These mock data give positions and velocities for stars in and around the Solar neighbourhood, relevant for recovering the local Galactic potential and e.g. dark matter content.
These first data assume a 1D population with precisely zero “tilt” term. The velocities are sampled from a 1D distribution function assuming as in Kuijken & Gilmore 1989. This should be an easy test, but highlights:
We use a disc model:
and vertical force law:
The vertical velocity dispersion (assuming no tilt) can be derived from the Jeans equations:
where sets the velocity dispersion at . However, we do not use this. Instead, we use the distribution function:
This is made more numerically tractable by the trigonometric substitution:
We set up several models by drawing stars from the above distribution function. These are detailed in the following table.
|Simple||; ; ; ; ;||simplenu_sigz_bin.dat simplenu_sigz.dat simplenu_sigz_raw.dat|
|Simplelow||As Simple, above, but with||simplelownu_sigz_bin.dat simplelownu_sigz.dat simplelownu_sigz_raw.dat|
|Simple2||; otherwise as Simple, above||simple2nu_sigz_bin.dat simple2nu_sigz.dat simple2nu_sigz_raw.dat|
|High||As Simple2, above, but with ; data cut on 2 < z < 4 kpc; just ~500 stars; and||highnu_sigz_bin.dat highnu_sigz.dat highnu_sigz_raw.dat|
where is the number of stars, and is the bin size (for the binned data).
The data files are as follows:
The system of units is kpc, Msun, km/s. Converting the vertical force to a surface density () via the Poisson equation (assuming no rotation curve contribution), we have:
. In the above system of units, the “baryonic” contribution .