Calibration of the Large Area X-ray Proportional Counter (LAXPC) instrument on-board AstroSat

TL;DR

This paper details the calibration process and background modeling of the LAXPC detectors on AstroSat, highlighting their timing capabilities, energy resolution, and effective area for X-ray observations.

Contribution

It introduces a comprehensive calibration and response model for LAXPC detectors, combining ground calibration, simulations, and in-orbit observations.

Findings

Energy resolution of 10-15% at 20 keV

Effective area of about 6000 cm²

Detectors suitable for timing studies

Abstract

We present the calibration and background model for the Large Area X-ray Proportional Counter (LAXPC) detectors on-board AstroSat. LAXPC instrument has three nominally identical detectors to achieve large collecting area. These detectors are independent of each other and in the event analysis mode, they record the arrival time and energy of each photon that is detected. The detectors have a time-resolution of 10 $\mu$s and a dead-time of about 42 $\mu$s. This makes LAXPC ideal for timing studies. The energy resolution and peak channel to energy mapping were obtained from calibration on ground using radioactive sources coupled with GEANT4 simulations of the detectors. The response matrix was further refined from observations of the Crab X-ray source after launch. At around 20 keV the energy resolution of detector is about 10--15\%, while the combined effective area of the 3 detectors is about 6000 cm$^2$.

Tables

Table 1. Table 1: Parameters, e 0 , e 1 subscript 𝑒 0 subscript 𝑒 1 e_{0},e_{1} and e 2 subscript 𝑒 2 e_{2} (Eq.  3 ) for the three LAXPC detectors

Detector	$e_0$	$e_1$	$e_2$
LAXPC10	$-3.46\pm 0.05$	$8.936\pm 0.010$	$-0.00198\pm 0.00010$
LAXPC20	$+0.08\pm 0.10$	$7.564\pm 0.015$	$-0.00267\pm 0.00010$
LAXPC30	$-7.67\pm 0.05$	$9.022\pm 0.015$	$-0.00197\pm 0.00010$

Table 2. Table 2: Pointing direction of each LAXPC detector as determined from the Crab scan and the estimated loss of efficiency due to pointing offset and collimator quality

Detector	RA	Dec	Offset	loss of
	${(}^{\circ })$	${(}^{\circ })$	${(}^{\circ })$	efficiency
Crab source	83.63	22.01
LAXPC10	$83.78\pm 0.01$	$22.01\pm 0.01$	0.15	21%
LAXPC20	$83.63\pm 0.01$	$22.08\pm 0.01$	0.07	25%
LAXPC30	$83.74\pm 0.01$	$22.03\pm 0.01$	0.11	23%
Mean	83.72	22.04	0.09

Table 3. Table 3: Blank sky coordinates observed by LAXPC

Target	RA	Dec	Date	Exposure	Count rate (s-1)
	${(}^{\circ })$	${(}^{\circ })$		(s)	LAXPC10	LAXPC20	LAXPC30
Sky9	237.22	46.92	19 Oct 15	37465	195	205	195
Sky5	57.37	$-47.09$	21 Oct 15	18643	199	186	180
Sky2	136.35	26.46	23 Nov 15	43326	239	197	192
Sky8	236.80	70.35	05 Jan 16	12124	259	190	193
Sky9	237.22	46.92	14 Mar 16	48250	263	201	114
Sky9	237.22	46.92	23 Mar 16	48062	263	205	202
Sky9	237.45	47.26	16 Aug 16	39297	288	210	160
Sky5	57.37	$-47.09$	30 Aug 16	33809	290	212	161
Sky6	77.42	12.42	16 Sep 16	47162	296	212	143
Sky10	321.13	-48.53	16 Oct 16	42760	293	217	137
Sky6	76.13	12.71	03 Dec 16	45812	285	204	150
Sky3	129.32	-27.97	25 Dec 16	36986	280	205	117
Blank Sky	183.47	22.81	23 Jan 17	45312	293	206	130
Sky8	237.33	70.20	13 Feb 17	52701	286	209	129
Blank Sky	183.47	22.81	13 Apr 17	59094	290	191	111
Blank Sky2	180.01	35.19	29 May 17	60314	277	189	094

Table 4. Table 4: Background count rates in LAXPC detectors in different layers and energy bins during March 2016

Layer	Energy bin	LAXPC10	LAXPC20	LAXPC30	Total
	keV	(s-1)	(s-1)	(s-1)	(s-1)
All	All	264	205	202	668
1	All	92.3	68.0	64.5	224.8
2	All	49.5	36.0	35.8	121.3
3	All	31.1	34.0	34.5	99.6
4	All	47.4	33.5	33.9	114.8
5	All	43.7	33.7	33.4	110.8
All	3–20	95.7	34.4	34.9	165.0
1	3–20	35.6	17.0	17.3	69.9
All	20–40	47.5	35.7	38.3	121.5
All	40–80	102	112	107	321
All	3–80	246	184	180	606

Table 5. Table 5: The background count rate in different ULD bins for each detector on 14 March 2016

Detector	ULD-1	ULD-2	ULD-3	ULD-4
	(s-1)	(s-1)	(s-1)	(s-1)
LAXPC10	248	262	275	299
LAXPC20	201	203	214	230
LAXPC30	190	204	217	230

Table 6. Table 6: High voltage adjustments carried out on LAXPC detectors

Detector	operation	Date	Voltage	remarks
			(Volt)
LAXPC10	HV	19 Oct 15	$2369\pm 15$	First ON
LAXPC10	HV	23 Oct 15	$2334\pm 15$	After purification
LAXPC10	HV	24 Oct 15	$2345\pm 15$	After purification
LAXPC10	HV	28 Nov 15	$2331\pm 15$	After purification
LAXPC10	HV	02 Jan 16	$2341\pm 15$
LAXPC10	HV	21 Apr 16	$2328\pm 15$
LAXPC10	HV	27 Jul 16	$2310\pm 15$
LAXPC10	HV	06 Jan 17	$2300\pm 15$
LAXPC10	HV	15 Mar 17	$2290\pm 15$
LAXPC20	HV	23 Oct 15	$2608\pm 15$	First ON
LAXPC20	HV	17 Oct 16	$2618\pm 15$
LAXPC20	HV	15 Mar 17	$2628\pm 15$
LAXPC30	HV	19 Oct 15	$2331\pm 15$	First ON
LAXPC30	HV	23 Oct 15	$2317\pm 15$	After purification
LAXPC30	HV	24 Oct 15	$2321\pm 15$	After purification
LAXPC30	HV	28 Nov 15	$2314\pm 15$	After purification
LAXPC30	HV	02 Jan 16	$2320\pm 15$
LAXPC30	HV	17 Mar 16	$2260\pm 15$

Equations

$$R=\frac{\mathrm{FWHM}(\mathrm{channels})}{\mathrm{Peak}(\mathrm{channels})}\times 100\%.$$

$$E_p=\frac{22.0}{w(E)}E.$$

$$n_c=e_0+e_1{E}_p(1+e_2{E}_p),$$

$$F(\rho )=\sum _{i=1}^5{\left(\frac{O_i-S_i}{O_i}\right)}^2,$$

$$\frac{\mathrm{d}N}{\mathrm{d}E}(E_{\gamma })=87.4E_{\gamma }^{-2.3}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{keV}}^{-1}{\mathrm{sr}}^{-1}.$$

$$F_x(\rho )=\sum _{i=2}^5(r_i-s_i{)}^2,$$

Full text

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., 2016a). AstroSat was launched on September 28, 2015 with 5 major astronomy payloads (Agrawal, 2006; Singh et al., 2014). Apart from LAXPC, these are the Ultra Violet Imaging Telescope (UVIT), Soft X-ray Telescope (SXT), Cadmium-Zinc-Telluride Imager (CZTI) and the Scanning Sky Monitor (SSM). The first four instruments are co-aligned so as to point to the same source. LAXPC instrument is described in detail by Agrawal et al. (2017). The LAXPC detectors have a collimator with about $1^{\circ}\times 1^{\circ}$ field of view. Each LAXPC detector is independent and can operate in event analysis mode where time of arrival of each photon is recorded to a time resolution of 10 $\mu$s giving an unprecedented sensitivity to a wide variety of timing phenomena. The detectors are filled with Xenon-methane mixture at 2 atmospheric pressure and detection volume has a depth of 15 cm, which gives large sensitivity at energies up to 80 keV.

This paper presents details of calibration for LAXPC detectors. The preliminary calibration for the energy scale and energy resolution was carried out in thermovac chamber on ground using radioactive sources. These observations were compared with GEANT4 (Agostinelli et al., 2003) simulation of the detectors to obtain preliminary response matrix, as well as background and field of view. These calibrations were refined by observations of Crab and other known astronomical calibrators after launch.

The rest of the paper is organized as follows: Section 2 gives an overview of the instrument. Section 3 describes ground calibration for energy resolution and energy scale. Section 4 describes the GEANT4 simulations and resulting response matrix. Section 5 describes on-orbit calibration using Crab and Cas A sources. Section 6 describes attempts to characterize the background. Section 7 describes the long term performance of LAXPC detectors in orbit. Section 8 gives the summary of calibration.

2 The LAXPC detectors

The LAXPC instrument consists of 3 nominally identical proportional counters each with a geometric collection area of $100\times 36$ cm2. The detectors are labelled as LAXPC10, LAXPC20, LAXPC30 (LX10, LX20, LX30 in brief). Figure 1 shows a schematic diagram of the LAXPC detector including the collimators and shield. Each detector has 5 anode layers, each of 12 anode cells of size $100\times 3\times 3$ cm. The top two layers are divided into 2 parts with alternate cells connected. These gives 7 main anodes, A1, A2 in the top layer, A3, A4 in the second layer from the top and A5, A6, A7 in the remaining three layers. The main anodes are surrounded on 3 sides with veto cells of thickness 1.5 cm. The veto-anode A9 covers the bottom area ($100\times 39$ cm), while veto-anodes A8, A10 cover the two sides ($100\times 15$ cm). The configuration of anodes is shown in Fig. 2. The two sides ($36\times 15$ cm) perpendicular to the length of the cells do not have any veto anode. The cells are labelled as C1, C2, $\ldots$, C11, C12 from right to left in the figure. Thus the cell C1 is adjacent to the veto-anode A8, while the cell C12 is adjacent to the veto-anode A10.

