Absolute polarization angle calibration using polarized diffuse Galactic emission observed by BICEP
ABSTRACT We present a method of cross-calibrating the polarization angle of a polarimeter using BICEP Galactic observations. \bicep\ was a ground based experiment using an array of 49 pairs of polarization sensitive bolometers observing from the geographic South Pole at 100 and 150 GHz. The BICEP polarimeter is calibrated to +/-0.01 in cross-polarization and less than +/-0.7 degrees in absolute polarization orientation. BICEP observed the temperature and polarization of the Galactic plane (R.A= 100 degrees ~ 270 degrees and Dec. = -67 degrees ~ -48 degrees). We show that the statistical error in the 100 GHz BICEP Galaxy map can constrain the polarization angle offset of WMAP Wband to 0.6 degrees +\- 1.4 degrees. The expected 1 sigma errors on the polarization angle cross-calibration for Planck or EPIC are 1.3 degrees and 0.3 degrees at 100 and 150 GHz, respectively. We also discuss the expected improvement of the BICEP Galactic field observations with forthcoming BICEP2 and Keck observations. Comment: 13 pages, 10 figures and 2 tables. To appear in Proceedings of SPIE Astronomical Telescopes and Instrumentation 2010
- SourceAvailable from: Denis Barkats[show abstract] [hide abstract]
ABSTRACT: The Robinson Telescope (BICEP) is a ground-based millimeter-wave bolometric array designed to study the polarization of the cosmic microwave background radiation (CMB) and galactic foreground emission. Such measurements probe the energy scale of the inflationary epoch, tighten constraints on cosmological parameters, and verify our current understanding of CMB physics. Robinson consists of a 250-mm aperture refractive telescope that provides an instantaneous field-of-view of 17 degrees with angular resolution of 55 and 37 arcminutes at 100 GHz and 150 GHz, respectively. Forty-nine pair of polarization-sensitive bolometers are cooled to 250 mK using a 4He/3He/3He sorption fridge system, and coupled to incoming radiation via corrugated feed horns. The all-refractive optics is cooled to 4 K to minimize polarization systematics and instrument loading. The fully steerable 3-axis mount is capable of continuous boresight rotation or azimuth scanning at speeds up to 5 deg/s. Robinson has begun its first season of observation at the South Pole. Given the measured performance of the instrument along with the excellent observing environment, Robinson will measure the E-mode polarization with high sensitivity, and probe for the B-modes to unprecedented depths. In this paper we discuss aspects of the instrument design and their scientific motivations, scanning and operational strategies, and the results of initial testing and observations. Comment: 18 pages, 11 figures. To appear in Millimeter and Submillimeter Detectors and Instrumentation for Astronomy III, Proceedings of SPIE, 6275, 2006Proc SPIE 06/2006;
- [show abstract] [hide abstract]
ABSTRACT: The Background Imaging of Cosmic Extragalactic Polarization (BICEP) experiment was designed specifically to search for the signature of inflationary gravitational waves in the polarization of the cosmic microwave background (CMB). Using a novel small-aperture refractor and 49 pairs of polarization-sensitive bolometers, BICEP has completed three years of successful observations at the South Pole beginning in 2006 February. To constrain the amplitude of the inflationary B-mode polarization, which is expected to be at least 7 orders of magnitude fainter than the 3 K CMB intensity, precise control of systematic effects is essential. This paper describes the characterization of potential systematic errors for the BICEP experiment, supplementing a companion paper on the initial cosmological results. Using the analysis pipelines for the experiment, we have simulated the impact of systematic errors on the B-mode polarization measurement. Guided by these simulations, we have established benchmarks for the characterization of critical instrumental properties including bolometer relative gains, beam mismatch, polarization orientation, telescope pointing, sidelobes, thermal stability, and timestream noise model. A comparison of the benchmarks with the measured values shows that we have characterized the instrument adequately to ensure that systematic errors do not limit BICEP's two-year results, and identifies which future refinements are likely necessary to probe inflationary B-mode polarization down to levels below a tensor-to-scalar ratio r = 0.1.The Astrophysical Journal 02/2010; 711(2):1141. · 6.73 Impact Factor
Article: MAXIPOL: Data Analysis and Results[show abstract] [hide abstract]
ABSTRACT: We present results from and the analysis of data from MAXIPOL, a balloon-borne experiment designed to measure the polarization in the cosmic microwave background (CMB). MAXIPOL is the first CMB experiment to obtain results using a rotating half-wave plate as a rapid polarization modulator. We report results from observations of a sky area of 8 deg2 with 10' resolution, providing information up to ℓ ~ 700. We use a maximum likelihood method to estimate maps of the Q and U Stokes parameters from the demodulated time streams, and then both Bayesian and frequentist approaches to compute the EE, EB, and BB power spectra. Detailed formalisms of the analyses are given. We give results for the amplitude of the power spectra assuming different shape functions within the ℓ bins, with and without a prior C = C = 0, and with and without inclusion of calibration uncertainty. We show results from systematic tests including differencing of maps, analyzing sky areas of different sizes, assessing the influence of leakage from temperature to polarization, and quantifying the Gaussianity of the maps. We find no evidence for systematic errors. The Bayesian analysis gives weak evidence for an EE signal. The EE power is 55 μK2 at the 68% confidence level for ℓ = 151-693. Its likelihood function is asymmetric and skewed positive such that with a uniform prior the probability of a positive EE power is 96%. The powers of EB and BB signals at the 68% confidence level are 18 and -31 μK2, respectively, and thus consistent with zero. The upper limit of the BB-mode at the 95% confidence level is 9.5 μK. Results from the frequentist approach are in agreement within statistical errors. These results are consistent with the current concordance ΛCDM model.The Astrophysical Journal 12/2008; 665(1):55. · 6.73 Impact Factor
arXiv:1007.2874v1 [astro-ph.IM] 16 Jul 2010
Absolute polarization angle calibration using polarized diffuse
Galactic emission observed by BICEP
Tomotake Matsumuraa, Peter Adeb, Denis Barkatsc, Darcy Barrond, John O. Battlee, Evan M.
