MNRAS 521, 3951–3961 (2023) https://doi.org/10.

1093/mnras/stad781
Advance Access publication 2023 March 16

On the cyclotron absorption line and evidence of the spectral transition in

SMC X-2 during 2022 giant outburst
G. K. Jaisawal ,1 ‹ G. Vasilopoulos ,2,3 S. Naik ,4 C. Maitra ,5 C. Malacaria ,6 B. Chhotaray ,4,7
K. C. Gendreau,8 S. Guillot ,9 M. Ng 10 and A. Sanna 11
1 DTU Space, Technical University of Denmark, Elektrovej 327-328, DK-2800 Lyngby, Denmark
2 Université de Strasbourg, CNRS, Observatoire Astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France
3 Department of Physics, National and Kapodistrian University of Athens, University Campus Zografos, GR-15783, Athens, Greece
4 Astronomy and Astrophysics Division, Physical Research Laboratory, Navrangpura, Ahmedabad, 380009, Gujarat, India
5 Max-Planck-Institut für Extraterrestrische Physik, Gießenbachstraße 1, D-85748 Garching, Germany
6 International Space Science Institute (ISSI), Hallerstrasse 6, CH-3012 Bern, Switzerland

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7 Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar, 382055, Gujarat, India
8 Astrophysics Science Division, NASA’s Goddard Space Flight Center, Greenbelt, MD 20771, USA
9 Institut de Recherche en Astrophysique et Planétologie, UPS-OMP, CNRS, CNES, 9 Avenue du Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France
10 MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
11 Dipartimento di Fisica, Università degli Studi di Cagliari, SP Monserrato-Sestu km 0.7, I-09042 Monserrato, Italy

Accepted 2023 March 10. Received 2023 March 10; in original form 2023 February 13

ABSTRACT
We report comprehensive spectral and temporal properties of the Be/X-ray binary pulsar SMC X-2 using X-ray observations
during the 2015 and 2022 outbursts. The pulse profile of the pulsar is unique and strongly luminosity dependent. It evolves
from a broad-humped into a double-peaked profile above luminosity 3 × 1038 erg s−1 . The pulse fraction of the pulsar is found
to be a linear function of luminosity as well as energy. We also studied the spectral evolution of the source during the latest
2022 outburst with NICER. The observed photon index shows a negative and positive correlation below and above the critical
luminosity, respectively, suggesting evidence of spectral transition from the sub-critical to supercritical regime. The broad-band
spectroscopy of four sets of NuSTAR and XRT/NICER data from both outbursts can be described using a cut-off power-law model
with a blackbody component. In addition to the 6.4 keV iron fluorescence line, an absorption-like feature is clearly detected in
the spectra. The cyclotron line energy observed during the 2015 outburst is below 29.5 keV, however latest estimates in the 2022
outburst suggest a value of 31.5 keV. Moreover, an increase of 3.4 keV is detected in the cyclotron line energy at equal levels of
luminosity observed in 2022 with respect to 2015. The observed cyclotron line energy variation is explored in terms of accretion
induced screening mechanism or geometrical variation in line forming region.
Key words: stars: neutron – pulsars: individual: SMC X-2 – X-rays: stars.

1 I N T RO D U C T I O N ≤1037 erg s−1 and occur close to the periastron passage of the binary
system. The second category of outbursts is giant in nature, where
Be/X-ray binaries (BeXRBs) represent two-thirds of the population the peak luminosity reaches ≥1037 –1038 erg s−1 . The latter usually
of high mass X-ray binaries. These systems consist of a massive (> lasts for a multiple or significant portion of the orbit and does not
10 M ) optical companion and a compact object (usually a neutron follow any orbital dependencies.
star) in a binary system. The optical companion in BeXRBs is a non- A significant population of BeXRBs is found in the Milky Way
supergiant OB spectral type star that shows Balmer series emission and the Magellanic Clouds with luminosities in the range of 1034 –
lines and infrared excess at a point in its life (Reig 2011). The above 1038 erg s−1 (Liu, van Paradijs & van den Heuvel 2006; Reig 2011).
characteristics originate from an equatorial circumstellar disk that is Our Galaxy hosts about 60–70 such systems (Reig 2011; Walter et al.
formed around the Be star due to its rapid rotation at velocities of 2015). The Small Magellanic Cloud (SMC; a neighbouring irregular
more than 75 per cent of Keplerian limit (Porter & Rivinius 2003). dwarf galaxy), however, contains about 68 pulsars (and a total of 122
The compact object in the system, on the other hand, accretes directly sources including candidates) despite being only a few per cent of the
from the Be-circumstellar disk. Two kinds of X-ray outbursts are mass of the Milky Way Galaxy (Reig 2011; Coe & Kirk 2015; Walter
observed from BeXRBs. First, Type-I outbursts are short (only a few et al. 2015; Haberl & Sturm 2016; Yang et al. 2017; Vinciguerra et al.
weeks long), (quasi-)periodic events that reach a peak luminosity of 2020).
SMC X-2 is a 2.37 s pulsating source in a BeXRB system located
inside SMC (Schurch et al. 2011) at a distance of 62 kpc (Hilditch,
 E-mail: gaurava@space.dtu.dk Howarth & Harries 2005; Graczyk et al. 2014). It was the second

© 2023 The Author(s)