The entire volume of the detectors, LAXPC10 and LAXPC20 is filled with a mixture of Xenon (90%) and Methane (10%) at a pressure of about 2 atmospheres. The LAXPC30 has a mixture of Xenon (84.4%), Methane (9.4%) and Argon (6.2%) at a pressure of about 2 atmospheres. The reason for using a different gas mixture in LAXPC30 was that after filling the first two detectors it was noticed that the energy resolution at 60 keV was about 13% with the high voltage employed to get the required energy range. Hence it was decided to add a small amount of Argon in LAXPC30 as that is expected to improve the energy resolution (Rao et al., 1987). The low energy threshold is kept at about 3 keV. The top of the detector is sealed by a 50 $\mu$m thick aluminised Mylar window which allows X-rays with energy $>3$ keV to pass through and dictates the low energy threshold of the detectors. Only events with larger energy can trigger the electronics. The Mylar window only covers the active detector volume. The veto-anodes on the two sides are covered by aluminium box and shield and are not expected to get incident photons coming from the top.

The LAXPC detectors are similar to the Rossi X-ray Timing Explorer, Proportional Counter Array (RXTE-PCA) which was launched in 1995 (Jahoda et al., 2006). The main differences are the increased pressure and depth of the detector, which gives high effective area at higher energies ($>30$ keV). At the same time a larger detector volume increases the background in LAXPC, thus making it difficult to study faint sources. Higher pressure in LAXPC also degrades the energy resolution to some extent. Another major difference is the availability of event mode data which gives the arrival time and energy of each photon that is detected. This allows a detailed timing studies for all sources that are observed. Apart from these, there are differences in the nature and distribution of veto layers which may also contribute to differences in the background.

An ADC converts the signal to 10 bits digital form, giving 1024 energy channels. Considering an energy resolution of about 10%, the number of channels can be reduced to 512 or 256 by combining 2 or 4 consecutive channels. This appears to be desirable as the output shows some fluctuations between even and odd channels. These fluctuations are of a few percent in magnitude and the ratio of counts in consecutive channels are independent of time. These can be seen in residuals after fitting the spectrum. For LAXPC10 and LAXPC30, 512 channels are adequate, while for LAXPC20 we need to go down to 256 channels. This truncated range is implemented in the LaxpcSoft software, while other level-2 pipeline software111http://www.tifr.res.in/~astrosat_laxpc/software.html produces 1024 channel output for all detectors.

The Mylar window is supported against the gas pressure by a collimator of height 7.5 cm made of square geometry aluminium cells, termed as the window support collimator. The field of view collimator of height 37 cm is placed above the window support collimator. Both these collimators have aligned gaps with a pitch of 7.0 mm. The field of view collimator has a tin sheet sandwiched between Copper and Aluminium using epoxy. This gives a field of view of about $0.9^{\circ}\times 0.9^{\circ}$. Since aluminium in window support collimator is almost transparent to higher energy X-rays, The field of view increases at high energies as only the field of view collimator of length 37 cm is effective. The detector is covered by a tin shield of thickness 1 mm, coated with Copper (50 $\mu$m) on five sides. On the sides of the detector the cover extends from the bottom to 23 cm above the top of the detector thus covering the lower part of the collimator housing. This shield is effective in cutting off the background from low energy photons and charged particles.

The outputs from the 7 main anodes and 3 veto anodes are fed to 10 Charge Sensitive Pre-Amplifiers (CSPAs). The high voltage is supplied to all main anodes (A1–A7) at the same point and its value is, therefore, the same. The veto anodes have a lower voltage but it cannot be controlled separately. The overall high voltage can be adjusted from ground in appropriate steps. But the high voltage of an individual anode cannot be adjusted. Hence, the gain equalization is achieved by varying the gain of the corresponding CSPA of the anode. This gain equalization is done on ground by matching the 30 keV Xe K-escape peak in background or Am241 source for each individual anode. The CSPA gain cannot be adjusted after launch. The high voltage is switched off when the satellite is passing through the South Atlantic Anomaly (SAA) region.

If more than one anode is triggered within the time resolution, the signal is simultaneously recorded in all these anodes. In order to reject background events the processing electronics is designed to reject any event that satisfies the following criteria:

Any event that triggers any of the veto anodes (A8–A10). 2. 2.

Any event that deposits more than the upper limit of about 80 keV in any anode. 3. 3.

Any event that is recorded in more than two main anodes (A1–A7). 4. 4.

Any event that is recorded in two main anodes (A1–A7) and the energy in both anodes is not in the Xenon K X-rays range covering about 25–35 keV. In this case if energy in any one or both anodes is in the K X-ray range then the event is accepted, energies in the two anodes are added and the event is recorded as a single event of combined energy.

This logic is found to be effective in reducing the background by about 99% (Section 4.4).

Thus the events that are accepted are either single-events where only one main anode is triggered or double-events where two main anodes are triggered but energy in at least, one of them is in the Xe K X-ray range. In both these cases, the energy deposited in these anodes should be below the upper energy threshold. Since the threshold is applied to each anode separately, the double-events can exceed the energy threshold by up to about 35 keV. Further, since the detector response is not linear, the double-events may not be recorded at the same channel as that of a single-event with the same total energy. The lower and upper threshold for Xe K X-ray range can be set remotely for each detector, but it applies to all anodes in a detector.

The energy resolution of detector can degrade with time if impurities accumulate in the gas. On ground this could happen by diffusion through Mylar window, but in the vacuum in space the rate of accumulation of impurities would be small. To take care of impurities, a gas purification system is included in the detector, which may be used from time to time to maintain the energy resolution close to the optimum value.

A System Time Base Generator (STBG) provides a stable and accurate time reference for each of the three LAXPC detectors. The time reference has a resolution of 10 $\mu$s, but has a slow drift. The STBG time is correlated to UTC time from an on-board SPS time to correct for the drift which is of the order of 1 part in $10^{5}$ or about 1 sec in a day. Extensive tests were carried out on ground and the corrected time is found to be satisfactory to the required accuracy even if SPS time is not available for an hour. In practice, SPS time is almost continuously available, thus giving the required timing stability. The STBG also provides time reference for other science payloads on AstroSat.

The LAXPC detectors have two main modes of operation, the Event Analysis (EA) mode and the Fast Counter (FC) mode. In the event analysis mode, which is the default, the timing of each event is recorded along with the information about the anode ID where it is recorded as well as the energy (Channel No.). Each event gives rise to 5 bytes of data. In this mode the dead-time of the detector is estimated to be about 42 $\mu$s (Yadav et al., 2016b). The LAXPC processing electronics is a non-paralysable system, so an event occurring during the dead time since the previous event is simply lost. Thus with an increasing event rate it will reach a saturating rate equal to the inverse of the dead-time. The dead-time was measured on ground using an X-ray gun to give high count rate. The measured count rate from the processing electronics, was compared with that obtained from a commercial MCA (MCA8000A) which gives the dead-time corrected count rate. The dead-time can also be measured by taking a Fourier transform of time series for a bright source, which would give a broad peak close to the inverse of the dead-time in the power spectrum. This can be compared with that expected for a dead-time corrected Poisson level power (Zhang et al., 1995). This yields an estimate of dead-time of around 42 $\mu$s (Yadav et al., 2016b). It is also possible to estimate the dead-time by comparing the observed count rate and the count rate estimated from the slope of $\delta t$ plot which shows the distribution of time-interval between two consecutive events, which should show an exponential behaviour for events with Poisson distribution. This technique also gives a value of about 42 $\mu$s. There is also a smaller dead-time of about 35 $\mu$s associated with rejected events, e.g., those which exceed the Upper Level Discrimination (ULD) threshold or the ones that trigger the veto anode or those that trigger more than two anodes simultaneously.

The event mode operation also generates a Broad-Band Counting (BBC) mode data simultaneously. These data contain counts in a predefined time-bin in four different energy bins in three layers, as well as some other counts for diagnostic purpose. The four energy bins are 3–6 keV, 6–18 keV, 18–40 keV and 40–80 keV. The layer 1 combines anodes A1 and A2, the layer 2 combines anodes A3 and A4, while the layer 3 combines A5, A6 and A7. The time-bin can be set from 16 ms to 2048 ms in steps increasing by a factor of 2, with a default value of 128 ms. Since these counters are 10 or 11 bits deep, they may overflow for bright sources if a time bin size towards the long end of the allowed range in selected. For example, for the Crab the counters may overflow if time-bin greater than 256 ms is used. It may be noted that in all cases the event mode data is always available to get the correct light curve in any energy and time bin. Apart from genuine events the BBC mode also has counters for rejected events, e.g., those exceeding the ULD in the main anodes (A1–A7), or those that trigger veto anodes.

In the FC mode the counts in only the top layer in a fixed time-bin of 160 $\mu$s are recorded in 4 energy bins. In this mode the rejection of events using veto anodes and mutual coincidence is suppressed and all events registered in anodes A1 or A2 are counted. The approximate energy bins are 3–6 keV, 6–8 keV, 8–12 keV, and 12–20 keV. These counters are 8 bit deep. This mode may be useful for bright or flaring sources where the count rate is very high. In this case the dead-time of the detector is about 10 $\mu$s and hence much higher count rates can be recorded.

Apart form these, there is also the Anti-Bypass (AB) mode where the rejection of events through veto anodes is suppressed. This is used for on-board calibration using a radioactive Am241 source which is placed in the veto anode A8. This is used to check the energy resolution and shift in gain. Even in default mode a fraction ($1/128$) of events in veto anodes are recorded and can be used for checking the energy resolution and gain, if sufficiently long observation is available. If the resolution degrades then we can perform purification of detector gas, while the shift in gain can be compensated by a change in high voltage. It is important to keep the gain close to the ground setting to ensure that the double-events are handled correctly. Energy spectrum of background or faint source also shows a peak around 30 keV due to Xe K fluorescence X-rays, which can also be used to monitor shift in gain.

3 Calibration on ground

To obtain the energy resolution and gain of detectors, three radioactive sources at different energies in the range of LAXPC detectors were used. The calibration was performed in a thermovac chamber and measurements were repeated at three temperatures of $10^{\circ}$ C, $20^{\circ}$ C and $30^{\circ}$ C to study the temperature dependence of detector response. The following 3 sources were used:

Fe55 with energy of 5.9 keV: These X-rays are absorbed in the top layer and hence only the two top anodes A1 and A2 register these events. Hence, the anodes A3–A7 are only calibrated using energy beyond 20 keV. 2. 2.

Cd109 with energies of 22.1 keV (54.5%), 21.9 keV (28.8%), 24.9 keV (13.7%) and 88 keV (3.0%): The first two peaks cannot be resolved by the detector, while the third one gives a small feature at the high end of the main peak, which can be fitted with some effort. The last peak is beyond the range of the detector, though because of finite resolution a small low energy tail of the peak, as well as the contribution from double events, or when the Xe K fluorescence X-ray escapes the detector should, in principle, be detected. However, the resulting peak is too weak and was not detected. At 22 keV about 50% of photons are absorbed in the top layer, but there are significant counts in all layers. The ratio of counts in different layers is determined by the gas density and we could use this to estimate the density in each detector, which is required to generate the detector response. 3. 3.

