The influence of magnetic fields on the Sunyaev Zel'dovich effect in clusters of galaxies

We study the influence of intracluster large scale magnetic fields on the thermal Sunyaev-Zel'dovich (SZ) effect. In a macroscopic approach we complete the hydrostatic equilibrium equation with the magnetic field pressure component. Comparing the resulting mass distribution with a standard one, we derive a new electron density profile. For a spherically symmetric cluster model, this new profile can be written as the product of a standard ($\beta$-) profile and a radius dependent function, close to unity, which takes into account the magnetic field strength. For non-cooling flow clusters we find that the observed magnetic field values can reduce the SZ signal by $\sim 10%$ with respect to the value estimated from X-ray observations and the $\beta$-model. If a cluster harbours a cooling flow, magnetic fields tend to weaken the cooling flow influence on the SZ-effect.