Systematics in the QUaD experiment

Clem Pryke for the QUaD Collaboration

University of Chicago, 5640 S Ellis Ave, Chicago, IL, 60637, USA

E-mail: pryke@focus.uchicago.edu

Abstract. QUaD was a ground breaking CMB polarization experiment, achieving for the first

time sufficient sensitivity to see the acoustic peaks in the E-mode power spectrum. Systematic

effects as they relate to the data analysis are discussed including relative gain calibration and

ground pickup. The observation of beam centroid offset between the two halves of the detector

pairs is also described and an empirical model presented.

1. Introduction

The QUaD experiment was designed to measure the polarization anisotropy of the CMB at 100and 150 GHz. It consisted of a Polarization Sensitive Bolometer (PSB; [1]) based receivermounted on a 2.6 m Cassegrain radio telescope, and supported by the platform originallyconstructed for the DASI experiment [2]. This is an az/el mount with a third axis allowingthe entire optics and receiver to be rotated around the line of sight (referred to as “deck”rotation). The secondary mirror was supported by a cone fabricated from polypropylene foamsheets (Zotefoam PPA30).

QUaD observed from the South Pole during the Austral winters of 2005, 2006 and 2007 andis now de-commissioned. Full details of the instrument have been published [3], as have scienceresults [4–8]. This paper focuses on some systematic effects.

2. Relative Gain Calibration

The halves of each PSB pair measure orthogonal linear polarizations. In the QUaD systemthere is no rapid polarization modulation. The pairs of detectors are read out separately anddifferenced to measure polarization in the off-line analysis. Accurate gain matching is requiredbefore the differencing operation to prevent total intensity leakage into polarization. It is thusnecessary that the relative gains be stable over the time period between measurement andapplication. In addition the detectors are DC sensitive so any differential baseline drift betweenthe two halves of a pair will appear as false polarization signal.

Before PSB direct pair differencing experiments like QUaD were proven in the field skepticismwas expressed that the necessary level of gain stability could be achieved. As described in [3]QUaD utilized active focal plane temperature stabilization. The relative gain of the detectorswas measured every 30 minutes by performing an “elevation nod” — the telescope was movedup and then down in elevation angle by one degree injecting an atmospheric ramp into the datastream. Regressing this signal versus airmass for each detector yields the relative gain factor involts/airmass. Figure 1 shows the relative gain timeseries for the first ten detector pairs. The

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Figure 1. Left: the relative gains of the first ten 150 GHz detector channels as measuredby elevation nods every half hour over two seasons. Right: a histogram of the percentagefluctuations of the timeseries at left including all channels. Reproduced from [5].

panel at right shows the percentage fluctuation of the timeseries with one histogram entry foreach detector pair.

It is very important to note that random errors in the relative gain measurements averagedown over time and do not lead to systematic leakage of temperature into polarization —sometimes a given pair will leak T into +Q and sometimes into −Q leading to zero net leakage.

3. Pair Sum and Difference Timestream Data

Figure 2 shows a sample of timestream data taken while the telescope was scanning on the CMBfield. Relative gain calibration has been applied and the sum and difference for each detector pairtaken. In the top panel we see the rounded triangle wave azimuth scan pattern superimposed ontop of the sidereal tracking rate. In the pair sum the common mode variation of the atmosphericsignal with time is very substantial but is not strongly correlated with the telescope motion — itappears that we are seeing structured “clouds” blowing through the telescope beam faster thanit scans. The pair difference timestream has dramatically less low frequency structure indicatingthat the atmospheric emission is largely unpolarized. The dark channels also show very littlelow frequency structure confirming that the pair sum signal originates outside the telescope andis not caused by, for instance, focal plane temperature instability.

Figure 3 shows the power spectral densities of the timestream data. We see that the lowfrequency structure seen in Figure 2 has the classic 1/f form at low frequencies. The cause ofthe “bump” at ∼ 0.25 Hz is unknown. We do see a small increase in the pair difference noise atlow frequencies. It is not clear if this is real or an artifact of imperfect relative gain calibration.Instead of using the elevation nod derived relative gains we can instead regress the A and Btimestreams within a pair against one another. Doing this does slightly reduce the amount ofpair difference 1/f . There may be subtle effects going here due to passband differences and thediffering spectra of the base thermal atmospheric emission versus that of the inhomogeneous(water line) component. However since the final maps are impressively free of temperature topolarization cross correlation and pass all jackknife tests we have not pursued this point further.

4. Ground Signal and Field Differencing

In initial QUaD observations it quickly became clear that ground pickup was a serious problemand we therefore adopted the commonly used lead-trail-field strategy. We scanned an area 0.5hours wide in R.A. for half an hour before switching to the area 0.5 hours behind in R.A. Thescan pattern in ground fixed azimuth/elevation coordinates was therefore repeated exactly halfan hour later — see Figure 4. By differencing the lead and trail field data point-by-point in the

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Figure 2. Timestream data for a sample scan set. The top panel shows the azimuth angle, andthe middle panels the pair sum and difference detector timestreams with relative gain calibrationapplied; red/orange colors are the 100 GHz pairs, while blue/green colors are the 150 GHz. Thebottom panel shows the dark channels. In all cases an approximate scaling to temperature unitshas been applied. For the purposes of this illustration the timestreams have been heavily lowpass filtered (to ≤ 1 Hz). Reproduced from [5].

timestream ground signal which is constant over half an hour is removed and a difference mapof the sky is obtained. Figure 5 illustrates the process.

