D
RAFT VERSION
M
ARCH
25, 2021
Typeset using L
A
T
E
X
twocolumn
style in AASTeX63
A Constraint on Primordial
B
-Modes from the First Flight of the S
PIDER
Balloon-Borne Telescope
S
PIDER
C
OLLABORATION
, P. A. R. A
DE
,
1
M. A
MIRI
,
2
S. J. B
ENTON
,
3
A. S. B
ERGMAN
,
3
R. B
IHARY
,
4
J. J. B
OCK
,
5, 6
J. R. B
OND
,
7
J. A. B
ONETTI
,
6
S. A. B
RYAN
,
8
H. C. C
HIANG
,
9, 10
C. R. C
ONTALDI
,
11
O. D
ORÉ
,
5, 6
A. J. D
UIVENVOORDEN
,
3, 12
H. K. E
RIKSEN
,
13
M. F
ARHANG
,
7, 14
J. P. F
ILIPPINI
,
15, 16
A. A. F
RAISSE
,
3
K. F
REESE
,
17, 12
M. G
ALLOWAY
,
13
A. E. G
AMBREL
,
18
N. N. G
ANDILO
,
19
K. G
ANGA
,
20
R. G
UALTIERI
,
21
J. E. G
UDMUNDSSON
,
12
M. H
ALPERN
,
2
J. H
ARTLEY
,
22
M. H
ASSELFIELD
,
23
G. H
ILTON
,
24
W. H
OLMES
,
6
V. V. H
RISTOV
,
5
Z. H
UANG
,
7
K. D. I
RWIN
,
25, 26
W. C. J
ONES
,
3
A. K
ARAKCI
,
13
C. L. K
UO
,
25
Z. D. K
ERMISH
,
3
J. S.-Y. L
EUNG
,
14, 27
S. L
I
,
3, 28
D. S. Y. M
AK
,
11
P. V. M
ASON
,
5
K. M
EGERIAN
,
6
L. M
ONCELSI
,
5
T. A. M
ORFORD
,
5
J. M. N
AGY
,
29, 30
C. B. N
ETTERFIELD
,
14, 22
M. N
OLTA
,
7
R. O’B
RIENT
,
6
B. O
SHERSON
,
15
I. L. P
ADILLA
,
14, 31
B. R
ACINE
,
13
A. S. R
AHLIN
,
32, 18
C. R
EINTSEMA
,
24
J. E. R
UHL
,
4
M. C. R
UNYAN
,
5
T. M. R
UUD
,
13
J. A. S
HARIFF
,
7
E. C. S
HAW
,
15
C. S
HIU
,
3
J. D. S
OLER
,
33
X. S
ONG
,
3
A. T
RANGSRUD
,
5, 6
C. T
UCKER
,
1
R. S. T
UCKER
,
5
A. D. T
URNER
,
6
J. F.
VAN DER
L
IST
,
3
A. C. W
EBER
,
6
I. K. W
EHUS
,
13
S. W
EN
,
4
D. V. W
IEBE
,
2
AND
E. Y. Y
OUNG
25, 26
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
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 Blvd., Pasadena, CA 91125, USA
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 Astronomy and Astrophysics, University of Toronto, 50 St George Street, Toronto, ON M5S 3H4 Canada
15
Department of Physics, University of Illinois at Urbana-Champaign, 1110 W. Green Street, Urbana, IL 61801, USA
16
Department of Astronomy, University of Illinois at Urbana-Champaign, 1002 W. Green Street, Urbana, IL 61801, USA
17
Department of Physics, University of Texas, 2515 Speedway, C1600, Austin, TX 78712, USA
18
Kavli Institute for Cosmological Physics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637 USA
19
Steward Observatory, 933 North Cherry Avenue, Tucson, AZ, 85721, USA
20
APC, Univ. Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cité, France
21
High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 60439
22
Department of Physics, University of Toronto, 60 St George Street, Toronto, ON M5S 3H4 Canada
23
Department of Astronomy and Astrophysics, Pennsylvania State University, 520 Davey Lab, University Park, PA 16802, USA
24
National Institute of Standards and Technology, 325 Broadway Mailcode 817.03, Boulder, CO 80305, USA
25
Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA
26
SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
27
Dunlap Institute for Astronomy and Astrophysics, University of Toronto, 50 St George Street, Toronto, ON M5S 3H4 Canada
28
Department of Mechanical and Aerospace Engineering, Princeton University, Engineering Quadrangle, Princeton, NJ 08544, USA
29
Department of Physics, Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63130, USA
30
McDonnell Center for the Space Sciences, Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63130, USA
31
Department of Physics and Astronomy, Johns Hopkins University, 3701 San Martin Drive, Baltimore, MD 21218 USA
32
Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510-5011, USA
33
Max-Planck-Institute for Astronomy, Konigstuhl 17, 69117, Heidelberg, Germany
ABSTRACT
We present the first linear polarization measurements from the 2015 long-duration balloon flight of S
PIDER
,
an experiment designed to map the polarization of the cosmic microwave background (CMB) on degree angular
Corresponding author: William C. Jones
wcjones@princeton.edu
arXiv:2103.13334v1 [astro-ph.CO] 24 Mar 2021
2
S
PIDER
C
OLLABORATION
scales. Results from these measurements include maps and angular power spectra from observations of 4
.
