<h3>Mass resolution of particles</h3>
<p>Usually, in an N-body or SPH simulation the term &quot;mass resolution&quot; refers to the mass of a single particle, which usually (but not always) all have the same mass.</p>
<p>A <em>single</em> particle can always be &quot;detected&quot; in the simulation, since we have control of the coordinates of all particles, but a <em>structure</em> of several particles becomes ill-defined if the number of particles is too small.</p>
<h3>Mass resolution of structures</h3>
<p>The mass of the smallest resolved structure depends on your definition of &quot;resolved&quot;. That could be, say, 10 or 100 particles, depending on what quantity you are interested in measuring, and how accurately you want it.</p>
<p>For instance, to define the mass of the structure, you need to be able to count the number of particles in the structure. But how does one know where to stop counting in a more or less continuous field of particles?</p>
<p>One way is to determine an approximate center of mass <span class="math-container">$x_\mathrm{CM}$</span> (approximate, since it can only be exact once all associated particles are defined), calculate the average density <span class="math-container">$\langle\rho\rangle$</span> inside a sphere centered on <span class="math-container">$x_\mathrm{CM}$</span> (which will be higher than the global average, since you started out on an overdensity), and increase the radius until <span class="math-container">$\langle\rho\rangle$</span> falls below some threshold (e.g. 200 times the global average). If the number of particles is too small, <span class="math-container">$\langle\rho\rangle$</span> will change rapidly between each iteration, making your mass inaccurate. From my experience, <em>at least</em> ten particles are needed.</p>
<p>If you're interested in the structure of the interstellar medium in a galaxy in a hydrodynamic (i.e. SPH) simulation, you probably need more particles than this. But I thinks it's fair to say that people disagree on how many particles are needed to resolve a galaxy.</p>

CC BY-SA 4.0
2015-03-19T08:16:11.090Z
2022-07-01T06:23:30.260Z
2022-07-01T06:23:30.260Z
pela
<p>Can someone define mass resolution in terms of cosmological simulations such as the millennium simulation? Is it just the smallest mass that a dark matter particle can have and still be detected by the simulation? </p>

<galaxy><cosmology><dark-matter><n-body-simulations>
Mass resolution
user
# Mass resolution

(Asked by: username_0 on 2015-03-19)

Can someone define mass resolution in terms of cosmological simulations such as the millennium simulation? Is it just the smallest mass that a dark matter particle can have and still be detected by the simulation?

**Tags:** galaxy, cosmology, dark-matter, n-body-simulations

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## 1 answers

### Answer by username_1 on 2015-03-19. Score: 5

### Mass resolution of particles

Usually, in an N-body or SPH simulation the term "mass resolution" refers to the mass of a single particle, which usually (but not always) all have the same mass.

A *single* particle can always be "detected" in the simulation, since we have control of the coordinates of all particles, but a *structure* of several particles becomes ill-defined if the number of particles is too small.

### Mass resolution of structures

The mass of the smallest resolved structure depends on your definition of "resolved". That could be, say, 10 or 100 particles, depending on what quantity you are interested in measuring, and how accurately you want it.

For instance, to define the mass of the structure, you need to be able to count the number of particles in the structure. But how does one know where to stop counting in a more or less continuous field of particles?

One way is to determine an approximate center of mass $x\_\mathrm{CM}$ (approximate, since it can only be exact once all associated particles are defined), calculate the average density $\langle\rho\rangle$ inside a sphere centered on $x\_\mathrm{CM}$ (which will be higher than the global average, since you started out on an overdensity), and increase the radius until $\langle\rho\rangle$ falls below some threshold (e.g. 200 times the global average). If the number of particles is too small, $\langle\rho\rangle$ will change rapidly between each iteration, making your mass inaccurate. From my experience, *at least* ten particles are needed.

If you're interested in the structure of the interstellar medium in a galaxy in a hydrodynamic (i.e. SPH) simulation, you probably need more particles than this. But I thinks it's fair to say that people disagree on how many particles are needed to resolve a galaxy.


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