In order to test for the presence of residual ground signal — or any other systematiccontamination — we perform a further level of differencing. The data is split into pairs ofapproximately equal subsets each of which should contain the same sky signal (i.e. cover thesame area of sky) but which are likely to contain different contaminating signal. The mostpowerful of these is our so called deck jackknife test in which the data subsets are the first andsecond halves of each day long data taking run. The run started at the same local sidereal time,and hence telescope azimuth angle, each day. The data halves were thus taken over completelydifferent parts of the horizon, and in addition the entire telescope was rotated by 60 deg aboutthe line of sight in the middle of the run. After taking the difference of maps made from thetwo data subsets we proceed to power spectra in the same way as for the un-differenced maps.Figure 6 shows the resulting power spectra — χ2 tests show that the jackknife spectra areconsistent with zero.

We can also difference the 100 and 150 GHz maps to look for evidence of foreground emission.Since the absolute calibration factor of both of these is determined by cross correlation with thesame (150 GHz) B2K map what we are really testing here is if the maps have the same spatialform at both frequencies. While the CMB is expected to do so foregrounds are not — forinstance synchrotron is known to have a spatially varying spectral index. As we see in Figure 7the 100 and 150 GHz maps cancel impressively well.

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Figure 3. Timestream PSDs averaged over a single day of data. Pair sum and pair differencespectra are shown; red/orange colors are the 100 GHz pairs, while blue/green colors are the150 GHz. Reproduced from [5].

5. Beam Centroid Offsets

The A and B halves of each detector beam should ideally have identical beam shapes on thesky. However as shown in Figure 8 in practice they are found not to do so. The principle effectis a centroid offset of ∼ 0.001 deg — < 5% of the beam width in all cases.

This effect is repeatable between beam mapping runs and rotates when the telescope is rotatedabout the line of sight — i.e. it is a property of the telescope rather than due to polarization of thesource. Additional evidence for this last statement comes from the fact that like aligned detectorpairs do not see the same offset magnitude and direction. Figure 9 shows the repeatability.

An empirical model has been constructed which appears to fit the data well as illustratedin Figure 10. For bolo pairs oriented radial/tangential to the focal plane radial direction theA-B centroid offset is radial. For pairs oriented at 45 deg to the focal plane radial direction thecentroid offset is tangential. i.e. For a half revolution of the A bolometer orientation startingfrom the radial direction, the A-B offset vector goes through a full revolution from inwards, tooutwards and back to inwards again. This effect is not understood; reflections from the metallicsurfaces of the primary and secondary cannot generate an offset of the observed magnitude. Thefeedhorns are axi-symmetric and aligned perpendicular to the bowl shaped focal plane surfaceso these also seem unlikely to generate an offset. This leaves the dielectric lenses. It might makesense for there to be an A-B offset for pairs oriented radially as A and B are then receivinglight which strikes the lens radially and tangentially to its direction of curvature. However it isunclear how a pair arranged at 45 deg — symmetrically with respect to the lens curvature —can have a tangential centroid offset.

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6. Conclusion

Some systematic related effects arising in the analysis of QUaD data have been described. After> 10 person years of effort the QUaD data remain imperfectly understood. In the final analysissystematic effects reduced the sensitivity of the results by only a small factor. However furtherincreases in sensitivity will need to be accompanied by corresponding decreases in systematiceffects to a) allow for the additional sensitivity to be fully exploited and b) to keep the analysiseffort to < 100 person years.

References

[1] Jones W C and et al 2003 Millimeter and Submillimeter Detectors for Astronomy.

Proceedings of the SPIE vol 4855 ed Phillips T G and Zmuidzinas J pp 227–238

[2] Leitch E M and et al 2002 ApJ 568 28–37 (Preprint astro-ph/0104488)

[3] Hinderks J and et al 2009 ApJ 692 1221–1246 (Preprint arXiv:0805.1990)

[4] Ade P and at al 2008 ApJ 674 22–28 (Preprint arXiv:0705.2359)

[5] Pryke C and et al 2009 ApJ 692 1247–1270 (Preprint arXiv:0805.1944)

[6] Wu E Y S and et al 2008 ArXiv e-prints (Preprint 0811.0618)

[7] Castro P G and et al 2009 ArXiv e-prints (Preprint 0901.0810)

[8] Friedman R B and et al 2009 ArXiv e-prints (Preprint 0901.4334)

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Figure 10. Centroid offset model. left: The mean pair centroid offset vector from Figure 9 isshown in red, the radial vector from the focal plane center is shown in black, and the A bolometergrid angle as projected on the sky is shown in blue. right: Scatter plot of the direction differences;the x-axis is the bolometer grid angle with respect to the radial direction (blue minus black atleft), and the y-axis is the centroid offset direction with respect to the radial direction (red minusblack at left).