11institutetext: IRAP, CNRS, Université de Toulouse, CNES, 9 Avenue du Colonel
Roche, 31028 Toulouse, France
e-mail<EMAIL_ADDRESS>22institutetext: INAF-Osservatorio Astronomico
di Roma, via Frascati 33, 00078 Monteporzio Catone, Italy 33institutetext:
INAF-Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano, via A. Corti
12, 20133 Milano, Italy 44institutetext: Dipartimento di Fisica, Università
degli Studi di Roma “Tor Vergata”, via della Ricerca Scientifica 1, I-00133
Rome, Italy 55institutetext: Scuola Universitaria Superiore IUSS Pavia,
Palazzo del Broletto, piazza della Vittoria 15, 27100 Pavia, Italy
66institutetext: INAF-Osservatorio Astronomico di Capodimonte, salita
Moiariello 16, I-80131, Napoli, Italy 77institutetext: Dipartimento di fisica
e chimica - Emilio Segrè, Università degli Studi di Palermo, Via Archirafi 36,
90123, Palermo, Italy

# On the nature of the 2.4 hr-period eclipsing cataclysmic variable W2 in 47
Tuc

R. Amato 1122 N. La Palombara 33 M. Imbrogno 4422 G.L. Israel 22 P. Esposito
55 D. de Martino 66
N.A. Webb 11 R. Iaria 77

(Received DD Month YYYY; accepted DD Month YYYY)

###### Abstract

Context. W2 (CXOGlb J002415.8–720436) is a cataclysmic variable (CV) in the
Galactic globular cluster 47 Tucanae. Its modulation was discovered within the
CATS@BAR project. The source shows all the properties of magnetic CVs, but
whether it is a polar or an intermediate polar is still a matter of debate.

Aims. This paper investigates the spectral and temporal properties of the
source, using all archival X-ray data from Chandra and eROSITA Early Data
Release, to establish whether the source falls within the category of polars
or intermediate polars.

Methods. We fitted Chandra archival spectra with three different models: a
power law, a bremsstrahlung and an optically thin thermal plasma. We also
explored the temporal properties of the source with searches for pulsations
with a power spectral density analysis and a Rayleigh test ($Z_{n}^{2}$).

Results. W2 displays a mean luminosity of $\sim 10^{32}$ erg s-1 over a
20-year span, despite lower values in a few epochs. The source is not detected
in the latest observation, taken with Chandra in 2022, and we infer an X-ray
luminosity $\leq 7\times 10^{31}$ erg s-1. The source spectral shape does not
change over time and can be equally well fitted with each of the three models,
with a best-fit photon index of 1.6 for the power law and best-fit
temperatures of 10 keV for both the bremsstrahlung and the thermal plasma
models. We confirm the previously detected period of 8649 s, ascribed to the
binary orbital period, and found a cycle-to-cycle variability associated with
this periodicity. No other significant pulsation is detected.

Conclusions. Considering the source orbital period, luminosity, spectral
characteristics, long-term evolution and strong cycle-to-cycle variability, we
suggest that W2 is a magnetic CV of the polar type.

###### Key Words.:

X-rays: individuals: CXOGlb J002415.8–72043, W2 – Stars: novae, cataclysmic
variables – globular clusters: individual: 47 Tuc

##  1 Introduction

Globular clusters (GCs) are the oldest stellar structures in the Milky Way,
usually showing nearly spherical distributions, with tens of thousands of
stars bound by gravity. Owing to their dense environments, GCs are good
laboratories for stellar dynamics and host abundant populations of compact
objects, often segregated in their core and formed dynamically (e.g. Pooley et
al., 2003). Examples include low-mass X-ray binaries (LMXBs), cataclysmic
variables (CVs), recycled millisecond pulsars, and – perhaps – even
intermediate mass black holes (Meylan & Heggie, 1997; Strader et al., 2012;
Lugaro et al., 2013). As the remnants of the least massive stars, which are
the most abundant types of stars, white dwarfs (WDs) should be the most common
compact objects in GCs. The identification of isolated WDs in GCs is a
challenging endeavour due to their intrinsic faintness. On the other hand, the
observation of accreting WDs in the UV and X-rays, their characteristics and
population ratio with respect to other X-ray emitters are important
diagnostics of the cluster evolution and tests of stellar dynamics.

47 Tucanae (NGC 104, 47 Tuc for brevity) is one of the brightest and most
massive GC in the Milky Way111A list of Milky Way GCs can be found at
https://physics.mcmaster.ca/~harris/mwgc.dat. It has a mass of $\simeq 7\times
10^{5}$ M⊙ (Marks & Kroupa, 2010), an age of 12-13 Gyr (Zoccali et al., 2001;
García-Berro et al., 2014; Thompson et al., 2020), and various distance
estimates: $4.521\pm 0.031$ kpc (Baumgardt & Vasiliev, 2021), $4.45\pm 0.01\pm
0.12$ kpc (Chen et al., 2018), and $4.47\pm 0.01\pm 0.08$ kpc (Simunovic et
al., 2023); for this work we shall simply assume 4.5 kpc. Several hundreds of
CVs are expected to be present in 47 Tuc, as results of both the evolution of
primordial binaries and dynamical encounters/three-body interactions (Pooley &
Hut, 2006; Belloni & Rivera, 2021). Data taken with the Chandra X-ray
Observatory (Weisskopf et al., 2000) of the core of 47 Tuc showed the presence
of more than one hundred faint X-ray sources within a few arcmin (Edmonds et
al., 2003b; Heinke et al., 2005). About one-third were tentatively identified
with CVs and many were confirmed with subsequent optical/ultraviolet
observations (see e.g. Edmonds et al., 2003a; Bhattacharya et al., 2017;
Rivera Sandoval et al., 2018). Recently, 47 Tuc has also been observed during
the calibration phase of the extended Roentgen Survey with an Imaging
Telescope Array (eROSITA, Predehl et al., 2021), where about 888 point-like
sources were detected, with a handful identified as CVs (Saeedi et al., 2022).

CXOGlb J002415.8–720436 (W2 hereafter) was first identified as a possible CV
candidate (or an enshrouded millisecond pulsar) by Grindlay et al. (2001), who
compared Chandra and ROSAT (Truemper, 1982) data of 47 Tuc. Edmonds et al.
(2003a, b) studied the optical counterparts of all X-ray sources of 47 Tuc
with the Hubble Space Telescope (HST) and found for W2 a V magnitude of 21.50
and U–V and V–I colours of 0.04 mag and 1.91 mag, respectively. The location
of this source in the U,U–V colour-magnitude diagram was blueward of the main
sequence, but close to the main sequence in the V,V–I colour-magnitude
diagram. They concluded that the source might have had a relatively faint
accretion disc, with the optical magnitude dominated by the companion star.
They also suggested that the system had a low accretion rate and estimated an
X-ray period of $\sim$6.3 hr, different from the optical periods of 2.2 hr,
5.9 hr, and 8.2 hr (Edmonds et al., 2003b). The spectral analysis of the
source was carried out by Heinke et al. (2005) on 2000 and 2002 Chandra data,
resulting in X-ray luminosities in the energy range 0.5–6 keV of $\sim 8\times
10^{31}$ erg s-1 and $\sim 16\times 10^{31}$ erg s-1, for the two epochs,
respectively.

