Supernova explosions of runaway stars and young neutron stars above the Galactic plane

Several supernova remnants and young neutron stars were recently discovered relatively high above the Galactic plane. One possibility is that they originate from runaway OB stars born in the Galactic disk. Understanding their origin will provide key insights into the properties of the Galactic halo. This paper aims to determine the spatial distribution of supernova explosions from runaway OB stars and to assess whether this model can explain certain observed neutron stars. We map the distribution of supernova events produced by runaway OB stars by incorporating their birth rate, initial spatial distribution, lifetime, ejection mechanisms, and velocity distributions. By tracking their motion in the Galactic potential, we determine their final distribution right before the explosion. We show that the neutron star Calvera, which is found at z around 2.2 kpc, could have originated from a runaway OB star. In addition, we compare the probabilities of finding a supernova remnant originating from Type Ia and core-collapse supernovae high above the Galactic plane, showing that supernova remnants related to core-collapse supernovae outnumber those related to Type Ia supernovae.