1School of Pure and Applied Physics, Mahatma Gandhi University, Kottayam
686560, India.
2Inter-University Centre for Astronomy and Astrophysics, Pune 411007, India.
3Indian Institute of Technology, Bombay 400076, India.
4Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, WI, USA
5Ashoka University, Sonipat 131029, India

# Pulsars in AstroSat-CZTI: Detection in sub-MeV bands and Estimation of
Spectral Index from Hardness Ratios

Anusree K.G.1,* Dipankar Bhattacharya2,5 Varun Bhalerao3 and Akash
Anumarlapudi4

###### Abstract

The Cadmium Zinc Telluride Imager (CZTI) onboard AstroSat, an open detector
above $\sim$100 keV, is a promising tool for the investigation of hard X-ray
characteristics of $\gamma$-ray pulsars. A custom algorithm has been developed
to detect pulsars from long integration ($\sim$years) of archival data, as
reported by us earlier. Here we extend this method to include in the analysis
additional $\sim$20% of the CZTI pixels that were earlier ignored due to their
lower gain values. Recent efforts have provided better and more secure
calibration of these pixels, demonstrating their higher thresholds and
extended energy range up to $\sim$1 MeV. Here we use the additional
information provided by these pixels, enabling the construction of pulse
profiles over a larger energy range. We compare the profiles of the Crab
pulsar at different sub-bands and show that the behaviour is consistent with
the extended energy coverage. As detailed spectroscopy over this full band
remains difficult due to the limited count rate, we construct hardness ratios
which, together with AstroSat Mass Model simulations, are able to constrain
the power-law index of the radiation spectrum. We present our results for the
phase-resolved spectrum of PSR J0534+2200 and for the total pulsed emission of
PSR J1513-5908. The recovered photon indices are found to be accurate to
within $\sim 20$%.

###### keywords:

Pulsars: individual (Crab, PSR J0534+2200) (PSR J1513-5908) —Calibration—LAT
pulsars—hard X-ray—CZTI pulsars—hardness ratio—power law —pulsar spectrum

<EMAIL_ADDRESS>
13 April 202223 July 2022

12.3456/s78910-011-012-3 #### 000 0000 1– 1

##  1 Introduction

Rotation powered pulsars usually emit broadband covering radio through
$\gamma$-rays. The geometry of the emission region and the radiation mechanism
in the pulsar magnetosphere shape the pulse profile. However, the nature and
origin of the non-thermal high energy emission still remains unresolved
despite a large variety of theoretical models proposed over the years (Arons
and Scharlemann 1979; Cheng, Ho and Ruderman 1986a,b; Romani and Yadigaroglu
1995; Kirk, Skjaeraasen and Gallant 2002; Dyks and Rudak 2003; Bai and
Spitkovsky 2010; Pétri 2012; Philippov and Spitkovsky 2018 among others). One
reason for the slow progress in this field has been the lack of detailed
broadband observations of a significant population of pulsars at X-ray and
$\gamma$-ray energies. The Fermi mission has been a game changer in the
$\gamma$-ray band, increasing the number of known pulsars from seven to over
270, and this continues to
grow111https://confluence.slac.stanford.edu/display/GLAMCOG/Public+List+of+LAT-
Detected+Gamma-Ray+Pulsars.

By modelling radio, X-ray, and $\gamma$-ray pulse profiles, important
constraints on the magnetospheric properties of pulsars can be obtained. (e.g.
Seyffert et al. 2011; Pierbattista et al. 2015; Lockhart et al. 2019; Pétri &
Mitra 2020) However, many of the Fermi-LAT $\gamma$-ray pulsars have no radio
counterpart. PSR J0633+1746 (Abdo et al. 2010), PSR J2021+4026 (Lin et al.
2013) and PSR J1836+5925 (Abdo et al. 2013) are some examples. For these
radio-quiet pulsars, the magnetospheric X-ray emission becomes the only
possible source of additional information. Unfortunately, instruments capable
of studying these pulsars in hard X-ray/soft $\gamma$-ray band have been rare.
Most instruments with high timing and spectral resolution, that can conduct
quality observations of known pulsars in this band, would still have to
contend with the low flux levels of the majority of these pulsars, requiring
prohibitively long pointed observations. Such long integrations, however,
become more feasible with open all-sky detectors where the target objects are
always present in the field of view.