8% of
the sky at 95 and 150 GHz, along with the results of internal consistency 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 significance; Galactic synchrotron emission is found to be negligible
in the S
PIDER
bands. We employ two independent foreground-removal techniques in order 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, employing a joint analysis of
S
PIDER
and
Planck
data in the harmonic domain, assumes a modified-blackbody model for the spectral energy
distribution of the dust with no constraint on its spatial morphology. Using a likelihood that jointly samples the
template amplitude and
r
parameter space, we derive 95% upper limits on the primordial tensor-to-scalar ratio
from Feldman–Cousins and Bayesian constructions, finding
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
S
PIDER
’s second flight will complement the
Planck
polarization maps, providing powerful measurements of
the polarized Galactic dust emission.
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 cos-
mological constant. The observed structure in the Universe
originates from primordial fluctuations of matter and energy
that grow through gravitational instability. These perturba-
tions evolve within a spacetime geometry that is spatially flat
on the largest observed scales. This simple paradigm has
proven to be in remarkable agreement with the overwhelm-
ing majority of all observational tests (Peebles 2012; Planck
Collaboration et al. 2020a,b).
Observational data place stringent constraints on the prop-
erties of these primordial density fluctuations; they must be
predominantly adiabatic in nature, Gaussian-distributed, fol-
low a nearly—but not quite—scale-invariant spectrum, and
encode correlations on scales larger than the horizon during
recombination. Mechanisms to generate such fluctuations
have been proposed within the context of inflationary, bounc-
ing, and cyclic models (Guth & Pi 1982; Starobinsky 1982;
Mukhanov & Chibisov 1982; Hawking 1982; Bardeen et al.
1983; Tanabashi et al. 2018; Shandera et al. 2019; Ijjas &
Steinhardt 2018, 2019; Cook et al. 2020).
In addition to the well-studied scalar perturbations, some
early-Universe models—particularly inflationary models—
predict a spectrum of tensor perturbations, or primordial
gravitational waves. Their amplitude is characterized by
the dimensionless tensor-to-scalar ratio,
r
.
1
The
Planck
data combine precision measurements of the scalar fluctua-
tions and the largest-scale CMB intensity fluctuations to con-
strain
r
to be less than
r
<
0
.
10 (Planck Collaboration et al.
2020d).
2
1
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
fixed to those of Planck Collaboration et al. (2020c).
2
This constraint relaxes to
r
<
0
.
16 when excluding the low-
`
data (2
≤
`
≤
29) that include the temperature deficit.
Local quadrupole anisotropies sourced by tensor fluctu-
ations can also imprint a unique “
B
-mode” (curl) com-
ponent to the polarization of the CMB at degree angular
scales (Kamionkowski & Jaffe 2001; Seljak & Zaldarriaga
1997). Though challenging to measure, this signature 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 fluc-
tuations would bring remarkable new insights into early-
Universe physics. This scientific potential has motivated
an ambitious observational effort to search for the signa-
ture of primordial gravitational waves in the polarization of
the CMB (Kamionkowski & Kovetz 2016; Abazajian et al.
2016).
The
Planck
polarization data, spanning 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 Col-
laboration et al. 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, im-
prove the constraint to
r
<
0
.
056 (Planck Collaboration et al.
2020d). In Tristram et al. (2021) this same constraint is ob-
tained 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 (Tris-
tram et al. 2021).
As anticipated even prior to the
Planck
results, any cosmo-
logical
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. 2020e).
