# Disentangling the neighbouring pulsars SXP 15.3 and SXP 305

I. M. Monageng1,3, M. J. Coe2, L. J. Townsend1,5, S. G. T. Laycock6, J. A.
Kennea7, A. Roy6, A. Udalski4, S. Bhattacharya6, D. M. Christodoulou6, D. A.
H. Buckley1,3,9 and P. A. Evans8
1South African Astronomical Observatory, P.O Box 9, Observatory, 7935, Cape
Town, South Africa
2Physics & Astronomy, University of Southampton, SO17 1BJ, UK
3Department of Astronomy, University of Cape Town, Private Bag X3, Rondebosch
7701, South Africa
4Astronomical Observatory, University of Warsaw, Al. Ujazdowskie 4, 00-478
Warszawa, Poland
5Southern African Large Telescope, P.O. Box 9, Observatory, 7935, Cape Town,
South Africa
6 Lowell Center for Space Science and Technology, University of Massachusetts
Lowell, MA, 01854, USA
7 Department of Astronomy and Astrophysics, The Pennsylvania State University,
525 Davey Lab, University Park, PA 16802, USA
8 University of Leicester, X-ray and Observational Astronomy Research Group,
Leicester Institute for Space and Earth Observation
9 Department of Physics, University of the Free State, PO Box 339,
Bloemfontein, 9300, South Africa
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

SXP 15.3 and SXP 305 are two Be X-ray binaries in the Small Magellanic Cloud
that are spatially separated by $\sim$7 arcsec. The small separation between
these sources has, in the past, resulted in confusion about the origin of the
emission from the combined region. We present long-term optical and X-ray
monitoring results of both sources, where we study the historic and recent
behaviour. In particular, from data collected as part of the S-CUBED project
we see repeating X-ray outbursts from the combined region of the two sources
in the recent lightcurve from the Neil Gehrels Swift Observatory, and we
investigate the origin of this emission. Using the H$\alpha$ emission line
from the Southern African Large Telescope (SALT) and photometric flux from the
Optical Gravitational Lensing Experiment (OGLE) to study the changes in the
size and structure of the Be disc, we demonstrate that the X-ray emission
likely originates from SXP 15.3. Timing analysis reveals unusual behaviour,
where the optical outburst profile shows modulation at approximately twice the
frequency of the X-ray outbursts. We consider either of these periodicities
being the true orbital period in SXP 15.3 and propose models based on the
geometric orientations of the Be disc and neutron star to explain the physical
origin of the outbursts.

###### keywords:

Be X-rays: binaries, stars: neutron

††pubyear: 2015††pagerange: Disentangling the neighbouring pulsars SXP 15.3
and SXP 305–A

##  1 Introduction

Be X-ray binaries (BeXBs) make up the largest fraction of the high mass X-ray
X-ray binary systems (HMXBs), with 49% of the total population composed of
them (Coleiro & Chaty, 2013). They primarily comprise a neutron star (NS) in
an eccentric orbit around a massive B-spectral type star with a circumstellar
disc. On rare occasions the compact object orbiting the Be star is a black
hole (Casares et al., 2014) or white dwarf (Coe et al., 2020). The interaction
between the NS and Be star can result in enhanced X-ray emission due to the
accretion of matter from the circumstellar disc by the NS. This transient
X-ray behaviour is classically defined by two types of outbursting events,
Type I and Type II. Type I outbursts have luminosities on the order of
$10^{37}$ erg. s-1 or less, and are typically associated with periastron
passage (Stella et al., 1986). Type II outbursts are typically an order of
magnitude brighter than Type I outbursts and are not associated with a
specific orbital phase. The origin of Type II outbursts have proved elusive,
with various explanations proposed alluding to complex circumstellar disc
variability and/or orbital geometry (e.g. Moritani et al. 2011; Martin et al.
2014; Monageng et al. 2017). Optical and infrared observations are used to
trace the circumstellar disc variability, primarily through the changes in the
H$\alpha$ emission line.
The Small Magellanic Cloud (SMC) hosts a large number of HMXBs (121; Haberl &
Sturm 2016), which is higher than those in the Milky Way (65; Rajoelimanana et
al. 2011) despite being $\sim$50 times less massive. This large abundance of
HMXBs in the SMC is likely due to a recent occurrence of star formation as a
result of an increase in the tidal force from its interaction with the Large
Magellanic Cloud (Gardiner & Noguchi, 1996; Diaz & Bekki, 2011).
In this manuscript we present analysis performed on two sources located in the
SMC, SXP 15.3 and SXP 305, which are separated spatially by just $\sim$7
arcsec - see Fig 1.

Figure 1: Optical (left) and X-ray (right) images of the 2 x 2 arcmin field
containing SXP 15.3 (south-west) and SXP 305 (north-east). The optical image
is an OGLE IV I-band image taken on 2010 September 14. The X-ray image is from
Chandra ACIS-I from 2006 November 22. The two sources are separated by 6.87
arcsec.

