A Constraint on Primordial
B
-modes from the First Flight of the
SPIDER
Balloon-borne
Telescope
P. A. R. Ade
1
, M. Amiri
2
, S. J. Benton
3
, A. S. Bergman
3
, R. Bihary
4
, J. J. Bock
5
,
6
, J. R. Bond
7
, J. A. Bonetti
6
, S. A. Bryan
8
,
H. C. Chiang
9
,
10
, C. R. Contaldi
11
, O. Doré
5
,
6
, A. J. Duivenvoorden
3
,
12
, H. K. Eriksen
13
, M. Farhang
7
,
14
,
15
,
J. P. Filippini
16
,
17
, A. A. Fraisse
3
, K. Freese
12
,
18
, M. Galloway
13
, A. E. Gambrel
19
, N. N. Gandilo
20
, K. Ganga
21
,
R. Gualtieri
22
, J. E. Gudmundsson
12
, M. Halpern
2
, J. Hartley
23
, M. Hassel
fi
eld
24
, G. Hilton
25
, W. Holmes
6
, V. V. Hristov
5
,
Z. Huang
7
, K. D. Irwin
26
,
27
, W. C. Jones
3
, A. Karakci
13
, C. L. Kuo
26
, Z. D. Kermish
3
, J. S.-Y. Leung
15
,
28
,S.Li
3
,
29
,
D. S. Y. Mak
11
, P. V. Mason
5
, K. Megerian
6
, L. Moncelsi
5
, T. A. Morford
5
, J. M. Nagy
30
,
31
, C. B. Netter
fi
eld
15
,
23
, M. Nolta
7
,
R. O
’
Brient
6
, B. Osherson
16
, I. L. Padilla
15
,
32
, B. Racine
13
, A. S. Rahlin
19
,
33
, C. Reintsema
25
, J. E. Ruhl
4
, M. C. Runyan
5
,
T. M. Ruud
13
, J. A. Shariff
7
, E. C. Shaw
16
, C. Shiu
3
, J. D. Soler
34
, X. Song
3
, A. Trangsrud
5
,
6
, C. Tucker
1
, R. S. Tucker
5
,
A. D. Turner
6
, J. F. van der List
3
, A. C. Weber
6
, I. K. Wehus
13
, S. Wen
4
, D. V. Wiebe
2
, and E. Y. Young
26
,
27
SPIDER
Collaboration
1
School of Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24 3AA, UK
2
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, BC V6T 1Z1, Canada
3
Department of Physics, Princeton University, Jadwin Hall, Princeton, NJ 08544, USA;
wcjones@princeton.edu
4
Physics Department, Case Western Reserve University, 10900 Euclid Ave, Rockefeller Building, Cleveland, OH 44106, USA
5
Division of Physics, Mathematics and Astronomy, California Institute of Technology, MS 367-17, 1200 E. California Boulevard, Pasadena, CA 91125, U
SA
6
Jet Propulsion Laboratory, Pasadena, CA 91109, USA
7
Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada
8
School of Electrical, Computer, and Energy Engineering, Arizona State University, 650 E Tyler Mall, Tempe, AZ 85281, USA
9
Department of Physics, McGill University, 3600 Rue University, Montreal, QC, H3A 2T8, Canada
10
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
11
Blackett Laboratory, Imperial College London, SW7 2AZ, London, UK
12
The Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, AlbaNova, SE-106 91 Stockholm, Sweden
13
Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway
14
Department of Physics, Shahid Beheshti University, 1983969411, Tehran, Iran
15
Department of Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, ON M5S 3H4, Canada
16
Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, IL 61801, USA
17
Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA
18
Department of Physics, University of Texas, 2515 Speedway, C1600, Austin, TX 78712, USA
19
Kavli Institute for Cosmological Physics, University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637, USA
20
Steward Observatory, 933 North Cherry Avenue, Tucson, AZ 85721, USA
21
Université de Paris, CNRS, Astroparticule et Cosmologie, F-75013 Paris, France
22
High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
23
Department of Physics, University of Toronto, 60 Saint George Street, Toronto, ON M5S 3H4, Canada
24
Department of Astronomy and Astrophysics, Pennsylvania State University, 520 Davey Laboratory, University Park, PA 16802, USA
25
National Institute of Standards and Technology, 325 Broadway Mailcode 817.03, Boulder, CO 80305, USA
26
Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA
27
SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
28
Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 Saint George Street, Toronto, ON M5S 3H4, Canada
29
Department of Mechanical and Aerospace Engineering, Princeton University, Engineering Quadrangle, Princeton, NJ 08544, USA
30
Department of Physics, Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63130, USA
31
McDonnell Center for the Space Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63130, USA
32
Department of Physics and Astronomy, Johns Hopkins University, 3701 San Martin Drive, Baltimore, MD 21218, USA
33
Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510-5011, USA
34
Max-Planck-Institute for Astronomy, Konigstuhl 17, D-69117, Heidelberg, Germany
Received 2021 April 6; revised 2021 August 5; accepted 2021 August 15; published 2022 March 14
Abstract
We present the
fi
rst linear polarization measurements from the 2015 long-duration balloon
fl
ight of
SPIDER
, which is an
experiment that is designed to map the polarization of the cosmic microwave background
(
CMB
)
on degree angular