S
PIDER
B
-
MODE
R
ESULTS
3
In this paper we report results from the first flight of S
PI
-
DER
, a balloon-borne instrument designed to measure the po-
larization of the CMB on degree angular scales. The paper is
organized as follows. After a brief description of the S
PIDER
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 complemen-
tary angular power spectrum estimators, while Section 6 dis-
cusses the consistency tests performed with each of these es-
timators, and Section 7 addresses sources of systematic error.
Results from several distinct methods of component separa-
tion are presented in Section 8, and Section 9 provides con-
straints on cosmological parameters for each method. The
main conclusions and S
PIDER
’s future prospects are summa-
rized in Section 10.
2.
THE S
PIDER
INSTRUMENT
The S
PIDER
payload consists of six monochromatic re-
fracting telescopes housed within a single liquid helium cryo-
stat, which is supported and pointed by a lightweight carbon
fiber gondola. Here we provide a brief overview of the pay-
load design, and a more detailed description can be found
in Runyan et al. (2010); Filippini et al. (2010); Rahlin et al.
(2014); Gualtieri et al. (2018).
2.1.
Receivers
Each S
PIDER
receiver is an axisymmetric two-lens cryo-
genic refractor with a 270 mm cold stop, designed to min-
imize 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
baffles surrounding the optics are cooled to 1
.
6 K in order
to reduce stray photon loading on the detectors. A sapphire
half-wave plate (HWP) mounted to a 4 K flange skyward of
each receiver’s stop is rotated to a new fixed orientation angle
twice daily to provide polarization modulation (Bryan et al.
2010a, 2016). Each receiver views the sky through a series of
reflective metal-mesh (Ade et al. 2006) and lossy nylon filters
to reduce infrared loading on the cryogenic system and detec-
tors, as well as a thin (
∼
3 mm) ultra-high-molecular-weight
polyethylene (UHMWPE) vacuum window. An appropriate
single-layer anti-reflection coating, matched to the receiver’s
band (95 or 150 GHz), is attached to each side of the HWPs,
lenses, vacuum windows, and relevant filters.
Each telescope focuses radiation onto four wafers (“tiles”)
of antenna-coupled transition-edge sensors (TESs), fabri-
cated 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 perpendic-
ular 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 polarization—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 opti-
cal power from these synthesized antennas through a band-
defining lumped-element filter before dissipating the power
incoherently on a thermally isolated island. Each island sup-
ports two TESs with different critical temperatures,
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; Stiehl et al. 2011; Battistelli et al. 2008).
The TESs and SQUIDs are housed within extensive magnetic
shielding (Runyan et al. 2010).
Table 1 summarizes the properties of all detectors used in
the analysis presented in this paper.
3
This flight of S
PIDER
deployed a total of 2400 TESs. The channel counts in Ta-
ble 1 account for intentionally dark (non-optical) TES chan-
nels, losses due to detector and readout performance, and the
conservative channel cuts used in the present analysis. No-
tably, one of the three 150 GHz receivers was excluded late in
the analysis due to a null test failure (see Section 6.1.3), but
should be recoverable with future work. Across the remain-
ing five receivers,
∼
80% of TESs are used in this analysis.
2.2.
Cryogenics
S
PIDER
’s cryogenic system (Gudmundsson et al. 2015),
the largest yet deployed on a long-duration balloon flight,
consists of two liquid helium reservoirs: a 1284-L main tank
and a 16-L superfluid tank. The main tank is maintained at a
pressure of roughly 1 bar during the flight, providing cooling
power at
∼
4 K for the receiver optics and the
3
He sorption
coolers. The boil-off from the main tank flows through heat
exchangers on each of two vapor-cooled shields, which inter-
cept the radiative and conductive parasitic loads on the cryo-
genic system and cool the infrared filter stack. The superfluid
system provides cooling power at 1
.
6 K to each telescope’s
3
He sorption cooler and internal optical baffles. The super-
fluid tank fills continuously from the main tank through a
capillary assembly, and is maintained at the ambient pressure
of the altitude at float (about 6 mbar). The superfluid system
is pumped down on the ground, and maintained at low pres-
sure 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.
3
In this paper, all temperatures used in reference to signal or noise are in
units of
∆
T
CMB
, the equivalent CMB fluctuation, in which the data are
natively calibrated.
4
S
PIDER
C
OLLABORATION
Table 1.
