The Astrophysical Journal Supplement Series, 208:20 (54pp), 2013 October doi:10.1088/0067-0049/208/2/20
C
2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A.
NINE-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP)
OBSERVATIONS: FINAL MAPS AND RESULTS
C. L. Bennett
1
, D. Larson
1
, J. L. Weiland
1
, N. Jarosik
2
,G.Hinshaw
3
, N. Odegard
4
,K.M.Smith
5,6
,
R. S. Hill
4
,B.Gold
7
, M. Halpern
3
, E. Komatsu
8,9,10
, M. R. Nolta
11
, L. Page
2
, D. N. Spergel
6,9
, E. Wollack
12
,
J. Dunkley
13
,A.Kogut
12
,M.Limon
14
, S. S. Meyer
15
, G. S. Tucker
16
, and E. L. Wright
17
1
Department of Physics & Astronomy, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218-2686, USA; cbennett@jhu.edu
2
Department of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08544-0708, USA
3
Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
4
ADNET Systems, Inc., 7515 Mission Drive, Suite A100, Lanham, MD 20706, USA
5
Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
6
Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544-1001, USA
7
School of Physics & Astronomy, University of Minnesota, 116 Church Street S.E., Minneapolis, MN 55455, USA
8
Max-Planck-Institut f
¨
ur Astrophysik, Karl-Schwarzschild Str. 1, D-85741 Garching, Germany
9
Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU, WPI),
Todai Institutes for Advanced Study, University of Tokyo, Kashiwa 277-8583, Japan
10
Texas Cosmology Center and Department of Astronomy, University of Texas, Austin, 2511 Speedway, RLM 15.306, Austin, TX 78712, USA
11
Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, Toronto, ON M5S 3H8, Canada
12
Code 665, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA
13
Oxford Astrophysics, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK
14
Columbia Astrophysics Laboratory, 550 West 120th Street, Mail Code 5247, New York, NY 10027-6902, USA
15
Departments of Astrophysics and Physics, KICP and EFI, University of Chicago, Chicago, IL 60637, USA
16
Department of Physics, Brown University, 182 Hope Street, Providence, RI 02912-1843, USA
17
UCLA Physics & Astronomy, P.O. Box 951547, Los Angeles, CA 90095–1547, USA
Received 2012 December 19; accepted 2013 March 5; published 2013 September 20
ABSTRACT
We present the final nine-year maps and basic results from the Wilkinson Microwave Anisotropy Probe (WMAP)
mission. The full nine-year analysis of the time-ordered data provides updated characterizations and calibrations
of the experiment. We also provide new nine-year full sky temperature maps that were processed to reduce
the asymmetry of the effective beams. Temperature and polarization sky maps are examined to separate cosmic
microwave background (CMB) anisotropy from foreground emission, and both types of signals are analyzed in
detail. We provide new point source catalogs as well as new diffuse and point source foreground masks. An updated
template-removal process is used for cosmological analysis; new foreground fits are performed, and new foreground-
reduced CMB maps are presented. We now implement an optimal C
−1
weighting to compute the temperature angular
power spectrum. The WMAP mission has resulted in a highly constrained ΛCDM cosmological model with precise
and accurate parameters in agreement with a host of other cosmological measurements. When WMAP data are
combined with finer scale CMB, baryon acoustic oscillation, and Hubble constant measurements, we find that big
bang nucleosynthesis is well supported and there is no compelling evidence for a non-standard number of neutrino
species (N
eff
= 3.84 ± 0.40). The model fit also implies that the age of the universe is t
0
= 13.772 ± 0.059 Gyr,
and the fit Hubble constant is H
0
= 69.32 ± 0.80 km s
−1
Mpc
−1
. Inflation is also supported: the fluctuations
are adiabatic, with Gaussian random phases; the detection of a deviation of the scalar spectral index from unity,
reported earlier by the WMAP team, now has high statistical significance (n
s
= 0.9608 ±0.0080); and the universe
is close to flat/Euclidean (Ω
k
=−0.0027
+0.0039
−0.0038
). Overall, the WMAP mission has resulted in a reduction of the
cosmological parameter volume by a factor of 68,000 for the standard six-parameter ΛCDM model, based on
CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor
117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces
the cosmological parameter volume even further. With no significant anomalies and an adequate goodness of fit, the
inflationary flat ΛCDM model and its precise and accurate parameters rooted in WMAP data stands as the standard
model of cosmology.
