# An Empirical Background Model for the NICER X-ray Timing Instrument

Ronald A. Remillard MIT Kavli Institute for Astrophysics & Space Research,
MIT, 70 Vassar St., Cambridge, MA 02139, USA  Michael Loewenstein  Department
of Astronomy, University of Maryland, College Park, MD 20742  X-Ray
Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD
20771, USA  James F. Steiner  Smithsonian Astrophysical Observatory, 60 Garden
St., Cambridge, MA 02138, USA  Gregory Y. Prigozhin  MIT Kavli Institute for
Astrophysics & Space Research, MIT, 70 Vassar St., Cambridge, MA 02139, USA
Beverly LaMarr  MIT Kavli Institute for Astrophysics & Space Research, MIT, 70
Vassar St., Cambridge, MA 02139, USA  Teruaki Enoto Extreme Natural Phenomena
RIKEN Hakubi Research Team, Cluster for Pioneering Research, RIKEN, 2-1
Hirosawa, Wako, Saitama 351-0198, Japan  Keith C. Gendreau  X-Ray Astrophysics
Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA  Zaven
Arzoumanian  X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA  Craig Markwardt  X-Ray Astrophysics Laboratory, NASA
Goddard Space Flight Center, Greenbelt, MD 20771, USA  Arkadip Basak Anton
Pannekoek Institute, University of Amsterdam, Science Park 904, 1098XH
Amsterdam, NL  Abigail L. Stevens Department of Physics & Astronomy, Michigan
State University, 567 Wilson Road, East Lansing, MI 48824, USA  Department of
Astronomy, University of Michigan, 1085 South University Avenue, Ann Arbor, MI
48109, USA  NSF Astronomy & Astrophysics Postdoctoral Fellow  Paul S. Ray
Space Science Division, U.S. Naval Research Laboratory, Washington, DC 20375,
USA  Diego Altamirano Department of Physics and Astronomy, University of
Southampton, Southampton, SO17 1BJ, UK  Douglas J. K. Buisson  Department of
Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, UK

(Revised this is submission V2; Accepted TBD)

###### Abstract

NICER has a comparatively low background rate, but it is highly variable, and
its spectrum must be predicted using measurements unaffected by the science
target. We describe an empirical, three-parameter model based on observations
of seven pointing directions that are void of detectable sources. Two model
parameters track different types of background events, while the third is used
to predict a low-energy excess tied to observations conducted in sunlight. An
examination of 3556 good time intervals (GTIs), averaging 570 s, yields a
median rate (0.4–12 keV; 50 detectors) of 0.87 c/s, but in 5% (1%) of cases,
the rate exceeds 10 (300) c/s. Model residuals persist at 20–30% of the
initial rate for the brightest GTIs, implying one or more missing model
parameters. Filtering criteria are given to flag GTIs likely to have
unsatisfactory background predictions. With such filtering, we estimate a
detection limit, 1.20 c/s (3 $\sigma$, single GTI) at 0.4–12 keV, equivalent
to $3.6\times 10^{-12}$ erg cm-2 s-1 for a Crab-like spectrum. The
corresponding limit for soft X-ray sources is 0.51 c/s at 0.3–2.0 keV, or
$4.3\times 10^{-13}$ erg cm-2 s-1 for a 100 eV blackbody. These limits would
be four times lower if exploratory GTIs accumulate 10 ks. Faint-source
filtering selects 85% of the background GTIs, and higher rates are expected
for targets scheduled more favorably. An application of the model to 1 s
timescale makes it possible to distinguish source flares from possible surges
in the background.

instrumentation: detectors — methods: observational — X-rays: general

††journal: AJ

##  1 Introduction

The Neutron Star Interior Composition Explorer (NICER) is a NASA mission for
X-ray astronomy that has been operating on the International Space Station
(ISS) since it was launched and deployed in 2017 June (Gendreau et al., 2016).
The NICER X-ray Timing Instrument (XTI) consists of 56 identical and co-
aligned cameras, each containing an X-ray Concentrator (XRC; Okajima et al.
(2016)) and a customized Si drift detector positioned in the concentrator’s
focal plane. The other primary components of NICER are a target acquisition
and tracking platform and seven electronics boxes, each of which services
event processing from eight detectors (Prigozhin et al., 2016). Each detector
package (detector, preamplifier, and thermoelectric cooler) is known as a
Focal Plane Module (FPM), and each electronic box is referred to as a
Measurement & Power Unit (MPU). The XTI sensitivity range is 0.2–12 keV, the
energy resolution is typical of Si detectors (e.g., 150 eV FWHM at 6.5 keV),
and detected events are time-tagged to an absolute accuracy of 100 ns. The
combined detector output from the 50 best-performing FPMs offers substantial
throughput, e.g. with 10,500 c/s from the Crab Nebula over the range 0.4–12
keV.

The FPM and MPU designs and interworking are described in Prigozhin et al.
(2016). Here we summarize the details that are most relevant to the background
model at hand. Each FPM is a single channel device that is collimated to view
a circular celestial area with radius of 3.17 arcmin. The multilayer the
collimator (1 mm radius) captures more than 90% of the light in the
concentrator’s point spread function, and it limits the travel time to the
anode for X-ray events, while the active area under the collimator extends to
a radius of 2.8 mm. All NICER observations contain events from both the
science target and the various types of background that are encountered while
operating in space. Scientific analyses thus require a model that can predict
the background spectrum so that the target spectrum can be isolated. The 3C50
background model uses detector measurements that characterize the background
but not the X-rays from the science target, analogous to past missions such as
the Photon Counting Array of the Rossi X-ray Timing Explorer (RXTE) Mission
(Jahoda et al., 2006). To assist modeling efforts, NICER routinely schedules
observations of seven sky positions that are void of detectable point sources.
These targets (inherited from RXTE) are named “BKGD_RXTE#”, with # ranging
1–6,8. Position #7 was eliminated as a NICER background target for the
presence of a soft X-ray source (bright star).

Pre-launch analyses predicted that the NICER background would primarily
consist of a very small contribution from the cosmic diffuse X-ray background
(e.g., Wu et al. (1991)), given the small FOV of the Instrument (31.6 square
arcmin), and particle interactions that deposit energy indistinguishable from
in-band X-rays. The 3C50 model covers these components. Additional background
sources that are not considered in the 3C50 model include enhanced diffuse
X-rays from hot gas in the Milky Way (dependent on galactic latitude),
possible soft X-rays related to Solar activity, and possible contamination
from the Earth limb or the radiation sources on Soyuz spacecrafts. In pre-
launch analyses, the primary background components were expected to yield, for
the majority of the ISS orbit, 0.2 counts per second (c/s) in soft X-rays at
0.4–2.0 keV, and an additional 0.15 c/s at 2–8 keV.

The Empirical Background Model, also known as the ”3C50” model, uses libraries
constructed by sorting and combining the spectra extracted from background
observations. Each library spectrum is the sum of spectra within a cell
defined by intervals in the adopted model parameters, as described below. The
model is named “3C50” because it is based on 3 parameters, the format assumes
that spectral extractions will be made from standard NICER “cleaned” event
lists, and the libraries are based on selection of 50 of the 52 FPMs operating
in the XTI, while the remaining 4 (of 56) are not operating).

Our choice of model parameters (see below) requires additional introductory
explanations about signal processing steps in the MPU (see Prigozhin et al.
(2016)). The signal line for each FPM is replicated, so that events can be
found and processed independently with “fast” and “slow” measuring chains that
use circuits with different time windows. The fast chain (84 ns nominal
shaping time) produces time tags with higher precision, while the slow chain
(465 ns shaping time) more effectively integrates the total electron yield,
with lower noise, providing better measurements of the event energy. Event
detections can trigger on either measuring chain, when the rate of change in
the signal line exceeds a trigger threshold held in the MPU, per FPM and per
chain. The trigger thresholds are chosen to admit a noise rate of $\sim 3$ c/s
per FPM, per measuring chain, as measured below 0.25 keV when there are no
sources in front of the detectors. Such noise events will be asynchronous,
i.e. they will trigger only one measuring chain. On the other hand, X-ray and
particle events will usually trigger both measuring chains, yielding a single
event that includes two measurements of the event energy. The caveat, here, is
that the fast chain, with a higher noise level than the slow chain, has a
lower trigger efficiency at energies below 1 keV. X-ray events from the source
that trigger the slow chain, but not fast chain, are likely to be in the range
0.2–0.6 keV, i.e., above the slow threshold and below the fast threshold.

When the travel path in the detector is long, from the point of incidence to
the charge-collecting anode at the center of the active Si region, then the
size of the charge cloud, and hence the temporal profile of the event, is
elongated by charge diffusion. With its longer shaping time, the slow chain is
more immune to such effects, since it has a longer time to integrate the
charge. Incomplete charge collection will lower the reported event energy, and
so the ratio of the slow chain energy and the fast chain energy systematically
increases when the point of incidence is near the outer edges of the detector,
i.e., beyond the inner ring of the collimator. This is an important detail for
the background model, since pre-launch simulations had shown that particle
interactions with the detector would generally produce event energies well
above the 12 keV limit of the concentrator’s effective area — and thus be
rejected — except for edge-clipping events near the outer edges of the active
Si area. NICER’s calibrated events lists are given in the ”pulse invariant”
(PI) convention, where PI is the calibrated energy value from the slow chain
in 10 eV units, PI_FAST is the calibrated energy in the fast chain, and
PI_ratio = PI / PI_FAST, for each event that triggers both of the measuring
chains (and PI_ratio = INDEF, otherwise). The events from the predicted edge-
clipping particles that can mimic X-ray events in PI value must travel a long
path to the anode, resulting in increased spread of the charge cloud
associated with the increased drift time. The measurement of such events would
then show anomalously high values in PI_ratio, since the “ballistic deficit”
in the fast chain will be more substantial, compared to the slow chain.

The final topic of NICER signal processing that is pertinent to the background
model is the system of NICER event flags. There are six flags, with assigned
value 1 or 0, which are interpreted as “yes” or “no”, respectively. Five of
these flags tie an event to a particular circuit latch in the MPU, and the
circuit is designed to help distinguish events as good or bad for inclusion in
scientific analyses. The flags are: first-event-in-packet (useful only for the
data pipeline software), triggered the fast chain, triggered the slow chain,
forced trigger, undershoot event, and overshoot event. Forced triggers result
from commands to sample the signal values in the absence of a trigger from a
detector, and they serve to monitor the zero point in the energy calibration
of each FPM/MPU signal processing combination. Since launch, forced triggers
have been operating at 5 Hz for each FPM. Undershoot events have latched a
circuit designed to detect the large negative pulse associated with a detector
reset, which causes a high-amplitude negative pulse when an FPM discharges the
capacitor that collects ambient charge running through the detector
(maintained at $-55^{\circ}$C). Overshoot events have latched a different
circuit designed to safeguard against large positive pulses (roughly
equivalent to 18 keV) that could cause a bit rollover in the analog-to-digital
converter. The keV assignments of undershoots and overshoot events are thus
meaningless. Any event with unity values in forced triggers, undershoots, or
overshoot flags are excluded from the “good events” that are passed into the
cleaned event lists created by the NICER pipeline. The cleaned event lists are
also limited to the slow chain energies in the range 0.2–15 keV. Returning to
the topic of background modeling, the strategy to recognize events associated
with energetic particles can be summarized as follows. Most particle events
would be excluded as bad events via the overshoot flag, while detector edge-
clipping events with in-band amplitude and no overshoot flag would be
identified via high values in the event’s PI_ratio. As shown below, NICER in-
flight data reveal an additional component with neither of these properties
that must be handled in order to predict the background spectrum.

