Simultaneous Chandra and HST observations of the quiescent neutron-star low-mass X-ray binaries in 47 Tucanae
Maureen van den Berg Liliana Rivera Sandoval Craig O. Heinke Haldan N. Cohn Phyllis M. Lugger Jonathan E. Grindlay Peter D. Edmonds Jay Anderson Andrei Catuneanu


firstpage–lastpage
BattleAgent: Multi-modal Dynamic Emulation on Historical Battles to Complement Historical Analysis
    
 Shuhang Lin^* 

 Rutgers University
 Wenyue Hua^* 

 Rutgers University
 Lingyao Li

 University of Michigan
 Che-Jui Chang

 Rutgers University
 Lizhou Fan

 University of Michigan
 Jianchao Ji 

 Rutgers University
 Hang Hua 

 University of Rochester
 Mingyu Jin 

 Rutgers University
 Jiebo Luo 

 University of Rochester
 Yongfeng Zhang^*Shuhang Lin and Wenyue Hua have equal contributions. Author Emails: {shuhang.lin,wenyue.hua, yongfeng.zhang}@rutgers.edu 

 Rutgers University

    April 29, 2024
============================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================





We present simultaneous Chandra X-ray Observatory and Hubble Space Telescope observations of three certain (X5, X7, W37)
and two likely (X4, W17) quiescent neutron-star low-mass X-ray
binaries (qLMXBs) in the globular cluster 47 Tuc. We study these
systems in the X-ray, optical and near-ultraviolet (NUV) using the
simultaneous data and additional non-contemporaneous HST data. We have
discovered a blue and variable NUV counterpart to W17. We have not
securely identified the eclipsing qLMXB W37 in the optical or
NUV. Deeper high-resolution imaging is needed to further investigate
the faint NUV excess near the centre of the W37 error circle. We
suggest that a previously identified optical astrometric match to X7
is likely the true counterpart. The Halpha emission and the location
of the counterpart in the colour-magnitude diagram, indicate that the
secondary is probably a non-degenerate, H-rich star. This is
consistent with previous results from fitting X7's X-ray spectrum. In
X4, the simultaneous X-ray and optical behaviour supports the earlier
suggestion that the X-ray variability is driven by changes in
accretion rate. The X-ray eclipses in X5 coincide with minima in the
optical/NUV light curves. Comparison of the 47 Tuc qLMXBs with the
cataclysmic variables (CVs) in the cluster confirms that overall the
qLMXBs have larger X-ray–to–optical flux ratios. Based on their
optical/NUV colors, we conclude that the accretion disks in the qLMXBs
are less prominent than in CVs. This makes the ratio of X-ray flux to
excess blue optical flux a powerful discriminator between CVs and
qLMXBs.





globular clusters: individual: 47 Tuc (NGC 104) – X-rays: binaries
– binaries: close – stars: neutron












§ INTRODUCTION
 

Low-mass X-ray binaries (LMXBs) consist of a neutron star or black
hole that accretes from a low-mass (≲1 M_⊙)
companion. Most known LMXBs are transient systems in which the X-ray
luminosity can change by orders of magnitude when they switch from an
actively accreting state to a quiescent, low-accretion rate state (or
the other way around). The majority of LMXBs are believed to be
quiescent most of the time. In neutron-star systems, quiescence can
offer a glimpse of the accretor: the quiescent X-ray emission may
feature a soft thermal component, thought to be radiated by the
neutron-star surface through the release of heat that is deposited
during episodes of accretion <cit.>. Harder non-thermal
emission can contribute to the X-rays as well; its origin is not well
understood, but suggestions include
synchrotron shock emission or low-level residual accretion (, ). Since the population of LMXBs
is concentrated towards the Galactic bulge, observations of quiescent
LMXBs (qLMXBs) with typical X-ray luminosities of L_X≈
10^31-33 erg s^-1 are often impeded by high levels of
extinction. As a result, quiescent systems can be difficult to find or
recognize.


It has been known since the early seventies () that a
good place to look for luminous LMXBs is in globular clusters, where
stellar encounters add new pathways to their formation. Thanks to the
sensitivity and spatial resolution of the Chandra X-ray
  Observatory, the number of quiescent LMXBs in globular clusters was
also found to be correlated with encounter rate
(e.g. , ,
). Due to their dynamical origin, it is not obvious
that globular-cluster (q)LMXBs can serve as a proxy for the field
population. For example, in regard to their orbital periods, it has
been suggested that ultra-compact systems (i.e. those with periods
≲80 min) are more common among cluster LMXBs, possibly a
signature of their different formation scenarios
<cit.>. Concerning their X-ray emission, it has been found
that the X-ray spectra of many cluster qLMXBs are dominated by the
soft and steady thermal component, and lack the additional harder (and
in many cases variable) non-thermal component that is often seen in
field qLMXBs[The class of transitional millisecond pulsars is
  an exception, see e.g. <cit.>.]  (,
). Small sample sizes and selection biases may
(partly) explain these apparent differences. We know of fewer than two
dozen (transient or persistently bright) LMXBs in globular clusters,
as well as a similar number of qLMXBs that are bright enough for an
X-ray spectral or variability study. LMXBs are typically discovered
when they go in outburst, but in clusters that are targeted with deep
Chandra pointings, LMXBs are also first identified in quiescence
by their distinct soft spectra. These separate discovery methods may
select systems with very different outburst histories or duty
cycles. Detailed studies of field and cluster systems can help clarify
to what extent the observed properties really signify different
underlying populations.


Another motivation for studying neutron-star qLMXBs is that fitting
their thermal X-ray emission with a suitable model can provide mass
and radius constraints when combined with a distance estimate
<cit.>. Since the mass-radius relation is determined by the
neutron-star equation of state, spectral fitting has become one of the
main methods to place limits on the equation of state of cold dense
matter (see e.g. ). The details of the adopted
model depend on the composition of the neutron-star atmosphere. This
composition in turn is determined by the nature of the mass donor:
accretion supplies fresh material to the outer layers of the neutron
star, which quickly stratifies with the lightest elements settling on
top (, ). Main-sequence donors
give rise to Hydrogen (H) rich atmospheres, while material accreted
from white-dwarf donors in ultra-compact systems is rich in Helium,
Carbon, and/or Oxygen. If the atmospheric composition is unknown, this
introduces systematic uncertainties in the mass and radius estimates
(, ). Another complication arises
when the X-ray spectrum is not purely thermal. To investigate whether
accretion could “contaminate” the spectrum, variability in X-rays or
at other wavelengths can be used as a diagnostic. Identifying the
nature and properties of the optical or near-ultraviolet (NUV)
counterpart can be crucial for inferring the composition of the
neutron-star atmosphere or to check for ongoing accretion (see
e.g. , ).

Finally, the non-thermal component of the X-ray emission also provides
an opportunity to study accretion physics at low mass accretion rates.
Accretion has been considered a likely origin of the non-thermal
component <cit.>, supported by the agreement of its spectral
shape with a bremsstrahlung model <cit.>. Accretion is
likely also responsible for a portion of the thermal spectrum,
evidenced by correlated variability in both components
<cit.>.  Different scenarios have been
proposed to explain the emergent spectrum in Cen X-4 and other weakly
magnetic systems. <cit.> discuss a model where the emission
largely originates in a boundary layer close to the neutron-star
surface, and constrain the properties of this layer and the dominant
radiation mechanism.  Qiao & Liu consider the radiative coupling
between the thermal (from the neutron-star surface) and non-thermal
(from the accretion flow) emission, and find that only a small
fraction of the energy transferred to the neutron star needs to be
thermalized and scattered back to the—radiatively
inefficient—accretion flow to explain the observations
(, ,
). Knowing the conditions in and around the
accretion region is also important to understand the observed
mass-donor properties (e.g. ).

The massive globular cluster 47 Tuc (NGC 104) hosts at least three
certain and two probable neutron-star qLMXBs, none of which have ever
been caught in outburst. These are, respectively, X5 (also known as
W58), X7 (also known as W46) and W37; and the candidates X4 (also known
as W125) and W17. The ROSAT sources X5 and X7 were already identified
as likely qLMXBs (also called soft X-ray transients) by
<cit.>, and their nature was confirmed by the first Chandra studies of the cluster (,
). The Chandra sources W37 and W17, and the
ROSAT source X4 were added as (candidate) qLMXBs by
<cit.>. X4 and W17 are notable because, unlike in many other
cluster qLMXBs, their X-ray spectra feature prominent non-thermal
emission, suggesting that accretion may be happening at a very low
rate. X5 and especially the extremely stable source X7 are among the
best-studied cluster qLMXBs, for several reasons. They are bright in
X-rays, and their spectra contain no discernible non-thermal
components (). Moreover, 47 Tuc suffers
from little foreground extinction and its distance is precisely
determined. From the known orbital periods of X5 (8.667 hr) and W37
(3.087 hr), we know that their neutron-star atmospheres must be
H-rich.


In this paper we study these five (candidate) qLMXBs in the X-ray,
optical and NUV. We investigate the known optical counterparts to X5,
which was found and studied in detail by <cit.>, and to X4,
which was briefly reported in <cit.>. We look for
counterparts to the three others, which so far have not been
identified in the optical or NUV. Our study is based on data from
several Hubble Space Telescope (HST) programs, including
images from the Advanced Camera for Surveys (ACS) that were taken
simultaneously with deep Chandra observations of 47 Tuc.  This
allows us to study correlated X-ray/optical behavior in our
sources. There is a sixth source in 47 Tuc that is also believed to
be an LMXB, viz. X9 (W42). It has been suggested that the accretor in
this ultra-compact system is a black hole, although a neutron-star
primary cannot be excluded. Details can be found in <cit.>,
<cit.>, <cit.>, and <cit.>.


For the cluster reddening, we assume E(B-V)=0.04±0.02
<cit.>. Following <cit.> who calculated the
weighted mean of published distances to 47 Tuc, we adopt a distance
to the cluster of 4.53^+0.08_-0.04 kpc.  This average
does not include the Gaia DR2 estimate <cit.>, but at
4.45±0.01±0.12 kpc (random and systematic errors, respectively)
the latter is consistent with our adopted value. We start with an
overview of the observations in Section <ref>, followed by a
description of the data reduction and analysis in
Section <ref>. In Section <ref> we present our
findings, which we discuss in the broader context of other
globular-cluster qLMXBs, and other faint cluster X-ray sources in
Section <ref>.




§ OBSERVATIONS
 



 §.§ Simultaneous X-ray and optical observations
 

We observed 47 Tuc simultaneously with Chandra and HST on
2002 September 30, October 2–3, and October 11. This temporal spacing
was chosen to sample variability on timescales from hours to
weeks. The HST data were taken with the Wide Field Channel (WFC)
on ACS under program GO 9281. The two CCD detectors of the WFC give a
combined field of view of 3.4 × 3.4 with a
2.5 gap in the middle. We obtained images through a blue
(F435W), red (F625W) and narrow-band Hα (F658N) filter for
total exposure times of 955 s, 1320 s, and 7440 s,
respectively. During each of the three visits, we obtained exposures
in all three filters; this way, we were able to construct
quasi-instantaneous colours that represent the stars' actual colours
as closely as possible, minimizing the effects of variability. In the
crowded fields of globular clusters, this filter choice has proven to
be efficient in separating the true optical counterparts of Chandra sources from optical sources that happen to lie in the
X-ray error circles by chance (see e.g. ,
).  Accreting binaries with low-mass donors
typically have strong Hα emission lines superposed on a blue
continuum coming from an accretion disk or stream (or, in the case of
cataclysmic variables (CVs), from the white dwarf as well), while the
stars in magnetically active binaries with enhanced coronal X-ray
emission can show chromospheric Hα emission lines.  For each
filter, we employed a dither pattern with fractional-pixel offsets so
that the native detector resolution of 0.05 per pixel could be
improved when combining the individual images. A summary of the
GO 9281 exposures can be found in Table <ref>.

