3.2 Galaxy cluster research: current perspectives
3.2.2 The Sunyaev-Zel’dovich effect
The Sunyaev-Zel’dovich effect is caused by inverse Compton scattering of Cosmic Mi- crowave Background photons off hot electrons in the intra-cluster gas (Fig. 3.5 a & b).
This causes the CMB spectrum to be shifted to higher frequencies (Fig. 3.5c), resulting in a CMB decrement/increment below/above 217GHz in the cluster direction (Fig. 3.5e, Fig. 3.6), when only considering the pure thermal SZ effect.
The preferential up-scattering of CMB photons can be derived by calculating the prob- ability of a single photon scattering event for a given frequency shift and electron velocity and by combining this with the properties of the electron velocity distribution (Birkinshaw et al. 1999). There is only a ≈ 1% chance of a CMB photon scattering off an electron (Carlstrom et al. 2002).
Figure 3.5: An illustration of the Sunyaev-Zel’dovich effect: CMB photons stream freely since the surface of last scattering (a) (image credit: NASA / WMAP Science Team).
When they traverse a galaxy cluster and thus also its gas plasma (b), ≈ 1% of these CMB photons are preferentially up-scattered towards higher frequencies (c) (image credit:
Carlstrom et al. 2002) through inverse-Compton scattering. This effect can be observed with radio telescopes (d) (image credit: ALMA (ESO/NAOJ/NRAO), W. Garnier (JAO)) which detect a decrement signature in the sky at frequencies below 217 GHz (assuming a pure thermal SZE) (e) (image credit: Carlstrom et al. 2002).
3.2. Galaxy cluster research: current perspectives 27
Figure 3.6: The spectral signature of the Sunyaev-Zel’dovich effect. Top: The thermal and kinetic SZ (vpeculiar = 500 km s−1) spectral CMB distorsions as a function of fre- quency taken from Carlstrom et al. (2002). Bottom: The frequency dependence is further illustrated through Planck multi-frequency cutouts of the galaxy cluster A2136 (Planck Collaboration Early results VIII 2011)
In the non-relativistic limit, the scattering process can be described by a so-called Kom- paneet’s scattering kernal, Fig. 3.7 (Birkinshaw et al. 1999), giving rise to the thermal Sunyaev-Zel’dovich effect, which fails to describe relativistic electron populations.
The spectral distorsion in terms of the dimensionless frequencyx≡hν/kBTCM B can be expressed as
∆T
TCM B =f(x)y , (3.6)
wherey is a dimensionless parameter, the Compton y-parameter, which denotes the elec- tron pressure integrated along the line of sight
y=, σTkBTe
mec2nedl . (3.7)
The spectral distorsion is therefore redshift independent, the redshift merely affecting the angular size of clusters in the sky. The parameter f(x) describes the spectral signature via
f(x) =)xex+ 1
ex−1 −4*(1 +δrel(x, Te)) , (3.8) where theδrel(x, Te) includes relativistic corrections. In terms of units of specific intensity, one can write
∆I = 2(kBTCMB)3
(hc)2 y x4ex (ex−1)2
)
xex+ 1
ex−1 −4*(1 +δrel(x, Te)) . (3.9) Recently, the Planck satellite has mapped galaxy clusters from 44GHz to frequencies that probe the increment region of the Sunyaev-Zel’dovich effect, illustrated in Fig. 3.6.
The relativistic SZ effect can either be obtained via a higher order expansion of the scattering equations in the electron temperature (Challinor et al. 1998, Itoh et al. 1998), or indeed via the Boltzmann equation numerical integration approach (Itoh et al. 2004), this method being more accurate up to higher temperatures and frequencies. A comparison of the scattering kernal for non-relativistic and relativistic electrons is given in Birkinshaw et al. (1999) and shown in Fig. 3.7 (top). Fig. 3.7 (middle) shows the spectral distorsion using the Itoh et al. (2004) numerical fits and Fig. 3.7 (bottom) compares this to the electron temperature expansion of Itoh et al. (1998) in order to illustrate the validity of the latter as a function of the dimensionless frequency range.
The kinetic SZ effect (kSZ) is caused by the effect of the bulk motion of the ICM and therefore lends itself well to non-thermal pressure ICM studies. Recently, the detection of the kSZ in MACS J0717.5+3745 has been reported (Sayers et al. 2013). Future in- struments such as CCAT will make kSZ measurements a promising tool for improving SZ power spectrum modeling (CCAT Scientific Memo in prep).
In the case of the isothermal beta model described in section 3.2.1, one can express the brightness temperature profile parametricallly as
∆T(θ) =∆T0
- 1 +θ2
θc2
.(1−3β)/2
(3.10) with ∆T0 being the central brightness temperature change andθ=rc/DA. Equivalently, one can define the central Compton-y parameter, y0. A variable that is proportional to a galaxy cluster’s total thermal energy content, is the spherically integrated Compton Y parameter
Ysph(r) = 4πσT
mec2 , r
0 Pe(r$)r!2dr . (3.11) The cylindrically integrated Y parameter in terms of the radial 3D pressure profilePe(r) integrated over a projected radius R, can be expressed as
Ycyl(R) = 2πσT
mec2 , ∞
−∞
dl , R
0 Pe(r)rdr . (3.12)
3.2. Galaxy cluster research: current perspectives 29
Figure 3.7: The relativistic SZ effect. Top: The scattering kernel as a function of the logarithmic frequency shift, s, for 5.1 keV (red) and 15.3 keV (blue) electron temperatures taken from Birkinshaw et al. (1999). This illustrates the necessity for using the relativistic formulation in the 15.3 keV case. Middle: The relativistic spectral distorsion for different electron temperatures as reported in the Itoh et al. (2004) numerical fits. Bottom: A comparison of the results by Itoh et al. (2004) (coloured lines) with the numerical higher order temperature expansion results of Itoh et al. (1998) (black lines) for different electron temperatures. As one can see, the disagreement is strongest for the highest electron temperatures.