NuSTAR Observations of the Unidentified INTEGRAL Sources: Constraints on the Galactic Population of HMXBs

We reduced the NuSTAR data using NuSTARDAS v.1.7.1, which is part of HEASOFT v.6.20, and CALDB version 20161021, setting saamode=strict and tentacle=yes in order to better remove the time intervals having an enhanced count rate due to the contamination created by the South Atlantic Anomaly.

We extracted the source lightcurves and spectra from a circular region having a 60'' radius and centered on the most precise soft X-ray position of each source provided by either Chandra, for IGR J10447–6027 (Fiocchi et al. 2010) and IGR J17402–3656 (Tomsick et al. 2009), or Swift/XRT, for IGR J16181–5407 (Landi et al. 2012) and IGR J20569+4940 (Landi et al. 2010), and listed in Table 2. The background lightcurves and spectra were extracted from a circular region having a 100'' radius and located at the other end of the chip in which the source was detected. The corresponding lightcurves are shown in Figure 2.

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Each NuSTAR spectrum was grouped to reach at least a 5σ significance in each energy bin, except for the highest energy bins for which we have a lower significance (2.2σ on average). For illustration purposes, the 5σ requirement was raised to 10σ for all NuSTAR spectra presented in Figures 3–6 and 8.

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The Swift/XRT was operated in photon counting (PC) mode, and the corresponding data were reduced using HEASOFT v.6.20. For each observation, we extracted a spectrum from a 30'' radius centered on the targeted source. We also made a background spectrum using a source-free annulus with inner and outer radii of 60''–300'' (IGR J10447–6027), 90''–300'' (IGR J16181–5407), or 120''–360'' (IGR J20569+4940). We used the most recent response matrix for a spectrum in PC mode (swxpc0to12s6_20130101v014.rmf), and we used xrtmkarf with an exposure map to make the ancillary response file.

Each Swift/XRT spectrum was grouped to obtain at least 25 counts (for IGR J20569+4940) or a 2σ significance (for IGR J10447–6027 and IGR J16181–5407) in each energy bin. IGR J17402–3656 has no simultaneous Swift/XRT coverage due to Moon constraints for the Swift spacecraft during the NuSTAR observation.

For each source, all spectra we obtained were fitted simultaneously, using xspec v.12.9.1, with the following two models:

$$\begin{eqnarray}&&{\rm{const}}\ast {\rm{tbabs}}\ast {\rm{pegpwrlw}}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&{\rm{const}}\ast {\rm{tbabs}}\ast {\rm{bremss}}.\end{eqnarray} \tag{ 2 }$$

Additional and more complex models were also tested, including:

$$\begin{eqnarray}&&{\rm{const}}\ast {\rm{tbabs}}\ast ({\rm{bremss}}+{\rm{gauss}})\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\rm{const}}\ast {\rm{tbabs}}\ast ({\rm{cutoffpl}}+{\rm{gauss}}).\end{eqnarray} \tag{ 4 }$$

Results obtained with the four models listed above are shown in Table 3 and in Figures 3–6. All error bars are given with 90% significance.

Table 3.  NuSTAR and Swift/XRT Simultaneous Spectral Fits Using xspec Models Presented in Section 2.3

