FIRST HARD X-RAY DETECTION OF THE NON-THERMAL EMISSION AROUND THE ARCHES CLUSTER: MORPHOLOGY AND SPECTRAL STUDIES WITH NuSTAR

The Arches cluster (G0.12+0.02; Cotera et al. 1996; Serabyn et al. 1998) is a massive star cluster with a core that is about 9'' (∼0.35 pc at 8 kpc) in radius (Figer et al. 1999), with an average mass density of ∼3 × 10⁵ M_☉ pc⁻³, containing more than 160 O-type stars (Figer et al. 2002). The Arches cluster is located in the inner Galactic center (GC) region at the projected angular distance of 11' from the dynamic center of the Galaxy—Sagittarius A* (Sgr A*).

The first serendipitous Chandra observations of the Arches cluster region revealed two bright sources (A1 and A2) located in the cluster's core which are surrounded by the cluster's diffuse X-ray emission (Yusef-Zadeh et al. 2002). A1 was later resolved into two distinct bright sources: A1N and A1S by Law & Yusef-Zadeh (2004) and Wang et al. (2006). Subsequent dedicated campaigns revealed a complicated picture of the Arches cluster X-ray emission, using spectral and morphological studies to establish the presence of thermal and non-thermal emission components. The thermal emission is thought to originate from multiple collisions between strong winds of massive stars (Chlebowski & Garmany 1991; Yusef-Zadeh et al. 2002; Wang et al. 2006; Capelli et al. 2011a). Diffuse non-thermal X-ray emission has been detected from a broad region around the cluster (Wang et al. 2006; Tsujimoto et al. 2007; Capelli et al. 2011b; Tatischeff et al. 2012). The non-thermal nature of this extended radiation is revealed by its bright fluorescent Fe Kα 6.4 keV line emission. The Fe Kα line at 6.4 keV, which is due to Fe that is neutral or in a low ionization state, is produced by ejecting a K-shell electron, either by hard X-ray photoionization from an external X-ray source, or by the collisional ionization induced by cosmic-ray (CR)-accelerated electrons or ions (mainly protons and α-particles).

The mechanism producing the fluorescent line emission around the Arches cluster is not completely understood. The fluorescence may be the result of irradiation of the cloud by hard X-ray photons with energies above 7.1 keV (the K-edge of neutral iron). The required X-ray illumination might be associated with a nearby transient X-ray source (e.g., Churazov et al. 1993, for 1E1740.7-2942) or with past activity of Sgr A*, as suggested by Sunyaev et al. (1993) to explain the fluorescent line emission of the giant molecular cloud Sgr B2 in the GC region (Koyama et al. 1996; Sunyaev & Churazov 1998; Murakami et al. 2000; Revnivtsev et al. 2004a; Terrier et al. 2010). Alternatively, the excitation of cold material might be through the collisional ionization by CR particles (e.g., Predehl et al. 2003; Yusef-Zadeh et al. 2007; Dogiel et al. 2009). Tatischeff et al. (2012, hereafter T12) argued that bright 6.4 keV line structures observed around the Arches cluster are very likely produced by bombardment of molecular gas by energetic ions, and they disfavored the possibility of accelerated electrons. T12 suggest that the required large flux of low-energy cosmic ray (LECR) ions could be produced in the ongoing supersonic collision between the star cluster and a nearby molecular cloud.

Previously, the lack of spectral and morphological studies above 10 keV precluded us from building a complete picture of the Arches cluster non-thermal emission and from making a definitive conclusion about the ionizing mechanism. With the first focused observations of the Arches cluster in the hard X-ray domain, we can shed light on the cause of the non-thermal X-ray emission detected around the cluster.

We assume a distance of 8 kpc to the GC (Gillessen et al. 2009) and the Arches cluster. Section 2 of the paper describes the Nuclear Spectroscopic Telescope Array (NuSTAR) observations and data reduction. In Section 3, we study the morphology of the Arches cluster using two-dimensional (2D) image fitting procedures and wavelet image decomposition techniques. In Section 4, we present a spectral analysis using the background approach specially developed for NuSTAR observations. The main results are discussed in Section 5 and summarized in Section 6.