Biermane, James J. Bocke,a, H. Cynthia Chiangf, Brendan P. Crille,a, C. Darren Dowelle,a,
Lionel Dubandg, Eric F. Hivonh, William L. Holzapfeli, Viktor V. Hristova, William C. Jonesf,
Brian G. Keatinge, John M. Kovacj, Chao-Lin Kuok, Andrew E. Langee,a, Erik M. Leitche,
Peter V. Masona, Hien T. Nguyene, Nicolas Ponthieul, Clem Prykem, Steffen Richtera,
Graca M. Rochae, Yuki D. Takahashii, Ki Won Yoonn.
aCalifornia Institute of Technology, Pasadena, USA;bUniversity of Wales, Cardiff, CF243YB,
Wales, UK;cJoint ALMA Office, Chile;dUniversity of California, San Diego, USA;eJet
Propulsion Laboratory, Pasadena, USA;fPrinceton University, Princeton, NJ, USA;g
Commissariat ` a l’´Energie Atomique, Grenoble, France;hInstitut d’Astrophysique de Paris,
France;iUniversity of California, Berkeley, USA;jHarvard University, USA;kStanford
University, Palo Alto, USA;lUniversite Paris XI, Orsay, France;mUniversity of Chicago, USA;
nNational Institute of Standards and Technology, Boulder, USA.
We present a method of cross-calibrating the polarization angle of a polarimeter using Bicep Galactic obser-
vations. Bicep was a ground based experiment using an array of 49 pairs of polarization sensitive bolometers
observing from the geographic South Pole at 100 and 150 GHz. The Bicep polarimeter is calibrated to ±0.01
in cross-polarization and less than ±0.7◦in absolute polarization orientation. Bicep observed the temperature
and polarization of the Galactic plane (R.A = 100◦∼ 270◦and Dec. = −67◦∼ −48◦). We show that the
statistical error in the 100 GHz Bicep Galaxy map can constrain the polarization angle offset of Wmap W band
to 0.6◦± 1.4◦. The expected 1σ errors on the polarization angle cross-calibration for Planck or EPIC are 1.3◦
and 0.3◦at 100 and 150 GHz, respectively. We also discuss the expected improvement of the Bicep Galactic
field observations with forthcoming Bicep2 and Keck observations.
Keywords: cosmic microwave background polarization, millimeter wave, calibration source, polarized galactic
emission, polarization calibration
The polarization of the cosmic microwave background radiation (CMB) provides a tool for probing the physics of
the early Universe. The CMB polarization field is decomposed into even parity E-mode and odd parity B-mode.1
Primordial density perturbations result in only E-mode polarization. The E-mode signal was discovered by
Dasi and characterized by experiments including Boomerang, CBI, Maxipol, QUaD, Wmap, and Bicep.2–8
Scientific interest in the CMB community moves toward detection of the B-mode signal, which originates from
a primordial inflationary gravitational wave background and weak gravitational lensing.9Numerous kilo-pixel
array experiments, including EBEX, Bicep2, Keck, PolarBear, Quiet, and Spider, are in operation or
under construction to search for B-mode polarization.10–13,15,16
While the sensitivity of an experiment increases by employing a large number of detectors, the requirements
for controlling systematic effects becomes also stringent.17Among systematic effects in the experiment, the
polarization angle of the detectors is one of the most important quantities to be calibrated. Any miscalibration
of the absolute polarization angle of a polarimeter mixes E-mode to B-mode signals, and therefore produces a
false B-mode signal. Furthermore, such mixed E and B-mode signals are correlated and non-zero EB correlation
indicates a false detection of the CPT violation or cosmic birefringence.18–20
(Send correspondence to T. Matsumura)
T. Matsumura: E-mail: email@example.com, Telephone: +1 626-395-2147.
The strategy for calibrating the absolute angle of a polarimeter may differ depending on the size of the tele-
scope and the platform of the observatory, i.e. ground-based, balloon-borne and space-borne. The polarization
angle of a small ground-based telescope like Bicep can be calibrated nearly end-to-end in the optical chain with-
out replying on a calibration source on the sky but rather with a precisely oriented polarized source in front of
the aperture in nominal observing conditions. On the other hand, large telescopes or any balloon- or space-borne
telescopes are difficult to calibrate in nominal observing conditions without using a polarized sky signal.
