Polarization Measurements of the Cosmic Microwave Background

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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 polarization 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’Accélérateur Linéaire, UniversitéParis Sud-11, Orsay, France present address: Laboratoire Astroparticules et Cosmologie, UniversitéParis 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 gravitational 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 environment 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 challenge 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 polarization 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 ensures 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 measurement 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 polarization 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 receivers 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 polarized 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 %.

To realize that, the two linear polarizations Ex, Ey are collected by an antenna (feed horn) while a quarter wave retarder (polarizer) and an orthomode-transducer (OMT) convert them into and extract ER and EL (Figure 35.2, right panel). After ampliﬁcation, the two polarizations are processed by a correlator to give the four outputs (ER + EL), (ER EL), (ER + i EL), and (ER i EL), which, once detected and diﬀerenced, give Q and− U as for Equations 35.2 (Cortiglioni− et al 2004).

Instrumental polarization

The low CMB polarization fraction makes the instrumental polarization a major challenge when designing experiments, and several studies have been made to investigate it (e.g., Carretti et al 2001; Franco et al 2003; O’Dea et al 2007)). It is generated by leakages between the two polarizations which give a polarized signal even in the case of a purely unpolarized input. Here we only present the case of the SPOrt architecture, which features best performances (see Cortiglioni and Carretti 2006 for other architectures). Major leakages occur in the optics, polarizer and OMT, where the two polarizations propagate together. The optics contribution is described by the so-called instrumental polarization beam Π (Carretti et al 2004). This is a complex combination of co- and cross-polar antenna patterns and can be significantly lower than 1 % of the main-beam peak in best devices. It features contributions of opposite sign which makes it negligible on large angular scales, but has to be considered when dealing with instrument resolution scales. The polarizer contribution is given by the differential attenuation between the two polarizations (Carretti et al 2001). Devices developed within the SPOrt programme give a fractional instrumental polarization of 0.1 %. The OMT is usually the most limiting device. Its contribution is related to≈ the square-root of the cross-talk between the two extracted polarizations, but the exact value is a complex combination of device parameters (Carretti et al 2001). Devices with fractional instrumental polarization of 0.2 % have been achieved, with best performances of 0.02 % at 30 GHz (Carretti≈ et al 2004). Such levels are sufficient to detect the E-mode and the B-mode of the most optimistic r values. The use of cleaning algorithms will be necessary to detect the B-mode of lowest r. 578 35. Polarization measurements of the CMB

Receivers based on bolometers

Measuring polarization with bolometers The increasing sensitivity of bolometers over the years and the large band ac- ceptance (typically 30 % of the central frequency) have made them the detectors of choice for CMB measurements. In recent years, all CMB bolometric experiments have used spider-web bolometers (SWB), developed at JPL. The absorbers of these bolometers have the shape of a spider-web, so that the absorbing part is only around 10 % of the detector surface. This reduces the cosmic-ray glitches in the signal and increases the detector sensitivity by lowering the heat capacity. The noise levels of these detectors reach the theoretical noise limit set by the photon noise of the background radiation. In space the background radiation can be made minimal, as there 1/2 is no atmospheric emission, and there the photon noise is typically 40 ñKs . ≈ However, by itself, a bolometer is not sensitive to the polarization state of the incoming radiation, as it absorbs all incoming power. The wish to take advantage of its high sensitivity to measure polarization of the CMB has driven considerable research in the last decade to develop bolometers sensitive to polarization. There are essentially two ways to do this: either by placing a polarizer on the radiation path, to select one polarization state, or by making the bolometer absorb only one direction of linear polarization. With the first solution, half of the incoming power is reflected back, reducing the efficiency of the device. To make it more efficient, the reflected part must be directed toward a second detector, so that the two polarization states are measured simultaneously: this is done by an OMT, with a polarizer tilted at 45◦. However, such a device is bulky as it uses the space of two detectors in the focal plane. The Archeops balloon experiment, primarily designed to map the CMB anisotropies, also successfully measured the Galactic dust polarization at 353 GHz (Benoˆıt et al 2004), using three OMTs associated with six spider-web bolometers, revealing highly polarized regions. The second method has made a breakthrough in recent years with the developments of the polarization-sensitive bolometer (PSB) device (Jones et al 2002).

It consists of a pair of silicon nitride micromesh absorbers, separated by 60 ñm, each coupled to one direction of linear polarization. This device, combining the advantages of OMT and spider-web bolometers, is much more compact, and the proximity of the two absorbers ensures very similar working conditions (background radiation, spectral bandpass).

The Planck High Frequency Instrument Planck is a third-generation satellite to map the full sky at millimetre wave- length, launched in 2009. The High Frequency Instrument (HFI) carries 32 PSBs at four frequency channels, from 100 GHz to 353 GHz, and 20 spider-web bolometers at ﬁve frequencies, from 143 GHz to 857 GHz. Originally, it was designed to map only temperature anisotropies, but given both the theoretical and instrumental developments, it was decided, in the early stage of the project, to replace some spider-web bolometers by PSBs to measure polarization as well. The sensi- 579

Figure 35.3: Expected E- (left) and B-mode (right) angular power spectra of Planck with uncertainty bars. The WMAP concordance model has been assumed (Spergel et al 2007) along with tensor-to-scalar perturbation power ratio r =0.1. tivity expected for the E-mode and B-mode polarization power spectra are shown in Figure 35.3 (it includes both HFI and LFI) . To make a full-sky map, Planck scans the sky along nearly great circles, the axis of which are along the Sun-Earth direction. That way, the full sky is covered after around six months. This scanning strategy allows each of the spider-web bolometers to make a full map. However, this is not true for the PSBs, as each one measures only one direction of polarization (except near the ecliptic poles). Even the combination of the two detectors (the sum and the diﬀerence) gives only I and Q Stokes parameters (in a local frame). Therefore, because of the scanning strategy, there is a need to combine at least three detectors to build full-sky I, Q and U maps. This makes the Planck-HFI instrument sensitive to various systematic eﬀects, as we shall see in the next section.