Published by Oxford University Press on behalf of Royal Astronomical Society
3952 G. K. Jaisawal et al.
outburst luminosity of 6 × 1038 erg s−1 (Kennea et al. 2015; Negoro
et al. 2015; Jaisawal & Naik 2016). Ionized emission lines from N,
O, Ne, Si, and Fe were detected in the data from the XMM–Newton
observation (La Palombara et al. 2016). Moreover, with broad-band
coverage of NuSTAR in the range of 3–79 keV, the neutron star
magnetic field was estimated for the first time to be ≈3 × 1012 G
based on the discovery of a cyclotron resonance scattering feature
(CRSF) at around 27 keV (Jaisawal & Naik 2016). A negative
correlation between the luminosity and cyclotron line energy was
also reported in the study. In addition to this, the pulsar is known
to show luminosity-dependent pulse profiles evolving from single
to double-peaked (Jaisawal & Naik 2016; Li et al. 2016; Roy et al.
2022). The onset of the propeller regime observed in late 2015 also
provided a measurement of the magnetic field to be ≈3 × 1012 G

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(Lutovinov et al. 2017), in agreement with the estimation through
CRSF detection.
After 7 yr of X-ray quiescence, SMC X-2 became active on 2022
June (Kennea, Coe & Evans 2022). The pulsar reached a peak
luminosity of 1 × 1038 erg s−1 , 3 weeks after its detection in the
soft X-ray band (Coe et al. 2022). Unlike the 2015 outburst, the
MAXI/GSC (Matsuoka et al. 2009) did not detect any significant
outburst peak in 2–20 keV band due to the relatively moderate
nature of the outburst in addition to the observational coverage gap
(see e.g. Fig. 1). We monitored the target closely with NICER and
NuSTAR to understand the spectral and temporal evolution during the
2022 outburst. We also analysed three NuSTAR observations from
the 2015 outburst to examine the cyclotron line and its evolution
Figure 1. The light curves of SMC X-2 during its 2015 (top) and 2022
(bottom) X-ray outbursts with MAXI (2–20 keV; red dot), NICER (0.5–10 keV;
and also studied the broad-band temporal and spectral properties
blue square), and Swift/XRT (0.3–10 keV; grey ellipse). The vertical dotted of the source. Section 2 reports the details of the observations
lines show the start date of the NuSTAR observations. In the bottom panel, and data analysis methods. The timing and spectral results are
the XRT light curve is scaled by a factor of seven to compare with the NICER presented in Section 3, followed by a discussion and conclusion in
light curve. Section 4.

brightest X-ray source in the galaxy when SAS 3 discovered it

in October 1977. The recorded luminosity was 8.4 × 1037 erg s−1 2 O B S E RVAT I O N S A N D DATA A N A LY S I S
(assuming a distance of 65 kpc) in the 2–11 keV energy band (Clark
et al. 1978; Clark, Li & van Paradijs 1979). Later observations 2.1 NICER
with the HEAO, Einstein, and ROSAT missions demonstrated the Launched in 2017 June, the NICER X-ray timing instrument (XTI,
X-ray transient nature of the source (Marshall et al. 1979; Seward & Gendreau, Arzoumanian & Okajima 2012; Gendreau et al. 2016) is
Mitchell 1981; Kahabka & Pietsch 1996). Thanks to RXTE (Rossi X- a soft XRT (0.2–12 keV) attached to the International Space Station.
ray Timing Explorer) and ASCA (Advanced Satellite for Cosmology The XTI consists of a total of 56 co-aligned concentrator optics. Each
and Astrophysics), coherent X-ray pulsations from SMC X-2 were optics collimates the soft X-ray photons on to a silicon drift detector
detected for the first time during the 2000 January–April outburst at the focus (Prigozhin et al. 2012). A high time resolution of ∼100 ns
(Corbet et al. 2001). This discovery made it possible to identify the (rms) and spectral resolution of ≈85 eV at 1 keV are achieved by
accreting object as a neutron star. The optical observations of the NICER. The effective area of the instrument is ≈1900 cm2 at 1.5 keV,
system, on the other hand, suggested two possible early-type stars with 52 active detectors. The total field of view of NICER is ≈30
at an angular separation of 2.5 arcsec as the potential counterparts arcmin2 .
of the pulsar. The Optical Gravitational Lensing Experiment I-band NICER monitored SMC X-2 after the onset of the 2022 outburst
photometric studies found variability at a period of 18.62 ± 0.02 in June. We used a total of 37 observations under the ObsIDs
d from one of the stars (northern star) (Schurch et al. 2011). This 52028301xx with a net exposure time of ≈39.6 ks for studying
periodicity closely matched the orbital period of ≈18.4 d measured the pulsar emission during the outburst between 2022 June 20
by studying the X-ray pulse-period modulation during the 2002 and and August 17. We reduced the NICER data using the nicerl21
2015 outbursts (Townsend et al. 2011; Li et al. 2016). The optical script available under HEASOFT version 6.30. The reprocessing is
counterpart (northern star) is identified to be an O9.5 III–V emission done in the presence of the gain and calibration database files of
star (McBride et al. 2008). version 20200722. The cleaned events obtained from the pipeline
The system displayed major outbursts during 1977 October (Mar- are used in our further analysis. In the beginning, the events from
shall et al. 1979; Seward & Mitchell 1981), 2002 January–April the South Atlantic Anomaly region were filtered out. We further
(Corbet et al. 2001), 2015 August–November (Kennea et al. 2015; applied standard filtering criteria based on the elevation angle from
Jaisawal & Naik 2016), and 2022 June–August (Coe et al. 2022). the Earth limb, pointing offset, and the offset from the bright
Detailed studies with XMM–Newton, Swift/XRT (X-Ray Telescope),
and NuSTAR were performed during the 2015 outburst when the
pulsar was accreting in the super-Eddington regime with a peak 1 https://heasarc.gsfc.nasa.gov/docs/nicer/analysis threads/nicerl2/.