Model	Param.a	Unit	IGR J10447–6027b	IGR J16181–5407	IGR J17402–3656	IGR J20569+4940
(1)	χ2/d.o.f.	⋯	275.1/271	350.4/332	516.0/302	526.6/485
	NH	1022 cm−2	16.7 ± 2.6	9.7 ± 1.7	${17.8}_{-2.2}^{+2.4}$	3.5 ± 0.4
	Γ	⋯	1.50 ± 0.06	1.71 ± 0.05	1.96 ± 0.06	2.60 ± 0.03
	F3–79 keV	10−12 erg cm−2 s−1	16.9	16.4	24.9	33.0
	CObs2	⋯	0.7 ± 0.1	⋯	⋯	⋯
	CSwift	⋯	0.4 ± 0.2	0.6 ± 0.2	⋯	0.81 ± 0.07
(2)	χ2/d.o.f.	⋯	267.2/271	376.3/332	476.6/302	675.0/485
	NH	1022 cm−2	13.2 ± 2.0	4.6 ± 1.2	9.3 ± 1.6	1.5 ± 0.2
	kT	keV	>65.7	${40.8}_{-5.1}^{+6.3}$	${25.3}_{-2.4}^{+2.8}$	7.0 ± 0.2
	F3–79 keV	10−12 erg cm−2 s−1	15.1	14.0	20.8	26.3
	CObs2	⋯	0.7 ± 0.1	⋯	⋯	⋯
	CSwift	⋯	0.4 ± 0.2	0.5 ± 0.2	⋯	0.86 ± 0.08
(3)	χ2/d.o.f.	⋯	⋯	⋯	308.5/299	⋯
	NH	1022 cm−2	⋯	⋯	6.0 ± 1.6	⋯
	kT	keV	⋯	⋯	${33.2}_{-3.7}^{+4.5}$	⋯
	Eline	keV	⋯	⋯	6.55 ± 0.05	⋯
	σline	keV	⋯	⋯	0.27 ± 0.06	⋯
	Nline	10−5 ph cm−2 s−1	⋯	⋯	5.9 ± 0.8	⋯
	F3–79 keV	10−12 erg cm−2 s−1	⋯	⋯	22.3	⋯
(4)	χ2/d.o.f.	⋯	⋯	⋯	283.8/298	475.2/484
	NH	1022 cm−2	⋯	⋯	<1.8	2.7 ± 0.3
	Γ	⋯	⋯	⋯	${0.78}_{-0.05}^{+0.14}$	2.22 ± 0.09
	Ecut	keV	⋯	⋯	${15.5}_{-2.0}^{+2.8}$	${23.9}_{-4.9}^{+7.9}$
	Eline	keV	⋯	⋯	6.53 ± 0.05	⋯
	σline	keV	⋯	⋯	${0.30}_{-0.04}^{+0.06}$	⋯
	Nline	10−5 ph cm−2 s−1	⋯	⋯	6.4 ± 0.8	⋯
	F3–79 keV	10−12 erg cm−2 s−1	⋯	⋯	20.6	29.6
	CSwift	⋯	⋯	⋯	⋯	0.80 ± 0.07

Notes.

^aF_{3–79 keV} denotes the flux of the source as measured by NuSTAR between 3 and 79 keV. ^bIGR J10447–6027 analysis combines the two NuSTAR data sets (Obs. 1 and Obs. 2 referring to Obs. ID 3016003004 and 3016003002, respectively) and the two Swift/XRT spectra (the value obtained for the cross-calibration constant C_Swift is the same for both observations; this is why a single value is reported in this table).

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We note that the Swift/XRT calibration constant (C_Swift in Table 3) is between ∼40% and 80%, which is lower than expected for the cross-calibration error between NuSTAR and Swift/XRT (see, e.g., Madsen et al. 2017). This discrepancy can be partly explained by the shortness of the Swift/XRT exposure compared to the NuSTAR exposure, making it more sensitive to the short timescale variability of the sources, but this is likely not the only reason. However, careful investigation of our data selection and reduction procedure did not provide any obvious cause for the discrepancies.⁶ In order to check the impact of the possibly erroneous Swift/XRT data on the fit results, we first fixed C_Swift to be equal to 1. In this case, the fits worsen, but the parameters remain consistent with the ones presented in Table 3. Then, we also performed spectral fits of the NuSTAR data alone. The values obtained for models (1) and (2) are once again within the error bars of the ones presented in Table 3, except for IGR J20569+4940, which gives a higher column density (N_H = (6.2 ± 0.9) × 10²² cm⁻²) and a steeper power law (Γ = 2.70 ± 0.04).