The close proximity of the two objects has resulted in confusion about their
optical counterparts, as they both fall within the X-ray error circles from
most missions (Haberl et al., 2000; Covino et al., 2001; Schurch et al.,
2011). Covino et al. (2001) presented the most accurate X-ray positions using
ROSAT HRI data and confirmed the association of SXP 15.3 with the B-spectral
type star listed as [MA93]552 in the optical catalogues of Meyssonnier &
Azzopardi (1993). These authors use medium resolution spectroscopy to classify
the optical counterpart as OIIIe or B0Ve. The optical counterpart of SXP 305
was noted to show no emission lines and to be a later B-spectral type than
[MA93]552. The 15.3 s pulse period of SXP 15.3 was derived by Lamb et al.
(1999) through the analysis of ROSAT and BATSE data. The detection of the 305
s pulse period of SXP 305 has for a long time proved elusive, having only been
detected recently using NuSTAR observations (Lazzarini et al., 2019).
In this paper we investigate the origin of recent outbursting behaviour coming
from the combined field of both sources as seen from Swift XRT observations.
We use optical photometry and spectroscopy to study the long-term variability
of the Be discs from both objects, where we see them exhibiting contrasting
behaviour.

##  2 Observations

###  2.1 OGLE

Long-term $I-$band photometry monitoring with a typical cadence of 1-3 days is
performed with the Optical Gravitational Lensing Experiment (OGLE) project
(Udalski et al., 1997; Udalski et al., 2015). The optical counterpart of SXP
15.3 has been observed for $\sim$23 years in the $I-$band, where it was
identified as SMC-SC6-99923 in OGLE II, SMC100.1 43671 in OGLE III and
SMC720.26 47 in OGLE IV. The optical counterpart of SXP 305 has also been
observed in the same period with identifiers SMC-SC6-99991 in OGLE II,
SMC100.1 43700 in OGLE III and SMC720.26 531 in OGLE IV. Both objects have
also been observed in the $V-$band with a lower cadence. The standard OGLE
pipeline (Udalski et al., 2015) was used for data reduction and calibrations.

###  2.2 SALT

We observed the optical counterpart of SXP 15.3 using the Robert Stobie
Spectrograph (RSS; Burgh et al. 2003; Kobulnicky et al. 2003) on the Southern
African Large Telescope (SALT; Buckley et al. 2006) between September 2017 and
October 2019. The PG1800 grating was used to cover the wavelength region that
includes the H$\alpha$ line ($\sim$6000$-7250$ Å). A single observation
covering the blue wavelength region ($\sim$3860$-$4900Å) was obtained using
the PG2300 grating.

The optical counterpart of SXP 305 was observed twice with the PG1800 grating
and once with the PG2300 grating. The close proximity of the two objects
allowed for simultaneous observations to be performed on them by arranging the
slit angle accordingly.

The primary reductions, which include overscan correlation, bias subtraction,
gain and amplifier cross-talk corrections were performed using the SALT
pipeline (Crawford et al., 2012). We then used iraf111Image Reduction and
Analysis Facility: iraf.noao.edu for the remaining steps: wavelength
calibrations, background subtraction and extraction of the one-dimensional
spectra.

###  2.3 Swift

The S-CUBED survey (Kennea et al., 2018) is a shallow weekly survey of the
optical extent of the SMC by the Swift X-ray Telescope (XRT; Burrows et al.
2005). Individual exposures in the S-CUBED survey are typically 60s long, and
occur weekly, although interruptions can occur due to scheduling constraints.
An automated pipeline based on the tools of Evans et al. (2009) was used to
analyse the data. The full details of the data reduction steps are given in
Kennea et al. (2018). The sources that are the subject of this paper have been
observed since June 2016 with S-CUBED.

###  2.4 RXTE

The X-ray monitoring of the SMC was carried out for over a decade using the
Rossi X-ray Timing Explorer space observatory (RXTE) (Jahoda et al., 1996).
The Proportional Counter Array (PCA) instrument on board RXTE was observing
the SMC 1997 - 2012, full details of these observations and analysis are found
in Laycock et al. (2005) and Galache et al. (2008). Positional identification
of SMC HMXBs is impossible with RXTE due to its 2 degree full width at zero
intensity field-of-view. Identification is performed solely through pulse
timing analysis and identification with related activity in optical light
curves. RXTE data on SXP 15.3 were initially presented in Schurch et al.
(2011).

###  2.5 Chandra

Chandra was launched in 1999 and resides in a highly elliptical 64-hour orbit.
It contains an assembly of grazing-incidence mirrors which focusses the
photons onto two scientific instruments namely the Advanced CCD Imaging
Spectrometer (ACIS) or the HighResolution Camera (HRC). The observations were
processed through standard CIAO data analysis threads. The data was barycenter
corrected and fluximage was run in the broad energy range (0.5-7.0 keV), with
creation of exposure maps. The point sources were detected by running
wavedetect with eavelet scales of 2,4,8 & 16\. The source and background light
curves were extracted in the broad energy band binned at 3.25 sec, the native
resolution for Chandra. For extraction the source region was defined as a
circle centered on the source coordinates with a 95% encircled-energy radius
at 2.3 keV as determined by the evalpos tool applied to the PSF map for that
observation. The background region was an annulus with an inner radius of
twice the source region radius and an outer radius of five times the source
region radius, also centered on the source coordinates.