MNRAS 521, 3951–3961 (2023)

 SMC X-2 with NICER and NuSTAR 3953
Table 1. Log of simultaneous observations of SMC X-2 with NuSTAR and
Swift/XRT or NICER during its 2015 and 2022 X-ray outbursts.

Observatory/ ObsID Start date Exposure

Instrument (ks)

NuSTAR 90102014002 2015-09-25T21:51:08 24.5

Swift/XRT 00034073002 2015-09-25T22:32:58 1.8
Swift/XRT 00081771002 2015-10-12T21:30:58 1.5
NuSTAR 90102014004 2015-10-12T21:41:08 23
Swift/XRT 00034073042 2015-10-21T14:08:58 4
NuSTAR 90101017002 2015-10-21T21:31:08 26.7
NICER 5202830119 2022-07-13T07:50:21 1.1
NuSTAR 90801319002 2022-07-13T20:18:43 42.7

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Earth. Good time intervals were produced using the nimaketime
task. Final spectra and light curves were created with the XSE-
LECT package of FTOOLS. The spectral background corresponding
to each observation is generated using the nibackgen3C502
tool (Remillard et al. 2022). The response matrix and ancillary
response files of version 20 200 722 are applied in our spectral
analysis.

2.2 NuSTAR
NuSTAR is the first hard X-ray focusing observatory launched in 2012
June (Harrison et al. 2013). It consists of two co-aligned grazing angle
incidence telescopes. The mirrors in each optic are coated with mul-
tilayers of Pt/SiC and W/Si that reflect the soft to hard X-ray photons.
A Cadmium–Zinc–Telluride detector at the focal point of each unit is
sensitive to the 3–79 keV photons. Following the recent outburst of
SMC X-2, we requested a NuSTAR target of opportunity observation.
The target was observed for an effective exposure of 42.7 ks on 2022
Figure 2. The 3–79 keV pulse profiles of SMC X-2, observed with NuSTAR,
July 13–14 (Table 1). Standard analysis procedures were followed arranged in order of luminosity. The top two (Obs-I and Obs-II) and bottom
for data reduction with NUSTARDAS 1.9.7 software. Unfiltered events (Obs-III) panels are from the 2015 outburst. The third panel (Obs-IV)
were processed in the presence of the CALDB of version 20 220 802 represents the pulse profile from the recent 2022 outburst. L38 stands for
using nupipeline task. Source products are extracted from a circular 0.5–100 keV unabsorbed luminosity in 1038 erg s−1 unit.
region of 120 arcsec radius around the central coordinates on each
detector using the nuproducts task. The background products are also 3 R E S U LT S
accumulated in a similar manner from a source-free circular region
of 120 arcsec radius. The background-subtracted light curves from 3.1 Timing analysis
both detector modules of NuSTAR were combined for our timing
studies. We searched for X-ray pulsations in the 3–79 keV NuSTAR light
We also reduced the data from the NuSTAR observations of SMC curves of SMC X-2 using the χ 2 -maximization technique (Leahy
X-2 during its 2015 major outburst (Table 1) by following the 1987). The barycentric corrected pulse period of the neutron star was
above procedure. The first observation was close to the peak of estimated to be 2.37197(2), 2.37141(2), 2.37257(2), and 2.37283(1) s
the outburst in 2015 September, whereas the other two were in the during Obs-I, Obs-II, Obs-III, and Obs-IV, respectively. The light
declining phase. Corresponding Swift/XRT observations are analysed curves from all the NuSTAR observations are folded with the
to perform broad-band spectroscopy (see also Jaisawal & Naik corresponding pulse period to obtain pulse profiles in the 3–79 keV
2016; Lutovinov et al. 2017 for XRT data analysis and descriptions; band, which are shown in Fig. 2. A double-peaked profile is clearly
Evans et al. 2009). All four NuSTAR observations in the 2015– evident at a luminosity3 of 6 × 1038 erg s−1 (top panel of Fig. 2).
2022 timeline are simply referred to as Obs-I, Obs-II, Obs-III, The shape of the pulse profile changes as luminosity decreases to
and Obs-IV in the paper. For spectroscopy, we have grouped each <3 × 1038 erg s−1 where a hump-like structure appears in the profile
NICER, NuSTAR, and XRT spectra for a minimum of 32 counts between 0.5 and 1.5 pulse phase. The pulse profiles exhibit similar
per channel bin to achieve a good signal-to-noise ratio using morphology at an equal level of luminosities observed during the
grppha. 2015 (Obs-II) and 2022 (Obs-IV) outbursts.

3 The 0.5–100 keV unabsorbed luminosity is calculated at a distance of 62 kpc

2 https://heasarc.gsfc.nasa.gov/docs/nicer/toolsnicer bkg est tools.html. after broad-band spectroscopy that is presented in Section 3.2.

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3954 G. K. Jaisawal et al.

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Figure 3. The energy resolved pulse profiles of SMC X-2 from the NuSTAR observations during its 2015 (Obs-I, Obs-II, and Obs-III) and 2022 (Obs-IV)
outbursts. L38 stands for 0.5–100 keV unabsorbed luminosity in units of 1038 erg s−1 .

