MULTI-WAVELENGTH OBSERVATIONS OF 3FGL J2039.6–5618: A CANDIDATE REDBACK MILLISECOND PULSAR

For our X-ray analysis, we selected only 0–4 pattern events from the pn and 0–12 from the two MOS detectors with the default flag mask. The source detection in the 0.3–10 keV energy range was run simultaneously on the event lists of each EPIC-pn and MOS detector using a maximum likelihood fitting with the SAS task edetect_chain invoking other SAS tools to produce background, sensitivity, and vignetting-corrected exposure maps. The final source list includes 90 X-ray sources from both the pn and MOS detectors, with a combined pn+MOS detection likelihood greater than 10, corresponding to a significance above 3.5σ. Figure 1 shows the 0.3–10 keV exposure-corrected XMM-Newton FOV that was obtained combining the images of the EPIC-pn and MOS detectors. We focused our analysis on the 16 X-ray sources detected within, or close to, the 95% confidence position error ellipse of 3FGL J2039.6−5618. We summarized the positions, spectral parameters, fluxes, and variability indices of these sources in Table 1.

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Table 1.  Spectral Properties of the XMM-Newton Sources Detected within, or Close to, the Error Ellipse of 3FGL J2039.6−5618. Spectral Models are: Power-law (PL), apec (AP), and Blackbody (BB)

Source ID	J2000 coord.	Counts Rate	Spectral	NH	ΓX	Flux[0.3−10 keV]	Variability
	R.A. Decl. (°) (stat. err.a)	10−3 cts s−1	Model	1022 cm−2		10−14 erg cm−2 s−1	χ2 (dof)
3	309.8956-56.2861 (03)	23.78 ± 0.99	PL	<0.04	1.36 ± 0.09	${10.19}_{-0.82}^{+0.87}$	66.18 (16)
11	309.8439-56.3292 (06)	10.76 ± 0.79	PL	<0.16	${1.33}_{-0.17}^{+0.24}$	${5.73}_{-0.63}^{+0.66}$	3.92 (8)
13	309.9995-56.3359 (05)	4.90 ± 0.57	PL/AP	<0.26	${2.07}_{-0.37}^{+0.55}$	${2.66}_{-0.45}^{+0.87}$	4.0 (8)
19	309.8170-56.2838 (09)	6.51 ± 0.72	PL/AP	<0.24	${1.54}_{-0.22}^{+0.52}$	${2.98}_{-0.60}^{+0.67}$	3.8 (8)
22	309.8713-56.3320 (07)	7.84 ± 1.36	PL/AP	<0.77	${1.80}_{-0.38}^{+0.74}$	${3.37}_{-0.59}^{+1.84}$	11.9 (8)
24	309.9619-56.2989 (08)	4.44 ± 0.46	PL/AP	<0.46	${1.86}_{-0.37}^{+1.08}$	${1.24}_{-0.31}^{+0.41}$	4.1 (8)
29	309.8415-56.3154 (10)	5.19 ± 0.71	PL/AP/BB	<1.05	${2.37}_{-0.70}^{+2.24}$	${1.36}_{-0.44}^{+1.15}$	6.2 (8)
31	309.8172-56.2948 (08)	4.21 ± 0.54	PL/AP/BB	<0.91	${1.80}_{-0.58}^{+0.72}$	${3.31}_{-0.68}^{+1.60}$	7.4 (8)
40	309.9936-56.3097 (11)	3.03 ± 0.50	PL/APb	0.05	2	${0.63}_{-0.22}^{+0.23}$	6.25 (6)
44	309.8651-56.2619 (15)	2.46 ± 0.44	PL/AP/BBb	0.05	2	${0.11}_{-0.04}^{+0.18}$	5.5 (5)
52	309.9451-56.3099 (13)	2.00 ± 0.35	PL/BB	<5.21	${1.11}_{-0.77}^{+3.00}$	${1.67}_{-0.70}^{+1.40}$	2.6 (5)
60	309.9159-56.3583 (14)	1.78 ± 0.32	PL/AP/BBb	<1.42	${2.33}_{-0.83}^{+1.01}$	${0.49}_{-0.25}^{+0.23}$	4.4 (4)
72	309.8419-56.3541 (16)	1.58 ± 0.41	PL/AP/BBb	0.05	2	${0.74}_{-0.23}^{+0.24}$	0.7 (3)
76	309.9548-56.3170 (20)	1.10 ± 0.29	PL/AP/BBb	0.05	2	${0.68}_{-0.21}^{+0.15}$	1.0 (3)
85	309.8740-56.3390 (16)	1.24 ± 0.43	PL/APb	0.05	2	${0.74}_{-0.27}^{+0.26}$	0.64 (3)
88	309.9357-56.2766 (17)	1.62 ± 0.43	...	...	...	...	8.89 (3)