Am241 with energy of 59.6 keV: This source also gives multiple peaks because of loss of energy due to Xe K fluorescence X-rays escaping the detector. The detector logic is built to add contributions in two anodes if at least one of them is in the range of Xe K fluorescence X-rays (25–35 keV). Hence, we get additional peaks at 29.8 keV (due to escape of Xe Kα) and 25.2–26.0 keV (due to escape of Xe Kβ). The Xe Kα X-rays account for about 81% of Xe K X-rays, thus giving a dominant peak at 29.8 keV. The second peak due to Kβ X-rays is barely resolvable with the detector resolution. Apart from these, the 59.6 keV peak is also split into two parts, one coming from single events where all energy is deposited in a single anode, and the second coming from double events where the energy is split between two anodes and the contribution is added by the detector logic. Since the detector gain is not strictly linear, but has a small quadratic term the channel number of a double events does not coincide with that for a single event, but the two peaks cannot be resolved properly, though they can be fitted with some effort. The contribution of single and double events can be separated by analyzing the single and double events separately. Since the quadratic term is negative the single event peak occurs at lower channel as compared to that from double events. The energy resolution of the two peaks are also different. The energy resolution of the double peak is determined by energy resolution at 29.8 keV as dominant component is from two 29.8 keV components. Thus the absolute energy resolution of 59.6 keV double event peak is $\sqrt{2}$ times that for 29.8 keV and the relative energy resolution is $1/\sqrt{2}$ times that for 29.8 keV. On the other hand, the resolution of peak due to single events is much worse as compared to that for double events. By fitting these two peaks around 59.6 keV, it is possible to estimate the quadratic term in the energy to channel number mapping.

To estimate the detector background, the counts are recorded without any source, before and after the source measurements are done. The background count rate is then subtracted from that for the source to get the contribution from the source.

In order to perform the calibration inside the thermovac chamber, an $x$–$y$ motion platform for movement of radioactive sources above the field of view collimator was designed. This can hold all three sources and expose one or more of them at a time. The $x$-$y$ motion platform can function in vacuum and its movements and source on/off status can be remotely controlled. The movement of sources is controlled by a program which moves the source with a predetermined pattern in $x$ or $y$ directions. The pattern was chosen to cover the entire area of the detector over about 2 hours. To study behavior of each cell, in some cases the source was moved along the length of each of the 12 cells.

To check the long term stability of detectors, periodic measurements were made on ground over a period of several months to check for drift in peak channel position. A slow decrease in peak channel with time was found due to accumulation of impurities in gas. The original position was restored when the gas was purified. Similar monitoring is continuing after launch. All detectors were filled with gas by 2011 and no leak was noticed before launch. This will put a limit of less than 0.5% per year for the leak rate before launch for all three detectors.

Apart from energy resolution, the timing characteristics of the detectors were also tested on ground. Fourier transform of the time series did not show any peak at frequencies less than 2 kHz. When strong source from X-ray gun was used the Fourier transform showed peak around 15 kHz which is expected from the dead-time effect. This is confirmed from the observations in orbit (Yadav et al., 2016b). The distribution of the time interval between two consecutive events in the LAXPC detectors follow the expected exponential behavior for Poisson distribution. It also shows a cutoff at 50 $\mu$s, in agreement with the measured dead time.

The operation of Fast Counter (FC) mode was also tested on ground using radioactive sources as well as X-ray gun, and again no peaks were found in the Fourier transform up to the Nyquist frequency of 3125 Hz. The nominal boundary of different energy bins were also tested by comparing the FC mode data with spectrum in EA mode for the same source. The energy bin boundaries were found to be correct to within about 1 keV.

3.1 Energy Resolution of LAXPC

For each of the X-ray lines, from the radioactive sources, the energy resolution $R$ of the LAXPC detector, averaged over the entire area was measured. The energy resolution is defined by

[TABLE]

To estimate the resolution, the observed spectrum for the source is corrected for the background and then fitted to a sum of Gaussian profiles to obtain the peak position and resolution. The observed spectra for the three sources and the background obtained by adding the counts in all anodes (A1–A7) are shown in Figure 3. These spectra were fitted to obtain the peak position and resolution and the results are shown in Figure 4 for three different temperatures and for different detectors at $20^{\circ}$ C.

The background spectrum in Figure 3 shows the lower and upper energy threshold beyond which the count rate drops sharply. On the lower side, it drops to zero below the lower energy threshold as the anodes are not triggered. Beyond the ULD the count rate does not drop to zero as the contribution from double events is still accepted. This is because this threshold is applied separately to each anode and sum of energy in two anodes can exceed the threshold. Thus in principle, LAXPC can detect photons with energies up to about 110 keV, though the efficiency reduces beyond 80 keV as only the double events contribute. From the magnitude of drop around channel 640, it appears that double events account for 25–30% of all events at these energies in the background spectrum.

It can be seen from Figure 4 that the resolution improves as temperature increases, while the peak channel shifts to lower value. In orbit, the temperature of detectors is maintained through heaters and its variation by less than $2^{\circ}$ C, may not be significant. This resolution is calculated when the counts in all anodes are added. If we consider single anode or a single cell in an anode the resolution is better by 1–2%. This is because the gains of all anodes may not be perfectly aligned and the scatter between different anodes broadens the peak slightly. Similarly, the two end cells in each layer (C1 and C12) have a different gain as compared to the middle cells. The difference being about 5% and has to be accounted for while constructing the response matrix. This variation also adds to the width of peaks. Below 20 keV the energy resolution varies as $1/\sqrt{E}$ as expected for a proportional counter (Knoll, 2000).

From the peak channel figure, it appears that the relation between energy and channel number is almost linear. This is misleading, as the peak around 59.6 keV is actually a combination of two peaks which are not resolved in the fit. Similarly, the energy resolution appears to remain flat at high energies, which is also misleading due to compound nature of the 59.6 keV peak. It can be seen that the gains of LAXPC10 and LAXPC30 are similar, but that for LAXPC20 is lower. Further, the gain in C1 cell of anode A4 in LAXPC10 is about 75% of that for other cells and this gives rise to a small second peak on lower energy side (see Figure 7). This difference has to be accounted for while generating the response matrix.

The veto anode A10 in LAXPC10 failed during thermovac test and has been disconnected. As a result, the background in this detector is higher as compared to the other two. After launch, the gain of LAXPC30 has been shifting steadily due to a suspected minor leak. As a result, the high voltage of this detector is periodically adjusted to keep the gain close to ground value.

The count rate was not uniform over the entire area of the detector and variations of a few percent were observed, presumably because of non-uniformity in the collimator. Figure 5 shows the scan over LAXPC10 detector using Fe55 source. The prominent dips at regular intervals are due to the source going outside the detector area during the scan. But there are other smaller dips which are likely to be due to blockages in some collimator cells. The blocked area was found to be less than 1% of scanned area. There were also some fluctuations in the count rate over a time-scale of minutes. These variations are most likely due to non-uniformity in the collimator. Apart from these, there are fluctuations over time scale of 10 s, due to the source crossing collimator cell boundary. These show up clearly in the Fourier transform. Since the radioactive sources are kept just above the collimator, they are expected to illuminate only one or two collimator cells at a time. If the source is moving almost exactly above the boundary of a cell, it can illuminate up to 4 cells simultaneously. As it moves from one cell to the next, a part of the beam will be blocked by the boundary of the cell, thus causing a dip in the counts. From these scans it is difficult to estimate the transmission efficiency of the collimator. This was later estimated in orbit using scan over standard Crab X-ray source.

4 GEANT4 simulation

In order to understand the characteristics of the LAXPC detectors and to construct the response matrix, GEANT4 (Agostinelli et al., 2003) simulations were carried out. For this purpose the basic detector geometry, including the aluminium box, shield, Mylar window and collimators were included to define the detector. Other features like electronics, purification system and the anode and cathode wires inside the detector were not included for simplicity. The advantage of using GEANT4 simulation is that all physical processes describing interaction of charged particles and photons are included and absorption coefficients of all relevant materials are incorporated. Similarly, all particles including secondaries, like photons, electrons, protons, muons etc. are tracked. Further, loss of efficiency due to escape of Xe K and L X-rays is automatically included in the simulations once the anode boundaries are specified. We did not include any dead zone between two anodes where the interaction may not be recorded. The GEANT4 package can deal with particles in energy range of 100 eV to 100 TeV. All secondary particles in this energy range are followed till they interact or go outside the defined volume. Apart from response matrix and efficiency of detector, the simulations were also used to estimate the field of view of the collimator as well as to estimate the background from photons and charged particles.

The simulations typically use $10^{6}$–$10^{7}$ photons, which in most cases were incident perpendicular to the Mylar window at the top. Further, these particles are uniformly distributed over the active detector area. These simulations were tested by comparing the results with observations from radioactive sources described in Section 3.1. For estimating the field of view of the collimator, the photons were assumed to be coming at a small angle to the axis of the detector. To estimate the background, the particles were assumed to be coming isotropically from all directions and were uniformly distributed on all bounding surfaces.

4.1 The detector response and efficiency

In order to approximate the observations of radioactive sources, simulations were carried out with the same distribution of energy as expected from these sources. The simulations yield the energy deposited in each anode cell from any event. The same logic as used in the detector electronics was applied to reject or accept the event. The result was compared with the observed spectrum. Since the absolute strength of the sources were not known, as they were collimated through a small hole in the container and placed over the field of view collimator, the number of events accepted by the simulation in a broad energy band covering the peak were normalized to match the number of counts observed in the same range. Thus the normalization was not a free parameter in the simulation. Once the normalization of the simulated spectrum was fixed, the counts in each anode and channel were compared with observed spectrum.

The voltage pulse in a proportional counter is only approximately proportional to the energy deposited in a given anode, instead the pulse is proportional to the number of electrons produced in the corresponding anode. The observed pulse height is essentially, the number of electrons produced in the gas multiplied by the electronic gain from the proportional counter and the amplifier. To generate the response matrix we need a mapping from the energy deposited to pulse height channel that is recorded. For this purpose, following Jahoda et al. (2006) we define an energy scale, $E_{p}$, proportional to the number of electrons produced, but is normalized such that it is approximately equal to the energy deposited $E$. The average energy $w(E)$ in eV required to produce one ionization electron in Xe is close to 22 eV (Dias et al., 1991, 1993, 1997). It is convenient to define

[TABLE]

The function $w(E)$ is shown in Figure 4 of Jahoda et al. (2006) and has discontinuities at the Xenon K and L edges. As a result of this, the energy to channel mapping may not be monotonic in this region. This function is used in the simulation to calculate $E_{p}$, which is then used to calculate the corresponding channel.