The Cadmium Zinc Telluride Imager (hereafter CZTI, Bhalerao et al. 2017)
onboard India’s first Astronomical Satelite AstroSat (Singh et al. 2014; Paul
2013) becomes an open detector above 100 KeV. We have developed a custom
algorithm that utilizes this property to detect pulsars, thus turning CZTI
into a promising hard X-ray pulsar monitor. A demonstration of this via the
detection of the Crab Pulsar from off-axis CZTI observations has been
presented by (Anusree et al. 2021).

The spectra of pulsars detected by Fermi-LAT in the $\gamma$-ray band (100
MeV-300 GeV) are usually described by a power-law with a high energy cutoff,
with the power-law photon indices lying in the range 0 to 2.04 (2PC Catalog,
Abdo et al. 2013). To understand whether the underlying non-thermal emission
continues to lower energies, determining the spectral properties at hard
X-rays is crucial. While we can recover hard X-ray profiles of pulsars in
CZTI, detailed spectroscopic analysis is rendered difficult by the strong
background in the open detector.

A crude estimate of the spectral slope may, however, be obtained from the
hardness ratio, namely the ratio of counts in two chosen energy bands. A
simple relation222https://asd.gsfc.nasa.gov/Craig.Markwardt//bat-cal/hardness-
ratio/ between the hardness ratio and power-law photon index has been derived
for the Swift-BAT instrument, using its pre-launch response matrix. We develop
this idea to establish a similar relation for off-axis CZTI observations, and
apply it to the hard X-ray pulsars detected by the instrument. We utilise
instrument responses derived from AstroSat mass model simulations (Mate et al.
2021) in the spectral fitting package XSPEC (Arnaud 1996) to predict photon
index values from hardness ratios measured in CZTI.

This work also uses the new calibration results of the low-gain pixels in
CZTI, discussed in Chattopadhyay et al (2021). This extends the detection of
pulsars in CZTI into sub-MeV bands. The Crab pulse profile has a well-
characterized energy dependence (Kuiper et al. 2001; Tuo et al. 2019). We
obtain the Crab pulse profile up to 1 MeV from the low-gain pixels. To verify
the new gain values of these pixels, we show that the observed ratios of the
counts at the two pulse peaks and at the bridge are consistent with the
literature.

This paper is structured as follows. Section 2 and 3 describe the data
analysis and methodology. Following a discussion of results in section 4,
which includes validating the new gain values of low-gain pixels and the
extension of detection in CZTI up to $\sim$1 MeV, we verify the photon index
prediction from hardness ratios using the Crab pulsar. We also estimate with
$\sim$80% accuracy the photon indices of canonical soft $\gamma$-ray pulsars
PSRJ1513-5908 and PSR J0835-4510. Finally, we show that the estimation of
photon index can be extended up to $\sim$1 MeV energies with proper
calibration of low-gain pixels.

##  2 Data & Background

This work is based on data from AstroSat-CZTI pointing observations released
for public use on or before 30th July 2020. The rotational parameters of the
pulsars under study have been obtained from the Timing programme pursued by
the Fermi mission. A part of the work utilizes AstroSat Mass Model
simulations. Information about the data and the analysis methods are described
in this section. Also discussed are the limitations and the scope of the
method in the present context.

###  2.1 AstroSat-CZTI

The CZTI instrument has four identical but independent quadrants. Each
quadrant consists of sixteen 40 mm × 40 mm × 5 mm sized CZT detector modules,
each further segmented into 256 pixels. A total of 16384 pixels results in a
total collecting area of $\sim$1000 cm2. The design and the function of the
payload are described in detail in Bhalerao et al (2017) and Rao et al (2016).
Primarily designed for imaging and spectroscopy up to 200 keV with $\sim
5^{\circ}$ field of view, the instrument becomes progressively transparent
above $\sim$60 keV and acts as an all-sky open detector above $\sim$100 keV.
Other than for detection of Pulsars as demonstrated in (Anusree et al. 2021),
this property of the instrument has also been utilized for the detection of
many Gamma Ray Bursts (Rao et al. 2016; Chattopadhyay et al. 2019).

###  2.2 Detection of Hard X-ray Pulsars

While CZTI makes pointing observations of a target in the main field of view,
photons from hard X-ray sources present elsewhere in the sky penetrate through
the walls and are recorded in the detector. This way, since the launch of
AstroSat, hard X-ray data has been continuously accumulating in the CZTI
archive for more than half a decade. Photons from a pulsar arrive at the
detector, modulated by its spin period. Availability of precise timing
ephemeris makes it possible to recover the pulse profiles from the CZTI
archival data. We use the ephemerides of LAT pulsars generated by Fermi Timing
programme (Ray et al. 2011; Kerr et al. 2015; Clark et al.2017) in conjunction
with the Tempo2 software package (Hobbs et al. 2006) to generate polynomial
coefficients (Polycos) describing the timing model of each pulsar. We have
developed an algorithm to fold both $\gamma$-ray and X-ray events using the
Solar System Barycentre Polycos. This algorithm can be used for data with gaps
from any X-ray mission. More details of this method and its validation are
described in Anusree et al (2021). We use the same method for obtaining all
the pulse profiles in this work. The spin ephemeris of pulsars derived from
Fermi observations and used in this work are listed in Tables 1 and 2
respectively for PSR J0534+2200 and PSRJ1513-5908, along with the reference
epochs.