Key words: cosmic background radiation – cosmology: observations – dark matter – early universe –
instrumentation: detectors – space vehicles – space vehicles: instruments – telescopes
Online-only material: color figures, machine-readable tables
1. INTRODUCTION
Since its discovery in 1965, the cosmic microwave back-
ground (CMB) has played a central role in cosmology. The
discovery of the CMB (Penzias & Wilson 1965) confirmed a
major prediction of the big bang theory and was difficult to
reconcile with the steady state theory. The precision measure-
ment of the CMB spectrum by NASA’s Cosmic Background
Explorer (COBE) mission (Mather et al. 1990, 1994) confirmed
the predicted CMB blackbody spectrum, which results from
thermal equilibrium between matter and radiation in the hot,
dense early universe. The COBE detection of CMB anisotropy
(Smoot et al. 1992; Bennett et al. 1992; Kogut et al. 1992; Wright
et al. 1992) established the amplitude of the primordial scalar
fluctuations and supported the case for the gravitational evolu-
tion of structure in the universe from primordial fluctuations.
1
The Astrophysical Journal Supplement Series, 208:20 (54pp), 2013 October Bennett et al.
While COBE mapped the full sky anisotropy on angular scales
>7
◦
, greater than the horizon size at decoupling, Wilkinson Mi-
crowave Anisotropy Probe (WMAP) mapped the full sky CMB
anisotropy on both superhorizon and subhorizon angular scales.
WMAP provided independent replication and confirmation of
the COBE maps on angular scales >7
◦
as well as the deter-
mination of precision cosmological parameters from fits to the
well-established physics of the observed sub-horizon acoustic
oscillations.
This paper together with its companion paper on cosmological
parameter determination (Hinshaw et al. 2013) mark the nine-
year and final official data release of the WMAP mission.
WMAP was designed to make full sky maps of the CMB in
five frequency bands straddling the spectral region where the
CMB-to-foreground ratio is near its maximum.
The overall WMAP mission design was described by Bennett
et al. (2003a). The optical design was described by Page et al.
(2003b) with the feeds and pre-flight beam patterns described by
Barnes et al. (2002). The radiometer design and characterization
was presented by Jarosik et al. (2003b).
The WMAP Science Team previously issued four major data
releases, each with an accompanying set of publications. The
first-year results included a presentation of the full sky maps
and basic results (Bennett et al. 2003b), on-orbit radiometer
characteristics (Jarosik et al. 2003a), beam profiles and win-
dow functions (Page et al. 2003a), Galactic emission contam-
ination in the far-sidelobes of the beams (Barnes et al. 2003),
a description of data processing and systematic measurement
errors (Hinshaw et al. 2003a), an assessment of foreground
emission (Bennett et al. 2003c), tests of CMB Gaussianity
(Komatsu et al. 2003), the angular power spectrum (Hinshaw
et al. 2003b), the temperature-polarization correlation (Kogut
et al. 2003), cosmological parameters (Spergel et al. 2003),
parameter estimation methodology Verde et al. (2003), impli-
cations for inflation (Peiris et al. 2003), and an interpretation
of the temperature–temperature and temperature–polarization
cross-power spectrum peaks (Page et al. 2003c).
The three-year WMAP results included full use of the po-
larization data and improvements to temperature data analysis.
The beam profile analysis, data processing changes, radiome-
ter characterization, and systematic error limits were presented
in Jarosik et al. (2007). An analysis of the temperature data
carried through to the angular power spectrum was described
by Hinshaw et al. (2007), and the corresponding polarization
analysis was presented by Page et al. (2007). An analysis of the
polarization of the foregrounds was presented by Kogut et al.
(2007). The cosmological implications of the three-year results
were summarized by Spergel et al. (2007).
The five-year WMAP results included updates on data pro-
cessing, sky maps, and the basic results (Hinshaw et al. 2009),
and updates on the beam maps and window functions (Hill et al.
2009). The five-year results also included improvements to char-
acterizing the Galactic foreground emission (Gold et al. 2009)
and the point source catalog Wright et al. (2009). The angular
power spectra (Nolta et al. 2009), likelihoods and parameter
estimates (Dunkley et al. 2009), a discussion of the cosmolog-
ical interpretation of these data (Komatsu et al. 2009), and a
Bayesian estimation of the CMB polarization maps (Dunkley
et al. 2009) completed the five-year results.
