Analysis of Temperature-to-Polarization Leakage in BICEP3 and Keck CMB Data from 2016 to 2018
BICEP/Keck Collaboration, T. St. Germaine, P. A. R. Ade, Z. Ahmed, M. Amiri, D. Barkats, R. Basu Thakur, C. A. Bischoff, J. J. Bock, H. Boenish, E. Bullock, V. Buza, J. R. Cheshire, J. Connors, J. Cornelison, M. Crumrine, A. Cukierman, E. Denison, M. Dierickx, L. Duband, M. Eiben, S. Fatigoni, J. P. Filippini, S. Fliescher, N. Goeckner-Wald, D. C. Goldfinger, J. A. Grayson, P. Grimes, G. Hall, M. Halpern, S. A. Harrison, S. Henderson, S. R. Hildebrandt, G. C. Hilton, J. Hubmayr, H. Hui, K. D. Irwin, J. Kang, K. S. Karkare, E. Karpel, S. Kefeli, S. A. Kernasovskiy, J. M. Kovac, C. L. Kuo, K. Lau, E. M. Leitch, K. G. Megerian, L. Minutolo, L. Moncelsi, Y. Nakato, T. Namikawa, H. T. Nguyen, R. O'Brient, R. W. Ogburn IV, S. Palladino, N. Precup, T. Prouve, C. Pryke, B. Racine, C. D. Reintsema, S. Richter, A. Schillaci, B. L. Schmitt, R. Schwarz, C. D. Sheehy, A. Soliman, B. Steinbach, R. V. Sudiwala, G. P. Teply, K. L. Thompson, J. E. Tolan, C. Tucker, A. D. Turner, C. Umilt?, A. G. Vieregg, A. Wandui, A. C. Weber, D. V. Wiebe, J. Willmert, C. L. Wong, W. L. K. Wu, E. Yang, K. W. Yoon, E. Young, C. Yu, L. Zeng, C. Zhang, S. Zhang
AAnalysis of Temperature-to-Polarization Leakage in BICEP3and Keck CMB Data from 2016 to 2018
T. St. Germaine a,b , P. A. R. Ade c , Z. Ahmed d,e , M. Amiri f , D. Barkats a,g , R. Basu Thakur h ,C. A. Bischoff i , J. J. Bock h,j , H. Boenish a , E. Bullock k , V. Buza l , J. R. Cheshire m , J. Connors n ,J. Cornelison a , M. Crumrine m , A. Cukierman e,d,o , E. Denison n , M. Dierickx a , L. Duband p ,M. Eiben a , S. Fatigoni f , J. P. Filippini q,r , S. Fliescher m , N. Goeckner-Wald e,o ,D. C. Goldfinger a , J. A. Grayson o , P. Grimes a , G. Hall m , M. Halpern f , S. A. Harrison a ,S. Henderson d,e , S. R. Hildebrandt h,j , G. C. Hilton n , J. Hubmayr n , H. Hui h , K. D. Irwin d,e,o,n ,J. Kang h,o , K. S. Karkare l , E. Karpel o , S. Kefeli h , S. A. Kernasovskiy o , J. M. Kovac a,b ,C. L. Kuo o,d,e , K. Lau m , E. M. Leitch l , K. G. Megerian j , L. Minutolo h , L. Moncelsi h ,Y. Nakato m , T. Namikawa s , H. T. Nguyen h,j , R. O’Brient h,j , R. W. Ogburn IV o , S. Palladino i ,N. Precup m , T. Prouve p , C. Pryke m,k , B. Racine a , C. D. Reintsema n , S. Richter a , A. Schillaci h ,B. L. Schmitt a , R. Schwarz m , C. D. Sheehy k , A. Soliman h , B. Steinbach h , R. V. Sudiwala c ,G. P. Teply t , K. L. Thompson e,o , J. E. Tolan o , C. Tucker c , A. D. Turner j , C. Umilt`a q,r ,A. G. Vieregg l , A. Wandui h , A. C. Weber j , D. V. Wiebe f , J. Willmert m , C. L. Wong a,b ,W. L. K. Wu d,e,o , E. Yang o , K. W. Yoon o,d,e , E. Young e,d,o , C. Yu o , L. Zeng a , C. Zhang h , andS. Zhang ha Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA 02138, U.S.A b Department of Physics, Harvard University, Cambridge, MA 02138, USA c School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA, United Kingdom d SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025 e Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 LomitaMall, Stanford, CA 94305 f Department of Physics and Astronomy, University of British Columbia, Vancouver, BritishColumbia, V6T 1Z1, Canada g Institut Laue-Langevin, 38042 Grenoble Cedex 9, France h Department of Physics, California Institute of Technology, Pasadena, California 91125, USA i Department of Physics, University of Cincinnati, Cincinnati, Ohio 45221, USA j Jet Propulsion Laboratory, Pasadena, California 91109, USA k Minnesota Institute for Astrophysics, University of Minnesota, Minneapolis, 55455, USA l Kavli Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637, USA m