scales. The results from these measurements include maps a
nd angular power spectra from observations of 4.8% of the
sky at 95 and 150 GHz, along with the results of internal co
nsistency tests on these data. While the polarized CMB
anisotropy from primordial density perturbations is the dominant signal in this region of sky, Galactic dust emission is
also detected with high signi
fi
cance. Galactic synchrotron emission is found to be negligible in the
SPIDER
bands. We
employ two independent foreground-removal techniques to
explore the sensitivity of the cosmological result to the
assumptions made by each. The primary method uses a dust template derived from
Planck
data to subtract the Galactic
dust signal. A second approach, whi
ch constitutes a joint analysis of
SPIDER
and
Planck
data in the harmonic domain,
assumes a modi
fi
ed-blackbody model for the spectral energy distribution of the dust with no constraint on its spatial
The Astrophysical Journal,
927:174
(
26pp
)
, 2022 March 10
https:
//
doi.org
/
10.3847
/
1538-4357
/
ac20df
© 2022. The American Astronomical Society. All rights reserved.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 4.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
1
morphology. Using a likelihood that joint
ly samples the template amplitude and
r
parameter space, we derive 95%
upper limits on the primordial ten
sor-to-scalar ratio from Feldman
–
Cousins and Bayesian constructions,
fi
nding
r
<
0.11 and
r
<
0.19, respectively. Roughly half the uncertainty in
r
derives from noise associated with the template
subtraction. New data at 280 GHz from
SPIDER
’
ssecond
fl
ight will complement the
Planck
polarization maps,
providing powerful measurements of the polarized Galactic dust emission.
Uni
fi
ed Astronomy Thesaurus concepts:
Cosmic microwave background radiation
(
322
)
;
Observational cosmology
(
1146
)
;
Cosmological parameters
(
339
)
;
Interstellar emissions
(
840
)
1. Introduction
In the standard cosmological model
(
Λ
CDM
)
, the universe
consists of a blend of radiation, baryonic matter, cold dark matter,
and a vacuum energy density consistent with a cosmological
constant. The observed structure in the universe originates from
primordial
fl
uctuations of matter and energy that grow through
gravitational instability. These perturbations evolve within a
spacetime geometry that is spatially
fl
at on the largest observed
scales. This simple paradigm has proven to be in remarkable
agreement with the overwhelming majority of all observational
tests
(
Peebles
2012
;
Planck
Collaboration et al.
2020a
,
2020b
)
.
Observational data place stringent constraints on the proper-
ties of these primordial density
fl
uctuations: they must be
predominantly adiabatic in nature, Gaussian-distributed, follow
a nearly
—
but not quite
—
scale-invariant spectrum, and encode
correlations on scales larger than the horizon during recombi-
nation. Mechanisms to generate such
fl
uctuations have been
proposed within the context of in
fl
ationary, bouncing, and
cyclic models
(
Guth & Pi
1982
; Hawking
1982
; Mukhanov &
Chibisov
1982
; Starobinsky
1982
; Bardeen et al.
1983
; Ijjas &
Steinhardt
2018
,
2019
; Tanabashi et al.
2018
; Shandera et al.
2019
; Cook et al.
2020
)
.
In addition to the well-studied scalar perturbations, some
early-universe models
—
particularly in
fl
ationary models
—
pre-
dict a spectrum of tensor perturbations, or primordial gravita-
tional waves. Their amplitude is characterized by the
dimensionless tensor-to-scalar ratio,
r
.
35
The
Planck
collabora-
tion combines precision measurements of the matter power
spectrum and the largest-scale cosmic microwave background
(
CMB
)
intensity
fl
uctuations to constrain
r
to be less than
r
<
0.10
(
Planck
Collaboration et al.
2020c
)
.
36
Local quadrupole anisotropies sourced by tensor
fl
uctuations
can also imprint a unique
“
B
-mode
”
(
curl
)
component to the
polarization of the CMB at degree angular scales
(
Seljak &
Zaldarriaga
1997
; Kamionkowski & Jaffe
2001
)
. Though
challenging to measure, this signa
ture is relatively free of sample
variance from the brighter scalar modes and thus allows
observational access to much smaller values of
r
. The detection
of the signature of tensor
fl
uctuations would bring remarkable
new insights into early-universe physics. This scienti
fi
cpotential
has motivated an ambitious observational effort to search for the
signature of primordial gravitatio
nal waves in the polarization of
the CMB
(
Abazajian et al.
2016
; Kamionkowski & Kovetz
2016
)
.
The
Planck
polarization data, which span more than half of the
full sky, constrain
r
<
0.158 using limits on the
B
-mode
contribution alone
(
Tristram et al.