The seven-year WMAP results comprised sky maps, system-
atic errors, and basic results (Jarosik et al. 2011), observations
of planets and celestial calibration sources (Weiland et al. 2011),
Galactic foreground emission (Gold et al. 2011), angular power
spectra and cosmological parameters based only on WMAP data
(Larson et al. 2011), cosmological interpretations based on a
wider set of cosmological data (Komatsu et al. 2011),andadis-
cussion of the goodness of fit of the ΛCDM model and potential
anomalies (Bennett et al. 2011).
All of the WMAP data releases have been accompanied
by an up-to-date Explanatory Supplement, including this final
nine-year release (Greason et al. 2012). All WMAP data are
public along with a large number of associated data products;
they are made available by the Legacy Archive for Microwave
Background Data Analysis (LAMBDA).
18
Each WMAP release improved cosmological constraints
through three types of advances: (1) the addition of WMAP
data from extended observations, (2) improvements in the anal-
ysis of all of the WMAP data included in the release, including
more optimal analysis approaches and the use of additional sea-
sons of data to arrive at improved experiment models (e.g., by
trending), and (3) improvements in non-WMAP cosmological
measurements that are combined into the WMAP team’s com-
bined likelihood analysis.
This paper is organized as follows. The data process-
ing changes from previous analyses are described in Sec-
tion 2. Beam patterns and window functions are discussed in
Section 3. Temperature and polarization sky maps are presented
in Section 4. In Section 5 updated masks and an updated point
source catalog are presented in addition to several different ap-
proaches to diffuse foreground evaluation, which are compared.
Angular power spectra are given in Section 6. An analysis of
the model goodness of fit and a discussion of anomalies are
in Section 7. Cosmological implications are then presented in
Section 8. Conclusions are given in Section 9. The accompany-
ing paper (Hinshaw et al. 2013) presents an in-depth analysis of
cosmological parameter solutions from various combinations of
data and models and offers cosmological conclusions.
2. DATA PROCESSING: OVERVIEW AND UPDATES
In this section we summarize changes in the WMAP data
processing since the previous (seven-year) data release.
2.1. Time-ordered Data
2.1.1. Data Archive Definition
The full nine-year WMAP archive of nominal survey data
covers 00:00:00 UT 2001 August 10 (day number 222) to
00:00:00 UT 2010 August 10 (day number 222). Individual
year demarcations begin at 00:00:00 UT on day number 222 of
a year and end at 23:59:59 UT on day 221 of the following year.
In addition to processing improvements, the WMAP nine-year
release includes new data accumulated during mission years 8
and 9. Flight operations during those final two years included
five scheduled station-keeping maneuvers, a lunar shadow
passage, and special commanding procedures invoked within the
last mission year to accommodate a compromised battery and
transmitter. Overall, WMAP achieved a total mission observing
efficiency of roughly 98.4%. The bulk of data excluded from
science analysis use are dominated by time intervals that do not
exhibit sufficient thermal stability.
2.1.2. Battery-driven Thermal Effects
The WMAP solar arrays were exposed to constant sunlight
so the battery was trickle charged for almost a decade. This
18
http://lambda.gsfc.nasa.gov/
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The Astrophysical Journal Supplement Series, 208:20 (54pp), 2013 October Bennett et al.
activated an internal battery design imperfection and caused
battery voltage fluctuations in the final months of the mission
(Greason et al. 2012). The resulting thermal variations were
beyond what had been experienced earlier in the mission.
A detailed analysis of time-ordered data (TOD) with sky
signal subtracted showed no detectable dependence on thermal
variations associated with battery events, and thus preservation
of data was preferred to excision. Out of an abundance of
caution, time sequences that contained some of the more
egregious temperature excursions were flagged as suspect and
omitted from use in the nine-year data processing even though
there was no specific evidence of adverse effects.
2.1.3. Pointing
For each observation, sky pointings of individual WMAP
feed horns are computed using boresight vectors in spacecraft
body coordinates coupled with the spacecraft attitude solution
provided by on-board star trackers. After the first mission year,
it was discovered that the apparent attitude computed by the
trackers includes small errors induced by thermal flexure of the
tracker mounting structure, as described by Jarosik et al. (2007).