School of Physics and Astronomy, University of Minnesota, Minneapolis, 55455, USA n National Institute of Standards and Technology, Boulder, Colorado 80305, USA o Department of Physics, Stanford University, Stanford, California 94305, USA p Service des Basses Temp´eratures, Commissariat `a lEnergie Atomique, 38054 Grenoble, France q Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 r Department of Astronomy, University of Illinois at Urbana-Champaign, Urbana, Illinois61801, USA s Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Cambridge CB3 0WA, UK t Department of Physics, University of California at San Diego, La Jolla, California 92093, USA
Send correspondence to T St. Germaine: [email protected] a r X i v : . [ a s t r o - ph . C O ] F e b BSTRACT
The
Bicep/
Keck Array experiment is a series of small-aperture refracting telescopes observing degree-scaleCosmic Microwave Background polarization from the South Pole in search of a primordial B -mode signature. Asa pair differencing experiment, an important systematic that must be controlled is the differential beam responsebetween the co-located, orthogonally polarized detectors. We use high-fidelity, in-situ measurements of the beamresponse to estimate the temperature-to-polarization ( T → P ) leakage in our latest data including observationsfrom 2016 through 2018. This includes three years of Bicep3 observing at 95 GHz, and multifrequency data from
Keck Array . Here we present band-averaged far-field beam maps, differential beam mismatch, and residual beampower (after filtering out the leading difference modes via deprojection) for these receivers. We show preliminaryresults of “beam map simulations,” which use these beam maps to observe a simulated temperature (no
Q/U )sky to estimate T → P leakage in our real data. Keywords:
Inflation, Gravitational waves, Cosmic microwave background, Polarization, BICEP, Keck Array
1. INTRODUCTION
Observations of the Cosmic Microwave Background (CMB) over the past few decades have given us a key viewof the early universe. These observations have played a central role in the development and validation of theΛCDM standard model of cosmology. Since the discovery of the 2.7 K CMB and its 3 mK dipole, therehave been detections of ∼ µ K temperature anisotropies, ∼ µ K E -mode anisotropies, and ∼
100 nK B -mode anisotropies due to gravitational lensing of E modes. There may exist a fainter B -mode signal in thepolarization of the CMB due to the presence of gravitational waves at the time of recombination. The resulting B -mode signal peaks at degree angular scales, and is parametrized by the tensor-to-scalar ratio r . A detectionof the B -mode signal due to primordial gravitational waves would constitute strong evidence for the existence ofthis period of inflation.The Bicep/
Keck Array (BK) series of CMB polarization experiments has been observing the sky in search forthis signal from the Amundsen-Scott South Pole Station since 2006. We use small-aperture, on-axis refractingtelescopes to search for the primordial B -mode signal at its (cid:96) ∼
100 peak. The compact telescope design alsoallows us to observe the CMB at multiple boresight rotation angles, which provides valuable cross-checks andsystematics control. The optical elements are cryogenically cooled to 4 K / 50 K to minimize internal loading (seeSection 2 for more details on optical design). The detectors are antenna-coupled transition-edge sensor (TES)bolometers that are cooled to 250 mK using a three-stage Helium sorption fridge. With each new telescope inour program, we have increased the detector count in order to reduce the statistical uncertainty and increasemapping speed.