The Chandra exposures that overlap with the HST
observations are part of a larger data set that consists of four pairs
of ACIS-S exposures, each pair made up of a long (∼65 ks)
full-frame exposure (ObsIDs 2735–2738) and a short (∼5 ks)
sub-array exposure (1/4 of an ACIS chip; ObsIDs 3384–3387). The HST data were taken during the first (ObsID 2735), third (ObsID
2737) and fourth (ObsID 2738) of the long exposures. Details of the
entire 2002 Chandra data set of 47 Tuc and its analysis are
given in <cit.>.




 §.§ Additional Chandra data



We take the positions of the qLMXBs and the sources we use for
registering the Chandra and HST astrometry (see
Section <ref>) from the catalog of 47 Tuc Chandra
sources by <cit.>. This deep source list is based on all
ACIS-S data from 2002 described in the previous section, as well as
ACIS-I data from 2000 and ACIS-S data from 2014–2015. The combined
data represent 540 ks of exposure time on the cluster, with some parts
receiving more exposure than others as a result of the use of
different imaging modes (full-frame, 1/4 or 1/8
sub-array). <cit.> applied the EDSER algorithm <cit.>
to the event files, improving the spatial resolution and the ability
to separate sources in the crowded cluster core. The 95% confidence
radii on the positions in the catalog were calculated using the
prescription by <cit.>, based on wavdetect runs on
mock ACIS-I data.











 §.§ Additional NUV and optical imaging with HST


We have analyzed NUV images of 47 Tuc from two HST programs. On
2013 August 13 we observed the cluster with the UVIS channel on the
Wide Field Camera 3 (WFC3) as part of program GO 12950. UVIS covers a
field of view of 2.7 × 2.7 with a scale of
0.04 per pixel. During two consecutive visits, 24 images were
obtained through the F300X filter for a total exposure time of 14 576
s, and eight images were taken through the F390W filter for a total
exposure of 4624 s. The dithering pattern included fractional-pixel
offsets. More details can be found in <cit.>.

We also analyzed archival images of 47 Tuc from program GO 9019 that
were obtained with the ACS High Resolution Camera (HRC) on 2002 April
12–13. The HRC offers a relatively small field of view of
29×25, but a superb detector scale of
∼0.025 per pixel. This data set comprises images taken
through ten filters, which are laid out in a mosaic pattern covering
the cluster centre. We only analyzed the exposures in the NUV and blue
filters F220W, F330W, F435W (only the 60 s exposures) and F475W that
include X7 and/or W37 in their field of view. The other three systems
are not covered by this data set. Basic information for the GO 12950
and GO 9019 data that we used can be found in Table <ref>.

Finally, we use the star catalogs of 47 Tuc from the HST UV
  Globular cluster Survey (HUGS; ). These are based
on ACS/WFC F606W and F814W images from program GO 10775
(P.I. Sarajedini; ) and ACS/WFC and WFC3/UVIS
images in the filters F275W (GO 12311, P.I. Piotto), F336W
(GO 11729, P.I. Holtzman; GO 12971, P.I. Richer), and F435W
(GO 9443, P.I. King; GO 9281—which is our data set as described
in Sect. <ref>). The HUGS images in the blue filters were
taken over a time span of more than eleven years: F275W images are
from 2010, F336W images from 2010–2013 and F435W images from
2002. This could impact the blue colours of stars if they are
(long-term) variables. The F606W and F814W images were taken within a
time span of <4 hours, so the derived red colour is only sensitive
to short-term brightness variations. We refer to Table <ref>
for the start and end times of all 47 Tuc HUGS data. We have used the
magnitudes extracted with the HUGS “method 3” photometry, which is
appropriate for very crowded environments.





§ DATA REDUCTION AND ANALYSIS
 



 §.§ X-ray data
 

We refer to <cit.> and <cit.> for details
on the reduction of the Chandra data. We extracted light curves
from the four long ACIS-S exposures from 2002 with time bins of 3000 s
(X4, W17, W37) or 500 s (for X5 and X7, which are much
brighter). Event times were converted to solar-system barycentre times
using the CIAO tools. X-ray luminosities from earlier works
<cit.> that assumed a cluster distance of 4.85
kpc, were adjusted for the distance we adopt here (4.53 kpc).

Neither X5 nor X7 show evidence for intrinsic X-ray luminosity
variability. We use the unabsorbed X-ray fluxes that were derived from
hydrogen-atmosphere spectral fits to the 2000 data in
<cit.>. The count rate for X5 is variable, but (apart from
the obvious eclipses) the variability appears to reflect changes in
the amount of obscuration in front of the X-ray source, instead of
changes in the intrinsic flux, as evidenced by the increased N_H fit
in periods of lower countrate <cit.>.  The X5
observation from 2000 appears to be the least affected by
obscuration. The adopted flux for W37 was taken from Table 3 of
<cit.>, and reflects the results of fitting the spectrum
extracted from the segment of ObsID 2735 that is least affected by
absorption. The model used is a combination of an absorbed hydrogen
atmosphere plus a non-thermal (power-law) component.  The flux values
for X5, X7 and W37 from <cit.> and <cit.> were
computed for the 0.5–2.5 keV band, but the spectra are so soft, with
no (X5, X7) or almost no (W37; ≲2% flux contribution)
power-law component, that these are consistent for the 0.5–10 keV
band as well. W17 is not significantly variable. The spectrum from the
2000 and 2002 data can be fit with a combination of a
hydrogen-atmosphere plus power-law model, with the latter the dominant
component. We convert the total intrinsic luminosity in the 0.5–10
keV band from Table 2 in <cit.> to an unabsorbed flux. The
flux of X4, on the other hand, is thought to vary intrinsically,
likely due to changes in the power-law component. <cit.>
identified a period of high flux in ObsID 2735, between 6.7 and 12.8
hr after the start of the observation. We use 0.5–10 keV X-ray fluxes
separately for this interval and the other three ObsIDs in 2002, and
paired each value with the overlapping GO 9281 F435W flux to compute
quasi-instantaneous X-ray–to–optical flux ratios.

We list the X-ray flux values and resulting X-ray–to–(optical or
NUV) flux ratios in Table <ref>. Estimated systematic errors
in the quoted X-ray fluxes are at least 5%, and arise from the use of
different energy bands, and from uncertainties in modelling the
spectra and the line-of-sight absorption column density N_H. Details
of the spectral modelling can be found in <cit.> and
<cit.>.




 §.§ Optical and NUV HST images


We started the reduction of the GO 9281 WFC data with the images that
were flat-fielded and corrected for charge transfer efficiency (CTE)
losses by the ACS calibration pipeline (CALACS version 8.2.0). These
flc images still suffer from significant geometric distortion,
which we corrected for by subsequent processing with the DrizzlePac
software <cit.>. First, the small relative offsets of the
flc images were corrected for with the routine tweakreg. The aligned individual images were then used as input for
astrodrizzle to create twice-oversampled (to
0.025 pixel^-1) stacked images in each filter that are
corrected for geometric distortion. Three short 10 s exposures, which
were taken to obtain photometry of bright cluster stars, were excluded
from the stacks. The stacked images are cosmic-ray cleaned with the
effects of bad columns and hot pixels removed as much as possible.

We reduced the GO 9019 HRC data in a similar way, starting from the
pipeline-processed (CALACS version 9.2.0) flat-fielded images. This
program was executed about a month after the installation of ACS on
HST in 2002 March. The effects of CTE degradation are therefore
negligible, and we have not corrected for it. As for the GO 9281
data, the GO 9019 flt frames were aligned with tweakreg
and stacked with astrodrizzle with a factor of two oversampling
to produce an image scale of 0.0125 pixel^-1 in the final
stacked images.

The starting point for the reduction of the GO 12950 UVIS data was
the flat-fielded images from the UVIS pipeline (CALWF3 version
3.1.2). We ran the dedicated STScI
software[<http://www.stsci.edu/hst/wfc3/tools/cte_tools>]
to correct for CTE losses, before aligning and stacking the images
with DrizzlePac. The scale of the image stacks is
0.02 pixel^-1. Details can be found in <cit.>.














  §.§.§ Astrometry
 

The Chandra ACIS-S absolute astrometry is tied to the
International Celestial Reference System (ICRS) with an accuracy of
∼1.1 (90%
confidence)[<http://cxc.cfa.harvard.edu/cal/ASPECT/celmon/>]. The
absolute astrometry of our distortion-corrected HST images on
the other hand, can be off by ∼1 or more <cit.>.
To make the optical identification of the Chandra sources
easier, we first tie the HST astrometry to the ICRS using UCAC2
stars, which have positional errors
≲0.070 <cit.>. However, the few UCAC2
standards in the GO 9281 images are often saturated even in the 10 s
exposures. Therefore, we do the astrometric calibration in several
steps. First, we astrometrically calibrated a ground-based image of
47 Tuc. From the ESO archive we obtained a 30 s V image taken with
the 2.2m/Wide Field Imager (WFI) at La Silla, Chile on 2002 October
29. An astrometric solution was derived based on 225 UCAC2 stars;
fitting for relative shift and rotation, pixel scale, and distortions,
gives rms residuals of ∼0.035 in right ascension and in
declination. Using 126 stars that are unsaturated and relatively
isolated in the WFI and the short GO 9281 F435W exposure, we derived
an astrometric solution for the latter, which has rms residuals of
∼0.030 in each direction. Finally, this solution was
transferred to the stacked GO 9281 images with negligible errors
using >10 000 stars. We estimate the final 1 σ accuracy of
the WFC absolute astrometry as the quadratic sum of the random errors
in the UCAC2 positions, the UCAC2–WFI tie and the WFI–HST tie,
augmented with the estimated systematic error in UCAC2 positions (10
mas, ). This results in an error of
∼0.095. We checked for a systematic offset between the
Chandra and HST astrometry by computing the weighted
average of the differences in Chandra and WFC positions of 29
known matches between X-ray sources and their optical counterparts
(see e.g. the finding charts in
). The resulting offset (X-ray
minus optical) is Δα=-0.027±0.006and
Δδ=+0.060±0.009.

The GO 12950 images were calibrated in a similar way, yielding a
final error in the astrometry of 0.074, and a small boresight
correction of Δα=-0.023±0.008and
Δδ=-0.003±0.009.

We apply the boresight correction to the Chandra positions and
looked for optical and NUV counterparts in the 95% error circles,
computed by adding the appropriate errors in the optical (or NUV)
positions, the X-ray positions, and the boresight errors (in
quadrature). The GO 9019 and HUGS images were not explicitly aligned
to the X-ray positions, but it was easy to cross-reference them to the
aligned GO 9281 and GO 12950 images by eye.