2021
)
.Using
BB
limits derived
from observations of less than 1% of the full sky, the Keck team
reports
r
<
0.072
(
BICEP2
/
Keck Array Collaboration
2018
)
.
Planck
measurements of the CMB intensity, the
E
-mode
polarization, and lensing over more than half the full sky,
together with the Keck
BB
limits, improve the constraint to
r
<
0.056
(
Planck
Collaboration et al.
2020c
)
. In Tristram et al.
(
2021
)
, this same constraint is obtained using only
Planck
temperature and polarization data. Combining the
B
-mode results
from the Keck experiment with this re-analysis of the
Planck
polarization data, the same team reports a somewhat tighter
constraint,
r
<
0.044
(
Tristram et al.
2021
)
.
As anticipated even prior to the
Planck
results, any
cosmological
B
-mode signal is subdominant to the diffuse
polarized emission from our Galaxy along any line of sight
(
Fraisse et al.
2013
)
. Current CMB observations must thus
contend with modeling uncertainties associated with diffuse
Galactic emission. To date, the
Planck
polarization data provide
the most accurate estimate of polarized Galactic emission across
the full sky
(
Planck
Collaboration et al.
2020d
)
.
In this paper, we report results from the
fi
rst
fl
ight of
SPIDER
,
which is a balloon-borne instrument that is designed to measure
the polarization of the CMB on degree angular scales. This paper
is organized as follows. After a brief description of the
SPIDER
instrument in Section
2
and observation strategy in Section
3
,
we discuss the low-level data processing leading up to maps of
the sky in Section
4
. Section
5
presents two complementary
angular power spectrum estimators, while Section
6
discusses the
consistency tests performed with each of these estimators,
and Section
7
addresses sources of systematic error. Results
from several distinct methods of component separation are
presented in Section
8
, while Section
9
provides constraints on
cosmological parameters for each method. The main conclusions
and
SPIDER
’
s future prospects are summarized in Section
10
.
2. The
SPIDER
Instrument
The
SPIDER
payload consists of six monochromatic refract-
ing telescopes that are housed within a single liquid helium
cryostat, which is supported and pointed by a lightweight
carbon
fi
ber gondola. Here we provide a brief overview of the
payload design, a more detailed description can be found in
Runyan et al.
(
2010
)
, Filippini et al.
(
2010
)
, Rahlin et al.
(
2014
)
, and Gualtieri et al.
(
2018
)
.
2.1. Receivers
Each
SPIDER
receiver is an axisymmetric two-lens cryogenic
refractor with a 270 mm cold stop, which is designed to
minimize polarized systematics. In each receiver, two high-
density polyethylene lenses cooled to 4 K focus light onto a
300 mK focal plane. The blackened cold stop and internal
baf
fl
es surrounding the optics are cooled to 1.6 K to reduce
stray photon loading on the detectors. A sapphire half-wave
plate
(
HWP
)
mounted to a 4 K
fl
ange skyward of each
receiver
’
s stop is rotated to a new
fi
xed orientation angle twice
35
Throughout we specify
r
at a scale of
k
0
=
0.05 Mpc
−
1
, and further assume
a scale-invariant tensor spectrum
(
n
t
=
0
)
. The six
Λ
CDM parameters are
fi
xed
to those of
Planck
Collaboration et al.
(
2020b
)
.
36
This constraint relaxes to
r
<
0.16 when excluding the low-
ℓ
data
(
2
ℓ
29
)
that include the temperature de
fi
cit.
2
The Astrophysical Journal,
927:174
(
26pp
)
, 2022 March 10
SPIDER
Collaboration
daily to provide polarization modulation
(
Bryan et al.
2010a
,
2016
)
. Each receiver views the sky through a series of
re
fl
ective metal-mesh
(
Ade et al.
2006
)
and lossy nylon
fi
lters
to reduce infrared loading on the cryogenic system and
detectors, as well as a thin
(
∼
3mm
)
ultra-high-molecular-
weight polyethylene
(
UHMWPE
)
vacuum window. An appro-
priate single-layer anti-re
fl
ection coating, which is matched to
the receiver
’
s band
(
95 or 150 GHz
)
, is attached to each side of
the HWPs, lenses, vacuum windows, and relevant
fi
lters.
Each telescope focuses radiation onto four wafers
(
“
tiles
”
)
of
antenna-coupled transition-edge sensors
(
TESs
)
, which were
fabricated at JPL
(
Ade et al.
2015
)
. Each wafer is patterned with
an array of polarimeter pixels, consisting of two inter-penetrating
arrays of slot antennas
(
one for each perpendicular polarization
mode
)
. This arrangement provides for an instantaneous
measurement of total intensity and one of two linear polarization
components. A complete measurement of partial linear polariza-
tion
—
Stokes
I
,
Q
and
U
parameters
—
is obtained for each pixel
through rotations of the HWP and the sky, which modulate the
polarization angle
(
Jones et al.