The amplitude of the flexure is time-dependent and driven by
spacecraft temperature gradients. The spacecraft temperature
responds both to solar heating and internal power dissipation,
and is monitored by thermistors mounted at different locations
on the spacecraft (Greason et al. 2012).
Telemetered spacecraft quaternions from the star trackers are
corrected for this thermal effect at the very beginning of ground
processing, when the raw science archive is created. Originally,
we adopted a simple linear model, assuming a fixed angular
rate of elevation change in units of arcsec per unit temperature
change. As the mission progressed and additional data was used
to improve the accumulated thermal profile history, the model
has evolved to include angular corrections both in elevation
(the dominant term) and azimuth. The nine-year quaternion
correction model updates the rate coefficients in both azimuth
and elevation, and uses readings from two separate thermistors
to characterize the spacecraft temperature gradients. A more
detailed description is provided by Greason et al. (2012). The
residual pointing error after applying of the correction algorithm
is computed using observations of Jupiter and Saturn. The upper
limit of the estimated error is 10
.
Beam boresight vectors have been updated based on the full
nine-year archive. The largest difference between the seven-
year and nine-year line-of-sight (LOS) vectors is 3
.Both
the calibrated and uncalibrated WMAP archive data products
include documentation of these LOS vectors.
2.1.4. Calibration
Calibration of TOD from each WMAP radiometer channel
requires the derivation of time-dependent gains (responsivity,
in units of counts mK
−1
) and baselines (in units of counts)
that are used to convert raw differential data into temperature
units. Algorithmic details and underlying concepts are set forth
in Hinshaw et al. (2007). Jarosik et al. (2011) outline the
calibration process as consisting of two general steps. The first
step determines baselines and preliminary gains on an hourly
or daily basis via an iterative process that combines a skymap
estimation with a calibration solution that updates with each
iteration. Baselines and gains are computed by fitting sky-
subtracted TOD to the dipole anisotropy induced by the motion
of the WMAP spacecraft with respect to the CMB rest frame.
The second calibration step determines absolute gain and fits
a parameterized gain model to the dipole gains derived in the
first step.
The form of the parameterized gain model is based on a
physical understanding of radiometer performance, and uses
telemetered measures of instrument temperatures and the radio
frequency (RF) biases. The model provides a smooth charac-
terization of the responsivity with time and allows higher time
resolution than provided by the dipole-fit gains. For the nine-
year analysis, we augment the gain model by adding a time-
dependent linear trend term, mΔt + c, to the parameterized form
presented in Jarosik et al. (2007). Here Δt is an elapsed mission
time in days, and m, c are additional fit parameters. Physically,
the linear trend can be thought of as a radiometer aging term.
Without the addition of this term, model fits to the nine-year
dipole gain measurements exhibited small systematic deviations
from zero-mean residuals for nine of the 40 WMAP channels.
The four Ka1 channels were most affected; the inclusion of the
gain model aging term prevents an induced total gain error of
about 0.1% in this band. Of the 40 WMAP radiometer channels,
W323 alone has shown poor convergence in the iterative pro-
cedure that determines dipole-fit gains. Upon investigation we
found that this problem is peculiar to the iterative algorithm and
not the data itself. The W323 calibration has not been substan-
tially affected in previous releases, but for the nine-year analysis
the diverging mode was identified and we disallowed it in the
gain model fit.
We continue to conservatively estimate an absolute calibra-
tion uncertainty of 0.2% (1σ ), based on end-to-end gain recov-
ery simulations. The overall change in calibration for the nine-
year processing relative to the seven-year release is −0.031%,
+0.048%, −0.005%, +0.041%, and +0.025% for K-, Ka-, Q-,
V-, and W-bands respectively; a positive change indicates that
features in the nine-year maps are slightly larger than those in the
equivalent seven-year maps (i.e., a slight decrease in nine-year
absolute gain compared to seven-year).
2.1.5. Transmission Imbalance Factors
The transmission efficiencies of sky signals through the
A-side and B-side optical systems into each WMAP radiometer
differ slightly from one another. This deviation from ideal
behavior is characterized in map-making and data analysis
through the use of time-independent transmission imbalance
factors. The method by which these factors are determined
from the WMAP data was described by Jarosik et al. (2007).
The determination improves with additional data. These factors
have been updated for the nine-year analysis and are presented
in Table 1. The nine-year values compare well against the
previously published seven-year values (Jarosik et al. 2011)
within the quoted uncertainties.