  §.§.§ Photometry
 

We used the IRAF DAOPHOT package to extract magnitudes from the
stacked GO 9281 and GO 12950 images with point spread function
photometry. For the GO 12950 images, we also carried out photometry
with the KS2 package <cit.> as an independent check. In
general, KS2 and DAOPHOT produce consistent results. Unless
mentioned otherwise, we report the DAOPHOT magnitudes in this
paper. All photometry is calibrated to the Vega-mag system using the
STScI zeropoints. We denote calibrated magnitudes in the F300X, F390W,
F435W, F625W, and F658N filters by U_ 300, B_ 390,
B_ 435, R_ 625, and Hα_ 658,
respectively. To compute dereddened magnitudes, we converted the
cluster reddening of E(B-V)=0.04±0.02 to filter-specific
extinction values. For the NUV filters, we obtained A(U_
    300)=0.26±0.13 and A(B_ 390)=0.18±0.08 using
the UVIS Exposure Time Calculator. For the optical filters, the
conversions given in Table 14 in <cit.> yield A(B_
    435)=0.16±0.08, A(R_ 625)=0.11±0.05, and
A(Hα_ 658)=0.10±0.05. Optical and NUV fluxes used
to estimate X-ray–to–optical or X-ray–to–NUV flux ratio's
(Table <ref>) were computed from the dereddened magnitudes
using the zeropoint fluxes provided by
STScI.[<https://acszeropoints.stsci.edu>]^,[
  <https://www.stsci.edu/hst/instrumentation/wfc3/data-analysis/photometric-calibration/uvis-photometric-calibration>]

In order to create optical light curves for the (candidate)
counterparts, we ran aperture photometry on the individual images
(except for the short exposures). Observation times were converted to
barycentric times. We created NUV light curves with the DOLPHOT
software <cit.>. DOLPHOT also produces average
photometry, which we find to be in general agreement with the DAOPHOT and KS2 photometry. More details about the photometric
analysis can be found in <cit.>.

We carried out aperture photometry on the twice-oversampled, drizzled
GO 9019 frames using the DAOPHOT FIND and PHOT
utilities. We used a 2 pixel radius (0.025 arcsec) aperture and
corrected the flux to an infinite aperture using the encircled energy
fractions from Table 4 in <cit.>. The magnitudes were
calibrated to the Vega-mag system using the zeropoints from Table 11
in <cit.>. In order to filter out outliers, such as blended
stars and PSF artifacts, we only included objects in the CMD for which
the positions across frames agreed to within 0.7 pixels.




§ RESULTS
 










 §.§ X4
 

X4 was first detected in ROSAT High Resolution Imager (HRI)
observations of 47 Tuc <cit.>. The source was identified
with W125 in the catalog of sources inside the cluster's half-mass
radius detected in the Chandra data from 2000 and 2002
<cit.>. The model for X4's X-ray spectrum requires a soft
component in addition to a dominant harder component to yield an
acceptable fit. Consequently, X4 was classified as a likely qLMXB
based on its spectral resemblance to other such sources. During the
2002 Chandra observations, X4 displayed variability on time
scales of ≲1 day. As X4 brightened in ObsID 2735, its
spectrum became harder, indicating that a reduction in N_H was not
responsible for the increase in count rate. <cit.> argued in
favor of changes in the power-law component driving the variability,
possibly a sign of ongoing accretion.

X4 lies ∼1.4 to the north-west of the centre of 47 Tuc,
and outside the field of view of the HST images analyzed by
<cit.> to look for optical counterparts to
     Chandra sources. <cit.> examined the GO 9281
     F658N (but not the F435W and F625W) images that we also analyze
     here, and reported a likely counterpart with excess Hα
     emission. In order to look for Hα-excess sources, they
     combined the Hα_ 658 magnitudes from GO 9281 with
     V (F606W) and I (F814W) magnitudes from ACS/WFC program
     GO 10775 (also included in HUGS), taken ∼3.5 yr after the
     GO 9281 data. As we show below, X4 is considerably variable in
     the optical as well. As a result, colours constructed from
     non-contemporaneous measurements can be affected by
     variability. We revisit X4's Hα_ 658 colour below.
     
In the GO 9281 data, we readily found a variable object at only
0.06  from the boresighted Chandra position of X4
(Fig. <ref>, top-left). Comparison of its coordinates with
those of the counterpart found by <cit.> shows that these are
the same object. X4 lies in an uncrowded part of the
cluster. Examination of the individual GO 9281 exposures, in which
X4's likely counterpart (X4_ opt henceforth) is easily
resolved, reveals that this star is clearly distinguishable in some
images but almost fades away in others. In Fig. <ref> we
compare images from 2002 September 30 and October 2. The counterpart
dimmed by Δ B_435≈1.2 mag in ∼2.8 days. Its
average magnitudes as derived from the stacked images, place it to the
blue and Hα-bright (i.e. left) side of the bottom of the main
sequence in the optical colour-magnitude diagram (CMD) of GO 9281
(Fig. <ref>; large red filled circle). At increasingly
shorter wavelengths, we see that X4_ opt becomes relatively
bluer. In the NUV CMD of GO 12950, the object lies between the
47 Tuc main sequence and the white-dwarf sequence
(Fig. <ref>), a region also occupied by background stars in
the Small Magellanic Cloud. The position and optical/NUV magnitudes of
X4_ opt can be found in Table <ref>.

In the HUGS B_ 435 versus U_ 336-B_ 435 CMD
X4_ opt lies in a similar region, and for the bluest HUGS CMD,
the counterpart falls right on the white-dwarf sequence
(Fig. <ref>, middle and left CMDs). Long-term brightness
variations add uncertainty to the blue HUGS colours of X4 since the
combined data sets are non-contemporaneous. The relative location of
X4_ opt with respect to the main sequence is qualitatively
different in the reddest (I_ 814 versus V_ 606-I_
  814) CMD, where it lies slightly to the red or above the main
sequence (Fig. <ref>, right CMD).  The HUGS catalogue does
not provide a proper-motion membership probability for X4_ opt.

In order to establish to what extent variability impacts the colours
of X4_ opt, we also examine its quasi-instantaneous GO 9281
colours. We created light curves in the B_ 435, R_ 625
and Hα_658 filters using aperture photometry on the
individual exposures, adopting a small aperture radius of 1.5 pixels
to minimise contamination by the nearby bright star to the east (see
Fig. <ref>, bottom row).  By combining pairs of R_
  625 and Hα_ 658 measurements that are closest in time
(∼6–7 min apart), we constructed fifteen Hα_
  658-R_ 625 measurements; these are plotted as small red
circles in the right panel of Fig. <ref>. The two small red
circles in the left panel represent B_ 435-R_ 625 colours
from images taken ∼19 min apart (the time separation is different
here because of the observing sequence). With plus-signs inside the
red circles we have marked one B_ 435-R_ 625 and one
Hα_ 658-R_ 625 measurement taken during a ∼31
min time span during the high X-ray flux interval in ObsID 2735
(individual data points are marked in the bottom-left panel of
Fig. <ref>). Similarly, we marked a pair of colours taken
during the low X-ray flux interval with x-shaped crosses (see also the
bottom-middle panel of Fig. <ref>). We find that X4_
  opt shows large optical brightness and colour variations that
appear to be correlated with its behaviour in X-rays. When the X-ray
flux is high, X4_ opt is brighter, bluer, and has a larger
Hα_658 excess than during the remainder of GO 9281 (see
middle and bottom rows of Fig. <ref>). The observed
X-ray/optical correlation supports the interpretation that the rise in
X-ray emission is caused by a temporary higher accretion rate. The
average colour of X4_ opt, as well as the colours during the
high and low X-ray flux intervals, are also plotted in the
colour-colour diagram (CCD) of Fig. <ref>. We infer that
the strength of the Hα_ 658 excess emission in terms of
equivalent width (EW) can vary at least between about -30 Å and
-80 Å. The average EW in the GO 9281 images is about -50 Å ,
larger than the EW estimate by <cit.> of -28 Å.

In the GO 12950 images, the object is significantly variable in
U_ 300 as well, by ∼1.6 mag (although at the faint end
magnitude errors are ∼0.4 mag). In B_ 390, the source is
more stable (Fig. <ref>).


















 §.§ X5
 

The Chandra light curve of X5 (or W58) shows eclipses at an
∼8.7 hr period as well as “dipping” activity due to rapid
changes in the column density obscuring the regions close to the
neutron star (; see top panel of
Fig. <ref>). These changes are likely caused by
inhomogeneities in the outer parts of an accretion disk seen (almost)
edge on. Using the precise Chandra position, <cit.>
identified the counterpart (X5_ opt) as a blue object in WFPC2
images that shows variability on long and short time scales (see
Fig. 1 in  and our Fig. <ref> for a finding
chart). In U (F300W), the short-term variations resemble eclipses
and ellipsoidal variations; no such variability was seen by Edmonds et
al. in V (F555W). The average U magnitude was found to change by
∼1 mag between epochs separated by years.  While the dipping in
X-rays, long-term U variability, and blue U-V colour point to the
presence of an accretion disk, <cit.> (and later
, with even more stringent constraints) found that
any contribution from non-thermal emission to the Chandra
spectrum is negligible. As suggested by <cit.>, gas from the
disk may not currently be reaching the neutron star. Possibly, gas is
building up in the disk, or it could be swept away by a pulsar wind or
propeller effect before arriving at the neutron-star surface.


In the GO 9281 photometry, X5_ opt is also blue (although not
as pronounced as in U-V) and shows Hα excess emission
(Fig. <ref>). The simultaneous X-ray and optical light
curves of X5_ opt show correlated variability in all three
filters, in the sense that the optical brightness also decreases
around the time of the X-ray eclipses (Fig. <ref>, middle
and bottom rows). This is illustrated more clearly in the folded light
curves of Fig. <ref>, where we adopted an orbital period of
31200.197(1) s (see Appendix <ref>). The folded X-ray
light curve in the top panel of Fig. <ref> only shows those
time intervals that are simultaneous with the optical data
(middle). Double maxima and minima per orbital phase are seen most
clearly in the R_625 light curve. These features could be the
combined effect of ellipsoidal variations and eclipses, or a signature
of multiple shocks that give rise to hot spots in the disk (see
e.g.  for the cataclysmic variable V455 And in
quiescence, and  for the neutron-star LMXB Cen X-4
in quiescence). Moreover, as the hot disk should be more extended than
the region from which the X-rays originate, the optical/NUV eclipse
should also last longer. This likely explains why the optical minimum
around phase 0 is broader than the X-ray eclipses, as was also noted
by <cit.> for the U band. Parts of the hot disk could be
obscured by the stream impact point, as well, which would shift the
midpoint of the optical/NUV eclipse to earlier phases. The sampling of
our light curve is not good enough to see this potential effect.

The quasi-instantaneous colours, computed in the same way as for
X4_ opt, show that X5_ opt moves closer to the main
sequence in Hα_ 658-R_ 625 around phase 0 (defined to
be the centre of the X-ray eclipse; Fig. <ref>). In the
bottom-middle panel of Fig. <ref>, the data points that were
combined to compute the colours around the X-ray eclipse are marked
with filled dots, which makes them easier to recognise in the folded
light curve of Fig. <ref>, the CMD of Fig. <ref>,
and the CCD of Fig. <ref>. Towards the end of this optical
dip, around 3.25 days after the start of GO 9281, the Hα_
  658-R_ 625 excess is again at the average level for X5_
  opt (see the left-most “dotted” blue square in the R_ 625
versus Hα_ 658-R_ 625 CMD in
Fig. <ref>). The B_ 435-R_ 625 colour at this
time also lies closer to the main sequence compared to the average,
but the corresponding individual B_ 435 and R_ 625 data
points lie in a part of the light curve where the brightness may be
changing relatively quickly, which could affect the colour. These
changes suggest that part of the region where the Hα (and
perhaps also blue) emission is relatively strong, is obscured together
with the X-rays.  Unlike <cit.>, who noted that X5_
  opt shows no signs of eclipses or ellipsoidal variability in V,
we do see variations at the redder wavelengths. This suggests
long-term qualitative changes in the light curve. The minima around
phase 0.5 in R_ 625 and Hα_ 658 could be
ellipsoidal variations. On the other hand, there is no obvious dip
around that phase in B_ 435; given the poor sampling, we cannot
draw firm conclusions. The light curve looks especially noisy around
phases 0.2–0.4 in Hα_ 658 (Fig. <ref>). This
interval overlaps with the part of the X-ray light curve most affected
by dipping.