###  2.6 XMM

The XMM-Newton observatory (Jansen et al., 2001) was launched by the European
Space Agency (ESA) in 1999 consisting of three high throughput X-ray
telescopes. The three telescopes focusses the photons onto European Photon
Imaging Camera (EPIC) and other spectrographic instruments. XMM-Newton looked
at the field of view containing the two pulsars four times (ObsIDs:
0110000101,0404680301,0601213001,0601211401). The data is processed through
standard tasks from Science Analysis Software (SAS) version 17.0.0. The event
files were cleaned for good time intervals using tabgtigen and barycenter
corrected with the barycen tool. We applied Standard filters to extract MOS
(Patterns <= 12) and PN (Patterns <= 4, single and double pixel events) event
files. The background subtracted lightcurves were extracted using the command
epiclccorr and binned at 2.7982 s with the source events extracted from a
radius of $20^{\operatorname*{\prime\prime}}$ and background region from an
annulus of inner radius $30^{\operatorname*{\prime\prime}}$ and outer radius
$60^{\operatorname*{\prime\prime}}$ about the detected source coordinate.

###  2.7 NuSTAR

The Nuclear Spectroscopic Telescope Array (NuSTAR ;Harrison et al. (2013)) is
the first focusing high-energy telescope in orbit, launched on 2012 June 13.
It operates in the 3 - 79 keV energy band, enabling us to overcome the $\sim$
10keV barrier set by previous X-ray telescopes. NuSTAR consist of two co-
aligned hard X-ray grazing incident telescopes (Wolter I) which focus on two
independent solid state focal plane detectors (focal length $\sim$ 10 m). The
two focal plane images can be added to gain sensitivity as the optics and
detectors are designed as identical as possible.

All the archival data(listed in Table1) for both FPMA and FPMB have been
analyzed using The NuSTAR Data Analysis Software (NuSTARDAS v1.8.0) and CALDB
(v20190513). This module is integrated in the Heasoft (v6.26.1) package
distributed by High Energy Archive Science Research Center (HEASARC). Using
the nupipeline command the level 1 event files are converted to level 2 event
files. Standard cleaning process has been used. The gti and barycenter
corrected high-level products (level3: spectra, lightcurves and skymap images)
were created using the nuproducts command. These products have been created in
the broad energy band. Source extraction region of
$20^{\operatorname*{\prime\prime}}$ was chosen centered at the known SXP 15.3
and SXP 305 coordinates, background extraction was done with a annular region
(inner:$30^{\operatorname*{\prime\prime}}$, outer:
$60^{\operatorname*{\prime\prime}}$) centered at the same source coordinate.
The net lightcuves, binned at 0.07s were background subtracted using lcmath
for both FPMA and FPMB and they were added to get the total background
subtracted light curve using the same command for each source in each
observations.

##  3 Results

###  3.1 X-ray variability

The bottom panels of Figs. 3 and 6 show the evolution of the X-ray flux from
S-CUBED monitoring of the combined field of SXP 15.3 and SXP 305. At the start
of the monitoring the flux displayed low values until an outburst associated
with SXP 15.3 was seen in July 2017 ($\sim$MJD57960) with a peak flux of $\sim
9\times 10^{-11}$ erg. s-1 cm-2. Period analysis was performed by Kennea et
al. (2017) during this outburst with the 15.3 s pulse period strongly
detected. Approximately four months later (November 2017) the X-ray flux of
SXP 15.3 reached its highest state to ever have been detected with peak
luminosity levels close to the Eddington limit ($F\sim 1.94\times 10^{-10}$
erg. s-1 cm-2, $L\sim 8.63\times 10^{37}$ erg. s-1). A cyclotron feature was
detected at 5 keV from AstroSAT and NuSTAR observations during this outburst
with an estimated surface magnetic field of $6\times 10^{11}$ G for the
neutron star (Maitra et al., 2018). A series of three outbursts followed, with
a recurring timescale of $\sim 150$ days at peak flux levels of $\sim 4\times
10^{-11}$ erg. s.-1 cm-2 ($L\sim 1.8\times 10^{37}$ erg. s.-1). We searched
for periodic modulation of the S-CUBED data using the Generalised Lomb-Scargle
technique of Zechmeister & Kürster (2009) where we excluded the Type II
outburst seen around MJD 58100 and the results are shown in Fig. 2. A strong
peak is seen at a period of 148 d. Interestingly, this recurring timescale is
approximately double the reported orbital period of SXP 15.3 ($P=74.5\pm 0.05$
d; Edge 2005). We discuss this further in Section 4.

Figure 2: Lomb-Scargle analysis of the S-CUBED data. The strongest peak has a
period of 148 d. The short dashed line shows the 1% False Alarm Probability,
the long dashed line the 10% FAP.

On delving into the RXTE archived power spectra in order to trace the history
of these two sources, we found evidences of pulsations in the range of 300-310
seconds in 29 ObsIDs by employing the PUMA/ORCA pipeline(Laycock et al., 2005;
Galache et al., 2008). The location of SXP305 lay in the central area of the
PCA field of view (Collimator response>0.5) in 385 separate ObsIDs.

However, there were possible chances of some of these peaks being spurious due
to aliases, spectral-leakage or due to contamination by the harmonics of other
pulsars in the vicinity. On excluding such ObsIDs, there remained 10 candidate
detections of SXP 305 which are listed in Table 2. For one of them, an overlap
was found for simultaneous detection for both SXP 15.3 and SXP 305.

