NuSTAR observation of Galactic Center diffuse emission

# NuSTAR Hard X-ray Survey of the Galactic Center region I: Hard X-ray morphology and spectroscopy of the diffuse emission

###### Abstract

We present the first sub-arcminute images of the Galactic Center above 10 keV, obtained with NuSTAR. NuSTAR resolves the hard X-ray source IGR J174562901 into non-thermal X-ray filaments, molecular clouds, point sources and a previously unknown central component of hard X-ray emission (CHXE). NuSTAR detects four non-thermal X-ray filaments, extending the detection of their power-law spectra with -2.3 up to keV. A morphological and spectral study of the filaments suggests that their origin may be heterogeneous, where previous studies suggested a common origin in young pulsar wind nebulae (PWNe). NuSTAR detects non-thermal X-ray continuum emission spatially correlated with the 6.4 keV Fe K fluorescence line emission associated with two Sgr A molecular clouds: MC1 and the Bridge. Broad-band X-ray spectral analysis with a Monte-Carlo based X-ray reflection model self-consistently determined their intrinsic column density ( cm), primary X-ray spectra (power-laws with ) and set a lower limit of the X-ray luminosity of Sgr A* flare illuminating the Sgr A clouds to  erg s. Above  keV, hard X-ray emission in the central 10 pc region around Sgr A* consists of the candidate PWN G359.950.04 and the CHXE, possibly resulting from an unresolved population of massive CVs with white dwarf masses . Spectral energy distribution analysis suggests that G359.950.04 is likely the hard X-ray counterpart of the ultra-high gamma-ray source HESS J1745290, strongly favoring a leptonic origin of the GC TeV emission.

Galaxy:center – X-rays: general – X-rays: ISM – radiation mechanisms: nonthermal
slugcomment: Accepted to Astrophysical Journal1919affiliationtext: Core of Research for the Energetic Universe, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan2121affiliationtext: INAF - Astronomico di Roma, via di Frascati 33, I-00040 Monteporzio, Italy

## 1. Introduction

The relative proximity of the Galactic Center (GC), at  kpc, allows for sensitive, high-resolution observations that are not possible for more distant galactic nuclei. Over the last two decades, the GC and Galactic Ridge have been extensively surveyed by X-ray telescopes, which have revealed various diffuse X-ray components including the Galactic Ridge X-ray emission (GRXE; Revnivtsev et al., 2006; Krivonos et al., 2007; Yuasa et al., 2012), an X-ray haze that extends out from the GC for degrees in longitude and a few degrees in latitude (Worrall et al., 1982), and large-scale diffuse Fe line emission (Koyama et al., 1989, 1996). In the inner 20 around the GC, a separate, unresolved  keV thermal component has been observed by Chandra and XMM-Newton (Muno et al., 2004; Heard & Warwick, 2013). Chandra has resolved thousands of point sources in the GC field, suggesting the keV thermal emission represents a population of unresolved magnetic CVs (Wang et al., 2002a; Revnivtsev et al., 2009; Muno et al., 2009). In addition, Chandra has performed arcsecond-scale mapping in the crowded soft X-ray (2-10 keV) band (Baganoff et al., 2003), identifying emission from the central supermassive black hole Sgr A*, hot gas from winds of the surrounding central stellar cluster, the supernova remnant (SNR) Sgr A East, non-thermal filamentary structures, molecular clouds and thousands of X-ray point sources (Muno et al., 2008).

In the GC region, Chandra has detected nearly two dozen X-ray filaments, most of which exhibit “cometary” or “filamentary” shapes and featureless non-thermal spectra with 1.5-2.5 (Johnson et al., 2009). Muno et al. (2008) and Lu et al. (2008) speculated that the X-ray filaments are young pulsar wind nebulae (PWNe) since they possess similar spectral and morphological properties, although there is as yet no direct evidence for a PWN. Whether X-ray filaments are PWNe or not, if synchrotron radiation is responsible for their non-thermal X-ray emission, hard X-ray spectroscopy probes the highest energy (-100 TeV) electrons that are accelerated since the synchrotron photon energy keV where is the electron energy and is the magnetic field strength typically 0.1-1 mG inside radio filaments (Yusef-Zadeh & Morris, 1987; Ferrière, 2009).

Many of the Galactic Center molecular clouds (GCMCs) in the Sgr A, B and C regions are known to produce diffuse Fe K fluorescence emission at 6.4 keV (Ponti et al., 2014). Two models, the so-called X-ray reflection nebula (XRN) model (Sunyaev et al., 1993) and the low-energy cosmic-ray (LECR) model (Yusef-Zadeh et al., 2002a), have been proposed to account for Fe K line emission by photo-ionization by an external X-ray source and collisional ionization by low-energy cosmic-rays, repectively (see Ponti et al., 2013, for a review). The XRN scenario seems more plausible since the XMM-Newton and Chandra surveys of the GC region over the last decade have revealed the year-scale time variation of strong Fe K line with equivalent width keV in the Sgr A clouds (Ponti et al., 2010; Capelli et al., 2012; Clavel et al., 2013) and Sgr B2 (Terrier et al., 2010). It has been proposed that the X-ray emission of GCMCs is associated with Sgr A* past flares, or nearby X-ray transients (Sunyaev et al., 1993; Koyama et al., 1996). However, it is still possible that the LECR emission contributes as an additional component given that a large population of cosmic rays are expected in the GC (Capelli et al., 2012). In either case, there has been no clear detection of X-ray continuum emission intrinsic to the Sgr A clouds. In the soft X-ray band, thermal diffuse emission as well as point sources heavily contaminate X-ray emission from the Sgr A clouds, while hard X-ray telescopes such as INTEGRAL were not able to resolve X-ray continuum emission from the Sgr A clouds.

In the gamma-ray band, the CANGAROO-II and HESS arrays of Cherenkov telescopes discovered the ultra-high energy gamma-ray source HESS J1745290 (Tsuchiya et al., 2004; Aharonian et al., 2004) and later its 0.1-10 TeV spectrum was well measured by different TeV telescopes such as HESS (Aharonian et al., 2009), VERITAS (Archer et al., 2014) and MAGIC (Albert et al., 2006). Both Sgr A* and the cometary PWN candidate G359.950.04 have been proposed as counterparts of the TeV source HESS J1745290, as both lie within its 13 error radius (Acero et al., 2010). This has led to two possible interpretations: a leptonic and a hadronic origin. In the leptonic scenario, high-energy electrons are accelerated by Sgr A* flares, PWNe, supernova remnants (SNRs) interacting with molecular clouds and stellar winds. These TeV electrons emit synchrotron radiation in the X-ray band in an ambient interstellar medium (ISM) magnetic field of G and also emit inverse-Compton radiation in the gamma-ray band by up-scattering ultraviolet and far-infrared photons in the high radiation density field of the GC (Hinton & Aharonian, 2007). In the hadronic scenario, relativistic protons accelerated from Sgr A* or SNRs interacting with the surrounding medium emit gamma-rays via pion decay, then secondary electrons emit X-rays via synchrotron or non-thermal bremsstrahlung radiation (Chernyakova et al., 2011). Both hadronic and leptonic models can also explain the 0.1-10 TeV spectrum of the GC, either via pion decay from protons injected into the diffuse interstellar medium by past Sgr A* outflows (Aharonian & Neronov, 2005; Ballantyne et al., 2007; Chernyakova et al., 2011) or via inverse-Compton emission from a population of electrons ejected from Sgr A* (Kusunose & Takahara, 2012) or the PWN candidate G359.950.04 (Hinton & Aharonian, 2007). As a more exotic scenario, dark matter annihilation at the GC has been also proposed (Cembranos et al., 2013). Since the soft X-ray emission of the GC is dominated by diffuse thermal emission and point sources that are mostly unrelated to the GeV to TeV emission, it is extremely important to identify a hard X-ray counterpart of HESS J1745290. However, the central 10 pc region of the GC has been difficult to localize due to the angular resolution of hard X-ray instruments (Winkler et al., 2003; Gehrels et al., 2004), leaving the origin and nature of HESS J1745290 a subject of controversy.

Above 20 keV, the INTEGRAL observatory discovered a persistent hard X-ray source IGR J174562901, which is particularly bright in the 20-40 keV range, within of the GC (Bélanger et al., 2006). The emission at energies above 40 keV, however, seems to shift several arcminutes to the east of both Sgr A* and Sgr A East. This variation in the position of the emission combined with the spatial resolution of the INTEGRAL/IBIS coded aperture mask has led to speculation that the emission results not from a single object, but from a collection of the many surrounding diffuse and point-like X-ray sources (Krivonos et al., 2007). However, without high-resolution, high-energy images of the region available, the existence of a new source of high-energy X-ray emission could not be ruled out.

The NuSTAR hard X-ray telescope (Harrison et al., 2013), with its arcminute angular resolution and effective area extending from 3 to 79 keV, can make unique contributions to understanding the emission mechanisms of X-ray filaments, GCMCs and the gamma-ray source HESS J1745290. Broadband X-ray spectroscopy with NuSTAR provides a powerful diagnostic that can distinguish between different models of GCMC X-ray emission and tightly constrain parameters when combined with self-consistent X-ray emission models. In addition, NuSTAR is the key to filling the gap between the well-studied soft X-ray populations and the persistent gamma-ray emission in the central parsec region of the GC.

In this paper, we report NuSTAR hard X-ray observations of diffuse emission in the GC region, while our companion paper (Hong et al., 2015) focuses on the hard X-ray point sources. §2 outlines the NuSTAR and XMM-Newton observations adopted for studying GC diffuse emission, followed by §3 describing our imaging and spectral analysis methods. §4 presents the hard X-ray morphology of the GC region above 10 keV. For three hard X-ray diffuse source categories, namely non-thermal X-ray filaments (§5), molecular clouds (§6) and the central 10 parsec region around Sgr A* (§7), we present our NuSTAR spectral and morphological analysis jointly with archived Chandra and XMM-Newton data, and discuss implications for their hard X-ray emission mechanisms. §8 summarizes our results from the NuSTAR GC survey. The Appendix describes NuSTAR background components and background subtraction methods, some of which are peculiar to the NuSTAR GC observations, as well as X-ray reflection models for GCMCs particularly on a Monte-Carlo based self-consistent MYTorus model. Throughout the paper, we assume a distance to the GC of 8 kpc (Reid, 1993).

## 2. NuSTAR Observations

NuSTAR consists of coaligned X-ray telescopes with corresponding focal plane modules (FPMA and FPMB) with an angular resolution of Half Power Diameter (HPD) and Full Width Half Maximum (FWHM; Harrison et al., 2013). NuSTAR operates in the 3-79 keV band with eV (FWHM) energy resolution below keV and eV at 68 keV. Soon after its launch in June 2012, NuSTAR initiated a large GC survey to study both point sources and diffuse emission in the hard X-ray band. A number of single pointing observations, occasionally coordinated with other telescopes, were performed to study Sgr A* flaring (Barrière et al., 2014), the newly discovered magnetar SGR 174529 (Mori et al., 2013; Kaspi et al., 2014), the Cannonball (Nynka et al., 2013), Sgr A-E (Zhang et al., 2014), X-ray transients in outbursts (Koch et al., 2014; Barrière et al., 2015), the Arches cluster (Krivonos et al., 2014) and Sgr B2 molecular cloud (Zhang et al., 2015).