We observed Arches cluster during the GC region campaign with the NuSTAR (Harrison et al. 2013) in 2012 October. NuSTAR operates in wide energy band from 3 to 79 keV, carrying two identical co-aligned X-ray telescopes with an angular resolution of 18'' (FWHM). The focal planes of each telescope, referred to as focal plane module A and B (FPMA and FPMB), provide a spectral resolution of 400 eV (FWHM) at 10 keV.

The first part of the survey was carried out in the inner GC region covering the area between Sgr A* and the persistent low-mass X-ray binary 1E 1743.1–2843 located 19' away (Porquet et al. 2003b; Del Santo et al. 2006). The Arches cluster serendipitously appears in the three NuSTAR observations listed in Table 1.

We processed the data from both modules using the NuSTAR Data Analysis Software (NuSTARDAS) v1.2.0, the 2013 June 28 version of the NuSTAR Calibration Database (CALDB), and HEASOFT v6.13. The data were filtered for periods of Earth occultation, high instrumental background due to South Atlantic Anomaly passages, and known bad/noisy detector pixels.

The NuSTAR detectors are not entirely shielded from X-rays that pass outside the X-ray optics modules and fall directly onto the detectors. Such an unfocused flux or "stray-light" can be significant if there are bright X-ray sources within 2–3 deg of the NuSTAR field of view. Stray-light from a point source has a uniform distribution on the detector and can be easily removed based on a geometrical model of the telescopes. We masked out the stray-light region of the FPMB detector (FPMA is clean) caused by two bright sources: GX 3+1 and the transient Swift J174510.8-262411 (see, e.g., Vovk et al. 2012 and references herein), which was active at the time of the NuSTAR observations. The contaminated detector pixels have been flagged as "bad" and removed from the analysis at the stage of data screening in the NuSTARDAS pipeline run. The observation 40010003001 (FPMB) has been completely disregarded because stray-light completely covered the Arches cluster region.

Stray-light photons from the extended sources and known celestial X-ray backgrounds cannot be so easily removed because they fill the whole detector area and have a non-uniform pattern depending on the emission morphology. We treated this background differently for the imaging and spectral analysis. Regarding the former, the non-uniform background of the individual observations is effectively averaged when it is combined into the mosaic, and therefore, can be considered as nearly flat (however, see the discussion in Section 3.1). In contrast, the non-uniformity of the background has a noticeable effect on the spectral analysis since it is done for individual observations. To overcome this issue we applied the approach described in Section 4.

After running the pipeline and screening the data, we end up with event lists for five NuSTAR observations containing the Arches cluster at different off-axis angles (Table 1). Note that the source appears at large off-axis distances, which causes the reduction of the efficiency (vignetting) and strong Point Spread Function (PSF) distortion. The total nominal (effective) dead-time corrected exposure time of 122.5 (76.7) ks comprises 73.8 (44.7) ks and 48.7 (32.1) ks for FPMA and FPMB, respectively.

The data from both detector modules were used to construct the mosaic images (Figure 1) around the Arches cluster in different energy bands. We used the 3–10 keV NuSTAR band as a proxy for the standard 2–10 keV energy range; 6–7 keV band as containing Fe Kα emission lines at 6.4 and 6.7 keV, which are unresolved by NuSTAR; and 10–20 keV as a hard X-ray band specific to NuSTAR. The mosaics in the energy bands 3–79, 20–40, and 40–79 keV are also shown in Figure 1. For each image an average (local) background level was determined within an annular region centered on the Arches cluster, as defined in Table 2 and illustrated in Figure 2. The background estimate was subsequently subtracted from each individual image, prior to the construction of the image mosaic. This is done because FPMB has a higher background count rate than FPMA, requiring that we adjust the relative detector background normalizations between modules. Note that the visible gradient in Figure 2 is produced mainly by the emission from the GC molecular clouds (see, e.g., Ponti et al. 2010).

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Table 2. Definitions of the Sky Regions

R.A. (J2000)	Decl. (J2000)	Parameters
Cluster (circle)
17h45m503	−28°49'19''	15''
Cloud (ellipse)
17h45m510	−28°49'16''	25'', 59'', 155°
17h45m503	−28°49'19''	15'' (excl.)
Background (annulus)
17h45m503	−28°49'19''	185''
17h45m503	−28°49'19''	100'' (excl.)

