Kampen eigenmodes in studies of collisonless stellar systems. Invoking the properties of these modes as rigorous eigenmodes of the collisionless system, they have made the surprising but interesting suggestion that the Landau approach, which does not produce eigenmodes of the system, is not useful for the study of such systems. However, in recent years the limit of zero collisions of a very weakly collisional plasma has been a subject of interest in the plasma physics community, and has led to new insights on the relative importance of Van-Kampen modes and Landau solutions. Using the Lenard-Bernstein collision operator, it has been shown that in the limit of zero collisions, the Case-Van Kampen continuous spectrum is eliminated and the discrete Landau solutions become true eigemodes of the weakly collisional system [2]. We apply the theory to the Jeans instability of stellar systems and demonstrate that in the limit of zero collisions of the collisional problem, large N-body simulations of stellar and galactic dynamics must reckon with Landau solutions as true eigenmodes of such systems. 

1. J. Y. Lau and J. Binney, arXiv e-prints: arXiv:2104.0744

2. C. S. Ng, A. Bhattacharjee and F. Skiff, Physical Review Letters 83, 1974 (1999)