2007
)
. A microstrip feed network
coherently couples optical power from these synthesized
antennas through a band-de
fi
ning lumped-element
fi
lter before
dissipating the power incoherently on a thermally isolated island.
Each island supports two TESs with different critical tempera-
tures,
T
c
, wired in series: a Ti sensor
(
T
c
∼
500 mK
)
for science
observations and an Al sensor
(
T
c
∼
1.3 K
)
for laboratory testing.
The 512
(
288
)
TESs of each 150 GHz
(
95 GHz
)
focal plane are
read out using a time-division SQUID multiplexing system
(
de
Korte et al.
2003
; Battistelli et al.
2008
; Stiehl et al.
2011
)
.The
TESs and SQUIDs are housed within extensive magnetic
shielding
(
Runyan et al.
2010
)
.
Table
1
summarizes the properties of all of the detectors used
in the analysis presented in this paper.
37
This
fl
ight of
SPIDER
deployed a total of 2400 TESs. The channel counts in Table
1
account for intentionally dark
(
non-optical
)
TES channels,
losses due to detector and readout performance, and the
conservative channel cuts used in the present analysis. Notably,
one of the three 150 GHz receivers was excluded late in the
analysis due to a null test failure
(
Section
6.1.3
)
, but should be
recoverable with future work. Across the remaining
fi
ve
receivers,
∼
80% of TESs are used in this analysis.
2.2. Cryogenics
SPIDER
’
s cryogenic system
(
Gudmundsson et al.
2015
)
,
which is the largest yet deployed on a long-duration balloon
fl
ight, consists of two liquid helium reservoirs: a 1284 l main
tank and a 16 l super
fl
uid tank. The main tank is maintained at
a pressure of roughly 1 bar during the
fl
ight, providing cooling
power at
∼
4 K for the receiver optics and the
3
He sorption
coolers. The boil-off from the main tank
fl
ows through heat
exchangers on each of two vapor-cooled shields, which
intercept the radiative and conductive parasitic loads on the
cryogenic system and cool the infrared
fi
lter stack. The
super
fl
uid system provides cooling power at 1.6 K to each
telescope
’
s
3
He sorption cooler and internal optical baf
fl
es. The
super
fl
uid tank
fi
lls continuously from the main tank through a
capillary assembly, and is maintained at the ambient pressure of
the altitude at
fl
oat
(
about 6 mbar
)
. The super
fl
uid system is
pumped down on the ground, and maintained at low pressure
during launch and ascent with a small diaphragm pump on the
gondola. The focal planes themselves are cooled to
∼
300 mK
by a dedicated
3
He sorption cooler within each telescope.
2.3. Gondola and Pointing System
The cryostat is supported within a lightweight carbon
fi
ber
gondola
(
Soler et al.
2014
)
. A reaction-wheel and motorized
pivot scan the gondola in azimuth, while a linear drive steps the
cryostat in elevation
(
Shariff et al.
2014
)
. Absolute referencing
of the payload orientation is provided by a suite of three star
cameras: one attached to the cryostat and oriented along the
boresight axis, the other two mounted to the outer gondola
frame on a rotating table that allows them to track the sky
during azimuthal scans. Information from the star cameras is
combined with that from GPS receivers, Sun sensors, encoders,
and gyroscopes to enable in-
fl
ight pointing and post-
fl
ight
pointing reconstruction
(
Gandilo et al.
2014
)
. Control and
monitoring of the pointing and cryogenic systems is performed
by a pair of redundant
fl
ight computers interfaced with the
custom BLASTbus electronics
(
Benton et al.
2014
)
. A Sun
shield protects the instrument and optics during the 24 hr
Antarctic summer daylight. Continuous electric power is
provided by a 2 kW solar panel system, while various antenna
arrays provide commanding, telemetry, and location informa-
tion during the
fl
ight.
3. Science Observations
SPIDER
was launched on 2015 January 1, from the NASA
/
NSF Long-Duration Balloon
(
LDB
)
facility near McMurdo
Station, Antarctica. All of the payload systems performed well
throughout the
fl
ight, with the exception of a differential GPS
unit failure that had no signi
fi
cant impact on
fl
ight operations
or pointing reconstruction.
SPIDER
’
s
fl
ight lasted 16.5 days at
an average altitude of 35 km. The
fl
ight was terminated when
cryogens were exhausted and the circumpolar wind system
began to fail. The payload touched down in a remote region of
Table 1
Summary of Instrumental Parameters for the Data Used in this Analysis
Center
Width
FWHM
#
Det.
NET
tot
Data Used
Map Depth
Band
(
GHz
)(
%
)(
arcmin
)
Used
(
m
Ks
)(
days
)(
μ
K arcmin
)
95 GHz
94.7
26.4
41.4
675
7.1
6.5
22.5
150 GHz
151.0
25.7
28.8
815
6.0
5.6
20.4
Note.
