View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server The Polatron: A Millimeter-Wave Cosmic Microwave Background Polarimeter for the OVRO 5.5 m Telescope B.J. Philhour1;2, B.G. Keating1, P.A.R. Ade3,R.S.Bhatia1, J.J. Bock1;4,S.E.Church2,J. Glenn5, J.R. Hinderks2, V.V. Hristov1,W.C.Jones1, M. Kamionkowski1,D.E.Kumar1, A.E. Lange1, J.R. Leong1, D.P. Marrone6, B.S. Mason1, P.V. Mason1;4,M.M.Shuman1, G.I. Sirbi1 ABSTRACT We describe the development of a bolometric receiver designed to measure the arcminute-scale polarization of the cosmic microwave background (CMB). The Polatron will be mounted at the Cassegrain focus of the 5.5 m telescope at the Owens Valley Radio Observatory (OVRO). The receiver will measure both the Q and U Stokes parameters over a 20% pass-band centered near 100 GHz, with the input polarization signal modulated at 0:6 Hz by a rotating, birefringent, ∼ quartz half-wave plate. In six months of observation we plan to observe 400 ∼ 2.5 arcminute pixels in a ring about the North Celestial Pole to a precision of 6 µK/pixel in each of Q and U, adequate to unambiguously detect CMB ∼ polarization at levels predicted by current models. Subject headings: cosmic background radiation — cosmology: observations — instrumentation: polarimeters — polarization 1. Introduction The detailed structure of the angular power spectrum of the cosmic microwave back- ground is currently being used to constrain a variety of cosmological parameters (see, e.g., 1California Institute of Technology, Observational Cosmology, M.S. 59{33, Pasadena, CA 91125 [email protected] 2Stanford University, Varian Building, Stanford, CA 94305 3Queen Mary and Westfield College, Astrophysics Laboratory, Department of Physics, London E1 4NS, UK 4Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109 5University of Colorado, Center for Astrophysics and Space Astronomy, Boulder, CO 80309 6University of Minnesota, School of Physics and Astronomy, Minneapolis, MN 55455 –2– Lange et al. (2000)). Thomson scattering of local quadrupole distributions of this radia- tion at the surface of last scattering should generate linearly polarized signal (Chandrasekar 1960). Consequently, the temperature anisotropies that are induced by density fluctuations and gravity waves in the early universe should themselves induce measurable polarization of the CMB (see, e.g., Jaffe, Kamionkowski, & Wang (2000)). Measurement of the pattern and amplitude of the CMB polarization field should ulti- mately allow tests of a number of cosmological theories. First, it will enable a check on the consistency of the theoretical model that describes CMB ∆T fluctuations as arising from den- sity fluctuations in the early universe; the cosmological models that predict the temperature angular power spectra predict corresponding polarization angular power spectra. Second, information gleaned from the polarization angular power spectrum will break degeneracies between cosmological parameters that arise in interpreting ∆T fluctuations. For example, it is difficult to use ∆T information alone to distinguish between dilution of signal at large angular scales due to early reionization and an overall change in the normalization of the pri- mordial power spectrum. However, early reionization should produce a recognizable signal — more power at large angular scales — in polarization (see Keating et al. (1998)). Third, a curl component to the CMB polarization vector pattern would indicate the presence of the stochastic gravity-wave background predicted by inflation models (Kamionkowski, Kosowsky, & Stebbins 1997a; Seljak & Zaldarriaga 1997; Kamionkowski, Kosowsky, & Stebbins 1997b). Should they exist, primordial gravity waves would carry information from an inflationary era never before open to investigation. The current observational status of this developing field is analogous to that of temper- ature anisotropy measurements some ten to fifteen years ago, with even the most sensitive upper limits an order of magnitude above the theoretically expected signal. This situation is set to change very soon with the ongoing deployment of a new generation of experiments specifically designed to measure CMB polarization. 