<p>I'm looking to better understand the stability of globular clusters for an n-body dynamical simulation, specifically with respect to initial data conditions.</p>
<p>I know that the total potential energy needs to be larger in magnitude than total kinetic energy for the cluster to be gravitationally bound, but I wasn't sure what kind of constraints on momenta would keep the cluster from collapsing in on itself.</p>
<p>I found this paper by Soviet physicist A. M. Fridman from about 50 years ago (link below) and it states that the &quot;total momentum of a globular cluster practically vanishes&quot;, and this sounds reasonable enough to me, but I realize this paper is a little older, and it doesn't really justify or cite this claim as far as I can tell. I also haven't found any other sources to verify this claim, is there anyone out there that works with globular clusters/ have some sources that can verify if this is the case?</p>
<p>Here is the English translation of the original paper <a href="http://adsabs.harvard.edu/full/1971SvA....15..250F" rel="nofollow noreferrer">The Stability of Globular Clusters and Spherical Galaxies</a> and it's abstract:</p>
<blockquote>
<p>A globular star cluster (or spherical galaxy) is modeled by a spherically symmetric system of rotating, gravitational masses. In accordance with observational evidence an r<sup>-2</sup> density profile is adopted, with particle trajectories <strong>such as the total momentum of the system vanishes.</strong> The stability of such a model against arbitrary perturbations has been demonstrated on the basis of results from plasma physics; rigorous mathematical proofs of stability have been given elsewhere [4-7].</p>
</blockquote>

CC BY-SA 4.0
2021-07-08T01:34:41.893Z
I found this very interesting! I've just asked [Which A. M. Fridman is the author of this paper on gravitational stability?](https://astronomy.stackexchange.com/q/44764/7982)
uhoh
CC BY-SA 4.0
2021-07-08T05:18:49.127Z
When I clicked the author for the website that had this paper, these came up as his other publications https://www.osti.gov/search/author:%22Fridman,%20A%20M%22
Justin T
CC BY-SA 4.0
2021-07-08T06:58:09.463Z
Those may be all papers containing "Fridman, A M" in the author field, not necessarily for one person. For example "[Smith, J](https://www.osti.gov/search/author:%22Smith,%20J%22) returns 4,752 results.
uhoh
<gravity><n-body-simulations><stellar-dynamics><globular-clusters>
Is this paper on globular cluster stability still up to date?
Justin T
# Is this paper on globular cluster stability still up to date?

(Asked by: username_0 on 2021-07-07)

I'm looking to better understand the stability of globular clusters for an n-body dynamical simulation, specifically with respect to initial data conditions.

I know that the total potential energy needs to be larger in magnitude than total kinetic energy for the cluster to be gravitationally bound, but I wasn't sure what kind of constraints on momenta would keep the cluster from collapsing in on itself.

I found this paper by Soviet physicist A. M. Fridman from about 50 years ago (link below) and it states that the "total momentum of a globular cluster practically vanishes", and this sounds reasonable enough to me, but I realize this paper is a little older, and it doesn't really justify or cite this claim as far as I can tell. I also haven't found any other sources to verify this claim, is there anyone out there that works with globular clusters/ have some sources that can verify if this is the case?

Here is the English translation of the original paper [The Stability of Globular Clusters and Spherical Galaxies](http://adsabs.harvard.edu/full/1971SvA....15..250F) and it's abstract:

> A globular star cluster (or spherical galaxy) is modeled by a spherically symmetric system of rotating, gravitational masses. In accordance with observational evidence an r-2 density profile is adopted, with particle trajectories **such as the total momentum of the system vanishes.** The stability of such a model against arbitrary perturbations has been demonstrated on the basis of results from plasma physics; rigorous mathematical proofs of stability have been given elsewhere [4-7].

**Tags:** gravity, n-body-simulations, stellar-dynamics, globular-clusters

> **Comments:**
> **username_1**: I found this very interesting! I've just asked [Which A. M. Fridman is the author of this paper on gravitational stability?](https://astronomy.stackexchange.com/q/44764/7982)  
> **username_0**: When I clicked the author for the website that had this paper, these came up as his other publications https://www.osti.gov/search/author:%22Fridman,%20A%20M%22  
> **username_1**: Those may be all papers containing "Fridman, A M" in the author field, not necessarily for one person. For example "[Smith, J](https://www.osti.gov/search/author:%22Smith,%20J%22) returns 4,752 results.  

---

## 0 answers