Commonly used polarized sources at millimeter wavelengths in the sky are the Crab nebula (Tau A) and
Centaurus A (Cen A). The Crab nebula is a supernova remnant that emits highly polarized radiation. Aumont et
al. presented the intensity and polarized signals of the Crab nebula observed by IRAM at 90 GHz.21Cen A is an
active galactic nucleus and Zemcov et al. reported the measurements of Cen A using the QUaD telescope.22The
reflection from the rim of the Moon is another source of the polarized calibration at millimeter wavelengths for a
detector that has a large dynamic range.23Wmap presented the measurements of the polarized celestial sources,
including the Crab nebula, from 23 to 94 GHz.24
The measurements of the Crab nebula show a consistent
polarization angle with Aumont et al.. Planck satellite is planning to use this source to calibrate the polarization
angle of LFI and HFI detectors.25,26
While these highly polarized compact sources are widely used for a polarization calibration, a high signal-to-
noise diffuse Galactic polarized signal observed by Bicep is another polarized source for the angle calibration on
the sky. Bicep was a millimeter-wave bolometric polarimeter that is designed to observe the CMB polarization.27
Bicep employs a refractive telescope with a small 24 cm aperture, simplifying the characterization of the end-to-
end performance of the polarimeter’s entire optical chain. While the observation of Bicep is concentrated on the
sky region that is minimally contaminated by the dust and synchrotron emissions, one-fifth of the observational
time is dedicated to the Galactic plane observations. With systematic effects well controlled, a high signal-to-
noise map of the diffuse polarized signal over the Galactic plane makes a standard calibration source on the sky
for ongoing and forthcoming CMB polarization experiments.
In Section 2 we discuss the statistical and systematic uncertainties in the Bicep polarized Galaxy map. In
Section 3 we discuss the formalism to cross-calibrate the polarization maps produced by an unknown absolute
polarization angle polarimeter using the Bicep polarization map. In Section 4, we apply this recipe to cross-
calibrate between the Bicep 100 GHz and Wmap W band maps, as well as compute the expected constraint on
the polarization offset angle for Planck and EPIC.
2. BICEP POLARIZED GALAXY MAP
Bicep was a ground based telescope observing from the geographic South Pole. The polarimeter consists of a
two lens refractive telescope with a 24 cm aperture and 49 pairs of polarization sensitive bolometers (PSBs) at
100 GHz and 150 GHz with a corresponding beam widths of 0.93◦and 0.60◦, respectively. A detailed description
of the Bicep instrument is presented in Yoon et al.27
Bicep observed two fields over the Galactic plane as shown in Figure 1. For each field, a telescope scans
back-and-forth in azimuth at 2.8◦/s over a 65◦range at a constant elevation. The elevation is stepped by 0.25◦
after 50 right and left ”half-scans” at a constant elevation. The telescope observed with four different orientations
about its boresight: 0◦,135◦,180◦, and 315◦. Each observation of the single field has a fixed boresight angle and
four observations cover all the boresight angles to increase the crosslinking coverage.
2.1 Map making
Figures 2 shows the Q and U maps observed by Bicep at 100 and 150 GHz. This section describes polarized map
making, focusing on processes unique to the Galactic field analysis. The map making process that is common to
the CMB analysis is described in Chiang et al.8
The low-level time stream cleaning is applied to the raw time stream in following steps, (i) deconvolution of
a bolometer transfer function, (ii) low-pass filtering at 5 Hz, and (iii) downsampling to 10 Hz. The jthsample
in a half-scan of a gain adjusted pair-differenced time stream is
Figure 1. (a) The two Bicep Galactic regions are indicated over the FDS model 8 at 150 GHz.28Right: The integration
time per nside=256 of Healpix pixel at 100 GHz (b) and 150 GHz (c).29
Figure 2. The Q and U maps of the Galactic fields are shown in the unit of µKcmb. Q and U are defined in the Galactic
coordinate with IAU convention.
where diA,Bare the individual low-level processed time streams of ithPSB pair, and giA,Bare the gain factors
for each PSB calibrated at every elevation step. Common mode noise between the PSB pair, such as thermal
fluctuations of the instrument and atmospheric fluctuations, is removed by differencing between the two PSB
pair time streams, and we fit a third order polynomial, Fi(tj), to the pair-differenced time stream in order to
remove residual 1/f noise below ∼ 0.1 Hz.
When the telescope sweeps over the Galactic plane the variations in the time stream due to the Galactic signal
and 1/f noise are degenerate. To prevent removing the Galactic signal we apply a mask within the Galactic
latitude of ±3◦. The mask is applied in the time domain and we only fit the polynomial to the pair-differenced
time stream where the mask is not applied. The fitted polynomial is subtracted from the time stream dijfor all
the samples in the half-scan.
In some cases one end of the half-scan lies inside of the Galactic mask. We did not include such half-scan in
the map making because the polynomial inside of the mask needs to be extrapolated from the edge of the mask
and the extrapolated polynomial does not represent the 1/f noise inside of the mask. The half-scans whose
two ends lie in the mask are also excluded. Consequently, the recovered maps become “pac-man” shaped. The
recovered region shrinks as the mask width increases.
We follow the formalism described by Jones et al.30and used for the Bicep CMB analysis described in Chiang
et al.8The Q and U values of the pixel in the direction on the sky ? p are computed from d′
ij= di(tj) −Fi(tj) as
αij= γiAcos2ψiAj− γiBcos2ψiBj
βij= γiAsin2ψiAj− γiBsin2ψiBj.
The weight wijis an inverse of a variance of d′
The angle ψ is the PSB orientations projected on the sky and γ =1−ǫ
ǫ is a cross-polarization response. Subscripts iAand iBrefers to the A and B bolometers of the ith pair. We use
nside=256 of Healpix pixelization to project Q and U on the sky.29
ijcalculated from the samples outside of the mask in each half-scan.