For the analysis of GC diffuse emission presented in this paper, we used the nine NuSTAR observations listed in Table 1. The first three observations were pointed at Sgr A*, while the next six observations, each with  ks depth, covered the area between Sgr A* and the low mass X-ray binary (LMXB) 1E1743.12843 (hereafter referred to as the “mini-survey”). The NuSTAR mini-survey was originally motivated to study the INTEGRAL source IGR J174562901. We did not use NuSTAR observations of Sgr A* in 2013 and 2014 since the data were heavily contaminated by outbursting X-ray transients. The other observations surveying larger regions, away from the GC, were primarily aimed at studying point sources, and so they are not included in this analysis. In addition, four XMM-Newton observations in 2012 (Table 1) were obtained in the Full Frame mode with the medium filter and their data are used for joint spectral analysis.

## 3. Data reduction and analysis

In this section, we describe our imaging and spectral analysis of the NuSTAR GC data. All the NuSTAR data were processed using the NuSTAR Data Analysis Software (NuSTARDAS) v1.3.1. After filtering high background intervals during South Atlantic Anomaly (SAA) passages, we removed additional time periods in which Sgr A* was in a flaring state, as observed by NuSTAR or during coincident Chandra observations (Barrière et al., 2014). An additional 70 ks was removed from the 2012 August observation (ObsID: 30001002003) due to a reduction in the event rate of FPMA, possibly due to debris blocking the detector. After all quality cuts, the effective exposure time ranges from 25-100 ks (mini-survey) to ks (Sgr A*) (Table 1 and Figure 1).

In most NuSTAR GC observations, the background below keV is dominated by photons from outside the field of view (FOV) entering through the aperture stop (so-called “stray-light background” or SLB hereafter Harrison et al., 2013; Krivonos et al., 2014; Wik et al., 2014). In particular, SLB patterns from nearby bright point sources ( erg cm s) within from the telescope’s pointing vector are visible at predictable locations on the FOV and completely dominate over other X-ray emission. We filtered out events in the region of heavy SLB contamination from the nearby bright source GX 3+1 (Seifina & Titarchuk (2012) see the Appendix for more details). As a result, % of FPMB events, mostly in detector chip 0, were removed from all observations, while FPMA data do not have significant SLB from bright point sources.

### 3.1. Imaging analysis

First, we applied astrometric corrections for individual NuSTAR event files by registering known soft X-ray sources to further improve our positioning accuracy for detailed morphological studies. These registration sources include bright Chandra point sources (Muno et al., 2009), the core of the Sgr A-E (Sakano et al., 2003), the Arches cluster (Yusef-Zadeh et al., 2002b) and the Cannonball (a neutron star candidate located outside the Sgr A East shell) (Park et al., 2005; Nynka et al., 2013). They all have Chandra counterparts with known positions to better than . Using the IDL centroiding routine gcntrd, we determined the centroid of each registration source in the 3-10 keV band, matching Chandra’s sensitive energy band (2-8 keV) for highly absorbed GC sources. Two of the Sgr A* observations (ObsID: 30001002001, 30001002004) contained several bright flares from Sgr A* itself (Barrière et al., 2014) that aided in determining the astrometric corrections. For these two observations, an image file was created that contained the bright flares from Sgr A* and we defined the offset as the difference between the radio position of Sgr A* (Reid et al., 1999) and the centroid of the NuSTAR emission. These event files, after removing Sgr A* flare intervals, were properly shifted using the Sgr A* flare position and used in the subsequent mosaic images presented here. Translational shifts by as much as were required to place the target source at its known position, and were applied to both event files and exposure maps.

Second, after each observation was corrected for its offset, we summed together all observations and normalized the resulting image by the effective exposure map. We neither subtracted background nor corrected for vignetting effects (so-called flat-fielding) in the subsequent imaging analysis since the background is not spatially uniform (see Appendix). Figure 2 shows the exposure-corrected count rate images in the 10-79 keV band, after combining both FPMA and FPMB data from the nine NuSTAR observations. For illustration purposes, we smoothed NuSTAR images with a Gaussian kernel of radius (5 pixels) unless otherwise instructed. We verified the applied astrometric correction by determining the position of one or several additional sources in each individual observation and in the final mosaicked image. The NuSTAR positions are within 5 of the reported Chandra positions.

There are two particularly bright regions seen in the NuSTAR images. One of them is the Sgr A* complex containing thermal diffuse emission, hundreds of X-ray point sources, X-ray filaments and thermal emission from Sgr A East. Although these X-ray sources are unresolved by NuSTAR in the 3-10 keV band, most of them have soft X-ray spectra and fade out beyond 10 keV making a subset of X-ray sources more prominent (§4). The other bright region near the left (east) side of the image is a persistent LMXB 1E1743.12843 at RA = and DEC = (J2000.0 Wijnands et al., 2006). The LMXB looks “extended” because it is so bright, with a 3-79 keV flux of erg cm s (Lotti et al., 2015), that its PSF wings extending beyond  are still dominant over other X-ray emission. Ghost-ray background (see its definition in the Appendix) from 1E1743.12843 is not visible, and our simulation confirmed that it is below the GC diffuse emission and SLB in most of the area covered by the NuSTAR mini-survey observations. The brightest X-ray filament is Sgr A-E (G359.890.08) at RA = and DEC = (J2000.0 Lu et al., 2003) and it is distinct from the Sgr A* complex. The molecular clouds in the region between the Sgr A* complex and 1E1743.12843 (Ponti et al., 2010) are also visible. The outer regions at or are dominated by SLB from the Galactic Ridge X-ray emission, and no GC emission is clearly visible there.

### 3.2. Trial probability map

In addition to the exposure-corrected images, we present a sky map of detection significance, dubbed a ‘trial map’, to illustrate detection significance of faint sources that are otherwise hidden in the count rate images (see Hong et al. (2015) for more details and applications to NuSTAR images). The value of the trial map at each sky position represents the number of random trials required to produce the observed counts by purely random Poisson fluctuations if no excess of X-ray sources relative to the background is present at the location. For every sky position, we first define a source cell (e.g., 20% encircled energy fraction of the PSF) and a background cell (an annulus around the position), and then, using the cells, we calculate the total observed counts () and their background counts (). For each image pixel, the random trial number is estimated to be a normalized incomplete gamma function of and (Weisskopf et al., 2007; Kashyap et al., 2010). We repeat the procedure for other pixels to generate the map by sliding cell windows across the field.

Throughout the paper, the negative logarithm of the trial probability is plotted in the trial map [e.g., ) = 6 for a trial probability of ]. Thus, a brighter spot indicates higher detection significance. When there are no significant systematic fluctuations, the presence of an X-ray source is indicated by a position where the trial probability is significantly smaller than the odds one can reach with the total number of independent searches (i.e. the inverse of the total number of searches). The total number of independent searches can be estimated as the maximal number of resolvable sources () in the field, which is the ratio of the number of pixels in the image ( pixels in this example presented in §4.3) to the NuSTAR angular resolution in pixels (FWHM  diameter circle: pixels). For a given confidence level (), one can claim a detection when . For instance, to detect a source at 99.7% confidence level (i.e. 3- detection), should be less than or its trial map value should be greater than 6.1. Similarly for 4- and 5- detections, the trial map value should be greater than 7.8 and 9.9, respectively. Note that trial maps are not used to infer the actual source brightness and they are presented without any smoothing.

### 3.3. Spectral analysis

For some of the hard X-ray sources discussed below, we have jointly analyzed the NuSTAR and XMM-Newton spectra to investigate their X-ray emission mechanisms by comparing with several existing models. We extracted NuSTAR source spectra and generated response matrices and ancillary files using nuproducts. Background subtraction and modeling require extra caution due to the high background level and to its complex multiple components (Appendix). Background substraction methods are specific to each source and they can be found in later sections (e.g., §6.1 and 7.1) where we clarify our data selection and filtering.

We processed all the XMM-Newton Observation Data Files (ODFs) with the XMM-Newton Science Analysis System (SAS version 13.5.0) and the most recent calibration files. We restricted our analysis to the XMM-Newton EPIC-PN data where photon pile-up effect is negligible for the sources we analyzed. After filtering out time intervals with high soft proton flaring levels, we selected EPIC-PN events with FLAG = 0 and PATTERN. For each XMM-Newton spectrum, the response matrix and effective area files are computed with the XMM-SAS tasks rmfgen and arfgen. For the background, we adopted the XMM-Newton calibration observations closest in time to each of the XMM-Newton observations, and used their EPIC-PN data with the filter wheel closed, thus blocking external X-rays and soft protons, and allowing us to measure internal background components accurately. First, we fit the so-called Filter Wheel Closed (FWC) spectra with several power-law continuum components and Gaussian lines to properly parameterize the background emission. Since the ratio between the lines and continuum in background spectra is stable between observations close in time, we scaled the overall normalization of the FWC model to match the count rates from the same source-free region between the FWC model and actual XMM-Newton science data, while we froze all the other parameters.

We combined NuSTAR FPMA and FPMB spectra and response files using the FTOOL addascaspec. XMM-Newton EPIC-PN spectra and response files from individual observations were similarly combined, after ensuring that individual spectra were consistent with each other. We grouped all spectra so that each bin had sufficient counts to ensure that it had a significance over background of at least . All spectral fitting and flux derivations were performed in XSPEC (Arnaud, 1996), with photoionization cross sections as defined in Verner et al. (1996) and abundances for the interstellar absorption as defined in Wilms et al. (2000). Chi-squared statistics were used for spectral fitting, and all quoted errors are for 1- level confidence.

## 4. Hard X-ray morphology of the Galactic Center region

### 4.1. 10-20 keV band morphology

Figure 3 shows the NuSTAR image in the 10-20 keV band. Some features are identified as point sources and marked with white circles (Hong et al., 2015). While 8 keV thermal emission and SNR Sgr A East emission are still dominant, the Cannonball (Nynka et al., 2013) is visible in the 10-20 keV image. Diffuse emission is present in the region east of the Sgr A* complex but west of the LMXB 1E1743.12843. This diffuse emission is likely a mixture of 8 keV thermal emission and molecular cloud X-ray continuum. Three molecular clouds, namely MC1, the Bridge and the Arches cluster indicated by green dashed ellipses (defined in Ponti et al., 2010), are clearly detected above 10 keV, while we do not detect diffuse emission from these clouds above 20 keV largely due to the high background level. The NuSTAR image is overlaid with Fe K line intensity contours obtained from the 2012 XMM-Newton observations (cyan contours). The continuum emission in the 4.5-6.28 keV band was subtracted from the 6.28-6.53 keV XMM-Newton image to emphasize just the Fe K line emission (Ponti et al., 2010). The 10-20 keV hard X-ray emission is well correlated with the Fe K line contours in these cloud regions.

