11institutetext:  School of Physics and Technology, Wuhan University, Wuhan
430072, China 22institutetext: WHU-NAOC Joint Center for Astronomy, Wuhan
University, Wuhan 430072, China 33institutetext: Aryabhatta Research Institute
of observational sciencES, Manora Peak, Nainital 263 001, India
44institutetext: Department of Physical Sciences, Indian Institute of Science
Education and Research Mohali, Sector 81, SAS Nagar, Manauli PO, 140306, India
55institutetext: Astronomy and Astrophysics Division, Physical Research
Laboratory, Navrangpura, Ahmedabad, 380009, India 66institutetext: Department
of Physics and Astrophysics, University of Delhi, 110007 Delhi, India
77institutetext: Indian Institute of Astrophysics, Koramangala, Bangalore 560
034, India

# X-ray confirmation of the intermediate polar IGR J16547-1916††thanks: Based
on observations obtained with NuSTAR and Swift.

A. Joshi X-ray confirmation of the intermediate polar IGR J16547-1916††thanks:
Based on observations obtained with NuSTAR and Swift.X-ray confirmation of the
intermediate polar IGR J16547-1916††thanks: Based on observations obtained
with NuSTAR and Swift. W. Wang<EMAIL_ADDRESS>confirmation of the
intermediate polar IGR J16547-1916††thanks: Based on observations obtained
with NuSTAR and Swift.X-ray confirmation of the intermediate polar IGR
J16547-1916††thanks: Based on observations obtained with NuSTAR and
Swift.X-ray confirmation of the intermediate polar IGR J16547-1916††thanks:
Based on observations obtained with NuSTAR and Swift.X-ray confirmation of the
intermediate polar IGR J16547-1916††thanks: Based on observations obtained
with NuSTAR and Swift. J. C. Pandey X-ray confirmation of the intermediate
polar IGR J16547-1916††thanks: Based on observations obtained with NuSTAR and
Swift.X-ray confirmation of the intermediate polar IGR J16547-1916††thanks:
Based on observations obtained with NuSTAR and Swift. K. P. Singh X-ray
confirmation of the intermediate polar IGR J16547-1916††thanks: Based on
observations obtained with NuSTAR and Swift.X-ray confirmation of the
intermediate polar IGR J16547-1916††thanks: Based on observations obtained
with NuSTAR and Swift. S. Naik X-ray confirmation of the intermediate polar
IGR J16547-1916††thanks: Based on observations obtained with NuSTAR and
Swift.X-ray confirmation of the intermediate polar IGR J16547-1916††thanks:
Based on observations obtained with NuSTAR and Swift. A. Raj X-ray
confirmation of the intermediate polar IGR J16547-1916††thanks: Based on
observations obtained with NuSTAR and Swift.X-ray confirmation of the
intermediate polar IGR J16547-1916††thanks: Based on observations obtained
with NuSTAR and Swift. G. C. Anupama X-ray confirmation of the intermediate
polar IGR J16547-1916††thanks: Based on observations obtained with NuSTAR and
Swift.X-ray confirmation of the intermediate polar IGR J16547-1916††thanks:
Based on observations obtained with NuSTAR and Swift. N. Rawat X-ray
confirmation of the intermediate polar IGR J16547-1916††thanks: Based on
observations obtained with NuSTAR and Swift.X-ray confirmation of the
intermediate polar IGR J16547-1916††thanks: Based on observations obtained
with NuSTAR and Swift.

Using X-ray observations from the NuSTAR and Swift satellites, we present
temporal and spectral properties of an intermediate polar (IP) IGR
J16547-1916. A persistent X-ray period at $\sim$ 546 s confirming the optical
spin period obtained from previous observations is detected. The detection of
a strong X-ray spin pulse reinforces the classification of this system as an
intermediate polar. The lack of orbital or side-band periodicities in the
X-rays implies that the system is accreting predominantly via a disk. A
variable covering absorber appears to be responsible for the spin pulsations
in the low energy range. In the high energy band, the pulsations are likely
due to the self occultation of tall shocks above the white dwarf surface. The
observed double-humped X-ray spin pulse profile indicates two-pole accretion
geometry with tall accretion regions in short rotating IP IGR J16547-1916. We
present the variation of the spin pulse profile over an orbital phase to
account for the effects of orbital motion on the spin pulsation. X-ray spectra
obtained from the contemporaneous observations of Swift and NuSTAR in the
0.5-78.0 keV energy band are modeled with a maximum temperature of 31 keV and
a blackbody temperature of 64 eV, along with a common column density of
1.8$\times 10^{23}$ cm-2 and a power-law index of -0.22 for the covering
fraction. An additional Gaussian component and a reflection component are
needed to account for a fluorescent emission line at 6.4 keV and the
occurrence of X-ray reflection in the system. We also present the spin phase-
resolved spectral variations of IGR J16547-1916 in the 0.5-78.0 keV energy
band and find dependencies in the X-ray spectral parameters during the
rotation of the white dwarf.

###### Key Words.:

accretion, accretion disks – stars: novae, cataclysmic variables – X-rays:
stars – stars: individual: IGR J16547-1916

Table 1: Log of the Swift and NuSTAR observations of IGR1654. Telescope | Date of | Observation | Instrument | Energy | Integration | Net Count Rate
---|---|---|---|---|---|---
| observation | ID |  | Band | Time (s) | (cts/s)
Swift | 21 Jan 2010 | 00090182001 | XRT | 0.3-10.0 keV | 1568.02 | 0.0938$\pm$0.0078
| 23 Jan 2010 | 00090182002 | XRT | 0.3-10.0 keV | 3993.48 | 0.0697$\pm$0.0043
| 13 Oct 2013 | 00040710001 | XRT | 0.3-10.0 keV | 843.16 | 0.0572$\pm$0.0083
| 25 Jan 2015 | 00040710002 | XRT | 0.3-10.0 keV | 223.14 | 0.1125$\pm$0.0225
| 29 Jun 2017 | 00040710003 | XRT | 0.3-10.0 keV | 864.25 | 0.0775$\pm$0.0096
| 30 Jun 2017 | 00040710004 | XRT | 0.3-10.0 keV | 180.51 | 0.1112$\pm$0.0249
| 08 Mar 2019 | 00088622001 | XRT | 0.3-10.0 keV | 6461.66 | 0.0862$\pm$0.0037
| 15 Mar 2019 | 00088622002 | XRT | 0.3-10.0 keV | 4873.64 | 0.0925$\pm$0.0045
| 17 Mar 2019 | 00088622003 | XRT | 0.3-10.0 keV | 1476.58 | 0.0629$\pm$0.0066
NuSTAR | 16 Mar 2019 | 30460016002 | FPMA/FPMB | 3-78 keV | 44565 | 1.1100$\pm$0.0857

Figure 1: X-ray light curves of IGR1654 obtained from (a) NuSTAR starting from
MJD 58558.2323 and (b) Swift starting from MJD 55217.8178 with 100 s binning
time in the 3-78 keV and 0.3-10.0 keV energy bands, respectively. The Swift-
XRT light curves are grouped in each snapshot.

##  1 Introduction

Magnetic cataclysmic variables (MCVs) possess a strong magnetic ($\sim$ 1-200
MG) white dwarf (WD) which accretes material from a Roche-lobe-filling red
dwarf companion star. The intermediate polars (IPs), a subclass of MCVs, are
known as asynchronized binaries (i.e., $P_{\omega}$ $<$ $P_{\Omega}$, where
$P_{\omega}$ and $P_{\Omega}$ are spin and orbital periods, respectively) with
a WD magnetic field strength of $<$10 MG. The orbital-period distribution of
MCVs shows that most of the IPs have orbital periods longer than the period
gap of 2-3 hr (Scaringi et al. 2010). In these systems, accreting material
forms an accretion disk up to a certain point where the magnetic pressure
exceeds the ram pressure and subsequently the accreting material flows along
magnetic field lines. The accretion mechanism in IPs is usually explained with
the three different scenarios viz disk-fed, disk-less, and disk-overflow (see
Hameury et al. 1986; Rosen et al. 1988). In these scenarios, the mode of
accretion can be identified with the presence of orbital, spin, beat, and
side-band frequencies. Along with these frequencies, various inner radii, such
as the magneto-spheric radius ($R_{mag}$), the radius of the closest approach
to the WD of a ballistic stream from the inner Lagrangian point ($R_{min}$),
and the circularization radius ($R_{circ}$), can also be used to describe
their accretion geometry (for details, see Warner 1995). From the sample of
Pretorius & Mukai (2014) and the Gaia DR2 parallaxes, a more updated space
density of IPs is derived as $<$ 1.3$\times$10-7 pc-3 (see Schwope 2018). With
Gaia distances, it has been observed that the majority of the IPs peak at the
hard luminosity of 1033-1034 erg s-1, while there is also evidence of the
existence of low-luminous IPs, mostly shorter-period systems below the period
gap, and they have the luminosity of $\sim$ 1030-1032 erg s-1 (Schwope 2018;
de Martino et al. 2020). In the IPs, the magnetically channeled accretion
column impacts the WD surface, and strong shocks are formed in the accretion
columns; this heats the plasma up to a high temperature, about $\sim$ 50-600
MK. The shocked gas subsequently cools as it falls toward the surface of the
WD via thermal bremsstrahlung emitting hard X-rays (Aizu 1973). However, some
IPs also possess soft X-ray emission which can be modeled by using a blackbody
component from the poles on the surface of the WD. Blackbody emission is
mostly dominant in polars and has a temperature of 20-40 eV. In recent
studies, a few IPs also possess a blackbody emission with a temperature more
than that of the polars and such IPs are referred to as ”soft-IPs” (see,
Haberl & Motch 1995; Evans & Hellier 2007). The observed X-ray emission in IPs
interacts with its surroundings and the part of X-ray emission undergoes
photoelectric absorption and produces X-ray modulations. Around half of the
intrinsic emission is also directed toward the WD and is expected to be
reprocessed and/or reflected from the WD surface. The detection of the
reflection can be confirmed with the two spectral features: a Compton
reflection hump, which is observed in between the 10-30 keV energy range, and
the presence of the fluorescent Fe K$\alpha$ emission line at 6.4 keV. Both
absorption and reflection are important to carry out an in-depth study of an
IP which requires broadband spectroscopy covering both soft and hard X-rays.

