y-type spectral distortions of the cosmic microwave background allow us to detect clusters and groups of galaxies, filaments of hot gas and the non-uniformities in the warm hot intergalactic medium. Several CMB experiments (on small areas of sky) and
theoretical groups (for full sky) have recently published y-type distortion maps. We propose to search for two artificial hot spots in such y-type maps resulting from the incomplete subtraction of the effect of the motion induced dipole on the cosmic microwave background sky. This dipole introduces, at second order, additional temperature and y-distortion anisotropy on the sky of amplitude few mu K which could potentially be measured by Planck HFI and Pixie experiments and can be used as a source of cross channel calibration by CMB experiments. This y-type distortion is present in every pixel and is not the result of averaging the whole sky. This distortion, calculated exactly from the known linear dipole, can be subtracted from the final y-type maps, if desired.
Mixing of blackbodies with different temperatures creates a spectral distortion which, at lowest order, is a y-type distortion, indistinguishable from the thermal y-type distortion produced by the scattering of CMB photons by hot electrons residing i
n clusters of galaxies. This process occurs in the radiation-pressure dominated early Universe, when the primordial perturbations excite standing sound waves on entering the sound horizon. Photons from different phases of the sound waves, having different temperatures, diffuse through the electron-baryon plasma and mix together. This diffusion, with the length defined by Thomson scattering, dissipates sound waves and creates spectral distortions in the CMB. Of the total dissipated energy, 2/3 raises the average temperature of the blackbody part of spectrum, while 1/3 creates a distortion of y-type. It is well known that at redshifts 10^5< z< 2x10^6, comptonization rapidly transforms y-distortions into a Bose-Einstein spectrum. The chemical potential of the Bose-Einstein spectrum is again 1/3 the value we would get if all the dissipated energy was injected into a blackbody spectrum but no extra photons were added. We study the mixing of blackbody spectra, emphasizing the thermodynamic point of view, and identifying spectral distortions with entropy creation. This allows us to obtain the main results connected with the dissipation of sound waves in the early Universe in a very simple way. We also show that mixing of blackbodies in general, and dissipation of sound waves in particular, leads to creation of entropy.
It is well known that Thomson scattering of CMB photons in galaxy clusters introduces new anisotropies in the CMB radiation field, but however little attention is payed to the fraction of CMB photons that are scattered off the line of sight, causing
a slight blurring of the CMB anisotropies present at the moment of scattering. In this work we study this {it blurring} effect, and find that it has a non-negligible impact on estimations of the kinetic Sunyaev-Zeldovich (kSZ) effect: it induces a 10% correction in 20-40% of the clusters/groups, and a 100% correction in $sim 5$% of the clusters in an ideal (noiseless) experiment. We explore the possibility of using this blurring term to probe the CMB anisotropy field at different epochs in our Universe. In particular, we study the required precision in the removal of the kSZ that enables detecting the blurring term $-tau_T delta T / T_0$ in galaxy cluster populations placed at different redshift shells. By mapping this term in those shells, we would provide a tomographic probe for the growth of the Integrated Sachs Wolfe effect (ISW) during the late evolutionary stages of the Universe. We find that the required precision of the cluster peculiar velocity removal is of the order of 100 -- 200 km s$^{-1}$ in the redshift range 0.2 -- 0.8, after assuming that all clusters more massive than 10$^{14}$ h$^{-1}$ M$_{odot}$ are observable. These errors are comparable to the total expected linear line of sight velocity dispersion for clusters in WMAPV cosmogony, and correspond to a residual level of roughly 900 -- 1800 $tau_T mu$K per cluster, including all types of contaminants and systematics. Were this precision requirement achieved, then independent constraints on the intrinsic cosmological dipole would be simultaneously provided.
If the peculiar motion of galaxy groups and clusters indeed resembles that of the surrounding baryons, then the kinetic Sunyaev-Zeldovich (kSZ) pattern of those massive halos should be closely correlated to the kSZ pattern of all surrounding electron
s. Likewise, it should also be correlated to the CMB E-mode polarization field generated via Thomson scattering after reionization. We explore the cross-correlation of the kSZ generated in groups and clusters to the all sky E-mode polarization in the context of upcoming CMB experiments like Planck, ACT, SPT or APEX. We find that this cross-correlation is effectively probing redshifts below $z=3-4$ (where most of baryons cannot be seen), and that it arises in the very large scales ($l<10$). The significance with which this cross-correlation can be measured depends on the Poissonian uncertainty associated to the number of halos where the kSZ is measured and on the accuracy of the kSZ estimations themselves. Assuming that Planck can provide a cosmic variance limited E-mode polarization map at $l<20$ and S/N $sim 1$ kSZ estimates can be gathered for all clusters more massive than $10^{14} M_{odot}$, then this cross-correlation should be measured at the 2--3 $sigma$ level. Further, if an all-sky ACT or SPT type CMB experiment provides similar kSZ measurements for all halos above $10^{13} M_{odot}$, then the cross-correlation total signal to noise (S/N) ratio should be at the level of 4--5. A detection of this cross-correlation would provide direct and definite evidence of bulk flows and missing baryons simultaneously.