In order to calculate the spectrum of simulated events we need a mapping from energy to channel. This was provided by the observed positions of the peaks in spectra for radioactive sources. We used a quadratic function

[TABLE]

to fix the energy to channel mapping. Here, $E_{p}$ is the effective energy in keV as defined above, and $n_{c}$ is the ADC channel where energy is mapped. The parameters $e_{0}$ and $e_{1}$ are determined by matching the 5.9 keV peak in Fe55 spectrum, the 22.1 keV peak in Cd109 spectrum and the 29.8 keV peak in Am241 spectrum. The parameter $e_{2}$ was determined by fitting the 59.6 keV peak in the Am241. One more iteration was performed by recalculating $e_{0}$, $e_{1}$ with fitted value of $e_{2}$. Since the position of low energy peaks is not sensitive to $e_{2}$ one iteration was found to be sufficient.

Near the absorption edges of Xe the mapping given by Eq. 3 is further tuned to fit the observed spectrum of Crab. Since the temperature in orbit is maintained constant to within $2^{\circ}$ C, no temperature dependence of coefficients in Eq. 3 is required. The same is true for energy resolution also.

The relative counts (total counts under a peak) in different anode layers depends on the absorption coefficient and density (or pressure) of the gas. Using this ratio for Cd109 source, which shows systematic variation in counts with layers, it is possible to estimate the density of the gas. It was found that varying the density by a few percent can get the relative count rates in better agreement. To estimate the density of the gas, simulations were done with different values of density and the relative difference in count rates

[TABLE]

where $O_{i}$ and $S_{i}$ are respectively, the counts in the observed and simulated spectra in $i$th layer. The sum is over the 5 layers. Since the total counts in observed spectrum are of order of $10^{6}$, the statistical errors in $O_{i}$ are very small and any departure in $F(\rho)$ from zero is due to systematic discrepancies in simulation. As a result, we have not tried to define a $\chi^{2}$ function for this purpose. This function shows a well-defined minimum as a function of density as shown in Figure 6. The difference in density could arise due to a small variation in pressure or temperature. This value of density is used in all further simulations. The density is found to be 10.0 mg cm*-3* in LAXPC10, 10.7 mg cm*-3* in LAXPC20 and 11.5 mg cm*-3* in LAXPC30.

Apart from the energy to channel mapping we also need the energy resolution as a function of energy to calculate the detector response. In principle, we can use the measured resolution shown in Fig. 4 for this purpose, but that is not satisfactory as that will not leave any free parameter in simulations to match the observed spectrum for the radioactive sources. Further, the peak at 59.6 keV in the Am241 spectrum is a multiple peak arising from single and double events with different resolution and channel. Thus we keep the energy resolution as a free parameter in simulations, which is determined by matching the observed spectrum. Thus we have 4 free parameters which give the energy resolution for the four peaks at 5.9, 22.0, 29.8 and 59.6 keV. The 5.9 keV peak is not seen in lower layers and its resolution is determined by the top layer only. In any case here we have assumed that all anodes have the same resolution. The 22.0 keV peak in Cd109, has a small component around 25 keV, but we assume the same relative resolution for the entire peak. Similarly, 29.8 keV peak in Am241 spectrum also has a contribution at lower energy from escape of Xe Kβ X-rays, but we assume the same relative resolution for the entire peak. The 59.6 keV resolution applies to the peak from single events where all energy is absorbed in the same anode. For the double events the two events have energy close to 29.8 keV and that resolution is used in each anode, before the channel number in the two anodes are added to get the final value. Thus we have only 8 free parameters, $\sigma_{1},\sigma_{2},\sigma_{3},\sigma_{4}$ to specify the energy resolution, $e_{0},e_{1},e_{2}$ (Eq. 3) and the density, to match the 3 spectra in each anode. Only the regions near the peaks are used to fit the spectra.

To determine these parameters we first determine $e_{0},e_{1}$ by matching the peak positions and then $\sigma_{2}$ and density are determined to match the Cd109 spectrum for all anodes. This fixes the value of density as explained above which is used in all further simulations. Then Fe55 spectrum is fitted to obtain the resolution $\sigma_{1}$. Since the low energy photons are absorbed in the top layer we only need to fit the spectrum in anodes A1, A2. The other three parameters, $\sigma_{3},\sigma_{4},e_{2}$ are used to match the spectrum for Am241. The resulting fits are shown in Figure 7 for LAXPC10. The anode A4 shows a secondary peak on the lower side, due to difference in gain in cell C1.

The resolution obtained by fitting the simulated spectrum for the $5.9,22.1,29.8$ keV lines are close to those determined by fitting the observed spectrum described in Section 3.1. However, for 59.6 keV peak the resolution obtained by fitting the simulated spectrum is much poorer than that from fitting the observed spectrum directly. This is because the simulated spectra give the resolution for the peak defined by single events, while the fit to observed spectra did not attempt to resolve the two peaks. It is possible to fit the two peaks but in that case the fit is not very stable. To illustrate the difference we show in Figure 8 the observed spectrum for Am241 when only single or double events are included. It can be seen that the peak in single events is broader and shifted to lower channel as compared to that in double events. The resolution obtained by fitting the simulated spectrum matches that for single event. The shift to the negative side occurs because the quadratic term in Eq. 3 is negative. The values of the parameters defining the gain for the detectors are listed in Table 1.

The inclusion of double events in the detector logic does introduce some complication in the construction of response matrix, but this is needed as above the K-edge of Xenon, typically 30% of the events are double events and their exclusion will reduce the efficiency significantly. The reduction in efficiency would be about 40% as in another 30% of the events the Xe K fluorescence X-ray escapes the detector and the event is recorded at lower energy. The event mode data from the detectors gives the channel information for each anode and it is possible to reject these double events in software, though the current pipeline software does not have that option. Figure 9 shows the observed spectrum of Crab in LAXPC10 when the double events are excluded. It can be seen that at high energies the efficiency is reduced by about 40% when double events are excluded. Further, excluding the double event will not remove all complications in response matrix, as at energies above the K-edge of Xenon a significant fraction of single events also correspond to cases where the Xenon K X-ray has escaped the detector and this will anyway have to be considered while generating the response, as there is no way this event can be distinguished from an event produced by a lower energy photon.

The observations of radioactive sources give the resolution at only four energy values, while for constructing the response matrix we need the energy resolution for all energies in the range of LAXPC. To obtain this we use a fit to $\sigma^{2}$ by a linear B-spline basis functions using 3 knots in $1/E$. We fix the knots at $1/80,1/28,1/3$ keV*-1*. This gives a piecewise linear approximation in $1/E$. Figure 10 shows the energy resolution and energy to channel mapping as determined from simulations. This can be compared with Figure 4 based on fitting the observed peaks in spectra for radioactive sources. The main difference arises for energies above 35 keV which is due to composite nature of the peak in this region. The larger nonlinearity in LAXPC20 is clearly seen in Figure 10. Because of this nonlinearity the effective ULD is higher in LAXPC20.

Using the energy to channel mapping and the energy resolution shown in Figure 10, it is possible to simulate the detector response for any incident energy in the relevant range. From these simulations it is possible to calculate the response matrix, which provides the information about the probability that an incident photon of any given energy will be observed in a particular channel of a particular anode. By summing over the probability in all channels and anodes we can get the detector efficiency at that energy, which is the probability that a photon of given energy will be observed in the detector. This efficiency multiplied by the geometric area of the detector would give the effective area of the detector.

4.2 The effective area of LAXPC detectors

To calculate the effective area we carry out simulations with incident photons at various energies and calculate the fraction that would be detected by the detectors. The geometric area of each LAXPC detector is $100\times 36=3600$ cm2. Assuming a perfectly aligned collimator in the simulations, we find that at best 79% of photons are detected as the rest of the area is blocked by the collimator. This gives an area of about 2800 cm2 for each detector. This would give a total effective area of three detectors around 8400 cm2. From the calibration on ground it was impossible to estimate the effect of imperfections in collimator. In particular, even the alignment of collimator may not accurately match that of the aluminium box containing the collimator which was used to align the detectors on satellite deck. Since all instruments on AstroSat are expected to be co-aligned it would be necessary to find the offset of each LAXPC detector with respect to the Satellite pointing axis. This offset as well as field of view of the collimator was expected to be estimated by scanning across the Crab. That should also give a better estimate of collimator misalignment.

For a perfect collimator the dead-time corrected count rate would vary linearly with pointing offset. The collimator of each detector consists of about 7000 square cells of side 7 mm. The fabrication and mounting of the collimator modules may introduce some level of misalignment between different individual cells in the collimator assembly. To produce a more realistic model of collimator, following Jahoda et al. (2006) we assume that the pointing direction of each cell is randomly displaced from the detector axis. The random offsets are assumed to have a Gaussian distribution centered at the detector axis and with standard deviation, $\sigma_{c}$, which quantifies the imperfection in the collimator. The standard deviation would need to be adjusted to approximate the observed scan profile. The actual collimator may have a misalignment in the mean also which would again be determined by the scan. Final effective area can only be obtained by cross calibration with other instruments after launch as described in Section 5.2.

4.3 The field of view

The field of view of the collimator could not be determined using radioactive sources on ground. Hence GEANT4 simulations were used for determining the field of view. Each simulation included $10^{6}$ photons of fixed energy which were uniformly distributed over the detector top and incident at a fixed angle to the detector axis. The number of events registered in the detector were noted for each angle. The secondary particles produced in the collimator are also tracked and all events which satisfy the selection criteria for the processing electronics were counted. The maximum counts were obtained when the photons were incident normal to the detector surface. The counts at other angles were divided by this maximum number to get the relative efficiency of the detector in different directions. There is some energy dependence in the field of view, as the window support collimator which is made of aluminium is almost transparent to high energy photons. As a result, at high energy the field of view increases marginally. For a perfect collimator the full-width at half maximum (FWHM) of the collimator is $43^{\prime}=0.72^{\circ}$ at 15 keV and $47^{\prime}=0.78^{\circ}$ at 50 keV when measured along diagonal of the detector. Along the sides of detector the FWHM turns out to be $50^{\prime}=0.83^{\circ}$ at 15 keV and $54^{\prime}=0.90^{\circ}$ at 50 keV. However, all cells in the collimator are unlikely to be perfectly aligned in the same direction and it is necessary to include this effect in simulations. On ground it was not possible to estimate the magnitude of dispersion in alignment of different cells and hence this was achieved by a scan across Crab after launch, by comparing the scan profile with simulations with different amount of dispersion in collimator alignment. The dispersion was assumed to have a Gaussian distribution and it was estimated that for LAXPC10 the standard deviation of the alignment is about $12^{\prime}=0.2^{\circ}$. This reduces the detector efficiency by about 14% which affects the effective area also. This estimate of 14% applies when photons are incident perpendicular to the top window, there is a mild dependence on the angle of incidence. Figure 11 shows the contours of constant efficiency for photons of 15 keV and 50 keV. The red contours which marks the region of half the maximum counts has a FWHM when scan is taken along the sides of detectors of $57^{\prime}=0.95^{\circ}$ at 15 keV and $62^{\prime}=1.03^{\circ}$ at 50 keV. These contours are not circular in shape because the cells in collimator are square.

