# Mass resolution

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?

### 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.