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Temperature asymmetry in the cosmic microwave background (CMB) data by thePlanck satellite has been discovered and analyzed toward several nearby edge-onspiral galaxies. It provides a way to probe galactic halo rotation, and toconstrain the baryon fraction in the galactic halos. The frequency independenceof the observed data provides a strong indication of the Doppler shift natureof the effect, due to the galactic halo rotation. It was proposed that thiseffect may arise from the emission of cold gas clouds populating the galactichalos. However, in order to confirm this view, other effects that might giverise to a temperature asymmetry in the CMB data, have to be considered andstudied in detail. The main aim of the present paper is to estimate thecontribution in the CMB temperature asymmetry data due to the free-freeemission by hot gas (particularly electrons) through the rotational kineticSunyaev-Zeldovich (rkSZ) effect. We concentrate, in particular, on the M31galactic halo and compare the estimated values of the rkSZ induced temperatureasymmetry with those obtained by using the SMICA pipeline of the Planck datarelease, already employed to project out the SZ sources and for lensingstudies. As an additional consistency check, we also verified that the hot gasdiffuse emission in the X-ray band does not exceed that detected in the softX-ray band by ROSAT observations. We note that our results clearly show thatthe rkSZ effect gives only a minor contribution to the observed M31 halotemperature asymmetry by Planck data.

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