For other detectors the dispersion in collimator cells is even larger giving even lower efficiencies. For LAXPC20 the dispersion $\sigma$ is estimated to be about $19^{\prime}$ giving a loss of efficiency by about 22%. For LAXPC30 $\sigma$ is estimated to be about $17^{\prime}$ giving a loss of efficiency by 18%. It is possible that this dispersion is overestimated as there would also be some contribution from misalignment between the field of view collimator and the window support collimator.

4.4 The detector background

The detector background arises from the photons and charged particles in space, apart from the X-rays coming from the source. The detector background can be estimated from simulation, if the flux of particles (photons and charged particles) responsible for the background is known at different energies. The high energy particles interact with shield and other surrounding material and may produce secondary X-rays or other particles of varying energies. The GEANT4 simulations keep track of all these secondaries. Although, the detector is not designed to detect high energy particles, many of these particles may deposit only a part of their energy inside the detector, thus triggering a valid event in the detector. Simulations include all secondaries produced in the shield, collimators and aluminium box enclosing the gas and collimator. But simulations do not include other materials surrounding the detector in the satellite and as a result, some differences may be expected. The main purpose of these simulations is to estimate the efficiency with which background events are rejected.

There are the following mechanism to reject the background:

The shield: The shield including the tin shield, aluminium box and collimators may not allow the particles to pass through. At low energies this is very effective and practically all background events are suppressed. 2. 2.

The detector efficiency: Since the low energy particles are shielded from the detector, only high energy particles will enter the detector volume. At these energies, the detector is fairly inefficient to photons and a large fraction of these photons will simply pass through the detector without registering an event. 3. 3.

Coincidence: The logic in processing electronics rejects all events which trigger more than one anode, except for the Xenon K X-ray peak as explained in Section 2. This can reject events due to charged particles. 4. 4.

Veto layers: Any event which deposits energy in a veto anode is rejected. This would also be effective for rejecting charged particles entering from the sides. 5. 5.

Excess energy: If the energy deposited in an anode exceeds the ULD of about 80 keV, it will be rejected.

The relative contributions of all these factors were estimated in the simulations. There can be multiple reasons why a given event is rejected. In particular, the last three options can have significant overlap. In the simulations, any event which registers in more than two anodes or two main anodes is accounted for in contribution from coincidence, while those events which are recorded in two anodes which include a veto anode are accounted for in contribution of veto layers. The excess energy refers to only those cases where only at most two main anodes are triggered. The overlap between different options was not estimated in these simulations.

The background flux was assumed to be isotropic and uniform. Only gamma, electrons and protons were considered separately as the primary particles. Each simulation run consisted of $10^{6}$ events for a chosen particle with energy uniformly distributed in a specified interval. The particles were incident on the virtual surface of a box of size $120\times 60\times 80$ cm with uniform probability of landing at any point on the surface. The detector was inside this virtual box. The initial direction of incident particles was also considered to be uniformly distributed in the solid angle of $2\pi$ constituting the particles directed inside the volume. With this size of virtual box, it was found that if the shield, aluminium box and collimator were removed, then on an average about 23% of the particles reached the active detector volume ($100\times 39\times 16.5$ cm). This is purely a geometric effect because the active detector is only a fraction of total volume considered. When the shielding material is included, the number of particles reaching the detector were much smaller at low energies, but at high energies they approached or even exceeded 23%. The latter is because of secondaries produced in the shield. Nevertheless, because of various rejection criterion, the number of events actually registered is much smaller. Thus for consistency all rates were normalized with this number.

For each event the total energy deposited in each anode volume was calculated and the rejection criteria outlined above were applied. In order to identify the contribution to background rejection from various measures, all contributions were separately counted. In addition, count of events rejected by each of the veto layers were also kept separately. These include only those events which also triggered one of the main anodes. These are counts which will be added if one of these veto anodes is not functioning, as is the case with LAXPC10.

The results are shown in Figure 12. Photons at energies below about 50 keV are almost completely absorbed by the shield. At higher energies an increasing fraction penetrates through the shield to reach the detector, but at these energies the efficiency of detector is rather low and a large fraction of these pass through the detector without interacting. For energies above 1 MeV the efficiency of the detector is very low and 70%–90% of the events are rejected because of this. The anti-coincidence logic accounts for rejection of up to 30% events at high energies, while veto layers reject up to 4% events at high energies. For energies above 10 MeV the anti-coincidence is about a factor of 4–7 more effective in rejecting background as compared to veto layers. The fraction of events which pass through all rejection criterion is about 1% or less at all energies. Also shown in the figure is the result if veto anode A10 is not functioning. It can be seen that the increase is typically about 60% at highest energies and drops down to 10%–20% at low energies, where the flux of gamma rays is likely to be larger.

Similarly, electrons up to energy of 1 MeV are almost completely absorbed in the shield, but the shield is totally ineffective beyond an energy of 10 MeV. For electrons the detector is fairly efficient and only about 20%–30% of events are rejected on that count. However, in this case anti-coincidence is very effective and about 90% of the events at highest energies are rejected by that. The fraction of events rejected by detector efficiency decreases to 10% at 5 MeV. The veto layers account for about 10% of the rejections at high energies and is typically less effective by a factor of 6 as compared to anti-coincidence at energies above 10 MeV. The net background recorded by the detector is about 2% of the incident flux at high energies and increases by about a factor of 2 when veto anode A10 is not functioning. At lower energies of 1-10 MeV, where the electron flux is likely to be large, the increase due to A10 not functioning is much less.

For protons the shield is effective up to an energy of 20 MeV, beyond that anti-coincidence is the dominant factor in suppressing the background, accounting for over 80% at high energies. The veto layers account for about 20% events at high energies. The net background recorded by the detector reaches 2% at high energies, but at these energies the flux of protons should be negligible. At energies below 500 MeV the background is less than 1%. If A10 is not functioning the background could be significantly higher and drops below 1% at about 50 MeV. The large contribution from A10 at intermediate energies comes because at these energies the protons get significantly attenuated in the shield and veto layer and after traveling through these they do not have much energy left and hence the event will be registered if the veto anode is not functioning. At higher energies the particles pass through multiple layers and can get rejected through anti-coincidence even when one veto anode is not functioning.

The charged particle flux in orbit outside of SAA region, where the detector is switched off, is rather small and most of the contribution is expected from cosmic X-ray background. The spectral form of this radiation flux can be approximated by (Mandrou et al., 1979; Schonfelder et al., 1980; Dean et al., 1991)

[TABLE]

The resulting background spectrum is compared with actual background observed in the orbit (Figure 13). The simulations suppressed all events with energy exceeding 80 keV and as a result there are no counts beyond the ULD in the simulated spectrum, while in the observed spectrum the double events contribute to counts in this energy range. It can be seen that considering the approximations made the agreement is reasonably good. More comparisons are discussed in Section 6. It may be noted that a smoothed version of this background spectrum was only used for simulating the LAXPC observations before launch. After launch the observed background is available.

5 Calibration in orbit

After the launch of AstroSat on September 28, 2015, LAXPC detectors were switched on in phases and on October 19, 2015 the high-voltage was raised to the value set during the ground calibration. The first round of gas purification was carried out during October 20–22, 2015. The energy resolution of the detector was estimated using the on-board calibration source in veto anode A8. The results are shown in Figure 14 which compares the spectrum before and after purification. Since the detectors were kept in air for several days before launch some impurities had accumulated in the detectors thus degrading the energy resolution. Before purification the energy resolution at 29.8 keV of LAXPC10, LAXPC20 and LAXPC30 was respectively, 17%, 12%, 13%, while after purification it improved to 14%, 12% and 10%, respectively. After purification, energy resolution was close to that on ground. As expected the gain also reduced after purification. Nevertheless, a second round of purification was performed on November 22, 2015. After this for LAXPC10 and LAXPC20 purification was done on August 18, 2016.

During the performance verification phase lasting till March 2016, various sources were observed to calibrate the instruments. Among them was Cas A, which shows an Iron line at 6.62 keV (Yamaguchi et al., 2014). The spectrum from observation on January 4, 2016, was fitted to check the peak channel mapping at low energies and the result is shown in Figure 15. The peak was found at energies of $6.7\pm 0.1$, $6.8\pm 0.1$ and $6.7\pm 0.1$ keV for LAXPC10, LAXPC20 and LAXPC30, respectively. The width of the peak was found to be consistent with the expected energy resolution of the detectors. Since the detector response was used in the fit, the fitted width was very small as compared to the expected energy resolution of about 20% at this energy. This confirmed that the used channel to energy mapping at this energy is within 0.2 keV of actual value.

All data received after launch have been analyzed using LaxpcSoft software222http://www.tifr.res.in/~astrosat_laxpc/LaxpcSoft.html for analyzing LAXPC data. All results reported in this work have been obtained using this software.

5.1 The field of view and alignment

To find the alignment of LAXPC detectors with respect to the satellite pointing direction we performed a scan across the Crab. The scan was performed along both right ascension and declination at a rate of $0.01^{\circ}$ s*-1* covering a range of $\pm 3^{\circ}$ from the nominal position of the source. This exercise was repeated three times and during each run three scans were done along right ascension and declination. The result obtained during the last run in February 2016 is shown in figure 16. It can be seen that all detectors do not show the peak counts at the same time and also not when the pointing direction matches Crab position. Analysis of these data gives the offset for each detector as listed in Table 2. It is possible to choose a pointing direction to maximize the total counts from LAXPC detectors and some observations have been made with such a pointing. However, other instruments on board AstroSat have a smaller field of view and placing the source at the LAXPC efficiency peak would place it far off the axis of some of these.