1+ǫis the polarization efficiency factor, where
2.2 Pixel noise in the map
Statistical errors in the Bicep maps are estimated using jackknife maps. We split the data into three pairs of
halves, (i) right and left half-scans, (ii) (0◦,315◦) and (135◦,180◦) boresight angles, (iii) two sets of detector
pairs located in alternating sectors of the 6-sector circular focal plane. We compute the Q and U maps of each
data set as (mQ1,mU1) and (mQ2,mU2). We compute the difference as
2(mQ1− mQ2)√N, δmU=1
2(mU1− mU2)√N, (6)
where N is the number of observations at each Healpix pixel. We compute the histogram of NEQ = δmQ/√2fs
and NEU = δmU/√2fs (where fs = 10 Hz sampling rate) from the map pixels that meet the criteria of (1)
N > 2000, (2) the Galactic latitude |θglat| < 3◦and (3) not being at the edge of the observed regions. (Hereafter
we call the region of the sky that meets these criteria a selected region.) We fit the histogram with a Gaussian
Aexp−(δm− ¯ m)2
Figure 3 shows the histograms of the jackknife maps. The noise property is well described by the Gaussian
distribution. The averaged NEQ and NEU from the three jackknives are 523 and 507 µK√s for 100 GHz, and
428 and 431 µK√s for 150 GHz, respectively. Among the three jackknives the worst NEQ is 16 % larger than
the best one that is from the right and left half-scan jackknife.
2.3 Systematic error
The polarization properties of a polarimeter are described by two quantities, PSB orientation ψ and the cross-
polarization response ǫ. The PSB orientation ψ is the angle at which the PSB is sensitive to the linear polarization.
The cross-polarization response is the response of the PSB to the orthogonally polarized incident radiation.
Figure 3. The histograms of δmQ and δmU for 100 and 150 GHz are shown for right/left (top), boresight angle (middle),
and detector sets (bottom) jackknives.
Figure 4. Comparison of the filtered Q (and U) values
of the simulated map against to the input unfiltered
Q (and U) values. The two linear lines are fits to the
100 GHz (blue) and 150 GHz (green) data. The red
line indicates the line that has a slope of 1 with zero
offset. The offsets of 100 and 150 GHz Q signals are
-5.6 and -18.1, respectively.
Figure 5. The difference of the polarization angle at
each pixel before and after applying the BICEP time
domain filtering to the simulated maps is plotted. The
points are selected from the pixels for the Galactic lat-
itude of |θ| < 1 (red), |θ| < 2 and |θ| > 1 (black),
|θ| < 3 and |θ| > 2 (blue). The four lines are |∆α|
from Equation 9 with the cases for αin of 0.1◦, 2◦, 5◦
Two calibration methods are used to measure the cross-polarization. One uses a modulated linearly polarized
broadband noise source mounted 200 m away from the Bicep telescope. Bicep observed the source by raster
scans with 18 different boresight rotation angles. The other method uses a rotating wire grid mounted at the
cryostat window. The signal is generated by chopping between an ambient absorber and the sky. The cross-
polarization response is measured to within ±0.01.
The PSB orientation is measured with a rotating dielectric sheet mounted in front of the cryostat window
in addition to the two methods described to measure the cross-polarization. The measurements were repeated
through each observing year and the uncertainty of the individual PSB orientation is 0.1◦rms. After the cryostat
was opened between 2006 and 2007 observing years, the PSB orientation measurements showed an average of 1◦
rotation in the absolute polarization angle. Thus, the absolute PSB orientation uncertainty is assigned to be less
than 0.7◦rms for three years of the observation periods. The detailed discussion of the polarization calibration
of the Bicep polarimeter is described in Takahashi et al.31
2.4 Effects due to time domain filtering
The subtraction of a polynomial fit from the pair-differenced time stream effectively acts as a high-pass filter in
the time domain. While the purpose of the high-pass filtering is to remove 1/f noise, this filtering also removes
some modes of the signal.
In order to quantify the amount of the time domain filtering of the Galactic signal, we prepare a simulated
polarization map (Healpix pixelization of nside=256) that consists of the sum of CMB and FDS maps at 100
and 150 GHz with a beam size of 0.93◦and 0.60◦, respectively.28The CMB map is generated by synfast using
the cosmological parameters of the standard ΛCDM model presented in Komatsu et al.20,29The Q polarization
of the FDS map is made based on the relationships of Q/T = c0(T/Tmax)c1observed by Bicep.32We have used
(c0,c1) = (0.007,−0.47) and (0.017,−0.29) for 100 and 150 GHz, respectively.
According to this polarization model, the Galactic Q depends on temperature signal. The FDS model 8 does
not have the same level of the emission as it is observed by the BICEP. In order to simulate the realistic level
of the Galactic emission we use the temperature T = βTFDS, where β = 1.30 and 0.87 for 100 and 150 GHz,
respectively. The U polarization of the FDS is set to be zero for all the pixels. The simulated maps are smoothed
to the beam size of 0.93◦and 0.60◦for 100 and 150 GHz, respectively.