Israel et al. (2016) unambiguously classified W2 as a CV based on the timing
analysis of Chandra ObsIDs. 953, 955, and 2735–8, that revealed an eclipse
with a period of 8649 s (2.4 hr), ascribed to the binary orbit. Their analysis
did not confirm the X-ray period of $\sim$6.3 hr derived by Edmonds et al.
(2003b). Rivera Sandoval et al. (2018) further studied the HST data of 47 Tuc
in the near ultra-violet (NUV) and optical wavebands. Using the ultraviolet
filter $U_{300}$, they did not find any periodicity of the source for any of
the periods previously proposed in the literature. However, the authors
selected only high-quality photometric data resulting in a sparse sampling
over 8 hr of observation, which could well have missed the 8 min long eclipse.
Notwithstanding, the light curve showed a variation of 3 mag during the time
of the observation. On the other hand, the period of 2.4 hr was confirmed in
the more intensive coverage with the $R_{625}$ filter, with the appearance of
a deep eclipse-like feature, hence confirming the optical counterpart to W2.
The source was classified as a candidate magnetic CV, very likely an
intermediate polar (IP), where the variations in magnitudes were attributed to
either precession of the accretion disc, or changes of its thickness, or
high/low state transitions. The most recent search for periodicity from the
source was performed by Bao et al. (2023), who found a first period of 8646.78
s, close to the one of Israel et al. (2016) and ascribed it to the orbital
period, and a second one of 3846.15 s, interpreted as the spin period of the
WD, supporting the IP scenario. Unfortunately, due to the source density in
the central region of 47 Tuc (within a radius of 1.7′), W2 is not resolved by
eROSITA (Saeedi et al., 2022).

In this manuscript, we aim to resolve the controversy on the presence and the
nature of the X-ray periods of W2 and classify the source through simultaneous
use of X-ray spectroscopic and timing analysis techniques. We use all
available Chandra data, including two new observations taken in 2022 (see Tab.
3). We also revisit eROSITA Early Data Release (EDR) and detect the source for
first time using this dataset, thanks to its period, even if it cannot be
spatially resolved from nearby sources. Data reduction, spectroscopic and
timing analyses are described in Sect. 2, 3 and 4, respectively. The nature of
the source is discussed in Sect.5 and our conclusions are presented in Sect.6.

##  2 Data reduction

###  2.1 Chandra

All available observations of the Galactic GC 47 Tuc in the Chandra Data
Archive span roughly 15 years, from early 2000 to 2015, with the addition of
two recent observations, taken in January 2022. For this work we considered
all the observations taken with ACIS-S or ACIS-I, as reported in Table 3. A
Chandra image of 47 Tuc is shown in Fig. 1, left panel.

All the data sets were reprocessed with the tool chandra_repro in the Chandra
Interactive Analysis of Observations software (CIAO, version 4.14), using
calibration files CALDB 4.9.8. The target was identified by means of its sky
coordinates, RA=$00^{h}24^{m}15.88^{s}$ and
DEC=$-72^{\circ}04^{\prime}36.38^{\prime\prime}$, in J2000 reference frame, as
in Israel et al. (2016). Spectra and light curves were extracted using the
CIAO tool specextract. We used circular regions for both the source and the
background, the former (1.8′′) centred on the source position, the latter
(10′′) on a nearby region, which contained no other X-ray sources, on the same
CCD. For each observation, we generated the source and background spectra, the
redistribution matrix and the auxiliary response files (rmf and arf). Each
spectrum was binned with a minimum number of 20 cts/bin. We used the same
regions to extract the light curves, after having barycentred the observations
at the source coordinates, with the JPL solar system ephemeris DE200. Amongst
all the observations, two data sets (954 and 16528) were rejected, because the
target was not on the illuminated CCDs.

The source was not visible by eye in the latest observation ObsID. 26286. We
ran the CIAO tool wavdetect to see if the algorithm could detect it. We first
created exposure-corrected images and exposure maps of the observation using
fluximage, in the broad energy band (0.5–7 keV), where the source flux peaks
(e.g. Heinke et al., 2005), with the option psfecf=0.99. We then ran
wavdetect, choosing the scales of 1 and 2 to enhance the detection of point-
like sources. Seeing as no source was detected at the position of W2, we used
the tool aplimits to obtain an upper limit on the count rate. For a false
detection probability of 0.1 (corresponding to 90% confidence level, c.l.), a
probability of missed detection of 0.5, and a background rate of $7.5\times
10^{-3}$ cts s-1, estimated from the circular background region of all other
observations, we obtained an upper limit of $1.2\times 10^{-3}$ cts s-1.

Figure 1: Chandra (left panel, ObsID. 2735) and eROSITA (right panel,1-2 Nov
2019 observations) images of the field of view of 47 Tuc. Solid and dashed
circles represent the source and background extraction regions for W2,
respectively, for Chandra (red) and eROSITA (blue). The black circle encloses
the inner region of the cluster excluded in the eROSITA analysis of Bao et al.
(2023) and has a radius of 1.7′. The box in the bottom left corner is a close-
up of the eROSITA source region as seen by Chandra, to show the X-ray sources
that are blended with W2 in the eROSITA image.

###  2.2 eROSITA

eROSITA observed 47 Tuc during the calibration phase on November 1-2, 2019
(ObsIDs. 700011, 700163, 700013, 700014) and November 19, 2019 (ObsIDs.
700173-175), for a total of $\sim$101 ks and $\sim$25 ks, respectively.
Another observation was carried out on September 28, 2019 (ObsID. 700012), but
we excluded it since no information about the satellite
orbit222https://erosita.mpe.mpg.de/edr/eROSITAObservations/OrbitFiles. is
available before October 2019 and no barycentric correction could be applied
to the data.