1.1. Polarization Angular Power Spectra Because of its vector nature, the formalism through which we compare measurement and theory is more complex for polarization than for intensity anisotropies. We begin with a CMB photon traveling in thez ˆ direction with wavelength λ and frequency ν,withanelectric field vector z −→E (x; y; z; t)=Ex(t)sin 2π νt + φx(t) xˆ λ − h z i +E (t)sin 2π νt + φ (t) y:ˆ (1) y λ − y h i –3– The degree to which φx(t)andφy(t) are correlated is the degree to which the light is polarized. Time-averaging over the electric field oscillations, we can describe the polarization with the Stokes parameters I E2 + E2 ; (2) ≡hxi h y i Q E2 E2 ; (3) ≡hxi−h y i U 2E E cos(φ φ ) ; (4) ≡h x y x − y i V 2E E sin(φ φ ) ; (5) ≡h x y x − y i where I refers to the intensity, Q and U describe the linear polarization and depend on the definition of the (x; y) coordinate system, and V describes the circular polarization of the photon. Thomson scattering does not produce circular polarization. Hence, the CMB is not expected to be circularly polarized, and we no longer consider V . The Stokes parameters are converted from units of flux density to CMB brightness temperature through cross- calibration with an astrophysical source of known temperature and emissivity. Maps for which the CMB temperature T is known in each directionn ˆ are routinely analyzed via expansion of the map in terms of the spherical harmonics Ylm: l ∞ T (ˆn) T =1+ almYlm(ˆn); (6) Tcmb l=1 m= l X X− where 1 aT = dnTˆ (ˆn)Y (ˆn); (7) lm T lm∗ cmb Z T and Tcmb is the average temperature of the CMB. The auto-correlation function Cl , defined by T T T a ∗ a = C δll δmm ; (8) h lm l0m0 i l 0 0 T is predicted by theory. The multipole moments alm are a realization of the underlying statistical theory that are specific to our universe and our unique viewpoint within it. Kamionkowski, Kosowsky, & Stebbins (1997a) have developed a formalism very similar to that described above for the analysis of polarization maps. (A separate and equivalent formalism has been developed by Zaldarriaga & Seljak (1997).) They define a symmetric, trace-free tensor Pab(ˆn) which describes the linear polarization observed in directionn ˆ = (θ, φ), 1 Q(ˆn) U(ˆn)sinθ P (ˆn)= − : (9) ab 2 U(ˆn)sinθ Q(ˆn)sin2 θ − − –4– By analogy to (6), Pab(ˆn) is expanded as a sum of appropriate orthonormal basis functions on the sphere, l ∞ Pab(ˆn) G G C C = almY(lm)ab(ˆn)+almY(lm)ab(ˆn) ; (10) Tcmb l=1 m= l X X− where G 1 Gab a = dnPˆ (ˆn)Y ∗(ˆn); (11) lm T ab lm cmb Z C 1 Cab a = dnPˆ (ˆn)Y ∗(ˆn); (12) lm T ab lm cmb Z G C and the basis functions Y(lm)ab and Y(lm)ab are covariant second derivatives on the sphere of the usual spherical harmonics Ylm, chosen because they are a complete, orthonormal basis set for symmetric, trace-free tensors. The expansion of the polarization tensor is broken into two natural sets of basis functions, labeled G and C, since a symmetric, trace-free 2 2 × tensor such as Pab can be written as a sum of two tensors, one with “electric” or “gradient” parity ( 1)l and one with “magnetic” or “curl” parity ( 1)l+1. − − G C T The multipole moments alm, alm, and the temperature multipole moments alm should completely describe a map of the CMB in both temperature and polarization. An expanded set of power spectra is needed to fully characterize the temperature and polarization state of the CMB: T T T a ∗ a = C δll δmm ; (13) h lm l0m0 i l 0 0 T G TG a ∗ a = C δll δmm ; (14) h lm l0m0 i l 0 0 G G G a ∗ a = C δll δmm ; (15) h lm l0m0 i l 0 0 G C GC a ∗ a = C δll δmm ; (16) h lm l0m0 i l 0 0 C C C a ∗ a = C δll δmm ; (17) h lm l0m0 i l 0 0 C T CT a ∗ a = C δll δmm : (18) h lm l0m0 i l 0 0 GC CT If the universe prefers no direction for CMB polarization, Cl and Cl are zero. The remaining Cl’s encode fundamental cosmological parameters. Generation of temperature anisotropies through scalar processes such as gravitational collapse will produce only G-type polarization since there is no preferred handedness or curl direction for such processes. Tem- perature anisotropies generated through tensor (and vector) processes such as the influence of primordial gravity waves will produce both G-andC-type polarization (Kamionkowski, Kosowsky, & Stebbins 1997a; Seljak & Zaldarriaga 1997). The reader is directed to Kamionkowski, Kosowsky, & Stebbins (1997a) for an extension –5– of this formalism which allows for the calculation of multipole moments and variances given measured polarization two-point correlation functions. 1.2. Measurements to Date G C Hedman et al. (2001) have placed the strongest limits on Cl and Cl with a ground- based correlation polarimeter, PIQUE. To simplify the comparison of one experimental result to another, polarization measurements are often expressed in terms of “flat band power” X 2 temperatures, such that l(l +1)Cl =2π = TX where X refers to G-andC-type polarization. +294 +229 In the multipole windows lG = 211 146 and lC = 212 135 they place 95% confidence limits h i − h i − on the flat band power of the G-andC-type power spectra of 10 and 9 µK respectively, and C a limit on the G-type spectrum of 7 µK if Cl is assumed to be zero.