We generate time ordered data using these simulated maps with the BICEP pointing and apply the same
map making as we apply to the real data. Figure 4 shows the correlation between the input and filtered Q
and U for the pixels inside of the selected sky region. The relationship of Q before and after applying the time
domain filtering is well described by a simple linear relationship. The offset generally depends on the amount
of the signal contained at the Galactic plane and the offset is higher when the Galactic signal is higher. This
is because the signal level at the mask boundary is significant as compared to the 1/f noise, and therefore the
interpolated polynomial inside of the mask follows the trend of the Galactic signal instead of the trend from the
1/f noise. On the other hand, the U polarization does not show any clear trend. This is because U polarization
do not contain any Galactic signal but only the polarization of the CMB. Therefore, there is no characteristic
signal increase at the Galactic plane.
Figure 5 shows the change of the polarization angle after time domain filtering. The change of the polarization
angle |∆α| is modeled as
where Qin= Ipcos2αin, Uin= Ipsin2αin and Ip=
the offset angle between the Bicep map and the map from other experiment is cross-calibrated it is important
to apply the same time domain filtering to the other map.
− αin), (9)
in. Q0is the offset to account for the filtering
effect. The time domain filtering effect to the polarization angle ranges from 0.1 to 100 degrees. Therefore, when
3. ESTIMATION OF THE OFFSET ANGLE AND ITS ERROR
We describe a method to detect the overall polarization angle offset between the two polarization maps. We
have two sets of Q and U maps. Ones are the Bicep maps as the calibrated maps. The others are maps to be
calibrated. In the case of comparing the maps from two different experiments, they do not necessarily have the
same beam sizes, and therefore we need to deconvolve the original beam and smooth the two maps to the same
beam size. The choice of the beam smoothing varies depending on the beam sizes of Bicep and other experiment
to be calibrated. In this section we assume that the two sets of maps have a same beam size and are pixelized
such that the noise among pixels are not correlated. We discuss the treatment of the different beam size between
the separate experiments as a case-by-case basis in Section 4.
We write the second and third components of the Stokes parameter of ith pixel in the two sets of maps as
(QiB± δQiB,UiB± δUiB),
(Qi± δQi,Ui± δUi),
where δQ and δU indicate the statistical noise. We assume that the parent distribution of the pixel noise is a
Gaussian described by the standard deviation of σQi(B), σUi(B), σQUi(B)with a mean of zero.
We relate Q and U of the same pixel on the sky between two experiments by two parameters, offset angle δα
and the ratio of the polarized amplitudes ρ as
We can solve Equation 12 for ρiand αias,
are identical, αi= 0 and ρi= 1.
2arctanUi/Qi. When the Q and U maps from two separate experiments
While the polarization calibration can be done in terms of Q and U, we express Q and U of two maps in terms
of δα and ρ. This choice was made to mitigate the effect due to the spectral dependence of the instrumental
bandpass location and shape mismatch between the two separate experiments.We discuss the spectral dependence
of the polarization angle in Section 5.
When the Q and U maps contain only signals, we have a perfect knowledge of the offset angle δα for every
pixel. When the noise is present in the maps, the noise in the map has to be propagated to an error in the offset
angle. The error of the offset angle in each pixel i is
where σQBi, σUBi, σQUBi, σQi, σUi, σQUiare the pixel noise associated with QBi and UBi, and Qi and Ui,
respectively. The derivative terms are
The derivative terms are inversely proportional to the square of the polarized intensity. This indicates that the
error of the offset angle is smaller when the polarized intensity is stronger. Figure 6 shows the angle uncertainty
as a function of the pixel noise in Q and U maps and the polarized intensity,
While a polarization angle αivaries from −90 to 90 degrees based on the signal and the pixel noise at the
given point on the sky, we assume that the distribution of the differenced angle δαiis a Gaussian. We validate
this assumption in Section 4 when we apply this formalism between Bicep and Wmap.
The Galaxy is not a single point source, and therefore the estimation of the polarization offset angle improves
by including all the available pixels in the map. In order to calculate the mean polarization offset angle, δα0,
between the reference and the uncalibrated polarimeter maps and the corresponding uncertainty of the mean,
we compute the likelihood of δα0as
L ∝ e−1
Figure 6. This plot shows the angle uncertainty of the
polarization signal at a given pixel as a function of a
pixel noise and a polarized intensity of the signal. For
an example, a map that has a pixel noise of 10 µK and
polarized intensity of 100 µK has a polarization angle
error of 3◦.
W band (black). Both spectra are normalized to the
maximum value of 1. The BICEP spectrum is the aver-
age of a PSB pair. The WMAP spectrum is the average
of the W band spectra.
The spectra of BICEP (red) and WMAP
We apply the method described in the previous section to Bicep and Wmap. We also compute the expected
constraint to Planck and EPIC, by using BICEP Galactic map.
4.1 Polarization angle offset between Bicep and Wmap
Wmap has been observing the temperature and polarization over the full sky.33The spectral bandwidth of
Bicep 100 GHz and the Wmap W band overlap as shown in Figure 7. In this exercise, we assume that the
absolute polarization angle of the Wmap polarimeter is unknown and we constrain the overall offset angle of the
Wmap polarization maps using the Bicep Galactic map as a polarization calibration source.
Before we apply the formalism described in Section 3, we need to correct the beam size difference between
the two experiments. The FWHM of the Bicep beam size at 100 GHz is 0.93◦. Each of the Q and U maps of the
four Wmap W band differencing assembly is deconvolved with the corresponding Wmap Bland convolved with
FWHM of 0.93◦Gaussian beam in nside=512 pixelization. We compute the weighted averaged map from the
four differencing assembly maps in W band. The weights are the inverse of the pixel variance of each differencing
assembly. We apply the Bicep time domain filtering to the averaged Wmap W band map. The filtered Q and
U maps are downsampled to 0.92◦pixel size (nside=64) maps in order to decorrelate the noise among pixels.