Notes. Results of the spectral analysis of the XMM-Newton sources detected within an error circle of 1.5 times the 95% confidence error ellipse of 3FGL J2039.6−5618. If the spectrum is well fitted by more than one model, we report only the PL parameters. Here, we report the best-fit X-ray position, the count rate of the best-fit spectral model, the best-fit column density, the best-fit photon index, the unabsorbed X-ray flux in the 0.3–10 keV energy band, and the variability test described in the text. The errors are at a 90% confidence and the upper limits at 3σ.

^aHere we report only the 1σ statistical error, the 1σ systematic error is about 15 for each X-ray source. ^bOwing to the low number of counts, we fixed the photon index (Γ_X) to 2 for a PL model and the temperature (kT) to 3.5 and 0.2 for an AP and a BB model, respectively.

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For each EPIC detector, we extracted the source photons using an extraction radius of 20'', while we extracted background photons from source-free regions in the same CCD chip as the source, with radii of 50''–120''. For each detector, we used the SAS task specgroup to rebin all the extracted spectra and have at least 25 counts for each background-subtracted spectral channel, as well as generated ad hoc response matrices and ancillary files using the SAS tasks rmfgen and arfgen. For each source, we fitted simultaneously the pn and MOS spectra using XSPEC v12.8, forcing the same set of parameters and considering three different spectral models: a power law (PL)—which is well suited for both AGN and pulsars—an apec (AP) for stellar coronae, and a blackbody (BB) for the pulsar thermal component. In all cases, the hydrogen column density N_H was left as a free parameter. For each emission model we computed the 90% confidence level error on the spectral parameters. When the best-fit N_H values were comparable to zero, we assumed the measured uncertainties to determine the 3σ confidence level upper limit. Spectra with very low counts were fitted after fixing the N_H to the estimated value along the line of sight (5 × 10²⁰ cm⁻²; Dickey & Lockman 1990), or fixing either the photon index or the temperature to typical values (i.e., Γ_X = 2 and kT = 3.5 keV or kT = 0.2 keV in case of an AP and a BB model, respectively).

As shown in Table 1, only Source 3 and 11, the two brightest X-ray sources in our sample, were best fitted by a simple PL model, with a χ² = 52.32 (42 degrees of freedom, dof) for the former and χ² = 16.06 (22 dof) for the latter. For the remaining 13 sources, at least two different models were required to obtain an acceptable fit with null hypothesis probability >0.01. Only for Source 88 was it not possible to obtain acceptable results with any of the selected spectral models. Indeed, this source is the faintest in our sample and is likely spurious. Figure 2 shows the binned spectrum of Source 3 extracted simultaneously from each of the EPIC detectors, together with the best-fit PL model. Since most MSPs are characterized by a significant thermal component to their X-ray spectra, we tried to fit the spectra of Source 3 and Source 11 with an absorbed BB plus PL model. This improved the accuracy of the fit only for Source 3, with a χ² = 34.9 (40 dof). From the F-test (Bevington 1969), we computed a 0.0003 probability that adding a thermal component to the model would produce a chance improvement to the fit. Since this probability only corresponds to a ∼3.6σ significance, hereafter we ignored the absorbed BB plus PL spectral model. Because the measured counts are too few to clearly discriminate among different spectral models in most X-ray sources, we checked whether we could extract qualitative spectral information from an hardness ratio (HR) analysis (Marelli et al. 2014). However, we found that the observed HRs are compatible with different spectral models and, therefore, are not constraining.