With a separation of , MC1 is the closest to Sgr A* in projection among the molecular clouds emitting the Fe K line. MC1 was one of the brightest clouds in 2012, and the Fe K line flux of the overall cloud stayed nearly constant from 2000 to 2010 (Ponti et al., 2010; Capelli et al., 2012). The bright 10-20 keV emission in MC1 coincides with the strong Fe K line emission seen in 2012. Using Chandra data, Clavel et al. (2013) found different time variations in sub-divided regions in the MC1 cloud between 2000 to 2010 — the Fe K line flux decreased in the two regions dubbed ’a’ and ’b’ while it increased in the four regions dubbed ’c’ to ’f’ in Figure 4. In 2012, XMM-Newton and NuSTAR detected the brightest Fe K line and hard X-ray continuum emission coinciding with the ’c’ region, where Fe K line flux has been most prominent in MC1 since 2002 (Clavel et al., 2013).

The so-called Bridge is located on the east side of MC1. It contains multiple clouds exhibiting a range of Fe K line flux light curves (Ponti et al., 2010; Capelli et al., 2012; Clavel et al., 2013). In the Bridge, there are two bright regions both in the Fe K line and hard X-ray continuum emission. They correspond to the two distinct regions observed in the NH map at molecular line velocity +50 km s (Jones et al., 2012), dubbed the Br1 and Br2 regions by Clavel et al. (2013). Spectral analysis of MC1 and the Bridge is presented in §6, while detailed imaging and spectral analysis of the Arches cluster can be found in Krivonos et al. (2014).

The east end of the Bridge is another molecular cloud, located at G0.110.11. In G0.110.11, there are two hard X-ray sources that do not emit a strong Fe K line at 6.4 keV. One is the X-ray filament G0.130.11 (§5.3), while the other is the bright magnetic CV CXOUGC J174622.7285218 (Muno et al., 2009). Unlike the GCMC, these two sources do not have strong Fe K line emission and thus do not appear in the 6.4 keV Fe K contours. Otherwise, we detected neither strong Fe K nor hard X-ray continuum emission associated with the molecular cloud in G0.110.11 probably because its X-ray flux has been decaying over the last decade (Capelli et al., 2012). No hard X-ray emission above 10 keV was detected from other clouds such as MC2, the 20 km s and 50 km s clouds. Continuing the linearly decreasing trend of Fe K line flux (Clavel et al., 2013), hard X-ray emission from MC2 may have slipped below the NuSTAR detection threshold. Our results are consistent with no apparent detection of Fe K emission from the 20 km s cloud and the 50 km s cloud (Ponti et al., 2010). However, given their small offsets ( pc) relative to the GC where X-ray transients are highly concentrated (Muno et al., 2005), X-ray outbursts lasting over a few years (e.g. SGR J174529) may illuminate these clouds, and thus X-ray reflection from there may be observed through time-varying Fe K line and hard X-ray continuum emission in the near future.

### 4.2. 20-40 keV band morphology

Above 20 keV, besides the LMXB 1E1743.12843 and Sgr A-E, hard X-ray emission is observed within a  radius region around Sgr A*. In order to investigate the central emission morphology precisely while avoiding image distortion of the Sgr A* region due to the off-axis PSF in the mini-survey data, we only used the three observations where Sgr A* was on-axis. Figure 5 shows the 20-40 keV NuSTAR image of the GC region. Diffuse emission from SNR Sgr A East (red contours in Figure 5), which is comprised of a  keV and -6 keV two-temperature thermal plasma (Sakano et al., 2004; Park et al., 2005), is no longer visible.

Instead, the central parsec of the persistent 20-40 keV emission is dominated by a point-like feature and a previously unknown diffuse X-ray component in the hard X-ray band (Perez et al., 2015). Perez et al. (2015) fit the raw count NuSTAR image in the 20-40 keV band with a two-dimensional model with two Gaussian profiles. The fitting range was restricted to the central to minimize the effect of background variations between different detector chips and bias from the molecular cloud region to the northeast. The fitting procedure used the Sherpa package (Freeman et al., 2001) to fully convolve the on-axis NuSTAR point spread function (PSF), telescope pointing fluctuation and vignetting function as well as fit a flat background component together.

Figure 6 shows NuSTAR 20-40 keV image zoomed in the central 3 region around Sgr A*. The dominant feature is not resolved by NuSTAR and therefore consistent with a point source, and its centroid at RA = and DEC = (J2000; white dashed circle in Figure 6 indicating 90% c.l position error of ) aligns well with the head of the PWN candidate G359.950.04. The compact size of G359.950.04 with  elongation as measured at  keV band by Chandra (Wang et al., 2006) (thus basically a point source with the  NuSTAR HPD) and spatial coincidence suggests that G359.950.04 is the likely counterpart to this point-like hard X-ray emission. This is further supported by our spectral analysis (§7) and the fact that the head of G359.950.04 has the hardest power-law spectrum and the highest 2-8 keV flux in the filament (Wang et al., 2006).

On the other hand, the central hard X-ray emission (CHXE) is centered at RA = and DEC = (J2000; green dashed circle in Figure 6 indicating 90% c.l position error of ), and it has an extent (FWHM) of  and  or 8 pc and 4 pc assuming a GC distance of 8 kpc (cyan ellipse in Figure 5). According to the detailed spectral study of two nearby intermediate polars and the CHXE by Hailey et al. (2015), the CHXE emission is likely an unresolved population of massive magnetic CVs with white dwarf masses .

### 4.3. 40-79 keV band morphology

The only significant emission above 40 keV in this field is concentrated within the central 1 region of the GC, likely because the three Sgr A* observations have a longer combined exposure than the NuSTAR mini-survey (Figure 1). Figure 7 shows a NuSTAR exposure-corrected smoothed image and the matching trial map of the central 1 region around Sgr A* in the 40-79 keV band, which is the only region with significant emission in this band. Given the fewer source counts, we smoothed the NuSTAR image with a larger Gaussian width of 17.5 (7 pixels) for better illustration. The view of the GC drastically simplifies above 40 keV — the emission is centered around G359.950.04 with some potential substructures.

The trial map clearly exhibits two distinct features above the 4- level. One is a point-like feature centered at the head of G359.950.04 and also spacially coincident with the TeV source HESS J1745290. This feature is persistent, observed in all individual observations. The other is a protrusion elongated in the south-west direction. Its significance is highest in the FPMA data of one of the Sgr A* observations (ObsID: 30001002003), and thus the protrusion should be taken with some caution as a potential artifact. The protrusion is not spatially coincident with the radio (Yusef-Zadeh et al., 2012) or X-ray jets (Li et al., 2013), but it intersects with the cooler molecular gas of the circumnuclear disk indicated by green contours (Morris & Serabyn, 1996; Christopher et al., 2005). There is no apparent counterpart in either the Chandra 2-8 keV image or the XMM-Newton 6.4 keV Fe K image. It is possible that soft X-ray emission from the protrusion may be heavily absorbed by the optically thick circumnuclear disk and also contaminated by 8 keV thermal emission.

## 5. Non-thermal X-ray filaments

Throughout the Sgr A* and GC mini-survey observations, NuSTAR detected four non-thermal X-ray filaments (G359.890.08 or Sgr A-E, G359.970.038, G0.130.11 and G359.950.04) above 10 keV. The 20-40 keV trial map (Figure 8), where Sgr A East diffuse emission is no longer dominant, illustrates the filaments Sgr A-E and G359.970.038. On the other hand, G0.130.11 is located in the molecular cloud G0.110.11 and it was detected by the mini-survey observation (shown as one of the green polygons in Figure 3). G359.950.04, which lies away from Sgr A*, appears in the zoomed images around Sgr A* shown in §4.2 and §4.3. These hard X-ray filaments are among the brightest in the soft X-ray band with 2-8 keV fluxes above erg cm s or an unabsorbed luminosity of  erg s at a distance of 8 kpc (Johnson et al., 2009). Although we detected hard X-ray emission from a part of G359.9640.052 shown in Figure 8, its spectral identification as the known X-ray filament is unclear since it might be confused with a bright Chandra source CXO J174543.7285947 with  photons cm  s within  of the filament (Muno et al., 2009), in addition to some contamination from 8 keV thermal emission and the CHXE. In the following sections, we individually discuss three out of the four hard X-ray filaments detected by NuSTAR above 10 keV. G359.950.04 will be later discussed in connection with the TeV source HESS J1745290 (§7).

### 5.1. g359.89−0.08 (Sgr A-E) — TeV electrons trapped in magnetic tubes

G359.890.08 is the brightest X-ray filament, with a 3-79 keV flux of erg cm s or an unabsorbed X-ray luminosity of  erg s assuming a distance of 8 kpc (Zhang et al., 2014). The filament was detected up to keV with a best-fit power-law index of . We do not detect another prominent radio filament Sgr A-F (G359.900.06), above 10 keV. This is consistent with the fact that Sgr A-F is significantly fainter than G359.890.08 (Lu et al., 2008). Based on the high-resolution radio and X-ray morphology of the filament as well as spectral analysis, Zhang et al. (2014) ruled out both a PWN scenario and a SNR-molecular cloud interaction. Instead, the most plausible scenario is that magnetic flux tubes trap  TeV electrons, which emits synchrotron X-rays up to keV. Since TeV electrons have cooling times as short as year for  mG, electrons must be accelerated nearby before entering the filament. One possible external source of TeV electrons is relativistic protons accelerated from Sgr A* or SNRs interacting with the nearby 20 km s cloud which produces secondary electrons via pion decays. The electrons can diffuse out of the cloud before they cool significantly by synchrotron radiation, and become trapped in the magnetic flux tubes. Another (less likely) possibility is that a population of unresolved year old PWNe accelerate electrons to TeV energies. Suzaku has detected extended X-ray emission from such year-old PWNe elsewhere in the Galactic Plane (Bamba et al., 2010), but low brightness X-ray emission from old PWNe may be contaminated by the strong GC diffuse emission or be below the NuSTAR detection level. We therefore cannot completely rule out this scenario.

### 5.2. g359.97−0.038 - The Sgr A East shell interacting with the 50 km s−1 cloud

G359.970.038 is located just outside the Sgr A East shell, and it is close to the “Plume” region. By jointly fitting the NuSTAR and Chandra spectra of the filament, Nynka et al. (2015) found that its non-thermal spectrum extends to keV with the best-fit photon index . The photon index of this filament is significantly harder than that of G359.890.08 (). Using the high-resolution radio and Chandra image of the filament as well as SED model fitting including the NuSTAR results, Nynka et al. (2015) found that the PWN scenario is again highly unlikely. Instead, the filament is likely illuminated by the interaction between the shell of SNR Sgr A East and the 50 km s cloud (Nynka et al., 2015), as evidenced by the large width of the CS -0 line, which exceeds the cloud bulk velocity of km s (Tsuboi et al., 2006). The harder X-ray power-law spectrum of is typical of non-thermal bremsstrahlung or inverse Compton emission of electrons accelerated at the SNR-cloud interaction site (Bykov et al., 2000, 2005). The lack of an apparent radio counterpart is also consistent with this picture. The GeV source 2FGL J1745.6-2858 detected by Fermi is coincident with the position of G359.970.038 (Nolan et al., 2012; Yusef-Zadeh et al., 2013). If the GeV source is associated with G359.970.038, it is additional evidence supporting the SNR-cloud interaction scenario since the SED model of Bykov et al. (2000) predicts a peak in the GeV band.