We adopted the following definition to evaluate the pulse fraction

(PF) of the pulsar, i.e. the relative amplitude of pulsed modulation:
Fmax − Fmin
PF = , (1)
Fmax + Fmin
where, Fmax and Fmin are the maximum and minimum intensities
observed in the pulse profile, respectively. The estimated PFs during
Obs-I, Obs-II, Obs-III, and Obs-IV are ≈45.7 ± 0.4 per cent,
29.2 ± 0.4 per cent, 17.6 ± 0.2 per cent, and 26.2 ± 0.3 per cent,
respectively. The observed PF is correlated with luminosity. This
means that the pulsed emission from the accretion column or the
hot spot contributes more than the unpulsed radiation (originating
from accretion flow or from the surface) when the source luminosity
increases.
To examine the evolution of pulsed beam geometry of the source,
we folded the energy-resolved light curves in 3–7, 7–15, 15–25, 25–
40, and 40–79 keV from the NuSTAR observations (Fig. 3). Doubled
peaked profiles are observed throughout soft to hard X-ray energy
ranges during Obs-I. The emission from both poles is clearly apparent
at this stage. As the luminosity decreases to a level of ∼3 × 1038
erg s−1 , the pulse profiles below 15 keV (Obs-II and Obs-IV) appear
with a hump-like structure that further evolves into a double-peak
at higher energies. The Obs-III is at around the Eddington limit of
Figure 4. The evolution of pulse fraction with energy, obtained from the
a classical neutron star. At this point, the soft to hard pulse profiles
energy resolved pulse profiles of the pulsar.
are single-peaked with a hump in the middle. We further studied
the energy evolution of the PF from the pulse profiles. Fig. 4 shows
(see Vasilopoulos et al. 2022). First, we adopted the epoch folding
positive dependencies between the energy and the PF. An extremely
Z-search test implemented through HENdrics and Stingray
low PF of about 11 per cent is found during Obs-III in the 3–7 keV
(Huppenkothen et al. 2019). Then, we refined the temporal solution
band.
and its uncertainty based on the ToA (time of arrival) of individual
pulses by using PINT4 (Luo et al. 2021). For some snapshot phases
3.2 Spin evolution connecting the ToAs was challenging to impossible due to multiple
peaks in the periodogram with similar intensity, a problem often
We used the barycentric corrected NICER data to investigate the encountered in slow pulsars observed with gaps (e.g. see appendix of
evolution of the temporal properties with the outburst and in partic-
ular, the spin evolution. To search for a periodic signal, we followed
the same methodology adopted for NICER monitoring of SXP 15.6 4 https://github.com/nanograv/pint/.

MNRAS 521, 3951–3961 (2023)

 SMC X-2 with NICER and NuSTAR 3955

10

Norm. counts s−1 keV−1

1

0.1

1.2

ratio
1

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0.8

0.5 1 2 5
Energy (keV)

Figure 6. Three representative NICER spectra in 0.5–10 keV fitted with an

absorbed cut-off power-law model. Black, red, and green correspond to an
unabsorbed luminosity of 4.4 × 1037 , 6.8 × 1037 , and 1.3 × 1038 erg s−1 in
the 0.5–10 keV range, respectively.

fit to the RXTE data yields a lower eccentricity consistent with the
one reported by Townsend et al. (2011). For comparison, we plotted
both solutions to the newly obtained and archival data shown in
Fig. 5.

Figure 5. Period evolution of SMC X-2 during the 2022 outburst using 3.3 The continuum emission during 2022 outburst
NICER and NuSTAR observations in top panel. The bottom panel shows
the pulse period evolution observed by RXTE during the 2000 January–May The soft X-ray energy spectrum of SMC X-2 is studied to understand
outburst. the emission at different phases of the 2022 outburst. We used NICER
observations at multiple epochs of the outburst in this study. Each
Zolotukhin et al. 2017; Vasilopoulos et al. 2018). The resulting period 0.5–10 keV NICER spectrum can be fitted statistically well with
measurements are shown in Fig. 5, In the same plot, we mark the an absorbed cut-off power-law model in XSPEC (Arnaud 1996). Fig.
NuSTAR measurement. We note that NICER observations where a 6 shows the energy spectra from these observations together. We
defined period was not obtained are marked as ‘bad’ and no error is considered TBabs model at Wilm abundance (Wilms, Allen &
given as their uncertainty is similar to the range of the plot. McCray 2000) and Verner cross-section (Verner et al. 1996) to
In the spin evolution, we see clear signatures of orbital motion, account for the local and interstellar medium absorptions along the
consistent with the 18.38 d period reported in the literature based on source direction in our spectral fit. We found that the equivalent
RXTE data (Townsend et al. 2011), whereas a similar periodicity is hydrogen column density (NH ) varies in the range of 1–3 × 1021
also seen in optical data of the system (e.g. Roy et al. 2022). Mod- atoms cm−2 during these observations. To reduce the spectral fitting
elling of the archival RXTE data has revealed an almost circular orbit degeneracy in the soft X-ray band, the column density is fixed at
with an eccentricity of about 0.07. The sampling of the RXTE data an average value of 1.43 × 1021 cm−2 , which is consistent with the
was sparse and in similar orbital phases. In contrast, the new NICER value observed with XMM–Newton in 2015 within error bars (La
data cover a smaller baseline but better sample the orbital cycle Palombara et al. 2016). We then fitted each individual spectrum with
near the peak of the outburst. Thus, their study could help improve an absorbed cut-off power-law model at the above-fixed column
the old orbital solution. To model the orbital evolution, we used a density. No signature of iron fluorescence line is detected in the
model composed of the orbital signature and the first derivative of the NICER spectra. The 0.5–10 keV unabsorbed flux is estimated using
frequency similar to Townsend et al. (2011). Moreover, we followed the cflux convolution model. The parameter errors are estimated
a Bayesian approach to effectively sample the whole parameter space for the 90 per cent confidence interval in this paper.
of the underline model (Karaferias et al. 2023). We applied the same The evolution of the spectral parameters during the outburst is
method to the NICER data, and the RXTE measurements.5 Given the shown in Fig. 7. The power-law photon index and cut-off energy are
issues with the NICER period determination at the later stages of the variable across the rise (blue) and decay (red) phases of the outburst.
2022 monitoring, we constrained our fit within MJD 59750–59790. The peak luminosity in the 0.5–10 keV range is found to be 1.3 × 1038
We find that the 2022 monitoring data yield a somehow eccentric erg s−1 (for a source distance of 62 kpc) around the outburst peak. To
orbit (e = 0.27), while the period is better constrained by the RXTE examine the spectral changes and associated spectral transition, the
data. Interestingly, if we maintain no priors for the eccentricity the parameters are studied with respect to the 0.5–10 keV unabsorbed
luminosity in Fig. 8. The photon index and cut-off energy follow a
positive correlation (with a Pearson correlation coefficient of 0.61
5 Data points were extracted from Townsend et al. (2011). and 0.66, respectively) with luminosity above 9 × 1037 erg s−1 . The