For other X-ray imaging telescopes like XMM-Newton, no pulsations were found
for either of the two pulsars lying in its field of view indicating towards
them being in the quiescent state. Table 1 shows the observations made by
Chandra, NuSTAR and Suzaku. NuSTAR was the only one to successfully register
strong pulsations from SXP 305 which was also reported by Lazzarini et al.
(2019) on 12th March 2017. The pulse profile for the same was a single broad
peak. SXP 15.3 was also detected thrice by NuSTAR during its outburst in the
period 2017-2018.

Apart from one Chandra observation (ObsID: 7156), no significant pulsation was
discovered for either of the two pulsars. However due to the excellent spatial
resolution of Chandra, it was able to resolve these closely paired X-ray
binaries. So, in order to remove any ambiguity, we calculated the fluxes at
the two X-ray position coordinates corresponding to the two pulsars for it.
The values in the 0.5-7 keV range resembled those for quiescent BeXRB pulsars
which ruled out any pulsation detection.

Figure 3: Long-term H$\alpha$ EW (top) and OGLE $I-$band (middle) lightcurves
of SXP 15.3, together with the S-CUBED lightcurve of the combined field of SXP
15.3 and SXP 305. The black circles in the bottom plot indicate detections
while the purple squares indicate upper limits. The blue markers indicate the
epochs of the 15-second pulse period detections.  Figure 4: The full OGLE
$I-$band lightcurve of the optical counterpart of SXP 15.3 Figure 5: Long-term
$I-$band (top) and $V-$band (bottom) OGLE lightcurves of the optical
counterpart of SXP 305. The blue markers indicate the epochs of the 305-second
pulse period detection. Figure 6: OGLE $I-$band lightcurve (top) of SXP 305
and the S-CUBED lightcurve of the combined field of SXP 15.3 and SXP 305. The
black circles in the bottom plot indicate detections while the purple squares
indicate upper limits. The blue marker indicates the epoch of the 305 s pulse
period detection with NuSTAR.

###  3.2 Optical variability

####  3.2.1 SXP 15.3

The spectroscopic monitoring of the optical counterpart of SXP 15.3 commenced
during its peak photometric state when the H$\alpha$ line was seen in strong
emission. Fig. 7 shows a typical example of the H$\alpha$ emission line. The
equivalent width (EW) of the H$\alpha$ line at the start of the monitoring
showed the largest values ever reported for the source, with values around
$\sim-19$ Å. The EW values continued to show correlated evolution with the
OGLE flux as seen in the slow decline of the two datasets from $\sim$MJD58360.

Figure 7: An example of the H$\alpha$ emission line in SXP 15.3 from an
observation taken on MJD59025 (25 June 2020).

The commencement of the SALT monitoring corresponds to the start of the large
X-ray outburst in November 2017 ($\sim$MJD58000). This suggests that the
circumstellar disc grew to a large extent, allowing enough matter to be
accreted by the NS to initiate the Type II X-ray outburst. The later portion
of the EW evolution ($\sim$MJD58360) shows similar high values as those seen
at the start, with a gradual decrease in EW to $\sim-16$ Å ($\sim$MJD58422).
This period corresponds to the second of the series of outbursts in the
S-CUBED lightcurve. The most recent EW measurements obtained at $\sim$MJD58785
and $\sim$MJD59025 display the lowest values ($-$10.5 Å and $-$13.2 Å,
respectively) of the monitoring campaign during its low X-ray state.

The $(V-I)-I$ colour-magnitude plot for SXP 15.3 is shown in Fig. 8. A strong
correlation is seen between the two quantities, which indicates a
low/intermediate viewing angle of the circumstellar disc. Another notable
feature of the colour-magnitude plot is a loop structure. The simultaneous
$I-$ and $V-$band observations were obtained during the period between
MJD53000 and MJD59000, covering the time when the system underwent its lowest
dip in flux (Fig. 4). From Fig. 8 it appears that the disc is lost from the
inside out since there was no evidence of the enhanced accretion (i.e. an
outburst) during that time that could have disrupted the outer parts of the
disc.

Figure 8: $(V-I)-I$ colour-magnitude plot of the optical counterpart of SXP
15.3 Figure 9: Lomb-Scargle analysis of OGLE IV I-band data. The strongest
peak has a period of 74.5 d. The short dashed line shows the 1% False Alarm
Probability, the long dashed line the 10% FAP. The peak at 94 d is the beat
period between the 74.5 d period and the annual sampling.

If the OGLE IV data are searched for periodic modulation in the range 50 – 200
d using the Generalised Lomb-Scargle then the result is shown in Fig 9. This
confirms the same period that has been identified by previous authors (Edge,
2005; Rajoelimanana et al., 2011) in the the earlier MACHO and OGLE III data
sets - 74.5 d. The precise updated ephemeris for the time of the optical
peaks, $T_{opt}$, is:

$T_{opt}=2452085.9+N(74.516)~{}\textrm{JD}$ (1)

####  3.2.2 SXP 305

The OGLE lightcurve shows repeating outbursts with I-band amplitudes in the
range $\sim 0.35-0.6$ mag that last for up to $\sim$600 days (Fig. 5). The
recurring timescale of these outbursts has a range $1100-1400$ days.
The first SALT observation of the optical counterpart of SXP 305 covering the
red region of the spectrum shows the H$\alpha$ line in absorption (Fig. 10,
top panel). This observation was taken during its OGLE photometric minimum
($\sim$MJD58785). In the most recent observation (MJD59025) the H$\alpha$ line
is seen in emission for the first time ever (Fig. 10, bottom panel),
confirming the Be nature of the optical companion. OGLE was unavailable during
this time for monitoring, however, the emission line suggests that SXP 305 is
undergoing another optical outburst. This variability is an indicator of
extreme changes in the circumstellar disc, suggesting that the system goes
through regular periods of complete disc-loss and recovery (see section 4.2).
Fig. 11 shows the $(V-I)-I$ colour-magnitude plot of the optical counterpart
of SXP 305. The relationship between the two quantities shows a strong
correlation, indicating a low/intermediate viewing angle of the circumstellar
disc. Growth in radius from a circumstellar disc that has a low inclination
angle relative to our line of sight results in excess flux and reddening due
to the temperature of the outer disc regions being cooler than the star.