Notes. Central position and radius for circular regions, and semi-minor/major axes and rotation angle for the elliptical regions. The rotation is defined counter clockwise relative to North (upward). "Cluster" and "Cloud" regions are illustrated in Figure 1. The excluded regions are marked as "excl."

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The exposure map, utilized for mosaic creation, has not been corrected for vignetting effects. We checked that the vignetting correction does not significantly improve the results of the imaging analysis. Hereafter, we assume no vignetting correction unless otherwise stated.

The primary goal of the current paper is to study the non-thermal emission surrounding the Arches cluster. The emission is revealed by fluorescent Fe Kα 6.4 keV line, as has been observed by XMM-Newton and reported in the recent papers by Capelli et al. (2011a) and T12. We adopted T12 sky regions describing the core of the Arches cluster prominent in Fe Kα 6.7 keV line ("Cluster" region) and the surrounding region characterized by the fluorescent 6.4 keV line (called "Cloud" region). The 6.7 keV line, attributed to the cluster core, originates from the hot, thermally ionized plasma, probably from the colliding winds of the massive stars. The 6.4 keV line emission clearly extends beyond the Arches cluster core, and comes from material in neutral or low ionization states filling (in projection) an extended area represented by an ellipse as illustrated in Figure 1. The ellipse is oriented approximately in the north–south direction with increased brightness to the south. The parameters of the background and reference regions are listed in Table 2.

3.1. Cluster Emission

The Arches cluster has been relatively well studied in the standard 2–10 keV energy band with the Chandra and XMM-Newton observatories. Close attention has been paid to the central part of the cluster, where thermal emission, thought to be from colliding winds of giant stars, is observed. With data from NuSTAR, we can obtain new insight into the hard X-ray emission of the Arches cluster. However, even with angular resolution that is unprecedented for hard X-ray astronomy (18'' FWHM), it is challenging to resolve emission in the core, which has a radius of ∼15''.

The 3–10 keV mosaic (Figure 1) demonstrates a strong excess in the core of the Arches cluster and apparent extended emission around it. To decouple these emission components and find the centroid position of the core, we fitted a spatial model convolved with an averaged PSF on the combined data set using the Sherpa package (Freeman et al. 2001), which is part of the CIAO-4.5¹² software (Fruscione et al. 2006).

To make a PSF function representing the average over the different source offsets in the ObsIDs, we used the inflight-calibrated PSF shape stored in the CALDB. The PSF images were weighted according to the exposure time of each data set. The resulting averaged PSF is shown in Figure 3. Its shape is strongly distorted because of the large off-axis angles (on-axis PSF would be symmetric). Importantly, the PSF elongation is not co-aligned with the 6.4 keV line cloud region. For the fitting procedure, we assume no significant change of PSF shape inside the radius of 60'' around the Arches cluster (see below). Note that 90% of the averaged PSF encircled energy is situated at or inside of the inner radius of the annular region used for the background estimation, depending on the adopted energy used. Using this fact, we estimated the background count rate in the separate fitting procedure without PSF convolution.

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Given the spatial extent of the emission around the Arches Cluster as found by Chandra and XMM-Newton, we want to confirm whether we can resolve this same emission with NuSTAR. This will give us confidence that we may also be able to spatially resolve the Arches cluster above 10 keV.

We represented the Arches cluster core emission by a 2D Gaussian. Due to the low count rate per pixel, we used Poisson statistics in the fitting procedure. The background term has been constrained in the annulus region shown in Figure 2. After running the fitting procedure with the 2D Gaussian model, we found that the 3–10 keV emission from the Arches cluster was not acceptably fitted with a single point source, and an extended "halo" around the cluster had to be considered. This finding is in line with the detection of extended emission surrounding the Arches cluster as observed by Chandra and XMM-Newton (Yusef-Zadeh et al. 2002; Law & Yusef-Zadeh 2004; Wang et al. 2006).