To extract eROSITA data from the EDR observations, we used the eROSITA
Standard Analysis Software System (eSASS, see Brunner et al., 2022) available
on the EDR
webpage333https://erosita.mpe.mpg.de/edr/DataAnalysis/esassinstall.html..
Following the online guide to
eSASS444https://erosita.mpe.mpg.de/edr/DataAnalysis/esasscookbook.html., we
selected all the events in the 0.2–5 keV band with valid patterns (PATTERN=15)
within the nominal field of view (FLAG=0xc0008000). In Fig. 1 (right panel) we
show a close-up view of the eROSITA field during the November 1-2
observations. The solid blue circle denotes the 15′′-radius region we used to
extract the source events. Note that eROSITA is not able to resolve W2 from
the other X-ray sources within the extraction area, which are instead resolved
by Chandra (see box in the bottom left corner of Fig.1). In particular,
another CV (W1, see e.g. Heinke et al., 2005), with luminosity comparable to
W2, falls within the eROSITA extraction region. This second CV was detected in
the 2000 and 2002 Chandra data sets by Heinke et al. (2005), while a visual
inspection of the 2014 and 2022 data sets revealed it to be switched off. We
have no means to say whether W1 is also present in the eROSITA observations.

##  3 Spectroscopic analysis

Spectral analysis was performed with the X-Ray Spectral Fitting Package Xspec
(Arnaud, 1996), version 12.9.1, using abundances from Wilms et al. (2000) and
cross-sections from Verner et al. (1996). At first, we considered only the
seven observations (ObsIDs. 955, 2735, 2736, 2737, 2738, 15747, 16527), where
the source spectrum has at least five data points in the range 0.5–6 keV,
suitable for a fit with $\chi^{2}$ statistics. Above 6 keV the spectrum is
dominated by the background. Following the analysis by Heinke et al. (2005),
we fit them separately with three different emission models: a power law (PL),
a thermal Bremsstrahulung (TB), and a vmekal (Mewe, 1991) model. Statistical
errors are at 90% c.l., unless specified otherwise.

We considered two different components for the interstellar absorption. The
first component ($N_{\mathrm{H}}^{\mathrm{GAL}}$, modelled with TBabs)
accounts for the total Galactic absorption in the direction of 47 Tuc and was
fixed to $5.5\times 10^{20}$ cm-2, according to the estimate provided by the
HEASARC $N_{\mathrm{H}}$ calculator tool555https://heasarc.gsfc.nasa.gov/cgi-
bin/Tools/w3nh/w3nh.pl, assuming Solar abundances. The second component
($N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$, described by the TBvarabs function)
represents both the interstellar absorption within the cluster and local to
the source. In this case, we fixed the chemical abundances to those derived
from Thygesen et al. (2014) for 47 Tuc, namely 33% of solar abundances for C,
N, O, and Ne, 27% for Na and Al, 46% for Mg, 35% for Si, S, and Ar, 34% for
Ca, 17% for Fe, and 13% for Ni.

For all three models, the local absorption
$N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ was consistent in all the spectra,
with the exception of ObsIDs. 15747 and 16527, where it was unconstrained.
Hence, we tied the $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ values and fitted
the seven observations again. The fit converged to
$N_{\mathrm{H}}^{\mathrm{47Tuc+local}}\sim 2\times 10^{21}$ cm-2. Detailed
tables with the best-fit results for both fits and for each model are reported
in Appendix B.

The best-fit power law photon index and the temperatures of the TB and vmekal
models were consistent for all observations, so that we also tied them
together to get more stringent constraints. We obtained a best-fit photon
index $\Gamma=1.53^{+0.13}_{-0.12}$ and best-fit temperatures of
$11^{+7}_{-4}$ keV for both thermal models. According to the fit statistics,
all models provide an equally good description of the spectra.

As a side note, for the vmekal model, we considered the same abundances we
used for the local absorption component (Thygesen et al., 2014). The total
spectrum was then computed by interpolating on a pre-calculated table
(parameter switch$=$1). Setting the chemical abundances to those of Heinke et
al. (2005), leads to little or no difference in the best-fit values. We also
note that there is little to no difference in the fit residuals between the
two thermal models (Fig.2), confirming that the two models are equivalent with
respect to the quality of the present data sets. We do not include eROSITA
data in the spectral analysis, because it is not possible to extract a clean
source spectrum, not contaminated by the nearby bright X-ray source W1 (cf.
Sect. 2.2 and Fig. 1). This will not be a problem for the timing analysis
(Sect. 4).

###  3.1 Combined data

The consistency of the best-fit parameters of the previous fits demonstrates
that W2 does not change its spectral state over time, in spite of changes in
flux (the normalisation is changing). Therefore, we decided to combine the
spectra of all observations in which the source was detected (Table 3), to
further constrain the best-fit parameters. To combine the spectra, we used the
CIAO tool combine_spectra, which sums the counts of each corresponding
spectral bin of different spectra and returns a total spectrum. In this way,
we increased the number of counts in each spectral bin and achieved a better
signal-to-noise ratio (S/N). The combined spectrum was again grouped with 20
cts/bin and fitted with the same models as above. Results of the fits are
shown in Table 6 and in Fig. 2, with fluxes and luminosities in the 0.3–10 keV
energy range. The fits returned a $\chi^{2}_{red}$(d.o.f) of 0.94(97) for the
PL and of 0.90(97) for both the TB and the vmekal models, with null hypothesis
probability (n.h.p.) values of 0.64, 0.75, and 0.74, respectively. The best-
fit values of the parameters $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$, $\Gamma$
and $kT$ were all consistent with those obtained in the previous fits. In all
cases, the unabsorbed flux is (6–7)$\times 10^{-14}$ erg cm-2 s-1, which
results in X-ray luminosities in the range $L_{\rm X}=(1.5-1.7)\times 10^{32}$
erg s-1, for a distance $d=4.5$ kpc.

Table 1: Best-fit values of the spectrum obtained by combining all the data
sets.

Model | PL | TB | vmekal
---|---|---|---
$N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ ($10^{21}$ cm${}^{-2})$ | 1.8$\pm$0.8 | 1.0$\pm$0.6 | 1.0$\pm$0.6
$\Gamma$ | 1.55${}^{+0.10}_{-0.09}$ | – | –
$kT$ (keV) | – | $10_{-2}^{+5}$ | $10_{-2}^{+4}$
Norm (10-6)aa$a$In units of photons keV-1 cm-2 s-1 at 1 keV for the PL model and of cm-5 for the TB and the vmekal models.  | $8.5\pm 0.8$ | $11.1\pm 0.5$ | $34_{-1}^{+2}$
$F_{\mathrm{abs}}$ ($10^{-14}$ erg cm-2 s-1) | 5.8$\pm$0.3 | $5.4_{-0.5}^{+0.3}$ | $5.5_{-0.7}^{+0.3}$
$F_{\mathrm{unabs}}$ ($10^{-14}$ erg cm-2 s-1) | $6.7\pm 0.3$ | $6.0^{+0.4}_{-0.3}$ | $6.1^{+0.3}_{-0.4}$
$L_{\mathrm{X}}$ ($10^{32}$ erg s-1) | $1.62\pm 0.07$ | $1.45^{+0.10}_{-0.07}$ | $1.48^{+0.07}_{-0.10}$
$\chi^{2}_{red}$(d.o.f.) | 0.94(97) | 0.90(97) | 0.90(97)
n.h.p. | 0.64 | 0.75 | 0.74
666

Figure 2: Summed spectra from all the Chandra data sets in which the source
was detected, together with the best-fit power-law model (top panel), and
residuals in units of $\chi^{2}_{red}$ in the case of the best-fit power-law
model (second panel), Bremsstrahlung model (third panel), and vmekal model
(bottom panel).