MNRAS 521, 3951–3961 (2023)

3956 G. K. Jaisawal et al.

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Figure 7. Spectral parameters of SMC X-2 after fitting each NICER energy Figure 8. The evolution of photon index and cut-off energy with the 0.5–
spectrum with an absorbed cut-off power-law model. The absorption column 10 keV luminosity of the pulsar. Square (blue) and squashbox (red) symbols
density is fixed at 1.43 × 1021 cm−2 . The unabsorbed luminosity is estimated correspond to the rising and declining parts of the 2022 outburst, respectively.
in 0.5–10 keV range for a source distance of 62 kpc. The outburst peaked
around 2022 July 10 with a luminosity of 1.3 × 1038 erg s−1 in the NICER column density to an average value of 1.25 × 1021 cm−2 . This resulted
band. The square (blue) and squashbox (red) symbols correspond to the rising in similar kinds of parameter variations as reported in Figs 7 and 8.
and declining parts of the 2022 outburst, respectively.

3.4 Broad-band spectroscopy of the pulsar during 2015 and

2022 giant outbursts
index stays close to a value of 0.35 at luminosity in the range of (6–9)
× 1037 erg s−1 . This could be identified as a critical limit of the pulsar We further performed broad-band spectroscopy of SMC X-2 in the
where the spectral shape changes. Below this limit, the source shows 1–70 keV range to investigate the continuum as well as the nature
a negative correlation (with a Pearson correlation coefficient of – of the cyclotron absorption line and its evolution. Three sets of XRT
0.57) between luminosity and the photon index. Similar behaviour is and NuSTAR quasi-simultaneous data from the 2015 outburst are used
observed between luminosity and the cut-off energy (with a Pearson along with the 2022 July NICER and NuSTAR pointed observations
correlation coefficient of –0.54). (Fig. 9). These spectra are additionally binned for representation
We also fitted each NICER spectrum with two absorption compo- purposes using setplot rebin command of XSPEC. The pulsar
nents together with a cut-off power-law model. One of the column spectrum can be described by standard models such as the Fermi–
densities was fixed at a foreground value 4 × 1020 cm−2 (Dickey & Dirac cut-off power-law, the negative and positive power-law with
Lockman 1990) at the Solar abundance. Another column density was exponential cut-off (NPEX; Makishima et al. 1999), and the cut-off
free in our study at the SMC abundance of 0.2 Solar (Russell & Dopita power-law with a blackbody component (see also Jaisawal & Naik
1992) to incorporate the local absorption. The SMC column density 2016). In our study, we used an absorbed cut-off power-law model
changes in the range 0.5–3 × 1021 cm−2 during the outburst. All the with a blackbody component (bbodyrad in XSPEC) to study all
fitted parameters, such as SMC column density, photon index, and four data sets. The column density was pegged at a lower limit of
the cut-off energy, however, were found to decrease with luminosity. 1 × 1020 cm−2 in the fit. A 6.4 keV Gaussian component for an
A gradual decline may be because of spectral degeneracy among iron fluorescence line is also needed. In addition to the emission,
these parameters in the soft X-ray band. This is similar to the findings a cyclotron absorption feature appears in the data and is fitted
discussed above in this section. Though we cannot totally disentangle with a Gaussian absorption line. The cyclotron lines are detected at
the variation of the local absorption during the outburst therefore <30 keV and at 31.5 keV in the 2015 and 2022 data sets, respectively
to reduce the degeneracy among the parameters, we fixed the SMC (Table 2). We used the Markov chain Monte Carlo model in XSPEC

MNRAS 521, 3951–3961 (2023)

 SMC X-2 with NICER and NuSTAR 3957

Norm. counts s−1 keV−1

Norm. counts s−1 keV−1

1 1

(a) (b)
0.1 0.1

0.01 0.01

10−3 10−3

2 2
0 0
χ

χ
−2 −2

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5 5
0 0
χ

χ
−5 −5
1 10 1 10
Energy (keV) Energy (keV)

1
Norm. counts s−1 keV−1

Norm. counts s−1 keV−1

10

0.1 (c) 1
(d)
0.1
0.01
0.01
10−3
10−3

2 2
0 0
χ

−2 −2
5 5
0 0
χ

−5
−5 −10
1 10 1 10
Energy (keV) Energy (keV)

Figure 9. The broad-band energy spectra of the pulsar during its 2015 and 2022 outbursts are fitted with an absorbed cut-off power-law model along with a
blackbody, and an iron emission line as well as a Gaussian absorption feature for a cyclotron line (top). The middle and bottom panels of each figure correspond
to the spectral residuals with and without an iron line and cyclotron feature component to the best-fitting spectra, respectively. (a)–(d) denote the sets of NuSTAR
and Swift/XRT (green) or NICER (magenta) data in Table 1, respectively.

