Open AccessCross‐terms and weak frequency‐dependent signals in the cosmic microwave background sky
Author(s) -
HernándezMonteagudo C.,
Sunyaev R. A.
Publication year - 2005
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1111/j.1365-2966.2005.08929.x
Subject(s) - physics , cosmic microwave background , astrophysics , redshift , cosmic variance , anisotropy , spectral density , amplitude , cosmic background radiation , multipole expansion , spectral line , reionization , sky , computational physics , optics , astronomy , galaxy , quantum mechanics , statistics , mathematics
In this paper, we study the amplification of weak frequency‐dependent signals in the cosmic microwave background (CMB) sky due to their cross‐correlation to intrinsic anisotropies. In particular, we centre our attention on mechanisms generating a weak signal, of peculiar spectral behaviour, such as resonant scattering in ionic, atomic or molecular lines, the thermal Sunyaev–Zel'dovich (tSZ) effect or extragalactic foreground emissions, whose typical amplitude (denoted by ε) is significantly smaller than the intrinsic CMB fluctuations. We find that all these effects involve either the autocorrelation of anisotropies generated during recombination ( z rec ) or the cross‐correlation of those anisotropies with fluctuations arising at redshift z i . The former case accounts for the slight blurring of original anisotropies generated in the last scattering surface, and shows up in the small angular scale (high multipole) range. The latter term describes, instead, the generation of new anisotropies, and is non‐zero only if fluctuations generated at redshifts z rec , z i , are correlated. The degree of this correlation can be computed under the assumption that density fluctuations were generated as standard inflationary models dictate and that they evolved in time according to linear theory. When the weak signal is frequency dependent (i.e. the spectral dependence of the secondary anisotropies is distinct from that of the CMB), we show that, by subtracting power spectra at different frequencies, it is possible to avoid the limit associated with cosmic variance and unveil weaker terms linear in ε. We find that the correlation term shows a different spectral dependence than the squared (∝ε 2 ) term usually considered, making its extraction particularly straightforward for the tSZ effect. Furthermore, we find that in most cases the correlation terms are particularly relevant at low multipoles due to the integrated Sachs–Wolfe effect and must be taken into account when characterizing the power spectrum associated with weak signals in large angular scales.