Band center and width are averages of per-detector measurements. Beam full-width at half-maximum is derived from a combined
fi
t to all detectors in a given
band. Noise-equivalent temperature is the quadrature average over all detectors used. Data used is the NET-weighted average of un
fl
agged data in each channel, and is
restricted to samples inside our sky mask
(
Section
5
)
with hits-weighted
f
sky
of 3.9%. Approximate map depths do not account for effects of
fi
ltering on signal-to-
noise. All sensitivities are reported in CMB temperature units.
37
In this paper, all of the temperatures used in reference to signal or noise are
in units of
Δ
T
CMB
, the equivalent CMB
fl
uctuation, in which the data are
natively calibrated.
3
The Astrophysical Journal,
927:174
(
26pp
)
, 2022 March 10
SPIDER
Collaboration
Ellsworth Land of West Antarctica. Data drives and key
fl
ight
hardware were recovered in February by personnel from the
British Antarctic Survey, while a second team recovered the
remainder of the instrument in November. The payload optics
and focal planes have subsequently been refurbished and
upgraded in preparation for a second
fl
ight
(
Shaw et al.
2020
)
.
During an Antarctic LDB
fl
ight, the Sun remains above the
horizon at all times. The accessible region of sky is therefore
constrained by the need for the
fi
eld center to remain roughly
anti-solar and, for CMB observations, to avoid the Galactic
plane. This favors a launch as early in the season as possible
because the anti-solar direction progresses to lower Galactic
latitude over time.
SPIDER
’
s launch opportunity came relatively
late in the Antarctic LDB season, which pushed the
fi
eld center
toward the lower range of possible
fi
eld centers.
SPIDER
scanned in azimuth throughout the
fl
ight, with a
sinusoidal speed pro
fi
le peaking as high as 4
°
s
−
1
. The
sinusoidal speed pro
fi
le allowed smooth torque variations in
the pivot and reaction-wheel motors, without sustaining peak
torque for long. For the
fi
rst two-thirds of the
fl
ight,
SPIDER
scanned a
∼
75
°
azimuthal range that was limited on either side
by the Galaxy and the Sun. To obtain more uniform coverage,
the azimuthal range was reduced for the
fi
nal third of the
fl
ight
to cover the middle half of this range. Scan turnarounds are
separated by as long as 36 s, shortening to as little as 22 s for
the narrower region later in the
fl
ight. Small steps in elevation
were made at every third scan turnaround, covering the full
22
°
–
50
°
range upwards and downwards once per day. A brief
scan over the bright Galactic source RCW38 was used to
con
fi
rm pointing in
fl
ight.
The in-
fl
ight pointing solution using only coarse sensors has
an error of 22
′
rms, which is less than a
SPIDER
beamwidth and
adequate for scan control. The post-
fl
ight pointing reconstruc-
tion integrates gyroscopes between star camera solutions, and
matches raw solutions of the boresight star camera to within
0
9 rms. The relative pointing between the boresight camera
and microwave detectors is calibrated with cross-correlation
and deprojection methods, which will be described in
Section
4.2.4
.
The half-wave plate is stepped in angle twice per sidereal
day
(
Bryan et al.
2010a
,
2016
)
. The nominal HWP angles are
chosen to rotate each receiver between Stokes
Q
and
U
sensitivity every half day, and to cover each rising and setting
raster in
Q
and
U
with every detector on alternate days. A total
of eight discrete HWP angles, separated by 22
°
.5 over a range
of 180
°
are cycled through an eight-day pattern to reduce
sensitivity to beam and HWP systematics
(
Bryan et al.
2010b
;
Nagy et al.
2017
)
. The HWP angles are measured with a
combination of absolute and relative encoders, which provides
an accuracy of 0
°
.1.
SPIDER
’
s
fl
ight control system implements a number of
autonomous watchdog routines that monitor the quality of data
returned from the detectors, perform limited corrective actions,
and package compressed summary data packets for return to
the ground system. Of particular note are the detector
monitoring systems, which are described more fully in Rahlin
(
2016
)
. These use regular measurements of the TES differential
resistance
(
dV
/
dI
)
from small 2 Hz square waves imposed on
the TES bias lines, which are carried out for 2 s intervals every
fi
fth scan turnaround. These values are used to automatically
identify channels that are superconducting or normal, have
accumulated a large DC offset, or have drifted signi
fi
cantly in
TES resistance. When the count of such anomalous channels
grows large enough, the system initiates a reset of the TES
feedback loop or an adjustment of the TES bias. Due to an
unforeseen software race condition, this monitoring system did
not function for most receivers during the latter portion of the
fl
ight; however, in practice this had little meaningful effect,
given
SPIDER
’
s excellent detector performance stability. Using
both electrical and optical measurements of the temporal gain
variations, the excursions on all timescales are found to be less
than 5%, and are not strongly correlated
(
Section
4.2.3
)
.
4. Data Processing and Map Making
In this section, we will present an abbreviated discussion of
SPIDER
’
s low-level processing from raw data to calibrated
maps and simulations of the sky. More details can be found in
Rahlin
(
2016
)
, Gambrel
(
2018
)
, Young
(
2018
)
.