2.2. Map-making
2.2.1. Standard Map-making
The standard WMAP map-making procedure is unchanged
from the previous release and the resulting maps are used for
the core cosmological analyses. Progress has been made on
the algorithm for estimating the noise properties of the maps.
The Stokes I noise levels (σ
0
) are now more self-consistent
between maps at angular resolution r9 and r10
19
than they had
been previously. Another difference from previous analyses is
19
The map resolution levels refer to the HEALPix pixelization scheme
(Gorski et al. 2005) where r4, r5, r9, and r10 refer to N
side
values of 16, 32,
512, and 1024, respectively.
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The Astrophysical Journal Supplement Series, 208:20 (54pp), 2013 October Bennett et al.
Tab le 1
Nine-year Fractional Transmission Imbalance
Radiometer x
im
Uncertainty Radiometer x
im
Uncertainty
K11 −0.00067 0.00017 K12 0.00536 0.00014
Ka11 0.00353 0.00014 Ka12 0.00154 0.00008
Q11 −0.00013 0.00046 Q12 0.00414 0.00025
Q21 0.00756 0.00052 Q22 0.00986 0.00115
V11 0.00053 0.00020 V12 0.00250 0.00057
V21 0.00352 0.00033 V22 0.00245 0.00098
W11 0.01134 0.00199 W12 0.00173 0.00036
W21 0.01017 0.00216 W22 0.01142 0.00121
W31 −0.00122 0.00062 W32 0.00463 0.00041
W41 0.02311 0.00380
W42 0.02054 0.00202
Notes. The fractional transmission imbalance, x
im
, and its uncertainty is
determined from the nine-year observational data. The fractional transmission
imbalance is defined as x
im
= (
A
−
B
)/(
A
+
B
), where
A
and
B
are the input
transmission coefficients for the A- and B-side optics (Jarosik et al. 2003a). For
an ideal differential radiometer, x
im
= 0.
that this procedure now determines the noise in the polarized
maps from the Stokes Q and U year-to-year differences while
including a spurious (“S”) map term, and a mean monopole is
subtracted from each S map, as is done separately for Stokes
I in the temperature map analysis. A detailed discussion is in
Section 4.1.
Data are masked in the map-making process when one
feed observes bright foregrounds (e.g., in the Galactic plane)
while the corresponding differencing feed observes a far fainter
sky. This masking prevents the contamination of faint pixels.
Previous WMAP data analysis efforts used a single processing
mask, based on the K-band temperature maps, to define which
pixel-pairs to mask for all of the frequency bands. In the current
processing we have changed to masking based on the brightness
in each individual band.
2.2.2. Beam Pattern Determination
The standard maps are used to subtract the background from
Jupiter observations to create beam maps, as has been done in
previous processing. We correct three seasons of Jupiter maps
in the latter part of the mission for the proximity of Uranus and
Neptune to Jupiter. Two-dimensional profiles from the newly
updated beam map data are now also used as inputs for the new
beam-symmetrized map-making procedure, described below.
2.2.3. Beam-symmetrized Map-making
In addition to the standard map-making, a new map-making
procedure, described in Section 4.2, effectively deconvolves
the beam sidelobes to produce maps with the true sky signal
convolved by symmetrized beams. As a result of this new
procedure, the previously reported map power asymmetry,
which we speculated was due to the asymmetric beams and
not cosmology (Bennett et al. 2011) has indeed been mitigated
in the new beam-symmetrized maps.
In this paper we use the beam-symmetrized maps for diffuse
foreground analysis (Section 5.3), but not for estimating the
angular power spectrum and cosmological parameters. This
is because the deconvolution process introduces correlations
in the pixel noise on the beam scale and it is impractical to
track these correlations at the full pixel resolution. Diffuse
foreground analyses, on the other hand, used maps smoothed to
a1
◦
scale. Appendix B of Hinshaw et al. (2007) demonstrated
that the cosmological power spectrum, C
l
, is insensitive to beam
asymmetry at WMAP’s sensitivity level. (It is the 4-point bipolar
power spectrum, not the 2-point angular power spectrum, that is
sensitive to beam asymmetry.) Use of the beam-symmetrized
maps for high-l angular power spectrum estimation would
invoke the need for high resolution noise covariance matrices,
along with far greater computational and storage demands than
are now feasible. Given that dense r9 noise covariance matrices
are computationally undesirable and the cosmological power
spectrum is insensitive to beam asymmetry, we do not use beam-
symmetrized maps for cosmology.
