A Deep Chandra View of a Candidate Parsec-scale Jet from the Galactic Center Supermassive Black Hole

Accretion onto a supermassive black hole (SMBH) can produce highly collimated, magnetized outflows of relativistic particles, i.e., jets. While the launching mechanism and composition of jets are still not well understood, it is generally believed that jets can mediate the transport of an enormous amount of energy from the central engine to much greater physical scales, thus playing an important role in regulating the coevolution of the SMBH and its environment (Meier 2012). As such, jets often manifest themselves as elongated features across a broad range of wavelengths, especially in the radio and X-ray bands where synchrotron and/or inverse Compton radiation from relativistic electrons are predominant. Spatially resolved studies of such features have greatly facilitated our general understanding of jet energetics and kinematics.

Rather ironically, our knowledge about jets emanating from the closest SMBH, the one located in the Galactic center (GC) and best known as Sgr A* (Melia & Falcke 2001), remains elusive. On the one hand, numerous theoretical studies have demonstrated that the centimeter-to-millimeter emission from Sgr A* can be interpreted as synchrotron radiation from a relativistic jet (e.g., Falcke et al. 1993; Falcke & Markoff 2000; Markoff et al. 2001; Yuan et al. 2002), which is likely symbiotic with a radiatively inefficient, advection-dominated accretion flow (Yuan & Narayan 2014). On the other hand, despite continuing efforts, observational searches for the putative jet, on sub-parsec to kiloparsec scales and over radio to γ-ray wavelengths, remain inconclusive (for an overview of the proposed jet candidates, see Li et al. 2013; hereafter LMB13; see also Shahzamanian et al. 2015; Yusef-Zadeh et al. 2016).

Among the proposed jet manifestations, a narrow linear X-ray feature named G359.944−0.052 (hereafter G359.944 for brevity), originally identified by Muno et al. (2008) with Chandra observations and further studied by LMB13, is of special interest for several reasons. First, this feature traces the putative jet on a sub-parsec scale, thus it can potentially help constrain any jet-driven feedback in the close vicinity of Sgr A*, as well as reveal short-term variations in the accretion process. Second, this feature is detected in X-rays and its power-law-shaped spectrum was found to be consistent with synchrotron emission. Due to the strongly magnetized environment of the GC, the synchrotron cooling timescale, on the order of ∼1 yr (see discussion in Section 6), requires continuous energy input, which was suggested to originate from the putative jet dissipating its internal energy upon collision with one of the gas streamers constituting the so-called mini-spiral (Figure 1), first discovered by Lo & Claussen (1983) and Ekers et al. (1983) with the Very Large Array (VLA). Third, and perhaps physically most attractive, the inferred spatial orientation of G359.944 (hence that of the underlying jet) is aligned with the angular momentum of the Galactic disk. This alignment is what one might expect if: (1) the jet orientation is dictated by the SMBH's spin axis, and (2) if the SMBH's angular momentum has resulted from the accretion of stars and gas that had an average angular momentum reflecting that of the Galaxy. This special geometry, if true, is highly instructive for modeling the process of accretion onto Sgr A*. Indeed, recent studies combining numerical models and millimeter data seem to agree on a high inclination angle (with respect to our line-of-sight) of the spin axis (e.g., Vincent et al. 2015; Broderick et al. 2016), lending support to the inferred jet path.

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The case for a jet can be reinforced if a relation between the variability of G359.944 and intrinsic variability of Sgr A* can be established. It has long been known that Sgr A* exhibits strong variability in its broadband radiation, a phenomenon commonly dubbed flares (Baganoff et al. 2001; Genzel et al. 2003; Ghez et al. 2004). In particular, the X-ray flares of Sgr A* can reach peak fluxes ∼10–100 times the quiescent level on a timescale of minutes (e.g., Baganoff et al. 2001; Porquet et al. 2003; Nowak et al. 2012; Zhang et al. 2017), strongly suggesting that they arise from merely a few gravitational radii from Sgr A*. At present, there is no consensus on the physical origin of the flares, but it is reasonable to associate flares with fluctuations or instabilities in the magnetized accretion flow (e.g., Chan et al. 2015; Ball et al. 2016; Li et al. 2017; Yuan et al. 2018). For this reason, when the G2 object, a hypothetical dusty cloud (with or without a central star; Gillessen et al. 2012; Witzel et al. 2014), was discovered to be moving on a highly eccentric orbit (e ≈ 0.98) and approaching periapsis around early 2014, there was heated anticipation that it might boost accretion onto Sgr A* and trigger strong radiation. Indeed, an increase in the frequency of bright X-ray flares a few months after the periapsis passage of G2 was suggested by Ponti et al. (2015) (see also Mossoux & Grosso 2017). On the other hand, no significant excess was seen at other wavelengths after the periapsis passage (for radio, see Park et al. 2015; Tsuboi et al. 2015; for infrared, see Witzel et al. 2018; for γ-rays, see Ahnen et al. 2017).