Bicep
Keck Array featured five receivers each housing 512(150/220/270 GHz) or 288 (95 GHz) detectors;
Bicep
3, with its larger aperture, holds 2,560 detectors at 95GHz. Prior to the start of the 2020 observing season, we installed the first
Bicep
Array receiver, which includes192 detectors at 30 GHz and 300 detectors at 40 GHz. Three other
Bicep
Array receivers at 95, 150, and220/270 GHz are currently in development. Our most recent published results, which includes observations from
Bicep2 and
Keck Array at 150, 95, and 220 GHz through 2015 (BK15), yields a constraint of r < .
06 whencombined with
Planck temperature measurements. At the focal plane, optical power couples to two co-located, orthogonally polarized planar antenna arrays,passes through an on-chip band-defining filter, and is eventually dissipated on a suspended bolometer islandand detected by two TES bolometers. This defines a single detector pair. Any mismatch in the beam patternbetween the two polarization states (which we call V and H in this paper) in a detector pair leaks temperatureanisotropies to the polarization measurement. This prominent systematic, temperature-to-polarization ( T → P )leakage, must be accounted for, as it may bias the final r estimate. Most of the leakage power, coming fromthe lowest-order main beam difference modes, is filtered out in analysis using a technique called deprojection(discussed in Section 3). We also utilize our vast library of far-field beam measurements in specialized “beammap simulations,” which estimates the higher-order, undeprojected T → P leakage in the CMB data. In theBK15 data set, when the measured T → P leakage is added to simulations, the resulting bias on r recoveredfrom multicomponent likelihood analysis is ∆ r = 0 . ± . rom 2016 to 2018, we observed the CMB with Bicep3 at 95 GHz and
Keck Array at 150, 220, 230, and 270GHz (with most of the
Keck data in that time at 220/230 GHz). Although the
Keck
220 and 230 GHz bandsare very similar, the spectral response of the receivers comprising these two bands have slightly different bandcenters, so they will be treated separately here. In future analyses they may be combined and presented as asingle band, after verification that the impact of this combination on the multicomponent likelihood analysis isnegligible.In these proceedings, we present a high-level analysis of the far-field beam measurements taken on
Bicep3 and
Keck Array during this time, including progress on quantifying the T → P leakage in these three years ofdata. We focus on the Bicep3
95 GHz and
Keck
220 and 230 GHz bands. In Section 2, we give a brief overviewof the differences in optical design between
Keck Array and
Bicep3 . We present far-field beam measurementsin Section 3, with emphasis on the differential beam patterns before and after deprojection. The preliminaryresults of the beam map simulations, including leakage Q maps, are shown in Section 4.
2. OPTICAL DESIGN
Bicep3 and
Keck Array both feature compact, two-lens on-axis refracting telescopes, although there are somedifferences in their optical design. Overall,
Bicep3 has a larger aperture (520 mm vs 264 mm for
Keck ), fasteroptics ( f / . f / . ◦ vs 15 ◦ ). In both cases, the lenses are cooled to 4 K duringobservations, and various IR filters at both 50 K and 4 K.Figure 1: Optical diagram for Keck Array (left) and
Bicep3 (right). Individual optical elements are labeledand drawn roughly to scale. The Zotefoam filter stack replaced the stack of metal-mesh reflective filters in the2016-2017 austral summer. The window was replaced with a
Bicep
Array-compatible window (also made ofHDPE) in the 2018-2019 austral summer. This figure is a slightly modified version of Figure 1 in Ref. 10.Figure 1 shows optical diagrams comparing
Bicep3 and
Keck Array telescopes. At 50 K,
Keck has a seriesof polytetrafluoroethylene (PTFE) and nylon IR filters, while
Bicep3 uses a high-density polyethylene foamfilter stack. This foam filter stack replaced the metal-mesh IR-reflective filters originally installed in
Bicep3 ,s part of an upgrade in the 2016-2017 austral summer. This resulted in significantly reduced thermal loadingon the 50 K stage. The lenses are kept at 4 K in both telescope designs, with
Bicep3 using alumina ceramicand
Keck using high-density polyethylene (HDPE). Also at 4 K are nylon IR filters and metal-mesh low-passfilters to prevent high-frequency photons from coupling directly to the detectors. The
Bicep3 window is madeof HDPE and is anti-reflection coated with expanded PTFE ∗ . In the 2018-2019 austral summer, this window wasupgraded to the slightly larger window design of Bicep
Array, without changing any other optical components.This allows future compatibility between
Bicep3 and
Bicep
Array windows and their associated hardware.