In the GO 12950 data, the counterpart to X5 is much bluer relative to
the main sequence than in the optical (Fig. <ref>). With
U_ 300≈22.3 at maximum brightness, the source is about as
bright as in 1997 November and 1999 October, but almost a magnitude
fainter than in 1995 October <cit.>.  The uncertainty in
the orbital period is small enough that we can phase-connect the
X-ray/optical light curves from 2002 with the NUV light curve from
GO 12950 taken about 11 years later (see Appendix A). In the bottom
panel of Fig. <ref>, we show the phased NUV light curve
taken over a time span of ∼6.5 hr. The U_ 300 light curve
looks smooth, and shows a broad dip centred around the X-ray eclipse.
The four B_ 390 data points show a lack of
variability. Unfortunately, in the other four F390W exposures, X5
falls in a chip gap.

In the HUGS CMDs, X5_ opt is blue except in the reddest
filters, where it lies ∼0.35 mag to the red of the main sequence
in V_ 606 - I_ 814. This excess may be explained by
periodic changes in the light curve on a time scale of hours affecting
the colours, or intrinsically anomalous colours of the donor.





 §.§ X7
 

X7 (or W46) is one of the best-studied X-ray sources in 47 Tuc. A
neutron-star atmosphere model gives an excellent fit to the Chandra spectrum. The lack of a harder power-law spectral
component, and the high level of stability in X-rays over the years,
suggest there is no accretion occurring in the system. This makes X7
an attractive source for deriving constraints on the neutron-star
equation of state <cit.>. Some systematic
uncertainties in X7's radius and mass measurements remain, because the
composition of the neutron-star atmosphere is unknown. Although an
H-rich atmosphere is deemed more likely than a He-rich atmosphere (see
the discussion in <cit.> and <cit.>), the nature of
the optical or NUV counterpart would shed more light on this
issue. However, no counterpart has been identified
yet. <cit.> found no variable or blue source in the X-ray
error circle.

We examined the colours of the three nearby stars that were also
considered by <cit.>, N1 to N3 (see Fig. <ref> top
right for a finding chart). Like these authors, we find that N2 and N3
have normal main-sequence colours in the GO 9281 and GO 12950
images, so we agree that these stars are not viable counterparts;
moreover, their angular separations from X7's Chandra position
are relatively large. At an offset of ∼0.07, N1 is an
excellent astrometric match to X7. However, its U-V colour resembles
that of a normal low-mass main-sequence star, and in the high-cadence
GO 8267 WFPC2 time series spanning 8.3 days N1 shows no variability
(see Fig. 3d in ). We find that the B_
  435-R_ 625 colour of N1 is also unremarkable, and consistent
with that of a ∼0.62 M_⊙ main-sequence star (based on
comparison with the isochrones from ). On the other
hand, its Hα_ 658-R_ 625 colour puts it slightly to
the Hα-excess side of the main sequence (see
Fig. <ref>). Interestingly, in the B_ 390 versus
U_ 300-B_ 390 CMD, N1 lies a little bit to the blue of the
main sequence (Fig. <ref>). This modest blue excess is also
found independently in the KS2 photometry of the same data, where the
apparent deviation from the main sequence is in fact a bit
larger. (Below, we quantify N1's blue excess in more detail for the
GO 9019 CMDs, where it is found in a similar location with respect to
the main sequence). Its U_ 300 light curve
(Fig. <ref>, top) shows scatter at a level that is higher
than ≳99% of stars with a similar magnitude
(Fig. <ref>). We also identify a faint star at an offset of
∼0.15 from X7 that is visible (but unnamed) in the V
finding chart in <cit.>, as well. We name this star N4 and
mark it in the finding chart of Fig. <ref>. N4 has a small
Hα excess that is more pronounced than that of N1, but lies on
the main sequence in the B_ 435-R_ 625 CMD. From the NUV
images, we find that B_ 390=24.18(4) but since this star is
undetected in U_ 300, we do not know its NUV colour. However,
the limit on U_ 300 suggests that U_ 300-B_
  390≳1.8.  There are two more stars inside the error circle
(N5 and N6); both lie on the main sequence, and therefore we do not
consider them plausible counterparts. These findings spurred us to
focus on N1 and N4, and look for coverage in other HST images.


In Fig. <ref>, we mark N1 and N4 in the HUGS CMD with the
orange and white diamond, respectively. N1 lies well to the blue of
the main sequence in the U_ 275 versus U_ 275-U_
  336 CMD, whereas the location of N4 is poorly constrained due to
the large errors in U_ 275. In the redder CMDs, both stars lie
on, or close to, the main sequence. Taking the HUGS colours at face
value, we conclude that N1 is the more likely counterpart given its
blue NUV colour and smaller offset from X7.  We caution that the value
of the “sharp” parameter, which indicates how well a star's profile
matches that of the PSF, is outside the optimal range in all HUGS
measurements of N1 and N4. This may be due to the crowding near X7 and
could indicate that their photometry is affected.

We examined N1 and N4 in the GO 9019 HRC data as well. N4 is not
detected in the GO 9019 F220W and F330W images, only in the F435W and
F475W images.  N1 is too faint to be detected in F220W. The average
U_ 330-B_ 435 and U_ 330-B_ 475 colours put N1
to the blue of the main sequence. To quantify this blue offset, we
first computed the width of the main sequence at the magnitude of N1
in the CMDs of Fig. <ref>. The solid red lines in the
panels represent the mean colour as a function of magnitude, while the
dashed red lines are the 1 σ deviations about the mean,
calculated using an iterated 3 σ clip. The curves were smoothed
by fitting third-order polynomials. We took half the separation
between the dashed lines as the 1 σ uncertainty on the colour
index, which for N1 is plotted as the error bar on the orange diamond
in each panel. N1 lies more than 1 σ to the blue side of the
main sequence in both CMDs, especially in the U_ 330-B_
  435 CMD, suggesting a blue (NUV) excess.

We also considered indications for variability in the individual
GO 9019 images. For B_ 435 and B_ 475, the DAOPHOT
errors are ∼0.08–0.1 mag, consistent with the scatter in the
magnitudes from the individual images (three in each filter). In
U_ 330, N1 shows a 0.35 mag variation between the three
images. Going from the first to the third exposure, N1 varies from
21.71(25) mag, to 21.36(18) mag (4 min later) and finally to 21.57(20)
mag (19 min after the first image). For all three filters, we compared
the standard deviation in the N1 data points with those of other stars
in the images, and found that N1 does not stand out. We conclude that
N1 is not significantly variable in the GO 9019 images that we
analyzed. Comparison between the HUGS magnitude for N1 in F336W from
2010 Sep (U_ 336=22.03(07)) with the value reported by
<cit.> from 1999 Jul (U_ 336=21.97 with an absolute
error ∼0.2 mag) also shows good agreement.

In conclusion, we consider it very likely that N1 is the true
optical/NUV counterpart of X7. The variability in F300X
(Fig. <ref>), the blue colours in the NUV filters and the
weak Hα excess emission suggest the presence of an accretion
disk. However, in X-rays X7 has not shown any signs of ongoing
accretion. Possibly, accretion from the secondary feeds the disk but
either the gas has not reached the neutron star just yet, or is
expelled from the system by a pulsar or propeller wind. Alternatively,
low-level accretion is taking place and generates faint X-ray
emission of the order ∼10^31 erg s^-1, but the
corresponding weak power-law component in the X-ray spectrum remains
hidden under the ∼10^33 erg s^-1 soft X-ray emission.
Another implication of N1 being the counterpart, is that the
atmosphere of the neutron star in X7 would be H-rich as N1 looks like
a main-sequence star with a small Hα excess. This is consistent
with the conclusions of <cit.> and <cit.> from X-ray
spectral fitting.




 §.§ W17


W17 is among the new sources that were discovered in the Chandra
observations of 2000. <cit.> identified this source as a
candidate qLMXB based on its relatively soft X-ray colours, and the
high X-ray–to–optical flux ratio (≳0.9) that is inferred
from its X-ray luminosity (L_X≈ 2 × 10^31 erg s^-1
(0.5–6 keV) for the distance adopted here) and the high upper limit
to the optical magnitude (U≳24). The proximity of a very
bright, saturated star at only ∼0.62 to the south-west
hampered their search for an optical counterpart in the deep GO 8267
WFPC2 V and I data.  Fits to the 2000 and 2002 Chandra
spectra led <cit.> to the conclusion that W17 is indeed a
qLMXB: its spectrum is dominated by a Γ≈ 1.9 power-law
component, but also shows a distinct soft component that can be fitted
with a neutron-star atmosphere model.  W17 does not show X-ray
variability on short time scales (days to weeks) or between the 2000
and 2002 observations.

In our GO 9281 data, the light of the nearby bright star also
inhibits a sensitive search for a counterpart, so we have no
simultaneous X-ray/optical measurements of this source. We estimate an
upper limit of B_435≳24, with an uncertainty of ∼0.5
mag given that the light of the saturated star makes it difficult to
account for the local background. The situation is much better in the
NUV. In the GO 12950 images we readily found a very blue star near
the centre of the Chandra error circle (see Fig. <ref>).
This star is highly variable with a full amplitude of Δ U_
    300≳ 1 mag in the ∼8 hr time span of the GO 12950
observations (Fig. <ref>). Its time-averaged U_
  300-B_ 390 colour puts it far to the blue of the main
sequence, in between the white dwarfs and the SMC sequence
(Fig. <ref>). The HUGS U_ 275-B_ 336 colour
puts it even closer to the white-dwarf sequence. In the F435W, F606W,
F814W filters, we do not consider the photometry reliable given the
proximity of the bright star.

The GO 12950 NUV colours of the counterpart are bluer than those of
X4_ opt and X5_ opt. A larger contribution from an
accretion disk could be the reason for this. However, the X-ray
luminosity of the power-law component in W17 is about the same as the
average power-law luminosity in X4, suggesting that on average the
level of accretion in these two systems is similar. The orbital period
would shed light on the nature of the companion. The shape of the
GO 12950 light curves show a hint of repetition at a time scale of
∼3.5–4 hr but do not display significant periodicity. If the
secondary is a white dwarf rather than a main-sequence star, it could
contribute to the blue colours as well.




 §.§ W37
 


W37 is also one of the sources discovered in the 2000 Chandra
observation.  Its spectrum is soft and can be fitted with a
neutron-star atmosphere model. W37's X-ray light curve shows eclipses
(at a period of 3.087 hr) as well as drastic changes in the count rate
due to variable obscuration. During the eclipses, a small amount of
residual soft emission of unknown origin was seen by
<cit.>. W37 has no known optical or NUV counterpart. No
nearby blue or variable object is seen in the HST data analyzed
by <cit.>, although the presence of two bright
main-sequence stars close to the X-ray position reduces the
sensitivity to finding faint counterparts. If the companion is a
main-sequence star, the orbital period indicates a secondary mass of
≲0.34 M_⊙.


