# Improved background model for the Large Area X-ray Proportional Counter
(LAXPC) instrument on-board AstroSat

H. M. Antia UM-DAE Centre of Excellence for Basic Sciences, University of
Mumbai, Kalina, Mumbai 400098, India<EMAIL_ADDRESS>P. C. Agrawal  Tata
Institute of Fundamental Research (retired), Homi Bhabha Road, Mumbai 400005,
India  Tilak Katoch Tata Institute of Fundamental Research, Homi Bhabha Road,
Mumbai 400005, India  R. K. Manchanda Department of Physics and Astronomy,
University of Southern Queensland, QLD 4300, Australia  Kallol Mukerjee Tata
Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Parag Shah Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai
400005, India

###### Abstract

We present an improved background model for the Large Area X-ray Proportional
Counter (LAXPC) detectors on-board AstroSat. Because of the large collecting
area and high pressure, the LAXPC instrument has a large background count
rate, which varies during the orbit. Apart from the variation with latitude
and longitude during the orbit there is a prominent quasi-diurnal variation
which has not been modelled earlier. Using over 5 years of background
observations, we determined the period of the quasi-diurnal variation to be
84495 s and using this period, it is possible to account for the variation and
also identify time intervals where the fit is not good. These lead to a
significant improvement in the background model. The quasi-diurnal variation
can be ascribed to the changes in charged particle flux in the near Earth
orbit.

Instrumentation: detectors; Space vehicles: instruments

##  1 Introduction

The Large Area X-ray Proportional Counter (LAXPC) instrument aboard the Indian
Astronomy mission AstroSat consists of 3 co-aligned large area proportional
counter units for X-ray timing and spectral studies over an energy range of
3–80 keV (Agrawal, 2006; Yadav et al., 2016; Agrawal et al., 2017). The
detailed calibration of LAXPC instrument, including the background model was
described by Antia et al. (2017, 2021). AstroSat was launched on 28 September
2015 and has completed six years in orbit. Currently, only one LAXPC detector,
i.e., LAXPC20 is working nominally. Because of large size of the detector and
a gas pressure of two atmospheres, the background rate is rather high, being
about 200 c s-1 in LAXPC20. There is also a strong variation in the background
rate during each orbit with the maximum count rate being achieved near the
South Atlantic Anomaly (SAA) passage. A large part of the orbital variation
can be modelled by fitting the count rate as a function of latitude and
longitude of the satellite (Antia et al., 2017, 2021). Apart from this, there
is a quasi-diurnal variation with an amplitude of about 20 c s-1 (Antia et
al., 2021) which is not accounted for by the existing background models. This
limits the effectiveness of background subtraction and hence the sensitivity
of the instrument for faint sources as well as spectral studies at high
energies for relatively bright sources. There is also a long term variation
over the period of 6 years in the background count rate as well as the
amplitude of quasi-diurnal trend.

An alternate background model has been implemented by Misra et al. (2021)
which is applicable only for faint sources and is restricted to the top layer
of the detector. This model is based on the assumption that for faint sources
the counts at high energies are only contributed by the background, which can
be scaled to get the background at low energies. This model is sensitive to
gain shift in the detectors and hence is only applicable to LAXPC20 which has
relatively stable gain. This happens to be the only detector which has been
working nominally after April 2018. This model can account for the quasi-
diurnal trend to some extent, but its applicability is limited to faint
sources and the top layer of the detector. Further, the calibration of this
model has not been updated and hence it doesn’t work so well on recent
observations and in fact the diurnal variation is not removed (Figure 15 of
Antia et al., 2021).

The main difficulty in accounting for the quasi-diurnal trend was that its
exact period was not known. During the initial years the amplitude of this
signal was also smaller. With increasing amplitude of the trend it became more
important to understand this trend. Using more than 5 years of background
observations and satellite orbital parameters, we have now identified the
period of quasi-diurnal variation to be 84495 s, which allows us to remove the
trend effectively and improve the background model.

The rest of the paper is organized as follows: Section 2 gives a summary of
various periodicities in AstroSat orbit so that the observed periodicity in
the background count rate can be identified with some of these. Section 3
describes the determination of periodicity in background count rate using over
five years of background observation. Section 4 describes the application of
this to background model and the resulting improvement. Section 5 gives the
summary of the results.

