<p>Your first question is about computing, not astronomy. You find a cumulative histogram of distance from the centre of mass and where that reaches 50% of the stars.</p>
<p>As to your second point, there is no tidal radius; you need two bodies in order to have a defined tidal radius. The tidal radius of a cluster is directly related to the gravitational potential external to it.</p>
<p>Stars can escape from a cluster because sometimes they can accumulate enough kinetic energy in weak interactions with each other, that their speed exceeds the escape speed of the cluster. It is a classic result that the &quot;evaporation&quot; timescale is of order 100 times the cluster relaxation timescale, even in the absence of an external gravitational field (e.g. <a href="https://arxiv.org/abs/astro-ph/0007258" rel="nofollow noreferrer">Gerhard 2000</a>).</p>

CC BY-SA 4.0
2020-01-07T15:41:06.607Z
Thanks, I checked out the paper. So in my case a star would (generally) escape the cluster if it's velocity is greater or equal than twice the root mean square of the velocities of all the stars ("Thus, on average, a particle with v≥2V=√12σ‖ will escape")
KGS
CC BY-SA 4.0
2020-01-07T12:40:18.283Z
2020-10-15T07:02:25.207Z
2020-10-15T07:02:25.207Z
ProfRob
<p>I am exploring a <a href="https://www.kaggle.com/mariopasquato/star-cluster-simulations" rel="nofollow noreferrer">dataset</a> of a direct N-body simulation of a star cluster, such that all particles have the <strong>same mass</strong> and</p>

<blockquote>
  <p>G = M = −4E = 1</p>
</blockquote>

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

<p>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:</p>

<ul>
<li><p>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?</p></li>
<li><p>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</p></li>
</ul>

<n-body-simulations><star-cluster>
how to calculate the half-mass radius and tidal radius of a (simulated) globular cluster
KGS
# how to calculate the half-mass radius and tidal radius of a (simulated) globular cluster

(Asked by: username_0 on 2020-01-07)

I am exploring a [dataset](https://www.kaggle.com/mariopasquato/star-cluster-simulations) 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

**Tags:** n-body-simulations, star-cluster

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## 1 answers

### Answer by username_1 on 2020-01-07. Score: 2 | Accepted answer

Your first question is about computing, not astronomy. You find a cumulative histogram of distance from the centre of mass and where that reaches 50% of the stars.

As to your second point, there is no tidal radius; you need two bodies in order to have a defined tidal radius. The tidal radius of a cluster is directly related to the gravitational potential external to it.

Stars can escape from a cluster because sometimes they can accumulate enough kinetic energy in weak interactions with each other, that their speed exceeds the escape speed of the cluster. It is a classic result that the "evaporation" timescale is of order 100 times the cluster relaxation timescale, even in the absence of an external gravitational field (e.g. [Gerhard 2000](https://arxiv.org/abs/astro-ph/0007258)).

> **Comments:**
> **username_0**: Thanks, I checked out the paper. So in my case a star would (generally) escape the cluster if it's velocity is greater or equal than twice the root mean square of the velocities of all the stars ("Thus, on average, a particle with v≥2V=√12σ‖ will escape")  

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