The jet power is generally thought to be correlated with the accretion rate (Yuan & Narayan 2014). In this regard, a parsec-scale jet may provide additional insight into the accretion process that is possibly affected by tidal interaction between Sgr A* and G2 or similar objects (e.g., G1; Witzel et al. 2017). In this work, we aim to revisit the case of G359.944 being the X-ray counterpart of the Sgr A* jet, taking advantage of the extensive Chandra observations of the GC in the past two decades. Our focus is devoted to probing flux and spectral variations in G359.944, and to further constraining the X-ray radiation mechanism and underlying jet properties.

We describe the Chandra data in Section 2. The spatial properties of G359.944 are reviewed in Section 3. Analysis of the flux variability is presented in Section 4. In Section 5, we examine the spatially resolved and time-dependent spectra of G359.944. Implications for the radiation mechanism and jet properties are discussed in Section 6, followed by a summary in Section 7. We adopt a distance of 8 kpc for the GC (Ghez et al. 2008; Gillessen et al. 2009).

The inner few parsecs centered on Sgr A* have been frequently visited by the Chandra X-ray Observatory since launch, chiefly with its Advanced CCD Imaging Spectrometer (ACIS). In this work, we utilize 47 ACIS-I observations taken between 1999 September and 2011 March, 38 ACIS-S observations with the High Energy Transmission Grating (HETG) taken between 2012 February and October, and 39 ACIS-S non-grating observations taken between 2013 May and 2017 July. All these observations had their aimpoint placed within 1' from Sgr A*,⁶ thus ensuring an optimal point-spread function for narrow features like G359.944. The ACIS-I data are essentially the same as used in LMB13. The ACIS-S non-grating (hereafter referred to as ACIS-S) observations, while taken in a 1/8 subarray mode, has a sufficiently large field of view to cover G359.944 and to substantially extend the temporal baseline, especially around the periapsis passage of G2.

Our data reduction procedure is detailed in Zhu et al. (2018), in which we have combined the ACIS-I and ACIS-S/HETG (hereafter simply referred to as HETG) observations to obtain the deepest ever X-ray source catalog of the GC. The main steps are briefly described below. We uniformly reprocessed the level 1 event files with CIAO v4.9 and the corresponding calibration files, following the standard pipeline.⁷ The light curve of each ObsID was examined, and when necessary, was filtered to remove time intervals contaminated by significant particle flares. This resulted in a total cleaned exposure of 1.42 Ms from ACIS-I, 2.83 Ms from HETG and 1.33 Ms from ACIS-S. The three data sets have comparable sensitivities,⁸ and when combined, they roughly double the signal-to-noise ratio (S/N), as achieved in LMB13 for G359.944. It is noteworthy that two ACIS-I observations, ObsID 5360 and 6639, suffer from relatively high particle background throughout their short exposures, thus they were excluded from the following analysis. In total, 122 observations spanning 5.58 Ms are included in this work. More specific information on the data sets are listed in Table 1. After the cleaned level 2 event file was created for each ObsID, we produced a merged event file by reprojecting all events to a common tangential point, i.e., the position of Sgr A* ([R.A., decl.] = [17:45:40.038, −29:00:28.07] at epoch J2000). We also generated exposure maps in the 2–8 keV band for each observation, assuming an incident spectrum of an absorbed bremsstrahlung. The lower energy cutoff is justified by the large foreground absorption column density N_H ∼ 10²³ cm⁻² (e.g., Zhu et al. 2018). The individual exposure maps of the same instrument (i.e., ACIS-I, HETG or ACIS-S) were then reprojected to form a combined exposure map.