3. BEAM MAPS AND WINDOW FUNCTIONS
The WMAP full beams are considered as a combination of
main beams and sidelobes. These are treated separately in the
data processing. The sidelobe beam patterns were determined
from early mission observations of the moon together with
pre-flight ground-based measurements, as described in Barnes
et al. (2003). Potential contamination from sidelobe pickup
was computed and removed from the calibrated TOD prior to
map-making (Hinshaw et al. 2009). In this section, we address
the main-beam response; treatment of the sidelobes remains
unchanged from the seven-year release.
WMAP beams are measured using observations of the planet
Jupiter that occur during the normal course of full-sky observing.
Two Jupiter observing seasons of ∼50 days each occur every
395–400 days. In the nine-year WMAP mission, a total of 17
seasons of Jupiter data were obtained. Time intervals for the four
observing seasons occurring during the last two mission years
are presented in Table 2; those for seasons 1–13 are presented
in Table 1 of Weiland et al. (2011).
The beams enter into CMB data analysis primarily through
the 10 beam transfer functions, b
l
, which give the beam response
in spherical harmonic space for each differencing assembly
(DA). Beam response on the sphere is measured in a coordinate
system fixed to the WMAP spacecraft (Barnes et al. 2003), and a
computation of several steps is required to generate b
l
. The nine-
year beam analysis follows the process described previously by
Hill et al. (2009) and Jarosik et al. (2011).
For a given DA, Jupiter is observed with only one feed at a
time, so initially the A- and B-side beams are mapped separately.
After correction for the static sky background, the data are
coadded in a planar grid surrounding each of the 20 A- and
B-side boresights. A physical optics code
20
is used to compute
beam models, which are optimized by χ
2
minimization using a
modified conjugate gradient algorithm. Two minor refinements
were added to this process for the nine-year analysis: first, a more
rigorous treatment of the removal of the Galactic signal was
adopted by including the common-mode loss imbalance term;
in practice this is a small effect since strong Galactic signals are
masked from use in the beam archive. Second, computation of
the interpolated beam model utilized an increase in secondary
mirror samplings from 200 × 200 to 235 × 235; this produced
a smoother far-field tail for the W 2 and W 3DAs.
Standard processing nominally rejects from analysis those
Jupiter observations whose sky positions lie within a 7
◦
radius
of other planets. Table 2 shows the seasonal range of projected
sky separations between Jupiter and planets that lie within the
exclusion radius for the last three observing seasons. Based
on projected proximity to Uranus or Neptune, application of
nominal exclusion criteria would have excised these three
20
DADRA: Rahmat-Sahmi et al. (1995, YRS Associates,
rahmat@ee.ucla.edu).
4
The Astrophysical Journal Supplement Series, 208:20 (54pp), 2013 October Bennett et al.
Tab le 2
WMAP Jupiter Observing Seasons (2008–2010)
Season
a
Begin End Nearby Planet
b
Projected Separation
c
% Excess
d
14 2008 Aug 21 2008 Oct 6 ··· ··· ···
15 2009 May 17 2009 Jul 3 Neptune 0.
◦
4–2.
◦
4 0.4–0.2
16 2009 Sep 26 2009 Nov 10 Neptune 3.
◦
8–6.
◦
8 0.08–0.0
17 2010 Jun 24 2010 Aug 10 Uranus 0.
◦
5–3.
◦
1 0.9–0.4
Notes.
a
An observing season is defined as a contiguous time interval during which an object is in the WMAP viewing
swath. Observing seasons 1–13 are listed in Weiland et al. (2011).
b
Jupiter sky coordinates are in proximity to those of the planet listed.
c
Seasonal range of projected separations between Jupiter’s position and that of the other planet.
d
Estimated excess integrated beam response, in %, that would have been contributed to the Jupiter beam by
contaminating planet, if no correction had been applied. Provided as a range; the first number is for K-band, the
last is for W-band; other frequencies are between these two values.
