Kinematics of young nearby neutron stars
There are ~100 young, nearby neutron stars (NSs) with distance and proper motion measurements known, most of them radio pulsars, plus a few radio-quiet thermal X-ray emitters. By tracing back the 3D motion of all those NSs, nearby young stellar associations, clusters and bubbles, and also all known young runaway stars, we can find close encounters in space and time, i.e. events, where NSs intersected with an association and/or a runaway star. Then, the NS may have been born in that association at that time in a supernova. An additional encounter with a runaway star would provide additional evidence.
Then, we know the kinematic age of that NS. We can compare the kinematic age with its characteristic spin-down age, which, in most cases, only gives the order of magnitude of the true (and kinematic) age. With kinematic ages we can probe cooling models for young NSs.
The difference between the association age (also age of the runaway star) and the kinematic age of the NS can be used to deduce the mass of the progenitor star. If we can find several NSs having possibly exploded within a few million years within the Local Bubble, we may be able to explain its origin by supernovae. For a recent (within a few million years) nearby supernova (within 100 to 150 pc), supernova debris like 60Fe should have been deposited in the Earth's crust. Such material has been detected. If we can find the NS formed by that supernova, we can constrain its distance and age, and maybe the mass (and, hence, debris yield) of the progenitor star, an important constraint for supernova and nucleosynthesis models.
By tracing back the travel paths of young neutron stars with known distances and proper motion, using a Monte-Carlo simulation (that takes all errors and the unknown radial velocity into account), we can identify the most probable kinematic age and distance of the supernova from the parent association/ cluster (figure below, RX J0720.4-3125 as an example). Using the kinematic ages and the temperatures from X-ray spectroscopy, we can compare both quantities with cooling curves (that depend on mass, composition/ EoS and cooling process).
Probability of the close encounter of RX J0720.4-3125 with its former companion candidate HIP 43158 (Tetzlaff et al. 2011, MNRAS, in press) near the Trumpler 10 association ~0.9 Myr ago.
Flight paths of RX J0720.4-3125, HIP 43158 and Trumpler 10 projected onto a galactic coordinate system (Tetzlaff et al. 2011, MNRAS, in press).