Table 1: Fermi-LAT $\gamma$-ray timing solution of PSR J0534+2200 by Fermi
Timing Observers. The numbers in parentheses denote $1\sigma$ errors in the
parameters

.  Parameters Right ascension, $\alpha$ 05:34:31.94 Declination, $\delta$
+22:00:52.1 Valid MJD range 54686-58767 Pulse frequency, $f~{}(s^{-1}$
29.7169027333 (0.0000148379) First derivative , $\dot{f}~{}(10^{-10}s^{-2})$
-3.71184342371 (4.6591493867e-17) Second derivative
,$\ddot{f}~{}(10^{-20}s^{-3})$ 3.3226958153 (1.1931513864e-24) Third
derivative , $\dddot{f}~{}(10^{-28}s^{-4})$ 1.2860657170 (9.2842295751e-32)
PEPOCH 55555 POSEPOCH 50739 TZRMJD 56730.15526586924 Solar system ephemeris
model DE405 Time system TDB

Table 2: Fermi-LAT $\gamma$-ray timing solution of PSR J1513-5908 by Fermi
Timing Observers. The numbers in parentheses denote $1\sigma$ errors in the
parameters

.  Parameters Right ascension, $\alpha$ 15:13:55.62 Declination, $\delta$
-59:08:09.0 Valid MJD range 54240-58647 Pulse frequency, $f~{}(s^{-1}$
6.5970919120 (0.0000000001) First derivative , $\dot{f}~{}(10^{-10}s^{-2})$
-0.6653060108 (1.8154387575e-18) Second derivative
,$\ddot{f}~{}(10^{-20}s^{-3})$ 0.1894558542 (1.1931513864e-24) PEPOCH 55336
POSEPOCH 54710 TZRMJD 55794.106598751587281 Solar system ephemeris model DE405
Time system TDB

###  2.3 Characterization of low-gain pixels

Soon after the launch of AstroSat, nearly 20% of the CZTI pixels seemed to
have an inadequate spectroscopic response (lower gain than expected). These
pixels had since been excluded from scientific analysis. However, a recent re-
calibration of these pixels has quantified their energy response and extended
the energy range of CZTI spectra up to $\sim$1 MeV (Chattopadhyay et al.
2021). As a preliminary experiment, we obtained the Crab pulse profiles using
0.5 Ms of on-axis observations and 10 Ms of archival data where the Crab
pulsar is within 5–70 degrees away from the pointing axis (hereafter off-axis
observations). This was done using both normal pixels and low-gain pixels. The
resulting high signal to noise ratio pulse profiles are shown in Figures 1(a)
and 1(b) respectively.

(a) Mode of Detection : On-axis, Channels :150-512
Profile: Black (normal pixels), Red (low-gain pixels)

(b) Mode of Detection : Off-axis, Channels :150-512
Profile: Purple (normal pixels), Red (low-gain pixels)

Figure 1:  According to Kuiper et al (2001), P2/P1 and Bridge/P1 ratio of Crab
pulsar increase with the increase in energy up to $\sim$1MeV. In CZTI on-axis,
P1 and P2 compared to normal pixels is seen diminishing and growing
respectively, resulting in an increased P2/P1 ratio ($\sim$1.38 in good pixels
and $\sim$1.50 in low-gain pixels) indicating higher energies of low-gain
pixels. In the off-axis case, the pulse profile from both type of pixels are
rather similar and can be attributed to the reduced sensitivity at lower
energies. However, a marginal rise in P2 is observed. The results support the
postulate by Chattopadhyay et al (2021) that the low-gain pixels have higher
energy thresholds than the normal pixels.

One way to verify the new gains of these pixels is by looking at the energy
dependent morphology of the Crab pulse profile. The profile consists of two
pulses P1 and P2, joined by a “Bridge”. In this work, we show that from low-
gain pixels alone, pulse profiles of Crab can be obtained in CZTI sub-bands up
to $\sim$1 MeV and the observed P2/P1 and Bridge/P1 ratios in these bands are
consistent with the literature (section 4.1). With these results, we show that
we can extend the study of pulsars up to sub-MeV energies by including these
pixels.