Once the best-fit parameters were constrained, we explored the long-term
variability of the source, studying the changes in flux over time. To do so,
we used the TB model and derived the fluxes for those observations excluded
from the previous analysis. We imposed
$N_{\mathrm{H}}^{\mathrm{47Tuc+local}}=1.1\times 10^{21}$ cm-2 and $kT=10$ keV
(see Table 6) and fitted the data, leaving only the normalisation free to
vary. For the latest Chandra observation, for which we do not have a spectrum,
we derived upper limits on the flux and luminosity from the upper limit on the
count rate estimated in Sect. 2.1. We used the online tool
WebPIMMS777https://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3pimms/w3pimms.pl.
with the best-fit parameters of the TB model and obtained an X-ray luminosity
$\leq 7\times 10^{31}$ erg s-1, in the energy range 0.3–10 keV, at 90% c.l.
All resulting fluxes and luminosities are shown in Table 8 and in Fig. 3. In
most observations, the source flux is in the range
$F_{\mathrm{abs}}\sim(4-9)\times 10^{-14}$ erg cm-2 s-1, corresponding to a
luminosity $L_{\mathrm{X}}\sim(1-2)\times 10^{32}$ erg s-1, while in a few it
is significantly lower. Some observations (marked with an asterisk in Table 8)
are shorter than the orbital period and their luminosities might be
unreliable.

Table 2: W2 unabsorbed fluxes and luminosities (0.3–10 keV) for each
observationaa$a$Fluxes and luminosities have been obtained for the thermal
Bremsstrahlung model, having $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ and $kT$
fixed at $1.1\times 10^{21}$ cm-2 and 10 keV, respectively. . An asterisk
marks those observations with exposure times shorter than the orbital period.

Obs. ID | $F_{\mathrm{unabs}}$ | $L_{\mathrm{X}}$
---|---|---
| (10-14 erg cm-2 s-1) | ($10^{32}$ erg s-1)
78* | 6$\pm$2 | 1.5$\pm$0.5
953 | 1.4${}^{+0.5}_{-0.3}$ | 0.34${}^{+0.12}_{-0.07}$
955 | 6.2${}^{+0.8}_{-0.7}$ | 1.5$\pm$0.2
956* | 6.5${}^{+2.0}_{-2.2}$ | 1.6$\pm$0.5
2735 | 6.4${}^{+0.5}_{-0.4}$ | 1.5${}^{+0.12}_{-0.09}$
3384* | 8$\pm$2 | 2.0$\pm$0.5
2736 | 5.8$\pm$0.4 | 1.42$\pm$0.09
3385* | 9$\pm$2 | 2.2$\pm 0.5$
2737 | 7.1${}^{+0.3}_{-0.2}$ | 1.73${}^{+0.07}_{-0.05}$
3386* | 2$\pm$1 | 0.5$\pm$0.2
2738 | 8.4$\pm$0.6 | 2.0$\pm$0.1
3387* | 2.6${}^{+1.1}_{-0.9}$ | 0.6${}^{+0.3}_{-0.2}$
16527 | 3.9${}^{+0.6}_{-0.4}$ | 0.95${}^{+0.14}_{-0.09}$
15747 | 5.7$\pm$0.6 | 1.4$\pm$0.1
16529 | 4.8$\pm$0.7 | 1.2$\pm$0.2
17420 | 4$\pm$1 | 1.0$\pm$0.2
15748 | 5$\pm$1 | 1.2$\pm$0.2
26229 | 2$\pm$1 | 0.5$\pm 0.2$
26286 |  $\leq$2.8bb$b$Upper limit at 90% c.l. |  $\leq$0.7bb$b$Upper limit at 90% c.l.
888

Figure 3: Light curve of W2. Empty data points are for those observations with
exposures shorter than the orbital period; the black arrow represents the
upper limit at 90% c.l. on the luminosity of the latest Chandra observation
(ObsID. 26286); the grey dotted line and area represents the average
luminosity of the source and its uncertainty at 90 % c.l., respectively.

##  4 Timing analysis

---
Figure 4: Left: Chandra 0.2-10 keV power density spectrum (PDS) of W2 by using
the 2002 datasets 2735–8 and one single interval. The 3.5$\sigma$ detection
threshold is also shown and marked by the blue solid line. The PDS is complex
and only one peak is above the threshold, corresponding to the harmonic of the
8649s period (both the fundamental and the harmonic are marked by I17 and 1/2P
I17, respectively). The period suggested by Bao et al. (2023) is indicated as
B23. Right: $Z^{2}_{N}$ search with $N=4$ harmonics of Chandra ObsIDs.
2735–2738. The fundamental and the first harmonic of the period at $P\simeq
8650$ s are marked with red dashed and solid lines, respectively, while the
period proposed by Bao et al. (2023) is marked with a black dash-dotted line.

Israel et al. (2016) found a phase-coherent solution for W2 in ObsIDs. 2735–8
corresponding to a period of 8649$\pm$1 s. The eclipse profile was asymmetric
and showed a total eclipse lasting about 8 min. The modulation was also
present in ObsIDs. 953 and 955, though the poor statistics did not allow an
independent period value to be inferred. Among the new available archival
observations we focused on ObsID. 15747–8, 16527 and 16529 where the source is
detected and the relatively long exposures ensure good statistics. A phase-
fitting procedure was applied revealing a period of 8653$\pm$3 s, in agreement
with that in the CATS@BAR catalogue although with a larger uncertainty.
Consequently, we keep the period reported in the catalogue as the reference
one in the subsequent analysis.

Figure 5: Phase-fitting of the 3846.15 s period of Bao et al. (2023), where
each data point corresponds to a duration of one orbital cycle (i.e. 8649 s).
The phases are highly scattered up to almost 40% of the period, suggesting
that this period is spurious and/or not coherent. The black solid and stepped
lines mark the best fit linear component and its 1$\sigma$ uncertainty,
respectively.