Figure 2: (a) Lomb-Scargle and (b) CLEANed power spectra of IGR1654. From top to bottom, the panels show the X-ray power spectra obtained for the epoch 16 March 2019 of the NuSTAR observation in the 3-78 keV, 3-6 keV, 6-10 keV, and 10-30 keV energy bands, respectively. The red horizontal dotted lines represent the 95% confidence level. Table 2: Periods corresponding to significant peaks in the power spectra of IGR1654 obtained from periodogram analysis of the NuSTAR and Swift data. Telescopes | Epoch | Scargle |  | CLEAN
---|---|---|---|---
|  | $P_{\omega}$ | P3ω |  | $P_{\omega}$ | P3ω
|  | ( s ) | ( s ) |  | ( s ) | (s)
NuSTAR | 16 Mar 2019 | 546.3$\pm$0.8 | 182.2$\pm$0.1 |  | 546.3$\pm$0.8 | 182.2$\pm$0.1
Swift | 08 Mar 2019 | 546.4$\pm$3.0 | 182.1$\pm$0.3 |  | 545.1$\pm$0.3 | 182.1$\pm$0.1
Swift | 15 and 17 Mar 2019 | 546.7$\pm$1.0 | .. |  | 548.5$\pm$0.3 | ..
Swift | 21 and 23 Jan 2010 | 546.6$\pm$0.4 | .. |  | .. | ..

In this paper, we present the first detailed analysis of the X-ray
observations of IGR J16547-1916 (hereafter IGR1654). This source was detected
in the ROSAT all-sky survey and cataloged in the INTEGRAL/IBIS survey (Bird et
al. 2010). Masetti et al. (2010) tentatively classified this system as an IP
based on the detection of strong Balmer and He II emission lines in its
optical spectrum along with the equivalent width ratio of HeII
$\lambda(4686)$/H$\beta$ $\geq$ 0.5. From the optical variability, Lutovinov
et al. (2010) derived a period of 549$\pm$15 s and hypothesized this as a spin
period of the WD. Later, Scaringi et al. (2011) provided a clear detection of
the orbital and spin periods of 3.7 hr and 546 s, respectively, using
photometric and spectroscopic observations and classified this system as an
IP. Recently, Shaw et al. (2020) presented a legacy survey of 19 MCVs,
including IGR1654 with the NuSTAR. They fit the NuSTAR spectra in the 20-78
keV energy band using the PSR X-ray spectral model (Suleimanov et al. 2016,
2019) and derived their WD masses. For IGR1654, they investigated the WD mass
as 0.74${}_{-0.08}^{+0.09}$ $M_{\odot}$. A detailed temporal and spectral
analysis in the broad X-ray energy range has not been done for this source
yet. We, therefore, present a detailed temporal and spectral analysis of
IGR1654 using the Swift and NuSTAR observations. The paper is organized as
follows: Section 2 summarizes archival X-ray observations and their data
reduction description. Analyses and the results of the X-ray data are
described in Section 3. Finally, we present a discussion and concise summary,
in Sections 4 and 5, respectively.

Figure 3: Folded X-ray light curves as obtained for the epoch 16 March 2019 of
the NuSTAR observation of IGR1654 in the 3-6 keV, 6-10 keV, and 10-30 keV
energy bands. The bottom panels show the hardness ratio curves HR1 and HR2,
where HR1 is the ratio of the count rate in 6-10 keV to the count rate in the
3-6 keV energy bands, i.e., HR1=(6-10)/(3-6), and HR2 is the ratio of the
count rate in 10-30 keV to the count rate in 6-10 keV energy bands, i.e.,
HR2=(10-30)/(6-10). Figure 4: Orbital-phase-resolved spin pulse profile as
obtained from the NuSTAR observations.

Figure 5: (a) Lomb-Scargle and (b) CLEANed power spectra of IGR1654. From top
to bottom, the panels show the X-ray power spectra obtained from the Swift
observations for the epochs 08 Mar 2019, 15 and 17 Mar 2019, and 21 and 23 Jan
2010 in the 0.3-10.0 keV energy band, respectively. The red horizontal dotted
lines represent the 90% confidence level.

Figure 6: Folded X-ray light curves as obtained for the epochs 15 and 17 March
2019 and 08 March 2019 of the Swift-XRT observations of IGR1654 in the 0.3-3.0
keV, 3-6 keV, and 6-10 keV energy bands. The bottom panels show the hardness
ratio curves HR3, HR4, HR5, and HR6, where HR3 and HR5 are the ratio of the
count rate in 3-6 keV to the count rate in 0.3-3.0 keV energy bands, i.e.,
HR3=HR5=(3-6)/(0.3-3.0), and HR4 and HR6 are the ratio of the count rate in
6-10 keV to the count rate in 3-6 keV energy bands, i.e.,
HR4=HR6=(6-10)/(3-6).

##  2 Observations and data reduction

X-ray observations of IGR1654 were taken from the NuSTAR and Swift satellites
and their log is given in Table 1. We describe the details of the NuSTAR and
Swift observations below.

###  2.1 NuSTAR

IGR1654 was observed with the hard X-ray focusing observatory NuSTAR (Harrison
et al. 2013) on 16 March 2019 at 05:16:09 (UT) for 44.6 ks. NuSTAR consists of
two co-aligned telescopes and two focal plane modules, FPMA and FPMB, and it
observes in the 3-79 keV energy range. Each detector module consists of four
32$\times$32 Cadmium-Zinc-Telluride detectors and provides a spectral
resolution (full width at half maximum, FWHM) of 0.4 keV at 10 keV and 0.9 keV
at 68 keV. The data reduction was accomplished by using the standard NuSTAR
Data Analysis Software (NuSTARDAS v1.4.1) as a part of HEASOFT v6.26.1. The
unfiltered events were first reprocessed by using nupipeline in the presence
of the updated version of calibration data files (CALDB 20191219) and then the
science quality events were obtained after reprocessing. Source light curves
and spectra were extracted by selecting a circular region of 70 arcsec around
the source position. We used different extraction regions for FPMA and FPMB
modules of the NuSTAR, based on respective images of each module, to consider
the relative astrometric offset between them. For background light curves and
spectra, the same size circular region located on the same detector chip and
centered $\sim$ 4 arcmin away from the source was chosen to avoid
contamination from the source photons. The barycentric corrected light curves,
spectra, effective area files, and response matrices were obtained via the
nuproducts package. All spectra were grouped using grppha to have at least 25
counts per bin.

###  2.2 Swift

IGR1654 has been observed with the Swift satellite on nine occasions from 2010
to 2019. Among which, two observations on 15 March 2019 (ObsID 00088622002)
and 17 March 2019 (ObsID 00088622003) are contemporaneous with NuSTAR
observations. Swift consists of three instruments: the wide-field Burst Alert
Telescope (BAT; Barthelmy et al. 2005), which covers the 15-350 keV energy
range, and the narrow-field instruments, including the X-ray Telescope (XRT;
Burrows et al. 2005) which observes in the 0.3-10.0 keV energy range, and the
UV/Optical Telescope (UVOT; Roming et al. 2005) with filters covering
1700-6500 Å. The task xrtpipeline (version 0.13.4) along with the latest
calibration files were used to produce the cleaned and calibrated event files.
The barycentric correction was applied to the event files of all the
observations using the task barycorr. The source and background events with
grades of 0-12 were extracted. The source product image, light curve, and
spectrum were extracted by selecting a circular region of 30 arcsec radius.
The background was chosen from several nearby source-free regions with a
similar size to that of the source. An ancillary response file (ARF) was also
calculated in order to correct the loss of the counts due to hot columns and
bad pixels using exposure maps with the task xrtmkarf and used the response
matrix file (RMF), $swxpc0to12s6$_2$0130101v014.rmf$, provided by the Swift
team. All spectra from the Swift/XRT were rebinned using the grppha for a
minimum of five counts per bin. Spectral fits were performed by using the
C-statistic for the fit, which is more suitable for low count per energy bin.