The Bicep Q and U maps are also downsampled to the same pixelization.
The pixel noise of the Wmap maps is computed by σ =
assemblies is (σW1,σW2,σW3,σW4) = (5.940,6.612,6.983,6.840) mK with nside=512 pixelization. We neglect the
correlated noise between Q and U for both experiments. The pixel noise of the Bicep maps is computed based
on the NEQ(U) derived from the right and left jackknife maps.
√Nhitswhere σ0for the Wmap W band differencing
Once the two sets of the maps and weights are computed in the same pixelization, we impose the criteria to
select the pixels. We choose the pixels that meet the criteria of |θglat| < 3◦, Nhitsof Bicep > 2000 and pixels
of which its neighbor do not have Nhits= 0. The second criterion assures that the most of the edge pixels of
the map are not included. The second criterion does not exclude the pixel around 282◦< φglon < 322◦and
|θglat| < 3◦where the edge of the map is not tapered by Nhits. Therefore, we include the third criterion to
exclude all the edge pixels in the maps.
Figure 8 shows the map of offset angle δαi and the weight 1/σ2
close to zero and the weight is higher at the Galactic plane. Figure 9 shows the weighted histogram of δαi. The
δαi. It is clear that the the offset angle is
Figure 8. The maps of δαi (left) in unit of degrees and weight = 1/σ2
downsampled to Healpix resolution of nside=64. The edge pixels are removed, and therefore the shape of the map does
not coincide with the ones in Figure 2.
δαi(right) in unit of degree−2. The maps are
Figure 9. The weighted histogram of δα between the
polarization maps of Bicep and Wmap and the Gaus-
sian fit are shown. The distribution is well described
as a Gaussian.
Figure 10. The likelihood of δα (solid black) with the
pixel noise estimated from the right and left jackknife
and δα (dash black) with the pixel noise increased by
16 % as a worst pixel noise estimation. The histogram
is a mean of the Gaussian fit to δα from the two sets of
the simulated signal (CMB+FDS) at 100 GHz and the
300 noise realizations. The red curve is the Gaussian
fit to the histogram.
mean and the standard deviation of the angle uncertainty of each pixel is −0.41◦and 11.2◦, respectively. The
distribution of the histogram is well described as a Gaussian distribution.
Figure 10 shows the likelihood of the offset angle calculated based on Equation 19 using the Bicep and the
filtered Wmap maps. The black line shows that the mean and the sigma are the 0.6◦and 1.4◦respectively. The
dashed line with the same mean has 16% larger sigma as a worst case pixel noise.
The histogram in Figure 10 is the results of the signal and noise simulations. We prepare two sets of maps by
adding the white noise of the Bicep 100 GHz and Wmap W band to the simulated signal only maps at 100 GHz
described in Section 2.4. We repeat computing the mean of the Gaussian fit to the histogram of δα from the
two sets of the map for the 300 noise realization. The fit to this histogram in Figure 7 is consistent with the
likelihood obtained by the using Equation 19.
4.2 Polarization offset angle between BICEP and future experiments
Any ongoing and forthcoming CMB polarization experiments which observe the Bicep Galaxy region can cross-
calibrate their polarization angle using the Bicep map. As examples, we compute the expected angle constraint
1σ error [◦]
Reference × Uncalibrated
Bicep × No noise experiment
Bicep × Wmap W-band
Bicep × Planck
Bicep × EPIC-IM (4K option)
(Bicep, Bicep2) × Planck
(Bicep, Bicep2, Keck) × Planck
Table 1. The 1σ statistical error of the polarization angle offset for various combinations of the experiments. The first
row, Bicep × No noise experiment, indicates the angle error only due to the Bicep statistical noise. Bicep2 only has
150 GHz band, and therefore the error in 100 GHz does not show any improvement.
for two cases, Bicep and Planck, and Bicep and EPIC.35
Table 1 shows the list of 1σ statistical error from the likelihood in Equation 19 for 100 GHz and 150 GHz for
the two experiments. In this comparison, we assume that the bandpass shape of the two separate experiments
is the same and the knowledge of the beam shape is perfect.
The expected pixel noise of Planck and EPIC-IM are from Planck bluebook and Bock et al., respectively.34,35
It is clear that the estimate of the 1σ error of the offset angle between Bicep and Wmap improves with Bicep
and Planck or EPIC-IM. This is because the noise contribution from Planck and EPIC-IM is much smaller than
the case from Wmap while the Bicep noise stays the same. On the other hand, there is negligible improvement
from Planck to EPIC-IM because the source of the noise in these two cases is limited by the pixel noise of the
While the observations of Bicep were completed, the ongoing Bicep2 and forthcoming Keck will improve
the sensitivity to the angle calibration. If we assume that Bicep2 and Keck will spend the same observational
time with the same detector sensitivity on the BICEP Galactic field, the expected reduction of the pixel noise is
and Keck. We assume that NBicepis 25 and 24 for 100 and 150 GHz, and N0is 256 for Bicep2 150 GHz and
144 × 4 and 256 × 2 for 100 and 150 GHz of Keck, respectively. The data combining with Bicep2 and Keck
provide the statistical errors of the offset angle smaller than the systematic errors of the Bicep polarimeter itself
for both 100 and 150 GHz bands.