###  2.4 Response generation from AstroSat Mass Model outputs

A key aspect of spectroscopy with an X-ray instrument such as the CZTI is
estimating the Redistribution Matrix (RMF) and the Auxiliary Response (ARF) of
the detector. We model the energy response (RMF) of each pixel as a Gaussian
spread about the incident energy, with the standard deviation determined from
ground calibration. We estimate the effective area from GEANT4 simulation of
the Astrosat mass model (Mate et al. 2020), in which monochromatic photons at
different energies between 20 keV and 2 MeV are incident and the effective
area as a function of both incident and detected energies is obtained to
generate the ARF. We then estimate the pixel wise detector response by
multiplying the RMF and the ARF. We apply a pixel mask, obtained from in-
flight performance, to include the desired pixels. Our previous work had been
carried out by including only the normal gain pixels at this stage, while in
the current work we extend the same to include the low gain pixels as well. To
the mass model simulation results, we apply appropriate Lower and Upper Level
Discriminators (LLD and ULD) to replicate the actual pixel behaviour. We then
generate the quadrant wise response by summing the responses of the
appropriate pixels.

##  3 Methodology for Estimation of Spectral Index

A Swift-BAT Calibration Note by C. Markwardt and D. Hullinger
333https://asd.gsfc.nasa.gov/Craig.Markwardt//bat-cal/hardness-ratio/
demonstrates that a reasonable estimate of the spectrum of a Gamma-Ray Burst
can be obtained using the hardness ratio, computed as the ratio of counts in
one energy band to that in another, if the incident spectrum is a power-law in
the bands of interest. A simple relation between the hardness ratio and the
power-law index is presented in the note. Here we extend this method to the
CZTI and obtain a calibration relation between the hardness ratio and photon
index of pulsars in the CZTI band (80–200 keV for off-axis observations with
normal gain pixels). We use the Crab pulsar as a test source.
We generate the instrument responses as described in section 2.4 and use them
to find a simple relation between the hardness ratio and the power-law photon
index. In the scenario of multiple directions, we generate an exposure-
weighted response by the weighted addition of responses using Heasoft-FTOOL
addrmf. After generating the response matrix, we use the X-ray spectral
fitting software (XSPEC, Arnaud 1996) to simulate power-law spectra with
photon indices ranging from 0.5 to 3.0, for a hypothetical count rate of 1 and
exposure 10ks. A statistically significant ratio of counts in 80.0-100.0 to
100.0-200.0 band is estimated from 100 such fake spectra. Then we define
photon index as a function of Hardness Ratio by obtaining a simple relation
between the two. This relation is then used to predict the photon index of
pulsars in CZTI by measuring hardness ratios from observed pulse profiles.

##  4 Results and Discussion

This section demonstrates the use of low-gain pixels to study Pulsars in CZTI
and validate the new gains from the re-calibration. We also present the power-
law indices we calculated using the method described in section 3.

###  4.1 Crab Pulse Profiles up to $\sim$1 MeV in low-gain pixels

The energy dependence of the Crab pulse profile has been well known for a long
time. Several models have been constructed over the years in an attempt to
explain the behaviour (e.g. Cheng et al. 2000; Takata et al. 2007; Tang et al.
2008; Bai and Spitkovsky 2010; Pétri 2012; Philippov and Spitkovsky 2018), via
a combination of magnetospheric structure and the position-dependent energy
distribution of electron-positron pairs. However a fully self-consistent
picture from first principles is yet to be developed. We use the
observationally well characterized profile changes of the Crab pulsar with
energy to assess the low-gain pixels in CZTI.

Obtained from the same channels, Figure 1 shows Crab pulse profiles of higher
P2/P1 ratio in low-gain pixels compared to good pixels, indicating that that
the low-gain pixels respond to higher energies. For a more quantitative
verification of the new gains of these pixels obtained from the re-
calibration, we applied it on 20 on-axis and 368 off-axis observations of Crab
to create energy-resolved pulse profiles. In Figure 2, we present energy-
resolved Crab pulse profiles for low-gain pixels up to 1 MeV.