In order to detect possible time variability during the XMM-Newton observation, we generated standard light curves from the pn-data for all 16 X-ray sources in Table 2. Starting from the source and background regions described in Section 3.1.2, we extracted source+background and background light curves, respectively, with the SAS task evselect and combined them into a background-subtracted light curve with the task epiclccorr. This task also corrects the time series for vignetting, bad pixels, chip gaps, quantum efficiency, dead time, exposure, and good time intervals. For each source, we generated a light curve with time binning of 2500 s, or multiple of this value, to have at least 25 counts per bin and we ran an χ² test to evaluate the variability significance. Only Source 3 is characterized by a significant variability during the observation (χ² = 66.18, with 16 dof), with a chance probability of 4.61 × 10⁻⁸ (>5σ). After combining the data from all three EPIC cameras, the Source 3 light curve shows a more apparent variability (Figure 3, left), with a chance probability of 7.43 × 10⁻¹⁴, whereas the other X-ray still shows no evidence of significant variability.

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The Source 3 light curve also hints at a possibly periodic modulation. We converted photon arrival times to the Solar system Barycentric Dynamical Time with the SAS task barycen and used the FTOOL task efsearch to find the best period in the light curve through a maximum χ² test. We folded the light curve with periods ranging from 100 to 43,000 s, with the latter comparable to the length of the XMM-Newton observation. We found the best-fit period at 0.2245 ± 0.0081 days, where the period uncertainty was obtained following Leahy (1987). The corresponding χ² of 104.5 (9 dof) gives a chance probability of 6.38 × 10⁻¹⁴, accounting for the number of trials, and makes the periodicity statistically significant (∼7.5 σ). The presence of a periodic signal at the corresponding frequency of ∼5 × 10⁻⁵ Hz was independently confirmed by the power spectrum produced with the FTOOL powspec. We note that the best-fit X-ray period of Source 3 is comparable to about half the length of the XMM-Newton observation, so that the observed periodicity might be spurious. We examined the light curves of other comparably bright X-ray sources detected in the whole XMM-Newton FOV and found that none showed evidence of periodicity at any timescale. Nonetheless, the fact that the length of the XMM-Newton observation only covers ∼2.3 cycles prevents us from firmly claiming that Source 3 is periodic. The X-ray light curve folded at the best-fit period (Figure 3, right) is characterized by two peaks separated in phase by 0.31 ± 0.04. Therefore, it cannot be described by a simple sinusoidal or Gaussian model, with a null hypothesis probability lower than 10⁻³. We checked whether the folded X-ray light curve of Source 3 varied as a function of the energy, and whether the X-ray spectrum changed as a function of the phase. In both cases, however, the available statistics is not sufficient to highlight significant differences in the energy-resolved light curves and the phase-resolved spectra.

We looked for archival X-ray images of the 3FGL J2039.6−5618 field to check for long-term variability of Source 3. The field was serendipitously observed with the X-ray Imaging Spectrometer (XIS) of Suzaku (Mitsuda et al. 2007) on 2010 October 28 for a total exposure time of 21.5 ks (OBSID 705028010). We extracted source counts from a circle of radius 13 around the best XMM-Newton coordinates of Source 3 and background counts from a nearby, source-free 2'-radius circle using the HEASOFT(v.6.16) tool xselect, and summed the spectra from the XIS cameras with the mathpha, addarf, and addrmf tools. We obtained 350 counts, of which ∼50% are from the source. A fit with a PL gives a null hypothesis probability of 0.06 (4 dof), with N_H < 5 × 10²¹ cm⁻² (90% upper limit), photon index Γ = 1.3 ± 0.4, and an unabsorbed flux in the 0.3–10 keV energy range of ${1.7}_{-1.0}^{+0.3}$ × 10⁻¹³ erg cm⁻² s⁻¹, which is fully compatible with the XMM-Newton results. The XMM-Newton count-rate and spectral parameters (Table 1) are also compatible with non-detection above the 3σ threshold (∼1.05 ×10⁻¹³ erg cm⁻² s⁻¹) of Source 3 in the short Swift/XRT images of Takeuchi et al. (2013), taken in 2010 and 2011. Therefore, we find no evidence of variability of Source 3 on timescales of three years.