Apart from the misalignment, the scan profile can also give some estimate of the quality of collimator, from the rate at which counts fall off with offset from the source. For an ideal collimator the counts should decrease linearly with offset. There is a significant deviation from this linear profile in the region where the count rate is close to maximum as well as where the count rate approaches the background. This departure can be modelled, if we assume that all cells in the collimator are not perfectly aligned with each other and that there is a scatter with Gaussian distribution. For LAXPC10 scan profile, the width of the distribution is found to be about $12^{\prime}$, while for other detectors it is somewhat larger. Figure 16 compares the observed profile with that expected for an ideal collimator as well as one with a scatter of $12^{\prime}$. Both the simulated profiles are scaled to give the maximum count rate that is observed during the scan. It can be seen that the profile for ideal collimator shown by blue lines in the figure does not match the observed profile and gives a somewhat smaller field of view. In some cases the peak counts in the profile for ideal collimator are below the observed counts. This is because in these scans the offset angle was never close to zero and at the minimum offset the ideal collimator gives significant reduction in count rate. For LAXPC10 the profile with a scatter of $12^{\prime}$ is close to the observed profile considering the assumptions made. The simulations only try to account for misalignment between different collimator cells, but do not account for other imperfections in the collimator and hence we do not expect a perfect agreement. Nevertheless, for LAXPC20 and LAXPC30 the deviations are somewhat larger and it appears that these detectors have larger scatter or other imperfections in their collimator. All collimators have the FWHM of field of view of about $55^{\prime}=0.92^{\circ}$ at low energies when measured along the sides of the detectors. These scans show the total count rate integrated over the entire energy range, but the count rate is dominated by low energy photons and hence the resulting field of view is applicable at low energies.

Figure 17 compares the observed profile during scan by combining all six scans as a function of calculated angular offset. It can be seen that the profiles of all scans merge into one which shows that the calculated offset is correct. Further, this figure compares the observed profile with simulated profiles with a few different levels of scatter in the alignment of collimator. The shape of the simulated profile does not perfectly match the observed profile, and it is likely that there are other imperfections in the collimator which contribute to the differences. Nevertheless, it is clear that LAXPC10 appears to be consistent with lower scatter in collimator, while for other detectors the scatter is larger, with LAXPC20 having the largest scatter. This is consistent with the estimated effective areas of the three detectors as discussed in the next subsection. It can be seen that for LAXPC10 the scatter is between $12^{\prime}$ and $17^{\prime}$. It may be noted that this result is only used to estimate the loss of efficiency due to collimator imperfection. The final effective area is estimated by simultaneous fit with NuSTAR observation and does not use this estimate.

We can estimate the field of view at higher energies by considering the counts in different energy bands. If we consider counts in the energy range of 40–60 keV the FWHM of field of view is about $63^{\prime}=1.05^{\circ}$. Figure 18 shows the results for this energy range and compares them with simulations with perfect collimator and one with dispersion of 12’.

The offset angle for the detectors range from $0.07^{\circ}$ to $0.15^{\circ}$. For an ideal collimator an offset of $0.15^{\circ}$ would reduce the efficiency by about 15%, but considering the scatter in alignment of individual cells at the level that matches observations the decrease is about 7%. The scatter in the collimator alignment reduces the efficiency by about 15%, which gives a total reduction of about 20% in efficiency for LAXPC10. For other detectors the reduction is comparable as the smaller offset compensates for larger scatter in collimator pointing. Table 2 also lists the estimated loss of efficiency for all detectors due to pointing offset and collimator quality. This reflects in the effective area considered in the next subsection. It may be noted that these offsets have been obtained with respect to the AstroSat satellite axis. However, all instruments are not perfectly aligned to this axis and as a result different pointings are used while observing with different instruments. Hence there could be an offset of about $0.1^{\circ}$ with respect to the pointing obtained here. As a result, it may be better to keep the normalization of effective area as a free parameter while simultaneously fitting spectra from different detectors or instruments.

5.2 Effective area

As mentioned in Section 4.2, the effective area of the combined LAXPC detector was expected to be about 8400 cm2 assuming nearly perfect collimator and alignment. From the scan across the Crab we have estimated that the misalignment with respect to the satellite pointing direction and imperfections in the collimator reduce the efficiency and hence the effective area by about 21% for LAXPC10.

Apart from the collimator imperfection the count rate would also be affected by the dead-time associated with rejected events. This count rate is more or less independent of the source being observed, though it varies during an orbit by about 25%. This rate may be estimated using appropriate counters in BBC mode. However, this rate in orbit is very different from that on ground and hence it could only be estimated after launch. From the BBC mode data the total counts in rejected events is estimated to be 2000–2500 s*-1*. With an estimated dead-time (from electronics design) of about 35 $\mu$s for rejected events, it gives a loss of efficiency by 7–9%. Combining both these factors gives a reduction in effective area by a little over 27% to about 6000 cm2.

Figure 19 shows the effective area of the three LAXPC detectors with correcting factor as explained below. The efficiency or the effective area is defined by the probability that a photon of given energy will register a valid event in the detector, the energy deposited may be less than the incident energy, for example, due to Xe K fluorescence X-ray escaping from the detector volume. Thus all these photons may not be detected at the correct energy. The difference between the effective areas of the three detectors is mainly from the collimator quality. For a perfect collimator all detectors show similar effective areas. The total effective area of the three detector is shown in the right panel. The sharp dip at low energies is due to absorption in the Mylar window at the top of the detector. The dip around 34 keV is due to reduced absorption coefficient just below the K-edge of Xenon. At high energies the efficiency decreases because of decrease in the absorption coefficient of the gas.

To get a better estimate of effective areas for each LAXPC detector, simultaneous observations of the Crab with NuSTAR (Harrison et al., 2013) were carried out on 31 March 2016. Simultaneous fit of NuSTAR and each of the LAXPC detectors to a power law spectrum gave the relative normalization of each detector assuming the response matrix for NuSTAR. The resulting fit for LAXPC10 is shown in Figure 20. From these fits the relative normalization with respect to NuSTAR of the three LAXPC detectors were calculated to be 0.92, 0.84 and 0.89, respectively for LAXPC10, LAXPC20 and LAXPC30. The simultaneous fit with NuSTAR including 1% systematics in LAXPC detector response gave a $\chi^{2}$ of 1.0 per degree of freedom. The effective area of each detector using the normalization as determined above and the combined effective area is shown in Figure 19. The maximum effective area of combined LAXPC detectors is about 6000 cm2 around 15 keV and reduces to about 5600 cm2, 4100 cm2 and 2200 cm2, respectively at 40 keV, 60 keV and 80 keV. These effective area estimates are for pointing as determined by the satellite axis. Since the pointing directions are not the same for all observations, there could be an uncertainty in effective area by 5%.

5.3 The response matrix

To calculate the response matrix we use GEANT4 simulations with energy resolution and energy to channel mapping as obtained in Section 4.1, for photons of fixed energy. We have used 338 energy bins in the range 2.05 to 145 keV to calculate the response. For each energy we use $10^{7}$ photons incident normally at the top of detector and uniformly distributed over the area. The efficiency of detection is multiplied by appropriate factor to take care of factors mentioned in the previous section. As explained in the previous section these factors are determined by a simultaneous fit to Crab spectrum with NuSTAR observations. Figure 21 shows the response of LAXPC30 for a few selected energies. All these are combined into a response file which incorporates the effective area and can be used with XSPEC package for fitting observed spectra.

For energies above the K-edge of Xe we get multiple peaks. The peaks at lower energies are due to escape of Xe K fluorescence X-rays outside the detector. For energies of 40.5 and 50.5 the two peaks due to escape of Kα and Kβ are resolved. For energies of around 80 keV or above, the main peak may not be complete as due to finite resolution a part of the peak may go beyond the ULD. However, the counts do not go to zero beyond this limit as the double events are still recorded. At high energies even the main peak due to single and double events may be resolved as the difference increases due to nonlinearity of response. This has not been verified from any source with known energy.

The calculated response matrix was used to fit the spectrum for Crab taken during January 2016. Although, the overall fit was good there were some differences around the Xe K- and L-edges. To correct for this the energy to channel mapping was locally modified in these regions. Another correction which was required to correct for excess events around 30 keV, which are coming from a gap in the shield. The aluminium box containing the collimator has some ribs of about 1 cm on all sides and the shield is put on this ribs. This leaves a small gap between the shield and collimator box (see Figure 1), through which high energy photons can pass through as the ribs made of aluminium are not enough to block them. Only photons coming in the direction close to the direction of pointing can pass through this gap. Although, this region is outside the volume covering the main anodes, the chamber enclosing the gas is larger and these photons can still interact with Xenon in this extra volume. Any Xe K fluorescence X-rays emitted in this region can enter the detector volume and trigger the detector. This contribution has been adjusted by matching the Crab spectrum. Typical contribution is about 1% of high energy photons above the Xe K-edge. This gap was not included in GEANT4 simulations.

This tuned response has been used for all calculations. The fits to Crab spectrum by a power-law for all 3 detectors with 1% systematics is shown in Figure 22. It can be seen that for all detectors the fit is good to within 2%. Further, for LAXPC10, LAXPC20 the fit is good even beyond 80 keV, while for LAXPC30 it deteriorates beyond 80 keV.

The drift in gain of detectors need to be accounted for while fitting the spectrum using a response matrix as well as while subtracting the background. Since the background spectrum is observed at a different time the gain may not be the same as that during source observation and it may be necessary to shift the background to the same gain as that during the source observations. The extent of shift required can be obtained by fitting the peak of calibration source in Anode A8. The gain shift is applied by assuming that the observed shift is due to change in coefficient $e_{1}$ in Eq. 3. This assumption may not be correct as other coefficients also could have changed, but it is not possible to determine the change in all coefficients from the shift in 30 keV peak.

A simple shift in gain will not give the correct spectrum at energies beyond about 35 keV as the logic for adding the double event checks for the energy to be in the interval of Xe K photons. The shift in gain will cause the double events to be missed and it is not possible to account for this while shifting the gain by a linear transformation in energy scale. This limits the ability to correct for gain shift between source and background and can introduce features in the resulting spectrum.

Another possibility is to use the spectrum obtained during the Earth occultation during the same orbits when the source was observed. This ensures that there is no gain shift between the source and background, but the observed spectrum during Earth occultation is not the same as real background as the Earth albedo would also contribute, but this may be the only option if no background observation with nearby gain is available. This issue is discussed in the next section. Once the background corrected source spectrum is available a response which has nearby gain can be used to fit the spectrum. The LaxpcSoft software also has option to shift background spectrum to align with source spectrum and it also identifies the response to be used. It may help to make finer adjustment in gain by applying a linear transformation to the energy scale, particularly the constant term, $e_{0}$ in Eq. 3.

5.4 Timing characteristics

Since the prime use of LAXPC instrument is for timing studies, the timing characteristics were investigated during ground calibration and the Fourier transform of the time series did not show any unexpected features. After launch this was checked in more detail with additional data for bright sources (Yadav et al., 2016b).