for error estimation on the spectral parameters. The Goodman Weare Moreover, to study the model-independency of the cyclotron line,
algorithm with 20 walkers and a total length of 200 000 is considered we show the parameter evolution using an absorbed NPEX model
in our study. The spectral parameters at a 90 per cent confidence with a GABS component. The cyclotron parameters are consistent
interval are presented in Table 2. We also show the 68 per cent, 90 between both models (Fig. 11).
per cent, 95 per cent, and 99.7 per cent confidence level contour maps Following the broad-band fit, we found that the 0.5–10 keV
for cyclotron line energy and width for second and fourth NuSTAR luminosity represents about 40 per cent of the total pulsar emission
observations in Fig. 10. in a 0.5–100 keV band. Therefore, an average bolometric correction
The cyclotron line energy, width, and line strength decreased with of 2.5 can be applied to the outburst emission measured by NICER.
the luminosity during the 2015 outburst (Fig. 11). The second and This is consistent with the typical estimates where the soft band
fourth NuSTAR observations (see Table 2) are at almost the same mostly contributes approximately 30–40 per cent of the pulsar
luminosity level. However, the cyclotron line parameters, especially emission (Anastasopoulou et al. 2022; Vasilopoulos et al. 2022).
the cyclotron line energies, are found to be marginally higher (within The 2022 outburst of SMC X-2 peaked at around MJD 59769.4 with
90 per cent level) in 2022 July. The magnetic field of the neutron star a bolometric corrected luminosity of 3.2 × 1038 erg s−1 . This is close
can be estimated to be 3.5 × 1012 G based on this recent detection. to half of the peak value the pulsar attained in the 2015 outburst.

MNRAS 521, 3951–3961 (2023)

3958 G. K. Jaisawal et al.
Table 2. Best-fitting spectral parameters (with 90 % errors) of SMC X-2 obtained from four simultaneous NuSTAR and Swift/XRT or NICER
observations. The fitted model consists of an absorbed cut-off power-law continuum with a blackbody and a Gaussian function for the iron
emission line and cyclotron absorption line components.

Parameters Obs-I + XRT Obs-II + XRT Obs-III + XRT Obs-IV + NICER

NH a 0.01+ 0.01
−0.01 0.01+ 0.08
−0.01 0.01+ 0.04
−0.01 0.01+ 0.6
−0.01
Photon index −0.16 ± 0.06 −1 ± 0.1 −1.33 ± 0.1 −0.77 ± 0.1
Ecut (keV) 6.4 ± 0.2 5.2 ± 0.3 5 ± 0.3 5.9 ± 0.3
kTbb (keV) 1.1 ± 0.1 0.95 ± 0.04 0.95 ± 0.04 0.85 ± 0.02
Normbb 5.5 ± 1.5 9.1 ± 1.1 5.8 ± 0.7 12.4 ± 0.7
Radiusbb (km) 14.5 ± 2 18.7 ± 1.1 14.9 ± 0.9 21.8 ± 0.6
Fe line energy (keV) 6.39 ± 0.09 6.32 ± 0.07 6.37 ± 0.07 6.3 ± 0.1
Fe line eq. width (eV) 71 ± 10 72 ± 14 88 ± 18 83 ± 18
Cyclotron line energy (Ec ) (keV) 26.8 ± 0.8 28.1+ 1.7
−1.4 29.5+ 2.7
−1.7 31.5+ 1.3
−1.1
5.5 ± 0.8 5.5+ 1.5
6.6+ 2.3
6.5+ 0.9

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Cyclotron line width (σ c ) (keV) −1.1 −1.4 −0.8
Cyclotron line strength (τ c ) 3.9+ 1.1
−0.8 4.4+ 2.9
−1.6 6.2+ 6.9
−2.5 8.7+ 3.1
−2.2
Luminosityb (0.5–10 keV) 2.75 ± 0.02 1.13 ± 0.01 0.7 ± 0.01 1.10 ± 0.01
Luminosityb (0.5–100 keV) 6.08 ± 0.02 2.87 ± 0.02 1.97 ± 0.01 2.82 ± 0.01
χν2 (ν) 1.04 (1276) 0.96 (1125) 1.06 (602) 1.09 (1549)
a Equivalent hydrogen column density (in 1022 atoms cm−2 ).
b Luminosity in 1038 erg s−1 units, assuming the source distance of 62 kpc (Hilditch et al. 2005; Haschke, Grebel & Duffau 2012; Graczyk
et al. 2014).