We cross-matched the positions of all the 16 XMM-Newton sources in Table 1 with the source catalogs obtained from the GROND observations. We performed the source detection on the single-band GROND exposures using the starfind tool in IRAF, matched the source catalogs over the different observations, and checked for variable sources against the median of all observations. Object photometry was computed using the task daophot in IRAF and the airmass correction was applied using the standard atmospheric extinction coefficients for the La Silla Observatory. For the cross-match we used a radius obtained by combining the statistical 1σ uncertainty on the X-ray source centroid, plus the 90% confidence level systematic error associated with the absolute accuracy of the XMM-Newton aspect solution, which is 15 per coordinate.¹³ The uncertainty on the absolute astrometry of the GROND images (03) is much lower than the XMM-Newton, and is accounted for by our choice of the matching radius. There are only six XMM-Newton sources (Source 3, 13, 22, 24, 40, 76) with at least a candidate optical or near-IR counterpart in the GROND data (Figure 4).

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We also cross-correlated the XMM-Newton source list with the VISTA, OM, and UVOT source catalogs. The source detection and photometry in the VISTA images were carried out as part of the CASU pipeline (Section 2.3). For the OM images, the source detection and photometry were carried out with the SAS tasks omdetect and ommag, respectively, and source detection and photometry for the UVOT images were carried out with the HEASOFT taks uvotdetect and uvotsource. As before, the matching radius accounted for the uncertainty on the absolute astrometry of the used source catalogs: ≲03 (VISTA; Emerson et al. 2004), 05 (UVOT; Breeveld et al. 2010), and 07 (OM; Page et al. 2012). The cross-correlations with these catalogs provided additional near-IR and near-UV magnitudes for some of the GROND sources and unveiled candidate counterparts for Source 11, 19, 29, 60, and 88. We found no counterparts in the OM/UVM2 filter, whereas only Source 3 was detected in the UVOT/UVW2 images. The optical, near-UV, and near-IR magnitudes of the candidate counterparts to the XMM-Newton sources are summarized in Table 2. Only for the candidate counterparts to Source 3, 40, and 76 do we have an adequate spectral coverage in at least the optical and near-IR.

Among the six XMM-Newton sources with a possible GROND counterpart, only Source 3 is associated with a clearly variable object (χ² = 1232, with 51 dof). Figure 5 (left) shows the multi-band light curves of this object for the three nights spanned by the GROND observations. As seen, the light curves seem to be modulated, with an amplitude of ∼0.4 mag in the g' band. In particular, the modulation seems to be periodic and feature a double-peaked profile (night 1), with the two peaks only partially seen in night 2 and 3, likely owing to the different sampling of the light curve. This modulation is also seen in the r', i', and z' light curves, with both shape and amplitudes similar to that of g', and is also recognized in the J- and H-band light curves, and very marginally in the that of K-band. This suggests that the observed modulation is real and not due, for instance, to possible problems with the photometry in a given filter. As a check, for all filters we extracted the light curves of several stars of comparable brightness detected in the GROND FOV, but found no evidence of such a modulation. This confirms that it is not due to random effects, such as variations in the sky conditions (transparency, background, moon illumination), or systematic effects, such as variations in the encircled flux due to the fixed size of the photometry aperture with respect to the seeing disk. Furthermore, the fact that the modulation seems to be periodic argues against the possibility that it is produced by any such effects, and implies that is associated with an intrinsic star variability.

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We computed the probability that the association between Source 3 and its candidate GROND counterpart is due to a chance coincidence. We computed the probability as $P=1-\mathrm{exp}(-\pi \rho {r}^{2}),$ where r is the matching radius used for Source 3 (18) and ρ is the density of stellar objects in the GROND field, regardless of their brightness, measured in the co-addition of all g'-band exposures. For a stellar density ρ ∼ 0.0019 square degree⁻¹ we estimated a chance coincidence probability P ∼ 0.02, which makes a chance coincidence unlikely.

