Intergalactic Wandering Stars in the Local Universe: Theoretical Predictions for Their Distance and Luminosity Distribution

Intergalactic wandering stars (IWSs) within 10 Mpc remain a poorly explored area of astronomy. Such stars, if they exist, are supposed to be wandering objects as they are not bounded by the gravitational potential of any galaxy. We set out to conduct dedicated studies for unraveling such a wandering stellar population. As the first paper of the series, in the present work we model the distance distribution and luminosity function of IWSs formed via the Hills mechanism of the Galactic central massive black hole (GCMBH). We implement a numerical simulation to generate IWSs taking the ejection history of the GCMBH and the stellar evolution process into consideration, and present their luminosity function in the distance range of 200kpc - 10Mpc. Our results suggest that a few hundred thousand IWSs have been generated by the GCMBH via the Hills mechanism in the past 14 billion years. These IWSs have an apparent magnitude peaking at 30 to 35 mag in SDSS $r-$band, which are hard to detect. However, a few thousand of them at the bright end are detectable by upcoming wide-field deep surveys, such as China Space Station Telescope (CSST) and Vera Rubin Observatory (LSST). The forthcoming discovery of such a wandering stellar population will open a door for precise understanding of the matter constitution of the nearby intergalactic space and the dynamical history of galaxies in the local universe.