# Calculating an Impact Parameter

**Estimate of NSs required to produce the observations**

If the neutron star is traveling 10 km/s and the length of the cube is 5 ly or 4.73*10^13 km, then it takes roughly 150,000 years to traverse the cube’s length.

meaning we’d need 272 Giant Stars to 1 Neutron Star to create 1 binary every 150,000 years. Considering we know of roughly 100 such binaries with a lifespan of around 10 million years we’d need to produce 1 binary every 100,000 years and would thus need

Alternatively, if we calculate the hit rate per 150000 years to produce 100 binaries in ten million years, we see that

or

an average of 1.5 hits per 150000. Thus we need a “hit rate” which is

times our current “hit rate.”

The easiest way to obtain this is to assume that there is not one neutron star per giant star but 181 giant stars per neutron star.

If we use a a “hit rate” of 1 in 10 billion and traversal time of 100,000 years, we have:

assuming there is one neutron star per regular star over the course of 100,000 years in the Milky Way. In ten million years this would produce:

so in ten million years we’d have 2000 Tidal Captures and would thus need to reduce the number of neutron stars by 20 for a ratio of 20 regular stars:1 neutron star in order to obtain 100 captures in ten million years.