To confirm the existence of a periodic modulation of the Source 3 candidate counterpart, we carried out a periodicity analysis based on the Generalized Lombe–Scargle periodogram method (Lomb 1976; Scargle 1982; Zechmeister & Kuerted 2009). To cross-check, we also used the phase dispersion minimization technique (Stellingwerf 1978) using the pdm code in IRAF and the Period04 software package (Lenz & Breger 2005), which is especially dedicated to the statistical analysis of large astronomical time series–containing gaps (see Figure 5). All methods indicate the presence of a periodicity with a period of ∼0.227 days. The analysis of the power spectrum of the optical time series shows a clear peak at the corresponding frequency, with a probability that is due to a chance noise fluctuation (false-alarm probability) of ∼1.8 × 10⁻¹⁵ (∼8σ). The best period was found at 0.22748 ± 0.00043 days in the optical bands and at 0.22799 ± 0.00062 days in the near-IR bands, where we estimated the period uncertainty following Gilliland & Baliunas (1987). The optical and near-IR best-fit periods of the Source 3 candidate counterpart are consistent within the uncertainties, which provides further evidence that the observed modulation is real.

The period of the optical/IR modulations seen in the GROND data for the Source 3 candidate counterpart is consistent with that seen in the XMM-Newton data for Source 3 (0.2245 ± 0.0081 days; Section 3.1.3), and so the detection of virtually the same periodicity clearly indicates that the two objects are associated. Therefore, based on the X-ray and optical variability at the same period and the relatively low chance coincidence probability, we regard the association between Source 3 and its GROND candidate counterpart as robust. Furthermore, since we based the selection of candidate X-ray counterparts to 3FGL J2039.6−5618 on the search for variable sources, the optical/X-ray periodicity of Source 3 makes it a very promising candidate. Another possible candidate X-ray counterpart to 3FGL J2039.6−5618 would be Source 11, which is the second brightest X-ray source detected in the 3FGL error circle, and the only other X-ray source with an obvious non-thermal spectrum (Table 1). However, Source 11 is not variable in X-rays and is not associated with a periodic optical/near-IR GROND counterpart. Therefore, although it cannot be firmly ruled out as a candidate X-ray counterpart to 3FGL J2039.6−5618, as of now, it is a less likely candidate by far than Source 3. The same is true for all other fainter X-ray sources in Table 1, whose poorly characterized X-ray spectra and sparse optical, near-UV, and near-IR flux measurements hamper a detailed multi-wavelength analysis of their properties and a non-ambiguous classification.

The optical/near-IR light curves of the Source 3 counterpart folded at the corresponding best-fit periods are shown in Figure 5 (right). A double-peak light curve is clearly visible, with a main peak and a secondary peak separated in phase by ∼0.5. For each band, we determined the phase of the two peaks by fitting a Gaussian function to their profiles to precisely compute their phase separations and errors. The peak phase separation remains constant in the optical (0.436 ± 0.003; g'), while it seems to slightly increase in the near-IR (0.517 ± 0.012; J). To better recognize the light curve evolution, we defined four regions: the main peak (ϕ = 0.2–0.5), the secondary peak (ϕ = 0.7–0.9), the "bridge" (ϕ = 0.5–0.7), and the "off-peak" (ϕ = 0.0–0.2 and ϕ = 0.9–1.0). The shape of the light curve is similar in all bands, but the profile of the modulation changes from the optical to the near-IR (Figure 6, left). In particular, the primary peak becomes broader and its amplitude decreases from ∼0.4 mag in the g' band to ∼0.2 mag in the H band; the difference between the primary and secondary peaks decrease from 0.133 mag in the g' band to ∼0 in the H band. Similarly, the amplitude of the "bridge" decreases, becoming comparable to that of the "off-peak" region. There is also possible evidence of a color variation as a function of phase (Figure 6, right), which might indicate that we are observing regions of the star surface at different temperatures. In particular, the colors seem to be bluer in coincidence with the two peaks, and bluer in coincidence with the primary peak than with secondary one. The colors also seem bluer in the "bridge" than in the "off-peak" region. The color variation seems consistently less marked at longer wavelengths because the light curve variations are smoother. Unfortunately, the errors on the GROND photometry calibration (Section 2.3) make it difficult to quantify the observed color variations.