##  2 Observations and Data Selection

The 3C50 model is a phenomenological approach to predict the in-band (0.4–12.0
keV) background spectrum using the observations of the NICER background
fields. The parent data set for the model libraries includes all such
observations from 2017 July 24, through 2020 March 21. The contributions from
each background field are given in Table 1. The selection filters leading to
the model libraries are summarized in Table 2, and they are described in
detail, below.

Table 1: Parent Observations for the 3C50 Background Model

Target | ObsID first | ObsID last | # GTIs | Exposure (ks)
---|---|---|---|---
BKGD_RXTE1 | 1012010101 | 3012010106 | 357 | 131.2
BKGD_RXTE2 | 1012010201 | 3012020201 | 545 | 309.8
BKGD_RXTE3 | 1012010301 | 3012030104 | 317 | 157.2
BKGD_RXTE4 | 1012010401 | 2012040241 | 451 | 248.4
BKGD_RXTE5 | 1012010501 | 2012050232 | 540 | 292.4
BKGD_RXTE6 | 1012010601 | 3012060201 | 830 | 548.4
BKGD_RXTE8 | 1012010801 | 3012080102 | 516 | 336.9

Note. — The sum of these background observations yields 3556 GTIs and 2.024 Ms
exposure time.

Data analyses utilized the NASA HEASoft package, version 6.26.1. Prior
software versions had different defaults for the use of nimaketime to define
good time intervals (GTIs; see below). The raw event lists from the NICER
pipeline for the observation IDs (ObsIDs) given in Table 1 were calibrated for
the 2020 gain revision specified by “GCALFILE”,
“nixtiflightpi20170601v005.fits”. When making the cleaned event lists, the
default filters for environmental conditions were adopted, excluding times in
the South Atlantic Anomaly (SAA), pointing elevations within 15∘ of the dark
Earth limb and within 30∘ of the sunlit Earth limb. However, the default
filters for bad-event count rates were effectively disabled by using extremely
high values (15000) for the maximum rates of overshoots, undershoots, and the
relationship between overshoots and magnetic cutoff rigidity. These filter
over-rides are required to populate the cleaned event lists with good events
during times when the background rates are high.

Table 2: Data Selections and Filters for the Spectrum Libraries

Selection | # GTIs | Exposure (ks) | Comment
---|---|---|---
All data | 3556 | 2024.2 | from Table 1
Selected 50 FPMs operating | 3435 | 1937.4 |
Filter noise outliers | 3357 | 1891.1 | any $i$: $nz_{i}>100$ and $nz_{i}>0.15nz$
Parameters within 3C50 limits | 3264 | 1818.3 | see Fig. 3
Subset ISS night | 1991 | 1068.6 |  $nz<200$, see Fig. 4
Filter out outliers | 1947 | 1038.2 | see Fig. 4 ; GTIs for night library
Subset ISS day | 1273 | 758.6 | $nz>=200$
Filter for high BG and stage 1 residuals | 1076 | 627.4 |  $ibg_{52}<0.4$ c/s; $-1.0<(C_{net}+D_{net})<1.0$

Note. — In summary, the 3C50 spectral libraries use 3023 (of 3556) GTIs,
corresponding to 1665.6 ks or 82% of the exposure time. There are 1947 GTIs
contributing to the night library and 1076 GTIs for the day library.

The ObsID directories from the NICER pipeline contain data for a given target,
accumulated on a given day. In this work, each GTI is an interval of
continuous exposure, and for NICER such intervals are usually less than 2 ks
because of interruptions imposed by the rotation of the ISS with respect to
celestial coordinates, imposed by the rotation of the ISS, once per 93 min
Earth orbit. Many ObsIDs contain more than one GTI. Since the NICER background
can change significantly at different locations in the ISS orbit, background
modeling is based on the timescale of GTIs, rather than ObsIDs. There is
further value to measuring the amount of parameter variability that occurs
within a given GTI, so as to exclude it or to redefine the time boundaries to
avoid strong flares in the background. Further practical considerations for
running the background model are given in 6.

The tool nimaketime was used to define the GTIs for every ObsID in each of the
background fields. This step repeats the same filter choices used to make the
revised cleaned event lists (see above). GTI selection was additionally
filtered to exclude GTIs with duration less than 60 s, while disregarding any
gaps of 1 or 2 s that might be imposed by a telemetry packet loss, which is
corrected for, via an adjusted exposure time, by the NICER pipeline. The
numbers of selected GTIs and the net exposure time accumulated per background
field, are given in Table 1. The total yield is 3556 GTIs, averaging 570 s per
GTI and accumulating 2.024 Ms.

Finally, we choose to build the background spectrum libraries with a selection
of 50 (of 56) FPMs. We label FPMs with two digits: the first for the MPU that
services it (0-6) and the second for the FPM slot (0-7) in the MPU. For
example, the first FPM on the first MPU is “00”, while the last FPM on th4e
last MPU is “67”. In this notation, the six excluded FPMs are the four that
are not operating (11, 20, 22, and 60) plus two (14 and 34) that have shown
episodes of unreliable spectra and high noise rates, respectively. The
selection of the remaining 50 FPMs adds an element of uniformity to the
background libraries. However, users can conduct target analyses with any
number of selected FPMs, and then apply the 3C50 model under the assumption
that the model metrics do not change, detector-by-detector, and the net
background spectrum can be simply scaled by the number of selected FPMs.

##  3 First Stage of the 3C50 Background Model

The strategy behind the 3C50 model is to sort out the background components
from an empirical point of view, based on event properties found in
observations of the background fields. The first stage of the model
distinguishes background components that have different spatial properties in
the detector focal plane, as determined by event distributions that have
different values of PI_ratio. The second stage of the model deals with the
soft X-ray excess due to noise encroachment induced by the seepage of sunlight
into the Instrument when observations are conducted in ISS sunlight, and this
is described in Section 4.

###  3.1 Two Parameters for Background Components Sorted by PI_ratio

Figure 1: Sample background observations showing every good event in the plane
of event energy vs. PI_ratio. The curved red line shows the NICER pipeline’s
boundary between events that appear as if in-focus (left of line), versus
events originating far from the detector anode (right of line). The
integration areas for the first two background model parameters, $ibg$ and
$hrej$, are also shown. The observations were chosen to illustrate how the two
background components are always present, but the fraction of events in each
group can vary widely.

The description of model parameter choices is framed by an examination of
Fig.1, where events are plotted in the plane of (effective) photon energy (PI)
versus PI_ratio, i.e. the ratio of slow-chain to fast-chain keV values for
good events that trigger both measuring chains. Each panel shows vertical
spectral tracks centered on PI_ratio values near 1.0 and in the range 1.7–2.2.
The curved red line shows the relationship, PI_ratio $=1.1+120.0/$PI, where PI
is the slow-chain photon energy in units of 10 eV. This relationship is the
standard cut in pipeline data processing, where events to the left of the
line, plus events with PI_ratio = INDEF, are passed to the cleaned event
lists. The value of 1.1 limits the exclusion of events to cases where the fast
chain energy differs by more than 10% from the slow chain energy. The second
term adds allowances for the broadening of the PI_ratio values due to
statistical noise, especially in PI_FAST. We note that the events displayed in
Fig.1 are drawn from the unfiltered but calibrated event lists (*ufa.evt) in
the pipeline’s $ObsID$/xti/event_cl/ directory, which contains all good events
(i.e., events with no undershoot, overshoot, or forced trigger flags), with no
PI_ratio screening.

The pipeline’s PI_ratio filter effectively separates the two vertical
distributions in background events seen in Fig.1. The right-side distribution
is consistent with the expected particle hits near the edges of the Si drift
detector that would mimic good events with anomalously high values in
PI_ratio. On the other hand, the left-side events are indistinguishable from
“in-focus” X-rays emitted by NICER targets, and we refer to this distribution
as the in-focus background component. This label is intended as a comparative
reference rather than a provable statement that the XRC is involved in the
process of detecting these events. Further considerations about the origin of
these events are given below.

To capture and monitor the rate of events with high PI_ratio, we define a
“hatchet” rejection line, shown in Fig. 1 as the blue vertical line at
PI_ratio = 1.54. This leads to the choice of the first 3C50 model parameter,
$hrej$, which is the count rate of hatchet-rejected events, PI_ratio $>=1.54$
in the range 3–18 keV. The high-energy cutoff represents an approximate
maximum energy in the NICER calibration, while the lower limit (3 keV) avoids
any overlap between in-focus and hatchet-rejected distributions. The tail-off
of rejected events below 3 keV represents the lower efficiency of the fast
chain triggers at lower energy, exacerbated by the charge-diffusion pulse
broadening that further decreases the probability of detection. There is also
laboratory evidence that the gain drops near the detector edges, affecting
both measuring chains. However, the energy content of particles is sometimes
sufficient to endure all of these effects and trigger a pulse with a telltale
high value in PI_ratio. In this sense, the NICER detector / electronics
package has a built-in particle monitor, albeit with low efficiency.

Figure 2: The in-focus background rate at 0.4–12 keV ($R_{BG}$) versus the
first two parameters of the 3C50 model, $ibg$ (top panel) and $hrej$ (bottom
panel). The plotted data corresponds to all of the 3556 GTIs represented in
Table 1. Rough correlations are seen in each panel, with a steeper dependence
in the case of $ibg$.

Fig. 1 shows two panels of background events, and each one represents an
overlay from three GTIs, using different FPMs, selected at widely different
times. The GTIs for the left panel were chosen for having roughly half of the
events located in the hatchet-rejected region, while the three GTIs selected
for the right panel have $\sim 10\%$ of events in the hatchet-rejected region.
The intent is to illustrate common features in the energy:PI_ratio plane,
while also showing that the fraction of events in each distribution can vary
significantly. To monitor the rate of in-focus events from the background
observations (i.e., the vertical track of events near PI_ratio $\sim 1$ in
Fig. 1), we define $ibg$, as the count rate of in-focus events (i.e., left of
the red curve) in the range of 15–18 keV. This restriction to high energy
events is needed to limit the $ibg$ capture range to energies well above 12
keV, where the XRC optics have negligible effective area, to avoid
contamination of $ibg$ by X-rays from bright sources.

