The effect of cluster magnetic field on the Sunyaev Zeldovich power spectrum

Precision measurements of the Sunyaev Zeldovich (SZ) effect in upcoming blank sky surveys require theoretical understanding of all physical processes with $\text{ga}10$ effects on the SZ power spectrum. We show that, observed cluster magnetic field could reduce the SZ power spectrum by $\sim 20$ at $l\sim 4000$, where the SZ power spectrum will be precisely measured by the Sunyaev Zeldovich array (SZA) and the Atacama cosmology telescope (ACT). At smaller scale, this effect is larger and could reach a factor of several. Such effect must be considered for an unbiased interpretation of the SZ data. Though the magnetic effect on the SZ power spectrum is very similar to that of radiative cooling, it is measurable by multi-band CMB polarization measurement.