### 5.3. g0.13−0.11 - pulsar wind nebula?

The third hard X-ray filament G0.130.11, shown in Figure 3, is located near the Radio Arc region and is embedded in the molecular cloud G0.110.11. The filament is a candidate PWN due to its cometary shape and a point-like feature CXOGCS J174621.5285256 (Wang et al., 2002b). It is one of the few X-ray filaments that has a radio counterpart. It is not possible to extract a clean NuSTAR spectrum of the filament due to the limited statistics, and contamination from the bright X-ray source CXOUGC J174622.7285218, away from the filament. CXOUGC J174622.7285218 is a magnetic CV with a 1745 s periodicity (Muno et al., 2009) and NuSTAR detected its hard X-ray extension above 10 keV (Hong et al., 2015). A deeper NuSTAR observation with more than ksec exposure will be required to perform useful spectral and timing analyses of this filament.

### 5.4. Heterogeneous origin of non-thermal X-ray filaments?

Two of the three hard X-ray filaments (G359.890.08 and G359.970.038) detected above 10 keV are unlikely to be PWNe, suggesting a heterogeneous origin for the X-ray filaments. G359.890.08 is likely powered by synchrotron radiation in magnetic flux tubes trapping TeV electrons, while G359.970.038 is illuminated by Sgr A East interacting with a 50 km s cloud. Our results indicate a reservoir of relativistic electrons and protons in the central 10 pc region, rather than production and acceleration of particles locally inside the filaments as in the PWN scenario. Electrons may be accelerated to TeV energies by faint year-old PWNe or they are by-products of hadronic interactions between relativistic protons and clouds.

Alternatively, Linden et al. (2011) proposed dark matter annihilation as a potential source of GeV electrons that are trapped in magnetic flux tubes and emit synchrotron radiation. In this scenario, light neutralinos with -10 GeV mass annihilate directly to leptons that decay to GeV electrons. The four radio filaments (G0.20.0, G0.160.14, G0.080.15 and G359.10.2) investigated by Linden et al. (2011) using their model are located outside the NuSTAR GC survey area or did not have sufficiently long exposure time in the NuSTAR mini-survey coverage to warrant study. Deep X-ray observations of these radio filaments could test the dark matter scenario since any X-ray detection of these radio filaments would indicate the presence of TeV electrons that cannot be produced in the annihilation of 5-10 GeV mass neutralinos. A more extensive hard X-ray survey of radio and X-ray filaments probe not only the spatial and energy distribution of cosmic-rays beyond the central 10 pc region but also dark matter physics.

## 6. Galactic center molecular clouds

All Sgr A clouds, including MC1, MC2, the Bridge and G0.110.11, were covered by the NuSTAR mini-survey as well as XMM-Newton observations in 2012. As Figure 3 in § 4.1 shows, we find that Fe K line emission (as measured by XMM-Newton) and hard X-ray continuum (as measured by NuSTAR) emission are spatially well-correlated in MC1, the Bridge and the Arches cluster. In October 2013, a 300 ks NuSTAR observation of the fading Sgr B2 spatially resolved hard X-ray emission from the Sgr B2 core and a newly discovered cloud feature G0.660.13 (Zhang et al., 2015). Sgr C is not suitable for NuSTAR observations because of strong ghost-ray background from the bright persistent LMXB 1A1742294.

Two models, the so-called X-ray reflection nebula (XRN) model (Sunyaev et al., 1993) and the low-energy cosmic-ray (LECR) model (Yusef-Zadeh et al., 2002a), predict distinct spectral and temporal properties for the X-ray emission from GCMCs. In the XRN scenario, molecular clouds can reflect X-rays from an illuminating source by scattering continuum X-rays and producing fluorescence line emission following photo-ionization of K-shell electrons. The XRN model predicts (1) variability of Fe K line and X-ray continuum emission over the light-crossing time of a cloud (1-10 years) or over the variability time scale of an illuminating source, (2) a strong Fe K line with equivalent width (EW) keV, (3) a Fe-K photo-absorption edge at 7.1 keV and (4) a Compton reflection hump (i.e. curved power-law spectrum) in the hard X-ray band if the cloud column density is high ( cm). Alternatively, low-energy cosmic ray electrons (LECRe), protons and ions (LECRp) can eject K-shell electrons via collisional ionization leading to fluorescence line emission. The LECR model predicts (1) a power-law spectrum orignating from non-thermal bremsstrahlung emission, (2) an Fe K line with EW  (0.25-0.4)  keV where is the Fe abundance relative to solar (Yusef-Zadeh et al., 2007, 2013), and (3) time variability of Fe K line and X-ray continuum emission over the electron cooling/diffusion time (LECRe) or long-term variability over years (LECRp). The shape of the X-ray continuum is sensitive to the incident cosmic ray energy spectrum.

Previous soft X-ray observations have been mainly focused on tracking time evolution of Fe K- line at 6.4 keV (see Ponti et al., 2013, for a review), due to their narrow bandpass (typically 4-8 keV) where different spectral components such as diffuse thermal emission, X-ray continuum from the cloud, Fe K edge and Fe K fluorescent lines are potentially all present and strongly degenerate. Both the EW of the Fe K line and the absorption depth () of the Fe K edge are highly sensitive to the underlying X-ray continuum level. Diffuse thermal emission, if not properly subtracted, will enhance the underlying continuum level and thus decrease both the Fe K line EW and . However, in the previous XMM-Newton, Chandra and Suzaku analysis, intrinsic X-ray continuum spectra either have been poorly constrained (Inui et al., 2009; Ponti et al., 2010; Nobukawa et al., 2011) or have been assumed to be a power-law spectrum with fixed to 1.9 (Capelli et al., 2012). More importantly, previous X-ray studies determined the parameters of the GCMCs and illuminating X-ray sources separately from individual components such as the Fe K line or absorption edge, therefore they lack self-consistency. In the XRN scenario, an Fe K line flux measurement yields a luminosity of the illuminating primary souce only at keV with some uncertainty associated with Fe abundance (Sunyaev et al., 1993).

In constrast, a broad-band X-ray continuum measurement provides the most robust determination of the X-ray spectrum of the primary source in the XRN scenario and a cosmic ray energy spectrum in the LECR scenario. The hard X-ray continuum provides an excellent measurement of the intrinsic column density () of the cloud (Ponti et al., 2014). In the subsequent sections, we fit self-consistent spectral models to the broad-band X-ray spectra of the Sgr A clouds using the NuSTAR and XMM-Newton data. This provides a powerful diagnostic that can distinguish between different models and tightly constrain parameters since it takes the full advantage of the broadband X-ray spectroscopy.

### 6.1. Spectral analysis of the Sgr A clouds: MC1 and the Bridge

We extracted NuSTAR and XMM-Newton EPIC-PN source spectra of MC1 and the Bridge using the same regions quoted in Ponti et al. (2010), as indicated by the green regions in Figure 3. XMM-Newton observations 0694641101 (35.5 ks total exposure) and 0694640401 (43.9 ks total exposure) were used for MC1 and the Bridge respectively since the sources are not intercepted by detector gaps and the signal-to-noise ratio is highest in these observations. This allows us to extend our energy band to 10 keV for the XMM-Newton spectra, while the background dominates above  keV in the other observations. We selected appropriate NuSTAR observations and focal plane module data that cover the full extent of the clouds that are free from high background counts. We extracted MC1 source spectra from FPMA data of one Sgr A* observation (ObsID: 30001002004) and three mini-survey observations (ObsID: 40010001002, 40010002001 and 40010004001), for a total exposure time of 125.7 ksec. We extracted the Bridge spectra from FPMA data of three NuSTAR mini-survey observation (ObsID: 0010003001, 0010004001 and 40010006001) with a total exposure time of 71.5 ksec. Although there are two bright regions in the Bridge (the so-called Br1 and Br2 region in Capelli et al., 2012), separate spectral analysis of each region does not yield sufficient photon statistics. Since we are not certain whether SLB or focused diffuse emission dominates as the background of these regions, we applied both the conventional and off-source background subtraction methods described in the Appendix. We found that the final results were not significantly different between the two methods because the contribution of SLB and focused diffuse emission is similar in these molecular cloud regions.

We fit the joint XMM-Newton and NuSTAR spectra with XSPEC models based on the XRN and LECR scenarios. For all spectral models considered here, we applied tbabs*[apec + apec + cloud_model] where cloud_model represents one of the X-ray spectral models that are intrinsic to the GCMCs and described in the subsequent sections. In either case, the common model components are tbabs and two apec models representing foreground (galactic) absorption, and  keV thermal components in the GC, respectively. We linked all the fit parameters between the XMM-Newton and NuSTAR spectra except the flux normalizations for the two thermal (apec) model components since background spectra mostly composed of the two thermal components were extracted differently for the XMM-Newton and NuSTAR spectra. Hereafter, we present the best-fit flux normalizations of the two thermal components from the XMM-Newton spectral fitting.

For the LECR scenario, we fit a self-consistent X-ray spectral model available in XSPEC for both the LECR electron and proton cases, by taking into account both X-ray continuum and fluorescent line components calculated from the energy loss of cosmic-rays penerating into a slab-like cloud of neutral gas at a constant rate (Tatischeff et al., 2012). Since the observed year-scale time variability of Fe K line flux in the Sgr A clouds rules out the LECR proton scenario, we fit an absorbed LECR electron model (tbabs*lecre) as the intrinsic cloud model cloud_model. 111A similar model was used to fit X-ray spectra of Sgr B2 clouds (Terrier et al., 2010; Zhang et al., 2015). The photo-absorption term takes into acount intrinsic absorption in the cloud with a characteristic column density . Although Fe K-shell electrons are ionized by cosmic-rays coming from an external source, continuum X-rays emitted via non-thermal bremsstrahlung can undergo photo-absorption before escaping from the cloud. We also set for the opposite case where continuum X-rays are emitted near the surface of the cloud, in which case most of them are not absorbed in the cloud. Although this is not a self-consistent treatment of the intrinsic absorption in the cloud, the two cases should bound the problem where the radiative transfer of continuum X-ray photons is not considered in the LECR models. Following Tatischeff et al. (2012) and Krivonos et al. (2014), we fixed the path length of cosmic-ray electrons to  cm since we find that the fitting results are insensitive to . In all cases, the LECRe models do not fit the XMM-Newton and NuSTAR spectra for MC1 and the Bridge as well as the XRN models, yielding -1.4 (Figure 9 and 10). The spectral fitting requires unreasonably high metallicity in order for the LECRe model to account for the strong Fe K line. Therefore, we conclude that the LECRe models are not consistent with the X-ray spectra of the two Sgr A clouds.