5.1 Comparison between the diffuse Galactic source and the Crab nebula as a polarized
simply scaled by
NBicep+N0, where NBicepis the number of detectors of Bicep and N0is of Bicep2 or Bicep2
We compare the Crab nebula and the BICEP Galactic region as a polarized source. The emission mechanism
of the Crab nebula at the millimeter wavelength is dominated by the synchrotron emission. Macias-Perez et al.
and Weiland et al. reported that the observed flux has a power law of ∝ (
polarization stays constant around 7 % over the millimeter wavelength.24,36On the other hand, the diffuse dust
emission at the Galactic plane increases as a function of frequency.32Therefore, the signal-to-noise increases as
the bandpass location increases.
40GHz)−0.3∼−0.35while the degree of
The Crab nebula is a point-like source and the Galaxy is a diffuse source. In order to compare the two
sources, we compute the integrated polarized flux of the Galactic field as shown in Table 2. We also show the
integrated polarized flux reported in Weiland et al. and Aumont et al.21,24The spatial area of the Galactic
field is much larger than that of the Crab nebula. Therefore, the integrated polarized flux of the Galactic signal
within the BICEP field is larger than that of the Crab nebula. The total pixel noise from the Galactic field is
added in quadrature. As a result, the polarized Galactic source at 150 GHz provides the same order of error as
compared to the Crab nebula at W band.
BandQ [Jy]U [Jy] Angle [◦]
WMAP, Crab nebula
all band combined
Aumont et al., Crab nebula
−88.5 ± 0.1
−87.7 ± 0.1
−87.3 ± 0.2
−87.7 ± 0.4
−88.7 ± 0.7
−88.8 ± 0.2
114.7 ± 6.0
573.4 ± 12.2
29.1 ± 6.2
195.6 ± 11.2
Table 2. The integrated polarized flux of the Crab nebula and the Bicep Galactic region is shown. The polarization
convention in this paper and Wmap are different, and thus the sign of U is changed from the original WMAP paper.
The angle error of the Bicep Galactic measurements is the quadrature sum of the pixel noise.
seen by 10′beam from Aumont et al. The original literature quoted the polarization angle in equatorial coordinates as
α = 148.8◦.
†The polarization angle
5.2 Effect of spectral mismatch between two experiments
When the two polarization maps from two separate experiments are cross-calibrated, the spectral bandpass of
the two experiments is not necessary the same. We assess the effect of the bandpass mismatch to the offset angle
estimation between the Bicep 100 GHz band and the Wmap W band.
Gold et al. derived the synchrotron and dust emission templates by the Markov chain Monte Carlo fitting.37
We compute the simulated Bicep and Wmap maps by integrating the sum of the synchrotron and dust template
maps over the Bicep 100 GHz bandpass and Wmap W band bandpass. We compute the offset angle δαiof each
pixel between the two bandpass maps. The median offset angle of all the pixels within the selected sky region is
0.005◦. We define the signal-to-noise for each pixel as the ratio of the polarized intensity to the pixel noise. We
compute the median and the maximum offset angle of which the pixels are the signal-to-noise > 3 are 0.01◦and
The Bicep 100 GHz map expects a higher contribution of the dust emission as compared to the Wmap
W band map because the Bicep 100 GHz bandwidth is slightly wider than Wmap W band bandwidth in higher
frequency side as shown in Figure 7. Gold et al. shows that in the Bicep Galactic field the polarization direction
of the synchrotron emission is −26◦< αsynch< 0◦and that of the dust emission is |αdust| < 0.3◦. Therefore,
the overall offset angle between the Bicep and Wmap maps is expected to show the positive rotation due to
the bandpass mismatch. The overall offset angle between the Bicep and Wmap maps, shown in Figure 7 , is
0.6◦± 1.4◦, and the positive mean value is consistent with the bandpass mismatch.
This effect is prominent when the passband of the instrument is located where more than two emission spectra
are mixed with nearly the same amplitude. This is because the two sources with different spectral shape can
have different polarization angles.
We present the polarized diffuse Galactic emissions observed by Bicep at 100 and 150 GHz and the method to
cross-calibrate the absolute angle between the Bicep map and any uncalibrated map. The absolute angle of the
Bicep polarimeter is calibrated to ±0.7◦and the 1σ error of the polarization angle due to the pixel noise of the
Bicep map is 1.24◦and 0.27◦for 100 and 150 GHz, respectively.
We apply this method between the Bicep and Wmap W band maps and cross-calibrate the angle to 0.6±1.4◦.
The expected 1σ errors for the Planck 100 and 150 GHz bands are 1.26◦and 0.27◦, respectively. The ongoing
and forthcoming Bicep2 and Keck are expected to reduce the statistical noise of the observations of the Bicep
Galactic region significantly.
The Bicep Galactic maps provide the polarized Galactic emission as a new angle calibration source for the
ongoing and forthcoming CMB B-mode experiments that require the absolute angle calibration to a fraction of
a degree. The method of using the Galactic signal as an angle calibration source can be applied to any two
experiments if one of the polarimeters is well calibrated. Therefore, when the Planck full sky polarization maps
are available, the future polarimeters should be able to use the Galactic signal as a calibration source not only
with respect to Bicep but also to Planck.