Figure 10: H$\alpha$ line of the optical counterpart of SXP 305 from SALT. The
top panel profile is from the first observation obtained on MJD58785 (29
October 2019) and the bottom panel is a profile obtained on MJD59025 (25 June
2020). Figure 11: $(V-I)-I$ colour-magnitude plot of the optical counterpart
of SXP 305

####  3.2.3 Spectral classification

Figure 12: SALT spectra of SXP 305 (top) and SXP 15.3 (bottom) covering the
blue region. The spectra are corrected for the heliocenter and redshift of the
SMC. The different line species are labeled at their expected rest
wavelengths.

The blue spectra of the optical counterparts of SXP 15.3 and SXP 305 are shown
in Fig. 12. Both spectra are clearly those of early-type stars, with a number
of Balmer and helium lines present in absorption. The H$\beta$ line in the
spectrum of SXP 15.3 is seen in emission due to the presence of the
circumstellar disc. A few of the absorption lines show infilling as a result
of the emission from the circumstellar disc.
Using the criteria in Evans et al. (2004), the presence of the CIII and OII
blend constrains the spectral type to earlier than B3. The presence of the
weak HeII 4686 line and absence of the He II 4541 line further constrains the
spectral type to B0.5. Using the faintest observed V-band magnitude of 15.15
and distance modulus of the SMC of 18.95 (Graczyk et al., 2013), we constrain
the luminosity class to V (Straizys & Kuriliene, 1981; Pecaut & Mamajek,
2013). We conclude that the spectral type of SXP 15.3 is therefore B0.5 V, in
agreement, to within errors, with Covino et al. (2001) and McBride et al.
(2008).

Using the same criteria, the presence of the CIII and OII blend at $\sim$4650
Å constrains the optical counterpart of SXP 305 to B3 or earlier while the
absence of the HeII 4686 line sets the spectral type to later than B0.5. The
spectrum reveals the SiIV 4088 line being weaker than the OII 4415-17 blend,
which constrains the spectral type to B1.5 or earlier. The low signal-to-noise
of the spectrum makes it difficult to confirm the presence/absence of the
other weaker indicators from the noise and so we conclude that the spectral
type of this object is in the range B0.5$-$B1.5. Using the faintest observed
V-band magnitude of 15.95 constrains the luminosity class to V (Straizys &
Kuriliene, 1981; Pecaut & Mamajek, 2013). In conclusion, the spectral type of
the optical counterpart of SXP 305 is B0.5$-$B1.5 V.

##  4 Discussion

###  4.1 BeXB nature of SXP 305

Lazzarini et al. (2019) confirmed the 305-sec pulse period and concluded that
SXP 305 is a BeXB system, although the Be nature of the optical companion had
not been determined. The presence of the H$\alpha$ emission line and the
B-type spectral classification presented in this work from SALT observations
confirms the Be nature of the massive companion. The previous observation
covering the red wavelength region was obtained during the optical minimum as
seen in the OGLE lightcurve when the disc was absent (Kahabka, 2000).

###  4.2 Origin of the recent series of Type I X-ray outbursts

A disc-less B1 V spectral class star would have an apparent I-band magnitude
of $\sim 16.3$ and $(V-I)$ colour index of $\sim-0.19$ (Straizys & Kuriliene,
1981; Pecaut & Mamajek, 2013). These values lie at the bottom left-hand corner
of Fig. 11. This implies that at its faintest state, the Be disc in SXP 305 is
almost completely diminished. This is further supported by the absence of the
H$\alpha$ emission line during the OGLE minima (Fig. 10). The shape and
repetition of the optical outbursts suggests quasi-periodic mass-loss from the
Be star. From an examination of the S-CUBED vs. I-band plots for both systems
(Figs. 3 and 6) it looks unlikely that the X-ray emission from the recent
outbursts is dominated by SXP 305 since this is the time of photometric
minimum, when the disc was depleted.
This recent series of X-ray outbursts occurred during the decline of the
optical emission (both photometric and EW) of SXP 15.3, with the spectroscopic
observations covering the second of the three outbursts (Fig. 3). Therefore,
it is likely that these outbursts come from SXP 15.3.
The pulse period detections of SXP 15.3 from NuSTAR were all obtained close to
outburst peaks, with the last of them occurring during the the second of the
three recent recurring outbursts (Fig. 3). The NuSTAR detection of the 305
second pulse period in SXP 305 corresponds to an epoch when there was no
enhanced X-ray activity which is also consistent with the time when the I-band
emission was on the rise (Fig. 6). This possibly suggests that there was some
low-level accretion from the Be disc in SXP 305 as it was forming during this
time. The fact that a strong pulse period was detected from SXP 15.3 during
one of the recent outbursts is further evidence that the outbursts are
associated with SXP 15.3 instead of SXP 305.