Finally, for two sources identified as AGN, we tested the presence of a neutral Compton reflection component by fitting:

$$\begin{eqnarray}&&{\rm{const}}\ast {\rm{tbabs}}\ast {\rm{pexmon}}\end{eqnarray} \tag{ 5 }$$

and for the source identified as a CV/IP, we adjusted the NuSTAR spectrum with the physical model IPM developed by Suleimanov et al. (2005), also including reflection, partial absorption, and the iron fluorescent lines at 6.4 and 6.7 keV:

$$\begin{eqnarray}&&\begin{array}{l}{\rm{const}}\ast {\rm{tbabs}}\ast {\rm{pcfabs}}\ast ({\rm{reflect}}\ast {\rm{ipm}}\\ \qquad +\ {\rm{gauss}}+{\rm{gauss}}).\end{array}\end{eqnarray} \tag{ 6 }$$

This allows the source parameters to be directly compared to the two previous CV/IPs that are among the faint persistent IGR sources and were observed by NuSTAR (see Clavel et al. 2016; Tomsick et al. 2016b, for more details).

The soft X-ray and near-IR (NIR; 2MASS J10445192–6025115) counterparts of this source have been identified (Landi et al. 2010; Fiocchi et al. 2010). In particular, previous soft X-ray observations with Swift and Chandra show a strongly absorbed X-ray source with no sign of variability. The Chandra spectrum can be fit with an absorbed power law (N_H = (22 ± 3) × 10²² cm⁻², ${\rm{\Gamma }}={1.0}_{-0.6}^{+0.3}$) for a total unabsorbed flux of F_{0.3–10 keV} ∼ 1.7 × 10⁻¹² erg cm⁻² s⁻¹. More recently, NIR spectroscopy from Very Large Telescope (VLT)/Infrared Spectrometer and Array Camera (ISAAC) provided a redshift measurement of this source (z = 0.047 ± 0.001, Fortin et al. 2018) demonstrating the extragalactic nature of IGR J10447–6027, possibly a Seyfert 2 AGN.

3.1.1. NuSTAR Results

3.1.2. Supplementary Information

The Swift/XRT counterpart was identified by Landi et al. (2012). It is located at R.A. = 16^h18^m0802, decl. = −54°06'098 (6'' uncertainty), consistent with three USNO/2MASS sources. The short Swift/XRT exposure did not provide enough statistics to derive spectral information, but its flux was F_{2–10 keV} = 4 × 10⁻¹³ erg cm⁻² s⁻¹ (assuming a power law with Γ = 1.8 and Galactic absorption N_H,Gal = 0.6 × 10²² cm⁻²). The recent Chandra observation covering this source also pinpoints the position of its soft X-ray counterpart, which is consistent with a single WISE source having an infrared excess (Ursini et al. 2018).

3.2.1. NuSTAR Results

IGR J17404–3655 (R.A. = 265112, decl. = −36913; Bird et al. 2007) is referenced as an X-ray binary in SIMBAD,¹⁰ and IGR J17402–3656 (R.A. = 265087, decl. = −36936; Krivonos et al. 2007) is referenced as the open cluster NGC6400 in SIMBAD. However, from an INTEGRAL point of view, these two names refer to a single source, hereafter IGR J17402–3656 (e.g., Krivonos et al. 2012). Its soft X-ray (CXOU J174026.8–365537, Tomsick et al. 2009), NIR (2MASS 17402685–3666374, Landi et al. 2008), and optical (USNO-A2.0 0525–28851523, Masetti et al. 2009) counterparts have been identified.

The optical spectrum shows only a single narrow Hα emission line superimposed onto a red continuum, which is typical of X-ray binaries. Furthermore, its optical colors do not match any star of early spectral type (which might rule out an HMXB), and its spectral appearance does not show the numerous emission lines expected in dwarf nova CVs. Based on this information and the fact that the source is likely distant (substantial spectral absorption), Masetti et al. (2009) identified IGR J17402–3656 as an LMXB.

