# how to calculate the half-mass radius and tidal radius of a (simulated) globular cluster

I am exploring a dataset of a direct N-body simulation of a star cluster, such that all particles have the same mass and

G = M = −4E = 1

for the whole cluster. The data available is the positions and velocities of all stars (at certain snapshots of the simulation).

I'd like to be able to calculate some basic characteristics of the cluster. First I did the center of mass (which is just the mean of all coordinates since all masses are equal), but I am not sure how to proceed for these two:

• The half mass radius - I can't seem to find an established (i.e. most efficient) way to calculate this. My first idea is to use a bisection method with the center of mass and the total radius as starting points, and do window queries with a spherical envelope until it contains half the stars. Is there something more efficient than that?

• The tidal radius - what I've found so far always involves variables drawn from the galaxy the cluster is in (like the total mass of the galaxy and so on). However, this being a simulation, there is no such data. Yet the dataset states that some stars escape the cluster over the length of the simulation... I must be missing something here