SPIDER
’
s raw data consist of 2.1 TB of time-ordered
samples. Bolometer and pointing data were recorded at
119 Hz, while a variety of gondola and cryogenic performance
parameters were recorded at reduced sample rates. All data
were recorded in-
fl
ight across multiple redundant drives. Data
from the six bolometer arrays and the
fl
ight system were
synchronized using data-valid clock signals and sequential
counter values distributed from a single crystal clock system.
For a number of data processing operations, samples are
grouped into contiguous
“
chunks
”
that are approximately
10 minutes in length. These evenly partition the periods between
HWP angle steps and divide only at turnarounds of the azimuthal
scan. Chunk length is a compromise between containing a
suf
fi
cient number of samples for analysis tasks such as
estimating low-frequency noise, while remaining short enough
to ensure that neighboring chunks have similar observing
conditions and sky signal. Ten minutes is long compared to
the azimuthal scan period, but short relative to the timescale for
changes in telescope elevation or cryogenic temperatures.
Similar chunk partitioning is also used to construct data subsets
for power spectrum estimation
(
Section
5
)
.
4.1. Timestream Flagging, Cleaning, and Filtering
In addition to the expected Gaussian uncorrelated noise, we
observe two broad classes of correlated noise in the
SPIDER
timestream data: intermittent and quasi-stationary.
Intermittent
noise encompasses noise sources that appear to be discretely on
or off at any given time. The primary sources of intermittent
noise are the telemetry transmitters on board the payload. In
particular, the three Iridium transmitters are active for about
two seconds at a time, operating asynchronously with periods
between 1 and 15 minutes. Other sources of intermittent noise
include cosmic ray interactions in the detectors
—
which are
discussed further in Osherson et al.
(
2020
)
—
and various
glitches or step discontinuities due to the multiplexing readout.
Quasi-stationary
noise consists of non-astrophysical signals
that are partially correlated across the
fi
eld of view and change
very little over multiple azimuthal scans. These have a peak-to-
peak amplitude that is typically less than 3 mK
CMB
, and vary
slowly over time. It is believed that the majority of this
contamination is sourced by sidelobe pickup, primarily from
the Earth
’
s limb; its variation with elevation is not consistent
with signal from any residual atmospheric emission. Addition-
ally, RF-coupled interference was observed in some of the
detector channels. One consequence of this is that a subset of
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detectors evidence a signal that is well-correlated with the
orientation of the reaction wheel, with couplings that vary in
strength both between warm readout electronics racks, and
within them channel by channel. During both pre-launch
testing and the
fl
ight, one of the three readouts serving the
150 GHz focal planes proved to be substantially more
susceptible to these effects than the others. As further discussed
in Section
6.1.3
, the data from this focal plane contribute to null
test failures and are not included in any other part of this
analysis.
Intermittent noise is mitigated by
fl
agging the affected
detector samples. Such samples are tagged, replaced with
constrained noise realizations, and excluded from map-making.
Step discontinuities arise intermittently in
SPIDER
’
s data, due
primarily to transmitter interference and large cosmic ray
interactions. In addition to
fl
agging the discontinuity itself, we
adjust the data to eliminate the discontinuity using a linear
fi
tto
data before and after the event. This procedure accounts
empirically for cross-talk of the discontinuity among channels.
This
“
stitching
”
operation improves low-frequency noise
signi
fi
cantly, and simulations show that it has negligible effect
on signal response.
Quasi-stationary noise is mitigated by time-domain
fi
ltering
of this
fl
agged data set, conducted at the full detector sample
rate. To reduce noise correlated with the reaction wheel,
detector timestreams are binned according to the angle of the
reaction wheel to form templates that are then subtracted. The
impact of this operation was checked using the full-
fl
ight time-
domain simulations described in Section
4.4
, and found to have
negligible effect on the astrophysical signal. This
fi
t is thus
performed only on data timestreams and is not performed on
the large simulation ensembles. To reduce low-frequency noise
and pickup more broadly, the data are
fi
ltered between each
scan turnaround by subtracting a
fi
fth-order polynomial
fi
tto
each detector
’
s data as a function of azimuth.
The effects of scanning,
fi
ltering, and
fl
agging are deter-
mined by applying the entire analysis pipeline to an ensemble
of time-domain signal simulations. The transfer functions due
to
fi
ltering and beams, which derive from these simulations, are
shown in Figure
1
and are discussed further in Section
5
. The
primary effect of
fi
ltering is a suppression of power on large
angular scales. Because the typical scan speed and direction
vary across the sky, the effect of
fi
ltering is both anisotropic
and inhomogeneous, with greater suppression on the edges of
the
fi
eld of view. This latter effect is not visibly evident in the
temperature or polarization maps
(
Figures
2
and
3
)
, and the net
impact of the
fi
ltering has been shown to be adequately
modeled with a simple multipole domain transfer function.