The Chandra spectrum is very hard (Γ ∼ −0.3, Tomsick et al. 2009), which would be very unusual for an LMXB, and is more commonly seen in either HMXBs that harbor more highly magnetized neutron stars or magnetic CVs. Moreover, the infrared spectrum obtained by Coleiro et al. (2013) shows that only the Brγ line is detected within the K_s-band. This line is mainly detected in supergiant and Be stars. Since no He i line was detected at 2.058 μm (generally present in supergiant stars), Coleiro et al. (2013) identified this source as a Be-HMXB candidate, even if the LMXB scenario could not be ruled out.

More recently, deeper infrared spectroscopy did detect the He i line, as well as Brγ and a weak C iv emission line (VLT/ISAAC, Fortin et al. 2018). Fortin et al. argue that the nondetection of Pfund emission rules out a hot B-type star and, based on the NIR study of CVs by Harrison et al. (2004), conclude that IGR J17402–3656 could be a CV with a K3–5 V companion if at a distance d = 530–700 pc.

3.3.1. NuSTAR Results

The NuSTAR lightcurve of IGR J17402–3656 shows no flaring activity, but there is a factor ∼2 variation between minimum and maximum count rates within the observation, consistent with the factor 2 difference observed between the fluxes previously measured by Chandra and Swift/XRT (both averaged over short observations, Landi et al. 2008; Tomsick et al. 2009).

We used the ${Z}_{1}^{2}$ (Rayleigh) test (Buccheri et al. 1983) to search for signals in the 3–24 keV lightcurve, making a periodogram extending from 0.0001 Hz (10,000 s) to 10 Hz. Between 1 and 322.5 s, there are no signals reaching the 3σ significance threshold (after accounting for trials). Starting from 322.58 s, there are five peaks above the 3σ threshold with increasing significance. Monte Carlo simulations of randomly distributed photon arrival times within the NuSTAR GTI reproduce these signals, with the first significant peak also at 322.58 s. Therefore, these peaks are not due to IGR J17402–3656 variability but to the discontinuity of the GTI. Between 0.1 and about 1 s, the IGR J17402–3656 periodogram has 12 peaks slightly above the 3σ significance threshold (none is above the 5σ threshold, and only two are above 4σ). To further understand the origin of these peaks, we folded the source light curve on 100,000 frequencies between 0.0001 and 10 Hz, using 10 phase bins. For each frequency, we then performed a fit of the folded light curve and recorded its amplitude, defined as the difference between maximum and minimum count rates divided by the sum of these two quantities. The folded lightcurves obtained at the peak frequencies are consistent with being constant (χ² ≪ 1) and have amplitudes ranging from 9.0% to 12.2%. So the 12 peaks described above are likely signatures of aperiodic variability. Furthermore, 95% of folded lightcurves corresponding to periods ranging from 0.1 to 322.58 s have amplitudes below 9.2%. Based on this 2σ upper limit on periodic signals in the 3–24 keV band, we cannot exclude the presence of a spin pulsation signal such as anticipated for CV/IPs (these spin modulations are energy dependent, and their amplitude in the NuSTAR band is limited, see e.g., Tomsick et al. 2016b).

The NuSTAR spectra are best fit by an absorbed thermal component, having a temperature kT ∼ 30 keV, plus a strong emission line around 6.55 keV (equivalent width EW ∼ 640 eV). The overall absorption fitted with this simple model (N_H ∼ 5 × 10²² cm⁻²) is higher than the value expected for Galactic absorption only (N_H,Gal = 0.6 × 10²² cm⁻²).¹¹ The temperature found is too high for an LMXB (e.g., Tauris & van den Heuvel 2006), while the properties of the emission line do not match what has been observed in HMXBs (Torrejón et al. 2010; Giménez-García et al. 2015). Instead, this spectrum is fully consistent with what is expected for a magnetic CV (e.g., Mukai 2017). To further investigate the physical parameters of this Galactic source, we adjust its spectrum with model (6). The best-fit parameters are listed in Table 4 and are fully consistent with other known IPs, such as IGR J18293–1213, which was also identified thanks to the NuSTAR Legacy program (Clavel et al. 2016).