###  4.3 Timing analysis of the recent series of Type I X-ray outbursts

####  4.3.1 The true orbital period of SXP 15.3

If data from the Type II outburst seen around MJD 58100 are removed from the
S-CUBED light curve, and the remaining data are folded at the period obtained
from the Lomb-Scargle analysis (Fig. 2), then the resulting profile clearly
indicates the presence of a very significant X-ray peak every 148.0 d - see
Fig. 13. Fig. 14 shows a similar version of this plot, but with the optical
data folded on the 74.5-day period.

Figure 13: S-CUBED data folded on the 148 d period obtained in Fig. 2. Figure
14: OGLE detrended data folded at the OGLE period given in Eqn 1.

It is clear from the timing analysis of the optical data and the recurrence
time of the X-ray outbursts in SXP 15.3 that there are two periodicities of
74.5 days and 148 days, respectively. Here, we explore the possible physical
interpretations of the recent X-ray outbursting behaviour, where we consider
either of these two periodicities being the true orbital period of the system.
Both the optical and X-ray peaks extend over a large fraction of the orbit for
both period considerations. While the optical peak is a proxy of the Be disc
distortion, the X-ray peak is a measure of the accretion of matter onto the
neutron star. The long time span of these peaks could be an indicator of a
relatively small misalignment between the Be disc and neutron star orbital
planes, as well as a relatively low eccentricity of the neutron star orbit.
This would imply that the neutron star is in the neighbourhood of the Be disc
and distorts it, while accreting matter for a significant portion of its
orbit.
For the case where the 74.5-day periodicity is the orbital period, this would
mean that the OGLE $I-$band outburst occurs once per orbit while the X-ray
outburst profile would occur at every other orbit of the neutron star (Fig.
14). In a geometrical setup where the Be disc and the orbital plane are
coplanar, with the neutron star in a nearly circular orbit, it is possible for
the disc eccentricity to grow through the 3:1 resonance (Franchini & Martin,
2019). If the disc precesses apsidally in a prograde direction, the time
interval of the X-ray outbursts can be greater than the orbital period.
In the instance where the 148-day periodicity is the true orbital period, this
would imply that the optical outbursts occur twice per orbit while the X-ray
outburst profile shows a peak once per orbit (Fig. 13). In this scenario, it
is possible for the orientation of the Be disc and neutron star orbital planes
to be close enough for the disc to be distorted for a large portion of the
orbit, but with enough misalignment to generate two optical outbursts per
orbit.
A further piece of evidence in support of the longer 148 d orbit comes from
interpreting the H$\alpha$ EW value as a circumstellar disc size. Using the
method described in Hanuschik (1989) and the measured value of -19Å the disc
radius is estimated to be $9.6\times 10^{10}$ m. Kepler’s Laws predict that
the radius of a circular orbit with these stellar components (1.4$M_{\odot}$
and 17.5$M_{\odot}$) and a period of 14 d will be $9.3\times 10^{10}$ m,
whereas a 75 d orbit size would only be $5.8\times 10^{10}$ m. Since it is
believed that the neutron star orbit naturally curtails the circumstellar disk
growth to be inside its orbit (Okazaki & Negueruela, 2001), then a 75 d orbit
would not work well under that paradigm. A 148 d orbit fits much better.

####  4.3.2 Optical and X-ray peak delays

As Fig. 13 shows, the X-ray peak tends to precede the optical one. There are 4
recognisable Type I X-ray peaks in the S-CUBED light curve, apart from the
large Type II outburst. These occurred at dates (OGLE phase): MJD 57962
(0.86), MJD 58259 (0.84), MJD 58410 (0.87) and MJD 58565 (0.95). So when the
regular Type I X-ray outbursts occur they are always at a phase 0.15 - 0.05
before the peak optical brightness. This type of phase delay has been seen in
several other systems (Coe et al., 2015) with values in the range 0.04 - 0.10,
corresponding to actual delays of 2 - 13 d. In the case of SXP 15.3, the delay
of the optical peak with respect to the X-ray peak of $0.1\pm 0.05$
corresponds to period of $7\pm 4d$, consistent with previous values. It is
suggested in Coe et al. (2015) that this delay is characteristic of the
circumstellar disk response times within the accretion process, and it is the
timing of the X-ray outburst that marks the periastron passage of the neutron
star. Unfortunately a lack of pulse period measurements around the orbit for
SXP 15.3 prevent an accurate orbital solution being obtained to confirm either
the exact moment of periastron or the true orbital period.

##  5 Conclusions

We have presented long-term optical and X-ray observations of two neighbouring
SMC Be X-ray binaries, SXP 15.3 and SXP 305. The recent X-ray data reveal
periodic outbursting behaviour from the combined region of the two objects,
the origin of which we demonstrate is likely due to SXP 15.3. We confirm the
previously reported 74-day modulation from the optical data of SXP 15.3, which
implies that the optical outbursts occur at twice the frequency of the X-ray
outbursts. We have considered either of the optical and X-ray modulation as
the true orbital period of SXP 15.3 and propose physical scenarios to explain
the observational behaviour. In both cases we suggest that the modulation is
caused by an unusual disc orientation as a result of a complex configuration
between the Be disc and the orbital plane. Further analysis in the form of
hydrodynamic modelling, or pulse period measurements around the orbit, are
necessary to distinguish between the two possible orbital periods.

