It was known that an ideal spherically symmetric stellar system with isotropic velocities and an inner core cannot reside in a Navarro, Frenk, and White (NFW) gravitational potential. The incompatibility can be pinned down to the radial gradient of the NFW potential in the very center of the system, which differs from zero. The gradient is

Measuring the obliquities of stars hosting giant planets may shed light on the dynamical history of planetary systems. Significant efforts have been made to measure the obliquities of FGK stars with hot Jupiters, mainly based on observations of the Rossiter–McLaughlin effect. In contrast, M dwarfs with hot Jupiters have hardly been explored because

White dwarfs (WDs) are the endpoint of evolution for 97% of stars. Most of these stars are in multiple systems, and a significant fraction of those are compact enough to exchange mass, altering the structures and subsequent evolution of both stars. The physical mechanisms that facilitate these mass exchanges include common envelope evolution, Roche