Table 4.  Spectral Parameters Obtained by Fitting the IPM Model to the NuSTAR Spectra of IGR J17402–3656 (χ²/d.o.f. = 284.4/297)

Model	Param.a	Unit	Best Fit
tbabs	NH	1022 cm−2	0.6 (fixed)
pcfabs	NH,pc	1022 cm−2	${45}_{-16}^{+18}$
	fraction	⋯	0.52 ± 0.06
reflect	Ω/2π	⋯	1.0 (fixed)
	A	⋯	>0.55
	AFe	⋯	1.0 (fixed)
	cos α	⋯	>0.42
ipm	Mwd	M⊙	${0.73}_{-0.07}^{+0.08}$
	F3–79keV	10−3 ph cm−2 s−1	1.3 ± 0.3
Gauss	${E}_{\mathrm{Fe}{\rm{K}}\alpha }$	keV	6.4 (fixed)
	${\sigma }_{\mathrm{Fe}{\rm{K}}\alpha }$	eV	50 (fixed)
	${{\rm{N}}}_{\mathrm{Fe}{\rm{K}}\alpha }$	10−5 ph cm−2 s−1	2.6 ± 0.8
Gauss	${E}_{\mathrm{Fe}\mathrm{xxv}}$	keV	6.7 (fixed)
	${\sigma }_{\mathrm{Fe}\mathrm{xxv}}$	eV	50 (fixed)
	${{\rm{N}}}_{\mathrm{Fe}\mathrm{xxv}}$	10−5 ph cm−2 s−1	2.6 ± 0.7

Notes. The uncertainties listed correspond to 90% confidence intervals. The normalization constant is fixed to 1 for FPMA and is 1.00 ± 0.03 for FPMB. The X-ray flux of the source is 2.0 × 10⁻¹¹ erg cm⁻² s⁻¹ in the 3–79 keV range.

^aParameters of the reflect model are: the reflection scaling factor (Ω/2π, set to 1 for an isotropic source above a disk), the abundance of elements heavier than He relative to solar (A), the iron abundance relative to the previous one (A_Fe), and the inclination angle of the white dwarf magnetic field (α). In the ipm model, M_wd refers to the mass of the white dwarf.

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3.3.2. Supplementary Information

Landi et al. (2010) identified the soft X-ray (later named 1SXPS J205642.6+494009 in Swift catalogs, e.g., Evans et al. 2014), NIR (2MASS J20564271+4940068), and radio (NVSS 205642+494005) counterparts of IGR J20569+4940. In the radio counterpart, the source is bright and has a 2.8–11 cm flat spectral index of −0.4 (Reich et al. 2000), making it a likely radio-loud object, i.e., either a microquasar or a blazar (Landi et al. 2010). This source is also associated with a Fermi source (2FGL J2056.7+4939, Martí et al. 2012), which was classified as a blazar candidate in the last Fermi catalog (3LAC J2056.7+4938, Ackermann et al. 2015), and it has recently been detected in the TeV energy range by the Very Energetic Radiation Imaging Telescope Array System (VERITAS; Mukherjee & VERITAS Collaboration 2016).

IGR J20569+4940 also appears to be variable both in radio (listed in the Variable 1.4 GHz radio sources from NVSS and FIRST, Ofek & Frail 2011) and in X-rays (fluxes different by a factor 2 reported for XMMSL1 J205642.7+494004 on the timescale of hours, Landi et al. 2010).