##  3 Analysis and results

###  3.1 NuSTAR

####  3.1.1 X-ray light curves and power spectra

Background-subtracted X-ray light curves of IGR1654 were obtained from the
FPMA and FPMB instruments of NuSTAR and were combined using the FTOOLS task
lcmath (Blackburn 1995). The combined X-ray light curve in the 3-78 keV energy
band is shown in Figure 1. To determine its periodic behavior, we performed a
Fourier transform using the Lomb-Scargle periodogram (LS) method (Lomb 1976;
Scargle 1982; Horne & Baliunas 1986) from the light curves with a time bin of
10 s. Figure 2 shows the Lomb-Scargle power spectra of the NuSTAR timing data
in the 3-78 keV, 3-6 keV, 6-10 keV, and 10-30 keV energy bands. The LS power
spectra in each energy band are dominated by two sets of signals $-$ one set
centered around the frequency of 0.00183049 $s^{-1}$ and the other set around
the frequency of 0.0054885 $s^{-1}$, which correspond to the frequencies
$\omega$ and $3$$\omega$, respectively. In this way, we observed a total of
six peaks in both sets of signals including $\omega$ and $3$$\omega$ (see
Figure 2). We calculated the false alarm probability (Horne & Baliunas 1986)
to check the significance of detected peaks and found that all six peaks in
the 3-78 keV energy band are more than 95% of the confidence limit. The peak
power of all these significant peaks is found to decrease toward the harder
energy bands. Among all significant peaks, the strong power of $\sim$ 342 is
found at frequency $\omega$, while a somewhat weaker peak with the power of
$\sim$ 71 is detected at frequency $3$$\omega$ in the 3-78 keV energy band.
Other side-band frequencies appear as the combination of spin and orbital
frequencies, that is $\omega$$-$$2$$\Omega$, $\omega$$+$$2$$\Omega$ and
$3$$\omega$$-$$2$$\Omega$, $3$$\omega$$+$$2$$\Omega$ on each side of $\omega$
and $3$$\omega$, respectively. These side-band frequencies are found to be
equally spaced from the central frequencies $\omega$ and $3$$\omega$ with
equal and unequal amplitudes, respectively. However, their spacing does not
correspond to the half of the orbital period of this system, which suggests
that these side-bands might be spacecraft orbital aliases. Therefore, to
further confirm the presence of true periodicities in the system, the light
curve variations were modulated by the CLEAN algorithm (Roberts et al. 1987).
The CLEANed power spectra of IGR1654 in the 3-78 keV, 3-6 keV, 6-10 keV, and
10-30 keV energy bands are shown in Figure 2. The CLEANed power spectra were
obtained with a loop gain of the 0.1 and 1000 iteration. In the CLEANed power
spectra, we have not detected any side-band frequencies or unwanted spacecraft
orbital aliases. However, only two strong peaks at frequencies $\omega$ and
$3$$\omega$ were detected in each energy band, which is well consistent with
the periods derived from the LS algorithm. The significant periods derived
from the LS and CLEAN algorithms in the 3-78 keV energy band for the epoch 16
March 2019 are given in Table 2.

####  3.1.2 Periodic intensity variations

We explored the periodic variability of IGR1654, using the NuSTAR data, in the
following three energy bands: 3-6 keV, 6-10 keV, and 10-30 keV ranges. The
X-ray light curves in the aforementioned energy bands were folded using the
spin period ephemeris reported by Scaringi et al. (2011). The orbital and spin
period ephemerides of Scaringi likely have a cumulative error of well over one
complete cycle by the time of the X-ray observations of the epoch 2019. In
this case, the zero phase is not securely known, while more accurate periods
are known. Therefore, we have considered a “phase” as a “relative phase”
during binary and rotational motion throughout the paper. All NuSTAR light
curves were folded with a phase bin of 0.05 and are shown in Figure 3. The
spin-phase-folded light curves were found to be double-humped in all of the
energy bands described above. The broad maxima or flat-topped hump was seen
during the first half cycle; however, a relatively lower amplitude hump was
observed during the subsequent half cycle. The spin modulations in each energy
band are not sinusoidal, thus, we estimated the degree of spin pulsations with
($I_{max}$-$I_{min}$)/($I_{max}$+$I_{min}$) $\times$ 100 %, where $I_{max}$
and $I_{min}$ are maximum and minimum intensities in a pulse profile,
respectively. The derived value of the spin modulations are 43$\pm$3% (3-6
keV), 28$\pm$3% (6-10 keV), and 29$\pm$5% (10-30 keV). The pulse profile was
found to be more prominent at lower energies. During the rotation of the WD,
we also extracted the hardness ratio curves (HR1 and HR2) between the hard and
soft counts defined as follows: HR1 is the ratio of the count rate in [6-10]
keV to the count rate in the [3-6] keV energy bands, that is,
HR1=(6-10)/(3-6), and HR2 is the ratio of the count rate in [10-30] keV to the
count rate in the [6-10] keV energy bands, that is, HR2=(10-30)/(6-10) and
they are shown in the bottom two panels of Figure 3. The HR1 curve displays a
strong modulation and is 180∘ out of phase with respect to the intensity
modulation, that is, the maximum in the HR1 curve is observed at the lowest
intensity. However, HR2 does not show any significant variation over the spin
cycle. X-ray light curves of IGR1654 were also folded using the orbital period
of 3.7 hr (Scaringi et al. 2011) in the 3-6 keV, 6-10 keV, 10-30 keV, and 3-78
keV energy bands. No orbital modulations in X-rays were noticed in these
energy bands which was further confirmed by the absence of the orbital
frequency in the NuSTAR power spectrum of IGR1654.

Using the NuSTAR observations, we also inspected the variation in the X-ray
spin-pulse profile over an orbit of IGR1654. Using the orbital and spin period
ephemerides reported by Scaringi et al. (2011), we extracted light curves for
the 0.1 orbital phase interval in the 3-78 keV energy band and folded them
with the spin period. We constructed an orbital-phase-resolved spin pulse
profile that explores the evolution of pulse over an orbital cycle and is
represented as the color composite plot (see Figure 4). A double or triple
hump-like spin pulse profile appears to be present during an orbital motion of
IGR1654. The shape and size of the pulse seem to vary during each orbital
phase. Around the orbital phase segment 0.3-0.4, two humps appear to be
merging in a single broad hump. Subsequently, the pulse shape again looks like
a double or triple hump in forthcoming orbital phase intervals.

Figure 7: Combined Swift-XRT (black), NuSTAR-FPMA (red), and NuSTAR-FPMB
(blue) X-ray spectra of IGR1654 as fitted with the models $A$, $B$, $C$, and
$D$ (see text for more details about these models). The bottom panel shows the
spectral residuals obtained after fitting the broad-band spectrum with respect
to all fitted models.

###  3.2 Swift

####  3.2.1 X-ray light curves and power spectra

Figure 1 shows the X-ray light curve of IGR1654 in the 0.3-10.0 keV energy
band as extracted for nine epochs of the Swift-XRT observations. Using the LS
method, we performed a periodogram analysis of the Swift data. Due to large
data gaps in the combined data set of the Swift observations, the real
frequencies were found to be absent in the power spectrum. We, therefore,
performed a power spectral analysis for each epoch separately from the light
curves with a time bin of 10 s in the 0.3-10.0 keV energy band. A significant
power spectrum was not obtained for the epochs 2013, 2015, and 2017 due to the
small data coverage. However, we obtained the significant power spectra for
the data of the epoch 08 March 2019 and a combined data set of the epochs 15,
17 March 2019 and 21, 23 January 2010. Figure 5 shows the LS power spectra of
the timing data in the 0.3-10.0 keV energy band for the epochs described
above. We detected two significant periods at frequencies $\omega$ and
$3$$\omega$ for the epoch 08 March 2019, which are well consistent with the
periods derived from the NuSTAR data. However, only a significant spin period
was observed for the combined data set of the epochs 15, 17 March 2019 and 21,
23 January 2010. Although, the $3$$\omega$ frequency is also present in the
power spectrum of these epochs, sadly they lie below the confidence level of
90%. Similar to the NuSTAR data, the spacecraft orbital aliases are also
present in the Swift LS power spectra of the epochs described above. Thus, to
further confirm the presence of a true signal for these epochs, we employed
the CLEAN algorithm to all of the epochs described above which are shown in
Figure 5. The CLEANed power spectra lead to the peaks at frequencies $\omega$
and $3$$\omega$ for the epoch 08 March 2019, while, only spin frequency
$\omega$ was detected for the combined data set of the epochs 15 and 17 March
2019. Both detected frequencies are well consistent with the periods derived
from their LS algorithm. However, no peaks at frequencies $\omega$ and
$3$$\omega$ were detected in the CLEANed power spectrum of the combined data
of the epochs 21 and 23 January 2010. The significant periods derived from the
LS and CLEAN algorithms in the 0.3-10.0 keV energy band for the above
mentioned epochs are given in Table 2.