3. FAR FIELD BEAM MEASUREMENTS
Every austral summer before starting CMB observations, we dedicate 1-2 months to measuring the far-fieldbeam patterns of all our telescopes in situ . The measurement process is described in detail in the BK15 BeamsPaper; here we give a brief overview. The small aperture design yields a far-field distance 2 D /λ <
200 m forall observing frequencies.
Bicep3 and
Keck Array are housed in buildings at the South Pole that are ∼
200 mapart, allowing us to observe a chopped thermal source from the opposite building to measure the beam response.A large, flat aluminum mirror is used to redirect the beams over the groundshield to the thermal source on theopposite building. The mirror over
Bicep3 intercepts all beams simultaneously, whereas the mirror over
Keck only intercepts the beams from, at most, two of the five receivers at a time.After demodulating the raw beam map timestreams at the chop rate (usually 16 Hz), we bin into “component”maps with 0 . ◦ square pixels using an instrument-fixed coordinate system. The portions of the component mapswhere the main beam intersects the ground are masked and removed, to prevent possible contamination afterdemodulation. Each component beam map is fit to a 2D elliptical Gaussian, allowing us to get estimates of beamwidth, pointing, and ellipticity for each detector. Detailed measurements of the beam parameters and differential( V − H ) beam parameters for Bicep3 and
Keck Array between 2016 and 2019 can be found in Ref. 12.In a given year of beam map measurements, one detector may have anywhere between 2 −
10 componentbeam maps (2 −
40 for
Bicep3 due to the better mirror coverage) after automatically cutting poor data usingthe fit Gaussian parameters. These component maps, which are taken at various boresight rotation angles, areall coadded into per-detector composite beam maps, which are the highest-fidelity measurements of the mainbeam response we have for each detector. These composite beam maps are used in the beam map simulationsdescribed in Section 4, and after being coadded over all detectors in a frequency band, are used to evaluate thebeam window functions. The
Bicep3 and
Keck Array beam window functions between 2016 and 2019 are alsofound in Ref. 12.It is the difference in beam response between the V polarization detector and H polarization detector thatleads to T → P leakage in the CMB data. We use a technique called deprojection to filter out the leading-order terms of this leakage (originally defined in BK-III ). To second order, the modes of a differential ellipticalGaussian couple to linear combinations of CMB T and its first and second derivatives. Since the beam shapesare constant in time, we can construct leakage template maps corresponding to these difference modes, samplethem using each detector pair’s real trajectory data, regress each detector pair’s signal timestream against itsleakage template, then subtract the fitted template from the signal. Any power remaining in the difference beamresponse after deprojection contributes T → P leakage to the CMB data which is not filtered or removed bythis technique. Through the rest of this proceeding we refer to this post-deprojection difference power as the“undeprojected residuals” or the “residual beam.”Before running full beam map simulations, one can compare the shapes and magnitudes of the differencebeams ( V − H ) and the undeprojected residuals to get a rough sense of leakage expected before and afterdeprojection. Figure 2 shows the V , H , V − H , and residual beams averaged over all detectors in Bicep3 , Keck
220 GHz, and
Keck
230 GHz. In general, we see that differential pointing dominates the V − H beam patternsfor Keck
220 GHz and
Keck
230 GHz, but less so for
Bicep3 . This is consistent with previous beam parameterestimates that showed
Bicep3 had much lower differential pointing than
Keck . The average residual beampower in
Keck
220 and 230 GHz has a very similar pattern, with slightly higher amplitude at 220 GHz. Thispattern is currently being investigated. Although there is value in quantifying the relative average difference ∗ igure 2: Plots of the V and H polarization beams, difference ( V − H ) beams, and undeprojected residualsaveraged across all detectors in a band. The left column shows averages over Bicep3 , the middle column showsaverages over
Keck
