— 35 — Polarization measurements of the Cosmic Microwave Background Ettore CarrettiI and Cyrille RossetII Abstract The polarization of the Cosmic Microwave Background (CMB) brings key in- formation of early stages of the Universe such as the epoch of re-ionization and the inflation time. Its faint signal asks for both high sensitivity and high polari- zation purity which requires cutting-edge and specifically designed instruments. In this chapter we review the instruments used in CMB space experiments to date and give an overview of the next developments aimed at detection of the elusive B-mode, which will permit us to look back in time to inflation. CMB polarization The Cosmic Microwave Background radiation (CMB) is the relic emission of the Big Bang and carries the signature of the primeval Universe conditions. The study of its temperature anisotropies by spacecraft like COBE, WMAP and now Planck has been enabling high-precision measurements of cosmological quantities like the density of the Universe, its expansion rate, and the composition of the matter–energy which fills it (Spergel et al 2007). The polarization is the next CMB “holy grail”. One of its two components (the E-mode) allows the study of the re-ionization history of the Universe and the formation of first stars and galaxies. The other component (B-mode) looks even further back in time. It is the signature of the gravitational-waves background emitted by the inflation and enables a direct probe of this epoch. The CMB polarization is weak and a tiny fraction of the temperature aniso- tropies (Figure 35.1). The anisotropy of the E-mode is about 0.3 ñK on large angular scales ( 1 % of the anisotropies). Only first detections have been carried out so far by WMAP≈ (Page et al 2007) and a few sub-orbital experiments (e.g., DASI and QUaD, see Pryke et al 2009, and references therein), while significantly more is expected from Planck. The B-mode is even fainter and only upper limits exist so IIstituto Nazionale di Astrofisica – Istituto di Radioastronomia, Bologna, Italy present address: CSIRO – Australia Telescope National Facility, Parkes, NSW, Australia IILaboratoire de l’Acc´el´erateur Lin´eaire, Universit´eParis Sud-11, Orsay, France present address: Laboratoire Astroparticules et Cosmologie, Universit´eParis Diderot, France 573 574 35. Polarization measurements of the CMB Figure 35.1: CMB angular power spectra assuming the concordance cosmological model after WMAP data (Spergel et al 2007): temperature (CT), E-mode (CE), and B-mode (CB). The latter is reported for three cases of the tensor-to-scalar perturbation power ratio r, which measures the power of the primordial gravita- tional wave background. The contribution to CB by gravitational lensing is also reported. The CMB has an intrinsic limit of ∆r 10−5, corresponding to a B-mode anisotropy of 1 nK. ≈ ≈ far. The emission range of interest runs from the present upper limit of 0.2 ñK down to the CMB intrinsic limit of 1 nK, four orders of magnitude lower≈ than the anisotropies of the total CMB emission≈ (Amarie et al 2005). These unusual conditions of both low signal and polarization fraction require specifically designed experiments: low-noise detectors to reach the required sensitivity; high polarization purity to minimize leakages from the unpolarized component; a highly stable en- vironment for high thermal stability and minimisation of spillover pollution. The latter requires a quiet space environment like the Sun-Earth L2 Lagrange point, where the telescope can be efficiently shielded from the Sun, Earth, and Moon, ensuring stable conditions. In fact, the best CMB measurements have been carried out from space so far. The tiny signal also makes relevant the contamination by foreground emissions, mainly of the Galaxy. Their minimum occurs at 70 GHz to 100 GHz, which sets the best CMB frequency range, where radio and bolometric technologies overlap. In addition, the need to trace these foregrounds asks for observations at both lower and higher frequencies. Consequently, both these two technologies are required, and a wide frequency range (from 30 GHz to 300 GHz) must be covered. In this paper we review radio and bolometric receivers used in CMB space experiments. Then we will introduce the new ideas under study to match the chal- lenge posed by the faint B-mode, i.e., the aim of the next-generation CMB space missions. 