In the GO 9281 and GO 12950 images we find seven optical/NUV sources
inside the 95% error circle, marked 1 to 7 in the panel for W37 in
Fig. <ref>. Five of these (2, 3, 5–7) look like regular
main-sequence or main-sequence turnoff stars, with some lying slightly
offset to the red side of the main sequence in B_ 435-R_
  625. We do not consider these stars plausible counterparts. Star 1
lies close to the main sequence in the R_ 625 versus
Hα_ 658-R_625 CMD (near the expected location of a
∼0.7 M_⊙ star) and the U_336 versus U_275-U_336
and I_814 versus V_606-I_814 CMDs, but in the R_ 625
versus B_ 435-R_ 625, B_ 390 versus U_
  300-B_ 390, and B_ 435 versus U_ 336-B_
  435 CMDs of Figs. <ref>, <ref> and
<ref>, respectively, it appears to be slightly offset to
the blue. Given the estimated upper mass limit of a main-sequence
donor (see previous paragraph), it is not likely that star 1 is the
true counterpart. It could be blended with an undetected fainter and
bluer object that draws its photometry to the blue side of the main
sequence, or the PSF wings of the nearby star 3 may not be properly
accounted for. The photometry for star 4 is ambiguous. In the optical,
it is only convincingly detected in the F435W images, at B_
  435≈20.1. Forcing DAOPHOT to extract R_ 625 and
Hα_ 658 magnitudes from the position of this F435W
detection, does not produce credible results. In the NUV, the
photometry of star 4 puts it either to the red (DAOPHOT) or the blue
(KS2, Dolphot) of the main sequence. Given the uncertain photometry,
we have omitted this star from Fig. <ref>. Perhaps the only
thing that can be concluded is that, at the time of the GO 9281
observations, this object was blue for it to be detected in the F435W,
but not in the F625W and F658N images. Stars 1 and 4 are highly
variable in the U_ 300 images of the GO 12950 data set; both
lie above the 99% percentile limit in Fig. <ref>. Star 1
was clearly detected in the NUV photometry and the variability seems
to be intrinsic, while star 4 seems to be closer to star 3 and
variability could be due to contamination from that star. In the HUGS
catalog and the GO 9019 images, star 4 is not detected.

Examination of the GO 9019 F220W image suggests the presence of
excess flux at a position about 0.06 to the north-west of star
2 and about 0.04 from the location of W37. This excess flux is
not apparent at longer wavelengths, which is consistent with the
presence of a blue star. This is illustrated in Fig. <ref>,
which shows the region around W37 in the F220W, F330W, and F435W
filters. These drizzled ACS HRC frames have been aligned with the HUGS
coordinate system, which itself is aligned with the Gaia
reference system. While the extension of the image of star 2 in F220W
is suggestive of the presence of a blue star near the position of W37,
it is by no means definitive. Deeper high-resolution imaging is
necessary to further investigate this issue.



In order to identify the counterpart of W37 through optical
variability on the known orbital period, we have performed a series of
light curve analyses on the GO 8267 WFPC2 data. The F555W and F814W
light curves of the four stars closest to the centre of the X-ray
error circle (stars 1 to 4) were kindly provided to us by
R. Gilliland. The light curves contain 636 (F555W) and 653 (F814W)
data points spread over 8.3 days in 1999 Jul. We refer to
<cit.> and <cit.> for more details about the data
and light curve extraction.  First, we phase-folded the V_ 555
and I_ 814 light curves on the known period from the X-ray
eclipses, but no periodicity was observed in either of the two
bands. To reduce the scatter in these light curves, we averaged the
measurements in phase bins of 0.001 and 0.003 days, well below the
duration of the X-ray eclipse. Still, no periodicity was observed for
any of the four stars.  Another attempt was carried out by using a
sigma-clipping approach on each of the previously defined phase bins.
We removed all photometric measurements that were smaller or larger
than m ± 3 σ, where m is the median value in each bin and
σ is the standard deviation. This approach was taken to remove
outliers, but did not reveal any periodicity.  Finally, we performed a
Lomb-Scargle <cit.> analysis to look for the X-ray period
in the optical data. The analysis was performed separately in both
filters. In multiple cases a period corresponding to the HST
orbit was observed (∼96.5 min, so very close to half W37's
orbital period, or 92.6 min), but none consistent with the X-ray
period of W37 or half of it.

In conclusion, we have not securely identified the counterpart to
W37. To compute limits on the X-ray–to–optical flux ratio (see
Table <ref>) we use the magnitudes of star 4, which is the
faintest of the stars near W37.




§ DISCUSSION
 






Our search for optical/NUV counterparts to the qLMXBs in 47 Tuc has
yielded the discovery of a blue and variable counterpart to W17. We
also find compelling indications that a known astrometric match to X7
is indeed a likely counterpart. Of the five (likely) neutron-star
qLMXBs in the cluster, only one (W37) remains unidentified as the
proximity of several stars near the centre of the X-ray error circle
complicates a sensitive search for a counterpart. Optical counterparts
have been identified for only two other globular-cluster
qLMXBs[and for a handful of globular-cluster transient LMXBs
  in quiescence, including IGR J18245-2452 in M 28
  <cit.>; Terzan 5 X-1 and Terzan 5 X-2
  <cit.>; and SAX J1748.9-2021 in NGC 6440
  <cit.>]: the source in ω Cen (discovered
by <cit.>, later named 44e by <cit.>) and U24 in
NGC 6397 <cit.>. With R_ 625=25.2 and R_
  625=26.2, respectively, these systems are much fainter than the
47 Tuc qLMXBs (with R_ 625 between 19.8 and 22.1, see
Table <ref>), making them unsuitable for detailed
follow-up studies. The ω Cen and NGC 6397 systems are also
intrinsically much fainter in the optical (M_ 625=11.6 and
M_ 625=13.7, respectively) than the 47 Tuc neutron-star qLMXBs
(M_ 625 between ∼6.5 and ∼8.8, see
Fig. <ref>). It is unlikely that similar
systems[with X-ray spectra dominated by a thermal component;
  note that a number of qLMXBs show a dominant non-thermal component
  <cit.>; such systems could be
  confused with CVs even in 47 Tuc <cit.>.] are also
present in 47 Tuc but have been missed; while in the optical they lie
below the sensitivity of the HST data, they would have been
easily detected by Chandra. For uncrowded sources, the
<cit.> 47 Tuc source catalogue is complete down to
L_X≈8×10^29 erg s^-1, whereas
L_X≈2×10^32 erg s^-1 for 44e <cit.> and
L_X≈8×10^31 erg s^-1 for U24 <cit.>).


In the optical, the counterparts of X4 and X5 and the likely
counterpart to X7 lie relatively close to the main sequence and show
Hα excess emission. This implies that the mass donors in these
systems are non-degenerate, H-rich main-sequence stars. For X5, the
non-degenerate nature of the secondary already followed directly from
the known orbital period and eclipse light curve. For X7, the
properties of the suggested counterpart are consistent with earlier
conclusions from fitting X7's X-ray spectrum.  Unfortunately, the
counterpart of W17 is not detected in Hα and the nature of the
donor remains unknown. Based on the large value of the lower limit on
the X-ray–to–optical flux ratio, <cit.> identified W17
as a likely qLMXB. Our limit on the flux ratio from the simultaneous
data (see Table <ref> and discussion below) confirms this
view. While we still cannot say with certainty whether X4 is a qLMXB
or not, the properties of the counterpart to X4 (modest blue optical
colour like X5 and X7, high flux ratio) make the case for X4 being a
qLMXB stronger.

In a diagram of X-ray luminosity versus X-ray colours, X5 and X7 stand
out as soft luminous sources in the cluster (see Fig. <ref>,
adapted from <cit.>). The more actively accreting
ultra-compact LMXB X9 is comparably bright, but has a harder
spectrum. Classification based on X-ray luminosity and colours alone
becomes more challenging for the less luminous sources X4, W17 and W37
(which could be classified as a qLMXB thanks to its X-ray light curve)
because members of other source classes can reach similar
luminosities. A case in point is X10 (also known as V3 or W27), which
is also a bright soft source.  X10 was classified as a probable
magnetic CV based on its X-ray spectrum and periodic (4.67 hr) X-ray
light curve <cit.> that are both typical for its
source class.

Taking into account the properties of the optical or NUV counterparts
helps to tell source classes apart. The known 47 Tuc CVs and qLMXBs
span similar ranges in absolute magnitude (see Figs. <ref>
and <ref>) and excess Hα emission (see
Fig. <ref>). The CVs, however, have counterparts that tend
to be bluer than the qLMXB counterparts. In particular in the optical
R_ 625 versus B_ 435-R_ 625 CMD, the counterparts
of X4, X5 and X7 are not far offset from the blue of the main
sequence. In other words, the relative contribution of an accretion
disk or stream (and in addition, for some CVs, the emission of the
white dwarf itself) to the combined light is more pronounced for CVs.

An often-used criterion for source classification is the ratio of the
X-ray flux to optical flux, which is highest for qLMXBs, followed in
order by CVs and ABs <cit.>. This can be understood based on
the different origins of the X-rays: emission from the heated surface
of the compact object and accretion in qLMXBs and CVs (and from a
shock region in magnetic systems) versus coronal activity of the
rapidly rotating stars in a close binary of main-sequence and/or
sub-giant stars. Neutron stars and black holes have the deepest
potential wells and give rise to the highest accretion-powered X-ray
luminosities. <cit.> demonstrated the diagnostic power of
the X-ray–to–optical flux ratio for the classified Chandra
sources in 47 Tuc. Since our 2002 Chandra and HST
GO 9281 observations were taken simultaneously, the resulting flux
ratios address concerns stemming from the X-ray and optical data being
taken at different epochs. For example, <cit.> found that X5
and X10 have similar flux ratios but cautioned that since X10 is
highly variable both in X-rays and in the optical, its actual F_
  X/F_ opt value could be lower. The filled symbols in
Fig. <ref> show the X-ray fluxes from the 2002 Chandra observation against the GO 9281 F435W fluxes F_ 435
(converted to unabsorbed absolute magnitudes)[Note that in
this figure, X-ray fluxes in the 0.5–6 keV band from the 2002 Chandra data are plotted (based on Table 2 in
). The corresponding X-ray–to–optical flux ratios
may be different from those in Table <ref>, which were
computed for specific (partial) ObsIDs or for a different epoch.]. We
include the securely identified CVs from <cit.> but omitted
W23 and W299 that have other candidate counterparts in the error
circle, turning their reported X-ray luminosities <cit.>
into upper limits. We find that at F_ X/F_
  435≈1.4, the flux ratio for X10 is somewhat lower than that
of X5 (∼1.7), but still not far off, even for the simultaneous
fluxes. The high flux ratio for X10 can be explained by its nature as
a magnetic CV: due to the high magnetic field of the white dwarf,
there is no accretion disk in the system to contribute to the blue
optical flux.  Furthermore, we find that W51 is also relatively bright
in X-rays compared to its optical flux.  This may be due to the large
flare produced by W51 in the 2002 Chandra observations
<cit.>, which substantially increased its average
flux; in the 2000 Chandra observations, its average flux was 5.7
times lower (which would bring W51 more in line with other CVs in 47
Tuc). We do not understand the nature of this flare.

In order to try to further separate the qLMXBs and CVs, we make use of
the finding that in the optical the qLMXB counterparts tend to lie
closer to the main sequence than the CV counterparts. We turn this
offset into an excess blue flux F_ 435,exc in the
following way. We assume that all the light in the F625W band is
contributed by a main-sequence secondary. In an isochrone (age 11 Gyr,
Z=0.004) generated with the PARSEC code <cit.>[see
  also <http://stev.oapd.inaf.it/cgi-bin/cmd>], we look up the
corresponding B_ 435 magnitude for such a star. The excess blue
flux F_ 435,exc is found by the difference between the observed
B_ 435 magnitude of the counterpart and the (theoretical)
secondary-star flux. This is likely a lower limit to the excess blue
flux, as the accretion flow may also contribute light in the redder
filters. But it does give us an upper limit on F_ X/F_
  435,exc and combined with the value of F_ X/F_ 435
this delineates the range inside which the true value of F_
  X/F_ blue,exc should lie. As can be seen in
Fig. <ref>, the distinction between the CVs and qLMXBs
becomes more pronounced when considering the excess blue flux.