Having defined $ibg$ and $hrej$ as the first two parameters for the 3C50
background model, Fig. 2 shows how each parameter varies with the in-focus,
in-band background count rate at 0.4–12 keV, hereafter $R_{BG}$. The lower
limit of the energy range, i.e., choosing 0.4 keV instead of the XTI
sensitivity limit at 0.2 keV, is a hedge against effects due to noise and the
optical light leak, which are described in the next section. The primary
objective of the background model is to predict the spectrum associated with
$R_{BG}$. Fig. 2 shows that both $ibg$ (top panel) and $hrej$ (bottom panel)
are roughly correlated with $R_{BG}$, with a steeper dependence in the case of
$ibg$.

The high degree of variability in $R_{BG}$ is apparent along the horizontal
axes. The median value is $R_{BG}=0.87$ c/s, but the distribution, even while
ignoring the 1% high and low extremes, still ranges from 0.33 to 300 c/s.
Values of $ibg$ can also vary by many orders of magnitude. Since $ibg$ is the
high-energy extension of $R_{BG}$), while the energy range is beyond the
effective area of the NICER optics, $ibg$ values can be used to normalize the
stage 1 library selection in the 3C50 model, tuning the model to converge with
the source spectrum at 15–18 keV (considered in extrapolation, since
extractions from cleaned event lists terminate at 15 keV under the default
pipeline settings).

While $hrej$ is a metric for the spatially extended events due to edge-
clipping particles, the origin(s) of the in-focus background component,
tracked with $ibg$, is not well understood. Background components with
PI_ratio near unity are expected from the cosmic diffuse X-ray background, as
well as possible soft X-ray emission from other sources (see Section 1). True
X-ray events are expected to appear in-focus, since the metal collimator above
the detector surface limits the path of X-rays to radii within 1 mm (3.17
arcmin) displacement from the anode (Prigozhin et al., 2016). However, the
count rate from these sources is expected to yield $R_{BG}\sim 0.5$ c/s over
most of the sky, while measured $R_{BG}$ values are sometimes far brighter and
highly variable. We are therefore led to view $ibg$ as representing a second
particle component that is either unable to penetrate the collimator or is
guided to the detector with assistance from the XRC.

###  3.2 3C50 Library for ISS Night

Fig. 3 shows a plot of $hrej$ versus $ibg$ for all of the 3556 GTIs
represented in Table 1. The $hrej$, $ibg$ plane is the parent for stage 1 of
the 3C50 model. A $5\times 7$ grid of parameter values in this plane is used
to bin the background spectra, per GTI, and the combined spectrum per grid
cell is computed to populate the stage 1 library in the 3C50 model. The cell
boundaries are chosen to follow the population pattern, rather than a regular
grid. The library cells on the upper left and lower right of the grid are left
vacant, and queries to those cells would select the nearest occupied neighbor,
moving horizontally along $hrej$.

Figure 3: Plot of $ibg$ versus $hrej$. This plane is divided into five cells
(horizontal) covering $hrej<5.0$ and seven cells (vertical) with $ibg<10.0$.
The cells are referenced by ($ibg$, $hrej$) number with 11 on the lower left
and 75 to the upper right. Cell boundaries in units of $ibg$, $hrej$ are given
in Table 3. These intervals define bins in which the background spectra per
GTI are combined to create the stage 1 background library for the 3C50 model.
The stage 1 library contains 33 such spectra, with cells 15 and 71 unoccupied.

The stage 1 model cells are labeled with two digits: $ibg$ number (1-7) and
$hrej$ number (1-5). The layout is shown in Fig. 3. The cell boundaries are
given in Table 3, along with the average $R_{BG}$ values, the cell
accumulation time, and the exposure-weighted normalization values in
$ibg_{lib}$. Library selections must be standardized to a fixed number of
FPMs, here chosen to be the maximum user choice of 52. However, users are free
to select and specify, for any GTIi, any number of FPMs ($nfpm_{i}$), along
with the model parameter measurements, $ibg_{i},hrej_{i}$. The 3C50 model will
then map a given GTI to a particular library cell, using values
($ibg_{52}=ibg_{i}*52/nfpm_{i};hrej_{52}=hrej_{i}*52/nfpm_{i}$), and the
matching library spectrum is presumed to have the correct spectral shape for
that GTI. The matching library spectrum is then re-normalized by a factor
$ibg_{i}/ibg_{lib}$, and the result is the stage 1 prediction for the
background spectrum in the 3C50 model.

Table 3: Stage 1 Cell Boundaries and Normalizations  Cell | $R_{BG}$ | GTI time |  $ibg_{52}$ start |  $ibg_{52}$ end |  $hrej_{52}$ start |  $hrej_{52}$ end |  $ibg_{lib}$ norm.
---|---|---|---|---|---|---|---
($ibg,hrej$) | (c/s) | (ks) | (c/s) | (c/s) | (c/s) | (c/s) | (c/s)
11 | 0.446 | 44.3 | 0.00 | 0.04 | 0.00 | 0.10 | 0.0218
12 | 0.493 | 149.4 | 0.00 | 0.04 | 0.10 | 0.15 | 0.0265
13 | 0.596 | 100.3 | 0.00 | 0.04 | 0.15 | 0.30 | 0.0285
14 | 0.775 | 28.5 | 0.00 | 0.04 | 0.30 | 0.60 | 0.0317
15 | … | … | 0.00 | 0.04 | 0.60 | 10.0 | …
21 | 0.689 | 95.7 | 0.04 | 0.08 | 0.00 | 0.15 | 0.0503
22 | 0.801 | 109.8 | 0.04 | 0.08 | 0.15 | 0.25 | 0.0517
23 | 0.855 | 71.4 | 0.04 | 0.08 | 0.25 | 0.35 | 0.0527
24 | 1.008 | 67.5 | 0.04 | 0.08 | 0.35 | 0.60 | 0.0567
25 | 1.242 | 8.0 | 0.04 | 0.08 | 0.60 | 10.0 | 0.0583
31 | 1.103 | 41.0 | 0.08 | 0.15 | 0.00 | 0.20 | 0.1006
32 | 0.955 | 29.5 | 0.08 | 0.15 | 0.20 | 0.30 | 0.0987
33 | 1.322 | 43.9 | 0.08 | 0.15 | 0.30 | 0.45 | 0.1013
34 | 1.302 | 20.4 | 0.08 | 0.15 | 0.45 | 0.60 | 0.1012
35 | 1.771 | 16.5 | 0.08 | 0.15 | 0.60 | 10.0 | 0.1088
41 | 2.020 | 18.6 | 0.15 | 0.40 | 0.00 | 0.20 | 0.2047
42 | 1.724 | 27.2 | 0.15 | 0.40 | 0.20 | 0.35 | 0.2370
43 | 1.904 | 15.6 | 0.15 | 0.40 | 0.35 | 0.50 | 0.2128
44 | 2.414 | 20.6 | 0.15 | 0.40 | 0.50 | 0.65 | 0.2314
45 | 2.673 | 16.9 | 0.15 | 0.40 | 0.65 | 10.0 | 0.2318
51 | 2.683 | 8.6 | 0.40 | 1.00 | 0.00 | 0.25 | 0.5002
52 | 2.763 | 20.1 | 0.40 | 1.00 | 0.25 | 0.40 | 0.5659
53 | 3.293 | 10.0 | 0.40 | 1.00 | 0.40 | 0.60 | 0.6039
54 | 4.446 | 7.5 | 0.40 | 1.00 | 0.60 | 0.80 | 0.7110
55 | 4.288 | 9.3 | 0.40 | 1.00 | 0.80 | 10.0 | 0.5986
61 | 4.527 | 7.3 | 1.00 | 3.00 | 0.00 | 0.25 | 1.4975
62 | 6.080 | 13.0 | 1.00 | 3.00 | 0.25 | 0.40 | 1.7515
63 | 6.644 | 4.9 | 1.00 | 3.00 | 0.40 | 0.63 | 2.0238
64 | 7.604 | 11.4 | 1.00 | 3.00 | 0.63 | 0.85 | 1.6836
65 | 11.644 | 7.7 | 1.00 | 3.00 | 0.85 | 10.0 | 2.1318
71 | … | … | 3.00 | 10.00 | 0.00 | 0.25 | …
72 | 9.944 | 2.5 | 3.00 | 10.00 | 0.25 | 0.40 | 3.8110
73 | 16.477 | 3.4 | 3.00 | 10.00 | 0.40 | 0.70 | 5.2374
74 | 15.311 | 2.9 | 3.00 | 10.00 | 0.70 | 0.90 | 3.6876
75 | 17.046 | 4.4 | 3.00 | 10.00 | 0.90 | 10.0 | 4.3715

Before proceeding to complete the stage 1 library spectra, we examine the
distribution in $R_{BG}$ that is found in each cell, as seen in the upper
panel of Fig. 4. Only the 1991 GTIs sorted for ISS-night conditions (see Table
1) are included here. Cells are noted by bin value, [$ibg:i=1-7,hrej:j=1-5$],
and we use the cell number plus the fractional order of membership within a
given cell to create an artificial horizontal axis that stretches out the data
points simply for viewing purposes. Data from cell i,j begin at value
$10*i+2*(j-1)+1$, and the last GTI in the cell is plotted one unit later. For
example, the GTIa in cell 11 are plotted in the range $11<x<12$, while cell 12
has range $13<x<14$, and cell 75 has range $79<x<80$. The larger gaps indicate
the vacant cells, 15 and 71.

Figure 4: top panel: Values of $R_{BG}$, the in-focus and in-band count rate
for the background GTIs, are plotted for each successive cell of the stage 1
library. The cells are counted by their $ibg,hrej$ number, ranging 11 to 75.
The cell id numbers and their ordinal number within the cell are used to
stretch out the points along the x-axis (see text). The dashed line shows the
high-rate filter that clips the brightest outliers to be excluded when
computing the library spectra. bottom panel: Reduced chi square values for
each cell, after filtering out the high points (top panel), assuming that
$R_{BG}$ is constant within each cell. The levels of intrinsic scatter in each
cell are $20-40$ %, motivating a step to normalize each library selection
using the $ibg_{i}$ value of each target spectrum.

