Measurement of the Polarization of the Cosmic Microwave Background with the Bicep2 and Keck Array Telescopes

On small angular scales, the aB mode pattern arises from the gravitational lensing of the E mode energy by the large-scale structure of the universe. This thesis is an overview of the results of the Bicep2/Keck Array and contains many details beyond the main publications.

Cosmic inflation

The locations of the peaks in the temperature angular power spectrum confirm that the modes are adiabatic [65]. Second, the scalar fluctuations that give rise to temperature anisotropy also give rise to linear polarization patterns with parity on the sky, discussed further in Section 1.2.

CMB polarization

The polarization pattern across the sky, E-mode or B-mode, depends on the symmetries of the primordial fluctuations and can be used to distinguish scalar from tensor fluctuations. The importance of the symmetries and the E-mode/B-mode basis was fully appreciated in 1996 by M.

Observational status

These possess an additional degree of freedom through the + and × polarization states of the gravitational waves, which translate to m = ±2 quadrupoles. All the other PhD theses are great resources and are in many ways more complete than what I offer here.

General overview

Testing and deploying the Bicep2/Keck Arraydetectors took up about half of my time in graduate school. The household electronics and Multi-Channel Electronics (MCE) attach to the bottom dish of the cryostat.

Figure 2.2: The Bicep2 telescope in the mount, looking out through the roof of the Dark Sector Laboratory (DSL) located 800 m from the geographic South Pole

Observing site

Readout and software

GCP synchronizes and merges the data streams from the MCE, BLASTbus and PMAC and records the data at 9 Hz (see Section 2.9).

Cryogenics

Each receiver is cryogenic, with a pulse tube cooler that cools the optics to 4 K and a three-stage sorption cooler that cools the focal plane to 270 mK.

Figure 2.3: Individual receiver of Keck Array. Each receiver is cryogenic, with a pulse tube refrigerator cooling the optics to 4 K and a three-stage sorption refrigerator cooling the focal plane to 270 mK

Transition-edge sensors

Major component layers of the focal plane design, with an enlarged view of the tile layers on the right. The gold winding microstrip terminal is on the right of the photo and the TESs on the left.

Figure 2.4: Focal plane pictures and cross-section. Upper: Top (left) of the Bicep2 focal plane and bottom with backshort removed (right)

Detector response

By shifting the bias to measure an I−V curve, the normal TES resistance can be derived from the slope of the linear region. Second, if the TES is at the very steep part of the transition with L 1, then so is the reaction.

Detector thermal conductance

SQUID readout

Noise performance and sample rate

Beam mapping

The upper panels show a typical detector pair from the focal plane in 2012, and the lower panels show a typical detector pair from the focal plane installed in 2013 with dramatically reduced differential directivity. Near-field beam mapping is a chopped heat source mounted on a biaxial translation stage that can be mounted directly in front of the cryostat window to perform this near-field measurement.

Figure 2.9: An example Keck Array detector pair that shows beam mismatch in the near field

Pointing

Absolute polarization angle and efficiency

The absorber is covered with a 1/8" thick sheet of closed-cell expanded polyethylene foam exactly as in the front (described in §3.5), the combination of which has about 95% emittance at 100 GHz. We use this polarization calibrator by placing it in place of the front part and fixing it to the azimuth mount.

Figure 2.10: A picture of the dielectric sheet calibrator installed on the Bicep1 telescope

Optical efficiency and spectral response

Furthermore, the cross-spectra between the angle-corrected BK150 data and the Planck143 GHz data (see Section 5.4 ) show neither evidence for a significant correlation in EE nor a significant leakage in EB [ 10 ]. If the source is uniformly filled with rays, then the integral angle over the solid gives the spectral flux.

Optical efficiency measurement

At the aluminum junction, where the FPU temperature is stable, one load curve determines the Joule power under optical load at room temperature and another determines this under optical load at liquid nitrogen temperature.

Spectral response measurement

Note that the top and bottom plots are of the same data but with different axis boundaries. The Fourier transform spectrometer (FTS) is a Martin–Puplett interferometer [48] that can be mounted directly on the front of the cryostat.

Figure 2.14: Interferogram of a 150 GHz detector. The data are of a detector on tile 1 of rx4

Detector screening program

The transformation from Q/U to E/B is given in Section 3.4 for full-sky and flat-sky approximations. The mode mixing and ambiguity issues are presented in Section 3.5 and the observation matrix and cleaning matrix that are correct for these issues are defined in Sections 3.6 and 3.7.

Figure 2.16: Sample far-field detector pattern measured in Short Keck, a test cryostat without an optical stop

Scan strategy

T/Q/U maps

The first scan of the G phase is shown in bold, showing the throw of the field scans (horizontal line) and the lifting nodes of the bracket (vertical line). Letxik =wikdsum,ik be the measurement of the sum of the pair while the detectors are pointed at a given map pixel indexed by the sajkth observation, weighted by wik.

Parallel accumulation

E/B maps

The transform is non-local and is performed in the Fourier domain, where the Fourier coefficients are related to. As in the case of the entire sky, it is possible to extract the components of Q and U that come only from E or B by setting them to zero in the above equation and returning to real space.

Mode mixing and ambiguity

Observation matrix

In parallel with the construction of the detector-pair maps and their accumulation, we construct pixel-by-pixel matrices which track how each true sky pixel maps into the pixels of the final map due to the various filtering operations. The construction of R from all the pointing and filtering operations is discussed in detail in J.

Purification matrix

Additional information on the construction of the cleaning matrix and its comparison with other methods is given in J.