####  3.2.2 Periodic intensity variations

We folded the Swift X-ray light curves in the 0.3-3.0 keV, 3-6 keV, and 6-10
keV energy bands for the combined data of the epochs 15, 17 March 2019 and 08
March 2019. Figure 6 shows the folded X-ray light curves with a phase bin of
0.05 for the Swift data. Similar to the NuSTAR, for the epochs 15 and 17 March
2019 which are contemporaneous with NuSTAR, the Swift X-ray folded light
curves seem to be double-humped in the 0.3-3.0 keV and 3-6 keV energy bands,
where the second peak is marginally visible (see Figure 6). Using a similar
approach as described in Section 3.1.2, we also estimated the degree of spin
pulsations as 67$\pm$25%, 59$\pm$22%, and 77$\pm$45% in the 0.3-3.0 keV, 3-6
keV, and 6-10 keV energy bands, respectively. The rotational hardness ratio
curves HR3 and HR4 are defined as the ratio of the count rates in [3-6] keV to
the count rate in [0.3-3.0] keV, that is, HR3=(3-6)/(0.3-3.0), and the count
rate in [6-10] keV to the count rate in [3-6] keV energy bands, that is,
HR4=(6-10)/(3-6), respectively, were also derived and are shown in the bottom
panels of Figure 6. Similar to the HR1 curve of the NuSTAR data, the HR3 curve
shows hardening at the minimum intensity phase, and vice versa. However, no
significant variation is seen in the HR4 curve. In contrast to the epochs 15,
17 March 2019 and 16 March 2019, the spin-phased Swift X-ray light curves in
the 0.3-3.0 keV energy band reveals a triple-hump pulse profile for the epoch
08 March 2019 due to a stronger dip observed near phase 0.3 (see Figure 6).
The first two humps seem to be prominent near the spin phases $\sim$ 0.15 and
$\sim$ 0.45, while the third hump is observed with the smaller amplitude
around spin phase $\sim$ 0.8. In 3-6 keV, a dip around 0.3 become
significantly weaker and the modulation appears to be similar to NuSTAR, but
the third peak after phase $\sim$ 0.6-0.7 seems to be negligible or marginally
visible. The pulse amplitudes were derived as 87$\pm$24 %, 51$\pm$21%, and
75$\pm$44% in the 0.3-3.0 keV, 3-6 keV, and 6-10 keV energy bands,
respectively. The hardness-ratio curves, HR5 and HR6 (defined as similar to
HR3 and HR4), were also extracted. The HR5 curve exhibits an anti-correlated
pattern with the intensity profile, that is, at the maximum intensity phase,
the hardness ratio is minimum (see bottom panel of Figure 6); however, the HR6
variation seems to be almost constant. The spin-phase-folded Swift X-ray light
curves were also extracted for the epochs 2017, 2015, 2013, and 2010. No
significant periodic variations were seen in the pulse profile of these epochs
probably due to their insufficient data coverage. Similar to NuSTAR, the
orbital-phase-folded Swift X-ray light curves were also explored for the
epochs 21 and 23 January 2010, 08 March 2019, and 15 and 17 March 2019 in the
0.3-3.0 keV, 3-6 keV, 6-10 keV, and 0.3-10.0 keV energy bands. Unfortunately,
their phase-coverage was found to be incomplete because the data length of
Swift is small compared to the orbital period of the system.

Table 3: Best-fit spectral parameters obtained from the spectral fitting of
the contemporaneous Swift/XRT and NuSTAR (FPMA and FPMB) observations of
IGR1654.

| pwab | reflect | mkcflow |  | bbody | gauss |  |
---|---|---|---|---|---|---|---|---
Models ($\downarrow$) | NH,max | $\beta$ | $R_{refl}$ | Cos$i$ |  $k$T | $A_{z}$ | $n_{mkcflow}$ |  | $kT_{bb}$ | $n_{bb}$ | $n_{g}$ | EW | $f_{X0.5-78.0}$ |  $\chi^{2}_{\nu}$/dof
A | .. | .. | … | … | 71${}_{-7}^{+7}$ | 1.0${}_{-0.3}^{+0.3}$ | 1.94${}_{-0.19}^{+0.23}$ |  | .. | .. | 4.83${}_{-0.59}^{+0.58}$ | 226${}_{-21}^{+16}$ | 4.83${}_{-0.05}^{+0.05}$ | 1.24/792
B | 2.1${}_{-0.2}^{+0.5}$ | -0.32${}_{-0.06}^{+0.05}$ | … | … | 56${}_{-3}^{+5}$ | 1.0${}_{-0.2}^{+0.2}$ | 2.22${}_{-0.18}^{+0.32}$ |  | .. | .. | 4.24${}_{-0.55}^{+0.58}$ | 195${}_{-12}^{+31}$ | 4.16${}_{-0.04}^{+0.04}$ | 1.13/791
C | 1.8${}_{-0.3}^{+0.3}$ | -0.26${}_{-0.07}^{+0.08}$ | 1.7${}_{-0.5}^{+0.6}$ | 0.45† | 30${}_{-3}^{+4}$ | 0.6${}_{-0.1}^{+0.1}$ | 3.36${}_{-0.28}^{+0.36}$ |  | .. | .. | 3.78${}_{-0.57}^{+0.58}$ | 163${}_{-31}^{+58}$ | 3.87${}_{-0.04}^{+0.04}$ | 1.05/790
| 2.0${}_{-0.3}^{+0.3}$ | -0.26${}_{-0.06}^{+0.06}$ | 1† | $>0.70$ | 30${}_{-2}^{+3}$ | 0.6${}_{-0.1}^{+0.1}$ | 3.51${}_{-0.41}^{+0.20}$ |  | .. | .. | 3.89${}_{-0.56}^{+0.56}$ | 181${}_{-28}^{+34}$ | 3.97${}_{-0.04}^{+0.04}$ | 1.05/790
D | 1.8${}_{-0.3}^{+0.3}$ | -0.22${}_{-0.07}^{+0.10}$ | 1† | $>0.70$ | 31${}_{-1}^{+3}$ | 0.6${}_{-0.1}^{+0.1}$ | 3.43${}_{-0.30}^{+0.31}$ |  | 64${}_{-58}^{+47}$ |  $<$ 1.22 | 3.82${}_{-0.55}^{+0.57}$ | 172${}_{-15}^{+26}$ | 3.93${}_{-0.04}^{+0.04}$ | 1.04/788

Notes: ($\dagger$) represents a fixed parameter (see text for details). NH,max
is the maximum equivalent hydrogen column in units of 1023 cm-2 and $\beta$ is
the power-law index for the covering fraction. $R_{refl}$ is the reflection
component, $Cosi$ is the inclination angle of the reflecting surface, $kT$ is
the high temperature of mkcflow model in units of keV, $n_{mkcflow}$ is the
normalization of the mkcflow model in units of $10^{-10}$ $M_{\odot}$ yr-1,
$kT_{bb}$ is the blackbody temperature in units of eV, $n_{bb}$ is the
normalization constant of the blackbody in units of $10^{-2}$, $n_{g}$ is
normalization constant of the Gaussian component in units of 10-5, EW is the
equivalent width of Fe K$\alpha$ in units of eV, and $f_{X}$ is the unabsorbed
X-ray flux derived in the 0.5-78.0 keV energy band in units of 10-11erg cm-2
s-1. All the errors are within a 90% confidence interval for a single
parameter ($\Delta$ $\chi^{2}$ =2.706).