Even after filtering out the points above the dashed line in Fig. 4, the
variations in $R_{BG}$ within each cell are much larger than the statistical
uncertainties. This is shown in the lower panel of Fig. 4, where the reduced
chi square value ($\chi^{2}_{\nu}$) are shown for each cell, after the bright
cases are removed, with the assumption that $R_{BG}$ is constant within a
cell. For cell 11, where the lowest $R_{BG}$ rates limit the statistical
precision, we find $\chi_{\nu}=8.7$, and $\chi^{2}_{\nu}$ increases for the
cells with higher rates (i.e., better statistics). The rms variations in
$R_{BG}$ within each cell correspond to intrinsic fractional fluctuations in
the range 20–40% of the mean values. This result suggests that the $ibg,hrej$
parameter scheme is far from a deterministic model, and additional background
parameters are likely to be important. These results also motivate the
strategy to normalize the library sections using the $ibg_{i}$ value of a
given source spectrum, to mitigate against the fractional errors of the cell
parents that would be otherwise inherited. Thus, the 3C50 model assumes that
the spectral shape per library spectrum is appropriate, while the
normalization is fine-tuned to the target spectrum at hand.

Figure 5: The stage 1 library for the 3C50 background model consists of these
33 spectra arranged with $ibg$ number (1–7) increasing vertically and $hrej$
number (1–5) increasing to the right. The spectra are substantially brighter
and flatter with increasing $ibg$ cell number (vertical steps), while a more
shallow brightness increase, a stronger soft component at 0.2–4 keV, and
brighter emission lines are seen with increased $hrej$ cell number (left to
right). Cell 11 (lower left) is the closest that the library comes to an
isolation of the cosmic diffuse X-ray background.

We note that for $R_{BG}$ or related quantities of central importance to
background modeling, the exercise represented in Fig. 4 can be conducted for
any hypothetical set of model parameters. Intrinsic variances within cells and
the progression of variances along each parameter axis can quantify how the
cells organize the background measurements with minimal variance, and whether
(from measurement slopes within each cell) the background properties are
divided into a grid with sufficient resolution.

The library spectra are made for each cell after filtering out the data points
that are above the dashed line in the top panel of Fig. 4, to avoid over-
weighting the results by such cases. There is a library spectrum for each
cell, which is simply the sum of all the counts in the selected GTIs of that
cell, divided by the total exposure time. Table 2 quantifies all of the
selection and filtering steps used to construct the 33 spectra for the stage 1
library, using 1947 selected GTIs (of 1991 during ISS night) that are below
the dashed line in Fig. 4. Day and night assignments are made on the basis of
the $nz$ value, as explained in the next Section.

The stage 1 library spectra are displayed in Fig. 5, using a rebinning scheme
that over-samples the XTI resolution uniformly by a factor $\sim 3$. In the
range 0.2–15 keV, the number of combined $PI$ bins is 3 (0.2–2.48 keV), 4
(2.48–6.00 keV), 5 (6.0–12.0 keV) and 6 (above 12 keV). As expected, the
spectra are substantially brighter and flatter with increasing $ibg$ cell
number (vertical steps), and there is an appearance of the Si K–$\alpha$
emission line (1.74 keV) in the highest two levels of $ibg$. With increasing
$hrej$ (i.e., from left to right), there is a more shallow increase in
continuum brightness, a stronger soft component at 0.2–3 keV, and increasing
emission lines indicating fluorescence at 7.47 keV (Ni K–$\alpha$), 9.71 keV
(Au L–$\alpha$), and 11.44 keV (Au L–$\beta$). These changing spectral
features over the surface of the $ibg,hrej$ plane offer some validation for
the utility of choosing those model parameters. The background component tied
to $ibg$ is the main source of the $R_{BG}$ count rate, while the $hrej$
parameter, despite its exclusion from $R_{BG}$ via $PI\\_ratio$ filtering in
the NICER pipeline, signals systematic changes in the spectrum of $R_{BG}$ for
both the continuum shapes and the characteristics of emission lines.

##  4 Second Stage of the 3C50 Background Model

The second stage of the 3C50 background model is required to subtract an
independent soft X-ray component tied to observations during ISS daytime. The
noise in the slow chain ($\sim 3$ c/s per FPM; see Section 1) always creates a
spectral component that is centered near 0.1 keV, and it is usually invisible
at 0.3 keV. However, it was recognized soon after launch that all of the NICER
FPMs exhibit systematically higher levels of this low-energy noise when the
XTI is illuminated by sunlight during the course of the ISS orbit (e.g,
Bogdanov et al. 2019). Optical photons cannot trigger events in the MPUs, as
such, but they liberate Si electrons, causing a number of secondary effects.
The increased detector current, in the presence of optical light, elevates the
undershoot rate (i.e., detector reset rates) and also causes modest changes in
detector gain and spectral resolution. The pipeline’s gain calibration makes
corrections for such effects, while the changes in spectral resolution are
also predictable, again allowing appropriate corrections for science
investigations. However, the spectral broadening of the low-energy electronic
noise can increasingly intrude above 0.2 keV as the optical load becomes more
intense. This is illustrated below in Subsection 4.2. Thus, the tail of the
low-energy noise distribution can encroach on a portion of the in-band source
spectrum during ISS daytime, making it necessary to include a quantification
of this effect in the background model. There is no expected or measured
correlation between excess noise and either $ibg$ or $hrej$, and so we treat
the daytime soft excess as an independent spectral component to be handled in
a second stage of the 3C50 model. When a GTI occurs during ISS daytime, the
derived spectra from model stages 1 and 2 are simply added together to form
the predicted background spectrum.

###  4.1 Third Model Parameter for Soft X-ray Excess during ISS Daytime

Figure 6: The 3C50 model was applied to GTIs of the background observations
using only the stage 1 library. Residuals from this exercise are shown at
0.4–12 keV (top panel) and 0.3-0.4 keV (bottom panel). The plot symbols
distinguish GTIs during ISS night (black cross) and ISS day (red triangle).
The positive residuals during ISS daytime are associated with the seepage of
sunlight into the XTI, which expands the $\sim 0.1$ keV noise component to the
point that it can encroach into the soft X-ray region that is valuable for
NICER science.

The need to correct for low-energy noise in spectra obtained during ISS
daytime is apparent in the residuals found after applying stage 1 (only) of
the 3C50 model to the background spectra. Fig. 6 shows the stage 1 residuals
in two energy bands: 0.4–12 keV and 0.3-0.4 keV. These model residuals should
display an average value of zero, in all bands, if the background model has
completed its job. GTIs during ISS night are plotted with a black cross, and
GTIs during ISS day are plotted with a red triangle. The stage 1 residuals are
plotted versus $R_{BG}$, i.e., the original background rate at 0.4–12 keV. The
horizontal axis is truncated at $R_{BG}=3.0$, covering 89.8 % of GTIs, for a
better view of the details. Residuals in the range 0.4–12 keV (top panel) are
fairly well contained during both day and night. But in the range 0.3–0.4 keV
(bottom panel), a region in soft X-rays that is valuable to NICER science
investigations, the GTIs during ISS daytime show the encroachment of noise.
The vertical axis scale is chosen to be identical in both panels to highlight
the significance of the problem.

To incorporate the effect of the soft X-ray excess during ISS daytime, we
choose to monitor the entire low-energy noise component for the 50 FPMs during
each GTI. The third parameter for the 3C50 background model, $nz$ is defined
as the total count rate in the slow chain in the range 0.0-0.25 keV. The GTIs
chosen for the stage 1 (nighttime) spectral library show a primary
distribution peak in $nz$ at $156\pm 5$ c/s, consistent with the $\sim 3$
c/s/chain target for trigger threshold settings for 50 FPMs (see 1). During
the analyses leading to the 3C50 model, it was determined that the effects of
optical light become measurable at 0.3–0.4 keV only when $nz>200$ c/s. This
value was then used to distinguish day and night categories for background
GTIs in the 3C50 model. Quantification of the relationships between $nz$ and
the soft excess in various energy bands are included in Table 4.

###  4.2 3C50 Library for ISS Daytime

An empirical strategy is adopted to model the soft excess during ISS daytime
with an additional one-dimensional set of spectra that comprise the stage 2
library in the 3C50 model. The stage 2 library captures the mean soft-excess
spectra left behind by stage 1 of the background model, using 12 steps in
value of $nz$, as given in Table 4. This library strategy appears to offer
better performance, compared to alternative efforts to fit the noise component
with a function with broad wings, e.g., a Lorentzian or modified Gaussian.

Table 4: Stage 2 levels and Quantified Soft Excess

Level | Min. $nz_{52}$ c/s | Max. $nz_{52}$ c/s | Normalized $nz_{lib}$ c/s | S0 c/s | S1 c/s | A band c/s
---|---|---|---|---|---|---
01 | 200 | 215 | 202.81 | 0.159 | 0.011 | -0.010
02 | 215 | 250 | 228.52 | 0.264 | 0.022 | -0.004
03 | 250 | 300 | 277.36 | 0.491 | 0.037 | 0.001
04 | 300 | 400 | 346.98 | 2.806 | 0.120 | 0.030
05 | 400 | 500 | 457.51 | 2.091 | 0.141 | 0.007
06 | 500 | 600 | 547.25 | 2.922 | 0.184 | 0.037
07 | 600 | 750 | 683.16 | 5.032 | 0.307 | 0.019
08 | 750 | 900 | 810.45 | 7.937 | 0.408 | 0.026
09 | 900 | 1100 | 1003.81 | 12.466 | 0.632 | 0.061
10 | 1100 | 1300 | 1198.35 | 31.528 | 1.230 | 0.114
11 | 1300 | 1600 | 1393.30 | 60.267 | 1.901 | 0.132
12 | 1600 | 0 | 1796.66 | 80.318 | 2.493 | 0.173

Note. — The last 3 columns give the soft excess rates per 50 FPMs, and the
energy bands are S0: 0.2–0.3 keV, S1: 0.3–0.4 keV, A band: 0.4–1.0 keV

Starting with 1273 daytime GTIs, we apply two filters before combining the
spectra within the designated levels in $nz$ (see Table 4). Both filters are
intended to reduce systematic problems that would be inherited by the stage 2
library. The first filter limits the input GTIs to moderate count rates, using
$ibg_{52}<0.4$ c/s, which corresponds to the first four $ibg$ levels (of 7) in
stage 1. The second filter excludes cases in which the stage 1 residuals at
2–12 keV (i.e., away from the soft excess) are outside the range $\pm 1.0$
c/s. This condition screens out the GTIs with stage 1 background spectra that
deviate from the predicted one. These filters exclude 137 and 60 GTIs,
respectively. The parent spectra for the stage 2 library then consist of 1076
GTIs, amounting to 83% of the total daytime exposure (see Table 2), divided
into 12 $nz_{52}$ levels, as defined in Table 4.

Figure 7: The stage 2 library for the 3C50 background model consists of 12
spectra that represent the soft excess caused by various levels of sunlight
intrusion into the XTI. These spectra were determined from the residuals of
the stage 1 model for 1076 GTIs during ISS day. The 12 spectra correspond to
different levels in the $nz_{52}$ parameter, which closely tracks the amount
of the optical light leak.