Cross maps

For this reason, cross-maps are only intended for the visual representation of the correlated components with reduced noise of maps and should generally be avoided in high-level analyses. The full description of the sign-flip noise model, complete with the accumulation of the noise covariance matrix, is presented in Sections 4.4–4.6, and an attempt at visualization of the noise correlation is given in Section 4.7.

Signal suppression and noise bias

Note that the suppression factor is partially degenerate with the absolute calibration of the experiment. Since the real data lie outside the noise distribution, D`0 is also estimated for all the 499 signal+noise simulations.

Single multipole simulations

The main effect of anisotropic filters is suppression along the kx = 0 line in the 2D Fourier plane. Since the observation and sweep matrices capture all filtering effects, they can be used to determine F`,`0.

Figure 4.1: F `,` 0 for D ` BB evaluated for Bicep2 using simulations at a single multipole containing no E-mode power and processed through the analysis pipeline, including matrix purification

Signal simulations

Tolan's thesis [87] discusses when lensing is assumed to be present or absent through the steps of the simulation pipeline. They are then converted to simulated time streams assuming instrument pointing information and deck angle and accumulated into maps, or they are simply multiplied by the observation matrix.

Noise models

The sign reversal noise simulation is a weighted accumulation of εkδm˜k, where εk is a +1 or −1 assignment. Here we show that this method is mathematically equivalent to subtracting the mean autospectrum of a sign-reversal noise simset.

Deviations

The term ˆfn,+(k) ˆfn,∗−(k) is the 2D cross spectrum between the two halves of the data distribution. As noted in Equation 3.68, only the real part of the 2D power spectrum contributes to the 1D power spectrum for a real-valued map.

Noise covariance blocks

Note that the sample noise covariance matrix as defined above is biased, but the bias is small if the number of scans or phases is large. Estimating the covariance matrix is computationally expensive, but manageable in size for Bicep2/Keck cluster maps.

Noise covariance and correlation maps

The ForT Q plot shows how the T noise of the selected pixel varies with the Q noise in all other pixels. For QT the plot shows how the T noise of the selected pixel varies with the T noise in all other pixels.

Figure 4.2: Noise covariance of a map pixel for T T , QQ, and U U . Each row of the covariance matrix is represented by a set of maps

Cross-spectrum noise distribution

There are some special cases of the variance-gamma distribution for which the probability density does not require Bessel functions.

Initial value estimation

Note that this is the standard deviation of the variance-gamma distribution, while σ is a parameter derived from the widths of the underlying Gaussian distributions.). In Section 5.9, we conclude with a summary of the results and a prediction of the further sensitivity of the Keck Array.

Maps

Based on the consistency of the 2010–2013 data set as assessed in Section 5.2 , the 150 GHz data are combined and reduced to angular power spectra in Section 5.3 . The total sensitivity is the depth divided by the square root of the effective area (about 390 deg2 for both telescopes), which accounts for apodization.

Consistency

The most extreme value is the χPTE for the Bicep2 tile nest, for which the real data spike is right at the end of 499 simulations and can be related to the difference in absolute calibration between the detectors. An example is the effect of residual ray effects beyond the elliptical Gaussian approximation.

Bicep2 /Keck Array power spectra

The error bars are the standard deviations of the noise simulations with the ΛCDM+ lens and therefore do not contain the sample variance on any additional signal components. The error bars are the standard deviation of the noise simulations with the ΛCDM+ lens and are not suitable for comparison of data values.

Figure 5.5: Keck Array power spectrum results for signal (black points) and early/late season jackknife (blue points)

Combination with Planck

The lens-ΛCDM+noise error bars as plotted are about a factor two smaller than those of the previous Bicep2only results—saturation on the (small) sample variance of the lens component occurs—the noise component is a factor 2.3 times smaller. The error bars are the standard deviation of the lensing ΛCDM+noise simulations and thus contain no sample deviation on any additional signal component.

Figure 5.7: The BB power spectrum of combined Bicep2 and Keck Array 150 GHz maps. The error bars are the standard deviation of the lensed-ΛCDM+noise simulations and hence contain no sample variance on any additional signal component.

Dust model

From dust astrophysics, we expect that variations of the dust SED in intensity and polarization will be correlated [50]. We therefore tested our assumption by measuring the spectral index of the total dust intensity in the Bicep2/Keck Array field using the template matching analysis reported in Planck Int.

Likelihood calculation

In the HL approach, the log-likelihood of the theoretical band strengths{D`0} for a model given the observation is {Dobs`0 }. An advantage of the HL approach is that (Df`0)12 and M−1 only need to be calculated once for the confidence model and not for other grid points in the model parameter space.

Parameter constraints

In the fiducial analysis, the amplitude of the lensing effect is held fixed at the ΛCDM expectation (AL= 1). Using their own and other data, the Planck Collaboration cites a limit on the amplitude of the lensing effect versus the ΛCDM expectation of AL.

Figure 5.12: Likelihood results for a fit allowing the lensing scale factor A L to float freely and using all nine bandpowers

Component-separated bandpowers

The probability of the fiducial analysis in Figure 5.11 is the combination of the nine bins together with their correlation. Therefore, it helps to visualize the results of the multicomponent analysis without invoking a specific theoretical model, apart from the assumptions about the frequency scale of dust.

Figure 5.13: Component-separated BB bandpowers using the HL likelihood analysis on individual ` bins.

Conclusion

Kernasovskiy.Measuring the polarization of the cosmic microwave background with the Keck Array and Bicep2. A measurement of the cosmic microwave background polarization power spectrum in B-mode on polar bear sub-degree scales.