220 GHz, and the right column shows averages over
Keck
230 GHz. Note the different colorscale in the V − H plots and the residual beam plots. The circular features at ∼ −
25 dB that are roughly 1degree from the main beam are due to crosstalk in the time-domain readout system and have been previouslycharacterized. beam power between frequency bands, averaging over entire receivers may disguise complex variations or trendsin these patterns across the detector array. There is ongoing work to evaluate simple, per-detector metrics of T → P leakage derived directly from the beam maps, to quantify these possible trends and identify possiblecorrelations with other optical measurements.Another factor that determines the leakage contributing to the final CMB maps from the undeprojectedresiduals is the coaddition over observations using multiple boresight rotation angles. Depending on the symmetryof a residual beam pattern and the amount of data at each angle contributing to the map, coaddition over manydifferent angles may significantly reduce the total T → P leakage from a detector pair in a given map pixel. KeckArray observes the CMB over eight boresight rotation angles each separated by 45 ◦ , which allows cancellationof any residual beam patterns that are invariant under 90 ◦ or 180 ◦ rotations. However Bicep3 only observesat four boresight angles (two separated by 45 ◦ and two that are their 180 ◦ compliments), due to the geometryof the cryocooler within the mount restricting boresight rotation. This means cancellation of residual beamspatterns invariant under 90 ◦ rotations cannot be achieved for Bicep3 . For a more complete discussion on theigure 3: Plots of the undeprojected residuals averaged across all detectors in a band ( ). The remainingplots show the effective residual beam after coadding over two boresight rotation angles separated by 180 ◦ ( ), four boresight rotation angles separated by 90 ◦ ( ), and infinitely many boresight rotation angles( )expected degree of cancellation of different leakage modes, see Ref. 13.Figure 3 shows the same band-averaged undeprojected residuals from the bottom row of Figure 2, nowcoadded over multiple boresight rotation angles to illustrate the effective total T → P leakage. This coaddingis done by averaging over the residual beam rotated to the specified boresight angles, weighted by cos 2 θ , where θ is the boresight angle. The similarity in the second row and third row for Bicep3 indicates that the penaltyfor using fewer rotation angles is small, on average. This is expected for a quadrupole-like pattern as seen inthe
Bicep3 average residual beam – a monopole-like pattern will cancel under 90 ◦ rotations and a dipole-likepattern will cancel under 180 ◦ rotations, but no such cancellation can be achieved with quadrupoles.
4. BEAM MAP SIMULATIONS
As CMB experiments increase detector count and sensitivity in future generations of telescopes, the ability toestimate and minimize T → P leakage is critical to our success at constraining cosmological parameters. Weuse “beam map simulations” to quantify the expected amount of T → P leakage due to beam shape mismatchin our real CMB maps. In this section, we present the latest leakage Q maps resulting from these simulations,nd discuss future efforts to estimate the resulting bias on r in our upcoming BK18 (all data through the 2018observing season) data set.The same analysis pipeline used for our real data and standard CMB simulations is also used for the beammap simulations. The input sky is the Planck temperature map, with no polarization (
Q, U = 0) and no addednoise. These input maps are convolved with the per-detector composite beam maps described in Section 3(truncated to a radius < ◦ from the main beam), then sampled using real detector pointing timestreams. Justas with the standard CMB simulations, the data cuts and weights applied are taken from the real data. Thesame deprojection method described in Section 3 is also applied. The timestreams are then binned into Q/U maps, where any non-zero polarization signal must be due to mismatch in the composite beam shapes.Although the input temperature maps in these simulations have no injected noise, the composite beam mapsinclude both signal and noise from the beam map measurement. To estimate the amount of noise in the leakage