### 6.2. Spectral fitting results with MYTorus model

Hereafter we present spectral fitting results primarily with MYTorus model, which is the only Monte-Carlo based XRN model that is available in XSPEC with finite cloud column density (Murphy & Yaqoob, 2009; Yaqoob, 2012). Unlike other XRN models that have been applied to GCMC X-ray data, the MYTorus model can determine the cloud and primary X-ray source parameters self-consistently. Indeed, we find that the MYTorus model yields better spectral fits than the other XRN models as shown in this section. The Appendix fully describes the MYTorus model application to the GCMC X-ray data and compare it with other widely-used XRN models. For comparison between the different models and also with the previous results, we present the fit results using an ad hoc XRN model  tbabs*(powerlaw + gauss + gauss) and a slab geometry model reflionx with infinite optical depth (Magdziarz & Zdziarski, 1995; Nandra et al., 2007; Ross & Fabian, 2005). Other slab geometry models such as pexmon yield similar results. In the ad hoc XRN model, we fixed the line energy and width of (weak) Fe K line to 7.06 keV and 0.01 keV, respectively and linked its flux normalization to that of Fe K line multiplied by 0.15, i.e. the ratio of the K and K line fluorescence yields (Murakami et al., 2001).

The MYTorus model includes three components, namely the transmitted continuum (MYTZ), scattered continuum (MYTS) and Fe fluorescent emission lines (MYTL), in a range of equatorial hydrogen column density through the tube of the torus  cm, power-law photon index -2.6 and incident angle (between an observer and the symmetry axis of the torus) . See Figure 15 in the Appendix for the geometry of the MYTorus model in comparison with the conventional geometry used in many publications on GCMCs. Note that and correspond to a face-on and edge-on observing view, respectively. Since we observe only the reflected X-ray emission from GC molecular clouds, we adopted two additive XSPEC models for scattered continuum (MYTS) and Fe fluorescent lines (MYTL):

atable{mytorus_scatteredH500_v00.fits} +
 atable{mytl_V000010pEp040H500_v00.fits}

in a “coupled” mode where the same primary X-ray spectrum is input for the both components. We selected the MYTS and MYTL tables with a power-law model with the highest energy cut-off at keV. Following the MYTorus manual , we selected the MYTL data table with an energy offset of +40 [eV] since the best-fit Fe K line centroids with a Gaussian line profile are 6.44 [keV] probably due to slightly ionized Fe in the clouds and/or instrumentral energy offset (note that NuSTAR has a systematic uncertainty of 40 eV near Fe emission lines; Madsen et al., 2015). We bound the incident angle to since we find that the MYTorus model is valid to fit the X-ray spectra of GCMCs in this range (Appendix).

The MYTorus model fits the joint XMM-Newton and NuSTAR spectra of MC1 and the Bridge well, yielding (MC1) and 1.13/524 (the Bridge), with all parameters well constrained (Figure 9, 10 and Table 2). We found that the intrinsic absorption and power-law continuum were accurately measured only by the joint fitting of XMM-Newton and NuSTAR spectra, as a result of combining high-resolution Fe line spectroscopy from XMM-Newton with broad-band X-ray spectroscopy from NuSTAR. The two thermal components have and keV and are consistent with the previous measurements in this region (Muno et al., 2004; Koyama et al., 2007). Although the abundance for the lower  keV temperature component is poorly constrained, we find that it does not affect the XRN model parameters. Although the ad hoc XRN model yields similar fit quality with (MC1) and 1.16/522 (the Bridge), the MYTorus model has fewer fit parameters due to its self-consistency - the power-law index and flux normalization are linked between the scattered continuum (MYTS) and the fluorescent line component (MYTL). The reflionx models do not fit MC1 and the Bridge spectra well with and 1.60/525, respectively. When we fit the MC1 spectra with the reflionx model, we fixed the plasma temperature of the second thermal component to 8 keV. Otherwise, the spectral fitting yields unreasonable parameters such as  keV and Fe abundance higher than 10 for the reflionx model.

#### Intrinsic column density

Our joint XMM-Newton and NuSTAR analysis using the MYTorus model measured the equatorial hydrogen column density (with 90% c.l. errors) with (MC1) and  cm (the Bridge). The ad hoc XRN model yields similar values in good agreement with the results of Capelli et al. (2012), who applied a similar ad hoc XRN model. Although one cannot simply compare the values from the MYTorus model and ad hoc XRN model (which has no geometry defined for ), our simulation shows that spectral fitting with the ad hoc XRN model “measures” an that deviates from the geometrical of the MYTorus model by a factor of , at  cm (Appendix). In comparison with the measurements of Ponti et al. (2010) (MC1: and the Bridge:  cm) based on the CS line intensity map (Tsuboi et al., 1999; Ponti et al., 2010), our value for MC1 is higher by a factor of while our result for the Bridge is close to their value. However, Ponti et al. (2010) and Capelli et al. (2012) pointed out the difficulty with constraining using molecular emission lines. For example, CS (Amo-Baladrón et al., 2009) and HCO (Handa et al., 2006) emission line measurements deduced nearly two orders of magnitude different values for another Sgr A cloud, G0.110.11. Still, the measured yields the Thomson depth of , indicating that these clouds are optically thin. Therefore, it is more accurate to apply XRN models properly suited for optically thin cases rather than the slab geometry models which assume infinite column density.

#### Power-law index

The power-law photon indices (with 68% c.l. errors) of the primary X-ray source are well constrained at (MC1) and (the Bridge) by the MYTorus model. The systematic errors associated with the angular dependence of the MYTorus model are smaller than the statistical errors for a measurement of at  cm (Appendix). Therefore, our results indicate that MC1 and the Bridge have consistent photon indices of the primary X-ray source at - level. The measured photon indices are both softer than those of Ponti et al. (2010): for MC1 and for the Bridge, based on XMM-Newton-only spectral analysis over a narrower band between 4 and 8 keV. The ad hoc XRN model measures similar photon indices to the MYTorus model since the clouds are optically thin and the primary X-ray spectrum shape is not significantly perturbed by photo-absorption and Compton scattering. The reflionx model yields softer photon indices ( and 2.3 for MC1 and the Bridge, respectively). Due to the infinite column density assumed in the reflionx model, low energy photons are overly absorbed thus requiring a softer power-law photon index to fit the X-ray spectra as similarly observed in NuSTAR spectral analysis of the Arches cluster and Sgr B2 (Krivonos et al., 2014; Zhang et al., 2015).

#### Fe Kα fluorescent line

Both the flux and the EW of the Fe K fluorescent line have often been used to track the time evolution of GC molecular clouds. Among our spectral models, only the ad hoc XRN model can provide Fe K line parameters separately since the Fe fluorescent lines and scattered continuum are coupled in the self-consistent models, which are not parameterized to easily provide Fe K fluorescent line fluxes or EWs in XSPEC. Using the fit results with the ad hoc XRN model, we calculated the Fe K line EW with respect to the power-law continuum, which is the only component instrinsic to the clouds and thus can be compared to the predictions from the XRN and LECR models (§6). For comparison with other results, it is crucial to specify which X-ray continuum component is used to calculate the Fe K line EW. Our EW values, (MC1) and keV (the Bridge), are larger than those of Ponti et al. (2010): 0.68 (MC1) and 0.75 keV (the Bridge), while the best-fit K line flux normalizations are consistent between our work and Ponti et al. (2010). Note that the Fe K line flux from the entire MC1 cloud has stayed nearly constant for years, although Chandra found different time variations across the cloud (Clavel et al., 2013). The discrepancy in Fe K line EWs is likely due to the fact that XMM-Newton continuum spectra are heavily contaminated by diffuse thermal emission, thus the continuum level is enhanced compared to the intrinsic non-thermal emission from the cloud. Indeed, using the Fe K line flux normalization and the power-law continuum parameters from Table 3 in Ponti et al. (2010), we obtain EW = 0.83 keV (MC1) and 1.16 keV (the Bridge) - they are similar to our measurements. Our Fe K line EW for MC1 is also consistent with Capelli et al. (2012), who measured EW keV.

#### Inclination angle

The inclination angle is constrained to for the Bridge, while is less constrained for MC1 likely because the overall X-ray reflection spectrum is rather insensitive to at  cm (Appendix) and the MC1 data have poorer photon statistics than the Bridge data. While it is tempting to suggest the Bridge with the best-fit is located close to the projection plane of the primary source, we cannot uniquely infer line-of-sight location of the cloud based on the measured inclination angle and also we cannot estimate systematic errors on in the MYTorus model (Appendix). A precise measurement of the cloud line-of-sight location should be performed with an improved XRN model implementing more realistic geometry for the Sgr A clouds in the future.

### 6.3. Implications for the primary source illuminating the Sgr A clouds

Table 3 summarizes the observed and derived parameters from MC1 and the Bridge using the self-consistent MYTorus model as well as the known geometrical parameters. For comparison with the Sgr A clouds, we adopted the Sgr B2 results from the 2003-2004 XMM-Newton and INTEGRAL observations (Terrier et al., 2010) soon after both the hard X-ray continuum and Fe K line fluxes started decaying in 2000, therefore they can determine the primary X-ray source spectra more accurately than the NuSTAR observation in 2012. Terrier et al. (2010) fit 2-100 keV spectra of a  circular region centered at the core of the cloud using a self-consistent XRN model, yielding the power-law index and 1-100 keV luminosity  erg  of an illuminating X-ray source (Table 3). 333The projected distance of 100 pc between Sgr A* and Sgr B2 was assumed for . The intrinsic column density  cm was also measured using an adhoc XRN model wabs*(apec+gaus+gaus+wabs*pegpw) (Terrier et al., 2010). Since the hydrogen column density distribution is highly non-uniform in the Sgr B2 region (Etxaluze et al., 2013), measured by X-ray spectral fitting may vary in the range of - cm depending on a choice of the extraction region (Zhang et al., 2015). Similar results ( and  erg s) were obtained by Revnivtsev et al. (2004) who analyzed ASCA, GRANAT and INTEGRAL data from a larger region () in Sgr B2 using a self-consistent XRN model.

MC1, the Bridge and Sgr B2 cloud have the consistent primary power-law indice . Since cannot be uniquely associated with the light-of-sight location of a cloud, the MYTorus model can give a lower bound of the illuminating source luminosity in which case the cloud and the primary X-ray source are located in the same projection plane. Using the best-fit primary X-ray fluxes at , we determined (MC1) and  erg s (the Bridge). Here, we assumed that the illuminating X-ray source is located at Sgr A* and we rescaled the primary X-ray flux following the recipe in the Appendix. For reference, using the observed Fe K line flux (which is also subject to Fe abundance uncertainty), Clavel et al. (2013) inferred higher X-ray luminosity of  erg s for MC1 since their estimate was based on the lower cloud column density ( cm) determined from the CS molecular line measurements (Ponti et al., 2010) contrary to our direct measurements of by fitting the broad-band X-ray spectra.

