The rotational kinetic Sunyaev-Zeldovich contribution to the temperature asymmetry toward the M31 halo

Temperature asymmetry in the cosmic microwave background (CMB) data by the Planck satellite has been discovered and analyzed toward several nearby edge-on spiral galaxies. It provides a way to probe galactic halo rotation, and to constrain the baryon fraction in the galactic halos. The frequency independence of the observed data provides a strong indication of the Doppler shift nature of the effect, due to the galactic halo rotation. It was proposed that this effect may arise from the emission of cold gas clouds populating the galactic halos. However, in order to confirm this view, other effects that might give rise to a temperature asymmetry in the CMB data, have to be considered and studied in detail. The main aim of the present paper is to estimate the contribution in the CMB temperature asymmetry data due to the free-free emission by hot gas (particularly electrons) through the rotational kinetic Sunyaev-Zeldovich (rkSZ) effect. We concentrate, in particular, on the M31 galactic halo and compare the estimated values of the rkSZ induced temperature asymmetry with those obtained by using the SMICA pipeline of the Planck data release, already employed to project out the SZ sources and for lensing studies. As an additional consistency check, we also verified that the hot gas diffuse emission in the X-ray band does not exceed that detected in the soft X-ray band by ROSAT observations. We note that our results clearly show that the rkSZ effect gives only a minor contribution to the observed M31 halo temperature asymmetry by Planck data.