The Sunyaev & Zeldovich (SZ) effect (Sunyaev & Zeldovich 1972) arises from the inverse Compton scatter of CMB photons against hot electrons. For a comprehensive background review see Birkinshaw (1999). The CMB intensity change is given by
where TCMB = 2.725 ± 0.002 K (Mather et al. 1999) is the CMB temperature and x = h / kTCMB.
The spectral form of this "thermal effect" is described by the function
which is negative (positive) at values of x smaller (larger) than x0 = 3.83, corresponding to a critical frequency 0 = 217 GHz.
where me, ne and Te are the electron mass, density and temperature respectively, T is the Thomson cross section, and the integral is over a line of sight through the plasma.
With respect to the incident radiation field, the change of the CMB intensity across a galaxy or a cluster can be viewed as a net flux emanating from the plasma cloud, given by the integral of intensity change over the solid angle subtended by the cloud
In the case of hot gas trapped in the potential well due to an object of total mass M, the parameter Y in eq. (20), called integrated Y-flux, is proportional to the gas-mass-weighted electron temperature <Te> and to the gas mass Mg = fgM:
At frequencies below 217 GHz, the Y-flux is negative and can therefore be distinguished from the positive signals due to the other source populations.
8.1. Sunyaev-Zeldovich (SZ) effects in galaxy clusters
The SZ effect from the hot gas responsible for the X-ray emission of rich clusters of galaxies has been detected with high signal-to-noise and even imaged in many tens of objects (Carlstrom et al. 2002, Benson et al. 2004, Jones et al. 2005, Bonamente et al. 2006, Halverson et al. 2009, Staniszewski et al. 2009). Detailed predictions of the counts of SZ effects require several ingredients, generally not well known: the cluster mass function, the gas fraction, the gas temperature and density profiles. All these quantities are evolving with cosmic time in a poorly-understood manner. Therefore, predictions are endowed with substantial uncertainties. Current models generally assume a self-similar evolution of the relationships between the main cluster parameters (mass, gas temperature, gas fraction, X-ray luminosity; Bonamente et al. 2008). Several predictions for the SZ counts are available (e.g. de Luca et al. 1995, Colafrancesco et al. 1997, De Zotti et al. 2005, Chamballu et al. 2008). SZ maps have been constructed, mostly using the output of hydrodynamical cosmological simulations, by Geisbüsch et al. (2005), Pace et al. (2008), Waizmann & Bartelmann (2009), amongst others.
Our understanding of the physics of the intra-cluster plasma is expected to improve drastically thanks to ongoing and forthcoming SZ surveys such as those with the South Pole Telescope (Carlstrom et al. 2009), the Atacama Cosmology Telescope (Kosowsky 2006), APEX-SZ (Dobbs et al. 2006), AMI (Zwart et al. 2008), SZA (Muchovej et al. 2007), OCRA_p (Lancaster et al. 2007), and the Planck mission (The Planck Collaboration 2006).
8.2. Galaxy-scale Sunyaev-Zeldovich effects
The formation and early evolution of massive galaxies is thought to involve the release of large amounts of energy that may be stored in a high-pressure proto-galactic plasma, producing a detectable SZ effect. (Note that the amplitude of the effect is a measure of the pressure of the plasma.) According to the standard scenario (Rees & Ostriker 1977, White & Rees 1978), the collapsing proto-galactic gas is shock-heated to the virial temperature, at least in the case of large halo masses ( 1012 M, Dekel & Birnboim 2006). Further important contributions to the gas thermal energy may be produced by supernova explosions, winds from massive young stars, and mechanical energy released by central super-massive black-holes. The corresponding SZ signals are potentially a direct probe of the processes governing the early phases of galaxy evolution and on the history of the baryon content of galaxies. They have been investigated under a variety of assumptions by many authors (Oh 1999, Natarajan & Sigurdsson 1999, Yamada et al. 1999, Aghanim et al. 2000, Majumdar et al. 2001, Platania et al. 2002, Oh et al. 2003, Lapi et al. 2003, Rosa-González et al. 2004, De Zotti et al. 2004, Chatterjee & Kosowsky 2007, Massardi et al. 2008b, Chatterjee et al. 2008).
Widely different formation modes for present day giant spheroidal galaxies are being discussed in the literature, in the general framework of the standard hierarchical clustering scenario. One mode (Granato et al. 2004, Lapi et al. 2006, Cook et al. 2009) has it that these galaxies generated most of their stars during an early, fast collapse featuring a few violent, gas rich, major mergers; only a minor mass fraction may have been added later by minor mergers. Alternatively, spheroidal galaxies may have acquired most of their stars through a sequence of, mostly dry, mergers (De Lucia & Blaizot 2007, Guo & White 2008).
The second scenario obviously predicts far less conspicuous galaxy-scale SZ signals that the first one. In the framework of the first scenario (Massardi et al. 2008b) find that the detection of substantial numbers of galaxy-scale thermal SZ signals is achievable by blind surveys with next generation radio telescope arrays such as EVLA, ALMA and SKA. This population is detectable even with a 10% SKA, and wide-field-of-view options at high frequencies on any of these arrays would greatly increase survey speed. An analysis of confusion effects and contamination by radio and dust emissions shows that the optimal frequency range is 10-35 GHz. Note that the baryon to dark matter mass ratio at virialization is expected to have the cosmic value, i.e. to be about an order of magnitude higher than in present day galaxies. Measurements of the SZ effect will provide a direct test of this as yet unproven assumption, and will constrain the epoch when most of the initial baryons are swept out of the galaxies.