Detectors with consistently high noise after cleaning are
completely cut from the analysis. A small fraction
(
=
1%
)
of
entire azimuth scans are also
fl
agged for having too much
residual noise after cleaning. In total, when weighting data by
their estimated noise level, complete detector cuts remove 5%
of the data, and 28% of samples on remaining detectors are
fl
agged, including periods of cryogenic recycling. All detectors
in the 150 GHz receiver most strongly affected by RF-coupled
interference are discarded, resulting in a further reduction of
22% at that frequency
(
10% overall
)
. Finally, 27% of un
fl
agged
samples lie outside the sky mask of the present analysis
(
Section
5
)
.
4.2. Detector Characterization
Both pre-launch and in-
fl
ight data are used to characterize
instrumental parameters needed to construct accurate temper-
ature and polarization maps. The pre-launch data include
spectroscopic and polarimetric measurements. In-
fl
ight data are
used for the absolute calibration, to monitor gain
fl
uctuations,
and to re
fi
ne pre-launch estimates of beam response and
pointing offsets.
4.2.1. Polarization Angle
The individual detector polarization angles were measured
prior to launch with a rotating polarized thermal source in the
near-
fi
eld of each receiver, as described in Nagy
(
2017
)
. The
uncertainty on each measured detector angle is approximately
0
°
.5, which is better than
SPIDER
’
s target of 1
°
(
Fraisse et al.
2013
)
. These measured angles are used directly by the map
maker, with no correction applied based on the
fl
ight data.
4.2.2. Frequency Response
The frequency response of each detector was measured prior
to launch with a custom high-throughput Fourier Transform
Spectrometer, which was mounted on top of the cryostat. Since
the hot thermal source did not illuminate the full telescope solid
angle, an actuated mirror steered the output over the full
fi
eld of
view. In total, 95% of all of the detectors used in the science
analysis were measured with band center and bandwidth
accurate to 1 GHz. Measurements of the band centers and
widths at different HWP angles and output mirror positions are
consistent within errors. Further details are provided in
Gambrel
(
2018
)
.
These per-detector measurements are not used directly in
making maps, which could result in leakage of spectrally
mismatched temperature signals into polarization. Instead, a
null test is constructed by splitting detectors with high and low
band centers
(
Section
6.1
)
. Since no difference is detected, we
conclude that the
SPIDER
data, including mitigation from
HWP and sky rotation, have negligible leakage from bandpass
mismatch.
Figure 1.
SPIDER
’
s
fi
lter transfer function
(
F
ℓ
)
, beam window function
(
B
ℓ
2
)
,
and total transfer function for 95 and 150 GHz. Quantities shown are the
average of the
EE
and
BB
transfer functions, which are similar but are not
assumed to be identical. In this work, signal estimation is achieved using a
simple binning of the data, which necessitates the
fi
ltering applied here. This
simple approach is driven by the desire to perform relatively ef
fi
cient analysis
of the signal and null tests in the time domain, but is unrelated to the
atmosphere and does not represent a limitation of the stratospheric balloon
platform.
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4.2.3. Calibration and Beam
SPIDER
’
s absolute calibration is derived by cross-calibrating
degree-scale power with
Planck
temperature anisotropy data at
100 and 143 GHz.
38
This procedure
fi
nds the absolute
calibration factor and parameterized beam model that mini-
mizes the difference with the
Planck
temperature spectra at a
per-detector level in the range 100
<
ℓ
<
275
(
100
<
ℓ
<
375
)
for the 95
(
150
)
GHz frequency band. The absolute calibration
is obtained by
fi
nding the scalar,
c
, that minimizes
()
åå
º-
==
Rc
C
C
b
b
1,
1
ℓℓ
ℓ
ℓ
ℓℓ
ℓ
ℓ
TT
ℓ
TT
ℓ
ℓ
,ref
Planck
SPIDER
1
2
1
2
where
ℓ
1
=
100 and
ℓ
2
=
275
(
375
)
for the 95
(
150
)
GHz
frequency band. We use
C
ℓ
TT
,ref
to represent a temperature power
spectrum calculated using maps obtained from re-scanning the
Planck
half-mission reference maps, while
C
ℓ
TT
is calculated
from single-detector maps cross-correlated with a
Planck
half-
mission map. The beam transfer functions,
b
ℓ
Planc
k
and
b
ℓ
SPIDER
,
Figure 2.
Left-hand panel: The total intensity map as observed by the
SPIDER
150 GHz receivers. No additional
fi
ltering is applied to the maps beyond that in the
timestream processing. The black outline indicates the sky region used to compute power spectra, though the additional point-source mask is not show
n. Middle panel:
The
Planck
143 GHz map as re-observed using the
SPIDER
scan strategy and
fi
ltering, indicating strong agreement in the temperature signal. Right-hand panel: The
raw
Planck
143 GHz map, shown to illustrate the impact of
SPIDER
’
s scan strategy and
fi
ltering, which suppresses power at large angular scales.
Figure 3.