We constrained the fitting area to a circle centered on the core and extending to a radius of 60''. The model includes (1) a narrow 2D Gaussian of fixed width (4'' FWHM, chosen to emulate the PSF smearing effect caused by incomplete aspect reconstruction), representing the cluster's core, (2) a wide 2D Gaussian describing the halo, and (3) a constant background term. Note that the visible in Figure 2 background gradient has no significant effect on the fitting procedure. The best-fit model parameters are listed in Table 3. Figure 4 shows the radial profile of the Arches cluster intensity distribution centered at the best-fit position of the core.

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Table 3. Best-fit Model Parameters for the PSF Fitting Procedure of the 3–10 keV Arches Cluster Core and Halo Emissions

Parameter	Value
Background (constant)
Norm. (× 10−5)	1.18 ± 0.01 counts s−1 pixel−1
Core (2D Gaussian)
Center R.A.a	17h50m5043
Center Decl.a	−28°49'2307
FWHM	40 (fixed)
Norm. (× 10−3)	2.2 ± 0.3 counts s−1 pixel−1
Halo (2D Gaussian)
Center R.A.a	17h45m5062
Center Decl.a	−28°49'4717
FWHM	$72{\buildrel{\prime\prime}\over{.}} 4^{+6{\buildrel{\prime\prime}\over{.}} 7}_{-4{\buildrel{\prime\prime}\over{.}} 7}$
Norm. (× 10−5)	$1.77^{+0.45}_{-0.37}$ counts s−1 pixel−1
Cash statistic	4661.91
Degrees of freedom	2820

Note. ^aJ2000 epoch, the 1σ positional uncertainty is less than 2'' and 6''–8'' for the core and halo components, respectively; see 2D confidence regions in Figure 6 for details. Model normalization factor is marked as "Norm."

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To demonstrate a surface brightness distribution of the Arches cluster halo, we show in Figure 5 the residuals after subtracting off a best-fit point source corresponding to the core emission.

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The position of the cluster's core is spatially consistent with the brightest source, A1, detected by Chandra in the Arches cluster (Yusef-Zadeh et al. 2002) and later resolved into the two sources A1S/N (Law & Yusef-Zadeh 2004; Wang et al. 2006). Figure 6 shows confidence regions for the position uncertainty of the core and halo components.

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Note that due to the NuSTAR optics design, the celestial coordinates of each incoming photon are determined during the post-processing. This task is complicated by distortions due to thermal bending and external forces acting on the mast during orbit. The systematic offset of the source position determination can be as high as 10''. However, the fact that the position of the Arches cluster core emission detected with NuSTAR is in agreement (within the angular separation of ∼15) with the catalogued coordinates of the two bright Chandra sources A1S/N, tells us that the described systematic offsets are negligible for these observations.

Our ability to centroid a weak source with NuSTAR is also subject to uncertainties based on how positions are probabilistically assigned to photons in the NuSTARDAS pipeline and the finite spatial resolution of the NuSTAR pixels. To estimate any scatter introduced by this process, we ran the NuSTARDAS pipeline 50 times, repeated out analyses, and found that the sky position of the Gaussian core has an rms scatter of 09. We adopt this as the systematic error on the cluster core position.

The width of the 2D Gaussian halo model component does not have strong physical meaning since this component is used specifically to describe local background of the core. However, we should note that the center position of the halo component does not coincide with the core centroid, and the trend suggests that the halo centroid falls outside the Arches cluster (Figure 6).

3.2. Wavelet Decomposition

We studied in Section 3.1 the morphology of the Arches cluster in the 3–10 keV band fitting data with a parametric model. We constrained the central part of the cluster, determined its centroid position, flux, and revealed strong excess outside the cluster core. Since we observe extended emission with a complicated projected morphology, it becomes quite difficult to represent this emission with an analytical model, i.e., to parameterize it. In this case, non-parametric methods can be used for morphological studies. One such method is a wavelet image transform.