Table 4: Best-fit spectral parameters derived from the Swift/XRT observations.  | pwab | mkcflow | bbody |  |
---|---|---|---|---|---
Swift/XRT | NH,max | $\beta$ | $n_{mkcflow}$ | $kT_{bb}$ | $n_{bb}$ | $f_{X0.5-10.0}$ |  $\chi^{2}_{\nu}$/dof
(Date of Obs.) | (1023 cm-2) |  | ($\times$10-10 $M_{\odot}$ yr-1) | (eV) | ($\times$$10^{-02}$) | ($\times$10-11 erg cm-2 s-1) |
21 and 23 Jan 2010 | 2.5${}^{+4.8}_{-1.2}$ | -0.21${}^{+0.17}_{-0.13}$ | 4.01${}^{+2.59}_{-0.98}$ |  $<$ 64 |  $<$ 3.2 | 4.63${}^{+0.40}_{-0.40}$ | 1.01/75
08 Mar 2019 | 2.0${}^{+4.8}_{-1.0}$ | -0.35${}^{+0.17}_{-0.12}$ | 3.00${}^{+1.78}_{-0.63}$ | 53${}^{+6}_{-11}$ |  $<$ 2.6 | 3.60${}^{+0.30}_{-0.30}$ | 1.00/96
Table 5: Best-fit spectral parameters derived from the spectral fitting of the contemporaneous Swift/XRT and NuSTAR (FPMA and FPMB) observations of IGR1654 at spin phases.  Model | Parameters | Spin Phase
---|---|---
|  | 0.0$-$0.1 | 0.1$-$0.2 | 0.2$-$0.3 | 0.3$-$0.4 | 0.4$-$0.5
pwab |  $N_{H,max}$ ($\times$1023 cm-2) | 1.26${}_{-0.36}^{+0.59}$ | 0.99${}_{-0.36}^{+0.59}$ | 1.73${}_{-0.47}^{+0.75}$ | 2.79${}_{-0.81}^{+1.33}$ | 1.41${}_{-0.43}^{+0.59}$
| $\beta$ |  $>$ -0.55 | -0.05${}_{-0.35}^{+0.59}$ | -0.26${}_{-0.15}^{+0.22}$ | -0.38${}_{-0.15}^{+0.21}$ | -0.30${}_{-0.17}^{+0.29}$
Mkcflow |  $n_{mkcflow}$ ($\times$10-10) $M_{\odot}$ yr-1 | 3.57${}_{-0.78}^{+0.75}$ | 3.73${}_{-0.61}^{+0.36}$ | 4.20${}_{-0.29}^{+0.33}$ | 4.38${}_{-0.29}^{+0.34}$ | 3.83${}_{-0.26}^{+0.29}$
Gaussian |  $n_{g}$ ($\times$10-5) | 2.25${}_{-1.51}^{+1.56}$ | 4.37${}_{-1.76}^{+1.68}$ | 3.93${}_{-1.78}^{+1.87}$ | 3.33${}_{-1.87}^{+1.99}$ | 5.00${}_{-1.74}^{+1.83}$
X-ray flux |  $f_{X0.5-78.0}$($\times$10-11erg cm-2 s-1) | 3.98${}_{-0.11}^{+0.11}$ | 4.19${}_{-0.12}^{+0.11}$ | 4.70${}_{-0.13}^{+0.13}$ | 4.90${}_{-0.14}^{+0.13}$ | 4.32${}_{-0.12}^{+0.12}$
|  $\chi_{\nu}^{2}$/(dof) | 1.26/(140) | 1.10/(147) | 1.08/(151) | 0.96/(147) | 1.08/(150)
|  | 0.5$-$0.6 | 0.6$-$0.7 | 0.7$-$0.8 | 0.8$-$0.9 | 0.9$-$1.0
pwab |  $N_{H,max}$ ($\times$1023 cm-2) | 2.02${}_{-0.64}^{+1.04}$ |  $>$ 6.22 | 1.99${}_{-0.73}^{+1.16}$ | 2.84${}_{-1.08}^{+2.27}$ | 4.04${}_{-1.58}^{+2.55}$
| $\beta$ | 0.01${}_{-0.31}^{+0.79}$ | -0.62${}_{-0.10}^{+0.15}$ | -0.11${}_{-0.33}^{+0.53}$ | -0.25${}_{-0.26}^{+0.42}$ | -0.26${}_{-0.21}^{+0.51}$
Mkcflow |  $n_{mkcflow}$ ($\times$10-10) $M_{\odot}$ yr-1 | 3.07${}_{-0.41}^{+0.37}$ | 3.67${}_{-0.43}^{+0.68}$ | 3.05${}_{-0.45}^{+0.10}$ | 2.89${}_{-0.33}^{+0.38}$ | 2.93${}_{-0.32}^{+0.36}$
Gaussian |  $n_{g}$ ($\times$10-5) | 3.68${}_{-1.53}^{+1.77}$ | 5.65${}_{-2.58}^{+3.18}$ | 2.60${}_{-1.50}^{+1.47}$ | 5.52${}_{-1.79}^{+1.95}$ | 4.80${}_{-1.98}^{+2.08}$
X-ray flux |  $f_{X0.5-78.0}$($\times$10-11erg cm-2 s-1) | 3.45${}_{-0.11}^{+0.11}$ | 4.14${}_{-0.15}^{+0.14}$ | 3.42${}_{-0.11}^{+0.11}$ | 3.27${}_{-0.12}^{+0.11}$ | 3.30${}_{-0.12}^{+0.12}$
|  $\chi_{\nu}^{2}$/(dof) | 0.82/(114) | 0.90/(96) | 0.99/(107) | 0.90/(99) | 1.05/(90)
Figure 8: Variations of the best-fit spectral parameters as a function of spin
phases. From top to bottom, the panels show the variation in the maximum
equivalent hydrogen column $N_{H,max}$, the normalization of the mkcflow model
($n_{mkcflow}$), and the unabsorbed X-ray flux ($f_{X}$) in the 0.5-78.0 keV
energy band. The unit of all parameters is similar as described in Table 3.
Error bars are plotted within a 90% confidence limit for a single parameter.

###  3.3 X-ray spectra

####  3.3.1 Swift and NuSTAR spectral fits

Background-subtracted X-ray spectra of IGR1654 are shown in Figure 7. The iron
line complex is present in both the NuSTAR and Swift spectra. The X-ray
spectral analysis was performed using XSPEC version-12.10.1 (Arnaud 1996;
Dorman & Arnaud 2001). The spectral fitting of the Swift observations was
performed in the 0.5-10.0 keV energy range due to poor signal-to-noise ratio
of individual Swift spectra below 0.5 keV. The spectral analysis of the NuSTAR
data was done in the 3-78 keV energy band. We investigated IGR1654 by the
spectral fitting of the contemporaneous Swift/XRT (15 March 2019 and 17 March
2019) and NuSTAR-FPMA/FPMB (16 March 2019) observations. To fit the broad
0.5-78.0 keV spectra, we used a multi-temperature cooling flow model mkcflow
(Mushotzky & Szymkowiak 1988) which is more appropriate for the accreting WDs
(see Mukai 2017) along with a Gaussian component with the fixed-line energy
and line width at 6.4 keV and 0.01 keV, respectively, and approximated with
the interstellar absorption model phabs using the abundance tables of Asplund
et al. (2009) and the photoelectric absorption cross-sections BCMC
(Balucinska-Church & McCammon 1992). To know the cross-calibration
uncertainties of the distinct instruments, a constant model component was also
included as model A=constant$\times$phabs(mkcflow + gauss). The abundances
were applied in the optically thin thermal model from Asplund et al. (2009).
The redshift required in the mkcflow model cannot be zero. It was thus fixed
to a value of 17.766$\times$$10^{-8}$ for a Gaia distance of
1066${}_{-54}^{+61}$ pc (Gaia Collaboration, Bailer-Jones et al. 2018) and a
cosmological Hubble constant of 50 km s-1 Mpc-1. The low temperature of the
mkcflow was fixed to the minimum value allowed by the model as 0.0808 keV. We
assumed a switch parameter at the value of 2 which determines whether the
spectrum is computed by using the AtomDB data. With model $A$, we observed an
equivalent hydrogen column (NH) of 8$\times$$10^{22}$ cm-2 from the phabs
model, which is very large at the Gaia distance of this source. A fully
covering absorber model phabs is not necessarily due to interstellar
absorption entirely $-$ a component of an absorber intrinsic to the IP may
well have the same energy dependence as phabs. In that case, the intrinsic
absorption might be affected due to the dominant local absorbers, resulting in
a high value of NH. Moreover, the spectrum did not fit at lower energies below
2 keV well (see Figure 7) with $\chi^{2}_{\nu}$ of 1.24 (792 dof) using a
phabs absorption model, which confirms the presence of the complex absorption.
Thus, to account for the complex absorption, we used the pwab model as
B=constant$\times$phabs$\times$pwab(mkcflow + gauss) which is a power-law
distribution of a covering fraction as a function of the maximum equivalent
hydrogen column NH,max and the power-law index for the covering fraction
$\beta$ (Done & Magdziarz 1998). Using model B, we found a low value of NH
$\sim$ 1018 cm-2 from phabs which is not physical. Thus, for further spectral
fitting, we fixed the NH value to the total Galactic column in the direction
of IGR1654, that is, at 1.27$\times$$10^{21}$ $cm^{-2}$ (Kalberla et al.
2005). Model B with a fixed NH provides a better fit to the spectra below 2
keV with an improved $\chi^{2}_{\nu}$ of 1.13 (791 dof). Using model B, we
obtained the large equivalent width (EW) of the Fe K$\alpha$ emission line,
and the column density of cold matter was found close to the value of
2$\times$$10^{23}$ cm-2 (see Inoue 1985). This suggests that the bulk of the
Fe K$\alpha$ emission line can be accounted by the absorbers, while a small
contribution, if any, is from reflection. Using models A and B, we also found
that the spectrum did not fit at higher energies well, which could be
associated with the absence of a reflection component. Therefore, to take the
occurrence of X-ray reflection in the system into account, we used a
convolution model reflect (Magdziarz & Zdziarski 1995) as model
C=constant$\times$phabs$\times$pwab(reflect$\times$mkcflow + gauss). With
model C, we found a better fit, but the value of the reflection scaling factor
was derived to be $\sim$ 1.7 (more than unity) at a fixed inclination angle of
the reflecting surface at the default value of cos $i$=0.45. The reflection
component describes the fraction of downward radiation that is reflected, so,
the observed value more than unity is not physical. Thus, we fixed this
parameter to unity, allowing cos $i$ to vary, and we obtained fits with a
similar quality as the best fit value cos $i$ ¿ 0.70. The inclusion of the
reflect model provides a more satisfactory fit at higher energies with an
improved $\chi^{2}_{\nu}$ of 1.05 (790 dof). However, model C was unable to
explain the positive residual below 1 keV, which is visible in the residual
plot of Figure 7. To account for this excess in soft X-rays, we fit the
spectra with a lower-temperature optical thin plasma component (APEC; Smith et
al. 2001), but this component adjusted the values of other parameters such
that the spectral fitting gave an unacceptable fit. After that, to account for
the soft energy residual pattern, an additional blackbody component was then
added as model
$D$=constant$\times$phabs$\times$pwab(reflect$\times$mkcflow+bb+gauss), which
provides a better fit to the spectra with a marginally improved
$\chi^{2}_{\nu}$ of 1.04 (788 dof). The F-test showed that the model D was
more significant with an F-statistics of 4.8 with a null hypothesis
probability of $8.2\times 10^{-3}$. However, the confinement of the soft X-ray
excess to only one spectral bin reduces its evidence in the IGR1654.
Unabsorbed X-ray flux in the 0.5-78.0 keV energy band was also calculated
using the “cflux” model. The best-fit parameters as obtained for each model
are given in Table 3, where the error bars are quoted with a 90% confidence
limit for a single variable parameter.