 W. Hu and M. White, “A CMB polarization primer”, New Astronomy, 2, pp. 323-344, 1997.
 J. M. Kovac, “Detection of polarization in the cosmic microwave background using DASI”, Nature, 420, 772
 T. Montroy et al., “A Measurement of the CMB EE Spectrum from the 2003 Flight of BOOMERANG”,
2006 ApJ 647 813.
 Sievers et al., “Cosmological Results from Five Years of 30 GHz CMB Intensity Measurements with the
Cosmic Background Imager”, ApJ, 660:976 987, 2007 May 10.
 J. H. P. Wu et al. “MAXIPOL: Data Analysis and Results”, 2007 ApJ 665 55.
 M. L. Brown et al. “Improved measurements of the temperature and polarization of the CMB from QUaD”,
2009 ApJ 705 978.
 L. Page, et al., “Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization
Analysis”, 2007, ApJS, 170, 335.
 H. C. Chiang et al. “Measurement of Cosmic Microwave Background Polarization Power Spectra from Two
Years of BICEP Data”, 2010 ApJ 711 1123.
 L. Pagano et al., “CMB Polarization Systematics, Cosmological Birefringence and the Gravitational Waves
Background”, Phys. Rev. D80:043522,2009.
 Reichborn-Kjennerud et al. “EBEX: A balloon-borne CMB polarization experiment”, Submitted to pro-
ceedings of SPIE Astronomical Telescopes and Instrumentation 2010.
 Ogburn et al., Submitted to proceedings of SPIE Astronomical Telescopes and Instrumentation 2010.
 Sheehy et al., Submitted to proceedings of SPIE Astronomical Telescopes and Instrumentation 2010.
 Arnold et al., “The polarbear CMB Polarization Experiment”, Submitted to proceedings of SPIE Astro-
nomical Telescopes and Instrumentation 2010.
 D. Samtleben et al., “Measuring the Cosmic Microwave Background Radiation (CMBR) polarization with
QUIET”, In the Proceedings ‘A Century of Cosmology’, San Servolo (Venezia, Italy), August 2007. arXiv:astro-
 Crill et al. “SPIDER: A Balloon-borne Large-scale CMB Polarimeter”, Proceedings of SPIE Volume 7010.
 Filippini et al. Submitted to proceedings of SPIE Astronomical Telescopes and Instrumentation 2010.
 Weiss et al. “Task Force on Cosmic Microwave Background Research”,’ arXiv:astro-ph/0604101v1.
 J. Q. Xia et al., “Probing CPT Violation with CMB Polarization Measurements”, Phys. Lett. B687:129-
 Wu et al. QUaD Collaboration. “Parity violation constraints using 2006-2007 QUaD CMB polarization
spectra”, Phys. Rev. Lett. 102, 161302 (2009).
 Komatsu et al. “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological
Interpretation”. Submitted to ApJ. http://lambda.gsfc.nasa.gov/
 Aumont et al. “Measurement of the Crab nebula polarization at 90 GHz as a calibrator for CMB experi-
ments”, A&A 514, A70 (2010).
 Zemcov et al. “CHARACTERIZATION OF THE MILLIMETER-WAVE POLARIZATION OF CENTAU-
RUS A WITH QUaD”, 2010 ApJ. 710 1541.
 Leitch et al., “Measuring Polarization with DASI”, Nature 420 (2002) 763-771.
 Weiland et al. “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Planets and
Celestial Calibration Sources”. Submitted to ApJ. http://lambda.gsfc.nasa.gov/
 Tauber et al., “The Planck Mission”, The Extragalactic Infrared Background and its Cosmological Impli-
cations. IAU Symposium, vol. 204 2001.
 Rosset, C. et al., “Planck pre-launch status: High Frequency Instrument polarization calibration”, Accepted
by Astronomy&Astrophysics, April 12, (2010).
 Yoon, K. W., et al., “The Robinson Gravitational Wave Background Telescope (BICEP): a bolometric large
angular scale CMB polarimeter”, 2006, Proceedings of SPIE Volume 6275,
 Finkbeiner, D. P., Davis, M., & Schlegel, D. J. “Extrapolation of Galactic Dust Emission at 100 Microns
to CMBR Frequencies Using FIRAS”, 1999, Astrophys. J. , 524, 867, astro-ph/9905128.
 Gorski, K.M. et al., 2005, Astrophys. J., 622,759.
 W. C. Jones et al., “Instrumental and Analytic Methods for Bolometric Polarimetry”, Astr. & Astroph. ,
470, Issue 2, 771785, August 2007, astro-ph/0606606.
 Y. D. Takahashi et al. “Characterization of the BICEP Telescope for High-Precision Cosmic Microwave
Background Polarimetry”, 2010 ApJ 711 1141.
 Bierman et al. Submitted to proceedings of SPIE Astronomical Telescopes and Instrumentation 2010.
 Jarosik et al. “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps,
Systematic Errors, and Basic Results”. Submitted to ApJ. http://lambda.gsfc.nasa.gov/
 Planck bluebook. ESA-SCI(2005)1. http://www.rssd.esa.int/Planck/
 J. Bock et al. “Study of the Experimental Probe of Inflationary Cosmology (EPIC)-Intemediate Mission for
NASA’s Einstein Inflation Probe”. arXiv:0906.1188v1.
 Marcias-Perez et al., “Global spectral energy distribution of the Crab Nebula in the prospect of the Planck
satellite polarisation calibration”, ApJ. 711:417-423, 2010 March 1.
 Gold et al. “Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Galactic Fore-
ground Emission”. Submitted to ApJ. http://lambda.gsfc.nasa.gov/