There are some known problems in time tagging of events. When the lowest time byte in time, T1, rolls over from FF to 00, the next higher byte, T2, does not increment at the same time. There is a delay of about 20 $\mu$s between updating the two bytes of time. If an event occurs in between the time when two time bytes are updated and if the count rate is sufficiently high, apparent time ordering of events may also get disturbed as apparently this event will precede the previous event. Similar problem is also present in roll over of higher time bytes, though these occur less often and are easier to correct. This problem has been corrected in software and after that all events are correctly ordered in time. However, the distribution of lowest time byte is not uniform and shows some features as shown in Figure 23. The origin of this effect is not known, but it can result in spurious periodicities if a period of exactly 2.56 ms (frequency of 390.625 Hz) or its multiples is used. The resulting pulse profile will match that shown in Figure 23. The reason for this distribution is not understood but it is independent of time. Since the profile is strongly peaked at one value, most of the power would be in higher harmonics of this frequency and this feature is not seen in Fourier transform, but it can show up if period folding is applied. This effect is seen if the instrument time as recorded through STBG is used. If the arrival times are converted to UTC (red line in Figure 23) the effect goes away because of a slow drift in the STBG clock. We do not believe that this reduces the time resolution as we have obtained power density spectrum up to a frequency of 50 kHz and it agrees with that expected from a Poisson distribution with dead-time (Yadav et al., 2016b).

After launch a peak around 50 Hz was found in the power density spectrum of bright sources in LAXPC20. This feature is present only in anode A1 and at energy of less than about 5 keV. It is also found in weak sources with a smaller significance. This has been traced to noise in the amplifier for anode A1. This anomaly was also present during ground tests.

Another source of possible instrumental feature in the power density spectrum is the calibration source in veto anode A8. To allow this spectrum to be observed, $1/128$ of the events registered in veto anodes are not rejected and get entered in the event mode file. Since the count rate in veto anodes is roughly constant, this gives a peak around 8-11 Hz in count rate from veto anodes. The lower frequency is seen in LAXPC10 where veto anode A10 is disabled and hence the count rate is lower. During observation of bright sources veto anodes count rate can be reduced due to effect of dead-time, thus reducing the frequency at which the peak occurs. For bright sources it is possible that this frequency will show up in the source counts also and in some cases a weak feature has been seen around this frequency in the power density spectra. This has to be accounted for while interpreting a power density spectrum.

6 The detector background

Although, the background in the laboratory was very stable, observations in orbit shows some variation with time and hence it is necessary to model the background, so that source contribution can be extracted from any observation. This is particularly important for faint sources. The total background counts averaged over an orbit in LAXPC10 is about 260 s*-1*, while in LAXPC20 and LAXPC30 it is about 200 s*-1*. The higher count rate in LAXPC10 is because one of the veto anode is switched off. The variation in background count rate is about 20% around the mean value.

The observed spectrum of background with counts in all anodes added is shown in Figure 24 for all LAXPC detectors during three different observations. One of these observations was when the satellite was pointing towards the Earth. For comparison simulated background spectrum calculated before launch is shown in one of the panels and it is clear that the agreement is reasonably good. Since the simulations did not include contribution from charged particles, it shows that this contribution is small in the orbit. There is some difference between the three spectra for all detectors as shown in the right panel. It can be seen that there is some energy dependence in the difference, hence scaling the spectrum by the total counts may not be enough. It is known that the cosmic X-ray background which is the main contributor to the LAXPC background, has spatial fluctuation of about 7% ($1\sigma$) (Revnivtsev et al., 2003) in the 2–10 keV band. These fluctuations cannot be modelled and set the flux limit below which faint sources may not be observable. It is not clear how these spatial fluctuations will contribute to LAXPC background, as the background is contributed by particles coming from almost all directions, much of these fluctuations will be averaged out. Even a bright X-ray source with hard spectrum which is off-axis can also contribute to the background as the typical rejection efficiency for hard photons above 100 keV is about 99% (Section 4.4), so 1% of these photons can be detected. For example, for Crab, we would expect a few counts per second when the source is shining on the side of the detector.

To cover some variation LAXPC has observed the blank sky coordinates listed in Table 3. The table also gives the total count rate observed in each detector. Considering the exposure time, the statistical error in these counts is less than 0.1 s*-1* and all the variation can be considered as systematic error. Some of the variation seen in LAXPC30 counts is due to shift in gain and decrease in density as discussed in the next section. The gain of the other detectors has also been drifting slowly and that could account for some of the variations. The background in LAXPC10 appears to be increasing with time, particularly, after August 2016 the count rate is higher than that during earlier observations. Table 4 shows the background counts in different layers and different energy bins as observed during March 2016. Some of the variation in background could be due to variation in satellite position and we attempt to model this. We have tried two models one based on observed correlation with the count rate of events which exceed ULD, and another based on satellite position. We also tried to model the background variation by using induced radioactivity during SAA passage, but did not find any improvement in the model with this addition and hence we have not included this effect.

6.1 Background model based on ULD counts

Figure 25 shows variation in background during one day in March 2016. All the three detectors show increase in counts as the spacecraft approaches the SAA region. In the SAA region the high voltage is switched off and hence no counts are recorded. The figure also shows ULD count rate which measures the number of events which exceed the upper energy threshold. This count rate also shows similar behavior. Further, the increase in the count rate as the satellite approaches SAA region is not the same in every orbit. It depends on the latitude at that point. AstroSat is placed in a nearly circular orbit with inclination of $6^{\circ}$ to the equator. If AstroSat is close to $6^{\circ}$ S while passing the SAA region, the effect is maximum. On the other hand when it is close to $6^{\circ}$ N, the SAA passage is short and the charged particle flux is also much smaller. The background counts are correlated to ULD counts as shown in the right panel of Figure 25. The correlation coefficient between the two is found to be 0.98, 0.93, 0.96 respectively for LAXPC10, LAXPC20, LAXPC30. Since the ULD counts do not vary too much with source counts, this correlation can provide a simple model for background. For high count rate sources we need to apply correction for dead-time in the ULD count rate also. To get the resulting model background spectrum the range of ULD counts is divided into 4 equal bins covering the full range for each detector. The boundary of these bins is marked by vertical lines in Figure 25. For LAXPC30 the background as well as ULD counts are shifted to lower values due to a shift in gain. The background count rate in each of these 4 bins is shown in Table  5.

The spectra obtained for each ULD bin is shown in Figure 26. For a given source observation, the time is divided into these ULD bins and the background spectra for these bins is weighted with time spent in the bin to get resulting background spectrum. The ULD counts need to be corrected for dead-time using the count rate of genuine events. This method is sensitive to shift in gain which affects the ULD counts. If the gain shifts on positive side some of events at high energy end will go beyond the ULD and the observed count rate would reduce while the ULD count rate will increase thus affecting the observed correlation. For LAXPC30 the ULD counts have reduced significantly due to leak and it is not possible to use this model. This background model does not give the background count rate as a function of time, but only corrects for the average background spectrum during an observation. Hence, it cannot be used to obtain the light curve for source counts.

6.2 Background Model Based on Satellite position

Since the SAA region is located mainly just south of the equator, the background counts depend on both longitude and latitude. A background observation over 1 day is expected to cover most of the region where the detector is not switched off. Thus using such an observation it is possible to fit the 2D dependence using product B-spline basis functions and this model was used. There is also some variation with altitude. Although, the AstroSat orbit is nearly circular there is a variation by about 15 km in altitude during the orbit, which may be enough to give some variation in background counts. Hence we also attempted to fit in 3-dimensions using product B-splines. Some regularization was also applied while calculating the fits (Antia, 2012). However, the fitted background did not show any significant improvement over the 2-dimensional fit. The fitted background for all three detectors are shown in Figure 27 for observations during March 2016. Since the detectors are off during SAA passage that region is excluded from the figure. The residuals obtained after subtracting the fitted background from the observed value is shown in Figure 28.

Until August 4, 2016 the SAA region was defined to be between the longitudes of $-110^{\circ}$ to $0^{\circ}$ (or $250^{\circ}$ to $360^{\circ}$). It was felt that this includes some region in the north where the charged particle flux may be low enough for the detectors to be operated. Hence, a modified definition based on a SAA model was implemented which accounted for the latitude dependence, and the entry to SAA was defined to be the point where longitude equals $-110^{\circ}+4(\hbox{latitude}+6^{\circ})$. With this change in definition of SAA region, a revised background model is needed and this was obtained from observations of background on August 16, 2016 and the results are shown in Figure 29. There appears to be some region in the north where background counts are quite large and it is necessary to eliminate this region from good time interval to get reliable model for background. There is also some variation in the average background count rate between the two background observations, mostly because of shift in the gain of detectors between the two observations (see Table 3 and Section 7).

This model gives the total background counts at any position of the spacecraft. For source observation, we take the mean counts over the period when the source was observed and scale the background spectrum to this mean count. Apart from the spectrum this model also gives the background counts at any time and this can be subtracted from the total light curve to get the source contribution. In most regions the background model agrees with actual counts to within 2%. But there is some unexplained variation with a period of slightly less than a day and an amplitude of a few counts per second, which is not modelled. The origin of this periodic variation is not known. The background spectrum obtained from this model does not account for variation in spectrum over the observed period. It only accounts for the total count rate, which is used to scale the spectrum.

In order to obtain the fits to background we need observations covering the entire range in longitude and latitude, which requires observations spanning at least one day. Apart from this we also require that the entire range of longitude and latitude are covered during the time when the satellite is not pointing towards the Earth. Some pointing directions are excluded by this criterion at a given time. For example, the observation of Sky-5 during August 30, 2016, did not include any region with latitude greater than $4^{\circ}$ and hence cannot be used to obtain the background fit.

6.3 Background from observation during Earth occultation

During observations of all sources with declination less than about $60^{\circ}$ there are periods during orbit when the source is occulted by the Earth and the satellite is facing the Earth. The source will not be visible during this period but the observed spectrum would not be identical to normal background as there would be some contribution from the Earth albedo and the Earth would block the diffuse X-ray background which directly goes through the collimator. The advantage of using the spectrum during the Earth occultation as a background is that a separate background observation is not required and more importantly it ensures that there is no shift in the gain between the source and background spectrum. Hence we have tried to study the difference between the true background, as obtained when the satellite is pointing in a direction where there are no X-ray source detectable by LAXPC, and the Earth occultation spectrum obtained when the satellite is pointing towards the Earth. This can be conveniently done during the background observations as most of the background regions observed are at latitudes low enough to have Earth occultation.

Figure 30 shows the ratio of counts during Earth occultation and background during five different background observations for all three LAXPC detectors. It can be seen that particularly, at low energies the ratio is far from 1 for LAXPC20 and LAXPC30. LAXPC10 shows a different behaviour because one of the veto anode (A10) has been disabled in that. It is clear that use of Earth occultation as background can introduce significant error at low energies, particularly for faint sources. However, in some cases it may be preferable to use this, particularly for LAXPC30 as its gain shifts significantly during a day and it is difficult to account for that from independent background observation.