For the decomposition of NuSTAR images in different energy bands, we used the so called à trous digital wavelet transform algorithm (Starck & Murtagh 1994; Slezak et al. 1994; Vikhlinin et al. 1997; Krivonos et al. 2010). The main advantage of this algorithm over other wavelet methods is the fact that it decomposes the image into a linear combination of layers or "scales," each of them emphasizes the structures with a characteristic size of ≈2^{J − 1} pixels, which is 2^J arcsec in the case of our NuSTAR mosaic image resolution (1 pixel = 2''). Thus, low (high) J values correspond to small (large) spatial variations. We used the WVDECOMP wavelet decomposition code developed by Vikhlinin et al. (1995, 1998) as a part of ZHTOOLS software package.¹³

We ran WVDECOMP on mosaic images for scales 1–7 (2''–128''), detecting all significant structures above the 5σ level. To keep the photon statistics on the images, we provided counts and exposure maps to WVDECOMP. As mentioned in Section 3, FPMB has a higher background count rate than FPMA. In fact, this can mimic extended structures on the exposure-corrected image. To diminish this effect, we built the background map for a given observation by multiplying the exposure map and background count rate measured in the annulus region shown in Figure 2. The individual background maps were combined into the mosaic and used as a part of the WVDECOMP algorithm.

Figure 7 shows wavelet scales 3–6 of the Arches cluster mosaic images in 3–10, 6–7, and 10–20 keV. The lowest scales (1, 2) do not contain significantly detected (5σ) structures. The highest scale (7) contains large-scale diffuse background attributed to the Galactic center molecular complex zone (Ponti et al. 2010) and Galactic Ridge X-ray Emission (GRXE; see, e.g., Revnivtsev et al. 2006). We combined scales 3–6, which only contain structures related to the Arches cluster into the mosaics shown in Figure 8. The main results from the WT decomposition can be summarized as follows (refer to Figures 7 and 8).

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3–10 keV. The core of the Arches cluster is clearly visible on the scales J = 3–4 and the halo emission is revealed on scale J = 5. The apparent position of the halo is consistent with fitting results in Section 3.1 showing a shifted position with respect to the cluster core.

6–7 keV. This energy band contains two blended Fe Kα lines at 6.4 and 6.7 keV. We speculate that these lines appear at scales J = 4 (6.7 keV) and J = 5 (6.4 keV). The 6.7 keV line is spatially consistent with core emission, while the 6.4 keV line emission follows the cloud region as expected. These results are in full agreement with XMM-Newton observations (T12). In contrast to the 3–10 keV band, the 6.7 keV line emission distribution does not demonstrate high-frequency detection at J = 3, which may indicate its broader spatial distribution in comparison with the 3–10 keV continuum emission of the Arches cluster. However, we should note that the 6–7 keV mosaic image is not continuum subtracted.

10–20 keV. The Arches cluster does not show any significant (>5σ) point-like structures in the core region, which is expected due to the rapid fall of the ∼1.7 keV thermal emission above 10 keV. On the other hand, the hard X-ray emission is significantly detected at scales J = 5–6. Note that the observed extended structure cannot be caused by the wide wings of the PSF—as is demonstrated in Figure 3, the PSF shape is not aligned with the cloud region morphology. The observed 10–20 keV continuum emission apparently coincides with Fe Kα fluorescent 6.4 keV line emission observed with XMM-Newton (T12). According to T12, the 6.4 keV line emission demonstrates brightening in the south-east part of the ellipse, which is also noticeable at scale J = 5.

20–40 keV. The mosaic map of the Arches cluster shown in Figure 1 does not allow to make a definitive conclusion about the source detection. However, wavelet decomposition shows weak excess at scale J = 6. This fact is implicitly confirmed by detection of the emission up to 40 keV in the spectral analysis of Section 4. The apparent hard X-ray emission is located outside the cluster and consistent with general extent of 10–20 keV emission.

We extracted spectral information for the Arches cluster from the circular region with radius of 50'' centered at the cluster's core (Table 2), including the core and extended emission. The spectra have been extracted from all observations using the nuproducts task applying PSF and ghost ray corrections to the effective area Ancillary Response File.

The extraction of the corresponding background spectra is complicated by the strong CXB and GRXE stray-light illumination causing a non-uniform pattern on the detectors with a gradient of a factor of two. For that reason, the background spectrum extracted from the source-free region over- or underpredicts the background count rate at the position of the source. This difficulty (not relevant for spectra of bright sources) causes strong systematic noise for the background-subtracted spectrum of weak sources such as Arches. To overcome this, we use the fact that the stray-light background does not significantly change for sky pointings separated by only 10'–20', and therefore we utilize nearby observations. Note that this method differs from that used in the imaging analysis. In the paired observation, we extract the background spectrum from the same detector region where the Arches cluster was observed. Obviously, this region should not contain any other diffuse or point-like source or stray-light from nearby bright sources. Table 4 lists the observations used for source and background spectrum extraction. For ObsID 40010006001, we had three observations which were suitable for background spectrum extractions and thus averaged together for better statistics.

