2.10 Observing Strategy
2.10.2 Sky Coverage
During each flight SPIDER will scan approximately 10% of the sky in a region near the galactic south pole that is exceptionally clear of galactic emission (see Fig. 2.21). The size of SPIDER’s observing region (which is approximately five times the area covered by ground based instruments) allows us to study polarization anisotropies at low multipoles, where the contribution to the B-mode power spectrum from lensing is sub-dominant. The larger sky fraction also allows us to reduce sample variance.
Chapter 3
Instrument Systematics
3.1 Introduction
To achieve the sensitivity necessary to reach SPIDER’s science goal, we will need an accurate and precise characterization of the detectors, optical components, and the resultant beams.
Non-idealities in any of these can result in systematic errors that have the potential to either leak temperature anisotropies into polarization or leak E-mode polarization into B-mode polarization. These systematic errors also include calibration uncertainties that can cause map distortions without necessarily causing false polarization signals.
A full description of SPIDER’s systematic errors requires both simulation and calibration efforts. We simulated many of the possible systematic errors to describe their effects on the final science result and set benchmark values for all of the simulated systematics. The benchmark values establish how precisely each source of systematic error must be measured or removed to achieve the design goal of measuring CMB polarization at a sensitivity equiv- alent to r = 0.03. It was our calibration goal during testing, both at Caltech in the test cryostat and in the flight cryostat during the integration of SPIDERat CSBF in Palestine, TX, to measure these systematics to the accuracy specified by the simulations. The actual measurements of these systematics will be covered in Chapters 4 and 5.
Ideally, the simulations described in this chapter would be done with variations in the instrument setup (e.g., with and without a half-wave plate, changing the flight parameters or sky coverage, different scan strategies, etc.), which would be helpful for building an intuitive understanding of the results. In practice, these simulations are too computationally intensive to allow this. It should be noted that these simulations often depend on the specifics of the observing and flight strategy, so many of the values in Table 3.1 are from
simulations that do not describe our current plan for an Antarctic flight from McMurdo Station. Most of the values listed in Table 3.1 are based on the residual of false B-mode signal in the r = 0.03 polarization spectrum for a four-day flight from Alice Springs, Australia.
Simulations that use a 20-30 day Antarctic flight will have reduced map noise, reduced sky rotation, and more time for rotation of the half-wave plate (HWP) to modulate polarization on the sky in comparison to an Alice Springs flight. These competing factors make it hard to predict how these benchmarks would change for an Antarctic simulation. As the use of the HWP ameliorates many systematic errors, we do not expect that the benchmarks would change significantly.
Our primary simulation pipeline is largely derived from the analysis pipeline used for the 2003 Antarctic flight of the BOOMERanG experiment [53]. The pipeline has several key components. The first step in the pipeline is to simulate flight pointing data for each detector (right ascension, declination, and polarization angle). Full-sky temperature and polarization maps are then simulated using the synfast program, which is part of the HEALPix software package. These maps are then smoothed by a Gaussian beam of the same width as the SPIDERbeam (which has been measured to be approximately Gaussian).
The full-sky maps are pixelized at a resolution which corresponds to ∼3.40 to ensure that the signal variation within a pixel is small. These full sky maps are then converted into timestreams using the pointing data from the flight simulator. The timestreams are high- pass filtered at 10mHz to approximate the filtering that will be done with real data in order to remove long timescale drifts (e.g., in gains or noise).
The timestream generation step includes the rotation of the half-wave plate, which is added to the polarization angle of each detector, and pointing effects such as pendulation and pointing jitter. The set of systematics we are simulating is also applied during this step.
Finally, a Jacobi-method-based iterative map-maker transforms the simulated time streams into maps of the observed Stokes parameters, Iobs, Qobs, and Uobs. The simu- lations were done with signal-only inputs, though the map-maker algorithm includes an inverse noise filtering of the timestreams. This is included because we would do this to real data in order to reduce 1/f noise, which can reduce map-making efficiency.
The simulations in this pipeline used 16 detectors, arranged in evenly-spaced pairs in a single column that extends the full height of the focal plane. The detectors in a pair have
orthogonal polarization sensitivities. These simulations assumed four days of operation during an Alice Springs flight in mid-November with a stepped half-wave plate operating mode.
There were two main simulation efforts, resulting in two papers which will be referred to from here forward by the first authors of the papers. The MacTavish [62] simulations explored the effects of polarization angle systematics, beam offsets, and gain drifts. The O’Dea simulations [68] investigated the impact of a non-ideal spectral response of half-wave plates, detector coupling to Earth’s magnetic field, beam mismatches and asymmetries, and the interaction of a foreground model with observing and flight strategies. The O’Dea simulations were done using the same simulation pipeline, but with the addition of a sky model that included a detailed model of foreground emission. This model includes polarized galactic dust emission (which requires a model of the galactic magnetic field), which is expected to be the dominant foreground for SPIDER. Synchrotron emission is expected to be sub-dominant at the SPIDER detector frequencies, and so it was not included in this model. As with the MacTavish simulations, the O’Dea simulations were done for a four- day Alice Springs flight. This is noticeably different from an Antarctic flight in that the observing time is much shorter and the fraction of the sky observed is much larger.
The simulations are evaluated by looking at the residuals (the difference between the input and output maps). However, to truly understand how the systematics will affect the science result, the maps must be transformed into power spectra. This is done usinganafast (also part of HEALPix) to do the spherical harmonic transforms. However, due to the fact that we are observing only a portion of the sky and not the full sky, the decomposition of the maps into E-modes and B-modes is not unique. The recovered B-mode spectrum is heavily biased by the input E-mode spectrum. This bias is removed by estimating the pseudo-spectra of the residual maps, which eliminates the true sky and leaves behind the systematic errors.
Table 3.1 summarizes the systematic errors and their r= 0.03 calibration goals, as well as their measured values. The following section describes each source of systematic error and how its benchmark value is derived, as well as the current scheme for measurement.
Table3.1:SPIDERSystematicsTable. SystematicTargetFakeBBSignal (%ofr=0.03)Currentstatus 90GHzCurrentStatus 150GHzNotes Relativegainuncertainty0.50%17%0.10%0.10%AchievedbyBoomerang DifferentialPointing10% 20%2.40%2.30%(X2,R6.1)and(X3,R8.0)measuredbySPIDER DifferentialBeamSize0.50%0.30%0.40%(X2,R6.1)and(X3,R8.0)measuredbySPIDER DifferentialEllipticity0.60%0.20%0.60%(X2,R6.1)and(X3,R8.0)measuredbySPIDER Absolutepolaranglecalibration1degree17%0.7degreeAchievedbyBICEP Relativepolaranglecalibration1degree6%0.1degreeAchievedbyBICEP Telescopepointinguncertainty10’6%5”AchievedbyBLAST Beamcentroiduncertainty1.2’12%1.2’AchievedbyBICEP Polarizedsidelobes-67dB8%-72dB-67dBAchievedbyBICEP Opticalghosting<2%6%1.5%-3.5%MeasuredbySPIDER HWPdifferentialtransmission0.70%10%TBDModeledbySPIDER Magneticshieldingatfocalplane10uKcmb/Bearth3%<5uKcmb/Bearth(X0,R4.0)measuredbySPIDER Cross-polarizationresponse0.80%TBD0.50%(X3,R8.0)measuredbySPIDER