7 Long term performance of LAXPC in orbit

The health parameters of the detectors, like the temperature, high voltage and various energy thresholds are monitored regularly. The temperature has been maintained at $18\pm 2^{\circ}$ C for LAXPC10 and LAXPC20, while that for LAXPC30 is maintained at $22\pm 2^{\circ}$ C. The energy thresholds have also remained steady, except for one instance when on 19 April 2016, the LLD of LAXPC10 was accidentally changed. This was corrected within a day. The high voltage has held steady, but as explained below it is being adjusted from time to time to maintain the gain of detectors. To monitor the long term stability of detectors the peak position and energy resolution of 30 and 60 keV peaks in the veto anode A8 from the on-board radioactive source is monitored regularly. Figure 31 shows the peak positions and energy resolution of the two peaks as a function of days after launch of AstroSat. Some of these variations are due to purification of gas and adjustment of high voltage. Table 6 shows the times when the gain was adjusted. The gain in LAXPC30 has been constantly shifting due to suspected leak. As a result, the high voltage is regularly adjusted for this detector. The 30 keV peak had shifted by up to 85 channels (out of 1024 channels) before the high voltage was adjusted downward for the first time on 17 March 2016 after the leak was verified. During October to December 2015 the shift in gain was small and similar to that in LAXPC10. During the first week of January 2016, the rate of gain shift in LAXPC30 started increasing. This gain shift has to be accounted for in the response matrix and these have been generated for different amounts of shift. Fig. 32 shows the peak position of 30 keV peak on a magnified scale.

Unfortunately, the on-board pressure gauge does not have adequate sensitivity to get accurate measure of the leak. Hence, we attempted to estimate the density of the gas using ratio of count rates in different layers as was done on ground (Section 4.1). For this purpose we use counts in the range of 20–24 keV. Since the background spectra is essentially flat we have to subtract the background from the source spectra for this purpose and we also need a bright source with soft spectrum to get sufficient counts in all layers. We found Cyg X-1 as a suitable source for this purpose. Following a procedure similar to that on ground as described in Section 4.1, we take the ratio of counts in energy interval 20–24 keV for different layers with respect to the top layer and minimize the function

[TABLE]

where $r_{i}$ is the ratio of counts in $i$th layer to the top layer in the observed spectrum and $s_{i}$ is the same ratio in simulations with prescribed density. Figure 33 shows the function defined above for 5 different observations of Cyg X-1 on January 8, April 29, June 1, July 1 and October 9, 2016. The density is shown in the units of initial density estimated on ground to estimate the loss due of leakage. This appears to indicate that density in LAXPC30 is decreasing by about 5% of original value every month and has now reached about 30% of the original value. During the first observation on January 8, 2016, which was the time when the leak became significant, the density is comparable to that estimated on ground. This gives us some confidence on this estimate. All observations before launch also did not show any significant gain shift.

Since the detector response depends on density, the response matrix has been generated for different values of density differing by steps of 5% of the original value. These responses have been used to fit the observed spectra for some of the sources to find the density which gives the best fit. That also gives an independent estimate of density which agrees with the previous estimate. By fitting the Crab observations during different times between February 2016 and February 2017 an estimate of the density in LAXPC30 has been obtained. These estimates are comparable to those obtained using Cyg X-1 observations described above and also with pressure estimated from the pressure gauge as shown in Figure 34. Since the absolute calibration of pressure gauge is not reliable, we have divided all values by the maximum value observed and we assume that pressure is proportional to the density. Figure 35 shows the effective area of the detector with different densities. It can be seen that at high energies the effective area has been steadily decreasing with density. But at energies of less than 10 keV, there is little difference even when the density is 10% of the original value.

The Figure 32 shows that the gain in LAXPC10 is also shifting steadily upwards, though at a much smaller rate as compared to LAXPC30. The rate was about 0.15 channels per day, which is more than 20 times smaller than that for LAXPC30. This rate has also increased to about 0.25 channels per day since September 2016. This could also be due to a very fine leak, which has been there at least, since launch. If this rate is held, the detector should function for several years. No change in density or pressure has been detected in LAXPC10 till now. Considering the rate of change of gain and density in LAXPC30, it can be estimated that the observed gain shift in LAXPC10 could be due to 2–3% reduction in density. This is at the limit of the sensitivities of techniques employed here. Fit to Crab spectrum observed during January 2017, with response using original density was very good and there is no indication of any reduction in density. For LAXPC20 the gain has been slowly shifting downwards, which is the expected behavior due to impurities accumulating in the detector. The resolution of this detector is also deteriorating with time. The gas purification was attempted on August 18, 2016, but it did not change the gain or resolution. Further, attempt needs to be made to purify the gas in LAXPC20. The gain appears to be drifting at a rate of about 0.06 channels per day. For LAXPC10 purification cycle on August 18, 2016 shifted the gain as expected, but the energy resolution did not improve. Nevertheless, the resolution of LAXPC10 appears to be stable for the last one year. The resolution of LAXPC30 is improving with time, presumably due to lower pressure.

A large part of the gain shift can be adjusted by changing the linear term, the coefficient $e_{1}$ in Eq. 3, but other coefficients may also be changing. Another measure of the change can be obtained by taking the ratio of channel for the 60 keV and 30 keV peaks. The energy ratio of the two peaks is close to 2 and for a linear gain the ratio in channels should be 2 and any departure from this value could be due to the other two terms in Eq. 3. Figure 36 shows the difference $2-p_{2}/p_{1}$ where $p_{1}$ and $p_{2}$ are peak positions for the 30 keV and 60 keV peaks. It can be seen that for both LAXPC20 and LAXPC30 this ratio has been decreasing in magnitude. Though for LAXPC20 it appears to have stabilized after May 2016. Thus it is clear that the coefficients, $e_{0}$ and $e_{2}$ are also changing with time. It is unlikely that all the observed variation can be accounted for variation in $e_{0}$ as that will require a large variation. Thus, it appears that $e_{2}$ is decreasing with time for these detectors.

To show the effect of long term variation in response, we have fitted the observed spectrum for the Crab during different observations using response which is adjusted for the shift in gain and for LAXPC30, decrease in density and the results are shown in Figure 37. The fit for LAXPC20 and LAXPC30 during August 2016 is poor due to shift in gain and decreasing density, respectively. There is also a general reduction in normalization for fit during this observation which is most likely due to a difference in pointing. For LAXPC30 the fitted power-law index, $\Gamma$, has also reduced. This is because the fit with lowest $\chi^{2}$ with different densities has been selected. This probably underestimates the density and $\Gamma$. The use of slightly higher density increases $\Gamma$, but also increases the $\chi^{2}$.

Because of the leak, the efficiency of LAXPC30 is also changing as shown in Figure 35. As a result of this, the background count rate in LAXPC30 is decreasing with time. Figure 38 compares the observed background during different times in the three detectors. It can be seen that for LAXPC30 the count rate is decreasing with time and the difference is more at high energies. There is also some shift in the gain of LAXPC10 and LAXPC30 which also affected the background. The shift in the gain for all detectors can be seen from the position of the hump near 30 keV due to Xe K fluorescence X-rays. The background in LAXPC10 has increased significantly during the last 6 months. The increase is mainly seen at low energies in all anodes that are adjacent to veto anode A10, which is disabled. The reason for this increase is not clear.

Apart from observing the scheduled sources, LAXPC has also detected a number of Gamma ray bursts. The probability of occurrence of a GRB in the $1^{\circ}\times 1^{\circ}$ FOV of LAXPC is very low (about 1/40000) and hence almost all the registered GRBs are those that occur on the sides of the detectors. Gamma-rays from GRBs have hard spectra extending to MeV and even beyond. The gamma-rays of hundreds of keV and MeV strike the side walls of the detector and produce secondary particles either in the walls of detector housing or in gas volume. Some of these may get detected as genuine event. As pointed out in Section 4.4, there is about 1% probability of high energy photons coming from random direction to register a valid event in the detector. From time tagged events accurate time profile of the GRBs and be derived. One of the events detected is shown in Figure 39. All detectors do not record the same count rate, as depending on the direction of the burst with respect to satellite, some detectors may be partially shielded by other material on the satellite. The bursts occurring during the SAA transit are obviously missed. Similarly, those bursts which are occulted by the Earth are also not seen. The timing of these GRBs match that recorded in LAXPC detectors. This gives us confidence in absolute timing accuracy at the level of 1 s. In principle, it is possible to obtain the spectrum of the recorded events in LAXPC detectors during GRB but the spectrum may not give much information as most of these events are from secondaries produced in the satellite. Since these photons are not coming from the top window, the response matrix for the detector is not applicable to study these events. Although LAXPC may not be useful for studying GRBs, the fact that it can detect these bursts should be kept in mind as some of these may be mistaken for bursts in the source being observed.

8 Summary

AstroSat has completed more than 620 days of operation and more than 9200 orbits so far. More than 600 pointings for about 250 distinct sources have been carried out. The response of the instrument is reasonably understood and has been used to produce scientific results (Yadav et al., 2016b; Misra et al., 2017; Verdhan Chauhan et al., 2017). The energy resolution of the detector at 30 and 60 keV is shown in Figure 31 which shows that LAXPC10 energy resolution is steady at $(15\pm 2)$%, while that in LAXPC20 is degrading slowly from about 12% just after launch to about 16% currently at 30 keV. On the other hand, the energy resolution of LAXPC30 has improved from about 11% just after launch to better than 10% currently. The effective area of the detectors is shown in Figure 19 and its normalization depends on the pointing direction. The uncertainties in normalization can be estimated by the results for Crab shown in Figure 37 which shows a variation of $\pm 5$%. The LAXPC10 detector has a higher background counts as one of the veto anodes is not functioning, while LAXPC30 has developed a leak and hence its sensitivity is decreasing at high energies as shown in Figure 35. The gain of all detectors is shifting with time and is controlled in a reasonable range by adjusting the high voltage from time to time. This shift has to be accounted for in spectral analysis.

The background model has uncertainties of up to 5% because of variation between different regions or satellite environment. The relatively large background in LAXPC detectors and its variation with time limits the capability to observe faint sources. The background uncertainty corresponds to about 10 counts per second, while the Crab yields about 3000 counts per second in each detector, which limits the study of faint sources. It may not be possible to study sources fainter than a few mCrab. Similarly, the variation in gain with time and understanding of detector response limits the scope of spectral studies. At the same time, a large area and consequently higher count rate and event analysis mode data allows detailed timing studies to be carried out. While interpreting the power spectrum possibility of instrumental features around 8–11 Hz in all detectors and around 50 Hz in LAXPC20 should be considered.

We acknowledge the strong support from Indian Space Research Organization (ISRO) in various aspect of instrument building, testing, software development and mission operation during payload verification phase. We acknowledge support of TIFR central workshop during the design and testing of the payload. We thank Dipankar Bhattacharya for arranging simultaneous observations with NuSTAR to calibrate the LAXPC instrument. We thank Tomaso Belloni for pointing out the feature around 50 Hz in the power spectrum of LAXPC20.