Benchmark Parameters for CMB Polarization Experiments

Abstract

The recently detected polarization of the cosmic microwave background (CMB) holds the potential for revealing the physics of inflation and gravitationally mapping the large-scale structure of the universe, if so called B-mode signals below 10^{-7}, or tenths of a uK, can be reliably detected. We provide a language for describing systematic effects which distort the observed CMB temperature and polarization fields and so contaminate the B-modes. We identify 7 types of effects, described by 11 distortion fields, and show their association with known instrumental systematics such as common mode and differential gain fluctuations, line cross-coupling, pointing errors, and differential polarized beam effects. Because of aliasing from the small-scale structure in the CMB, even uncorrelated fluctuations in these effects can affect the large-scale B modes relevant to gravitational waves. Many of these problems are greatly reduced by having an instrumental beam that resolves the primary anisotropies (FWHM << 10'). To reach the ultimate goal of an inflationary energy scale of 3 \times 10^{15} GeV, polarization distortion fluctuations must be controlled at the 10^{-2}-10^{-3} level and temperature leakage to the 10^{-4}-10^{-3} level depending on effect. For example pointing errors must be controlled to 1.5'' rms for arcminute scale beams or a percent of the Gaussian beam width for larger beams; low spatial frequency differential gain fluctuations or line cross-coupling must be eliminated at the level of 10^{-4} rms.

Figures (5)

• Figure 1: Block diagram for simple polarimeters. The orthomode transducer (OMT) separates two orthogonal linear polarization states with a leakage between the two characterized by $(\epsilon_1,\epsilon_2)$. After amplification with gain fluctuations $(g_1,g_2)$ the polarization state is detected by one or more of the following techniques: differencing the lines to produce $Q$, correlating the lines to produce $U$, correlating the lines with a phase shift $\phi = \pi /2$ to produce $V$. The roles of $Q$ and $V$ may be interchanged by placing a quarter-wave plate at the front end.
• Figure 2: Scalar CMB power spectra in temperature ($\Theta\Theta$) and $E$-mode polarization ($EE$) compared with $B$-mode polarization due to gravitational lensing and gravitational waves at the maximum allowable $2.6 \times 10^{16}$ GeV WanTegZal02 and minimum detectable $3.2 \times 10^{15}$ GeV level KnoSon02. The $\Lambda$CDM model shown has parameters given in \ref{['sec:bfield']}.
• Figure 3: Coherence dependence of $B$-mode contamination (a) for calibration $a$ with rms $A_a=10^{-2}$ (b) for monopole-leakage $\gamma_a$, $\gamma_b$ with $A_{\gamma_a}=A_{\gamma_b}=10^{-3}$ added in quadrature. The beam scale is FWHM = $(8 \ln 2)^{1/2}\sigma = 1'$ to remove beam effects and the FWHM coherence $(8 \ln 2)^{1/2}\alpha$ is stepped from $256'$ to $4'$ in factors of 2. Other effects follow the trend of calibration errors not monopole leakage. For a coherence large compared with the CMB acoustic peaks, $B$ contamination picks up their underlying structure. Here and in the following figures, the gravitational lensing and minimum detectable gravitational wave ($E_i=3.2 \times 10^{15}$GeV) $B$-modes are shown for reference (thick shaded lines). The scaling with $E_i$ of the peak in the $B$-mode spectrum is shown on the right hand axis.
• Figure 4: Beam dependence of $B$-mode contamination for (a) pointing with an rms $A_{p_a} = A_{p_b} = 10^{-2}$ (in units of the Gaussian beam width) added in quadrature (b) quadrupole leakage with an rms $A_{q}=0.002$ (in units of differential beam ellipticity). The coherence $\alpha$ is set to max($\sigma$, $10'/(8\ln 2)^{1/2}$) and the beam is stepped from $128'$ to $2'$ in factors of 2.
• Figure 5: All effects for a beam and coherence of FWHM = $(8\ln 2)^{1/2} \sigma =10'$. (a) Polarization distortion for an rms of $A=10^{-2}$ from calibration $a$, rotation $\omega$ ($0.6^\circ$ rms), pointing ($p_a$,$p_b$) ($2.5"$ rms) , and spin flip ($f_a$,$f_b$). (b) Temperature leakage for an rms of $A=10^{-3}$ from monopole ($\gamma_a$,$\gamma_b$), dipole ($d_a$,$d_b$) and quadrupole ($q$) terms. The "$b$" component of each effect is shown with dashed lines.