Summary of instrumental parameters for the data used in this analysis. Band center and width are averages of per-detector mea-
surements. Beam full-width at half-maximum is derived from a combined fit 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 unflagged 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 filtering on
signal-to-noise. All sensitivities are reported in CMB temperature units.
Center
Width
FWHM
# Det.
NET
tot
Data Used
Map Depth
Band
[GHz]
[%]
[arcmin]
Used
[μK
√
s]
[days]
[μK
·
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
2.3.
Gondola and Pointing System
The cryostat is supported within a lightweight carbon fiber
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 ref-
erencing 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 sen-
sors, encoders, and gyroscopes to enable in-flight pointing
and post-flight pointing reconstruction (Gandilo et al. 2014).
Control and monitoring of the pointing and cryogenic sys-
tems is performed by a pair of redundant flight computers
interfaced with the custom BLASTbus electronics (Benton
et al. 2014). A sun shield protects the instrument and op-
tics during the 24-hour Antarctic summer daylight. Continu-
ous electric power is provided by a 2 kW solar panel system,
while various antenna arrays provide commanding, teleme-
try, and location information during the flight.
3.
SCIENCE OBSERVATIONS
S
PIDER
was launched on January 1, 2015, from the
NASA/NSF Long-Duration Balloon (LDB) facility near Mc-
Murdo Station, Antarctica. All payload systems performed
well throughout the flight, with the exception of a differen-
tial GPS unit failure that had no significant impact on flight
operations or pointing reconstruction. S
PIDER
’s flight lasted
16.5 days at an average altitude of 35 km. The flight was ter-
minated when cryogens were exhausted and the circumpolar
wind system began to fail. The payload touched down in a
remote region of Ellsworth Land of West Antarctica. Data
drives and key flight hardware were recovered in February
by personnel from the British Antarctic Survey; a second
team recovered the remainder of the instrument in Novem-
ber. The payload optics and focal planes have subsequently
been refurbished and upgraded in preparation for a second
flight (Shaw et al. 2020).
During an Antarctic LDB flight the Sun remains above the
horizon at all times. The accessible region of sky is therefore
constrained by the need for the field 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,
since the anti-solar direction progresses to lower Galactic lat-
itude over time. S
PIDER
’s launch opportunity came relatively
late in the Antarctic LDB season, pushing the field center to-
ward the lower range of possible field centers.
S
PIDER
scanned in azimuth throughout the flight, with a
sinusoidal speed profile peaking as high as 4 ° s
−
1
. The si-
nusoidal speed profile allowed smooth torque variations in
the pivot and reaction wheel motors, without sustaining peak
torque for long. For the first two-thirds of the flight, S
PIDER
scanned a
∼
75° azimuthal range limited on either side by the
Galaxy and the Sun. In order to obtain more uniform cover-
age, the azimuthal range was reduced for the final third of the
flight to cover the middle half of this range. Scan turnarounds
are separated by as long as 36 s, shortening to a little as 22 s
for the narrower region later in the flight. Small steps in el-
evation were made at every third scan turnaround, covering
the full 22° to 50° range upwards and downwards once per
day. A brief scan over the bright Galactic source RCW38
was used to confirm pointing in flight.
The in-flight pointing solution using only coarse sensors
has an error of 22
′
RMS, less than a S
PIDER
beam width
and adequate for scan control. The post-flight pointing re-
construction integrates gyroscopes between star camera so-
lutions, and matches raw solutions of the boresight star cam-
era to within 0
.
9
′
RMS. The relative pointing between the
boresight camera and microwave detectors is calibrated with
cross-correlation and deprojection methods described in Sec-
tion 4.2.4.
The half-wave plate is stepped in angle twice per sidereal
day (Bryan et al. 2016, 2010a). The nominal HWP angles are
chosen to rotate each receiver between Stokes
Q
and
U
sen-
sitivity 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 in an eight-day pattern
to reduce sensitivity to beam and HWP systematics (Bryan
et al. 2010b; Nagy et al. 2017). The HWP angles are mea-
sured with a combination of absolute and relative encoders,
providing an accuracy of 0
.
1°.