##  2 The AstroSat orbit

AstroSat has been placed in a nearly circular orbit with eccentricity of $\sim
0.001$, altitude of about 640 km and a inclination of about $6^{\circ}$ to the
equator. The altitude has been decreasing slowly with time, resulting in a
slow decrease in the orbital period. During April 2021, the sidereal orbital
period was 5844.38 s, while the period as measured by latitude variation was
5836.57 s, that from longitude was 6269.66 s and the altitude had a period of
5851.71 s. The frequency difference between the latitude and longitude gives a
period of 84494 s. This differs from the sidereal rotation period of the
Earth, 86164 s because of precession of the orbit.

Figure 1: The maximum and minimum altitude during each orbit and the maximum
latitude during each orbit, is shown in the left panel as a function of days
since the launch of AstroSat. The arrows in the top panel mark the times of
AstroSat orbit maneuvers. The right panel shows the same quantities over a
limited time to show the variations on scale of days.

Since the eccentricity of the orbit is very small the rate of precession of
the nodes or the plane of the orbit can be estimated by considering the
perturbation due to gravitational quadrupole moment, $J_{2}$ ($=0.00108$ for
the Earth) to get the precession rate

$\frac{3\pi R^{2}}{Ta^{2}}J_{2}\approx 1.44\times
10^{-6}\;\mbox{rad}\;\mbox{s}^{-1},$ (1)

where, $R$ is the radius of the Earth, $a$ is the semi-major axis of the
satellite orbit and $T$ is the orbital period of the satellite. This gives the
precession period of about $4.36\times 10^{6}$ s. For nearly circular orbit
this is also the period of precession of the orbital plane. Since the maximum
latitude during the orbit is changing with time the orbital plane should be
precessing.

To determine the actual period of precession of AstroSat orbit we examined the
orbital data for over five years and determined the minimum and maximum of
altitude and latitude during each orbit and the results are shown in Figure 1.
The minimum in latitude is not shown as it is almost same in magnitude to the
maximum. The right panel of the figure shows the blowup of the same, which
clearly shows variation on quasi-diurnal period as well as variation on time
scale of order of 50 days. For the maximum latitude these periods averaged
over the last five years are 84496 s and 4363843 s. The latter should be the
precession period. If the corresponding frequency is added to the Earth’s
rotation frequency we get a period of 84496 s, which is close to the frequency
difference between the latitude and longitude periods. This is also close to
the period of quasi-diurnal variation found in the LAXPC background. The three
arrows in the figure mark the times when some orbital maneuvers were carried
out. These maneuvers can change the orbital period, but it was found that the
change in the period of quasi-diurnal variation due to the last two maneuvers
is less than 1 s and hence is not considered. We have not considered the
period before April 4, 2016, when the first maneuver was performed as that
would have changed the period significantly and we do not have enough data
before that to determine the period accurately. There was also only one long
background observation before this time. It is difficult to model the
background during this initial period as there were some adjustments made to
various parameters in the detector.

While analyzing the orbital data it was discovered that during four periods of
about one day each, there is some anomaly in the orbital data. Since the LAXPC
analysis software relies on the satellite position to determine the time of
Earth occultation and SAA passage these data may not be processed correctly.
The affected observations are listed in Table 1, which also gives the time
interval that is affected in MJD. The data from this period should be rejected
during analysis. The version v3.4 onward of
LaxpcSoft111https://www.tifr.res.in/~astrosat_laxpc (backshiftv3.f) would
issue a warning if these data are processed.

Table 1: LAXPC observations affected by anomaly in orbital data Observation ID | Source | Affected Period (MJD)
---|---|---
20180529_G08_025T01_9000002130 | Cyg X-3 | 58268.25 – 58269.25
20200123_A07_138T09_9000003458 | J164754.90+443345 | 58872.00 – 58873.30
20200910_A09_079T01_9000003864 | CAL 83 | 59103.90 – 59105.00
20210120_A10_123T08_9000004126 | BCD T8 | 59234.95 – 59235.90
20210121_A10_093T01_9000004128 | 2MASS J05215658+4359220 | 59234.95 – 59235.90

With the precession period obtained above, all the periodicities in AstroSat
orbit can be explained. If $f_{A}=1/5844.38$ Hz is the sidereal frequency of
AstroSat orbit, $f_{E}=1/86164$ Hz is the Earth’s rotation frequency and
$f_{P}=1/4363843$ Hz is the precession frequency of AstroSat orbit, the
frequencies, $f_{\mathrm{lat}},f_{\mathrm{lon}},f_{\mathrm{alt}}$ of the
orbital period in longitude, latitude and altitude, respectively, can be
determined as follows:

$\displaystyle f_{\mathrm{lon}}$ $\displaystyle=$ $\displaystyle
f_{A}-f_{E}={1\over 6269.64}\;\mathrm{Hz},$ (2) $\displaystyle
f_{\mathrm{lat}}$ $\displaystyle=$ $\displaystyle f_{A}+f_{P}={1\over
5836.56}\;\mathrm{Hz},$ (3) $\displaystyle f_{\mathrm{alt}}$ $\displaystyle=$
$\displaystyle f_{A}-f_{P}={1\over 5852.22}\;\mathrm{Hz},$ (4)

These values are all close to the observed periods mentioned earlier. Further,

$f_{\mathrm{lat}}-f_{\mathrm{lon}}=f_{P}+f_{E}={1\over 84496}\;\mathrm{Hz}.$
(5)

This is close to the actual frequency difference as noted earlier. As shown in
the next section this is also close to the period of quasi-diurnal variation
in the LAXPC background.

##  3 The period of quasi-diurnal variation in the background

To determine the period of quasi-diurnal variation in the background we use
all background observations after April 4, 2016 covering a stare time of
approximately a day or more. The light curves of all these observations with a
time-bin of 10 s were combined into one time series. Only the Good Time
Intervals (GTI) were considered, which exclude the passage through the South
Atlantic Anomaly (SAA) and when the satellite is pointing to the Earth as the
target location is occulted by the Earth. The dominant variation in the time-
series is due to the orbital period of longitude, which gives the maximum
count rate when the satellite is close to the SAA passage. Apart from this the
quasi-diurnal oscillations are also seen (Antia et al., 2021). To fit both
these periodic variations we fit the combined time series, $c(t)$, to the
function

$c(t)=a_{0}+\sum_{j=1}^{N}\left(a_{j}\cos(2\pi jf_{1}t)+b_{j}\sin(2\pi
jf_{1}t)+d_{j}\cos(2\pi jf_{2}t)+e_{j}\sin(2\pi jf_{2}t)\right),$ (6)

where, $f_{1},f_{2}$ are respectively, the frequencies of the orbital and
quasi-diurnal variations and $N$ is the number of harmonics used in the fits.
The parameters $a_{j},b_{j},d_{j},e_{j}$ and frequencies $f_{1},f_{2}$ are
fitted to minimize the resulting $\chi^{2}$ deviation. $N=5$ was used in the
fits as that was found to be sufficient.

Figure 2: The least square fit to background light curves, showing the reduced
$\chi^{2}$ as a function of the quasi-diurnal period in the bottom panel and
the resulting profile as a function of phase in the top panel. Figure 3: The
light curves for a few selected background observations in LAXPC20 with a
time-bin of 32 s are shown as a function of $\mathrm{mod}(t,84495\;{\rm s})$.
Since the background observations cover a period longer than 84495 s, there is
some time period where multiple values are available.

The resulting least squares fit gives the two periods as 6270.40 s and 84495
s. The statistical errors in the fits were small and hence are not shown. The
value of 6270.40 s is in agreement with the period in longitude. Likewise, the
second period of 84495 s agrees with the period of quasi-diurnal variation in
the maximum of latitude obtained in the previous section. Figure 2 shows the
$\chi^{2}$ value as a function of the quasi-diurnal period and the resulting
profile of diurnal variation. It is clear that there is a very clear minimum
in $\chi^{2}$ giving a reliable estimate of the period of quasi-diurnal
variation. The profile obtained matches with the observed profile as shown in
Fig. 3 which shows the light curves for a few selected background
observations. The time axis in this figure is $\mathrm{mod}(t,84495)$ and it
can be seen that in all cases spanning about 5 years the maximum occurs around
the same phase, thus confirming that the variation has maintained the phase
over the entire duration of AstroSat observations. This can be compared with
Figure 12 of Antia et al. (2021) which shows the light curves for the same
background observations with time measured from the beginning of observation.
That figure naturally shows peak in quasi-diurnal variations at different
times.

From the discussion in the previous section it is clear that this is
essentially the diurnal variation due to the rotation of the Earth. The period
differs from the rotation period of the Earth because of precession of the
AstroSat orbit.