Using the excess blue fluxes versus X-ray fluxes, we see three groups
in Fig. <ref>. At logF_ X/F_ 435,exc > 2.0,
only qLMXBs are seen. Between 1.5 <logF_ X/F_ 435,exc
<2.0, we see a qLMXB without NS surface emission (X9, likely a black
hole qLMXB) and a CV without an optically bright accretion disk (X10,
a polar CV). We also find W51 here, which is classified as a CV, but
has a higher F_ X/F_ 435,exc than either X9 or X10,
spurring us to speculate that W51 might be a magnetic CV or a hidden
qLMXB (with a dominant nonthermal X-ray spectral component). Then at
logF_ X/F_ 435,exc < 1.5, we see only CVs.

As a final note, we point out that the (likely) optical/NUV
counterparts to X4, X5, X7 and W17 lie well within the error circles
(Fig. <ref>). Since the radii of these error circles are
dominated by the X-ray errors, this suggests that the prescription by
<cit.> for the 95% positional uncertainty on the Chandra positions overestimates the actual uncertainties. For the
five sources that we consider here, we have also computed the X-ray
errors using the formula in <cit.>. We find that for these
bright sources the resulting 95% X-ray errors are about 3–5 times
smaller than the Hong errors. The optical/NUV counterparts lie very
close to, or within, the Kim error radii. We suggest that for future
studies of bright Chandra sources, the use of the Kim errors is
more appropriate as they eliminate many astrometric counterparts that
would otherwise fall inside the (larger) error circles.




§ CONCLUSIONS
 


We have performed a detailed study of three certain (X5, X7 and W37)
and two likely (X4 and W17) qLMXBs in 47 Tuc using simultaneous Chandra and optical HST data, complemented with
non-contemporaneous optical and NUV HST data. We have discovered
a blue and variable NUV counterpart to W17. The emission of a nearby
bright star overwhelms this star in the optical. For X7, we suggest
that the star N1, a previously identified astrometric match to this
source, is the likely true counterpart. Since N1 looks like a
main-sequence star, the atmosphere of the neutron star is probably
H-rich. N1 has blue colours (in particular in the NUV), shows a modest
Hα excess and enhanced variability in U_ 300. These
properties point at the presence of an accretion disk, but at the same
time X7 has not shown any signs of accretion in X-rays. We suggest
that either gas from the disk has not reached the neutron star (yet),
or that the power-law component associated with accretion is
overwhelmed by the soft X-ray emission. We find a possible NUV
counterpart for W37 but deeper higher-resolution imaging is needed to
investigate the association with the X-ray source.

We have investigated the properties of the known optical/NUV
counterparts to X4 and X5. For X4, we find that the simultaneous X-ray
and optical light curves confirm that the X-ray variability is driven
by changes in the accretion rate. In X5, minima in the optical and NUV
light curves accompany the X-ray eclipses. The simultaneous X-ray and
optical data suggest that the regions in the binary system that give
rise to the blue and Hα excess emission are obscured together
with the X-rays. We find evidence for long-term variations in the
optical from comparing our light curves with those taken about three
years earlier.

Overall, based on the smaller blue (F435W) excess fluxes for X4_
  opt, X5_ opt, and X7_ opt compared to the CV optical
counterparts, we conclude that the accretion disks in the 47 Tuc
qLMXBs are less prominent than in CVs. This makes the ratio of X-ray
flux to excess blue optical flux a powerful discriminator between CVs
and qLMXBs.



§ ACKNOWLEDGEMENTS

  The authors thank R. Gilliland for providing GO 8267 light
  curves. This work is supported by Chandra grant GO3-4033A. This work
  made use of data from ESO telescopes obtained from the ESO/ST-ECF
  Science Archive Facility.
  CH is supported by NSERC Discovery Grants RGPIN-2016-04602 and RGPIN-2023-04264.




§ DATA AVAILABILITY

The Chandra data used in this work are available in the Chandra Data Archive at <https://cxc.harvard.edu/cda>. The HST data used in this work can be retrieved from the Mikulski Archive for Space Telescopes (MAST) Portal at <https://mast.stsci.edu/search/ui/#/hst>.












@urlcharsothermakeother $&#_%
@doi@urlcharsother ifnextchar [ @doi@
  @doi@[]
@doi@[#1]#2tempa#1tempaempty http://dx.doi.org/#2 doi:#2http://dx.doi.org/#2 #1
@eprint#1#2@eprint@#1:#2::nil
@eprint@arXiv#1http://arxiv.org/abs/#1 arXiv:#1
@eprint@dblp#1http://dblp.uni-trier.de/rec/bibtex/#1.xml
  dblp:#1
@eprint@#1:#2:#3:#4niltempa #1tempb #2tempc
  #3tempc empty tempc tempb tempb tempa tempb empty tempb arXivifundefined
  mn@eprint@tempbtempb:tempcmn@eprint@tempbtempc

[Albrow, Gilliland, Brown, Edmonds,
  Guhathakurta  & SarajediniAlbrow et al.2001]albrea01
Albrow M. D.,  Gilliland R. L.,  Brown T. M.,  Edmonds P. D.,
  Guhathakurta P.,   Sarajedini A.,  2001, @doi [] 10.1086/322353,
  http://adsabs.harvard.edu/abs/2001ApJ...559.1060A 559, 1060

[Alcock & IllarionovAlcock &
  Illarionov1980]alcoilla80
Alcock C.,  Illarionov A.,  1980, @doi [] 10.1086/157656, https://ui.adsabs.harvard.edu/abs/1980ApJ...235..534A 235, 534

[Anderson et al.,Anderson
  et al.2008]andea08
Anderson J.,  et al., 2008, @doi [] 10.1088/0004-6256/135/6/2055,
  http://adsabs.harvard.edu/abs/2008AJ....135.2055A 135, 2055

[Bahramian, Heinke, Degenaar, Chomiuk,
  Wijnands, Strader, Ho  & PooleyBahramian
  et al.2015]bahrea15
Bahramian A.,  Heinke C. O.,  Degenaar N.,  Chomiuk L.,  Wijnands R.,
   Strader J.,  Ho W. C. G.,   Pooley D.,  2015, @doi []
  10.1093/mnras/stv1585, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2015MNRAS.452.3475B
  452, 3475

[Bahramian et al.,Bahramian
  et al.2017]bahrea17
Bahramian A.,  et al., 2017, @doi [] 10.1093/mnras/stx166, http://adsabs.harvard.edu/abs/2017MNRAS.467.2199B 467, 2199

[Bao, Li  & ChengBao
  et al.2023]baoea23
Bao T.,  Li Z.,   Cheng Z.,  2023, @doi []
  10.1093/mnras/stad836, https://ui.adsabs.harvard.edu/abs/2023MNRAS.521.4257B 521, 4257

[Beccari, De Marchi, Panagia  &
  PasquiniBeccari et al.2014]beccea14
Beccari G.,  De Marchi G.,  Panagia N.,   Pasquini L.,  2014, @doi
  [] 10.1093/mnras/stt2074, http://adsabs.harvard.edu/abs/2014MNRAS.437.2621B 437, 2621

[Bernardini, Cackett, Brown, D'Angelo,
  Degenaar, Miller, Reynolds  & WijnandsBernardini
  et al.2013]bernardini13
Bernardini F.,  Cackett E. M.,  Brown E. F.,  D'Angelo C.,  Degenaar
  N.,  Miller J. M.,  Reynolds M.,   Wijnands R.,  2013, @doi []
  10.1093/mnras/stt1741, https://ui.adsabs.harvard.edu/abs/2013MNRAS.436.2465B 436, 2465

[Bhattacharya, Heinke, Chugunov,
  Freire, Ridolfi  & BogdanovBhattacharya et al.2017]bhatea17
Bhattacharya S.,  Heinke C. O.,  Chugunov A. I.,  Freire P. C. C.,
  Ridolfi A.,   Bogdanov S.,  2017, @doi []
  10.1093/mnras/stx2241, http://adsabs.harvard.edu/abs/2017MNRAS.472.3706B 472, 3706

[Bogdanov, van den Berg, Heinke, Cohn,
  Lugger  & GrindlayBogdanov et al.2010]bogdea10
Bogdanov S.,  van den Berg M.,  Heinke C. O.,  Cohn H. N.,  Lugger
  P. M.,   Grindlay J. E.,  2010, @doi []
  10.1088/0004-637X/709/1/241, http://adsabs.harvard.edu/abs/2010ApJ...709..241B 709, 241

[Bogdanov, Heinke, Özel  &
  GüverBogdanov et al.2016]bogdea16
Bogdanov S.,  Heinke C. O.,  Özel F.,   Güver T.,  2016,
  @doi [] 10.3847/0004-637X/831/2/184, http://adsabs.harvard.edu/abs/2016ApJ...831..184B 831, 184

[Bressan, Marigo, Girardi, Salasnich,
  Dal Cero, Rubele  & NanniBressan et al.2012]bresea12
Bressan A.,  Marigo P.,  Girardi L.,  Salasnich B.,  Dal Cero C.,
  Rubele S.,   Nanni A.,  2012, @doi []
  10.1111/j.1365-2966.2012.21948.x, http://adsabs.harvard.edu/abs/2012MNRAS.427..127B 427, 127

[Brown, Bildsten  & RutledgeBrown
  et al.1998]browea98
Brown E. F.,  Bildsten L.,   Rutledge R. E.,  1998, @doi []
  10.1086/311578, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/1998ApJ...504L..95B
  504, L95

[Cackett, Brown, Miller & WijnandsCackett et al.2010]cackea10
Cackett E. M., Brown E. F., Miller J. M., Wijnands R.,  2010, @doi [] 10.1088/0004-637X/720/2/1325, https://ui.adsabs.harvard.edu/abs/2010ApJ...720.1325C 720, 1325

[Cameron, Rutledge, Camilo, Bildsten,
  Ransom  & KulkarniCameron et al.2007]cameron07
Cameron P. B.,  Rutledge R. E.,  Camilo F.,  Bildsten L.,  Ransom
  S. M.,   Kulkarni S. R.,  2007, @doi [] 10.1086/512229, https://ui.adsabs.harvard.edu/abs/2007ApJ...660..587C 660, 587

[Campana, Colpi, Mereghetti, Stella  &
  TavaniCampana et al.1998]campea98
Campana S.,  Colpi M.,  Mereghetti S.,  Stella L.,   Tavani M.,
  1998, @doi [] 10.1007/s001590050012, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/1998A   ARv...8..279C
  8, 279

[Campana et al.,Campana
  et al.2002]Campana02
Campana S.,  et al., 2002, @doi [] 10.1086/342505, https://ui.adsabs.harvard.edu/abs/2002ApJ...575L..15C 575, L15

[Campana, Israel, Stella, Gastaldello & MereghettiCampana et al.2004]campea04
Campana S., Israel G. L., Stella L., Gastaldello F., Mereghetti S. 2004, @doi [] 10.1086/380194, https://ui.adsabs.harvard.edu/abs/2004ApJ...601..474C 601, 474

[Chakrabarty et al.,Chakrabarty
  et al.2014]chakea14
Chakrabarty D.,  et al., 2014, @doi [] 10.1088/0004-637X/797/2/92,
  https://ui.adsabs.harvard.edu/abs/2014ApJ...797...92C 797, 92

[Chen, Richer, Caiazzo  & HeylChen
  et al.2018]chenea18
Chen S.,  Richer H.,  Caiazzo I.,   Heyl J.,  2018, @doi []
  10.3847/1538-4357/aae089, http://adsabs.harvard.edu/abs/2018ApJ...867..132C 867, 132