Kuiper et al. (2001) provide a detailed characterization of the pulse profile
of the Crab pulsar over the 0.75–30 MeV band. The P2 and the Bridge emission
intensity increases with increasing energy up to $\sim$1 MeV and above $\sim$1
MeV, P1 dominates P2, and the bridge emission becomes less significant. In
Table 4, we report the P2/P1 ratio and the Bridge/P1 ratio in low-gain pixels
obtained by adopting the phase definitions used by Kuiper et al. (2001) (P1:
0.94-1.04, P2: 0.32-0.43, Bridge/Ip: 0.14-0.25, Off Pulse: 0.52-0.88).
Increasing the integration to 1 MeV resulted in an increased P2/P1 and
Bridge/P1 ratio, agreeing well with the trend seen in Kuiper et al (2001).

A more recent study by Tuo et al. (2019) characterizes the energy dependence
of Crab profile in the 15–250 keV band using the Insight-HXMT mission and
present a lower limit of 1 for the P2/P1 ratio. Adopting their definitions of
peaks, with P1 and P2 as the local maximum of the leading and trailing peak
respectively, we compute the ratio in the 100–1000 keV band in CZTI low-gain
pixels. The ratios thus obtained in CZTI as reported in Table 3 are well above
the lower limit of 1.

We obtained the energy-resolved Crab pulse profile from low-gain pixels, as
shown in Figure.2 which, together with the observed profile characteristics
reported in Tables 3 and 4 verify the higher energy thresholds of low-gain
pixels in CZTI and validates the new gains from re-calibration. We also note
that the P2/P1 ratio is more prominent in the off-axis data than in the on-
axis, consistent with the increased sensitivity to high energy photons in the
off-axis scenario.

Table 3:  P2/P1 ratio of Crab Profile from low-gain pixels in CZTI compared
with corresponding lower limit by Insight-HXMT (Tuo et al. 2019)

E-band | Mode of Detection | P2/P1 (this work)) | P2/P1 (Insight-HXMT) | S/N
---|---|---|---|---
100-1000 keV | On-axis | 1.15$\pm$0.04 |  $>$1 | 58.6
100-1000 keV | Off-axis | 1.32$\pm$0.06 |  $>$1 | 45.0

P1 and P2 here are the local maxima of Peak1 and Peak2 and S/N is the signal
to noise ratio of the pulse profile in CZTI.

Table 4: P2/P1 ratio and Bridge/P1 ratio of Crab Profile from low-gain pixels
in CZTI compared with literature.

E-band | Mode of Detection | P2/P1(this work) | P2/P1∗ | Bridge/P1(this work) | Bridge/P1 ∗ | S/N
---|---|---|---|---|---|---
100-200 keV | On-axis | 1.38$\pm$0.07 | 1.4-1.9 | 0.41$\pm$0.04 | 0.4-0.7 | 42.6
100-1000 keV | On-axis | 1.46$\pm$0.04 | 1.4-1.9 | 0.51$\pm$0.04 | 0.4-0.7 | 39.9
100-200 keV | Off-axis | 1.58$\pm$0.07 | 1.4-1.9 | 0.52$\pm$0.06 | 0.4-0.7 | 23.1
100-1000 keV | Off-axis | 1.66$\pm$0.06 | 1.4-1.9 | 0.65$\pm$0.04 | 0.4-0.7 | 29.7

Here, P2/P1 and Bridge/P1 are the intensity ratios of the profile features
estimated from the background-subtracted counts in respective phase intervals.
S/N is the signal to noise ratio of the pulse profile in respective CZTI
bands.
∗ The range in which P2/P1 and Bridge/P1 ratios increase as energy is
increased from 100 keV to 1 MeV, as observed by Kuiper et al (2001).

(a) Mode of Detection: On-axis

(b) Mode of Detection: Off-axis

Figure 2: The energy-resolved pulse profile of Crab pulsar in low-gain pixels
of all the CZTI quadrants after the gain correction. The increase in P2 and
the bridge emission intensities relative to that of P1 is evident from the On-
axis profiles. A more quantitative discussion of the profile shape, done
towards verifying low-gain pixel gains, is available in Tables 3 and 4

###  4.2 Photon Index from hardness ratios

In order to verify the method, we estimated the power-law index for our test
source Crab as described in Section 3. The results thus obtained are presented
in this section for validation. We also present our results of power-law index
prediction for the pulsar PSR J1513-5908.

####  4.2.1 Phase Resolved Spectra of Crab:

The total pulsed spectrum of Crab is a broken power-law in the 60-200 keV
band, with power-law indices 1.85 and 2.20 with a break around $\sim$130keV
(Ulmer et al. 1995); hence can not be estimated by our method. However, the
phase-resolved spectrum of Crab is consistent with a simple power law. In a
study using INTEGRAL data, power-law fits to the spectrum of selected phase
intervals of Crab profile in the 80-200 keV yield photon indices 2.30 ±0.05,
1.98 ±0.10, and 2.14 ±0.05, respectively, for the phase intervals that define
P1, Bridge/Ip and P2 (Massaro et al. 2006).