S
PIDER
B
-
MODE
R
ESULTS
5
S
PIDER
’s flight 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 de-
tector monitoring systems, described more fully in Rahlin
(2016). These use regular measurements of the TES dif-
ferential resistance (
dV
/
dI
) from small 2 Hz square waves
imposed on the TES bias lines; these are carried out for 2-
second intervals every fifth scan turnaround. These values
are used to automatically identify channels that are super-
conducting or normal, have accumulated a large DC offset,
or have drifted significantly 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 ad-
justment 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 flight; in prac-
tice this had little meaningful effect, given S
PIDER
’s excel-
lent detector performance stability. Using both electrical and
optical measurements of the temporal gain variations, the ex-
cursions on all timescales are found to be less than 5%, and
not strongly correlated (see Section 4.2.3).
4.
DATA PROCESSING AND MAP MAKING
Here we present an abbreviated discussion of S
PIDER
’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).
S
PIDER
’s raw data consist of 2
.
1 TB of time-ordered sam-
ples. Bolometer and pointing data were recorded at 119 Hz,
while a variety of gondola and cryogenic performance pa-
rameters were recorded at reduced sample rates. All data
were recorded in-flight across multiple redundant drives.
Data from the six bolometer arrays and the flight 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” approximately 10 minutes
in length. These evenly partition the periods between HWP
angle steps and divide only at turn-arounds of the azimuthal
scan. Chunk length is a compromise between containing a
sufficient number of samples for analysis tasks like estimat-
ing low-frequency noise, while remaining short enough 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 S
PI
-
DER
timestream data: intermittent and quasi-stationary.
In-
termittent
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. The three Iridium transmitters in par-
ticular are active for about two seconds at a time, operat-
ing asynchronously with periods between 1 and 15 minutes.
Other sources of intermittent noise include cosmic ray inter-
actions in the detectors—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 field of view and change very little over multiple az-
imuthal scans. These have a peak-to-peak amplitude typi-
cally 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 resid-
ual atmospheric emission. Additionally, RF-coupled inter-
ference was observed in some of the detector channels; one
consequence of this is that a subset of detectors evidence a
signal that is well-correlated with the orientation of the reac-
tion 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 flight, 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 flagging of affected de-
tector samples. Such samples are tagged, replaced with con-
strained noise realizations, and excluded from map-making.
Step discontinuities arise intermittently in S
PIDER
’s data,
due primarily to transmitter interference and large cosmic ray
interactions. In addition to flagging the discontinuity itself,
we adjust the data to eliminate the discontinuity using a lin-
ear fit to data before and after the event. This procedure ac-
counts empirically for cross-talk of the discontinuity among
channels. This “stitching” operation improves low-frequency
noise significantly, and simulations show that it has negligi-
ble effect on signal response.
Quasi-stationary noise is mitigated by time-domain filter-
ing of this flagged data set, conducted at the full detector
sample rate. To reduce noise correlated with the reaction
wheel, detector timestreams are binned according to the an-
gle of the reaction wheel to form templates that are then sub-
tracted. The impact of this operation was checked using the
full-flight time-domain simulations described in Section 4.4,
and found to have negligible effect on the astrophysical sig-
6
S
PIDER
C
OLLABORATION
nal; this fit is thus performed only on data timestreams,
but not on the large simulation ensembles. To reduce low-
frequency noise and pickup more broadly, the data are fil-
tered between each scan turnaround by subtracting a fifth-
order polynomial fit to each detector’s data as a function of
azimuth.
The effects of scanning, filtering, and flagging are deter-
mined by applying the entire analysis pipeline to an ensem-
ble of time-domain signal simulations. The transfer functions
due to filtering and beams, which derive from these simu-
lations, are shown in Figure 3 and are discussed further in
Section 5. The primary effect of filtering is a suppression
of power on large angular scales. Because the typical scan
speed and direction vary across the sky, the effect of filtering
is both anisotropic and inhomogeneous, with greater suppres-
sion on the edges of the field of view. This latter effect is not
visibly evident in the temperature or polarization maps (Fig-
ures 1 and 2), and the net impact of the filtering has been
shown to be adequately modeled with a simple multipole do-
main 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 flagged 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 flagged, 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 unflagged samples lie outside the sky mask of the
present analysis (Section 5).
4.2.
Detector Characterization
Both pre-launch and in-flight data are used to characterize
instrumental parameters needed to construct accurate tem-
perature and polarization maps. The pre-launch data include
spectroscopic and polarimetric measurements. In-flight data
are used for the absolute calibration, to monitor gain fluctu-
ations, and to refine 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-field of each receiver as described in Nagy (2017).
The uncertainty on each measured detector angle is ap-
proximately 0
.