3.4.1. NuSTAR Results

3.4.2. Optical Spectrum

In complement of the NuSTAR Legacy program, we obtained a spectrum from the Keck LRIS from two 900 s integrations on UT 2016 August 6 (PI: F. Harrison) centered on the candidate optical counterpart to IGR 20569+4940 (see Figure 7). The object is extremely red and featureless (other than telluric absorption). This is compatible with a highly absorbed BL Lac object optical spectrum, as expected from both the high Galactic absorption in the direction of IGR J20569+4940 (N_H,Gal = 1 × 10²² cm⁻²) and the column density derived from the X-ray spectra.

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Taking full advantage of the better sensitivity and higher spectral resolution of NuSTAR, we have been successfully investigating the fainter population associated with the unidentified INTEGRAL sources, focusing only on persistent sources (see also Lutovinov et al. 2013).

NuSTAR provided crucial inputs for the spectral studies of three magnetic CVs (see also Clavel et al. 2016; Tomsick et al. 2016b) and three AGNs. The corresponding unfolded spectra are presented in Figure 8. The spectral coverage extending up to ∼80 keV allowed for a constraint on the intrinsic hardness of the sources with, for instance, measurements of Bremsstrahlung temperatures above kT ≳ 15 keV for all sources classified as IPs (Figure 8, right panels). The iron line properties also were revealed to be a compelling NuSTAR diagnostic for our study since they are particularly prominent in magnetic CVs (Figure 8, right panels), and a reshifted reflected emission was also detected in one of the extragalactic sources (see Section 3.2.1). In addition, variability studies performed on the NuSTAR lightcurves were powerful tools to describe the properties of faint IGR sources, especially the detection of eclipses in IGR J18293–1213 (Clavel et al. 2016) and the confirmation of both a pulsation period and a decrease of the pulse fraction with energy in IGR J14091–6108 (Tomsick et al. 2016b). Therefore, combined with observations at other wavelengths, NuSTAR can be efficiently used to classify faint hard X-ray sources toward the Galactic plane and to better constrain their individual characteristics.

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Among the sample observed by NuSTAR, three CVs were identified, which is not surprising since this population of Galactic sources is expected to be dominant at low fluxes (see, e.g., Lutovinov et al. 2013). The individual properties of these three sources are consistent with the overall population of hard X-ray sources already classified as CV/IPs (see e.g., Pretorius & Mukai 2014; Schwope 2018), and constraints on their distance demonstrate that they are relatively fainter only because they are further away. Moreover, the classification of IGR J14091–6108, IGR J17402–3656, and IGR J18293–1213 as CV/IPs highlights the importance of X-ray diagnostics in pinpointing the right identification for this type of source, whereas optical or infrared spectral information alone may be misleading (see, e.g., Section 3.3). Therefore, deep X-ray observations would help classify the remaining unidentified IGR sources listed in Table 1, including IGR J18256–1035, which is currently classified as an LMXB candidate (Masetti et al. 2013, mostly based on its optical spectrum), although this is in contradiction with the hard spectrum measured by Chandra (Tomsick et al. 2008). These diagnostics are similar to the ones we originally had for IGR J17402–3656, which has now been classified as a CV/IP based on its NuSTAR spectrum.

The successful identification of several faint persistent IGR sources summarized in Table 1 allows for new constraints on the surface density of HMXBs toward low fluxes. To derive the logN-logS from the properties of known persistent HMXBs, we use the following equation, which also accounts for the incompleteness of the source classification:

$$\begin{eqnarray}&&N\left(\gt {f}_{X}\right)=\displaystyle \sum _{\mathop{i=1}\limits_{{f}_{i}\gt {f}_{X}}}^{{n}_{\mathrm{src}}}\displaystyle \frac{{P}_{i}}{A\left({f}_{i}\right)},\end{eqnarray} \tag{ 7 }$$