For $\sim$1000 ks CZTI observations of Crab pulsar, following the procedure
described in Section 3, we obtained relations between power-law index and
hardness ratios defined by the ratio of counts in the 80.0–100.0 keV band to
those in 100.0–130.0 keV, 100.0–160.0 keV, 100.0–180.0 keV and 100.0–200.0 keV
respectively. In each case, as shown in Figure 3, the relation was described
by a straight line. We then used these relationships to predict the power-law
index describing the phase-resolved spectrum of Crab. The power-law indices
predicted from the hardness ratios observed in the phase intervals for P1, P2,
and Bridge defined by Massaro et al (2006) (P1: 0.98-1.01, P2: 0.38-0.41,
Bridge/Ip: 0.08-0.27, Off Pulse: 0.60-0.80) presented in Table 5 is $\sim$90%
accurate and verifies our method.

(a) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-130\;{\rm keV}}$

(b) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-160\;{\rm keV}}$

(c) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-180\;{\rm keV}}$

(d) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-200\;{\rm keV}}$

Figure 3: Straight line fits to the variation of power-law photon indices with
hardness ratios in good pixels. The hardness ratios are obtained from simple
power-laws simulated using the instrument responses derived from AstroSat mass
model (Mate et al. 2021) in the spectral fitting package XSPEC (Arnaud 1996).
The relations presented here are used to predict the photon indices in Table 5
Table 5: Phase Resolved Spectrum of Crab in CZTI Normal Pixels

Profile Feature of Crab |  a80-100 keV |  b100-130 keV |  c Hardness Ratio |  dPL (Pred.) |  e PL (Ref.)
---|---|---|---|---|---
P1 | 136961$\pm$2450 | 121623$\pm$3230 | 1.13$\pm$0.040 | 2.27$\pm$0.22 | $2.30\pm 0.05$
P2 | 163395$\pm$2450 | 150454$\pm$3230 | 1.09$\pm$0.028 | 2.12$\pm$0.19 | $2.14\pm 0.05$
Bridge/Ip | 217869$\pm$2450 | 200605$\pm$3230 | 1.09$\pm$0.021 | 2.12$\pm$0.18 | $1.98\pm 0.10$
| 80-100 keV | 100-160 keV |  |  |
P1 | 136961$\pm$2450 | 183735$\pm$5145 | 0.75$\pm$0.025 | 2.44$\pm$0.20 | $2.30\pm 0.05$
P2 | 163395$\pm$2450 | 232691$\pm$5145 | 0.70$\pm$0.019 | 2.20$\pm$0.18 | $2.14\pm 0.05$
Bridge/Ip | 217869$\pm$2450 | 311160$\pm$5145 | 0.70$\pm$0.014 | 2.20$\pm$0.17 | $1.98\pm 0.10$
| 80-100 keV | 100-180 keV |  |  |
P1 | 136961$\pm$2450 | 208870$\pm$5784 | 0.66$\pm$0.022 | 2.47$\pm$0.19 | $2.30\pm 0.05$
P2 | 163395$\pm$2450 | 265015$\pm$5784 | 0.62$\pm$0.016 | 2.27$\pm$0.17 | $2.14\pm 0.05$
Bridge/Ip | 217869$\pm$2450 | 360941$\pm$5784 | 0.60$\pm$0.012 | 2.17$\pm$0.16 | $1.98\pm 0.10$
| 80-100 keV | 100-200 keV |  |  |
P1 | 136961$\pm$2450 | 222896$\pm$6287 | 0.61$\pm$0.021 | 2.47$\pm$0.19 | $2.30\pm 0.05$
P2 | 163395$\pm$2450 | 285071$\pm$6287 | 0.57$\pm$0.015 | 2.27$\pm$0.17 | $2.14\pm 0.05$
Bridge/Ip | 217869$\pm$2450 | 388893$\pm$6287 | 0.56$\pm$0.011 | 2.22$\pm$0.16 | $1.98\pm 0.10$

a,b Background subtracted counts in the CZTI bands specified and c is the
ratio of the two
d Power-Law index predicted from observed hardness ratios in CZTI
e Power-Law index obtained using INTEGRAL  data in 80-200 keV band (Massaro et
al. 2006)