Q
and
U
polarization maps as observed by
SPIDER
’
s 95 and 150 GHz receivers. The maps have been smoothed with a 10
′
Gaussian for clarity. The
temperature-to-polarization leakage from the map maker is subtracted
(
Section
4.4
)
, although this effect is not visible by eye. The dominant
E
-mode pattern of the
cosmological signature is evident in the maps, although it is diluted by the Galactic signal. The white outline indicates the sky region used to comput
e power spectra,
though the additional point-source mask is not shown.
38
Throughout this paper, we use release 3.01 of the
Planck
HFI maps
(
Planck
Collaboration et al.
2020e
)
.
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quantify the relative sensitivity the
Planck
and
SPIDER
spatial
response as a function of multipole.
We use a simple Gaussian beam model,
b
ℓ
SPIDER
, to extend
this calibration to other angular scales included in our analysis;
note that this extrapolation is small, and primarily to larger
angular scales. Each
SPIDER
telescope is
fi
tted with a single
common beam model, which is then used to determine an
independent calibration factor for each individual detector.
Various consistency tests show that our analysis is not
sensitive to a more physically motivated beam model because
signi
fi
cant deviations from a simple Gaussian are only evident
below multipoles used in constructing bandpowers. By using
beam models informed by physical optics simulations, we have
quanti
fi
ed the potential bias in our absolute calibration on the
largest angular scales caused by the Gaussian beam model
assumption. At most, this results in a 5% bias in the beam
transfer function in the lowest bin
(
33
ℓ
57
)
, which has a
negligible impact on the results. The
“
Inner
/
Outer Focal Plane
Radius
”
null test
(
Section
6.1
)
shows no detectable difference
between the detectors expected to be the best and worst
matches to our beam model.
We further explore the possibility of time-varying detector
calibrations in several ways. We use our regular TES resistance
measurements
(
Section
3
)
to generate a rough proxy for small
changes in the TES bias state, and hence responsivity. When
TES monitoring is not available late in the
fl
ight, we use the
average level of the TES current to calibrate a similar proxy.
We
fi
nd that these estimates are consistent with one another.
Additionally, we
fi
nd that gain excursions on all timescales are
less than 5%, and are not strongly correlated. While we correct
our timestreams for an interpolated version of our TES-
monitoring gain, simulations and null tests show that this has
negligible impact on our analysis
(
see Figure
4
)
.
Time domain simulations are used to quantify errors in the
absolute calibration and effective beamwidth on both per-
detector and full focal plane bases. Statistical error in the
determination of those parameters is caused by noise in the
SPIDER
and
Planck
data, both of which are incorporated in our
simulations with appropriate noise models. At the telescope
level, statistical error is relatively small because of the data
’
shigh
signal-to-noise ratio. For example, the fractional error in the per-
telescope beam transfer function,
b
ℓ
, at degree angular scales, is
approximately 0.1%. The likelihood analysis described in
Section
9
incorporates a model of the statistical beam error.
Some potential systematic effects are also investigated and found
to be subdominant at our sensitivity level
(
Section
7
)
.
4.2.4. Pointing Offset
Each detector
’
s pointing relative to the boresight star camera
solution, averaged over the full
fl
ight, is initially characterized by
maximizing the cross-correlation between single-detector
SPIDER
temperature maps and
Planck
maps. To reduce error, a model for
each detector tile
—
allowing free translation, rotation, and plate
scale
—
is
fi
tted to the individual detector offsets.
These initial pointing offsets are re
fi
ned using a time-domain
“
deprojection
”
technique based upon Bicep2 Collaboration
(
2015
)
. The deprojection method involves
fi
tting for perturba-
tions in leading-order beam systematics
—
calibration, pointing
offset, width, and ellipticity
—
using time-domain templates
generated from
Planck
temperature maps and their derivatives.
Unlike the BICEP2 implementation, we
fi
t for perturbations not
between paired detectors but between each detector
’
s data and
a simulation thereof, which is generated by re-observing
Planck
maps using the Gaussian beam model and initial pointing
estimates from cross-correlation. The per-detector pointing
offsets measured this way are consistent with the cross-
correlation results but have greater precision. In addition to
measuring the average pointing offset of each detector over the
full
fl
ight, the average offset of all detectors in each 10-minute
chunk is used to measure and correct a slow thermal
/
mechanical drift over the course of the
fl
ight relative to the
boresight position estimated by the pointing sensors.
Deprojection
fi
ts are also used to measure per-detector
calibration, beamwidth, and ellipticity. The estimated calibra-
tions are in good agreement with those found in Section
4.2.3
Figure 4.
Simulated residual
B
-mode power from several systematic effects at
150 GHz. The top panel shows the residuals from offset detector orientation
angles and beam model extensions simulated using the
beamconv
algorithm.
The bottom panel shows residuals determined from time-domain deprojection
templates. In the legend,
“
PO
”
refers to physical optics simulations; the entries
are described further in Section
7
. Also shown for comparison are total
BB
spectra with lensing
(
solid gray
)
and without
(
dashed gray
)
for two benchmark
values of
r
.
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