##  4 Improved background model

The observed background light curve for each background observation is fitted
to a function of latitude and longitude to account for the variation during
the orbit. To account for the quasi-diurnal variation an additional periodic
function of time is added in the improved model to get

$c(t)=\sum_{ij}g_{ij}\phi_{i}(\theta)\psi_{j}(\phi)+\sum_{j=1}^{N}\left(d_{j}cos(2\pi
f_{2}jt)+e_{j}\sin(2\pi f_{2}jt)\right),$ (7)

where $\theta,\phi$ are the latitude and longitude of satellite position at
time $t$, $f_{2}$ is the frequency of the quasi-diurnal variation determined
in the previous section and $\phi_{i}(\theta)$ and $\psi_{j}(\phi)$ are the
cubic B-spline basis functions over a suitably chosen knots in latitude and
longitude, respectively. The coefficient $g_{ij},d_{j},e_{j}$ are determined
by a regularized least squares fit (e.g., Antia, 2012) to the observed light
curve. A time bin of 32 s was used in the light curve. The number of
harmonics, $N=5$ is used, which is the same as that used for fitting the
period of quasi-diurnal period in the previous section. In order to cover the
entire range of latitude and longitude, all background observations extend
over a period of more than one day. The Eq. 7 defines the background model
which is implemented in the LAXPC analysis software (laxpcl1.f) which is
available from the LAXPC website222https://www.tifr.res.in/~astrosat_laxpc.
The LaxpcSoft v3.4.2 onward implement the revised background model.

Figure 4: The long term variation in the background count rate after
correcting for gain shift and quasi-diurnal variations in LAXPC10 (left panel)
and LAXPC20 (right panel).

Even after including the quasi-diurnal variation, the background model defined
above does not fit the observed variation (Figure 5) over the entire region.
There is a significant deviation in the few orbits near the maximum in quasi-
diurnal variation, just after the satellite exits the SAA. This region also
shows variation in the spectrum (Antia et al., 2021). Thus in the revised
software a period of 10 min after the exit from SAA in orbits close to the
maximum in quasi-diurnal variation is removed from the Good Time Interval
(GTI). These orbits are determined by the time, $t$ (in sec), of exit from
SAA, which satisfies, $10000\leq{\rm mod}(t,84495)\leq 35000$. The inclusion
of quasi-diurnal variation and the improved definition of GTI leads to a
significant improvement in background model as seen in the following
discussion.

Figure 5: The residuals in the fit to background of LAXPC20 for the two
background observations obtained using the improved background model. The left
panel shows the residuals in the light curve with a time-bin of 32 s. The red
points mark the time interval that is now removed from the GTI. The right
panel shows the residuals in the energy spectrum.

Apart from the orbital and quasi-diurnal variation, the LAXPC background also
shows some long term variation as shown in Figure 4. This figure shows the
average count rate during the background observations corrected for gain shift
and quasi-diurnal variation. It can be seen that the background counts in
LAXPC20 have increased by about 20% over the last 6 years, but the gradient
has reduced since 2019 and the counts are relatively stable during 2020–21.
Figure 5 shows the residuals in the background fit to the light curve and the
spectrum for two representative background observations. This figure can be
compared with Figure 14 of Antia et al. (2021) which shows the results for the
same background observations using old background model. It can be seen that
there is some improvement in the fit to both the light-curve and the spectrum.
It may be noted that the $y$-axis range in the spectrum fit is reduced as
compared to that in the old figure due to significant improvement in the fit.
Since the typical count rate in LAXPC spectrum is 2 c s-1 keV-1, the
difference is less than 1% in all cases. For the February 2017 background
observation it appears that there was no need to restrict the GTI. This is a
special case, while for almost all background observations it is needed to
remove some part of GTI. The reason for this is not clear, but out of about 60
background observations only in 3 cases the GTI adjustment may not be needed.
For the sake of uniformity we have applied this correction to all observations
after 4 April 2016. For earlier observations the GTI correction is not
applied. There is only one long background observation during March 2016 in
this earlier period.