Other parameters in Table 2 such as the blackbody temperature was SMC X-2 was observed with NuSTAR at luminosities above the
found to be in a narrow range of 0.85–1.1 keV during both outbursts. Eddington limit of a classical neutron star during the 2015 and 2022
We also measured the corresponding emission radius (Radiusbb ) to outbursts. The NuSTAR pulse profiles are found to be luminosity
examine the possible origin and location of thermal emission. The dependent. At a luminosity of 6.1 × 1038 erg s−1 (Obs-I), a doubled
observed Radiusbb is estimated to be in the range of 14–22 km (see peaked profile appears throughout soft to hard X-rays suggesting the
Table 2), which is close to the size of a neutron star. This suggests that emission from both the poles of the neutron star as the observed
the thermal component may originate from the neutron star surface peaks are separated by 0.5 phase in the pulse profile. The emission
or from the accretion column during the 2015 and 2022 outbursts. geometry, however, evolves below this luminosity, where the soft
X-ray profiles are mainly broad or contain a hump-like structure.
The emission from both poles is clearly apparent in the hard X-
4 DISCUSSION AND CONCLUSIONS rays in the case of Obs-II and IV. The pulse fraction of the pulsar
increases with energy clearly up to 40 keV, indicating an increase in
The broad-band emission from the accreting X-ray pulsars is un-
the pulsating photons contributing to emission at higher luminosities.
derstood to be due to thermal and bulk Comptonizations of seed
This suggests the rising height of the accretion column or mound.
photons from the hot spots within the accretion column mounted on
The profile changes with luminosity can be understood in terms of
the magnetic poles of the neutron star (Becker & Wolff 2007). The
evolving emission geometry, where the significant contribution of
underlying physical phenomena of these sources can be understood
the fan beam is anticipated in the supercritical regime.
by studying the pulse emission geometry and the spectral evolution
We also detected a spectral transition in SMC X-2 during the
of the pulsar during X-ray outbursts. At lower luminosities such as
2022 outburst with NICER. The photon index shows a positive and
1034 –1035 erg s−1 , the accreted material falls freely until it gets halted
negative dependency on luminosity below and above a range of
and settled by Coulomb interactions in a hydrodynamical shock near
value in the range of 6–8 × 1037 erg s−1 in 0.5–10 keV range.
the surface (Basko & Sunyaev 1975). This leads to a simplistic
Considering a bolometric correction factor of 2.5, we expect a critical
pulsed emission geometry in the form of a pencil beam where the
luminosity of 1.5–2 × 1038 erg s−1 at which the emission pattern is
X-ray photons propagate along the magnetic field lines. At this stage,
expected to change. According to Becker et al. (2012), the critical
the radiation is mostly dominated by bulk Comptonization (Becker &
luminosity depends on the magnetic field assuming disk accretion on
Wolff 2005, 2007). When the accretion rate increases, a radiation-
to a classical neutron star with a 1.4 M mass and a 10 km radius.
dominated shock is expected to be formed in the accretion column
at a critical luminosity that leads to geometrical changes or spectral
transition in the emission (Basko & Sunyaev 1976; Becker & Wolff  16/15
B
2007). The infalling material interacts closely with the shock and gets Lcrit = 1.49 × 1037 erg s−1 (2)
1012 G
decelerated through it before settling down on to the neutron star. The
photons below the shock region diffuse through the column side-wall
in the form of a fan beam pattern. The anticipated emission geometry Using equation (2), the magnetic field B can be estimated to be
is a mixture of fan and pencil beam patterns at a luminosity of ∼1036 – in the range of 8.7–11.4 × 1012 G for the above range of luminosity
1037 erg s−1 . The thermal as well as bulk Comptonization processes values. The estimated magnetic field differs by a factor of 3–4 from
contribute significantly to the observed broad-band emission at this the measurement based on the detection of a cyclotron line in the
stage. In the supercritical luminosity regime (>1037 erg s−1 ), a pure spectrum (Jaisawal & Naik 2016). In case no bolometric correction
fan beam pattern is expected because of a strong radiative shock that is applied, the magnetic field from equation (2) turns out to be 3.7–
makes the accretion column optically thick for photons propagating 4.8 × 1012 G, i.e. much closer to the estimates based on cyclotron
along the magnetic field lines. line energy.

MNRAS 521, 3951–3961 (2023)

 SMC X-2 with NICER and NuSTAR 3959

1
8

0.8
0.6
σc (keV)

6
+

0.4
4 (b)

0.2

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26 28 30
Ec (keV)

1
9
0.8

8
σc (keV)

0.6

7
+
0.4

6
Figure 11. Change in the cyclotron line parameters such as line energy,
width, and its strength (τ cyc ) with 0.5–100 keV unabsorbed luminosity. The
0.2

5 (d) measurements from the 2015 and 2022 outbursts are shown in solid circles and
squares, respectively. The red and blue colours correspond to line parameters
obtained after an absorbed cut-off power-law model along with blackbody
30 32 34 and GABS, and an absorbed NPEX model with a GABS model, respectively.
Ec (keV)

depending on the line energy since it is expressed as Ecyc = 11.6B12 ×

Figure 10. The 68 per cent, 90 per cent, 95 per cent, and 99.7 per cent (from
(1 + z)−1 keV, where B12 is the magnetic field in 1012 G unit, and z
innermost to outermost) confidence intervals contour maps between cyclotron
is the gravitational red-shift.
line energy and width at an equivalent level of luminosity from 2015 (upper)
and 2022 (bottom) outbursts. (b) and (d) have the usual meaning as denoted in The centroid energy of the cyclotron line in principle measures the
Fig. 9. The ‘+’ sign corresponds to the best-fitting values for both parameters. field strength at the line-forming region. A change in line energy with
The colour bars denote the parameter confidence range from 68 per cent to luminosity is observed in several accretion-powered X-ray pulsars
99.7 per cent on a scale of zero to one, respectively. during outbursts (Nakajima et al. 2006; Tsygankov, Lutovinov &
Serber 2010; Jaisawal, Naik & Epili 2016; Staubert et al. 2019).
In some cases like Her X-1 (Staubert et al. 2007), the cyclotron
4.1 The evolution of cyclotron absorption line and its
energy and luminosity are positively correlated, whereas there are
implication on the magnetic field
pulsars such as 4U 0115+63 (Nakajima et al. 2006; Tsygankov
Both the 2015 and 2022 X-ray outbursts of SMC X-2 lasted for et al. 2010) and V 0332+53 (Tsygankov et al. 2010) that show a
more than 2 months with peak bolometric luminosities of 6 × 1038 negative correlation between these parameters (Becker et al. 2012).
erg s−1 and 3 × 1038 erg s−1 , respectively (see Fig. 1). We report The positive correlation is expected in the sub-critical region (below
broad-band spectral properties of the pulsar during the latest giant the critical luminosity) when the pressure of the accreting plasma
outburst using data from NICER and NuSTAR observations. The pushes the hydrodynamical shock or line-forming region closer to the
2015 NuSTAR and Swift/XRT observations are also used to study neutron star surface with an increasing accretion rate (luminosity).
the cyclotron absorption line and its long-term evolution. We found On the other hand, a formation of radiation-dominated shock is
relatively higher cyclotron line energy (with an increase of 3.4 keV) expected in the accretion column at higher accretion rates. The shock
during the current outburst in comparison to the 2015 measurement drifts upwards in the column due to strong radiation pressure with
made around a similar luminosity. In addition, the line energy is increasing mass accretion rate in the supercritical regime (Becker
anticorrelated with luminosity in the 2015 outburst. The cyclotron et al. 2012). Therefore, a negative correlation between the cyclotron
line is a unique absorption-like feature that is observed in the 10– line energy and luminosity is expected at this phase. This is observed
100 keV spectrum of X-ray pulsars (Meszaros 1992). They appear in SMC X-2 when the pulsar was accreting in the supercritical regime
due to a resonance scattering of photons with electrons in quantized during the 2015 outburst. Alternatively, the formation of a cyclotron
Landau energy states in the presence of a strong magnetic field. line and its observed negative correlation can be understood by the
The field strength can be estimated directly using a 12-B-12 rule reflection of accretion column photons on to the neutron star surface