## Acknowledgements

We thank an anonymous referee for the useful comments. IMM, DAHB and LJT are
supported by the South African NRF. Some of the observations reported in this
paper were obtained with the Southern African Large Telescope (SALT), as part
of the Large Science Programme on transients 2018-2-LSP-001 (PI: Buckley).
This work was partially supported by the NASA ADAP grants NNX14AF77G and
80NSSC18K0430.

## Data Availability

All X-ray data are freely available from the NASA Swift archive. The OGLE data
in this article will be shared on any reasonable request to Andrzej Udalski of
the OGLE project. The SALT data in this article will be shared on any
reasonable request to David Buckley of the South African Astronomical
Observatory.

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##  Appendix A X-ray data

Table 1:

Obs. ID | Time | MJD | RA | Dec |  Flux/$10^{-14}$ |  Lx/$10^{34}$ | Period |
---|---|---|---|---|---|---|---|---
| (ks) | (d) | (deg) | (deg) |  (erg s-1 cm-2) |  (erg s-1) | (s) |
Chandra | ACIS-I |  |  |  |  (0.5-7 keV) |  |  |
7156 | 38.67 | 54061 | 13.0583 | -73.3219 |  2.44$\pm$0.57 |  1.12$\pm$0.26 | 15.239 |
|  |  | 13.0644 | -73.3209 |  5.52$\pm$0.81 |  2.53$\pm$0.37 | … |
8479 | 42.10 | 54060 | 13.0583 | -73.3219 |  3.82$\pm$0.66 |  1.75$\pm$0.30 | … |
|  |  | 13.0644 | -73.3209 |  4.73$\pm$0.72 |  2.18$\pm$0.33 | … |
8481 | 15.98 | 54062 | 13.0583 | -73.3219 |  3.3$\pm$1.1 |  1.52$\pm$0.50 | … |
|  |  | 13.0644 | -73.3209 |  4.71$\pm$1.18 |  2.16$\pm$0.54 | … |
Chandra | ACIS-S |  |  |  |  (0.5-7 keV) |  |  |
3907 | 50.19 | 52698 | 13.0583 | -73.3219 |  2.68$\pm$0.55 |  1.23$\pm$0.25 | … |
|  |  | 13.0644 | -73.3209 |  5.90$\pm$0.77 |  2.71$\pm$0.35 | ….. |
11095 | 38.67 | 55334 | 13.0583 | -73.3219 | … | … | … |
|  |  | 13.0644 | -73.3209 | … | … | … |
11096 | 38.67 | 55349 | 13.0583 | -73.3219 | … | … | … |
|  |  | 13.0644 | -73.3209 | … | … | … |
11097 | 29.60 | 55300 | 13.0583 | -73.3219 |  0.33$\pm$0.32 |  0.15$\pm$0.15 | … |
|  |  | 13.0644 | -73.3209 |  1.97$\pm$0.48 |  0.91$\pm$0.22 | …. |
11980 | 22.75 | 55307 | 13.0583 | -73.3219 |  0.65$\pm$0.31 |  0.30$\pm$0.14 | … |
|  |  | 13.0644 | -73.3209 |  1.76$\pm$0.51 |  0.81$\pm$0.23 | ….. |
11981 | 33.60 | 55317 | 13.0583 | -73.3219 |  1.01$\pm$0.31 |  0.46$\pm$0.14 | … |
|  |  | 13.0644 | -73.3209 |  1.69$\pm$0.42 |  0.77$\pm$0.19 | …. |
11982 | 24.57 | 55319 | 13.0583 | -73.3219 |  1.36$\pm$0.78 |  0.62$\pm$0.36 | … |
|  |  | 13.0644 | -73.3209 |  1.01$\pm$0.76 |  0.46$\pm$0.35 | …. |
11983 | 29.34 | 55328 | 13.0583 | -73.3219 | … | … | … | -
|  |  | 13.0644 | -73.3209 | … | … | … |
11984 | 20.48 | 55338 | 13.0583 | -73.3219 | … | … | … | -
|  |  | 13.0644 | -73.3209 | … | … | … |
11985 | 21.04 | 55341 | 13.0583 | -73.3219 | … | … | … | -
|  |  | 13.0644 | -73.3209 | … | … | … |
12200 | 26.73 | 55308 | 13.0583 | -73.3219 |  0.55$\pm$0.28 |  0.25$\pm$0.13 | … |
|  |  | 13.0644 | -73.3209 |  1.91$\pm$0.51 |  0.88$\pm$0.23 | … |
12208 | 15.97 | 55318 | 13.0644 | -73.3209 |  1.22$\pm$0.52 |  0.56$\pm$0.24 | … |
12210 | 27.55 | 55323 | 13.0583 | -73.3219 |  0.68$\pm$0.43 |  0.31$\pm$0.20 | … |
|  |  | 13.0644 | -73.3209 |  1.06$\pm$0.87 |  0.49$\pm$0.40 | ….. |
12211 | 34.99 | 55320 | 13.0583 | -73.3219 |  1.13$\pm$0.44 |  0.52$\pm$0.20 | … |
|  |  | 13.0644 | -73.3209 |  0.95$\pm$0.57 |  0.44$\pm$0.26 | ….. |
XMM | EPIC |  |  |  |  (0.2-12 keV) |  |  |
0110000101 | 28.00 | 51832 | 13.0639 | -73.3204 |  |  3.70$\pm$2.44
---
|  1.70$\pm$1.12
---
… |
0404680301 | 23.90 | 54201 | 13.0642 | -73.3203 |  |  8.12$\pm$1.51
---
|  3.73$\pm$0.69
---
… |
0601213001 | 42.01 | 55087 | 13.0617 | -73.3212 |  |  13.93$\pm$3.74
---
|  6.41$\pm$1.72
---
… |
0601211401 | 46.81 | 55139 | 13.0611 | -73.3214 |  |  15.52$\pm$1.83
---
|  7.14$\pm$0.84
---
… |
Suzaku |  |  |  |  |  (0.5-7 keV) |  |  |
503094010 | 120.48 | 54629 | 13.0583 | -73.3219 |  48.41$\pm$45.65 |  22.26$\pm$20.99 | … |
NuSTAR | FPM-A |  |  |  |  (3-10 keV) |  |  |
50311002002 | 169.75 | 57824 | 13.0612 | -73.3209 |  211.56$\pm$15.3 |  97.32$\pm$7.04 | 305.49 |
50311002004 | 76.77 | 57953 | 13.0548 | -73.3197 |  2110$\pm$352 |  970.66$\pm$161.93 | 15.28 |
50311002006 | 29.94 | 57974 | 13.0552 | -73.3218 | … | … | … |
30361002003 | 0.31 | 58418 | 13.0545 | -73.3219 | … | … | … |
30361002004 | 58.35 | 58421 | 13.0545 | -73.3209 |  2899$\pm$233 |  1333.62$\pm$107.18 | 15.24 |
30361002002 | 70.65 | 58087 | 13.0535 | -73.3230 |  5136$\pm$94 |  2362.7$\pm$43.24 | 15.26 |