####  3.3.2 Swift/XRT spectral fits

We examined the spectral evolution of IGR1654 using other Swift/XRT
observations. The same best-fit model D as described in the Section 3.3.1 was
used for the spectral fitting of the Swift/XRT observations, keeping fixed the
plasma temperature and abundance values of the mkcflow and the parameter of
the Gaussian component to those determined from the average spectral fitting
of the NuSTAR and Swift observations as presented in Table 3. We also used the
same fixed parameters which were adopted for the average spectral fitting. For
the epochs 2013, 2015, and 2017, the spectra were found to be under-fitted as
per their low value of reduced chi-square. Thus, due to their poor statistics,
we did not include the data of these epochs further for spectral analysis.
However, we estimated their fluxes using webpimms
111https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3pimms/w3pimms.pl as $\sim$
3.4$\times$$10^{-12}$ erg cm-2 s-1, $\sim$ 6.7$\times$$10^{-12}$ erg cm-2 s-1,
and $\sim$ 5.6$\times$$10^{-12}$ erg cm-2 s-1 for the epochs 2013, 2015, and
2017, respectively. Here, we considered $\sim$ 27 keV plasma and Galactic NH
of 1.27$\times$$10^{21}$ cm-2. For the epochs 2010 and 2019, the unabsorbed
X-ray fluxes were found to be variable. During the epoch 2019, the flux was
found to decrease by $\sim$ 22% from the epoch 2010. The best-fit spectral
parameters derived from the Swift/XRT observations are summarized in Table 4.

###  3.4 Phase-resolved spectroscopy

Using contemporaneous Swift/XRT and NuSTAR (FPMA and FPMB) observations,
phase-resolved spectroscopy was also performed to trace the dependence of
X-ray spectral parameters during the rotation of the WD. For this, we simply
divided the spin pulse into ten equally spaced phase intervals from 0 to 1 in
the phase interval of 0.1 by applying phase filters on the barycentric-
corrected event file in xselect package. The spectra of each phase segment
were fitted with the best-fit model $D$, keeping fixed the plasma temperature
and abundance values of the mkcflow, and the parameters of the blackbody
components at the values obtained from the average spectral fitting. Resulting
spectral parameters are summarized in Table 5. The free parameters are pwab
components ($N_{H,max}$ and $\beta$), the normalization of the mkcflow model
($n_{mkcflow}$), and the normalization of the Gaussian component ($n_{g}$).
The significance of the variation of all of the components was measured using
the $\chi^{2}$-test. We found that the variations of $N_{H,max}$,
$n_{mkcflow}$, and $f_{X}$ are significant above a 90% confidence level.
Variations of these parameters are shown in Figure 8. However, for the
parameters $\beta$ and $n_{g}$, we did not find significant variations along
with the spin phases. The variation of the absorption component ($N_{H,max}$)
was found to be anti-correlated with the X-ray flux. However, an opposite
pattern is seen in the variations of the X-ray flux and $n_{mkcflow}$, that
is, the variation of $n_{mkcflow}$ is correlated with the variation of the
X-ray flux.

##  4 Discussion

We have carried out a detailed X-ray analysis of an intermediate polar
IGR1654. From the NuSTAR and Swift observations, we derived two significant
periods, $P_{\omega}$ and $P_{3}$ω in the 3-78 keV and 0.3-10.0 keV energy
bands for the epochs 16 March 2019 and 08 March 2019, respectively. The
periods derived for these epochs are well consistent (see Table 2). A
significant spin period was also derived for the epoch 15 and 17 March 2019 of
the Swift observations in the 0.3-10.0 keV energy band, which is similar to
the period derived for the epochs described above. The derived X-ray spin
period matches well with the optical spin period reported by Scaringi et al.
(2011). The strong X-ray spin signal at $\sim$ 546 s is seen at all X-ray
energies is characteristic of IPs and confirms the nature of the object. With
the presence of optical beat ($\omega$$-$$\Omega$) and spin frequencies,
Scaringi et al. (2011) reported that IGR1654 displayed a mixture of disk and
stream accretion. In contrast to Scaringi et al. (2011), we did not detect the
beat or orbital frequencies in the X-ray power spectrum of IGR1654. The
dominance of the spin frequency and the lack of beat frequency in the X-rays
indicates that the system is accreting predominantly via a disk (for details,
see, Mason et al. 1988; Hellier 1991; Wynn & King 1992; Norton 1993; Norton et
al. 1996). Although the existence of the beat modulation is not seen in the
X-ray power spectrum of IGR1654, the spin modulations during an orbital cycle
(Figure 4) do have, however, substantial implications for its accretion
geometry. The observed spin modulations in IGR1654 might be affected due to
absorption or occultation by a structure fixed in the binary frame or due to
reprocessing of the spin pulse from the secondary star, the disk-stream
region, or the inner Lagrangian point (Norton et al. 1992).

Energy dependence of the spin pulse profile is one of the unique properties of
IPs. The observed energy-dependent rotational modulations and hardening at the
minimum intensity of the pulse profile as obtained from the NuSTAR and Swift
data in the low energy ($<$ 10 keV) range can be attributed to the accretion
curtain scenario and generally explained with variable complex absorbers
(Rosen et al. 1988). In this scenario, the accreting material falls onto the
WD poles from the inner edge of the truncated disk at the magnetospheric
radius and flows along the magnetic field lines in an arc-shaped curtain. In
this model, the optical depth of the infalling material in the curtain is
larger along the field lines rather than perpendicularly. Thus, photoelectric
absorption is maximum when the accretion curtain points toward the observer
and provides minimum spin modulations, and vice versa. No significant
variations seen in the hardness ratio along with the spin phases above 10 keV
imply that the accretion curtain scenario is not expected to produce
significant spin modulations above 10 keV. Mukai (1999) and De Martino et al.
(2001) suggested that either reflection or tall shocks (shock height $>$ 0.1
$R_{WD}$) are responsible for the hard X-ray spin modulations in IPs. If
reflection is the main mechanism for the hard X-ray modulations, then it
should provide an anti-phased spin pulse profile with respect to a low energy
pulsation. This is contrary to what we observe for IGR1654 (see Figure 3). On
the other hand, the self occultation of tall shocks would provide the same
phase spin modulations at both high and low energies and both accreting poles
would be visible over a range of viewing geometry. To have the same-phased
spin modulations at both hard and soft energies, $i$ \+ $\delta$ $<$ 90∘,
where $i$ is the binary inclination and $\delta$ is the magnetic colatitude
(Mukai 1999). This would suggest that the upper pole dominates the hard X-rays
at all phases. In a few cases, where the hard X-ray amplitudes are observed on
the order of 10 % or less, the complex absorbers are found to be responsible
for their modulations via Compton scattering (Rosen 1992). For IGR1654, the
observed strong (29 %) hard X-ray spin modulations are in the same phase with
the low energy spin modulations, indicating that the hard X-ray spin
modulations can be attributed to tall shocks above the accreting poles.
Moreover, the height of the shock can be estimated using the reflection
amplitude as described by Tsujimoto et al. (2018). If the reflector subtends
$2\pi$ steradian of the sky, as seen from the X-ray emitter, then it provides
a negligible shock height and only one pole is visible at all phases. However,
when both emission regions are simultaneously observable and the value of the
reflection amplitude is relatively small, then it implies a large shock
height. Present X-ray data did not allow us to constrain the reflection
amplitude (see Section 3.3.1). Because of this, we were unable to constrain
the shock height, but the high energy ($>$ 10 keV) spin modulation suggests
that it is not small. Such hard X-ray modulations were also observed in the
other two short-rotating period IPs V709 Cas and V2731 Oph, where a finite
shock height was proposed as a solution for the spin modulations above 10 keV
(De Martino et al. 2001; Mukai et al. 2015; Lopes de Oliveira & Mukai 2019).

Following Norton et al. (1999), the observed double-humped pulse profile for a
short rotating period ($P_{\omega}$$\sim$ 546 s) of the WD in IGR1654 can be
explained with the two-pole accretion model. Two-pole accretion is believed to
be a ”normal” mode behavior in disk-accreting IPs, which can produce both
either single-peaked or double-peaked pulse profiles, depending on the
strength of the magnetic field of the WD and the visibility of two accreting
poles during rotation of the WD (see Hellier 1996; Allan et al. 1996). Norton
et al. (1999) suggested two processes to produce a double-peaked spin pulse
profile in the two-pole accretion scenario, which are briefly described below.