Figure 6: Top panel: Chandra ACIS eclipse profiles of W2, folded to the best
period of $P=8649$ s, for the three different epochs where the modulation was
detected: 2000 (red line and filled circles), 2002 (black lines), and 2014
(blue line and filled squares). A correction of about 20% was applied to the
2000 datasets in order to take into account the difference in CCD efficiency
between ACIS-I and ACIS-S. We used the reference epoch MJD 52551.999(1)
(1$\sigma$ c.l.) for the 2002 datasets, while the 2000 and 2014 light curves
have been arbitrarily shifted along the x-axis in order to align the minima,
corresponding to the 8-min eclipse. All light curves have 20 phase-bins of
$\sim$432 s duration each. Bottom panel: Folded light curves of the four
longest observations, carried out in 2002 a few days apart from each other.
From top to bottom: ObsID. 2735, 2736, 2737 and 2738. The profiles are complex
and variable on time scales of less than a day.

Figure 7: Energy-resolved profiles of the summed 2002 data sets, in units of
normalised intensity, for the following energy ranges: 0.3–2 keV (first
panel), 2–6 keV (second panel), 6–10 keV (third panel). Bottom panel: hardness
ratio (2–6 keV)/(0.3–2 keV).

Figure 8: Phase-folded profile ($P=8649$ s) in eROSITA data from the
observations on November 1-2, 2019 (black profile, reference epoch MJD
58787.991(1), 1$\sigma$ c.l.) and on November 19, 2019 (red profile, shifted
on the y-axis for better visualization). The latter has also been arbitrarily
shifted along the x-axis to align the eclipse phase.

Recently, Bao et al. (2023) reported a second coherent signal, detected by a
Gregory-Loredo algorithm (Gregory & Loredo, 1992), corresponding to a period
$P=3846.15$ s. Our PDS analysis of Chandra observations 2735–8, performed
following Israel & Stella (1996), shows no significant peak above the
3.5$\sigma$ threshold at the corresponding frequency (see Fig.4, left panel),
although the high PDS peak at the frequency of the second harmonic of the 2.4
hr modulation, at about 4325 s, hampers the detection sensitivity around the
peak itself. To further check for the presence of the reported modulation at
$\sim 3846$ s, we also performed a Z${}^{2}_{n}$ search (Buccheri et al.,
1983) for periodicity in the 0.1–0.6 mHz range, using the henzsearch tool
included in the HENDRICS package (Bachetti, 2018). The right panel of Fig. 4
shows the results of our analysis. Both the fundamental ($\nu\simeq
116\,\mathrm{\mu Hz}$, $n=4$) and the second harmonic ($\nu\simeq
231\,\mathrm{\mu Hz}$, $n=1$) are clearly detected, while the $P=3846.15$ s is
below the 3.5$\sigma$ detection threshold.

In order to further check the possibility that the peak at $P=3846.15$ s might
be a spin period we carried out a phase-fitting analysis by using time
intervals of 2.4 hr length (i.e. over one orbital cycle). If the $P=3846.15$ s
is real, we expect to see either a constant or a linear trend in the phases.
In Fig. 5 we show the results of this analysis ($\chi^{2}_{\mathrm{red}}$ of
40 for a linear component model) where it is evident that the phases are
highly scattered up to almost 40% of the period, suggesting that the peak is
spurious and/or marks a variability with a low coherence level such as a QPO-
like component. Regardless of the exact origin of the 3846.15 s peak, we can
reasonably exclude that it is a strictly coherent signal and, therefore, that
it is the spin period of the accreting WD.

Fig. 6 shows the eclipse profile evolution as a function of time, for $P=8649$
s, for the three different epochs (2000, 2002, and 2014, left panel), while
the bottom panel shows the eclipse profiles for the 2002 ObsIDs.2735–8. Note
that the sparseness of the observations does not allow for a phase alignment
of the three epochs. Hence, we shifted the profiles arbitrarily in order to
have the centre of the eclipse aligned at the same phase. In Fig. 7 we show
the eclipse profiles of the summed 2002 spectra at different energy ranges
(0.3–2 keV, 2–6 keV, and 6–10 keV) and the hardness ratio (2–6 keV/0.3–2 keV).
The profiles clearly display a double hump, more evident at soft than hard
energies, with the relative intensity of the humps changing both from epoch to
epoch and within the same epoch, often on time scales less than a day. The
hardness ratio is constant within the uncertainties, except for the eclipse
phase, where the counts in all bands are consistent with zero.

To complete our analysis, we searched for the same periodicity of $P=8649$ s
in the eROSITA data. Both the PDS and $Z^{2}_{N}$ search did not reveal any
signal with a significance $\geq 3.5\sigma$, but epoch folding at the period
found in Chandra data returned the same eclipse profile at $P=8649$ s. Fig. 8
shows the phase-folded profiles of both eROSITA epochs, where the background
has been inferred by also correcting for the expected count rate of the other
bright source W1 within the source extraction region (see box in Fig.1) in the
eROSITA energy band, based on the analysis of Heinke et al. (2005) of Chandra
archival observations where W1 is detected. W2’s eclipse profile shape is
consistent with the one found in the Chandra data (cf. Fig. 6), ultimately
proving the detection of the source. We also tried to fold eROSITA light
curves at the period of $P\simeq 3846.15$ s and obtained a profile similar to
the one reported by Bao et al. (2023). However, we also found that similar
profiles are obtained with any period within the 3746–3946 s range, and indeed
at these frequencies both the Z${}^{2}_{n}$ and PDS analysis shows an excess
of power with respect to a pure white noise level (see Fig. 4, right panel).

##  5 Discussion

This work attempts at ascertaining the nature of the CV W2 in the Galactic GC
47 Tuc. To do so, we carried out a comprehensive spectral and temporal
analysis, using all available data sets of the Chandra Data Archive and six
eROSITA EDR observations.

We found that the X-ray spectrum of the source can be described equally well
using three different models: a power law, a thermal bremsstrahlung, and an
optically thin thermal plasma (vmekal). All fits need to include the
absorption of the interstellar medium, in excess of $\sim 1\times 10^{21}$
cm-2. The power law model returned a best-fit photon index of $\Gamma=1.55$,
while the thermal models resulted in the best-fit temperatures of $kT=10$ keV.
The latter result is in agreement with those of Heinke et al. (2005) for the
2002 data set (ObsIDs. 2735–8, 3384–7), but not for the 2000 one (ObsIDs. 78,
953–6), which had a higher temperature of the vmekal model. However, it has to
be noted that we only used one (ObsID. 955) out of the five 2000 observations
to determine the best-fit parameters, which resulted consistent with those of
the 2002 data sets.