575 Correlation receivers Radiometric receivers are based on direct amplification at the frequency of the signal. Usually, low-noise amplifiers (LNA) of high electron-mobility transistors (HEMT) are used because of their high sensitivity especially if cooled down to cryogenic temperatures (typically 20 K or 80 K). On the other hand, HEMT-LNAs are affected by gain instabilities. This adds an extra term to the white noise, called 1/f noise after its power spectrum (Wollack 1995). Its contribution increases with the integration time τ instead of decreasing as τ −1/2, and thus prevents any benefit of long exposures. A key parameter is the knee frequency, i.e., the frequency at which the 1/f noise component equals the white noise. This defines the longest useful integration time (τ 1/f ). max ≈ knee Total-power receivers feature fknee in the range from 100 Hz to 1 kHz (at 100 GHz) resulting in too short integration times. Correlation receivers therefore are needed to correlate signals amplified by different LNAs and largely reduce the common mode and, in turn, the fluctuations induced by gain instabilities (Cor- tiglioni and Carretti 2006). In this case, fknee typically ranges from 0.01 Hz to 0.1 Hz, which can keep the instrument stable for tens of seconds. This is sufficient for a space experiment. In fact, with an appropriate scanning strategy (e.g., by spinning and precessing the spacecraft) it is possible to modulate the signal on time scales from 1 min to 2 min, which enables data-reduction software to remove instability effects on longer times (cf., for example, Delabrouille 1998; Sbarra et al 2003). Correlation receivers can come in several flavours. In the following we will describe those of the last generation of space experiments: Planck–LFI, WMAP, and SPOrt. CMB polarization observations Planck-LFI. ESA’s Planck has been launched on 14 May 2009. The Low Fre- quency Instrument (Planck-LFI) consists of radiometers to cover three frequency bands from 30 GHz to 70 GHz and is expected to significantly improve the polari- zation results of WMAP (see Page 578). Planck is primarily devoted to CMB temperature anisotropies and measures the 2 2 2 total power of the two linear polarizations Ex , Ey . The sensitivity to both Ex and E 2 gives it polarization capabilities.| Stokes| | Q| is measured by the difference| |1 | y| E 2 E 2 Q = | x| − | y| . (35.1) 2 Stokes U is obtained by a second receiver spun by 45◦, as two receivers are needed to get Q and U. The total-power measurement is obtained by a pseudo-correlation (which en- sures the needed stability) based on the difference between the sky signal ( 2.725 K) and a reference-load of comparable intensity: a black body kept at 4 K≈ by a li- quid 4He bath. Each linear polarization gathered by the optics is extracted by an orthomode-transducer (OMT) and combined with the reference load signal by a 1See Chapter 33 (Stenflo 2010) for the definition of the Stokes parameters. 576 35. Polarization measurements of the CMB Figure 35.2: Schemes of Planck–LFI, WMAP, and SPOrt receivers. ◦ sky load 180 hybrid (Figure 35.2, left panel). The two outputs, proportional to Ex +Ex sky load and Ex Ex (for Ex polarization) are then amplified and combined back by a − sky load second hybrid to Ex and Ex . After the detection, sky and load are differenced. The two signals are both amplified by the two LNA chains, and their difference cancels out most of the gain fluctuations (Mennella et al 2004). WMAP. NASA’s WMAP (Bennett et al 2003) has been observing since 2001 and covers five bands from 23 GHz to 94 GHz. Besides providing a precise mea- surement of the CMB anisotropy spectrum, it performed the first detection of the large-scale E-mode polarization (Page et al 2007). As for Planck, its primary goal is the temperature anisotropy, but it can measure 2 2 the polarization through the difference of Ex and Ey . WMAP uses differential receivers forming the difference of signals| collected| by| two| independent telescopes looking at two sky positions spaced by 140◦. The receiver scheme is similar to that of Planck-LFI, except that the signal from the second telescope is subtracted instead of the reference load (Figure 35.2, mid panel). The other polarization extracted by the two OMTs feeds a second receiver. The basic instrument element thus consists of a pair of radiometers which provide the anisotropy of two pixels 140◦ spaced for both the two polarizations. The equations to derive Stokes Q and U are given in Page et al (2007). SPOrt. Unlike the other two instruments, the Sky Polarization Observatory (SPOrt) has been specifically designed for polarization measurements (Cortiglioni et al 2004). It was expected to fly on board the ISS and provide sensitivities in pola- rization comparable to WMAP, but it was stopped at the end of Phase B because of the ISS schedule uncertainties following the Columbia accident. The SPOrt re- ceivers were designed with no compromise with other needs (like the detection of the temperature anisotropies) and the instrumental polarization performances of its prototypes are still the best ever achieved by CMB space experiments (Carretti et al 2004). 577 The architecture is based on the cross-correlation of the two circularly polar- ized components (ER and EL) which simultaneously gives both the two Stokes parameters Q and U as ∗ Q = Re(EREL) ∗ U = Im(EREL) , (35.2) which (in contrast to the 50 % efficiency of both Planck and WMAP) gives a time efficiency of 100 %.