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We tried to align in phase the X-ray and optical light curves of Source 3 to check the relative alignments between the X-ray and optical peaks. However, the difference between the epochs of the XMM-Newton and GROND observations (MJD = 56885–56887 and MJD = 56575, respectively) corresponds to a maximum time difference of 312 days. The accuracy on the best-fit optical period derived from the GROND observations is 0.00043 days (Section 3.2.2), which corresponds to a phase uncertainty of ∼0.0019. Thus, building a phase-coherent solution for the optical light curve backward to the epoch of the XMM-Newton observation would bring an uncertainty of ∼0.59 on the absolute phase determination, which is larger than the phase separation between the two peaks (∼0.3 in the X-rays and ∼0.45 in the optical).

We computed the time-average multi-band photometry of the Source 3 counterpart from the GROND data and obtained g' = 19.40 ± 0.02, r' = 18.71 ± 0.02, i' = 18.59 ± 0.02, z' = 18.52 ± 0.02, J = 18.13 ± 0.03, H = 18.33 ± 0.03, and K = 18.35 ± 0.06, with all magnitudes in the AB system. The photometry errors account for both statistical errors and the systematic uncertainty on the photometry calibration. We also identified the Source 3 counterpart in the U and UVW1-filter exposures from the XMM-Newton/OM with AB magnitudes U = 21.26 ± 0.26 and m_UVW1 = 21.88 ± 0.4 (Table 2), whereas it is not detected in the UVM2 filter down to a 3 σ limiting magnitude of 21.99 and in the Swift/UVOT UVW2 image down to a limiting magnitude of 23.34 (AB). In the near-IR, we also identified the Source 3 counterpart in the VISTA images, with AB magnitudes J = 18.24 ± 0.03, H = 18.24 ± 0.04, and K_s = 18.64 ± 0.09, converted from the native Vega survey system.¹⁴ We found that the VISTA magnitudes (epoch 2010.6) are all compatible with the GROND ones (epoch 2014.7), after accounting for the difference between the K and K_s filters, which excludes long-term variability on year timescales from the Source 3 counterpart.

We used the time-averaged g', r', i', and z'-band magnitudes of the Source 3 counterpart as a reference for its classification by analyzing its location in the observed (i.e., not corrected for the reddening) color–magnitude (CM) and color–color (CC) diagrams of the field. The diagrams are shown in Figure 7, where the location of the field stars is shown by the black filled circles and that of the Source 3 counterpart as a red filled triangle. Red and green triangles correspond to the location computed from the single-image photometry. In order to reject outliers and include only high-confidence measurements, we plotted only field stars for which at least 20 measurements per filter were available and with σ < 0.08. We compared the observed CM and CC diagrams with simulated stellar sequences computed from the Besançon models (Robin et al. 2004) for different stellar populations and distance values up to 15 kpc. The simulated sequences are shown in Figure 7 as the grayscale map. The dark gray regions in the CM diagrams correspond to a likely distance range (200 ≲ d ≲ 900 pc) for Source 3, whereas in the CC diagram the dark gray region corresponds to simulated magnitudes that are within ±0.05 the g'-band magnitude of the Source 3 counterpart.

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The distance to Source 3 is unknown a priori. The upper limit on the hydrogen column density derived from the fits to the X-ray spectrum of Source 3 (N_H < 4 × 10²⁰ cm⁻²; Table 1) indicates a distance lower than ≈0.9 kpc, assuming the relation between distance and N_H used by He et al. (2013). Without a parallax measurement, the distance to Source 3 cannot be precisely constrained from kinematic measurements of its optical counterpart. The NOMAD catalog (Zacharias et al. 2005) gives a proper motion of μ_αcos(δ) = 14 ± 4 mas yr⁻¹ and μ_δ = −16 ± 9 mas yr⁻¹ in right ascension and declination, respectively. This corresponds to a spatial velocity of ${101}_{-30}^{+32}$ × (d/1 kpc) km s⁻¹. If we equate it to the median of the transverse velocity distribution of MSPs (∼108 km s⁻¹, with a standard deviation of ∼86 km s⁻¹) computed from the Australia National Telescope Facility (ATNF) Pulsar Catalog¹⁵ (Manchester et al. 2005), we obtain a distance of ∼770–1500 pc that is compatible with the estimate inferred from N_H. Any determination of a lower limit on the distance is more uncertain. Again, if Source 3 were a binary MSP, the distance distribution of known binary MSPs from the ATNF Pulsar Catalog gives a probability of ∼0.006 to find one within a radius of 0.2 kpc. Thus, the assumed distance range for Source 3 (200 ≲ d ≲ 900 pc) is reasonable.