MNRAS 521, 3951–3961 (2023)

3960 G. K. Jaisawal et al.
(Poutanen et al. 2013). The hypothesis suggests that the cyclotron 2019. There was also a period in 1993–1996 when the line energy
line gets formed on the surface rather than in the accretion column was increased by a few keV. The time evolution of the cyclotron
where the gradient is high to explain the observed changes in the line line energy is still a matter of study. It is believed that the observed
energy. As the accretion rate increases, a larger accretion column decay/increase in line energy represents a geometrical change within
covers a substantial portion of the atmosphere from the pole to the the emission region or in the configuration of the local magnetic
equator (high to low magnetic field regions). This can also explain field rather than a change in the global dipolar magnetic field of the
the origin of the observed negative correlation between the cyclotron neutron star (Mukherjee, Bhattacharya & Mignone 2013; Staubert
energy and luminosity in SMC X-2 resulted due to a change in et al. 2019). This could be further understood in terms of a marginal
illumination pattern. imbalance between the accretion rate and the losing or settling rate
It is important to note that the cyclotron line energy of SMC X- of the accreted material on the accretion mound. If the settling rate
2 is different at a given luminosity observed at Obs-II and Obs-IV is slightly higher than the leakage of the material from the bottom
during different outbursts. The MAXI/GSC light curves in Fig. 1 of the mound, this may lead to an increase in the column height
show a clear rise in the source intensity after MJD 57259 and 59738 as well as a change in the local magnetic field configuration of
during the 2015 and 2022 outbursts, respectively. The source reached the line forming region. A line decay is expected naturally in this

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a luminosity of 2–3 × 1038 erg s−1 (Obs-II and IV) after 49 and 36 d case. Over time, the excessive accumulation of the material and its
since the onset of respective outbursts. Our measurements suggest an pressure on the mound may result in a forced redistribution of the
increase of 3.4 keV in the cyclotron line energy between these data material across the surface. This would adjust the accretion mount
sets at comparable luminosities. This difference in the cyclotron line to its unperturbed configuration where higher line energy would be
energy corresponds to a change in the magnetic field of 3.8 × 1011 expected. The time-scale for such redistribution is unclear. But, it
G, assuming a classical neutron star and gravitational redshift of 0.3. may happen after continuous accumulation of matter over a long
Such an enhancement in the cyclotron energy can be understood by period or (multiple) strong outbursts like those observed in 2002 and
an accretion-induced screening of the magnetic field or geometrical 2015 of SMC X-2. Future observations of the source during outbursts
changes in the line-forming region. Theoretical studies suggest that will allow understanding the behaviour of the cyclotron line better.
the accretion flow distribution from poles to lower latitudes may drag
the field lines (Choudhuri & Konar 2002 and references therein). This
AC K N OW L E D G E M E N T S
mechanism could effectively lower down the original field strength
even on a shorter time-scale in the top layer of the distributed material, We thank the referee for constructive suggestions on the paper.
considering no effect of magnetic buoyancy. However, in reality, the This research has made use of data obtained through HEASARC
screening mechanism depends on the ratio of time-scales for field Online Service, provided by the NASA/GSFC, in support of NASA
burial by the advection mechanism and the re-emerging of the field High Energy Astrophysics Programs. This work used the NuSTAR
through magnetic buoyancy and Ohmic rediffusion (Choudhuri & Data Analysis Software (NUSTARDAS) jointly developed by the ASI
Konar 2002). An increase of 3.4 keV in cyclotron line energy in the Science Data Center (ASDC, Italy) and the California Institute of
latest modest outburst suggests that the screening mechanism is not Technology (USA). SG acknowledges the support of the CNES. GV
effective as it is in the case of the 2015 giant outburst, where a similar acknowledges support by H.F.R.I. through the project ASTRAPE
luminosity is achieved in the decay phase almost 49 d after the onset. (Project ID 7802).
The neutron star by this point would accumulate a factor of two or
more mass with an integrated value of 3.5 × 1024 g in 2015. DATA AVA I L A B I L I T Y
A similar possibility is discussed for V 0332+53 during its
2004/05 outburst where the cyclotron line energy at a given lu- We used archival data of NICER, NuSTAR, Swift, and MAXI obser-
minosity in the decay got reduced by ≈1.5 keV with respect to vatories for this work.
the rising phase of the outburst (Cusumano et al. 2016). However,
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MNRAS 521, 3951–3961 (2023)