The inferred unabsorbed fluxes are almost all consistent with each other
within uncertainties, resulting in luminosities around the average value of
$1.3\times 10^{32}$ erg s-1 (Fig. 3), typical of magnetic CVs (e.g. Mukai,
2017). In the latest observations (ObsIDs.26229 and 26286), both taken in
2022, the source appears to have weakened, with a luminosity of $5\times
10^{31}$ erg s-1 for ObsID.26229 and an upper limit of $7\times 10^{31}$ erg
s-1 for ObsID.26286.

The period $P=8649$ s found by Israel et al. (2016) for the epochs 2000 and
2002 is confirmed also for the observations taken in 2014–15. The presence of
a $\sim$8 min eclipse strongly indicates that this period can be ascribed to
the orbital period of the system, placing W2 among the CVs in the period-gap.
The eclipse was also confirmed by Rivera Sandoval et al. (2018) in HST data
(in the red filter R625).

This is the first time that the source is detected using eROSITA data.
Although W2 falls within the dense central region of 1.7′ that eROSITA cannot
spatially resolve, we detected the same eclipse profile from the source events
extracted from a 15′′-radius circular region. The folded eROSITA light curves
resemble those of Chandra (cf. e.g. Fig. 6 and 8), hence confirming the
identification of W2.

Our analysis did not detect (above the 3.5$\sigma$ threshold) any other
periodicity, neither in Chandra nor in eROSITA data. The detection of the
3846.15 s modulation of Bao et al. (2023) can be probably attributed to the
different approach (peak-removal of the fundamental and first harmonic of the
orbital period) adopted by the authors. Our in-depth analysis of the candidate
signal identified by Bao et al. (2023) shows that this modulation is unrelated
to the source and/or not coherent (see Fig. 5), indicating that it is not the
spin period of the WD. Moreover, we note that the power spectrum shows an
excess of power in the frequency range 1–4$\times 10^{-4}$ Hz, with several
peaks below the detection threshold of 3.5$\sigma$. Epoch-folding at each of
these individual peaks lead to all sort of sinusoidal profiles. Due to the
lack of detection of other significant periodicities, we classify the source
as a candidate polar CV, rather than an IP.

The source displays a double-humped phase-folded profile, which is also
sometimes observed in polar CVs, as seen for example in AM Her (Heise et al.,
1985) and V496 UMa (Kennedy et al., 2022). This profile shape is typically
attributed to the emission from both magnetic poles of the WD, with one being
more intense than the other, due to the inclination at which the WD is
observed. Concerning W2, the energy-resolved folded light curves of the 2002
data sets (e.g. Fig. 7) show similar amplitudes of the two peaks at hard
energies, while they are unequal at soft energies. This would suggest that the
less active pole is harder than the main pole. The hardness ratio of the
source does not give further information, being constant within the error
bars. The high cycle-to-cycle variability (Figs. 6), despite no significant
changes in the X-ray flux (Fig. 3), would point to a behaviour typical of
magnetic CVs of the polar type, as observed for instance for the eclipsing
polars 2PBC J0658.0-1746 (Bernardini et al., 2019) or 3XMM J00511.8+634018
(Schwope et al., 2020), which also fall in the period gap.

###  5.1 The CV populations in GCs

47 Tuc has the highest number of CVs among all Galactic GCs, with a total of
43 CVs and candidate CVs identified so far in HST optical and NUV data (Rivera
Sandoval et al., 2018). Among them, several have also been detected and
identified in X-rays, thanks to Chandra and eROSITA data (Edmonds et al.,
2003a, b; Heinke et al., 2005; Bao et al., 2023; Saeedi et al., 2022). For
instance, the most recent work claimed 11 X-ray CVs in the cluster,
identifying the CVs based on their periodic signals (Bao et al., 2023).

We confirm that W2 has the second shortest orbital period ($\sim$2.4 hr) of
all the X-ray CVs in the cluster. 4 out of the 11 CVs have periods within the
period gap, close to the ratio for the CVs in the Galaxy bulge, but higher
than that for CVs in the solar neighbourhood (20% and 8%, respectively, as
reported by Bao et al., 2023). However, it should be noted that the period gap
for magnetic CVs is much less marked than that of non-magnetic systems
(Webbink & Wickramasinghe, 2002). Remarkably, as noted by Bao et al. (2023),
in 47 Tuc all the CVs in the period gap are located within the half-light
radius (3.17′) and the core radius (0.36′) of the cluster, while longer-period
CVs are more centrally concentrated and are found within the core radius.
Moreover, no known CV in the GC has a period below the period gap, and the
majority of them show longer periods than those of the CVs in the Galaxy bulge
and solar neighbourhood. These peculiarities would suggest different formation
channels for the GC CVs compared to those in the Galactic bulge and the solar
neighbourhood, contributing to the idea that dynamical encounters may have
played a significant role in the GC history (e.g. Belloni et al., 2019). This
might be especially true for those CVs outside the core radius, such as W2,
although a selection bias cannot be entirely excluded (CVs below the period
gap are generally less bright). However, observational biases might be present
towards the brightest X-ray CVs (i.e. magnetic CVs), which appear to be more
abundant in GCs than non-magnetic CVs. Whether this is true or not is still a
matter of debate (Knigge, 2012; Belloni & Rivera, 2021).

Apart from 47 Tuc, three other GCs have a high number of hosted CVs: NGC 6397,
NGC 6752, and $\omega$ Cen (see Belloni & Rivera, 2021, for a review). All
these GCs show a bi-modal distribution of the faintest and the brightest CVs
when observed in X-rays. However, while in core-collapsed GCs this
distribution persists also in optical, in non-core-collapsed GCs, like 47 Tuc,
there is no evidence of bimodality at optical wavelengths. Another difference
between these GCs lies in the spatial distribution of their CVs. In NGC 6397
and NGC 6752 the bright CVs are concentrated more towards the centre than
faint CVs. The same holds for $\omega$ Cen, though less evident. Instead, in
47 Tuc CVs are uniformly distributed. This difference can be due to the
evolution and relaxation time of the cluster. Nonetheless, with a
$L_{\mathrm{X}}\sim 10^{32}$ erg s-1, W2 is among the brightest CVs in all the
aforementioned GCs. This is consistent with its magnetic nature, as magnetic
CVs are typically brighter (e.g. Mukai, 2017).

