Dark Matter and Gas in Clusters of Galaxies

Joachim Köppen Kiel March 2017

### Some brief explanations

- For a spherical cluster of galaxies we show the distribution of dark matter and
hot intracluster gas (ICM), and their properties: density, mass inside radius
*r*,
the speeds of circular orbits and for escape from radius *r*, and the maximum
ram pressure that would be experienced by a galaxy when it comes as close as radius
*r* of the centre, on a circular or a radial orbit.
- The central densities can be entered in various units. Click on a field to make it
the currently valid input field (marked in light green).
- The radial distributions of dark matter and ICM follow beta profiles with the
parameters specified by the user.
- The hot ICM is observed in the X-rays, and its distribution is often described by
a beta profile. From this and the observed (or assumed) temperature on then deduces
the distribution of the dark matter by assuming hydrostatic equilibrium:
- To compute this, select
**acceleration** vs. **log. radius**. Clicking the
**wipe&plot** button will show two curves:
- red: deduced from the ICM distribution and the hydrostatic equilibrium
- blue: the dark matter distribution with its current (guessed) beta profile parameters

Now change the parameters for the dark matter beta-profile until the blue curve
matches the red curve in the range of radii for which you seek a good representation
of the deduced dark matter with a beta profile.
- Another way is to select
**masses** vs. **log. radius**. Clicking the
**wipe&plot** button will show three curves:
- blue: the ICM distribution
- red: the deduced dark matter distribution
- black: the dark matter distribution with its current beta profile parameters

Change the parameters for the dark matter beta-profile until the black curve
matches the red curve.
- The
**escape speed** is given to reach the specified finite **escape to radius**.
Note even during the entire age of the Universe an object with a speed of 1000 km/s
cannot cover distances more than about 13 Mpc! Hence the theoretical concept of the
escape speed as the one to reach zero speed at infinite distance from the cluster
centre runs into our real world's limit.
- Selecting e.g.
**pressures** you then get the range of maximum ram pressures
that a galaxy will encounter at different radii on circular and radial orbits.