Given that MC1 and the Bridge require as low as erg s, it is possible that an outbursting X-ray transient could have illuminated these clouds. Previously, Chandra found short temporal evolution of two Fe K features in G0.110.11, and their Fe K emission was attributed to reflection of an outburst of Sgr A* or an X-ray binary with a few year duration (Muno et al., 2007). Also, Capelli et al. (2012) proposed that one of the Sgr A clouds emitting an Fe K line could be illuminated by the nearby X-ray transient XMMU J174554.4285456. Within the inner 10 of the GC, about a dozen X-ray transients have been detected, with their maximum 2-10 keV luminosities ranging from to erg s (Muno et al., 2005; Degenaar et al., 2012). Only 1A 1742289 had its maximum outburst X-ray luminosity ( erg s) exceed the inferred for MC1 and the Bridge. The only outburst from 1A 1742-289, observed in 1975, decayed rapidly over a few months (Branduardi et al., 1976), which is far shorter than the time variation of Fe K line flux observed from MC1 and the Bridge (Clavel et al., 2013). Similarly, none of the other X-ray transients in the GC had persistent outbursts over a long enough period ( years) to illuminate MC1 and the Bridge at the observed flux levels. In general, it is extremely rare for a bright outburst with erg s to last for a few years (Chen et al., 1997). Therefore, we rule out the known X-ray transients in the GC as primary sources for MC1 and the Bridge. Alternatively, an undetected X-ray transient with X-ray outburst luminosity erg s and year burst duration, such as the black hole binary GRS 1915105 (Fender & Belloni, 2004), could be a primary source. However, Clavel et al. (2013) found this scenario implausible since it requires unrealistic cloud distribution around the GC to account for the observed Fe K flux variation in the Sgr A clouds.

As a result, Sgr A* is the most likely illuminating source for MC1 and the Bridge. This is supported by the fact that the measured power-law indices (-2.1) for Sgr A clouds as well as for Sgr B2 (Terrier et al., 2010) are consistent with those from the current Sgr A* flares (Baganoff et al., 2001; Nowak et al., 2012; Degenaar et al., 2013; Neilsen et al., 2013; Barrière et al., 2014), and low-luminosity AGNs typically with (Reeves & Turner, 2000). Several studies based on Fe K line and X-ray continuum flux measurements suggest that Sgr B2 was illuminated by a giant Sgr A* flare with  erg s about 100 years ago (Koyama et al., 1996; Murakami et al., 2001; Terrier et al., 2010; Ponti et al., 2010; Capelli et al., 2012). Based on the different temporal variations of Fe K line emission from various GCMCs, Capelli et al. (2012) and Clavel et al. (2013) claimed that Sgr A* flaring activity in the past hundred years had multiple distinct periods with vastly different flaring powers before declining to the current flaring state with erg s (Nowak et al., 2012). Given the error bars in and the lower bounds of in Table 3, our analysis shows that the primary X-ray spectra are consistent between MC1, the Bridge and Sgr B2, thus it is still inconclusive whether these clouds were illuminated by different Sgr A* flares in the past or not. Continuing long-term monitoring of the Sgr A clouds by NuSTAR, with improved XRN models and photon statistics, will be able to constrain Sgr A* flaring activity (e.g., number of giant Sgr A* flares, their X-ray luminosities, and durations) over the last few hundred years more tightly.

## 7. The central 10 pc around Sgr A*

The central 10 pc around Sgr A* is a highly crowded region with an extremely rich variety of radio, IR, soft X-ray, GeV and TeV sources. However, the NuSTAR view of the GC above keV exhibits only two hard X-ray features — a point-like feature coincident with G359.950.04 and the CHXE (Figure 6). In the gamma-ray band, HESS detected a single source, HESS J1745290 at RA = and DEC = (J2000) (Acero et al., 2010), that is spatially consistent with both Sgr A* and G359.950.04. In this section, we investigate a connection between the hard X-ray sources and the HESS source as well as their emission mechanisms, based on our spectral analysis results using NuSTAR, XMM-Newton and Chandra data. A multi-wavelength SED analysis is discussed in the subsequent section to elucidate the TeV emission mechanisms.

### 7.1. Joint NuSTAR and XMM-Newton spectral analysis

We extracted NuSTAR spectra from a circular region of radius 40 around the Chandra position of G359.950.04 (Wang et al., 2006), at RA= and DEC = (J2000). This radius was chosen to maximize the significance of the highest-energy spectral bins and minimize contamination from diffuse thermal emission given the NuSTAR PSF (e.g., HPD). The NuSTAR background spectra were extracted from a region from the same detector chip but excluding Sgr A East, the “Plume” (Park et al., 2005), and the molecular clouds (Ponti et al., 2010). We extended the energy band for spectral fitting to 50 keV, above which the internal detector background dominates.

To better constrain the low-energy components of this spectrum, we used EPIC-PN data from the two XMM-Newton observations (ObsID: 0694640301 and 0694641101) carried out in 2012 for which Sgr A* was placed near the center of the FOV (See Table 1). X-ray spectroscopy with XMM-Newton EPIC instruments constrains the Galactic column density better than NuSTAR by fitting the spectrum below 3 keV, and it resolves Fe lines at 6.7 keV (He-like) and 6.9 keV (H-like), thus measuring the plasma temperature accurately. We extracted an XMM-Newton spectrum from the same region as used for the NuSTAR analysis. We generated response files and background spectra following the procedured described in §3.3. We used the 2-8 keV band for fitting the XMM-Newton spectra.

To fit the 2-50 keV spectrum of XMM-Newton and NuSTAR, we used the model const * tbabs * (apec + apec + pegpwrlw + gauss). To account for the different overall normalization between NuSTAR and XMM-Newton, a constant relative normalization factor was allowed to vary. The abundances of the two thermal components were fit freely within the range measured by the previous analysis (Baganoff et al., 2003; Sakano et al., 2004). The NuSTAR and XMM-Newton spectra of the central 40 region are shown in Figure 11 and the best-fit parameters are listed in Table 4. The lower-temperature component, at  keV, corresponds to a combination of the thermal emission from stellar winds in the central 10 region (Baganoff et al., 2003) and the low-temperature component of Sgr A East (Sakano et al., 2004). The higher-temperature component, at  keV, is consistent with the high-temperature component of Sgr A East in the region near Sgr A* (Sakano et al., 2004). The power-law component has a best-fit photon index and a 20-40 keV flux of  erg cm s.

### 7.2. Can G359.95−0.04 and the CHXE account for the 20-40 keV emission in the central 10 pc region?

In order to assess the presence of a hard X-ray extension of G359.950.04 above 10 keV, we performed spatially-resolved spectral analysis using the Chandra data. Chandra measured a photon index of for G359.950.04, but with a spectral softening from the pulsar head to tail ranging from 1.3-3.0 (Wang et al., 2006). The high-energy spectrum of this object is then most accurately modeled as a summation of spectra with different photon indices rather than a simple extrapolation of the best-fit photon index. We refit the spectrum extracted from the same region used by Wang et al. (2006) using a more extensive set of Chandra data. This yields a photon index of , consistent with the previous measurements. We then divide the Wang et al. (2006) region into three sub-regions of equivalent areas, yielding , and , listed in order from the head toward the tail. Then, we constructed a composite spectral model for G359.950.04 from a set of Chandra fluxes and photon indices from the three segmented regions in the filament, and extrapolated it to the hard X-ray band. The composite model gives a 20-40 keV flux of erg cm s.

Perez et al. (2015) showed the south-west and north-east region symmetrically located inside the CHXE ellipse have identical hard X-ray spectra, described equivalently well by either a power-law with or thermal bremsstrahlung with  keV. By repeating the same spectral analysis with the latest NuSTAR pipeline version, we determined the 20-40 keV flux of erg cm s in the southwest region of the CHXE. Using the spatial model of the CHXE presented in §4.2, we calculate the 20-40 keV flux of the CHXE to be erg cm s in the central 40 region around Sgr A*, assuming that the CHXE has a power-law spectrum with throughout its entire region.

The sum of the estimated G359.950.04 and CHXE flux ( erg cm s) matches with the observed 20-40 keV flux in the central 40 region ( erg cm s) within the error bars. In addition, the spectral model consisting of a hard X-ray extension of G359.950.04 and the CHXE emission reproduces the 20-40 keV NuSTAR spectrum since the measured PL index of is similar to those of G359.950.04 and the CHXE. This result confirms that 20-40 keV emission in the central 40 region is predominantly due to the CHXE and G359.950.04. Our imaging analysis in §4.3 shows G359.950.04 is more prominent above 40 keV likely because G359.950.04 has a slightly harder X-ray spectrum and is more compact than the CHXE. While other X-ray sources may contribute to the hard X-ray emission in the central 40 region, our error analysis indicates their contribution should be less than erg cm s in the 20-40 keV band. This upper limit will be useful in constraining models of X-ray and particle emission in the central parsec region around Sgr A*.

### 7.3. Connection with the TeV source HESS J1745−290

Our imaging and spectral analysis shows that above 20 keV hard X-ray emission in the central 10 pc region is composed of the CHXE and G359.950.04. No gamma-ray emission is expected from the CHXE since it is likely an unresolved population of massive magnetic CVs, while only a rare subclass of HMXBs are known to emit TeV gamma-rays (Dubus, 2013). Thus, it leaves only G359.950.04 as a hard X-ray counterpart candidate for HESS J1745290.

Previously, any models proposing that leptons are emitted from Sgr A* or its vicinity within a few pc have had great difficulties with explaining the large extent of the diffuse hard X-ray source IGR J174562901 since the synchrotron cooling time of TeV electrons emitting hard X-ray photons is as short as years (Neronov et al., 2005; Hinton & Aharonian, 2007). Now that NuSTAR has revealed the compact hard X-ray emission above 40 keV is centered around G359.950.04, this “cooling time” problem associated with IGR J174562901 no longer exists.

In order to explore whether G359.950.04 alone can account for the GC TeV emission spectroscopically, we developed a one-zone PWN model following Zhang et al. (2008) and used it to fit the broad-band SED data in the central parsec region. Our model inputs are PWN age, magnetic field strength at present, a broken power-law spectrum for electron injection [ at and at ] with the lower and upper energy limits, the radiation density in the IR, optical and UV bands, as well as pulsar spin-down parameters. For the SED data, we adopt the X-ray spectrum of G359.950.04 from our Chandra and NuSTAR spectral analysis and the TeV spectrum of HESS J1745290 from Aharonian et al. (2009). The radio non-detection with an upper limit of erg cm s from 6 cm observations (Hinton & Aharonian, 2007) is also taken into account in our analysis. Hereafter, we do not consider the Fermi GeV source 2FGL J1745.62858 at RA= and DEC = (J2000) since it lies outside the error circle of HESS J1745290 (Nolan et al., 2012; Yusef-Zadeh et al., 2013). 2FGL J1745.62858 may well be associated with the aformentioned X-ray filament G359.970.038 (Nynka et al., 2015).