Using the above-mentioned method, we have constructed one FPMB and three FPMA spectra. The latter have been further grouped together using the FTOOL task MATHPHA. The corresponding background spectra and responses have been averaged accordingly. Finally, we have grouped spectrum channels to have at least 30 counts bin⁻¹ using GRPPHA tool. Figure 9 shows the FPMA and FPMB spectra of the Arches cluster.

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According to the morphological studies presented in Section 3, we attribute the hard spectral component above 10 keV to the fluorescing cloud around the Arches cluster.

We first approximated the observed spectra with the collisionally ionized plasma emission model APEC representing the cluster's core thermal emission, and a non-thermal power-law continuum with a Gaussian line at 6.4 keV, modeling the cloud emission outside the cluster (Figure 9). Due to the fact that NuSTAR has a limited spectral resolution, the centroid energy of the Gaussian line and its width have been fixed at 6.4 keV and 0.1 keV, respectively. All the emission components were subject to a line-of-sight photoelectric absorption model WABS in XSPEC. The fitting procedure does not allow us to constrain the absorption, and we fixed it at N_H = 9.5 × 10²² cm⁻² measured by T12 (also using WABS) in the core of the Arches cluster. The metallicity of the X-ray emitting plasma was not constrained either, and we fixed it to Z = 1.7 Z_☉ as per T12. The best-fit results obtained with this model (referred to as model 1 in the discussion) are shown in Table 5. All fitted parameters in this table and in the following discussion contain uncertainty estimation at the 90% confidence level.

Table 5. Spectral Analysis of the Arches Cluster X-Ray Emission.

Parameter	(Unit)	Model 1	Model 2	Model 3
C		1.06 ± 0.14	1.05 ± 0.14	1.07 ± 0.14
NH	(1022 cm−2)	9.5 (fixed)	9.5 (fixed)	9.5 (fixed)
Z/Z☉		1.7 (fixed)	1.7 (fixed)	1.7 (fixed)
kT	(keV)	$1.76^{+0.36}_{-0.29}$	$1.69^{+0.31}_{-0.26}$	$1.64^{+0.37}_{-0.23}$
IkT	(see notes)	$36.0^{+17.8}_{-12.9}$	$39.6^{+16.7}_{-11.9}$	$43.2^{+16.9}_{-15.0}$
E6.4 keV	(keV)	6.4 (fixed)	⋅⋅⋅	⋅⋅⋅
F6.4 keV	(10−5 ph cm−2 s−1)	1.24 ± 0.5	⋅⋅⋅	⋅⋅⋅
Γ		1.62 ± 0.31	⋅⋅⋅	⋅⋅⋅
Ip.l.	(10−12 erg cm−2 s−1 over 3–20 keV)	$1.49^{+0.26}_{-0.24}$	⋅⋅⋅	⋅⋅⋅
EW6.4 keV	(keV)	$1.1^{+0.7}_{-0.5}$	⋅⋅⋅	⋅⋅⋅
Λ	(H-atoms cm−2)	⋅⋅⋅	5 × 1024 (fixed)	⋅⋅⋅
s		⋅⋅⋅	$1.65^{+0.59}_{-0.55}$	⋅⋅⋅
Emin	(keV/n)	⋅⋅⋅	104 (fixed)	⋅⋅⋅
NLECR	(10−8 erg cm−2 s−1)	⋅⋅⋅	$8.08^{+1.82}_{-1.62}$	⋅⋅⋅
ΓRX		⋅⋅⋅	⋅⋅⋅	2.93 ± 0.31
ξ	(erg cm s−1)	⋅⋅⋅	⋅⋅⋅	10 (fixed)
IRX	(10−5)	⋅⋅⋅	⋅⋅⋅	6.09 ± 5.00
Reduced χ2 (d.o.f.)		0.91 (134)	0.89 (136)	0.91 (140)

