### Site Tools

tests:discs:mockread1d

## Local models/mocks

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.

### Simple 1D data sampled from a distribution function of vertical energy

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:

• The importance of systematic errors due to over-restrictive assumptions about the potential;
• The role of sampling - i.e. how many stars are needed for what type of error;
• The importance of having different populations split by chemistry (and the errors introduced if we get this wrong);
• The importance of sampling high or low as compared to the disc plane; and
• The role of uncertainties in the baryonic mass model

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:

where:

This is made more numerically tractable by the trigonometric substitution:

which gives:

We set up several models by drawing stars from the above distribution function. These are detailed in the following table.

Model Parameters Data files Plots
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:

• simplenu_sigz_bin.dat :: Binned data:
• simplenu_sigz.dat :: Smooth model
• simplenu_sigz_raw.dat :: Raw particle data in
• simple.png :: Plots of the above.

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:

where:

. In the above system of units, the “baryonic” contribution .

tests/discs/mockread1d.txt · Last modified: 2015/05/01 10:42 by justin