Figure 12 shows the best-fit SED model along with the radio, X-ray and TeV data. Following Hinton & Aharonian (2007), we assumed G359.950.04 is a year-old PWN with a spin-down power of  erg s and its magnetic field strength is 300 G at present. We find that these parameters fit the SED data reasonably well. In the central parsec region, the radiation density can be as high as  eV cm (Davidson et al., 1992). We adopted the FIR, optical and UV radiation density from Hinton & Aharonian (2007) who quoted the original work of Davidson et al. (1992). We found that a broken power-law electron spectrum with , and  TeV represents the shape of the X-ray and TeV spectrum well. These electron injection parameters are typical of young PWNe (Zhang et al., 2008). The maximum electron energy was set to 200 TeV to account for the energy cut-off at 4 TeV in the gamma-ray spectrum (Aharonian et al., 2009). A low energy cut-off at  TeV was required so that the model is consistent with the non-detection of G359.950.04 in the radio band. Alternatively, Hinton & Aharonian (2007) proposed fast electron diffusion to account for the lack of a radio counterpart. Both the upper and lower limit in the electron injection spectrum are similar to those of Hinton & Aharonian (2007) who analyzed the same SED data except using the X-ray spectrum of the INTEGRAL source IGR J174562901. In conclusion, we find that G359.950.04 alone, likely a year-old PWN with nominal electron injection parameters, can account for the broad-band SED of the central parsec region including HESS J1745290. It is noteworthy that the other distinct TeV gamma-ray source within a degree from the GC is associated with another young PWN in SNR G0.9+0.1 (Aharonian et al., 2005).

As an alternative leptonic scenario for the GC TeV emission, stellar wind shocks from massive stars in the central stellar cluster can efficiently accelerate electrons (Quataert & Loeb, 2005), or Sgr A* itself can eject high-energy electrons (Kusunose & Takahara, 2012). Due to the fast electron cooling time either by synchrotron radiation or inverse Compton scattering in the GC, hard X-ray emission should be localized around an electron acceleration site. While these emission mechanisms may be in action, our NuSTAR analysis indicates that their contribution is insignificant since the hard X-ray emission above 40 keV is spatially and spectroscopically consistent with G359.950.04. Therefore, the PWN candidate G359.950.04 seems to be the most plausible hard X-ray counterpart of the TeV source HESS J1745290.

The hadronic scenario may be plausible as well based on the fact that diffuse TeV emission is spatially well correlated with molecular clouds in the GC (Aharonian et al., 2006). One potential source of ejecting high energy protons is Sgr A* (Aharonian et al., 2006; Ballantyne et al., 2007; Dogiel et al., 2009b; Ballantyne et al., 2011). Among a number of hadronic models proposed for the gamma-ray emission in the GC, there has been no specific prediction for X-ray spectra in the central parsec region. Rather, they have been focused on larger degree-size regions over which protons can propagate without losing kinetic energies significantly (Dogiel et al., 2009c). Similar to the LECR model, either non-thermal bremsstrahlang or synchrotron is expected to be the primary X-ray emission mechanism via secondary electrons produced by hadronic interactions between high energy protons and molecular clouds (Dogiel et al., 2009b, c; Gabici et al., 2009). Such X-ray emission must be most prominent at the location of molecular clouds or high-density gas in the vicinity of Sgr A*, potentially with Fe K line emission at 6.4 keV (Dogiel et al., 2009a). In addition, X-ray emission in the hadronic scenario should have a larger extent than in the leptonic scenario since protons have significantly longer cooling times than electrons in the GC where both magnetic field and radiation density are high. To the contrary, hard X-ray emission above 40 keV is highly concentrated around G359.950.04, and Chandra did not detect strong Fe K emission within 10 pc around Sgr A*, including the circumnuclear disk (Baganoff et al., 2003). Therefore, the hadronic scenario is unlikely to be a major contributor for the hard X-ray and TeV emission in the central parsec region.

## 8. Summary

The initial 450 ksec phase of the NuSTAR GC program, with its high-resolution imaging and spectroscopic capability from 3 to 79 keV, has made unique contributions to understanding high-energy phenomena in the crowded GC region as listed below.

• NuSTAR resolved the INTEGRAL source IGR J174562901 into non-thermal X-ray filaments, molecular clouds, point sources and the previously-unknown central hard X-ray emission (CHXE) above 20 keV.

• The X-ray emission from Sgr A East is thermal with  1-6 keV with no evidence of non-thermal emission, and is consistent with the previous soft X-ray observations (Maeda et al., 2002; Sakano et al., 2004).

• In the 20-40 keV band, NuSTAR discovered hard X-ray emission (CHXE) centered on Sgr A*. The CHXE is elongated along the Galactic Plane with an elliptical extent of  pc (Galactic longitude) and  pc (Galactic latitude) (Perez et al., 2015). The most likely explanation for the CHXE is an unresolved population of massive magnetic CVs (largely intermediate polars) with (Hailey et al., 2015).

• NuSTAR detected four non-thermal X-ray filaments (G359.890.08, G359.970.038, G0.130.11 and G359.950.04) above 10 keV. The origin of non-thermal X-ray filaments may be heterogeneous and associated with different emission mechanisms such as magnetic flux tubes trapping TeV electrons (Zhang et al., 2014), SNR-cloud interaction and PWNe (Nynka et al., 2015).

• For the first time, NuSTAR resolved hard X-ray emission from the Sgr A clouds above 10 keV and unambiguously detected hard X-ray continuum emission from MC1 and the Bridge. Hard X-ray continuum emission is spatially correlated with Fe K line emission (EW  keV) from these clouds. We fit the Monte-Carlo based MYTorus model to the XMM-Newton + NuSTAR spectra of MC1 and the Bridge, and determined their intrinsic column densities ( cm) and the primary X-ray spectra with self-consistently. We set a firm lower bound for X-ray luminosity of Sgr A* flares illuminating MC1 and the Bridge to  erg s. It is still unclear whether the Sgr A and Sgr B clouds were illuminated by different Sgr A* flares in the past.

• A point-like hard X-ray source observed in the 20–60 keV band is identified as the PWN candidate G359.950.04, away from Sgr A*. The hard X-ray emission in the central 10 pc region is predominantly composed of two sources, G359.950.04 and the CHXE.

• In the central 10 pc around Sgr A*, G359.950.04 is the primary hard X-ray feature that is expected to emit TeV gamma-rays via inverse Compton scattering of IR, optical and UV photons. Our SED study suggests that G359.950.04 is the hard X-ray counterpart of the persistent TeV source HESS J1745290, thus strongly favoring the leptonic origin of the TeV emission at the very center of our galaxy.

Follow-up deep observations by NuSTAR will lead to further spectral identification of X-ray filaments and point sources. Monitoring time variation of the GC molecular clouds jointly by NuSTAR and XMM-Newton will elucidate their X-ray emission mechanism and probe the primary illuminating source or Sgr A* flaring activity in the past. Starting from April 2015, the NuSTAR Legacy program will follow up some of the hard X-ray sources discussed in this paper with deeper exposures.

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). R. Krivonos acknowledges support from Russian Science Foundation through grant 14-22-00271. G. Ponti acknowledges support via an EU Marie Curie IntraEuropean fellowship under contract no. FP-PEOPLE-2012-IEF-331095, the Bundesministerium für Wirtschaft und Technologie/DeutschesZentrum füÌr Luf-und R fahrt (BMWI/DLR, FKZ 50 OR 1408) and the Max Planck Society. F.E. Bauer acknowledges support from CONICYT-Chile (Basal-CATA PFB-06/2007, FONDECYT 1141218, “EMBIGGEN” Anillo ACT1101), and the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. S. Zhang is supported by NASA Headquarters under the NASA Earth and Space Science Fellowship Program - Grant “NNX13AM31”. D. Barret acknowledges support from the French Space Agency (CNES). We thank Tahir Yaqoob for useful discussions on the MYTorus model.

## Appendix A NuSTAR background in the Galactic Center observation

NuSTAR imaging and spectral analysis of GC sources is challenging due to the high background level and to its complex multiple components. The NuSTAR background is generally characterized by four different components as outlined below. More detailed discussion on the CXB and internal background can be found in Wik et al. (2014).

• Focused diffuse background (2-bounce background photons): diffuse background photons in the FOV are reflected twice by the optics and focused on the detector plane.

• Ghost-rays (1-bounce background photons): Photons from outside the FOV are reflected once by the optics and reach the detector plane. Ghost-ray photons from a bright persistent source or X-ray transient can be significant, with a visible pattern in the NuSTAR image. Although some observations of the GC and Norma field have been severely affected by ghost-ray background (Bodaghee et al., 2014), it is not important in the NuSTAR mini-survey and Sgr A* observations.

• Stray-light or aperture background (0-bounce background photons): Photons from any X-ray source at - away from the telescope pointing vector, that are not blocked by the aperture stop, illuminate the detector plane. Stray-light background (SLB) is not uniform over the detector plane, and it is not identical between the two focal plane modules. The location of SLB is sensitive to the position angle (PA) of the telescope.

• Internal detector background (cosmic-ray induced background photons): atmospheric albedo and activation components with several emission lines in the 20-40 keV band. Above keV, this component usually becomes more important than the other background components.

Figure 13 shows example NuSTAR images (FPMA and FPMB images from ObsID: 40032010001) exhibiting both ghost-ray background and SLB. The radiating pattern in the lower-left corner of both the FPMA and FPMB image is due to the ghost-ray background photons from the bright persistent LMXB 1A1742294 at RA= and DEC = (J2000) (Wijnands et al., 2006). On the other hand, the bright region in the upper-left corner of the FPMA image is due to the SLB from the bright X-ray source GX 3+1 (Seifina & Titarchuk, 2012).

### a.1. Stray-light background removal from bright X-ray point sources

In some observations, SLB from a point source brighter than erg cm s can be easily visible in raw NuSTAR images (Figure 13). For a given position angle (PA) and a list of nearby bright point sources, we can exactly predict the SLB pattern on the detector plane. Using a code developed specifically for calculating the SLB pattern from a point source with known position, we can generate a bad-pixel map for each detector module and observation, and then filter out events and exclude exposure map in regions of high SLB. This is one of the NuSTAR data filtering processes discussed in §2, before proceeding to further imaging and spectral analysis.

### a.2. Background spectrum subtraction

For all GC sources discussed in this paper, the primary background component below keV is focused diffuse background and SLB, while the instrumental background dominates above keV. For example, Figure 14 shows a NuSTAR background spectrum extracted from a region free from point sources and molecular clouds in one of the NuSTAR mini-survey observations (ObsID 40032001002). As shown in Figure 14, SLB from the Galactic Ridge X-ray emission (sGRXE) is usually dominant over that of cosmic X-ray background (sCXB). This background spectrum is typical to NuSTAR GC observations. Focused CXB and GRXE components are not shown in the figure since their fluxes are lower than their stray-light components by an order of magnitude. Both the CXB and internal background are modeled by the nulyses or nuskybkg software package using the high-latitude NuSTAR data (Wik et al., 2014). The sGRXE spectrum is well represented by an absorbed thermal spectrum (APEC model in XSPEC) with keV and an Fe K emission line at 6.4 keV.

The background count rate per detector area [cm] extracted from relatively source-free regions in the NuSTAR mini-survey observations varies between and  cts sec cm in the 3–20 keV band. After subtracting the model count rates from the sCXB component and internal detector background (Wik et al., 2014), the 3–20 keV sGRXE count rate ranges from (ObsID: 40010003001) to  cts sec cm (ObsID: 40010001002) with the mean count rate of  cts sec cm. The sGRXE component accounts for % of the total background count rate in the 3-20 keV band. Both sGRXE count rate and its fraction to the overall background varies between different observations, position angles and detector modules.