First possibility invokes large accretion areas due to the weak magnetic field
of the short period rotating WD. The radius at which material is captured by
the field lines is relatively small due to the low magnetic field of the WD.
Consequently, the vertical optical depth is lower than the horizontal optical
depth. Thus, when the upper pole is moving toward the observer, the minimum
attenuation of the X-ray flux occurs and maximum emission is seen from it and
gives the first peak in the pulse profile. At this phase, the lower pole is
generally occulted since this pole is in anti-phase with that from the upper
pole. However, when the upper pole is moving away from the observer, the lower
pole is at its most visible, giving a second peak in the pulse profile.

Second possibility invokes tall accretion regions, but with the vertical
optical depths being larger than the horizontal optical depths, as in the
classical accretion scenario. The shock height is proportional to the size of
the accreting area (Frank et al. 1992), so the accretion regions in the short
period rotating IPs are tall due to a weak magnetic field of the WD. When the
upper pole points away from the observer giving maximum flux, the lower pole
is viewed essentially from the side and its flux adds to the first maximum.
However, when the upper pole points toward the observer giving minimum flux,
the lower pole may still be visible and give rise to a second maximum. Norton
et al. (1999) also reported that slow rotators do not exhibit X-ray beat
periods and they are an indicator of a WD with a relatively weak magnetic
field. For IGR1654, we did not detect the X-ray beat signal in its power
spectra; also, the spin modulations are double-humped where high energy spin
modulations suggest that it has a tall shock. Therefore, the second
possibility seems to be the most feasible to produce a double-humped spin
pulse profile in a short period IP IGR1654. In contrast to NuSTAR, triple-hump
profiles of the Swift data for the epoch 08 March 2019 are difficult to
explain using the two-pole accretion model. To accommodate for them in a two-
pole accretion model, two adjacent peaks with the presence of a narrow dip (at
a spin phase $\sim$ 0.3) could represent the emission from one dominant pole,
whereas a relatively smaller amplitude hump after a wider dip (at spin phase
$\sim$ 0.6-0.7) may represent the emission from the second pole. If two nearby
peaks represent one dominant pole, then the pole should remain in the line of
sight for a longer time. This is also evident from the observed pulse profile
of IGR1654 in which the dominant pole remains in view for almost half of the
spin cycle. A narrow dip between two adjacent peaks is not prominent in all
energy bands, indicating that the possibility of absorption is more likely the
cause for the appearance of the triple-hump pulse profile. Some short-period
IPs, such as V405 Aur, AE Aqr, YY Dra, DQ Her, XY Ari, GK Per, V709 Cas, V667
Pup, V515 And, and V2731 Oph (see Allan et al. 1996; Hellier 1996; Kamata &
Koyama 1993; Norton et al. 1988, 1999; Butters et al. 2007, 2008; de Martino
et al. 2008; Lopes de Oliveira & Mukai 2019), have shown double-peaked X-ray
spin pulse profiles on some occasions and they are explained with the two-pole
accretion scenario. Also, these short-period IPs did not exhibit clear X-ray
beat periods in their lives. The absence of a beat signal and observed double-
humped pulse profile at a spin period of $\sim$ 546 s from two-pole accretion
suggests that IGR1654 can also be placed in the list of the short-period IPs
described above. In contrast to X-rays, Scaringi et al. (2011) detected a
single-peaked and quasi-sinusoidal spin modulation in the optical domain for
IGR1654. This seems to be very interesting since the X-ray spin pulse profile
is double-peaked for this system. This can be interpreted with the standard
accretion-curtain model. In this model, optical emission originates from the
accretion curtains between the inner disk and the WD. If they are optically
thick, their varying aspect produces modulations during WD rotation. In this
case, both poles of the WD act in phase due to which the changing visibility
of the curtains results in a single-peaked pulse with a maximum when the upper
pole points away from the observer (Hellier 1991, 1995; Kim & Beuermann 1996).

The average X-ray spectrum of IGR1654 is well modeled by a complex absorber
with a maximum equivalent hydrogen column of $\sim$ 1.8$\times$$10^{23}$ cm-2
and a power-law index of -0.22 for a covering fraction, a multi-temperature
cooling flow model at temperatures 0.0808 keV (fixed) and $\sim$ 31 keV, along
with a blackbody with an average temperature of $\sim$ 64 eV. In contrast to
other soft-IPs (see Mason et al. 1992; Haberl et al. 1994, 2002; Evans &
Hellier 2004; De Martino et al. 2004; Vrielmann et al. 2005; Anzolin et al.
2008; Joshi et al. 2016, 2019), the evidence of a soft X-ray excess is meager
in the X-ray spectrum of IGR1654. If the soft X-ray excess is really present
in IGR1654, then it can be due to the heated region near the accretion
footprints which is not hidden by the accretion column depending upon the
system inclination and the magnetic colatitude (see Evans & Hellier 2007). We
also derived unabsorbed soft ($F_{s}$) and hard ($F_{h}$) X-ray fluxes of
5.02${}_{-6.90}^{+3.55}$$\times$$10^{-12}$ erg cm-2 s-1 and
3.00${}_{-0.03}^{+0.03}$$\times$$10^{-11}$ erg cm-2 s-1 in the energy band of
0.5-78.0 keV from the blackbody and mkcflow models, respectively. The softness
ratio, $F_{s}$ /4$F_{h}$, was then calculated as $\sim$ 0.04 for IGR1654,
which seems to be matched with the softness ratios observed for other soft-IPs
(Evans & Hellier 2007). We also determined the size of the accretion footprint
from the soft X-ray flux. The unabsorbed soft X-ray flux of
5.02$\times$$10^{-12}$ erg cm-2 s-1 and the temperature of 64 eV imply an
emitting area of 3.95$\times$$10^{13}$ cm-2. The WD mass of
0.74${}_{-0.08}^{+0.09}$ $M_{\odot}$ in IGR1654 implies the observed blackbody
emitting area covers $\sim$ 6$\times$10-4 of the WD surface, which is
consistent with other estimates for the accretion area in IPs (Hellier 1997).
The above discussion is purely based on the presence of a soft X-ray excess
only in the X-ray spectra of IGR1654.

From spin-phase-resolved spectroscopy, we have found that the variation in the
absorption component is anti-correlated with the X-ray flux, that is, the
absorption component is found to be maximum when the X-ray flux is minimum.
Such variations can be explained with the widely accepted classical curtain
scenario. During the rotation of the WD, when the curtain points toward the
observer, the X-ray flux is minimum due to the maximum absorption, however,
the X-ray flux is maximum when the accretion curtain moves away from the line
of sight of the observer.

##  5 Summary

To summarize, the detection of the X-ray spin period at $\sim$ 546 s is well
consistent with the previously obtained optical spin period and unambiguously
confirms the IP nature of this system. The presence of the strong spin pulse,
with no sign of orbital or side-band periodicities in the X-rays, indicates
that the system is accreting predominantly via a disk. A variable covering
absorber appears responsible for the spin pulsations in the low energy range,
however, the modulations above 10 keV can be attributed to tall shocks. The
observed double-humped X-ray pulse profiles at low and high energies reveal
two-pole accretion geometry with tall accretion regions in short rotating IP
IGR1654, which is probably caused by a weak magnetic field of the WD. The
X-ray spectrum of IGR1654 is affected by complex absorption with an equivalent
hydrogen column of $\sim$ 1.8$\times$$10^{23}$ cm-2 and a power-law index of
-0.22 for a covering fraction, as well as described by a soft X-ray blackbody
component at $\sim$ 64 eV and an optically thin plasma emission component at
$\sim$ 31 keV. Variations in the absorption component and X-ray flux along
with the WD rotation are compatible with the classical accretion curtain
scenario.

## Acknowledgements

We acknowledge the referee for useful comments and suggestions that improved
the manuscript considerably. This research has made use of data obtained with
the NuSTAR mission, a project led by the California Institute of Technology
(Caltech), managed by the Jet Propulsion Laboratory (JPL) and funded by NASA.
This research has made use of the XRT Data Analysis Software (XRTDAS)
developed under the responsibility of the ASI Science Data Center (ASDC),
Italy. This work is supported by the National Program on Key Research and
Development Project (Grants No. 2021YFA0718503, 2021YFA0718500), and the NSFC
(12133007, U1838103, 11622326). One of the authors Ashish Raj acknowledges the
Research Associate Fellowship with order no. 03(1428)/18/EMR-II under Council
of Scientific and Industrial Research (CSIR).