The stage 2 model spectra are shown in Fig. 7. The amplitude and extent in keV
of the soft excess increases with the $nz_{52}$ level, as expected. These
spectra have been smoothed with a 15 PI-bin “boxcar” at energies above 0.4
keV. Above 0.7 keV, the continuum levels are very faint, even at the highest
$nz$ rates (i.e., levels 10–12), where the integrated count rates correspond
to an addition of less than 0.06 c/s to the count rate (i.e., 0.7–12 keV)
during ISS daytime.

The normalization scheme for the stage 2 library selection follows the
practices used for the stage 1 library. For any spectrum ($GTI_{i}$), a user
can select and specify any number of FPMs ($nfpm_{i}$), along with the noise
level $nz_{i}$, that is consistent with $nfpm_{i}$. The stage 2 library
intervals are again based on a standard 52-FPM scale (Table 4), so that a
library selection is based on the value $nz_{52}=nz_{i}*52/nfpm_{i}$. If
$nz_{52}$ corresponds to level $j$ of the stage 2 library, then that spectrum
is selected and re-normalized by a factor, $nz_{i}/nz_{j}$, and then added to
the background prediction in stage 2 of the 3C50 model.

Table 4 also specifies the count rates of library spectra integrated for the
softest NICER bands, $S0$ (0.2–0.3 keV), $S1$ (0.3–0.4 keV), and $A$ (0.4–1.0
keV). The Table quantifies the soft excess that would be suffered if stage 2
of the model were ignored. Stage 2 is therefore a required part of the 3C50
model for studies of faint and soft X-ray sources, including the rotation-
powered pulsars that are the prime targets for NICER, since their count rates
are often $<1$ c/s.

Table 4 can further help to evaluate residual count rates in background-
subtracted spectra for science targets. We retain our conventions for labeling
NICER energy bands, and we use the subscript “net” to indicate count rate
queries applied to background-subtracted spectra. The manner in which noise
events leak into the different energy bands (Table 4) gives some guidance as
to how to use $S0_{net}$ as a quality metric to estimate, per GTI, the likely
level of residual contamination that may be present in $S1_{net}$, which we
want to preserve for science. This is relevant because systematic errors in
the background model can leave behind many more counts in $S0_{net}$, compared
to the X-ray brightness of the target, since the effective area of the NICER
XTI is very low in $S0$ and this band is strongly attenuated by absorption in
the interstellar medium. Depending on the brightness and softness of a given
X-ray target, such filtering steps using $S0_{net}$ can, for example, inform
users as to whether the soft X-ray light curve (e.g., 0.3–2.0 keV) is free
from contaminated GTIs, or when spectral fitting down to to 0.3 keV is likely
to be safe. We offer specific recommendations and examples for filtering
results via the background-subtracted spectra, in part using $S0_{net}$, in 6
and 7, below.

##  5 Model Evaluation

To close the loop on the background observations we apply the full 3C50 model
to all of the 3477 background GTIs that have parameter values within the model
limits. Residual count rates are shown vs. $R_{BG}$ in Fig. 8. The top panel
displays residuals in the in-band energy range ($R_{BGnet}$), and the bottom
panel shows residuals at 0.3–0.4 keV ($S1_{net}$). The night/day observations
are distinguished with a black cross / red triangle, respectively. What can
these residual rates tell us about systematic uncertainty when applying the
3C50 background model? Considering first the in-band residuals (top panel),
the 3C50 model is shown to be most effective when the background count rates
is low. The need to bifurcate the evaluation into high and low count rates is
tied to the pattern of points in the top panel. When $R_{BG}<2$ c/s, which
corresponds to 82% of all background GTIs, then $R_{BGnet}$ has $rms$ value
0.33 c/s. In Sections 6 and 7 below, we show that the quality of these results
can be improved by quality-filtering the background-subtracted spectra in off-
target energy bands. In Fig. 8, the 3C50 model residuals above 2 c/s becomes
more random, losing the population near zero, in marked contrast with the
bottom panel. We interpret this as evidence that an additional model
parameter, which has not been identified, has first-order significance when
the background rate is high. Below, we also provide methods to identify and
filter out some of the GTIs associated with high background rates, to protect
the integrity of NICER science while further studies of the NICER background
go forward.

Figure 8: Final residuals from the application of the 3C50 model to the
background observations, plotted versus the original count rate at 0.4–12 keV,
$R_{BG}$. The horizontal axis is truncated at 5 c/s for clarity; only 6% of
the observations exceed this level. Model residuals are shown at 0.4–12 keV
($R_{BGnet}$, top panel) and 0.3-0.4 keV ($S1_{net}$, bottom panel). The plot
symbols distinguish GTIs during ISS night (black cross) and ISS day (red
triangle).

The bottom panel of Fig. 8 shows very small residuals in $S1_{net}$ during ISS
nighttime (black crosses), but the daytime GTIs have higher residuals,
particularly when the $nz$ rates are high. High residuals in $S1_{net}$ are
matched with much higher residuals in $S0_{net}$, and this provides a method
to use $S0_{net}$ to safeguard $S1_{net}$ or $A_{net}$, taking guidance for
the relationship between noise leaks in $S0,S1,$ and the $A$-band given in
Table 4. Users can screen for problematic GTIs by choosing a maximum tolerable
light leak in $S1_{net}$ or $A_{net}$ for their science, finding that level in
Table 4 : $S1$ or $A$, and then use the corresponding $S0$ value as the filter
criterion for $S0_{net}$ to exclude GTIs that are likely to exceed the chosen
noise limit. Systematic differences within any $nz$ bin in the Stage 2 library
will leave residuals of either sign in $S0_{net}$, $S1_{net}$, and $A_{net}$,
and filtering efforts should mirror the rejection criteria accordingly.

Figure 9: Map of the background observations in Earth longitude and latitude,
with the magnitude of 3C50 model residuals, $R_{BGnet}$, represented in the
symbols type. The c/s ranges and symbols are: $\pm 0.1$ (black “x”); $\pm
1.0$, excluding the previous level (small black triangle); $\pm 2.0$,
excluding previous levels (cyan filled circles); $-5.0$ to $-2.0$ (medium size
magenta square); 2.0 to 5.0 (medium green triangle); $<-5.0$ (large red
triangle); and $>5.0$ (large blue square). The points terminate in latitude at
the inclination of the ISS orbit ($52\deg$). The highest residual count rates
from the 3C50 model reside in the polar horns in the ISS orbit. The region
void of points in the lower-right quadrant is the exclusion zone for the SAA,
and there are no indications of problems near the chosen SAA boundaries.

The origin of GTIs with high background model residuals is revealed in Fig. 9,
where different intervals in $R_{BGnet}$ (see the Fig. caption) are plotted on
a grid of Earth longitude and latitude, using the orbit location at the
midpoint of each GTI. It is clear that the GTIs with the largest residuals
coincide with the polar horns in the ISS orbit. The first two intervals (i.e.,
residuals within $\pm 1.0$ c/s) account for 90% of all GTIs, while the
intervals with largest residuals (1.2% of the total and $|R_{BGnet}|>5.0$ c/s)
are largely (86%) confined to high latitude: $|lat|>42.0\deg$. On the other
hand, the NICER exclusion zone for the SAA (Southern area void of points)
appears to effectively exclude any background-related problems. This exclusion
zone coincides with keyword NICER_SAA = 1 in the pipeline’s information files.

##  6 Practical Considerations for the 3C50 Background Model

###  6.1 Implementing the 3C50 Background Model

The prototype ftool task ”nibackgen3C50” is the recommended tool to run the
3C50 background model. Although not yet formally part of the HEASoft NICER
software suite, it is compliant with NASA HEASARC standards and is supported
by the NICER Guest Observer Facility. There are two time intervals that are
important in the use of nibackgen3C50. The first is the particular
investigation interval for which a predicted background spectrum is desired.
This is driven by the input given to the tool, which is nominally an ObsID,
i.e., the reference number and top level directory for a daily accumulation of
GTIs for a single target. Users can obtain background spectra on timescales
shorter than an ObsID (which generally contains multiple GTIs) by
alternatively inputting the combination of a single unfiltered event file and
GTI file. In either case, one background spectrum is output, per call to
nibackgen3C50. Thus, users who plan to investigate target spectra on
timescales shorter than one day would sort the unfiltered event files (i.e.,
the pipeline’s $ObsID/xti/event_cl/ni*ufa.evt.gz files) into a series of
smaller files with the intended time boundaries and the run nibackgen3C50
sequentially on these files along with their associated GTI files.

The second important time interval is internal to nibackgen3C50, which
generally computes the background in sub-intervals and then provides the
exposure-weighted results in the output file. The sub-intervals may be the
GTIs within the input file, or a shorter timescale directed by the user. Sub-
intervals are never allowed to cross GTI boundaries, since the gaps between
GTIs can be many hours, with a likelihood of different background conditions
on either side of the gap. The background rate systematically varies with the
ISS location in its 93 min orbit. As noted above, NICER GTIs are seldom as
long 2 ks, and a typical monitoring program has an average GTI $\sim$600 s, or
11% of the orbit. As a fraction of the ISS orbit, GTIs are an acceptable
choice for nibackgen3C50 sub-intervals. Shorter intervals are also acceptable,
but below $\sim$100 s, Poisson noise in $ibg$, the parameter that normalizes
the nighttime library selections, can be a concern.

Another option of nibackgen3C50 is the ability to control the FPM selections
by listing the ones to ignore. Then, for each sub-interval, nibackgen3C50
reads the event lists and calculates the average count rates in $ibg$, $hrej$,
and $nz$ for the selected FPMs, scales these rates to the level of 52 FPMs to
make library selections (Tables 3 and 4), normalizes the nighttime library
selection by $ibg/ing_{lib}$ (Table 3), and then, if $nz_{52}>200$, adds the
selected daytime library spectrum, normalized by $nz/nz_{lib}$ (Table 4).
Then, as noted abve, the sub-interval spectra are exposure weighted to produce
the modeled background spectrum. Further information about the control of time
intervals and other command parameters for nibackgen3C50 are available via the
HEASARC NICER tools website
111https://heasarc.gsfc.nasa.gov/docs/nicer/tools/nicer_bkg_est_tools.html,
from where it may be downloaded and locally installed.

Additional implementation notes are as follows. The 3C50 model enforces a
minimum $ibg_{52}$ value of 0.016 c/s, to avoid cases where short intervals
and low $ibg$ rates would lead to occasions when $ibg_{i}$ is zero, and the
background prediction would also be zero, since $ibg_{i}/ibg_{lib}$ is the
normalization factor for the stage 1 contribution to the predicted background.
This lower limit on $ibg_{52}$ was estimated from the distributions in
$R_{BG}$ and $ibg_{52}$ for the 3556 GTIs examined in this study. Finally, the
current version of the nibackgen3C50 tool described above allows for
application of the $hbg_{net}$ quality check, with the user selecting the
maximum allowed absolute value. The $SO_{net}$¡ check is not implemented the
current release, but will be in subsequent releases.