5°, which is better than S
PIDER
’s target of
1° (Fraisse et al. 2013). These measured angles are used di-
rectly by the map maker, with no correction applied based on
the flight data.
4.2.2.
Frequency Response
The frequency response of each detector was measured
prior to launch with a custom high-throughput Fourier Trans-
form Spectrometer (FTS) mounted on top of the cryostat.
Since the hot thermal source did not illuminate the full tele-
scope solid angle, an actuated mirror steered the output over
the full field of view. 95% of all detectors used in the science
analysis were measured with band center and band width
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, and this could result in leakage of spectrally
mismatched temperature signals into polarization. Instead, a
null test is constructed splitting detectors with high and low
band centers (Section 6.1). Since no difference is detected,
we conclude that the S
PIDER
data, including mitigation from
HWP and sky rotation, have negligible leakage from band-
pass mismatch.
4.2.3.
Calibration and Beam
S
PIDER
’s absolute calibration is derived by cross-
calibrating degree-scale power with
Planck
temperature
anisotropy data at 100 and 143 GHz
4
.
This procedure
finds the absolute calibration factor and parameterized beam
model that minimizes the difference with the
Planck
temper-
ature spectra at a per-detector level in the range 100
< ` <
275 (100
< ` <
375) for the 95 (150) GHz frequency band.
The absolute calibration is obtained by finding the scalar,
c
,
that minimizes
`
2
∑
`
=
`
1
R
`
≡
`
2
∑
`
=
`
1
∣
∣
∣
∣
∣
c
̂
C
T T
`
̂
C
T T
`
,
ref
b
Planck
`
b
SPIDER
`
−
1
∣
∣
∣
∣
∣
,
(1)
where
`
1
= 100 and
`
2
= 275 (375) for the 95 (150) GHz
frequency band. We use
̂
C
T T
`
,
ref
to represent a temperature
power spectrum calculated using maps obtained from re-
scanning the
Planck
half-mission reference maps while
̂
C
T T
`
is calculated from single-detector maps cross-correlated with
a
Planck
half-mission map. The beam transfer functions,
b
Planck
`
and
b
SPIDER
`
, quantify the relative sensitivity the
Planck
and S
PIDER
spatial response as a function of multipole.
We use a simple Gaussian beam model,
b
SPIDER
`
, to extend
that calibration to other angular scales included in our analy-
sis; this extrapolation is small, and primarily to larger angular
scales. Each S
PIDER
telescope is fit 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 sen-
sitive to a more physically motivated beam model, as sig-
4
Throughout this paper we use release 3.01 of the
Planck
HFI maps (Planck
Collaboration et al. 2020f)
S
PIDER
B
-
MODE
R
ESULTS
7
−
200
−
100
0
100
200
Temperature [
—
K]
0
10
20
30
40
50
60
70
80
Right Ascension
−
2
:
0
−
1
:
5
−
1
:
0
−
0
:
5
0
:
0
Declination
−
48
◦
−
36
◦
−
24
◦
−
12
◦
+25
◦
+50
◦
+75
◦
Spider
150 GHz
+25
◦
+50
◦
+75
◦
Reobserved
Planck
143 GHz
+25
◦
+50
◦
+75
◦
Planck
143 GHz
Figure 1.
(
left
) The total intensity map as observed by the S
PIDER
150 GHz receivers. No additional filtering 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 shown. (
middle
) The
Planck
143 GHz map as re-observed using the S
PIDER
scan strategy and filtering, indicating strong agreement
in the temperature signal. (
right
) The raw
Planck
143 GHz map, shown to illustrate the impact of S
PIDER
’s scan strategy and filtering, which
suppresses power at large angular scales.
−
2
−
1
0
1
2
Polarization [
—
K]
0
10
20
30
40
50
60
70
80
Right Ascension
−
2
:
00
−
1
:
75
−
1
:
50
−
1
:
25
−
1
:
00
−
0
:
75
−
0
:
50
−
0
:
25
0
:
00
Declination
−
48
◦
−
36
◦
−
24
◦
−
12
◦
Q
Spider
95 GHz
Q
Spider
150 GHz
−
48
◦
−
36
◦
−
24
◦
−
12
◦
+25
◦
+50
◦
+75
◦
U
+25
◦
+50
◦
+75
◦
U
Figure 2.
Q
and
U
polarization maps as observed by S
PIDER
’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 compute power spectra, though the additional point source mask is not shown.