where n_src is the total number of IGR sources considered as HMXBs, HMXB candidates, or unidentified; P_i is the probability of each source i of flux f_i to be an HMXB; and A is the sky coverage corresponding to the INTEGRAL catalog used for the present study (Krivonos et al. 2012, but restricted to $| b| \lt 5^\circ$). In this work, we consider all 53 HMXBs listed in Lutovinov et al. (2013, Table 1) to have P_i = 1. The probability P_i of the former HMXB candidate IGR J17586–2129,¹³ recently identified as a CV (Fortin et al. 2018), is instead set to zero. Then, we add the 20 previously unidentified sources listed in Table 1 with the following probabilities: P_i = 1 for the 2 sources now identified as HMXBs, P_i = 0 for the 18 sources for which the persistent HMXB identification is ruled out, P_i = 0.5 for the source identified as a pulsar (either high- or low-mass X-ray binary), and following our HMXB detection rate, P_i = 0.1 for the remaining 5 unidentified sources (see Table 1). The result is shown as an orange line in Figure 9. The 95% confidence interval corresponding to our best prediction was computed using the bootstrap method. To show the full range allowed for N(>f_X) by the present data set, extreme cases where the pulsar and the five unidentified sources are all set to either HMXBs (P_i = 1) or non-HMXBs (P_i = 0) are also displayed in Figure 9.

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We compare our results with the continuous extension of the luminosity function of persistent HMXBs anticipated by Lutovinov et al. (2013) in the flux range that can be investigated with INTEGRAL. Based on this hypothesis, they predicted that there should be at least 12 HMXBs having a flux below F_{17–60 keV} < 1 × 10⁻¹¹ erg cm⁻² s⁻¹ within their sample and possibly up to 14% more, when correcting their function for the number of known HMXBs with unknown distances that were not included in their study. This gives a probability between P_i = 6/26 and P_i = 7.68/26 for the 26 sources that were unidentified at the time. The corresponding range of surface densities is reported by the bold black line in Figure 9and is significantly above our best prediction.

Six sources, including the pulsar XTE J1824–141, are still unidentified. We cannot exclude the possibility that four of these sources could be HMXBs, in which case their surface density would be in full agreement with the prediction of Lutovinov et al. (2013). However, given the ratio of HMXBs currently identified among the faint IGR sources, this scenario seems unlikely. Instead, the confidence interval associated with what we believe to be a reasonable prediction (one of the six unidentified sources is expected to be an HMXB) is showing a significant deviation from the continuous extension proposed by Lutovinov et al. (2013), pointing toward a lower number of persistent HMXBs toward low fluxes. If this is confirmed, the break in the log N-log S could be right below F_{17–60 keV} ∼ 1 × 10⁻¹¹ erg cm⁻² s⁻¹ (see Figure 9).

Multiwavelength efforts to identify the nature of IGR J17315–3221, AX J1753.5–2745, XTE J1824–141, IGR J18497–0248, IGR J19113+1413, and Swift J2037.2+4151 will be key to test the trend described above. However, to fully understand accretion processes occurring in persistent HMXBs, it will be important to also enlarge the sample of classified faint hard X-ray sources. In this respect, the latest INTEGRAL Galactic plane survey catalog contains a set of 72 newly detected sources, including 59 below F_{17–60 keV} < 1 × 10⁻¹¹ erg cm⁻² s⁻¹ (Krivonos et al. 2017). Most of these faint sources have no clear identification yet, but once they do, adding this sample to our study will also improve the description of the logN-logS for F_{17–60 keV} = 10⁻¹²–10⁻¹¹ erg cm⁻² s⁻¹.

In parallel, NuSTAR has also been used to constrain the surface density of hard X-ray sources below the detection limit of INTEGRAL. The NuSTAR serendipitous survey and the survey of the Norma arm region led to the detection of four new HMXB candidates. Nevertheless, with no secure classification, it is also not yet possible to discriminate between the different predictions regarding the number of persistent HMXBs at these even fainter fluxes (Fornasini et al. 2017; Tomsick et al. 2017).