The systematic effects The signal from a single detector of a PSB pair can be written in the following form: g m = (1 + η)II˜+ (1 η) QQ˜ + UU˜ dΩ , (35.3) 2 − Z n h io where I˜, Q˜ and U˜, are the beams in term of Stokes parameters, η is the detector cross-polarization and g is the calibration factor. Ideally, a PSB should have η =0 and spider-web bolometers η = 1, but typical values are rather η 0.05 and PSB ≃ ηSWB 0.95. Similarly, in ideal conditions, the intensity beam I˜ is Gaussian and symmetric,≃ and Q˜ and U˜ are given by I˜cos2ψ and I˜sin2ψ, respectively, where ψ is the angle of the PSB with respect to the sky. It is clear that if the detectors have different properties, the reconstructed Stokes parameters will be a mix of the sky Stokes parameters. Since the deviation of the polarized anisotropy signal from that of the total CMB radiance is at most 10 %, the most damaging effect is a leakage from I to Q and U. Typical effects that can lead to such leakage are uncertainties in calibration, beam differences or time-constant differences (which lead to different effective beams, see Rosset et al 2007). Other 580 35. Polarization measurements of the CMB effects, like angle or cross-polarization errors, will mix Q and U, which essentially leads to a leakage from E- to B-mode, since the former is much larger than the latter (O’Dea et al 2007; Hu et al 2003). For example, a relative fractional calibration uncertainty of 1 % will lead to corresponding uncertainties in Q and U of typically 1 % of I, and hence to un- E −2 TE −4 T TE certainties in power spectra of typically ∆Cl 10 Cl + 10 Cl , where Cl is the cross-spectrum between temperature and≈ E-mode. At small angular scales (multipole l 1000), where the E-mode is large, the relative uncertainty on the E-power spectrum≈ is typically 1 %. On the other hand, the uncertainty on the B-mode at l 100 (typical scale of primordial gravitational waves) is typically 10 times larger than≈ the B-mode spectrum! This example shows clearly that the measurement of the B-mode will require an exquisite control of systematic effects. Future experiment design must minimize such systematics, and the most important is certainly to avoid using different detectors to build a polarization map.

The future of CMB observation from space

The next step of CMB science is to measure the elusive B-mode and probe the inflation epoch. The CMB community has already moved on: NASA has started Inflation Probe with three feasibility studies, while the European community has proposed B-POL for the first call of ESA’s Cosmic Vision Programme. As discussed on Page 573, the major challenge of the B-mode is its faintness: its signal is far weaker than the temperature anisotropy and the other polarized component (E-mode). This requires both high sensitivity to detect it and polarization purity to limit contamination by the other two components. The basic idea is to take advantage of the best of each of the two technologies used so far, realizing an instrument with the purity of radiometer front-ends along with bolometer sensitivity. The simplest architecture is based on front-ends made of a feed horn, collecting the two linear polarizations, and an OMT to separate them as in a radiometer. The signal is then detected by bolometers, instead of being amplified by HEMTs as in a normal radiometer, to take advantage of their better sensitivity. The two detected polarizations must then be subtracted to provide the Stokes parameter Q. A second receiver spun by 45◦ gets U. A major issue is the need for more detectors to make polarization maps. An architecture that is a bit more complex uses the circular polarizations like the SPOrt receivers. This requires a polarizer between horn and OMT and a correlation device before the signals are detected with bolometers (Cortiglioni and Carretti 2006). This scheme has the advantage of simultaneously measuring both Q and U with just one unit, with clear advantage in term of calibration. Furthermore, this can reduce by a factor of two the number of receivers necessary to reach the wanted sensitivity, with clear benefit for a space mission in terms of mass and volume reduction. Architectures of this kind are under development for both ground-based and balloon-borne experiments (e.g., CLOVER, North et al 2007; and EBEx, Oxley 581 et al 2004, for the linear polarization scheme) and are the baseline for B-POL (both schemes). Another original architecture, combining advantages of bolometric detectors and interferometry, is also under investigation. It aims at combining the sensitivity of bolometers and low systematic effects of interferometers. The main advantage is to have a very basic optical system (no telescope is needed, feed horns are looking directly at the sky). MBI and BRAIN are two experiments based on this concept (Polenta et al 2007; Timbie et al 2006). Furthermore, the required sensitivity asks for arrays of thousands of receivers and, in turn, mass production technologies. Studies to produce cheap and high- performance OMTs are ongoing, both in waveguide and planar technology. The latter has evident cost and mass production advantages, but the polarization purity performances are poorer than for the former. Efforts are thus aimed at both improving the performance with the planar technology and reducing the cost of the waveguide devices. The selection will depend on which one will reach the best cost–performance compromise.

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