As described by Jahoda et al. (2006) the detector background is expected to be
contributed by (i) the cosmic X-ray background, (ii) charged particle flux in
the local environment (iii) induced radioactivity in the spacecraft.
Simulation of the detector background (Antia et al., 2017) appears to suggest
that the first component is dominant as far as total count rate is concerned.
However, the temporal variations are predominantly caused by the other two
components. The secular long term variation are likely to be from the induced
radioactivity, while the shorter term variations on time-scale of a day or
shorter may be from the charged particle flux in the satellite environment.
This component is likely to be correlated with the geographic position of the
satellite relative to the Earth. As a result, we can expect this variation to
show diurnal variation with the period estimated above. In fact, the region
with high background count rate in LAXPC is correlated to region where the
Charged Particle Monitor (CPM) on board AstroSat (Rao et al., 2017) finds high
count rate. The Proportional Counter Array (PCA) on board the Rossi X-ray
Timing Explorer (RXTE) also appears to show similar variation (Figure 25 of
Jahoda et al., 2006) which has been attributed to the correlation with apogee
precession (Jahoda et al., 2006). Similarly, the Large Area Counter (LAC) on
board Ginga also shows similar variations (Hayashida et al., 1989). This
appears to be similar to what we find in the LAXPC detector. The orbital
parameters of Ginga/LAC, RXTE/PCA and AstroSat/LAXPC are quite different.
Ginga and RXTE had higher orbital inclination of $31^{\circ}$ and $23^{\circ}$
(Jahoda et al., 1996), respectively, while AstroSat is in near equatorial
orbit with an inclination of $6^{\circ}$. The Ginga orbit also had a higher
eccentricity with altitude ranging from 517 km to 708 km. Similarly, RXTE
altitude ranged from 580 km just after launch to 490 km at the end of
operation. While AstroSat altitude is in a narrow range of 630 km to 650 km
(Figure 1). AstroSat passes through the northern end of SAA where the charged
particle flux is order of magnitude or more lower than that for latitudes of
$15^{\circ}$ to $30^{\circ}$, traversed by Ginga and RXTE. As a result, we
would expect the induced radioactivity in AstroSat to be much lower than that
in Ginga or RXTE. The short term variations in the background rates of LAC,
PCA and LAXPC are therefore, expected to show some differences, but the basic
features of the background are the same. The short term variations in LAC and
PCA have been modelled using induced radioactivity. For LAXPC we have been
able to model most of the variation by treating the count rate as a function
of latitude and longitude, supplemented by a diurnal variation. The remaining
part in a few orbits is discarded from the GTI as that shows a rather large
deviation, which has significant variation on long time-scales.

Figure 6: The position of 30 keV peak in the calibration source as a function
of time since 20 March 2017, just after the last adjustment of HV. The solid
line shows a straight line fit to the data.

Another improvement is made in applying the gain shift to the background
spectrum to match that in the source spectrum. This was done using the
measurement of gain obtained from the calibration source in veto anode A8. It
was found that apart from a steady linear trend the gain also has some
fluctuations of the order of 2 channels (out of 1024). If the calculated gain
shift is not correct it can introduce some features around 30 keV where there
is a prominent peak in the background spectrum due to Xe K florescence. To
improve the situation for LAXPC20 data taken after 1 April 2017 (after the
last HV adjustment in the detector on 16 March 2017) the gain is fitted to a
straight line and gain shift between the background and source spectrum is
calculated using this fit. Figure 6 shows the peak position of 30 keV line in
LAXPC20 after the last adjustment and the straight line fit to it. The fit
gives a variation of 1 channel in the peak position in about 150 days. Since
typical separation between the background and source observations is less than
one month, it gives a shift of less than 0.2 channels in most cases, which
should not introduce any artifact. This measure is not applied to older data
and to other two detectors as there the slope of gain change was much larger
and adjustment in HV or gas purification were more frequent (figure 2 of Antia
et al., 2021).

##  5 Summary

The LAXPC background shows a prominent quasi-diurnal variation which was not
accounted for in the earlier background models. Using over 5 years of data the
period of the quasi-diurnal variation is determined to be 84495 s, which is
the diurnal variation corrected for the precession of the orbit.
Identification of this period also made it possible to identify the orbits
where a large deviation was observed just after exit from SAA. After
incorporating this period in the background fit and removing some interval
from GTI, there is a significant improvement in the background model and this
model is incorporated in the latest version of the software.

We acknowledge the strong support from Indian Space Research Organization
(ISRO) in various aspect of instrument building, testing, software development
and mission operation and data dissemination.

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