Table displaying Pulsations and other X-ray data for all sources falling in
the FoV of either of the two pulsars SXP15.3 and SXP305, from Chandra ACIS,
XMM-Newton EPIC, Suzaku and NuSTAR(FPM-A). SXP305 was found pulsating by
NuSTAR while SXP15.3 pulsations were detected once by Chandra and thrice by
NuSTAR. The Chandra rows which are empty corresponds to the ACIS-S
observations where the targeted source lay outside the chip edges. For each of
the individual Chandra observations, the first sub row in the flux column
refers to the flux obtained about the SXP15.3 coordinate(Coe & Kirk, 2015) and
the next entry corresponds to the flux obtained about the SXP305(Lazzarini et
al., 2019) coordinate.

Table 2:

Obs. ID | Time | MJD | RA | Dec | Flux |  Lx/$10^{34}$ | Period
---|---|---|---|---|---|---|---
| (ks) | (d) | (deg) | (deg) |  (count PCU${}^{-1}~{}s^{-1}$) |  (erg s-1) | (s)
RXTE | PCA |  |  |  |  (keV) |  |
50088-02-01 | 7.37 | 51918 | 12.4999 | -73.0999 |  |  | …
|  |  |  |  | 0.32 | 1.8 |  306.74$\pm$5.41
92076-04-42 | 8.98 | 54242 | 12.4999 | -73.0999 |  |  | …
|  |  |  |  | 0.17 | 1.0 |  307.69$\pm$3.19
93037-02-14 | 6.90 | 54380 | 13.3999 | -73.3999 |  |  | …
|  |  |  |  | 0.5 | 2.8 |  301.20$\pm$8.62
93037-02-15 | 7.85 | 54391 | 13.3999 | -73.3999 |  |  | …
|  |  |  |  | 0.25 | 1.4 |  303.95$\pm$4.15
93037-02-29 | 7.42 | 54491 | 13.3999 | -73.3999 |  |  | …
|  |  |  |  | 0.24 | 1.35 |  301.20$\pm$4.08
94037-04-41 | 9.30 | 55153 | 12.4999 | -73.0999 |  |  | …
|  |  |  |  | 0.21 | 1.2 |  304.87$\pm$4.64
95037-04-22 | 6.88 | 55345 | 12.4999 | -73.0999 |  |  | …
|  |  |  |  | 0.28 | 1.6 |  303.03$\pm$2.06
95037-04-48 | 12.37 | 55532 | 12.4999 | -73.0999 |  |  | …
|  |  |  |  | 0.17 | 1.0 |  307.69$\pm$3.31
95037-04-52 | 10.70 | 55556 | 12.4999 | -73.0999 | 0.11 |  | 15.24
|  |  |  |  | 0.19 | 1 |  306.74$\pm$2.82
96037-04-25 | 11.13 | 55732 | 12.4999 | -73.0999 |  |  | …
|  |  |  |  | 0.25 | 1.4 |  308.64$\pm$3.33

Table displaying all RXTE-PCA candidate detections of SXP305 around P=305 secs
(n=1). The exposure times are in ksecs and the RA and Dec are the pointing RA
and Dec of the telescope for that ObsID. There was a single ObsID: 95037-04-22
for which both the pulsars SXP15.3 as well as SXP305 showed pulsations.