##  6 Conclusions

We investigated the nature of the CV W2 in the Galactic GC 47 Tuc. The source
shows characteristics which are common among magnetic CVs: a luminosity of
$\sim 10^{32}$ erg s-1, a temperature of 10 keV, and an orbital period of 8649
s (2.4 hr). The flux of the source is found to be constant in almost all
Chandra observations, taken in 2000, 2002, 2014–15, and 2022. In the latest
2022 observation, W2 is not detected, but the upper limit on its flux is
consistent with the previous observation in the same epoch. Our search for
pulsations confirms the previous orbital period and finds no other significant
signal. The source is also detected for the first time in eROSITA data and the
same orbital period is recovered. This source has been proposed to have a
second, shorter period of 3846 s, indicating that it might be an asynchronous
magnetic CV of the IP type. However, our analysis does not confirm the
presence of this second period, based also on the low coherence of the
candidate signal which is inconsistent with being originated by a spin
modulation. Instead, the cycle-to-cycle variability of the amplitude at the
2.4 h period, as well as its X-ray luminosity, suggests that it is a polar.

###### Acknowledgements.

This research is based on data obtained from the Chandra Data Archive and has
made use of the software package CIAO provided by the Chandra X-ray Center
(CXC). The eROSITA data shown here were processed using the eSASS software
system developed by the German eROSITA consortium. The authors thank the
anonymous referee whose constructive feedback significantly improved the
scientific quality and the readability of this manuscript. RA and GLI
acknowledge financial support from INAF through grant “INAF-Astronomy
Fellowships in Italy 2022 - (GOG)”. MI is supported by the AASS Ph.D. joint
research programme between the University of Rome ”Sapienza” and the
University of Rome ”Tor Vergata”, with the collaboration of the National
Institute of Astrophysics (INAF). PE and GLI acknowledge financial support
from the Italian Ministry for University and Research, through the grants
2017LJ39LM (UNIAM) and 2022Y2T94C (SEAWIND), and from INAF through LG 2023
BLOSSOM. DdM acknowledges support from INAF Astrofund2022. RA and NW are
grateful for support provided by the CNES for this work.

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##  Appendix A Chandra observations of 47 Tuc

Table 3: Log of Chandra observations in chronological order. Upper limit on
the latest observation is given at 90%c.l.

Obs. ID | Date | Exp. (ks) | Net count rate ($10^{-3}$ cts/s) | Instrument | Ref.
---|---|---|---|---|---
78 | 2000-03-16 07:17:27 | 3.88 | $5.9\pm 1.2$ | ACIS-I | (a)
953 | 2000-03-16 08:38:40 | 31.68 | $1.2\pm 0.2$ | ACIS-I | (a,b)
954 | 2000-03-16 18:01:59 | 0.85 | – | ACIS-I | (a)
955 | 2000-03-16 18:32:00 | 31.68 | $4.5\pm 0.4$ | ACIS-I | (a,b)
956 | 2000-03-17 03:55:20 | 4.69 | $5.3\pm 1.1$ | ACIS-I | (a)
2735 | 2002-09-29 16:57:56 | 65.24 | $6.4\pm 0.3$ | ACIS-S | (a,b)
3384 | 2002-09-30 11:37:18 | 5.31 | $9.0\pm 1.3$ | ACIS-S | (a)
2736 | 2002-09-30 13:24:28 | 65.24 | $6.0\pm 0.3$ | ACIS-S | (a,b)
3385 | 2002-10-01 08:12:28 | 5.31 | $8.8\pm 1.4$ | ACIS-S | (a)
2737 | 2002-10-02 18:50:07 | 65.24 | $7.6\pm 0.3$ | ACIS-S | (a,b)
3386 | 2002-10-03 13:37:18 | 5.55 | $2.1\pm 0.6$ | ACIS-S | (a)
2738 | 2002-10-11 01:41:55 | 68.77 | $7.4\pm 0.3$ | ACIS-S | (a,b)
3387 | 2002-10-11 21:22:09 | 5.74 | $2.1\pm 0.6$ | ACIS-S | (a)
16527 | 2014-09-05 04:38:37 | 40.88 | $3.1\pm 0.3$ | ACIS-S |
15747 | 2014-09-09 19:32:57 | 50.04 | $4.4\pm 0.3$ | ACIS-S |
16529 | 2014-09-21 07:55:51 | 24.7 | $3.9\pm 0.4$ | ACIS-S |
17420 | 2014-09-30 22:56:03 | 9.13 | $2.7\pm 0.6$ | ACIS-S |
15748 | 2014-10-02 06:17:00 | 16.24 | $4.5\pm 0.5$ | ACIS-S |
16528 | 2015-02-02 14:23:34 | 40.28 | – | ACIS-S |
26229 | 2022-01-26 15:20:22 | 9.65 | $1.0\pm 0.4$ | ACIS-S |
26286 | 2022-01-27 02:10:56 | 9.83 |  $\leq$1.2 | ACIS-S |
999(a) Heinke et al. (2005), (b) Israel et al. (2016).

##  Appendix B Best-fit results

The following tables show the best-fit parameters obtained from fitting the
seven data sets 955, 2735, 2736, 2737, 2738, 15747, 16527 individually
(columns 2–6) and from imposing the same local absorption
$N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ (columns 7–8).

Table 4: Best-fit values of the seven data sets 955, 2735, 2736, 2737, 2738,
15747, 16527 with the power law model, assuming
$N_{\mathrm{H}}^{\mathrm{GAL}}=5.5\times 10^{20}$ cm-2, in two different
cases: independent fits for each spectrum (columns 2–6) and simultaneous fit
with the same local absorption (columns 7–8). The latter fit resulted in
$N_{\mathrm{H}}^{\mathrm{47Tuc+local}}=(2.6^{+1.2}_{-1.1})\times 10^{21}$
cm-2, with $\chi^{2}_{red}$(d.o.f.)$=$1.22(81) and n.h.p.$=$0.08. Fluxes are
computed in the energy range 0.5–6 keV.