The NICER data archive contains event files that were calibrated with a series
gain solutions, which can be identified by the keyword ”GCALFILE”. Users are
recommended to bring their data sets to a uniform calibration level with the
”nicerl2” tool, using either the calibration used in this paper,
nixtiflightpi20170601v005.fits (2020), or the more recent one
nixtiflightpi20170601v006.fits (2021), for which there are no differences
below 12 keV. The nibackgen3C50 tool attempts to match the GCALFILE in the
input event lists with an appropriate set of library spectra, and 3C50 Model
libraries have been prepared for two previous gain calibrations, governed by
GCALFILEs nixtiflightpi20170601v002.fits (2018) and
nixtiflightpi20170601v004.fits (2019)). By default, if a match cannot be made,
then the user is warned, but a background spectrum is produced using the most
recent model library.

Tables 3 and 4 the details in this Section provide sufficient information
(i.e., cell boundaries, library normalizations, minimum $ibg_{52}$ value, and
GCALFILE issues) for users who wish to download the model library files, which
are a simple directory of standard ”pha” files, and script their own
implementation of the 3C50 background model. The calculation steps would be
the same as those given above in the functional outline of nibackgen3C50, and
the scripts would need to include commands to sort out the events
corresponding to definitions of $ibg$, $hrej$, and $nz$, e.g., using ”fselect”
on the unfiltered and calibrated event lists, given choices of time intervals
and lists of FPMs (”DET_ID”) to exclude. The conversion of the model-parameter
event lists to event rates would complete the assembly of required 3Crp
parameters: $N_{FPM}$, $ibg$, $hbg$, and $nz$, for each time interval needing
a background prediction.

###  6.2 Variations in ibg, hrej, and nz within a GTI

The selection of GTIs to populate the model libraries did not have an explicit
screening step for variations in the values of model parameter within a GTI
(Table 2). We address this issue here. To evaluate the 3C50 parameter values
for each GTI interval, we extracted both the spectra and light curves (1 s
bins) for each parameter. The light curves were routinely used to calculate
the mean ($\mu$), standard deviation ($\sigma$), and the variance in excess of
Poisson statistics ($\sigma_{int}^{2}=\sigma^{2}-\mu$) for each parameter.
Trends with brightness were investigated, and we explored several filtering
criteria and their ramifications.

For $ibg$ and $hrej$, the low values of $\mu$ make it inappropriate to use the
fraction of intrinsic deviations (i.e., sqrt($\sigma_{int}^{2})/\mu$) as a
screening tool. Instead, an ad hoc relationship was favored, with a rejection
criterion: $\sigma_{int}>1.0+0.2\times\mu$. At the lowest count rates (see
Fig. 2), the intrinsic deviations must be above 1 c/s to prompt rejection,
while at the highest rates (i.e., 10 c/s), the intrinsic deviation must be 20%
of the mean rate. Considering all of the GTIs with average parameter values
within the 3C50 model limits, $hrej$ variations fail this test in only 0.8% of
the intervals, while the $ibg$ rejection rate is 5.4%, and this group includes
all of the $hrej$ failures. Furthermore, all but 50 of the $ibg$ failures were
already rejected for library use by other criteria listed in Table 2. These
remaining 50 cases are all among the 183 GTIs in the brightest three levels of
the night library, i.e., in cells 51-75. Rather than exclude these cases, we
concluded that variability in $ibg$ is another characteristic of the high
background conditions that do not fall in line with the 3C50 model.

Variations in $nz$ are an entirely different matter. The count rates are high,
and systematic differences in the response of individual FPMs to the optical
light leak may occur during ISS daytime. The effects of the light leak on the
X-ray spectrum are not the same, at a given FPM-integrated count rate in $nz$,
if the distribution is skewed toward one FPM rather than being more evenly
distributed. The most striking example is FPM #34, which was eliminated from
this study because of its frequent extreme response to ISS daytime. In
practice, it was found that the disparity in FPM noise rates was a more
important issue than the changes in $nz$ within a given GTI. Different
rejection criteria were investigated, using 3C50 model residuals in the S1 and
A bands as the metrics for quality assessment. We adopted the criterion that a
GTI would be excluded from consideration (during ISS daytime) if $FPM_{i}$
with the highest noise rate yields a GTI-average rate $nz_{i}>100$, while
$FPM_{i}$ also contributes more than 15% of the total noise counts. This step
is included in the data selection outline given in Table 2. GTIs that fail
this test were rejected from further consideration , in order to maintain the
strategy to use the same 50 FPMs to build the model libraries. For general
investigations with NICER, users could alternatively choose to excluding the
offending $FPM_{i}$ and recompute the extractions from the event lists for
that GTI with a reduced set of selected FPMs.

###  6.3 Filtering Steps After Background Subtraction to Improve Data Quality

To deal with systematic errors in the background subtraction process, the
strategy was introduced in Section 5 to filter out results on the basis of
residual count rates in spectral bands that are not needed for science. The
energy range for any spectra extracted from cleaned event lists is 0.2–15.0
keV, and in the context of this background investigation, this can be seen as
$S0+S1+A+B+C+D+gap+hbg$, corresponding to energy bands 0.2–0.3 0.3–0.4,
0.4–1.0, 1–2, 2–4, 4–12, a gap, and 13–15 keV. Background-subtracted rates are
expected to be near zero in $S0_{net}$ and $hbg_{net}$, while the other bands
contain the target spectrum to be used for science analyses. Tabulating the
count rates in $S0_{net}$ and $hbg_{net}$ provides a basis for quality
fitering the background modeling process. One can view $hbg_{net}$ as a
quality diagnostic for the Stage 1 background component, while $S0_{net}$ is a
diagnostic for the Stage 2 component.

Three levels of filtering are advised for NICER investigations of targets with
different levels of X-ray brightness. They are detailed below in the sense of
data selections for quality purposes, to be applied to GTIs prior to science
analyses of light curves or spectra. The next Section offers two examples of
this process. The filter levels given below are illustrative, and users should
explore the tradeoffs in coverage versus data quality to decide the optimal
filter criteria that are consistent with the investigation goals and
requirements.

  * •

Level 1 filter selects GTIs with (($-30.0<S0_{net}<30.0)$ c/s &&
$(-0.5<hbg_{net}<0.5$)) c/s. This filter should be applied to even the
brightest X-ray sources.

  * •

Level 2 filter selects GTIs with (($-10.0<S0_{net}<10.0)$ c/s &&
$(-0.1<hbg_{net}<0.1$)) c/s. The level 2 filter is appropriate for moderately
bright sources, e.g., $20.0<R_{net}<300$ c/s. For moderately bright sources
with very soft spectra (e.g., with detections limited to energy below 2 keV),
filter level 2S can additionally impose: $-0.5<D_{net}<0.5$ c/s, where the
D-band (4–12 keV) is given up as an additional background band.

  * •

Level 3 filter selects GTIs with (($-2.0<S0_{net}<2.0)$ c/s &&
$(-0.05<hbg_{net}<0.05$)) c/s. This filter is appropriate for faint sources,
e.g., $R_{net}<20.0$ c/s). For a faint source with a very soft spectrum,
filter level 3S can again impose: $-0.5<D_{net}<0.5$ c/s.

  * •

It has been shown that the majority of GTIs with the highest background rates
and largest model residuals occur in the polar regions of the ISS orbit (Figs.
8 and 9). However, there is no effective way to screen results by orbit
position without incurring significant data losses. To illustrate this, we
define the a group of “bad” model residuals as 153 GTIs (of 3477) with
$R_{BGnet}<-2.0$ or $R_{BGnet}>2.0$ c/s. A broad definition of the polar
region, with latitude $lat<-42\deg$ or $lat>42\deg$, captures 80% of the bad
GTIs. However, only 9.4 % of the polar GTIs are bad, and GTI exclusion on this
basis would be costly. An ad hoc definition of the polar horns can be made
from Fig. 9, using the same polar region with additional constraints for
longitude intervals: $200<lon<320$ (North) and $60<lon<180$ (South). This
region captures 63% of the bad GTIs, but only 19 % of the GTIs are bad.

###  6.4 Model and Filtering Considerations for the Brightest Source

Considerable attention has been paid to the brightest and the softest X-ray
sources observed with NICER, to investigate the effects of source counts on
the background parameters and also the background-subtracted count rates
pertinent to quality filtering. We first consider the the high-energy range of
the spectrum, specifically $ibg$, a 3C50 model parameter (15-18 keV, in-
focus), and $hbg_{net}$ (13-15 keV, in-focus), which used as a data quality
filter. We note that $ibg$ is a raw measurement, while $hbg_{net}$ is a
background-subtracted quantity (subscript ”net”). Both of these energy bands
are outside the imaging effective areas of the concentrator, but there is
still a finite probability that a high energy photon may pass straight through
to the detector, without interacting with the concentrator foils. Thus, it is
relevant to investigate whether any extremely bright X-ray sources may elevate
the count rates of either parameter. Of particular interest are Scorpius X-1,
the brightest X-ray source in the sky (116,000 c/s when normalized to 50
FPMs), the black hole transients, MAXI J1820+070 (65,000 normalized c/s at
maximum) and MAXI J1348-630 (47,000 normalized c/s), and the neutron star
transients with high-mass companion stars (HMXBs) and relatively hard X-ray
spectra, Swift J0243.6+6124 (28,000 c/s at maximum) and A0535+26 (6,000 c/s).
The first three cases are the only targets (2017-2020) for which there was a
commanded reduction of the number of active FPMs, so that the telemetry rate
would remain below the maximum event rate ($\sim$ 30,000 c/s) for the cables
connecting the output of the MPUs to the telemetry stream. For all of these
sources, we find that contamination of $ibg$ is not an issue. Values of $ibg$
are found to be uncorrelated with changes in source intensity, when comparing
these quantities on the GTI timescales. Variations in $ibg$ are dominated by
seemingly random changes in the background conditions, with no evidence of the
outburst profile of the X-ray sources.