Notes. Model 1: C × WABS × (APEC + Gaussian + power law); Model 2: C × WABS × (APEC + LECRp); Model 3: C × WABS × (APEC + REFLIONX). The cross-calibration constant term C is fixed at unity for FPMA data and fitted for FPMB. The absorption column density is noted as N_H. APEC thermal plasma model is characterized by kT, Z/Z_☉, and I_kT parameters, respectively, describing temperature, metallicity relative to solar, and normalization in units of 10⁻¹⁸∫n_en_HdV/(4πD²), where n_e and n_H are the electron and proton number densities in units of cm⁻³, and D is the distance in cm. E_6.4 keV and F_6.4 keV: centroid energy and flux of the neutral or low-ionization Fe Kα line. Γ and I_p.l.: index and 3–20 keV pegged normalization of the power-law component (model PEGPWRLW). EW_6.4 keV: EW of the 6.4 keV line with respect to the power-law continuum. Λ, s, E_min, and N_LECR: LECR ions path length, source spectrum index, minimum energy, and model normalization. By definition dW/dt = 4πD²N_LECR is the power injected in the interaction region by primary CR protons with energies between E_min and E_max = 1 GeV, where D is the distance to the source. Γ_RX, ξ, and I_RX: the power-law slope of the incident radiation, ionization parameter (defined as ξ = 4πF_tot/n_H where F_tot is the total illuminating flux, and n_H is the density of the reflector), and normalization of REFLIONX model (Ross & Fabian 2005). The metallicity parameter Z for LECR and REFLIONX models is fixed at 1.7 Z_☉. Reduced χ² (d.o.f.): reduced χ² and degrees of freedom.

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Model 1 provides a reliable fit to the data by constraining the temperature of the core emission, the power-law component and the intensity of the 6.4 keV line. The $1.76^{+0.36}_{-0.29}$ keV temperature of the thermal component is in agreement with that recently measured by T12 in the cluster's core ($1.79^{+0.06}_{-0.05}$ keV from "model 1" in T12). The power-law slope Γ = 1.62 ± 0.31 is consistent with $\Gamma =1.6^{+0.3}_{-0.2}$ from T12, measured in the cloud region. T12 finds the slope and 6.4 keV line equivalent width (EW_6.4 keV) of the cloud region compatible with the LECR ion model, where collisional ionization of the cloud by CR protons produces the 6.4 keV fluorescence line. According to the XMM-Newton study of the Arches cluster by T12, the LECR electron model (LECRe) requires an ambient Fe abundance ≳ 3 times the solar value to account for the measured EW of 1.2 ± 0.2 keV, which makes the measured properties of the non-thermal cloud region emission hardly compatible with the LECR electron model. We consider only the LECR proton (LECRp) model in the following analysis.

We fitted the spectra with the XSPEC model WABS × (APEC + LECRp), henceforth "model 2." The model depends on the LECR path length in the ambient medium, Λ, the minimum energy of the CR particles entering the cloud, E_min, the power-law index of the CR source energy spectrum, s, and the metallicity of the X-ray emission region, Z. We fixed Λ and E_min parameters of the LECRp model according to T12, making free slope s and normalization N_LECR. The best-fit results obtained with model 2 are given in Table 5 and the spectral components are shown in Figure 9.

The NuSTAR-measured spectral index of the injected low-energy protons $s=1.65^{+0.59}_{-0.55}$ is in general agreement with the T12 value ($1.9^{+0.5}_{-0.6}$). The best-fit LECR model normalization for the fixed E_min = 10 MeV nucleon⁻¹$N_{{\rm LECR}}=(8.08^{+1.82}_{-1.62})\times 10^{-8}\; {\rm erg\,cm}^{-2}\; {\rm s}^{-1}$ is somewhat higher than that measured by T12 ($N_{{\rm LECR}}=(5.6^{+0.7}_{-0.3})\times 10^{-8}\; {\rm erg\,cm}^{-2}\; {\rm s}^{-1}$). The corresponding power injected by LECR protons lies in the range (5–8) × 10³⁸ erg s⁻¹.