Jupiter seasons from use. To preserve the ability to characterize
the beam response during the latter part of the mission, we
chose instead to correct the last three seasons of Jupiter data
for excess contributions from Uranus and Neptune. Excess
response from these planets is computed and removed from each
Jupiter observation assuming that the response to Uranus and
Neptune may be modeled using a symmetrized beam template
with peak response inferred from Weiland et al. (2011). An
estimate of the magnitude of the correction is provided in the
last column of Table 2, provided as a percentage contribution in
excess of the uncontaminated integrated Jupiter beam response
for each season. Observations which occur when Jupiter’s sky
coordinates lie within the confines of a spatial “Galaxy mask”
are also excluded from use in the analysis (Weiland et al.
2011). During observing season 14, the Galactic latitude of
Jupiter is ∼−18
◦
, close enough to the Galactic plane that
some observations are rejected based on the masking criterion.
Masking is frequency dependent: roughly 30% of season 14 K-
band observations are excluded, decreasing to 17% for Ka, 13%
for Q and less than 0.1% for V- and W-bands.
For each DA, the Jupiter data for sides A and B are combined
with the best-fit models in a “hybrid” beam map, which is
used to construct the symmetrized radial beam profile, b(θ). A
Legendre transform gives b
l
. The beam hybridization procedure
is described in detail by Hill et al. (2009). Essentially, the
process edits the Jupiter TOD by replacing faint, noisy Jupiter
samples with noise-free predicted values taken from the two-
dimensional beam model. This process is controlled by one
parameter for each DA, the threshold gain, B
thresh
: all observed
beam samples with gain lower than B
thresh
are replaced with
their counterpart model values. This test is applied to the model
samples, rather than the observed ones, in order to avoid bias
from observational noise. B
thresh
is optimized statistically for
each DA using a Monte Carlo method, whereby uncertainty
belonging to the beam model is traded against the noise in the
observed data points. The figure of merit to be minimized is
the uncertainty of the resultant solid angle in the hybridized
beam. For this purpose, the error in the model is assumed to be
a 100% uncertainty in the overall scaling of the low-sensitivity
“tails,” which is the only portion of a beam model that is used
in the hybrid. For the nine-year data, B
thresh
is set 1 dB lower
than for the seven-year data; values are 2, 3, 5, 6, and 9 dBi for
K- through W-bands, respectively.
Hill et al. (2009) give the procedure for transforming the
hybrid beam profiles into beam transfer functions. This com-
putation also yields main-beam solid angles and estimates of
the temperature of the Jupiter disk. Beam-related quantities are
summarized in Table 3. The last three columns list quantities
that are valid for a point source with spectral index α =−0.1
(flux F
ν
∝ ν
α
), typical of sources in the WMAP point source cat-
alog. They were determined as described in Jarosik et al. (2011),
except a small correction for bandpass drift was included in the
calculation of effective frequency for K-, Ka-, Q-, and V-bands
as described in Appendix A.
The nine-year and seven-year b
l
are consistent with each
other, although the b
l
for W 4 is about 0.6% higher in the nine-
year analysis than in the seven-year analysis for l>100, a shift
that is at the edge of the error band.
The error bands for b
l
are computed using Monte Carlo
simulations of the beam map hybridization; details of the
simulations follow the description provided in Hill et al. (2009).
As Jupiter observations have accumulated over the WMAP
mission lifetime, the contribution of the model tails to the hybrid
beam has become less important. The nine-year hybrid beams
are data dominated: for each of the ten beams, less than 0.25% of
the integrated hybrid beam response is attributable to the model
tails.
4. MAP-MAKING
4.1. Standard Map Processing
4.1.1. Individual Band Processing Masks
The algorithm used to reconstruct sky maps from differential
data masks selected observations to minimize artifacts associ-
ated with regions of high foreground intensity. (Jarosik et al.
2011). Observations for which one of the telescope beams is in
a region of high foreground intensity gradients while the other
is in a low gradient region are only applied to the pixel in the
high foreground region as the map solutions are generated. This
“asymmetric” masking suppresses map reconstruction artifacts
in the low foreground emission regions used for CMB analysis.
These artifacts arise from small variations in the power sam-
pled by the telescope beams for different observations that fall
within the same map pixel. The variations result from a com-
bination of the finite pixel size and beam ellipticity that both
couple to spatial intensity gradients. A processing mask is used
to delineate the regions of high foreground intensity gradients.
Previous data releases used a common processing mask for all
frequency bands based on the K-band temperature maps, even
though the foreground intensities vary greatly by band. The cur-
rent release uses different masks for each frequency band and
therefore utilizes the data more efficiently.
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