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
---|---|---|---|---|---|---|---
Obs. | $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ | $\Gamma$ | $F_{\mathrm{abs}}$ |  $\chi^{2}_{red}$(d.o.f.)aa$a$Degrees of freedom (d.o.f). | n.h.p.bb$b$Null hypothesis probability (n.h.p.). | $\Gamma$ | $F_{\mathrm{abs}}$
| ($10^{21}$ cm-2) |  | ($10^{-14}$ erg cm-2 s-1) |  |  |  | ($10^{-14}$ erg cm-2 s-1)
955 | 2.0${}^{+14.2}_{-2.0}$ | 1.3${}^{+1.1}_{-0.5}$ | 8 $\pm$ 4 | 0.18(2) | 0.84 | 1.3${}^{+0.5}_{-0.4}$ | 7${}^{+4}_{-2}$
2735 | 1.7${}^{+2.2}_{-1.7}$ | 1.4${}^{+0.3}_{-0.2}$ | 7 $\pm$1 | 1.03(15) | 0.42 | 1.5 $\pm$ 0.2 | 6.4${}^{+1.2}_{-0.8}$
2736 | 4.0${}^{+3.7}_{-2.9}$ | 1.6 $\pm$ 0.3 | 6 $\pm$ 1 | 1.31(14) | 0.19 | 1.5 $\pm$ 0.2 | 6.2${}^{+1.0}_{-0.8}$
2737 | 3.8${}^{+2.6}_{-2.2}$ | 1.5${}^{+0.3}_{-0.2}$ | 8 $\pm$ 1 | 2.02(18) | 0.01 | 1.4 $\pm$ 0.2 | 8 $\pm$ 1
2738 | 2.7${}^{+2.5}_{-2.3}$ | 1.8 $\pm$ 0.3 | 7 $\pm$ 1 | 0.93(18) | 0.54 | 1.75 $\pm$ 0.2 | 7.0${}^{+1.2}_{-0.8}$
15747 | 2.9 (frozen) | 1.7 $\pm$ 0.3 | 5 $\pm$ 1 | 0.47(7) | 0.86 | 1.65 $\pm$ 0.3 | 5.1${}^{+1.1}_{-0.8}$
16527 | 2.9 (frozen) | 1.3${}^{+0.5}_{-0.4}$ | 4${}^{+2}_{-1}$ | 2.33(3) | 0.07 | 1.3${}^{+0.5}_{-0.4}$ | 4${}^{+2}_{-1}$

101010

Table 5: As before, for the thermal Bremsstrahlung model. For the simultaneous fit with the same local absorption (columns 7–8) the best-fit local absorption was of $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}=(2.0\pm 0.9)\times 10^{21}$ cm-2, with $\chi^{2}_{red}$(d.o.f.)$=$1.21(81) and n.h.p.$=$0.1. (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
---|---|---|---|---|---|---|---
Obs. | $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ | kT | $F_{\mathrm{abs}}$ |  $\chi^{2}_{red}$(d.o.f.) | n.h.p. | kT | $F_{\mathrm{abs}}$
| ($10^{21}$ cm-2) | (keV) | ($10^{-14}$ erg cm-2 s-1) |  |  | (keV) | [$10^{-14}$ erg cm-2 s-1]
955 | 1.7${}^{+11.3}_{-1.7}$ | 60${}^{+50}_{-30}$ | 7${}^{+16}_{-7}$ | 0.17(2) | 0.84 | 46${}^{+45}_{-24}$ | 7${}^{+3}_{-7}$
2735 | 1.3${}^{+1.8}_{-1.3}$ | 18${}^{+66}_{-11}$ | 6${}^{+1}_{-6}$ | 1.01(15) | 0.44 | 13${}_{-7}^{+35}$ | 6${}^{+1}_{-2}$
2736 | 3.3${}_{-2.3}^{+2.9}$ | 9${}_{-5}^{+26}$ | 5.4${}^{+0.6}_{-2.4}$ | 1.22(14) | 0.25 | 13${}_{-6}^{+37}$ | 5.6${}^{+0.8}_{-2.6}$
2737 | 3.1${}^{+2.1}_{-1.7}$ | 12${}_{-6}^{+54}$ | 7${}^{+1}_{-5}$ | 1.99(18) | 0.01 | 20${}_{-10}^{+140}$ | 8${}^{+1}_{-6}$
2738 | 1.5${}_{-1.5}^{+2.0}$ | 6${}_{-3}^{+7}$ | 6.3${}^{+0.8}_{-2.0}$ | 0.92(18) | 0.55 | 5${}_{-2}^{+4}$ | 6${}^{+1}_{-2}$
15747 | 2.2 (frozen) | 8${}_{-4}^{+30}$ | 4.6${}^{+0.7}_{-2.4}$ | 0.57(7) | 0.78 | 8${}_{-4}^{+37}$ | 4.7${}^{+0.8}_{-1.5}$
16527 | 2.2 (frozen) | 38${}^{+44}_{-23}$ | 4${}^{+1}_{-4}$ | 2.30(3) | 0.07 | 42${}^{+47}_{-25}$ | 4${}^{+2}_{-4}$
Table 6: As before, for the vmekal model. The simultaneous fit of the seven spectra with the same local absorption (columns 7–8) resulted in $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}=(1.9\pm 0.9)\times 10^{21}$ cm-2, with $\chi^{2}_{red}$(d.o.f.)$=$1.22(81) and n.h.p.$=$0.09. (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
---|---|---|---|---|---|---|---
Obs. | $N_{\mathrm{H}}^{\mathrm{47Tuc+local}}$ | kT | $F_{\mathrm{abs}}$ |  $\chi^{2}_{red}$(d.o.f.) | n.h.p. | kT | $F_{\mathrm{abs}}$
| ($10^{21}$ cm-2) | (keV) | ($10^{-14}$ erg cm-2 s-1) |  |  | (keV) | ($10^{-14}$ erg cm-2 s-1)
955 | $1.8^{+12.5}_{-1.8}$ | 50$\pm$30 | $7^{+13}_{-7}$ | 0.17(2) | 0.84 | 50${}^{+30}_{-46}$ | 7${}^{+9}_{-7}$
2735 | $1.2_{-1.2}^{+1.8}$ | 19${}^{+61}_{-12}$ | $6.5_{-6.0}^{+0.9}$ | 1.01(15) | 0.44 | 13${}_{-6}^{+36}$ | 6${}_{-5}^{+1}$
2736 | $3.3_{-2.3}^{+2.8}$ | $9_{-4}^{+23}$ | $5.4_{-2.1}^{+0.8}$ | 1.21(14) | 0.26 | 13${}_{-6}^{+35}$ | 5.7${}_{-3.0}^{+0.8}$
2737 | 3.1${}^{+2.0}_{-1.8}$ | $12_{-6}^{+55}$ | $7.2_{-2.7}^{+0.8}$ | 2.01(18) | 0.01 | 19${}^{+61}_{-10}$ | 8${}_{-4}^{+1}$
2738 | $1.4_{-1.4}^{+1.8}$ | $6_{-2}^{+7}$ | $6.4_{-1.6}^{+0.7}$ | 0.93(18) | 0.55 | 5${}_{-1}^{+4}$ | 6.2${}_{-1.2}^{+0.7}$
15747 | 2.2 (frozen) | $8_{-4}^{+30}$ | $4.7_{-2.3}^{+0.8}$ | 0.57(7) | 0.78 | 8${}_{-4}^{+36}$ | 4.8${}_{-2.9}^{+0.8}$
16527 | 2.2 (frozen) | 31${}^{+49}_{-26}$ | $4^{+3}_{-4}$ | 2.31(3) | 0.07 | 50$\pm$30 | 4${}_{-4}^{+5}$