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

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

Diffuse emission in the outskirts of galaxies, such as stellar tidal streams, galaxy stellar halos and intracluster light, provides important constraints on the structure and evolution of the Universe. However, such low surface brightness diffuse emission can be up to thousands of times dimmer (>29 AB mag/[square arcseconds]) than the sky