Q/U maps due to noise in the beam maps, we generate “split” beam maps alongside the standard compositebeam maps. For a given detector, its split beam map is evaluated by randomly dividing all component maps(that pass automatic cuts) into two halves, and taking the difference. These split maps are used in beam mapFigure 4: Apodized Q maps of T → P leakage from beam map simulations coadded over the 2016, 2017, and2018 observing seasons. The left column shows the signal as predicted using composite beam maps, and theright column shows noise predicted by split beam maps. Top:
Bicep3
95 GHz, middle: Keck
220 GHz, bottom:Keck
230 GHz. Note the scale of the RA and Dec axes are slightly different between the
Keck maps and the
Bicep3 maps. All plots use the same colorscale.imulations in the same way as the composite beam maps, and the resulting
Q, U leakage maps are treated asestimates of noise on the leakage estimates.Figure 4 shows the resulting leakage Q maps from beam map simulations coadded over the 2016, 2017,and 2018 seasons. The Keck
220 GHz and 230 GHz leakage signal maps have very similar structure, which issomewhat expected due to the similarity of the average residual beams shown in Figure 2 and Figure 3. Thenoise in the beam maps (and therefore the leakage Q noise map) is smaller for Bicep3 , mostly due to the highernumber of component beam maps used to form the per-detector composites (due to the better coverage of theredirecting mirror). Although detailed power spectrum analysis of these maps is still in progress, preliminaryanalysis indicates that the amount of leakage seen in
Bicep3 is smaller than any
Keck band in the relevantmultipole range ( (cid:96) ∼ − Keck
220 and 230 GHz seems consistent with previouspublished 220 GHz results. Future work for this T → P analysis includes calculating power spectra after using our matrix-based purifica-tion that reduces E → B leakage due to partial sky coverage and filtering. We will then use the same quadraticestimator ρ as defined in the BK15 Beams Paper to evaluate the systematic contribution to the single-frequency BB spectra. Finally, we plan to take these maps (after coadding with previous observing seasons) and formcross spectra with the real BK18 Q/U maps.
5. CONCLUSIONS
In these proceedings we have presented a preliminary, high-level analysis of the far-field beam response of the
Bicep3 and
Keck Array
CMB polarimeters in the 2016, 2017, and 2018 observing seasons. We show the frequencyband-averaged V polarization, H polarization, V − H , and residual beam response for Bicep3 and the
Keck Q maps from beam map simulations that are estimates of the T → P leakage expected in our real CMB maps. As expected from comparisons of the residual beams, the amount of Q leakage in Bicep3 between 2016 and 2018 is lower than that of
Keck
220 and 230 GHz (based on preliminarypower spectrum analysis). Leakage seen in 220 and 230 GHz is roughly consistent with previous T → P analysisof Keck
220 GHz.
ACKNOWLEDGMENTS
The BICEP/
Keck project (including BICEP2, BICEP3 and BICEP Array) have been made possible through aseries of grants from the National Science Foundation including 0742818, 0742592, 1044978, 1110087, 1145172,1145143, 1145248, 1639040, 1638957, 1638978, 1638970, 1726917, 1313010, 1313062, 1313158, 1313287, 0960243,1836010, 1056465, & 1255358 and by the Keck Foundation. The development of antenna-coupled detector tech-nology was supported by the JPL Research and Technology Development Fund and NASA Grants 06-ARPA206-0040, 10-SAT10-0017, 12-SAT12-0031, 14-SAT14-0009, 16-SAT16-0002, & 18-SAT18-0017. The developmentand testing of focal planes were supported by the Gordon and Betty Moore Foundation at Caltech. Readoutelectronics were supported by a Canada Foundation for Innovation grant to UBC. The computations in thispaper were run on the Odyssey cluster supported by the FAS Science Division Research Computing Group atHarvard University. The analysis effort at Stanford and SLAC was partially supported by the Department ofEnergy, Contract DE-AC02-76SF00515. We thank the staff of the U.S. Antarctic Program and in particularthe South Pole Station without whose help this research would not have been possible. Tireless administrativesupport was provided by Kathy Deniston, Sheri Stoll, Irene Coyle, Donna Hernandez, and Dana Volponi.
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