[Church, Strader, Davies  &
  BobrickChurch et al.2017]churea17
Church R. P.,  Strader J.,  Davies M. B.,   Bobrick A.,  2017, @doi
  [] 10.3847/2041-8213/aa9aeb, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2017ApJ...851L...4C
  851, L4

[Cohn et al.,Cohn
  et al.2010]cohnea10
Cohn H. N.,  et al., 2010, @doi [] 10.1088/0004-637X/722/1/20, http://adsabs.harvard.edu/abs/2010ApJ...722...20C 722, 20

[D'Angelo, Fridriksson, Messenger  &
  PatrunoD'Angelo et al.2015]dangea15
D'Angelo C. R.,  Fridriksson J. K.,  Messenger C.,   Patruno A.,  2015,
  @doi [] 10.1093/mnras/stv465, https://ui.adsabs.harvard.edu/abs/2015MNRAS.449.2803D 449, 2803

[D'Avanzo, Campana, Casares, Israel,
  Covino, Charles  & StellaD'Avanzo et al.2005]davaea05
D'Avanzo P.,  Campana S.,  Casares J.,  Israel G. L.,  Covino S.,
  Charles P. A.,   Stella L.,  2005, @doi []
  10.1051/0004-6361:20053517, https://ui.adsabs.harvard.edu/abs/2005A   A...444..905D 444, 905

[Deutsch, Margon  & AndersonDeutsch
  et al.2000]deutea00
Deutsch E. W.,  Margon B.,   Anderson S. F.,  2000, @doi []
  10.1086/312486, https://ui.adsabs.harvard.edu/abs/2000ApJ...530L..21D 530, L21

[DolphinDolphin2000]dolp00
Dolphin A. E.,  2000, , http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2000PASP..112.1383D   db_key=AST
  112, 1383

[Echiburú, Guillot, Zhao, Heinke,
  Özel  & WebbEchiburú et al.2020]echiea20
Echiburú C. S.,  Guillot S.,  Zhao Y.,  Heinke C. O.,  Özel
  F.,   Webb N. A.,  2020, @doi [] 10.1093/mnras/staa1456, https://ui.adsabs.harvard.edu/abs/2020MNRAS.495.4508E 495, 4508

[Edmonds, Heinke, Grindlay  &
  GillilandEdmonds et al.2002a]edmoea02a
Edmonds P. D.,  Heinke C. O.,  Grindlay J. E.,   Gilliland R. L.,
  2002a, @doi [ApJL] 10.1086/338776, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002ApJ...564L..17E   db_key=AST
  564, L17

[Edmonds, Gilliland, Camilo, Heinke  &
  GrindlayEdmonds et al.2002b]edmoea02b
Edmonds P. D.,  Gilliland R. L.,  Camilo F.,  Heinke C. O.,
  Grindlay J. E.,  2002b, @doi [ApJ] 10.1086/342985, http://adsabs.harvard.edu/abs/2002ApJ...579..741E 579, 741

[Edmonds, Gilliland, Heinke  &
  GrindlayEdmonds et al.2003a]edmogillea03a
Edmonds P. D.,  Gilliland R. L.,  Heinke C. O.,   Grindlay J. E.,
  2003a, @doi [ApJ] 10.1086/378193, http://adsabs.harvard.edu/abs/2003ApJ...596.1177E 596, 1177

[Edmonds, Gilliland, Heinke  &
  GrindlayEdmonds et al.2003b]edmogillea03b
Edmonds P. D.,  Gilliland R. L.,  Heinke C. O.,   Grindlay J. E.,
  2003b, @doi [ApJ] 10.1086/378194, http://adsabs.harvard.edu/abs/2003ApJ...596.1197E 596, 1197

[Ferraro, Pallanca, Lanzoni, Cadelano,
  Massari, Dalessandro  & MucciarelliFerraro
  et al.2015]ferrea15
Ferraro F. R.,  Pallanca C.,  Lanzoni B.,  Cadelano M.,  Massari D.,
  Dalessandro E.,   Mucciarelli A.,  2015, @doi []
  10.1088/2041-8205/807/1/L1, https://ui.adsabs.harvard.edu/abs/2015ApJ...807L...1F 807, L1

[Gilliland et al.,Gilliland
  et al.2000]gillea00
Gilliland R. L.,  et al., 2000, @doi [] 10.1086/317334, http://adsabs.harvard.edu/abs/2000ApJ...545L..47G 545, L47

[Gonzaga, Hack, Fruchter  &
  MackGonzaga et al.2012]gonzea12
Gonzaga S.,  Hack W.,  Fruchter A.,   Mack J.,  eds, 2012, The
  DrizzlePac Handbook

[Grindlay, Heinke, Edmonds  &
  MurrayGrindlay et al.2001]grinea01a
Grindlay J. E.,  Heinke C.,  Edmonds P. D.,   Murray S. S.,  2001,
  @doi [Science] 10.1126/science.1061135, http://adsabs.harvard.edu/abs/2001Sci...292.2290G 292, 2290

[Haggard, Cool, Anderson, Edmonds,
  Callanan, Heinke, Grindlay  & BailynHaggard
  et al.2004]haggea04
Haggard D.,  Cool A. M.,  Anderson J.,  Edmonds P. D.,  Callanan
  P. J.,  Heinke C. O.,  Grindlay J. E.,   Bailyn C. D.,  2004, @doi
  [] 10.1086/421549, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2004ApJ...613..512H   db_key=AST
  613, 512

[Haggard, Cool  & DaviesHaggard
  et al.2009]haggard09
Haggard D.,  Cool A. M.,   Davies M. B.,  2009, @doi []
  10.1088/0004-637X/697/1/224, https://ui.adsabs.harvard.edu/abs/2009ApJ...697..224H 697, 224

[Hasinger, Johnston  &
  VerbuntHasinger et al.1994]hasiea94
Hasinger G.,  Johnston H. M.,   Verbunt F.,  1994, , http://adsabs.harvard.edu/abs/1994A

[Heinke, Grindlay, Lloyd  &
  EdmondsHeinke et al.2003a]heinea03a
Heinke C. O.,  Grindlay J. E.,  Lloyd D. A.,   Edmonds P. D.,  2003a,
  @doi [ApJ] 10.1086/374039, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2003ApJ...588..452H   db_key=AST
  588, 452

[Heinke, Grindlay, Lugger, Cohn,
  Edmonds, Lloyd  & CoolHeinke et al.2003b]heinea03b
Heinke C. O.,  Grindlay J. E.,  Lugger P. M.,  Cohn H. N.,  Edmonds
  P. D.,  Lloyd D. A.,   Cool A. M.,  2003b, @doi [ApJ]
  10.1086/378885, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2003ApJ...598..501H   db_key=AST
  598, 501

[Heinke, Grindlay  & EdmondsHeinke
  et al.2005a]heinea05a
Heinke C. O.,  Grindlay J. E.,   Edmonds P. D.,  2005a, @doi [ApJ]
  10.1086/427795, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005ApJ...622..556H   db_key=AST
  622, 556

[Heinke, Grindlay, Edmonds, Cohn,
  Lugger, Camilo, Bogdanov  & FreireHeinke
  et al.2005b]heinea05b
Heinke C. O.,  Grindlay J. E.,  Edmonds P. D.,  Cohn H. N.,  Lugger
  P. M.,  Camilo F.,  Bogdanov S.,   Freire P. C.,  2005b, @doi [ApJ]
  10.1086/429899, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2005ApJ...625..796H   db_key=AST
  625, 796

[Heinke, Rybicki, Narayan  &
  GrindlayHeinke et al.2006]heinea06
Heinke C. O.,  Rybicki G. B.,  Narayan R.,   Grindlay J. E.,  2006,
  @doi [ApJ] 10.1086/503701, http://adsabs.harvard.edu/abs/2006ApJ...644.1090H 644, 1090

[Heinke et al.,Heinke
  et al.2014]heinea14
Heinke C. O.,  et al., 2014, @doi [] 10.1093/mnras/stu1449, https://ui.adsabs.harvard.edu/abs/2014MNRAS.444..443H 444, 443

[Henleywillis, Cool, Haggard, Heinke,
  Callanan  & ZhaoHenleywillis et al.2018]henlea18
Henleywillis S.,  Cool A. M.,  Haggard D.,  Heinke C.,  Callanan P.,
   Zhao Y.,  2018, @doi [] 10.1093/mnras/sty675, https://ui.adsabs.harvard.edu/abs/2018MNRAS.479.2834H 479, 2834

[Hong, van den Berg, Schlegel, Grindlay,
  Koenig, Laycock  & ZhaoHong et al.2005]hongvandea05
Hong J.,  van den Berg M.,  Schlegel E.,  Grindlay J.,  Koenig X.,  Laycock S.,
    Zhao P.,  2005, ApJ, 635, 907

[Jonker, Galloway, McClintock, Buxton,
  Garcia  & MurrayJonker et al.2004]Jonker04
Jonker P. G.,  Galloway D. K.,  McClintock J. E.,  Buxton M.,  Garcia
  M.,   Murray S.,  2004, @doi []
  10.1111/j.1365-2966.2004.08246.x, https://ui.adsabs.harvard.edu/abs/2004MNRAS.354..666J 354, 666

[KatzKatz1975]katz75
Katz J. I.,  1975, @doi [] 10.1038/253698a0, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/1975Natur.253..698K
  253, 698

[Kim et al.,Kim
  et al.2007]kimkimea07
Kim M.,  et al., 2007, @doi [] 10.1086/511634, https://ui.adsabs.harvard.edu/abs/2007ApJS..169..401K 169, 401

[Koekemoer, McLean, McMaster  &
  JenknerKoekemoer et al.2005]koekea05
Koekemoer A.,  McLean B.,  McMaster M.,   Jenkner H.,  2005, Technical report,
  Instrument Science Report ACS 2005-06.
STScI

[Kononov, Lacy, Puzin, Kozhevnikov,
  Sytov  & LyaptsevKononov et al.2017]konoea17
Kononov D.,  Lacy C.,  Puzin V. B.,  Kozhevnikov V. P.,  Sytov A. Y.,
    Lyaptsev A. P.,  2017, in The Golden Age of Cataclysmic Variables and
  Related Objects IV. p. 31 (@eprint arXiv 1607.00265),
  @doi10.22323/1.315.0031

[Li, Kastner, Prigozhin, Schulz,
  Feigelson  & GetmanLi et al.2004]liea04
Li J.,  Kastner J. H.,  Prigozhin G. Y.,  Schulz N. S.,  Feigelson
  E. D.,   Getman K. V.,  2004, @doi [] 10.1086/421866, https://ui.adsabs.harvard.edu/abs/2004ApJ...610.1204L 610, 1204

[LinaresLinares2014]lina14
Linares M.,  2014, @doi [] 10.1088/0004-637X/795/1/72, http://adsabs.harvard.edu/abs/2014ApJ...795...72L 795, 72

[LombLomb1976]lomb76
Lomb N. R.,  1976, @doi [] 10.1007/BF00648343, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/1976Ap   SS..39..447L
  39, 447

[Lugger, Cohn, Cool, Heinke  &
  AndersonLugger et al.2017]luggea17
Lugger P. M.,  Cohn H. N.,  Cool A. M.,  Heinke C. O.,   Anderson J.,
   2017, @doi [] 10.3847/1538-4357/aa6c56, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2017ApJ...841...53L
  841, 53

[Miller-Jones et al.,Miller-Jones
  et al.2015]millea15
Miller-Jones J. C. A.,  et al., 2015, @doi []
  10.1093/mnras/stv1869, http://adsabs.harvard.edu/abs/2015MNRAS.453.3918M 453, 3918