####  4.2.2 Photon index of PSR J1513-5908:

PSR J1513-5908, a canonical soft $\gamma$-ray pulsar, is among the 18 hard
X-ray pulsars detected in CZTI off-axis data to date (K.G Anusree et al.
2022b, In Prep.). The total pulsed spectrum of J1513 in the 94.0–240.0 keV
band is well-fit with a simple power-law of photon index of 1.64$\pm$0.40
(Gunji et al. 1994). For a better comparison with the known spectrum, we
obtained CZTI pulse profiles in 94–100 keV and 100-200 keV as shown in Figure
4(b), using archival data spanning $\sim$3 years where the pulsar is within
5–70 degrees of the pointing. In Figure 5, we present the relationship
connecting power-law index and hardness ratio defined as the ratio of counts
in 94.0–100.0 keV band to those in 100.0–200.0 keV band, obtained by the
method described in section 3. The photon index of $1.64\pm 0.58$ reported in
Table.6, predicted from the hardness ratio measured from the profiles in
Figure 5 is consistent with the results of (Gunji et al. 1994).

(a)

(b) Hardness Ratio = $\frac{{\rm counts~{}in}\;94-130\;{\rm keV}}{{\rm
counts~{}in}\;130-200\;{\rm keV}}$

Figure 4: The 94–130 keV & 130–200 keV pulse profiles of PSRJ1513-5908 in good
pixels of all the CZTI quadrants. The photon index predicted from the hardness
ratios obtained from these profiles are shown in Table 6. Table 6: Total Pulse
Spectrum of PSR J1513-5908 in CZTI Good Pixels

Pulsar Name |  a94-130 keV |  b130-200 keV |  cHardness Ratio |  dPL (Pred.) |  e PL (Ref.)
---|---|---|---|---|---
PSRJ1513-5908 | 824904$\pm$71525 | 909280$\pm$83324 | 0.91$\pm$0.11 | 1.64$\pm$0.41 | $1.64\pm 0.40$

a,b Background subtracted counts in CZTI bands specified and c is the ratio of
two
d Power-Law index predicted from observed hardness ratios in CZTI
e Power-Law index obtained using WELCOME data in 94-240 keV band (Gunji et al.
1994)

###  4.3 Photon Index prediction from low-gain pixels

It is clear from Section 4.1 that the inclusion of the low-gain pixels extends
the energy band of CZTI up to $\sim$1 MeV. We repeated the power-law index
prediction for phase-resolved Crab spectra similar to that in Section 4.2.1
but using the low-gain pixels. For this purpose, we generated response
matrices from Mass Model using updated calibration files. We present the
comparison of our results with the well-known spectrum of Crab in Table 7.
With these results, we argue that with proper calibration, the inclusion of
low-gain pixels can extend the power-law index prediction in CZTI up to
$\sim$1 MeV.

(a) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-130\;{\rm keV}}$

(b) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-160\;{\rm keV}}$

(c) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-180\;{\rm keV}}$

(d) Hardness Ratio = $\frac{{\rm counts~{}in}\;80-100\;{\rm keV}}{{\rm
counts~{}in}\;100-200\;{\rm keV}}$

Figure 5: Straight line fits to the variation of hardness ratio with power-law
photon index in low-gain pixels. The hardness ratios are obtained from simple
power-laws simulated using the instrument responses derived from AstroSat mass
model (Mate et al. 2021) in the spectral fitting package XSPEC (Arnaud 1996).
The relations presented here are used to predict the photon indices in Table
7. Table 7: Phase Resolved Spectrum of Crab in CZTI Low-Gain Pixels