The relative significance between the focused diffuse background and the SLB varies between different regions in the NuSTAR image. When focused diffuse emission is dominant, one can extract a background spectrum from a region away from the source on the same detector chip over which the instrumental background is uniform (Harrison et al., 2013). When SLB is dominant, we extract a background spectrum using the same detector region used for extracting a source spectrum from another nearby observation with a similar position angle (off-source background subtraction) (Krivonos et al., 2014). For instance, the Sgr A* complex has significant GC thermal emission so the former conventional background subtraction should be applied. On the other hand, the off-source background subtraction is more appropriate for the Arches cluster where the SLB is more significant than the focused GC diffuse emission (Krivonos et al., 2014).

While the sCXB component can be accurately modeled using NuSTAR extragalactic deep survey data (Wik et al., 2014), there is no reliable background model for the sGRXE component due to the complex and unknown spatial distribution of the GRXE. Instead, as guidance, we used the sGRXE count rates determined from the NuSTAR mini-survey data to estimate whether the sGRXE is dominant over other background components for a given source region. For some sources, the situation is “mixed” where both the focused diffuse background and SLB have similar count rates. In this case, we applied both background subtraction methods to bound the problem.

### a.3. Comparison of X-ray reflection models applied to GC molecular clouds

In general, the X-ray reflection spectrum from a GC cloud is composed of scattered continuum, Fe fluorescent lines and photo-absorption edges. A popular XRN model for GCMCs is an absorbed power-law continuum with two Gaussian emission lines for the Fe K and K lines respectively:  tbabs*(powerlaw + gauss + gauss) where tbabs model, sometimes replaced by wabs, represents intrinsic absorption in the cloud. This model assumes that Fe fluorescent photons come from the center of a cloud, while another form  tbabs*powerlaw + gauss + gauss assumes that Fe fluorescent photons come from the surface and are therefore not subject to photo-absorption in the cloud. In practice, there is almost no difference between these two cases unless the cloud column density is extremely high. However, this ad hoc XRN model lacks self-consistency since photo-absorption, scattered continuum and fluorescent lines are decoupled and fit separately. The scattered continuum is represented by a single power-law model assuming that the primary X-ray spectrum shape is unperturbed by Compton scattering. This assumtion is valid only for low energy photons where Compton scattering is negligible, and when a cloud is optically thin ( cm).

In the other extreme case, slab geometry models such as  pexrav, pexmon and  reflionx calculate X-ray reflection spectra self-consistently from a slab with infinite optical depth (Magdziarz & Zdziarski, 1995; Nandra et al., 2007; Ross & Fabian, 2005). Ponti et al. (2010) applied the pexrav model to Sgr A molecular clouds, while reflionx has been used to fit X-ray spectra of the Arches cluster (Krivonos et al., 2014) and the Sgr B2 cloud (Zhang et al., 2015). However, the major drawback of these slab geometry models is that they are applicable only for Compton-thick clouds ( or  cm), and they do not allow for a measurement of the column density. Both our spectral analysis and independent measurements suggest that the Sgr A clouds are optically thin with  cm.

None of the above models can determine the intrinsic column density of a cloud and the primary X-ray spectrum self-consistently. As demonstrated by recent X-ray studies of Compton-thick AGN, Monte-Carlo simulation is the only viable approach to build a self-consistent X-ray reflection model (Murphy & Yaqoob, 2009). In the past, Sunyaev & Churazov (1998), Revnivtsev et al. (2004) and Odaka et al. (2011) studied X-ray morphology and spectra of GCMCs using Monte-Carlo based X-ray reflection models. These models explored some limited parameter space primarily for Sgr B2, but they are not implemented in XSPEC for spectral fitting. At present, the MYTorus model is the only X-ray reflection model that is available in XSPEC that can measure the intrinsic column density self-consistently for GCMCs (Murphy & Yaqoob, 2009; Yaqoob, 2012). The MYTorus model employs Monte-Carlo simulation of reprocessing X-ray photons from a toroidal reprocessor, and it enables “real-time” spectral fitting in XSPEC using tabulated Green’s function data. The other X-ray reflection models available in XSPEC either assume infinite column density or do not separate a reflected component (Brightman & Nandra, 2011). Although the MYTorus model was originally developed to study Compton-thick AGNs with a toroidal X-ray reflector, we find that it is applicable to X-ray spectral analysis of GCMC data with some restrictions as shown in the next section. Table 5 compares the three XRN models used in our analysis, their assumptions, limitations and valid parameter ranges.

### a.4. Applicability of MYTorus model to X-ray spectroscopy of GC molecular clouds

Since the MYTorus model was developed primarily for studying X-ray reflection spectra of Compton-thick AGN, it assumes a torus with completely neutral material and uniform density (Murphy & Yaqoob, 2009). The MYTorus model covers a range of the equatorial column density - cm and power-law photon indices -2.6. Note that the MYTorus model defines the inclination angle between an observer’s line of sight (LOS) and the symmetry axis of the torus (), while most publications on GCMCs use a scattering angle () of illuminating photons off the cloud to the observer (Capelli et al., 2012). See Figure 15 for the geometry of a cloud and the torus as well as the definition of the incident and scattering angle. A face-on viewing case for the MYTorus model () corresponds to the scattering angle when a cloud is in the same projected plane as the primary X-ray source. For each of the three key assumptions associated with the MYTorus model, below we investigate the valid parameter space where the model is applicable to analyze X-ray reflection spectra of molecular clouds in general.

• The reflector geometry is toroidal.

We explored a large range of and to investigate the validity of MYTorus model application to a quasi-spherical cloud. To begin with, a face-on case () provides an accurate solution for a cloud since the axial symmetry is preserved for X-ray photon reflection with respect to a distant observer. We can obtain reflected X-ray flux from the cloud (which is a part of the virtual torus, i.e. the red circle in Figure 15) by scaling the best-fit primary X-ray flux by a solid angle ratio of the torus (fixed to ) and the cloud. In this way, we ’collect’ X-rays reflected from the cloud only and ’abandon’ X-rays reflected from the rest of the torus (the grey area in Figure 15). and remain the same regardless of the cloud geometry. As deviates from the face-on case, different azimuthal parts around the torus can scatter X-rays at different angles therefore the MYTorus model spectrum may show some variation with the inclination angle and become inaccurate for a quasi-spherical cloud.

However, we find that the scattered continuum component (MYTS) does not vary with strongly as long as and the cloud is optically thin ( cm). Figure 16 shows MYTS model spectra at various inclination angles for and  cm. There are two reasons for the strong angular dependence at . First, since the half-opening angle of the torus is fixed to , some back-scattered X-ray photons from one side of the torus can hit the other side thus they are subject to further absorption before reaching an observer at . This is peculiar to the assumed torus geometry of the MYTorus model. Second, multiple scattering can induce some angular dependence of X-ray reflection spectra but it is negligible at  cm. Odaka et al. (2011), who simulated X-ray reflection spectra for the Sgr B2 cloud (with a spherical shape assumed), found that the scattered X-ray continuum spectrum and morphology do not depend on the location of the cloud and incident angle significantly when the cloud is not Compton thick. Moreover, the scattered X-ray flux is proportional to the total mass (or solid angle for a given ) of a cloud regardless of its shape, if it is optically thin (Cramphorn & Sunyaev, 2002).

To quantify the (in)sensitivity to or assumed geometry, we made simulated MYTS spectra for at - cm, then we fit the simulated spectra with the MYTS model with fixed at . We measured the deviation of , and normalization from their input values, and adopted them as systematic errors associated with the MYTorus model. At  cm, and normalization deviate from the input values by %, 1% and 7%, respectively. At  cm, the deviation increases to %, 3% and 10%.

We also compared an absorbed power-law model (tbabs*powerlaw) with the MYTorus model spectra in Figure 16. We adopted the mean column density of over all LOS through the torus (Murphy & Yaqoob, 2009), power-law index of and flux normalization roughly adjusted to the MYTorus model spectra in high energy band where photo-absorption is negligible. Note that the ad hoc XRN models predict significantly lower X-ray fluxes than the MYTorus models in low energy band. This is due to the fact that the ad hoc XRN model uses a single absorption term with a charateristic column density whereas photo-absorption takes place in various locations in the cloud with different optical depths. Based on simulation, we find that the ad hoc XRN model yields a column density lower than the equatorial column density () from the MYTorus model by a factor of 2-3 in the range of - cm.

Our primary goal is to determine the primary X-ray spectrum (e.g., Sgr A* flares) therefore we set  cm as a valid range of MYTorus model application to molecular clouds because otherwise the systematic errors for and normalization become larger than our statistical errors. We conclude that the reflected X-ray spectrum model in the NuSTAR energy band (3-79 keV) is not sensitive to the geometry of a reflector as long as and  cm. In this range, similarly to the face-on case, the incident X-ray flux for a given cloud can be obtained by scaling the best-fit X-ray flux from the MYTorus fit by the solid angle ratio of a cloud (typically for GCMCs) and the torus of the MYTorus model () with % errors. The best-fit power-law index from the MYTorus model fit can be adopted as that of the primary X-ray source with % errors. On the other hand, a relation between and LOS distance of a cloud as well as its systematic errors cannot be well established. A modified version of the MYTorus model for more realistic cloud geometry (e.g. sphere) is under development and it will be used to determine the location of the GC molecular clouds and their primary X-ray source spectra more precisely without the restrictions described above.

• The torus density profile is uniform.

Since we extract X-ray spectra from the entire cloud and collect all X-ray photons reflected toward us, we assume that any effects due to the non-uniformity of the density profile will be negligible at  cm as multiple scattering is insignificant at these column densities. Also, the reflected X-ray flux is proportional to the total mass of a cloud if it is optically thin (Cramphorn & Sunyaev, 2002). Thus, the primary X-ray flux will not be affected by different density profiles. It is, however, more important to take into account non-uniform density profile for X-ray morphology studies of GCMCs (Sunyaev & Churazov, 1998; Odaka et al., 2011).

• Fe abundance is fixed to solar.

Non-solar Fe abundance primarily affects Fe fluorescent lines at 6.4 and 7.0 keV and the Fe K absorption edge at 7.1 keV. While an unknown Fe abundance adds some uncertainty when one attempts to determine the primary X-ray luminosity solely from the Fe K line EW, broadband X-ray spectroscopy with NuSTAR extends to keV where the contribution of Compton scattering dominates over that of Fe fluorescent lines or photo-absorption. We confirmed that the fit parameters did not vary significantly when we fit the MYTS (scattered continuum) model only to the XMM-Newton + NuSTAR spectra of MC1 and the Bridge without 6-10 keV energy bins where the Fe fluorescent lines and the K-edge are prominent. A new self-consistent XRN model based on the MYTorus model will implement data tables for different Fe abundances in the range of -3 (private communication with T. Yaqoob).

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