However, the impact of these bright or hard sources on $hbg_{net}$ is somewhat
different. After background subtraction, a residual count rate in $hbg_{net}$
is seen in Sco X-1 (up to 1 c/s), and similar residuals are seen for the pair
of bright HMXBs at times of maximum intensity. All of the other bright
transients show $hbg_{net}<0.2$ c/s when the sources are near maximum
intensity. Since the prescription for the level 1 quality filter is to reject
background-subtracted GTIs with $hbg_{net}<-0.5$ or $hbg_{net}>0.5$,
observations would be falsely rejected, at level 1 filtering, for the Sco X-1,
Swift J0243, and A0535-26. The solution to this problem is to either refrain
from filtering these three sources, near times of maximum intensity, or to
predict the NICER background with the ”Space Weather” Model (see Section 9.3),
which has no parameters related to measured count rates. Users of the 3C50
background model are advised to compare the light curves for exceptionally
bright or hard X-ray sources with the light curve of derived $hbg_{net}$
values in order to determine customized filtering values that are appropriate.
Furthermore, the level of filtering should be approached as a function of
source count rate, particularly for transients that NICER observes with more
than 5 magnitudes of dynamic range between intensity maxima and the final
measurements as the source returns to quiescence. The increased susceptibility
to X-rays from bright and hard sources for $hbg$ (13–15 keV), relative to
$ibg$ (15–18 keV), can be understood as a combination of the decreasing
absorption cross section at 13–18 keV in silicon, combined with the decreasing
photon spectrum in that same range, for most X-ray subclasses.

An analogous search was made for target contributions to $nz$, the raw count
at 0.0–0.25 keV, and the filtering parameter, $S0_{net}$, the count rate at
0.2–0.3 keV in the background subtracted spectrum. The investigation included
the same bright sources noted above, plus very soft X-ray transients, e.g.,
MAXI J0637-430 (6,000 c/s at maximum) and the coronal flares in HR1099
(reaching 675 c/s). It was found that the model parameter $nz$ is dominated by
variations in the Sun angle and is not significantly affected by exceptionally
bright or soft source. However, the level 1 filtering condition,
$S0_{net}<30c/s$ is exceeded in the brightest GTIs for four sources: MAXI
J1820, Sco X-1, MAXI J0637, and HR1099. Again, users can suspend data
filtering near times of maximum intensity for these sources, or alternatively
they can use the ”Space Weather” background model (Section 9.3). The
comparison of light curves in $S0_{net}$ versus the broadband source intensity
(0.4 – 12 keV) is a prudent step in the effort to customize filtering and
optimize data quality for exceptional sources.

##  7 Background-Subtracted Light Curves

###  7.1 Observations of the Crab Nebula

The Crab Nebula is commonly used as a bright reference source in X-ray
astronomy. However, the Crab intensity is not truly constant; long term
variations up to 7% were detected in multi-satellite observations (Wilson-
Hodge et al., 2011). NICER observations (with target name “PSR_B0531+21”) over
the interval 2017 August 5 to 2020 April 27 were reprocessed, applying the
same calibrations used for the background fields (Section 2). The query for
GTIs, again using nimaketime while excluding the undershoot/overshoot rate
filters, netted 418 GTIs with duration $>50$ s.

Figure 10: top panel: NICER light curve of the Crab Nebula at 0.3–12 keV,
after background subtraction with the 3C50 model. The plot shows 408 GTIs with
an average exposure of 816 s. The selected sample has a mean: $10531\pm 60$
c/s, and most of the the 0.6% variations can be seen as a gentle 900 day wave
in the light curve. Observations with other satellites are needed to determine
whether these variations in the Crab are real. bottom panel: the Hard Color,
defined as the ratio of count rate at 4–12 keV, relative to that at 2–4 keV.
Measurements have a mean and rms, $0.251\pm 0.001$.

Application of the 3C50 model yielded background predictions for 416 GTIs,
while the remaining two cases had $ibg_{52}$ values that exceeded the model
limits (10 c/s). Count rates were integrated from the background-subtracted
spectra in the range of 0.3–12 keV, and Level 1 filtering was applied (see
Section 6). This filtering step excluded eight GTIs as quality risks, and the
count rates for the remaining 408 are shown in Fig. 10, scaled to 50 FPMs.
These data display mean and rms values: $10531\pm 60$ c/s. In contrast, the
eight filter-eliminated GTIs average $10414\pm 226$ c/s at 0.3–12 keV. Fig. 10
also shows the hard color, which is the ratio of count rates at 4–12 and 2–4
keV (or D/C in terms of energy band labels). The hard color measurements have
a mean and rms, $0.251\pm 0.001$. The hard color results indicate the
photometric precision that can be achieved with NICER spectra, using modest
quality filtering, over the 2017-2020 time interval.

The Crab light curve shows that the 0.6% variations have a systematic temporal
profile that can be seen as a gentle $\sim 900$ d wave in intensity. These
results are not corrected for deadtime, but the latter depends on the total
event rate (all energies and all event flags), and the total event rate for
the Crab varies on an annual timescale, due to the correlation between the
noise rate and the solar angle. Observations of the Crab by other space
missions will help to determine whether the changes in the NICER light curve
are intrinsic to the Crab or arise from systematic factors that have escaped
the current investigation.

###  7.2 Light Curve of 1E 0102.2–7219

The supernova remnant in the Small Magellanic Cloud (SMC), 1E0102.2$-$7219
(hereafter “E0102”), is a faint calibration source that serves as a flux and
spectral line reference for many X-ray instruments (Plucinsky et al., 2017).
The NICER observations from 2017 July 17 to 2020 June 12 netted 965 GTIs with
an average exposure of 438 s. The 3C50 model yielded 941 background subtracted
spectra, while filtering steps (see Section 6) left 916 GTIs at level 1 and
804 GTIs at level 2. We note that the fraction removed by the level 2 filter
(15%) is larger than normal, because E0102 is observed in a wider range of
conditions, as a calibration source, compared to many NICER science targets.

Figure 11: NICER observations of the SNR in the SMC, E0102, yielded background
subtracted spectra with the 3C50 model for 941 GTIs through 2020 June 12,
accumulating 408 ks exposure time. The soft light curve (0.3–2.0 keV)
extracted from all of the GTIs is shown in the left panel, while the same data
with level 2 filtering (804 GTIs, 352 ks) is shown in the right panel (see
Section 6). These measurements have mean and rms: $25.60\pm 0.62$ c/s and
$25.63\pm 0.42$ c/s, respectively, while the rms statistical uncertainty is
0.32 c/s.

Since the source is soft, we examine the background-subtracted light curve in
the range 0.3–2.0 keV. Fig. 11 shows the results for level 1 filtering (left
panel) and level 2 filtering (right panel). The measurements have mean and
rms: $25.61\pm 1.15$ c/s and $25.62\pm 0.41$ c/s, respectively. The average
statistical uncertainty at 0.3–2.0 keV is 0.3 c/s. This demonstrates the
utility in using $S0_{net}$ and $hbg_{net}$ as metrics for filtering GTIs,
sacrificing some amount of temporal coverage to improve quality.

##  8 Background Modeling at 1 s Timescale

The background parameters, $ibg$ and $hrej$, normally have count rates below 1
Hz, and one must integrate for a few hundred seconds to produce an average
value with reasonable statistical precision. However, the occasional surges in
the background rates show corresponding variations in $ibg$ and $hrej$ and the
relationship between these quantities can help to diagnose whether rapid
changes in NICER light curves may originate from either the X-ray target or
the in-band background.

Figure 12: Estimate of the in-band background rate using the relationship,
$R_{est}=2.91*ibg+4.67*hrej$. Each point corresponds to one GTI, and the
equation is determined with a least-squares fit confined to the range
$0.5<R_{BG}<300$ c/s. The dashed line is a reference for the match between
this relationship and the measured rate ($R_{BG}$). The estimator is more
precise at low count rate, showing again the systematic error for the 3C50
model when the background rate is high. Nevertheless, the estimator is an
effective aid to diagnose whether observed variability at short timescales
originates from the target or from activity in the background.

In Fig. 2 it was shown that $ibg$ and $hrej$ are both roughly correlated with
$R_{BG}$, with somewhat different average slopes. This motivates a strategy to
estimate $R_{BG}$ as a linear combination of $ibg$ and $hrej$ with different
coefficients. Using a least-squares fit confined to the range $0.5<R_{BG}<300$
c/s, the best fit relationship is $R_{est}=2.91*ibg+4.67*hrej$, with results
shown in Fog. 12. There is significant scatter in the ability of the
background estimator to predict $R_{BG}$ at high count rates, pointing to the
same problem seen with the 3C50 model residuals (Fig. 8). Nevertheless, the
background estimator might show rapid increases and temporal structure that
resemble the NICER light curve in short time bins, and this would convincingly
implicate the background as the origin of the fast flares.

Figure 13: Application of the 1-s background estimator to two GTIs from
observations of SwiftJ1858 when the source, an X-ray binary system containing
an accreting neutron star, was in a flaring state. The first GTI shows that
the rapid flaring is from the X-ray source (blue), and this behavior has been
observed many times with NICER and other instruments. However, the second GTI
shows a light curve with unusual rapid flaring in the background (red),
demonstrating that this particular sequence of flares is from the background,
rather than the X-ray source.

To illustrate the use of the background estimator, we consider the case of the
X-ray transient source, Swift J1858.6$-$0814 (Krimm et al., 2018), hereafter
“SwiftJ1858”. NICER observations from 2018 November 1 through 2019 November 17
show dozens of GTIs containing fast variability, when the source intensity
ranges from non detectable levels to multiple sharp maxima in the range 100 to
1600 c/s (Ludlam et al., 2018). It was later shown that much of this ”flaring”
is actually driven by variable absorption along the line of sight to a nearly
eclipsing binary system (Buisson et al., 2021). After a data gap imposed by
low Sun angle during the interval MJD $58805-58903$, NICER found SwiftJ1858 to
be in a more conventional state of quasi-steady emission with eclipses and
absorption dips. Then type I X-ray bursts were detected, identifying the
source as an accreting neutron star (Buisson et al., 2020).

Despite the propensity of Swift J1858 to vary rapidly, during the first part
of its outburst, it is necessary to distinguish the few cases in which rapid
flaring originated in the background, rather than the X-ray source. Fig. 13
shows two GTI light curves, in 1 s bins, with contrasting findings regarding
the origin of the fast flares. In both cases, the light curve shown in blue is
the background-subtracted count rate using the 3C50 model with parameters
averaged over the respective GTIs. Values for the background estimator are
shown in red. In the first case (the second GTI on MJD 58426), the background
intensity remains low and quiet, implying that the flares originate in
SwiftJ1858.

In the second case (the second GTI on MJD 58429), the BG estimator show that
the high-amplitude variations coincide with significant activity in $ibg$ and
$hrej$. A precise match is not expected between blue and red curves, since an
effort has been made to background-subtract the blue curve on the GTI
timescale (note the negative values at times before 800 s), and since the
predictability of the background is compromised by systematic error in the
model at high background rates. Nevertheless, it is clear that the second set
of flares originated in the background and not in SwiftJ1858. In this example,
the background flares did occur in the Southern polar horn, during a time
interval with a range in orbit latitude and longitude:
$-51.7\deg<lat<-47.5\deg$ and $79.0\deg<lon<107.2\deg$.