[Nardiello et al.,Nardiello
  et al.2018]nardea18
Nardiello D.,  et al., 2018, @doi [] 10.1093/mnras/sty2515, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2018MNRAS.481.3382N
  481, 3382

[Özel & FreireÖzel &
  Freire2016]ozelfrei16
Özel F.,  Freire P.,  2016, @doi []
  10.1146/annurev-astro-081915-023322, https://ui.adsabs.harvard.edu/abs/2016ARA   A..54..401O 54, 401

[Pallanca, Dalessandro, Ferraro,
  Lanzoni  & BeccariPallanca et al.2013]pallea13
Pallanca C.,  Dalessandro E.,  Ferraro F. R.,  Lanzoni B.,   Beccari
  G.,  2013, @doi [] 10.1088/0004-637X/773/2/122, https://ui.adsabs.harvard.edu/abs/2013ApJ...773..122P 773, 122

[Pooley & HutPooley &
  Hut2006]poolhut06
Pooley D.,  Hut P.,  2006, @doi [ApJL] 10.1086/507027, http://adsabs.harvard.edu/abs/2006ApJ...646L.143P 646, L143

[Pooley et al.,Pooley
  et al.2003]poolea03
Pooley D.,  et al., 2003, @doi [] 10.1086/377074, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2003ApJ...591L.131P
  591, L131

[Qiao & LiuQiao & Liu2018]qiaoliu2018
  Qiao, E., Liu, B. F., 2018, @doi []
  10.1093/mnras/sty2337, https://ui.adsabs.harvard.edu/abs/2018MNRAS.481..938Q 481, 938

[Qiao & LiuQiao & Liu2020]qiaoliu2020
  Qiao, E., Liu, B. F., 2020, @doi []
  10.1093/mnras/stz3510, https://ui.adsabs.harvard.edu/abs/2020MNRAS.492..615Q 492, 615

[Qiao & LiuQiao & Liu2021]qiaoliu2021
  Qiao, E., Liu, B. F., 2021, @doi []
  10.1093/mnras/stab227, https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.3870Q 502, 3870

[Rivera Sandoval et al.,Rivera Sandoval
  et al.2015]riveea15
Rivera Sandoval L. E.,  et al., 2015, @doi []
  10.1093/mnras/stv1810, http://adsabs.harvard.edu/abs/2015MNRAS.453.2707R 453, 2707

[Rivera Sandoval et al.,Rivera Sandoval
  et al.2018]riveea18
Rivera Sandoval L. E.,  et al., 2018, @doi []
  10.1093/mnras/sty058, http://adsabs.harvard.edu/abs/2018MNRAS.475.4841R 475, 4841

[RomaniRomani1987]roma87
Romani R. W.,  1987, @doi [] 10.1086/165010, https://ui.adsabs.harvard.edu/abs/1987ApJ...313..718R 313, 718

[Rutledge, Bildsten, Brown, Pavlov  &
  ZavlinRutledge et al.2002]rutlea02
Rutledge R. E.,  Bildsten L.,  Brown E. F.,  Pavlov G. G.,   Zavlin
  V. E.,  2002, @doi [] 10.1086/342306, https://ui.adsabs.harvard.edu/abs/2002ApJ...578..405R 578, 405

[Salaris, Held, Ortolani, Gullieuszik
  & MomanySalaris et al.2007]salaea07
Salaris M.,  Held E. V.,  Ortolani S.,  Gullieuszik M.,   Momany Y.,
  2007, @doi [] 10.1051/0004-6361:20078445, http://adsabs.harvard.edu/abs/2007A

[Sarajedini et al.,Sarajedini
  et al.2007]saraea07
Sarajedini A.,  et al., 2007, @doi [] 10.1086/511979, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2007AJ....133.1658S
  133, 1658

[ScargleScargle1982]scar
Scargle J. D.,  1982, ApJ, 263, 835

[Servillat, Heinke, Ho, Grindlay,
  Hong, van den Berg  & BogdanovServillat et al.2012]servea12
Servillat M.,  Heinke C. O.,  Ho W. C. G.,  Grindlay J. E.,  Hong J.,
   van den Berg M.,   Bogdanov S.,  2012, @doi []
  10.1111/j.1365-2966.2012.20976.x, https://ui.adsabs.harvard.edu/abs/2012MNRAS.423.1556S 423, 1556

[Shahbaz, González-Hernández, Breton, Kennedy, Mata Sánchez & LinaresShahbaz et al.2022]shahea22
  Shahbaz, T.,  González-Hernández, J. I., Breton, R. P., Kennedy, M. R., Mata Sánchez, D., Linares, M., 2022, @doi []
  10.1093/mnras/stac492, https://ui.adsabs.harvard.edu/abs/2022MNRAS.513...71S 513, 71

[Sirianni et al.,Sirianni
  et al.2005]siriea05
Sirianni M.,  et al., 2005, @doi [] 10.1086/444553, http://adsabs.harvard.edu/abs/2005PASP..117.1049S 117, 1049

[Steiner, Heinke, Bogdanov, Li, Ho,
  Bahramian  & HanSteiner et al.2018]steiea18
Steiner A. W.,  Heinke C. O.,  Bogdanov S.,  Li C. K.,  Ho W. C. G.,
  Bahramian A.,   Han S.,  2018, @doi [] 10.1093/mnras/sty215,
  https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2018MNRAS.476..421S
  476, 421

[Testa et al.,Testa
  et al.2012]testea12
Testa V.,  et al., 2012, @doi [] 10.1051/0004-6361/201219904, https://ui.adsabs.harvard.edu/abs/2012A   A...547A..28T 547, A28

[Tudor et al.,Tudor
  et al.2018]tudoea18
Tudor V.,  et al., 2018, @doi [] 10.1093/mnras/sty284, http://adsabs.harvard.edu/abs/2018MNRAS.476.1889T 476, 1889

[Verbunt, van Kerkwijk, in't Zand  &
  HeiseVerbunt et al.2000]verbea00
Verbunt F.,  van Kerkwijk M. H.,  in't Zand J. J. M.,   Heise J.,
  2000, @doi [] 10.48550/arXiv.astro-ph/0005337, https://ui.adsabs.harvard.edu/abs/2000A   A...359..960V 359, 960

[Verbunt, Pooley  & BassaVerbunt
  et al.2008]verbea08
Verbunt F.,  Pooley D.,   Bassa C.,  2008, in Vesperini E.,  Giersz
  M.,   Sills A.,  eds,  International Astronomical Union Symposium no. 246
  Vol. 246, Dynamical Evolution of Dense Stellar Systems. pp 301–310
  (@eprint arXiv 0710.1804), @doi10.1017/S1743921308015822

[Walsh, Cackett  & BernardiniWalsh
  et al.2015]walsea15
Walsh A. R.,  Cackett E. M.,   Bernardini F.,  2015, @doi []
  10.1093/mnras/stv315, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2015MNRAS.449.1238W
  449, 1238

[Wijnands, Heinke, Pooley, Edmonds,
  Lewin, Grindlay, Jonker  & MillerWijnands
  et al.2005]Wijnands05
Wijnands R.,  Heinke C. O.,  Pooley D.,  Edmonds P. D.,  Lewin W.
  H. G.,  Grindlay J. E.,  Jonker P. G.,   Miller J. M.,  2005, @doi
  [] 10.1086/426127, https://ui.adsabs.harvard.edu/abs/2005ApJ...618..883W 618, 883

[Wijnands, Degenaar, Armas Padilla, Altamirano, Cavecchi, Linares, Bahramian & HeinkeWijnands
  et al.2015]wijnea15
Wijnands, R., Degenaar, N., Armas Padilla, M., Altamirano, D., Cavecchi, Y., Linares, M., Bahramian, A., Heinke, C. O., 2015, @doi []
  10.1093/mnras/stv1974, https://ui.adsabs.harvard.edu/abs/2015MNRAS.454.1371W
  454, 1371

[Zacharias, Urban, Zacharias, Wycoff,
  Hall, Monet  & RaffertyZacharias et al.2004]zachea04
Zacharias N.,  Urban S. E.,  Zacharias M. I.,  Wycoff G. L.,  Hall
  D. M.,  Monet D. G.,   Rafferty T. J.,  2004, @doi []
  10.1086/386353, http://adsabs.harvard.edu/abs/2004AJ....127.3043Z
  127, 3043

[in't Zand, van Kerkwijk, Pooley,
  Verbunt, Wijnands  & Lewinin't Zand et al.2001]intzea01
in't Zand J. J. M.,  van Kerkwijk M. H.,  Pooley D.,  Verbunt F.,
  Wijnands R.,   Lewin W. H. G.,  2001, @doi [] 10.1086/338361,
  https://ui.adsabs.harvard.edu/abs/2001ApJ...563L..41I 563, L41

[in't Zand et al.,in't Zand
  et al.2003]intzea03
in't Zand J. J. M.,  et al., 2003, @doi []
  10.1051/0004-6361:20030681, https://ui-adsabs-harvard-edu.ezp-prod1.hul.harvard.edu/abs/2003A   A...406..233I
  406, 233





  


§ REFINING THE ORBITAL PERIOD OF X5
 


The eclipses of X5 are total eclipses, averaging 2500 s long, which
can be explained by the X-rays coming exclusively from the neutron
star surface. Only occasional background photons fall within the
eclipse.  To provide the photon list, we extract lightcurves at the
instrument time resolution (for ACIS, or 2.0 s for HRC) from
barycentred event files. We use the 0.5–2 keV energy range for ACIS
data (which includes most source photons, while reducing background)
and a 1.0 extraction region to create the lightcurves. We use
ACIS observations from 2000 (ObsIDs 953, 955; ),
2002 (ObsIDs 2735–3386 in Table <ref>, described in
2.1), 2014 (ObsIDs 16527–15748, ), and 2022
(ObsID 26229, PI Paduano), along with HRC observations in 2005-2006
(ObsIDs 5542–6240, ).

The countrate from X5 is low enough (typically 0.1 counts/second, or
lower) that we choose not to try to fit the eclipse with a specified
function, nor to fit the ingresses and egresses, as when studying
eclipses of bright LMXBs <cit.>. Instead, we find
the best approach is to find the midpoint of each eclipse using the
last photon recorded before the eclipse, and the first photon after
it.  The uncertainty in the eclipse midpoint is thus σ_mid =
√((σ^2_in+σ^2_out)/2),
where e.g. σ_in is the inverse of the measured counts in the
100 seconds up to the last photon.  This requires some iteration, to
identify likely background photons interrupting eclipses (we find only
14 such interlopers). We omit using eclipses if the continuum
countrate is so low that the eclipse is substantially longer than
average (>2700 s), or if we measure only an ingress or an
egress. This leaves us with 35 complete and high-quality eclipses,
spread from 2000 to 2022, with 20 observed during the 2005–2006 HRC
data. The eclipse midpoints, and their associated errors, are given in
Table <ref>, including three not used for our
calculation, in units of TDB seconds since MJD_REF=50814.0
(barycentred).

We calculate the orbital period iteratively, using eclipses close in
time to find the orbital period and its error, and then predict more
distant eclipses, which then refine the orbital period and its error.
If the error in the orbital period for the next eclipse is less than
half an orbital period, we maintain cycle count.

We begin with ObsID 6238 in 2005, which has two well-measured
eclipses, which give P=31195±30 s. We then extrapolate this
solution 3 cycles to ObsID 5546, refining the period to
P=31204±7.5 s, and continue similarly.  We include the cycle
count (from the 2nd eclipse of ObsID 6238) in
Table <ref>.  Using the full range of eclipses, we
arrive at an orbital period solution for X5's X-ray eclipse midpoints,
measured from MJD_REF=50814.0, of TDB=251975445(±16)+n ×
31200.192(±0.002) s, where n is an integer.