## References

  * Aizu (1973) Aizu, K. 1973, Progress of Theoretical Physics, 49, 1184
  * Allan et al. (1996) Allan, A., Horne, K., Hellier, C., et al. 1996, MNRAS, 279, 1345
  * Anzolin et al. (2008) Anzolin, G., de Martino, D., Bonnet-Bidaud, J.-M., et al. 2008, A&A, 489, 1243
  * Arnaud (1996) Arnaud, K. A. 1996, in Astronomical Society of the Pacific Conference Series, Vol. 101, Astronomical Data Analysis Software and Systems V, ed. G. H. Jacoby & J. Barnes, 17
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481
  * Balucinska-Church & McCammon (1992) Balucinska-Church, M. & McCammon, D. 1992, ApJ, 400, 699
  * Barthelmy et al. (2005) Barthelmy, S. D., Barbier, L. M., Cummings, J. R., et al. 2005, Space Sci. Rev., 120, 143
  * Bird et al. (2010) Bird, A. J., Bazzano, A., Bassani, L., et al. 2010, ApJS, 186, 1
  * Blackburn (1995) Blackburn, J. K. 1995, in Astronomical Society of the Pacific Conference Series, Vol. 77, Astronomical Data Analysis Software and Systems IV, ed. R. A. Shaw, H. E. Payne, & J. J. E. Hayes, 367
  * Burrows et al. (2005) Burrows, D. N., Hill, J. E., Nousek, J. A., et al. 2005, Space Sci. Rev., 120, 165
  * Butters et al. (2007) Butters, O. W., Barlow, E. J., Norton, A. J., & Mukai, K. 2007, A&A, 475, L29
  * Butters et al. (2008) Butters, O. W., Norton, A. J., Hakala, P., Mukai, K., & Barlow, E. J. 2008, A&A, 487, 271
  * de Martino et al. (2020) de Martino, D., Bernardini, F., Mukai, K., Falanga, M., & Masetti, N. 2020, Advances in Space Research, 66, 1209
  * De Martino et al. (2004) De Martino, D., Matt, G., Belloni, T., Haberl, F., & Mukai, K. 2004, A&A, 415, 1009
  * De Martino et al. (2001) De Martino, D., Matt, G., Mukai, K., et al. 2001, A&A, 377, 499
  * de Martino et al. (2008) de Martino, D., Matt, G., Mukai, K., et al. 2008, A&A, 481, 149
  * Done & Magdziarz (1998) Done, C. & Magdziarz, P. 1998, MNRAS, 298, 737
  * Dorman & Arnaud (2001) Dorman, B. & Arnaud, K. A. 2001, in Astronomical Society of the Pacific Conference Series, Vol. 238, Astronomical Data Analysis Software and Systems X, ed. F. R. Harnden, Jr., F. A. Primini, & H. E. Payne, 415
  * Evans & Hellier (2007) Evans, P. & Hellier, C. 2007, ApJ, 663, 1277
  * Evans & Hellier (2004) Evans, P. A. & Hellier, C. 2004, MNRAS, 353, 447
  * Frank et al. (1992) Frank, J., King, A., & Raine, D. 1992, Accretion power in astrophysics.
  * Gaia Collaboration, Bailer-Jones et al. (2018) Gaia Collaboration, Bailer-Jones, C. A. L., Rybizki, J., Fouesneau, M., Mantelet, G., & Andrae, R. 2018, AJ, 156, 58
  * Haberl & Motch (1995) Haberl, F. & Motch, C. 1995, A&A, 297, L37
  * Haberl et al. (2002) Haberl, F., Motch, C., & Zickgraf, F.-J. 2002, A&A, 387, 201
  * Haberl et al. (1994) Haberl, F., Throstensen, J. R., Motch, C., et al. 1994, A&A, 291, 171
  * Hameury et al. (1986) Hameury, J.-M., King, A. R., & Lasota, J.-P. 1986, MNRAS, 218, 695
  * Harrison et al. (2013) Harrison, F. A., Craig, W. W., Christensen, F. E., et al. 2013, ApJ, 770, 103
  * Hellier (1991) Hellier, C. 1991, MNRAS, 251, 693
  * Hellier (1995) Hellier, C. 1995, in Astronomical Society of the Pacific Conference Series, Vol. 85, Magnetic Cataclysmic Variables, ed. D. A. H. Buckley & B. Warner, 185
  * Hellier (1996) Hellier, C. 1996, The intermediate polars, ed. A. Evans & J. H. Wood, Vol. 208, 143
  * Hellier (1997) Hellier, C. 1997, MNRAS, 288, 817
  * Horne & Baliunas (1986) Horne, J. H. & Baliunas, S. L. 1986, ApJ, 302, 757
  * Inoue (1985) Inoue, H. 1985, Space Sci. Rev., 40, 317
  * Joshi et al. (2019) Joshi, A., Pandey, J. C., & Singh, H. P. 2019, AJ, 158, 11
  * Joshi et al. (2016) Joshi, A., Pandey, J. C., Singh, K. P., & Agrawal, P. C. 2016, ApJ, 830, 56
  * Kalberla et al. (2005) Kalberla, P. M. W., Burton, W. B., Hartmann, D., et al. 2005, A&A, 440, 775
  * Kamata & Koyama (1993) Kamata, Y. & Koyama, K. 1993, ApJ, 405, 307
  * Kim & Beuermann (1996) Kim, Y. & Beuermann, K. 1996, A&A, 307, 824
  * Lomb (1976) Lomb, N. R. 1976, Ap&SS, 39, 447
  * Lopes de Oliveira & Mukai (2019) Lopes de Oliveira, R. & Mukai, K. 2019, ApJ, 880, 128
  * Lutovinov et al. (2010) Lutovinov, A. A., Burenin, R. A., Revnivtsev, M. G., Suleimanov, V. F., & Tkachenko, A. Y. 2010, Astronomy Letters, 36, 904
  * Magdziarz & Zdziarski (1995) Magdziarz, P. & Zdziarski, A. A. 1995, MNRAS, 273, 837
  * Masetti et al. (2010) Masetti, N., Parisi, P., Palazzi, E., et al. 2010, A&A, 519, A96
  * Mason et al. (1988) Mason, K. O., Rosen, S. R., & Hellier, C. 1988, Advances in Space Research, 8, 293
  * Mason et al. (1992) Mason, K. O., Watson, M. G., Ponman, T. J., et al. 1992, MNRAS, 258, 749
  * Mukai (1999) Mukai, K. 1999, Astronomical Society of the Pacific Conference Series, Vol. 157, The X-ray Light Curves of Magnetic Cataclysmic Variables with Non-zero Shock Heights, ed. C. Hellier & K. Mukai, 33
  * Mukai (2017) Mukai, K. 2017, PASP, 129, 062001
  * Mukai et al. (2015) Mukai, K., Rana, V., Bernardini, F., & de Martino, D. 2015, ApJ, 807, L30
  * Mushotzky & Szymkowiak (1988) Mushotzky, R. F. & Szymkowiak, A. E. 1988, in NATO Advanced Science Institutes (ASI) Series C, Vol. 229, NATO Advanced Science Institutes (ASI) Series C, ed. A. C. Fabian, 53–62
  * Norton (1993) Norton, A. J. 1993, MNRAS, 265, 316
  * Norton et al. (1999) Norton, A. J., Beardmore, A. P., Allan, A., & Hellier, C. 1999, A&A, 347, 203
  * Norton et al. (1996) Norton, A. J., Beardmore, A. P., & Taylor, P. 1996, MNRAS, 280, 937
  * Norton et al. (1988) Norton, A. J., Watson, M. G., & King, A. R. 1988, MNRAS, 231, 783
  * Norton et al. (1992) Norton, A. J., Watson, M. G., King, A. R., Lehto, H. J., & McHardy, I. M. 1992, MNRAS, 254, 705
  * Pretorius & Mukai (2014) Pretorius, M. L. & Mukai, K. 2014, MNRAS, 442, 2580
  * Roberts et al. (1987) Roberts, D. H., Lehar, J., & Dreher, J. W. 1987, AJ, 93, 968
  * Roming et al. (2005) Roming, P. W. A., Kennedy, T. E., Mason, K. O., et al. 2005, Space Sci. Rev., 120, 95
  * Rosen (1992) Rosen, S. R. 1992, MNRAS, 254, 493
  * Rosen et al. (1988) Rosen, S. R., Mason, K. O., & Cordova, F. A. 1988, MNRAS, 231, 549
  * Scargle (1982) Scargle, J. D. 1982, ApJ, 263, 835
  * Scaringi et al. (2010) Scaringi, S., Bird, A. J., Norton, A. J., et al. 2010, MNRAS, 401, 2207
  * Scaringi et al. (2011) Scaringi, S., Connolly, S., Patterson, J., et al. 2011, A&A, 530, A6
  * Schwope (2018) Schwope, A. D. 2018, A&A, 619, A62
  * Shaw et al. (2020) Shaw, A. W., Heinke, C. O., Mukai, K., et al. 2020, MNRAS, 498, 3457
  * Smith et al. (2001) Smith, R. K., Brickhouse, N. S., Liedahl, D. A., & Raymond, J. C. 2001, ApJ, 556, L91
  * Suleimanov et al. (2016) Suleimanov, V., Doroshenko, V., Ducci, L., Zhukov, G. V., & Werner, K. 2016, A&A, 591, A35
  * Suleimanov et al. (2019) Suleimanov, V. F., Doroshenko, V., & Werner, K. 2019, MNRAS, 482, 3622
  * Tsujimoto et al. (2018) Tsujimoto, M., Morihana, K., Hayashi, T., & Kitaguchi, T. 2018, PASJ, 70, 109
  * Vrielmann et al. (2005) Vrielmann, S., Ness, J.-U., & Schmitt, J. H. M. M. 2005, A&A, 439, 287
  * Warner (1995) Warner, B. 1995, Cambridge Astrophysics Series, 28
  * Wynn & King (1992) Wynn, G. A. & King, A. R. 1992, MNRAS, 255, 83