##  9 Discussion

###  9.1 Sensitivity Limits with the 3C50 Background Model

Quantitative analysis of the residuals in a background model, when applied to
observations of blank sky regions, provides information on both the instrument
sensitivity limits and systematic problems regarding model performance. Given
the large range in $R_{BG}$ (Fig. 2) and the limited success of the 3C50 model
when $R_{BG}>2.0$ (Section 5), these topics must be approached with
qualifications. After applying the 3C50 model to 3447 GTIs with model
parameters within limits, the residuals at 0.4–12 keV are within $\pm 0.5$ c/s
in 80% of the GTIs. Applying level 3 filtering criteria (see Section 6), which
excludes 15% of these GTIs, the rms value of $R_{BGnet}$ is 0.40 c/s. This, in
turn, implies a detection limit (3 $\sigma$ in a single GTI) of 1.20 c/s at
0.4–12 keV, which is equivalent to $3.6\times 10^{-12}$ erg cm-2 s-1 at 0.4–12
keV. assuming the spectral shape of the Crab Nebula. In the soft X-ray band,
the corresponding detection limit ($3\sigma$, single GTI) is 0.51 c/s at
0.3–2.0 keV. These limits would improve by a factor of 4 if the exploratory
GTIs for a given target accumulate 10 ks of exposure. We note that the
percentage of GTIs that pass level 3 filtering should exceed 90%, since the
scheduling of science targets would be more favorable than the program to
widely sample the background conditions.

###  9.2 Model Limitations at High Background Rates

Our assessment of the 3C50 model noted evidence of a missing model parameter
that is particularly important at high values of the raw background rate at
0.4–12 keV ($R_{BG}$). The correlation between $R_{BG}$ and $ibg$ implies that
the most of these events are associated with the in-focus component implied by
values in PI_ratio. This is reminiscent of the early Chandra discovery that
protons could scatter off the mirrors and come into focus on the detectors
when the satellite passed through the radiation belt (O’Dell et al., 2010).
The hypothesis that a similar condition is affecting NICER would imply that
the background model should consider the angle between the camera pointing
direction and the local magnetic field lines during the course of the NICER
orbit. Such attention was suggested by Fukazawa et al. (2009) in the
background model for the Suzaku HXD Instrument.

Further motivation to track the camera viewing direction, relative to its
position in the Earth orbit, is provided by a study of an archive of particle
rate measurements built with a series of NOAA polar-orbiting satellites
(Fidani et al., 2010). Since 1998, these satellites have been equipped with
the Space Environment Monitor (SEM-2) system, which contains two sets of
instruments that monitor the energetic charged particle environment above the
Earth. One of these systems, the Medium Energy Proton and Electron Detector,
has two sets of detectors mounted perpendicular to each other. The different
viewing angles produce differential particle fluxes for electrons in the
ranges of both 30-100 and 100-300 keV (see Fig. 1 of Fidani et al. (2010)).
The pitch angle, i.e., the angle between the charged particle flow and the
local magnetic field, varies systematically with the position in low Earth
orbit, suggesting that the particle flux should depend on the longitude,
latitude, the camera angle with respect to the local magnetic field, and the
local pitch angle. This context will be explored further in the effort to link
the direction of particle flow to the in-focus component in the NICER
background.

The limitations of the 3C50 model were first apparent in Fig. 4, where the raw
background rates showed significant variations when binned in model cells for
the nighttime library. This, in part, motivated the strategy to re-normalize
the selected library spectrum for a given GTIi, by the factor
$ibg_{i}/ing_{lib}$. An assessment of the impact of this step can be made by
comparing the residuals with and without the re-normalization step, while
making use of the quality filtering criteria described in Section 6.3. Closing
the loop on the background pointings with (without) $ibg$ re-normalization
leaves residuals that pass level 1 filtering in 93% (88%) of all GTIs, while
passing level 2 filtering 85% (85%) of the time. The conclusion is that $ibg$
re-normalization does provide a modest improvement in the quality of the 3C50
model when the background rate is high.

###  9.3 Comparisons with Parameters of the Environmental Background Model

The “Space Weather” Background Model is an alternative to 3C50 that predicts
NICER background spectra on the basis of the local spacecraft environment
(Gendreau et a. in prep.), and it is implemented in the FTOOL,
“nicer_bkg_estimator”, which is also available via the HEASARC NICER tools
website (prior footnote). The principal model parameters are the local cutoff
rigidity (“COR” ; Smart & Shea (2005)), which is a measure of the shielding
provided by the Earth’s magnetic field, and the $K_{p}$ index, which is a
global measure of disturbances in the magnetic field. The NICER pipeline
furnishes the values of “$COR\\_SAX$”, every second, in the filter files, and
the values of the cutoff rigidity are computed with a particular model
developed for the $BeppoSAX$ Mission (Amati et al., 2002). $COR\\_SAX$
shielding has units in the range $0-17$, while the $K_{p}$ index is given for
each 3 hr interval, with a range $0-6$ quantized in steps of 0.333. Values for
the $K_{p}$ index are obtained from the GFZ site in Potsdam (https://www.gfz-
potsdam.de/en/kp-index/).

The relationship between model pairs for the 3C50 and Space Weather models is
examined in Fig. 14. It is immediately apparent that $hrej$ and $COR\\_SAX$
are measuring the same phenomenon, i.e., the amount of magnetic shielding at
the ISS position is inversely proportional to the rate of spatially extended
events due to particles, as measured with $hrej$. The $COR\\_SAX$ parameter
would be a desirable substitute for $hrej$, in future versions of the 3C50
model, because it is readily accessible in NICER filter files, and it is free
from the statistical accuracy limits that confronts $hrej$, due to its low
count rate.

Figure 14: Relationship between 3C50 model parameters and those of the NICER
Environmental Model. The plot of $hrej$ vs. the cutoff rigidity ($COR\\_SAX$)
is the best correlation seen between any two hypothetical background
parameters in this study. On the other hand $ibg$ and $K_{p}$ pair with their
model partners in different ways.

##  10 Summary

NICER has a comparatively low background rate, typically $10^{-4}$ times the
broad-band count rate of the Crab Nebula, but it is highly variable in both
amplitude and spectral shape. The silicon drift detectors are high-throughput,
but single-channel devices, and so the background spectrum must be predicted
using measurements that are not affected by the targeted X-ray source. The
3C50 model predicts the background spectrum using an empirical approach and
three model parameters. Data analyses are based on recurrent observations of
seven pointing directions that are void of detectable sources. Spectra from a
wide range of observing conditions are sorted by values of the model
parameters to build a two-stage library of spectra that are the core of the
background model. It is noted that most particle hits are automatically
excluded from either the target spectrum or the background model because the
energy of the event trips the overshoot flag, removing such events from
spectral consideration.

Two model parameters, $ibg$ and $hrej$, track background components associated
with particle-induced events. They are distinguished by values of PI_ratio,
which is the ratio of event energies in the fast measuring chain, relative to
the slow chain in the instrument electronics. Values of PI_ratio can
discriminate detector ionization locations near the center of the silicon
drift detector (i.e., events appearing ”in-focus”, from those near the outer
edges of the detector (hence associated with spatially extended events). We
define $ibg$ as the rate of in-focus events at 15–18 keV (beyond the effective
area of the optics), while $hrej$ is the rate of particle events at 3–18 keV
that originate near the outer edges of active silicon, underneath the metal
collimator. A grid of values in these two parameters is used to bin and
average the GTI-based collection of background spectra to form the stage 1
library of the model. Measured values in these parameters for any given target
observation are then used to select a matching library spectrum. That spectrum
is re-normalized by $ibg/ibg_{lib}$ to form the stage 1 prediction of the
NICER background. The third parameter, $nz$ (count rate at 0–0.25 keV), allows
predict of a low-energy excess that is tied to observations conducted in
sunlight, when $nz>200$ c/s. Twelve intervals in $nz$ are used to sort and
average the residual spectra from the stage 1 process, applied to all of the
background observations, to form the stage 2 library of the model. For target
observations, the measured value, $nz_{i}$ is used to select a spectrum from
the stage 2 library. That spectrum is re-normalized by $nz_{i}/nz_{lib}$, and
the result is added to the stage 1 background spectrum to complete the
background prediction.

The small contribution from the cosmic diffuse X-ray background is carried
into the background model by the manner in which the stage 1 library is
constructed. This component is always present in the NICER field of view, and
its inclusion in the 3C50 model is guaranteed by the imposition of a minimum
value for $ibg$, 0.016 c/s. There are no provisions in the model for diffuse
Galactic emission, components local to the Earth or the solar system, or
contaminating sources in the field of view. Such contributions, when
anticipated, must be considered externally.

An examination of 3556 GTIs, with an average duration of 570 s, shows that the
in-band cont rate of good events at 0.4–12 keV, scaled to 50 selected
detectors, has a median value 0.87 c/s. However, the distribution is quite
broad, ranging from 0.33 to 300 c/s, after excluding 1% outliers on each end.
After applying the 3C50 model to 3447 GTIs with model parameters within
limits, the residuals at 0.4–12 keV are within $\pm 0.5$ c/s in 80% of the
GTIs. However, residuals persist at 20–30% of the initial rate for the
brightest cases, which tend to occur in the polar horns of the ISS orbit
(mixed with many quiet GTIs at the same polar locations). The inaccuracy of
the model, when the background rate is high, suggests one or more missing
model parameters. Quality filtering criteria are developed to warn users when
the predicted background spectrum is not likely to be satisfactory. When such
filtering criteria are applied at the level appropriate for faint X-ray
sources, the systematic uncertainty in the model, which is an estimate of the
detection limit, is 1.20 c/s at 0.4–12 keV (3 $\sigma$, for a single GTI), and
0.51 c/s at 0.3–2.0 keV. For a Crab-like spectrum, the detection limit at
0.4–12 keV is equivalent to $3.6\times 10^{-12}$ erg cm-2 s-1. The limiting
count rate in soft X-rays is equivalent to $4.3\times 10^{-13}$ erg cm-2 s-1,
assuming a 100 eV blackbody spectrum, with an ISM column density of $5\times
10^{20}cm^{-2}$. These limits would improve by a factor of 4 if the
exploratory GTIs accumulate 10 ks. The GTIs that pass such filtering criteria
amount to 85% of the total, while higher success rates would be expected for
general targets scheduled more favorably than the background observations.

Under normal conditions, the empirical model’s background predictions are
limited to timescales of minutes or longer, because of Poisson noise in $ibg$
and $hrej$, which often have count rates $<1$ c/s. However, the crude
background estimator, $R_{est}=2.91*ibg+4.67*hrej$, can be applied on
timescales of seconds or less, to help assess whether observations of fast
variability originate in either the source or the background. Background
flares that are associated with significant variations in the raw, in-band
count rate produce momentarily high values of $ibg$ and $hrej$, and the
temporal structure in $R_{est}$ will be highly correlated with the in-band
variations under scrutiny.

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