To test the X-ray reflection scenario of the Arches cluster non-thermal emission, we applied the self-consistent reflection model REFLIONX¹⁴ in XSPEC describing the reflected spectrum for an optically thick atmosphere of constant density, illuminated by radiation with a power-law spectrum (Ross & Fabian 2005), henceforth "model 3." The REFLIONX spectrum contains modeled fluorescence lines and continuum emission (Figure 9). Developed for the surface of hot accretion disks, REFLIONX can still be applied for cold material around the Arches cluster, fixing the ionization parameter ξ at the lowest allowed value of 10 erg cm s⁻¹. The best-fit parameters of model 3 are shown in Table 5.

In this section, we discuss the results of this work in the context of two scenarios proposed to explain the excitation mechanism of the fluorescent emission around the Arches cluster.

5.1. CR Bombardment Hypothesis

5.2. X-Ray Reflection Hypothesis

In this paper, we present results on the first focused hard X-ray observation of the Arches cluster performed by NuSTAR. We report on significant detection of the hard X-ray emission around the cluster with a spectrum that extends for the first time up to ∼40 keV. The main results can be summarized as follows.

• 1.  
  The NuSTAR mosaic image of the Arches cluster shows a core component and extended halo emission in the 3–10 keV energy band. The centroid position of the core emission coincides with the bright sources A1N/S resolved with Chandra in the Arches cluster. The halo emission around the cluster also follows the morphology observed with Chandra. The centroid position of the halo emission does not coincide with the core and tends to be outside the Arches cluster.
• 2.  
  Wavelet decomposition of sky mosaics does not show any significant (5σ) detection of point-like sources in the core of the Arches cluster above 10 keV. The continuum 10–20 keV emission is significantly detected well beyond the Arches cluster with a spatial morphology consistent with the Fe Kα fluorescent 6.4 keV line emission observed with XMM-Newton (T12).
• 3.  
  The spectral analysis of the Arches cluster region, including the extended emission around it, reveals a ∼1.7 keV temperature plasma, which is consistent with the optically thin thermal plasma measured by T12 in the cluster's core and associated with thermalization of massive star winds and several colliding stellar wind binaries within the cluster (T12).
• 4.  
  The power-law slope Γ = 1.62 ± 0.31 and ${\rm EW}_{{\rm 6.4 \,keV}}=1.1^{+0.7}_{-0.5}$ keV are in agreement with that measured by T12 around the Arches cluster and expected for the LECR ion model.
• 5.  
  The X-ray emission of the Arches cluster is well fitted with a model composed of an optically thin thermal plasma and a non-thermal component produced by LECR ions (T12). The best-fit CR spectral index is $s=1.65^{+0.59}_{-0.55}$. The LECR model normalization gives the corresponding power of the injected LECR protons in the cloud region at the level of (5–8) × 10³⁸ erg s⁻¹ (with D = 8 kpc and CR minimum energy E_min = 10 MeV nucleon⁻¹).
• 6.  
  The luminosity of the primary source required by the X-ray reflection model is 1–2 orders of magnitude higher than that observed in the Arches cluster, which is in agreement with similar constraints drawn from the 6.4 keV line flux.

The X-ray photoionization and CR-induced emission models can reproduce the data equally well. Additional NuSTAR observations with the Arches cluster on-axis would be useful to detect the difference between the emission models above 20 keV. At this point, we can conclude that explaining the non-thermal emission around the Arches cluster with an X-ray reflection scenario in which the illuminating source is located in or close to the cluster is unlikely. However, irradiation by a long outburst of Sgr A* can still be considered, and would imply long-term variability of the 6.4 keV line flux should be detected. The excitation of the neutral material around the cluster by CR interactions also looks plausible, though a large flux of LECR protons is needed to produce the observed fluorescent emission.

This work was supported under NASA Contract No. NNG08FD60C, and made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software, and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). F.E.B. acknowledges support from Basal-CATA (PFB-06/2007) and CONICYT-Chile (FONDECYT 1101024 and Anillo ACT1101). R.K. thanks Eugene Churazov for fruitful discussions and valuable suggestions to the paper.

Facility: NuSTAR - The NuSTAR (Nuclear Spectroscopic Telescope Array) mission