Profile Feature of Crab |  a80-100 keV |  b100-130 keV |  c Hardness Ratio |  dPL (Pred.) |  e PL (Ref.)
---|---|---|---|---|---
P1 | 18146$\pm$1128 | 22706$\pm$1176 | 0.80$\pm$0.060 | 2.21$\pm$0.36 | $2.30\pm 0.05$
P2 | 20336$\pm$1128 | 26004$\pm$1176 | 0.78$\pm$0.060 | 2.10$\pm$0.36 | $2.14\pm 0.05$
Bridge | 24565$\pm$1128 | 33012$\pm$1176 | 0.74$\pm$0.040 | 1.88$\pm$0.27 | $1.98\pm 0.10$
| 80-100 | 100-160 keV |  |  |
P1 | 18146$\pm$1128 | 38870$\pm$1678 | 0.47$\pm$0.035 | 2.29$\pm$0.30 | $2.30\pm 0.05$
P2 | 20336$\pm$1128 | 44391$\pm$1678 | 0.46$\pm$0.031 | 2.22$\pm$0.27 | $2.14\pm 0.05$
Bridge | 24565$\pm$1128 | 57839$\pm$1678 | 0.42$\pm$0.023 | 1.94$\pm$0.22 | $1.98\pm 0.10$
| 80-100 | 100-180 keV |  |  |
P1 | 18146$\pm$1128 | 45000$\pm$1845 | 0.40$\pm$0.030 | 2.29$\pm$0.27 | $2.30\pm 0.05$
P2 | 20336$\pm$1128 | 53066$\pm$1845 | 0.38$\pm$0.025 | 2.14$\pm$0.24 | $2.14\pm 0.05$
Bridge | 24565$\pm$1128 | 67717$\pm$1845 | 0.36$\pm$0.019 | 1.99$\pm$0.21 | $1.98\pm 0.10$
| 80-100 | 100-200 keV |  |  |
P1 | 18146$\pm$1128 | 50175$\pm$1849 | 0.36$\pm$0.026 | 2.28$\pm$0.25 | $2.30\pm 0.05$
P2 | 20336$\pm$1128 | 60312$\pm$1849 | 0.34$\pm$0.021 | 2.12$\pm$0.22 | $2.14\pm 0.05$
Bridge | 24565$\pm$1128 | 76759$\pm$1849 | 0.32$\pm$0.017 | 1.97$\pm$0.20 | $1.98\pm 0.10$

a,b Background subtracted counts from low-gain pixels in the CZTI bands
specified and c is the ratio of the two
d Power-Law index predicted from observed hardness ratios in CZTI
e Power-Law index obtained using INTEGRAL  data in 80-200 keV band (Massaro et
al. 2006)

##  5 Conclusion

The CZTI instrument onboard AstroSat, an open detector above $\sim$100 keV, is
a promising tool for studying the hard X-ray properties of pulsars. As
reported earlier, a custom algorithm detects pulsars in the CZTI band from
long integration of the archival data spanning $\sim$years (Anusree et al.
2021). In this work, we have extended this method to include an additional
$\sim$20% of the CZTI pixels that were excluded earlier due to their lower
gain values. A recent re-calibration of these pixels demonstrated higher
thresholds that extend the energy range in CZTI up to $\sim$1 MeV
(Chattopadhyay et al. 2021). One way to verify the corrected gains of these
pixels is to look at the pulse profiles of Crab in these pixels. In this work,
we use the gains of low-gain pixels from re-calibration and recover energy-
resolved pulse profiles of Crab up to $\sim$1 MeV. Also, we calculate from
these pixels the P2/P1 and Bridge/P1 ratios of Crab pulsar at sub-MeV CZTI
bands and verify that the ratios are consistent with the known values. Our
results show that with proper calibration, the inclusion of these pixels can
extend the detection of pulsars in CZTI up to $\sim$1 MeV.

Detailed spectroscopy of these pulsars over the full CZTI band is impossible
due to the limited count rate. We have presented a successful method to
predict the spectrum of pulsars detected in CZTI, assuming the radiation
spectrum is a power law in the CZTI band. Using AstroSat Mass Model
simulations, we calibrate the variation of hardness ratio with power-law index
in CZTI. We then use it to predict the power-law index from the hardness
ratios obtained from actual data. We present our results for the phase-
resolved spectrum of PSR J0534+2200 and the total pulsed emission of PSR
J1513-5908. The recovered photon indices are accurate to within $\sim 20$%.
The results are promising as this enables the comparison of the AstroSat-CZTI
(80.0–200 keV) and Fermi-LAT (0.1–300 GeV) spectrum of LAT pulsars to check
whether the hard X-ray and $\gamma$-ray emission have a common continuum.
Inferences from this work will be used to obtain sub-MeV profiles and
constrain the power-law spectral index of other pulsars using CZTI.

## Acknowledgements

We thank the anonymous referee for comments and suggestions that significantly
improved the paper. This work uses data from the Indian astronomy mission
AstroSat, archived at the Indian Space Science Data Centre (ISSDC). The
instrument CZTI was built by a TIFR-led consortium of institutes across India,
including VSSC, IUCAA, URSC, PRL, and SAC. The Indian Space Research
Organisation funded, facilitated and managed the project. We extend our
acknowledgement to the team members of the CZTI POC at IUCAA for helping with
the aggregation of data. We also thank Fermi Timing Observers Paul Ray and
Matthew Kerr for their timely and favorable response in providing LAT
ephemeris for the pulsars. We thank the HPC facility at IUCAA, where we
carried out all the data analysis. Anusree K. G. acknowledges support for this
work from the DST-INSPIRE Fellowship grant, IF170239, under the Ministry of
Science and Technology, India.

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