We also used the upper limit on the N_H to infer an interstellar extinction along the line of sight $E(B-V)\lt 0.072,$ after applying the relation of Predehl & Schmitt (1995). Then, we computed the extinction in the different filters using the extinction coefficients of Fitzpatrick (1999). The reddening vectors are shown in Figure 7 for the limit case $E(B-V)=0.072.$ Since the field stars are affected by an unknown interstellar extinction, and the simulations based on the Besançon models simply compute a reddening scaled proportionally to the assumed distance in a given direction, introducing a reddening correction in our simulations might bias a direct comparison between the observed and the simulated stellar sequences. Therefore, for simplicity, in all cases we simulated the stellar sequences assuming a null reddening. Then, we used the reddening vectors as a reference to trace the extinction-corrected locations of the observed points for the Source 3 counterpart (red points) along the simulated stellar sequences. As seen, the location of the Source 3 counterpart in the diagrams falls between the regions of the simulated MS and WD stellar sequences. Only for distances as low as ∼0.1 kpc would the counterpart location in the diagrams be compatible with a WD. However, if Source 3 is an MSP, this possibility is unlikely (see above). Thus, we conclude that the star is most likely not a WD.

We built the optical/near-UV/near-IR spectrum of the Source 3 counterpart using the available multi-band photometry (Section 3.3.2). In all cases, we used the measured AB magnitudes as a reference to compute the spectral fluxes at the filter peak wavelengths. In addition, as a reference for the interstellar extinction correction, we used a maximum extinction value of E(B − V) = 0.072 that is derived from the upper limit on the hydrogen column density N_H (Predehl & Schmitt 1995) obtained with the fit with a PL spectral model (Section 3.1.2).

We fit the spectrum with both a single- and a double-BB spectral model. However, we found that the optical/near-UV/near-IR data cannot be simultaneously fitted by a single BB and that a double BB is required to fit the entire spectrum (χ² = 20.6, 6 dof). The inferred temperatures are T_H ∼ 3700 K for the hotter BB, which fits the optical/UV fluxes, and T_C ∼ 1600 K for the colder one, which fits the near-IR part of the spectrum. The double-BB model is also consistent with the upper limits obtained in the OM/UVW2 and UVOT/UVM2 filters. The overall spectral shape and spectral parameters do not change significantly when adding the correction for the maximum estimated interstellar extinction (T_H ∼ 3800 K, T_C ∼ 1600 K). While the temperature of the hot BB is compatible with the surface temperature of a mid-MS companion star, the temperature of the colder one is too low to be entirely ascribed to the emission from the star surface. Although this can contribute to part of the observed near-IR emission, as indicated by the periodic modulation of the J-, H-, and K-band light curves, an additional source external to the star is required to account for the low temperature of the BB that fits the near-IR part of the spectrum. This source might be associated with emission from cold intrabinary gas or dust, may be the residual of an accretion disk left over by a past phase of matter accretion on the neutron star.

The analysis of the counterpart colors as a function of phase (Figure 6, right) suggests that its spectrum slightly changes along the ∼0.2245 days period. To quantify this possible evolution, we fitted the multi-band spectrum in the four phase intervals defined in Section 3.3.1. Like in our phase-resolved color analysis, we cannot use the single-epoch flux measurements in the U and UVW1 bands obtained with the XMM-Newton/OM. As mentioned previously, we fitted the four phase-resolved spectra using a double-BB model, considering both null and maximum interstellar extinction. However, we did not find evidence of a significant spectrum evolution across the different phase intervals. This is partially ascribed to the fact the spectra are less constrained at shorter wavelengths without the flux measurements in the U and UVW1 bands.