In addition, we have acquired ancillary VLA and NuSTAR images, chiefly to obtain constraints on the flux of G359.944 at radio frequencies and in hard X-rays. Details of the VLA images can be found in Zhao et al. (2009; see also LMB13). We analyzed the NuSTAR data obtained in 2012 (ObsIDs: 30002001001, 30002001003, and 30002001004), an epoch with no X-ray transient contaminating the inner few parsecs around Sgr A* (S. Zhang et al. 2019, in preparation). Using the selected data set, we extracted the source spectrum and the background spectrum from an annular region that can properly represent the PSF contamination from the bright pulsar wind nebula (PWN) candidate G359.95−0.04 (Wang et al. 2006) at the location of G359.944. We found that G359.944 is detected at only the 1σ confidence level in 3–79 keV, and lower than 1σ in the 3–10, 10–20, and 20–40 keV energy bands. In 10–40 keV, the 3σ flux upper limit is 1.5 × 10⁻¹³ erg cm⁻² s⁻¹, assuming a representative photon index of 1.0 (see Section 5).

A 2–8 keV counts image combining the 122 Chandra observations is shown in Figure 1, highlighting the X-ray filament G359.944 and the X-ray-bright Sgr A complex. Also shown are VLA 8.4 GHz intensity contours tracing the ionized gas streamers of the mini-spiral (Zhao et al. 2009). The highly linear morphology of G359.944 and its almost perfect alignment with Galactic latitude can be clearly seen in the figure. The fact that the extrapolation of the straight line defined by G359.944 points back to Sgr A* had led Muno et al. (2008) and LMB13 to associate G359.944 with the putative jet. LMB13 further identified a shock front on the Eastern Arm of the mini-spiral (at an offset of [Δα, Δδ] = [128, 77] from Sgr A*, as marked by the white "X" in Figure 1), which they interpreted as the site where the jet penetrates through and dissipates energy to the ionized gas. Consequently, G359.944 can be understood as the synchrotron radiation from shock-induced relativistic electrons cooling in a finite post-shock region downstream from the shock along the jet path.

We revisit the above qualitative picture with the updated X-ray data. For a quantitative analysis, we follow LMB13 to adopt the hypothetical jet path as pointing away from Sgr A* at a position angle of 1245. Visual examination indicates that this remains an optimal definition for the linear filament in the current X-ray image of significantly enhanced counting statistics. LMB13 suggested that the filament is unresolved along its short axis. We update this view by comparing the intensity distribution of G359.944 along its short axis with that of nearby point sources. The derived FWHM is ∼11 for the former and ∼08 for the latter, suggesting that the filament is marginally resolved along its short axis, having a linear width of ∼0.04 pc at the assumed distance of 8 kpc. We emphasize that the average PSF should have a negligible variation along G359.944.

The exposure-map-corrected 2–8 keV intensity profile along the long axis of G359.944 is shown in the upper row of Figure 2, with the three panels displaying the ACIS-I, HETG, and ACIS-S data in order. To account for the local background, we have adopted an adjacent box running in parallel with the filament. It is clear that the intensity profile looks similar among the three data sets, indicating no drastic changes in the morphology of G359.944 over the past two decades. According to the presumed physical picture, X-ray emission can be induced immediately downstream the shock front (taken in Figure 2 as the zero-point of the intensity profile). However, as already noted in LMB13 and illustrated in Figure 1, the presence of relatively strong and non-uniform diffuse emission around the shock front hampers an accurate determination of the local background thereof. To test this possibility, we subtract no background for the first bin (≲3'') of the intensity profile, which thus represents a firm upper limit at the position. It turns out that this upper limit is compatible with the X-ray filament starting from the shock front. In practice, however, we define the filament as starting at 3'' and ending at 105 (i.e., an apparent length of 75, corresponding to a physical length of ∼0.3 pc), beyond which point the filament again loses its trace into the diffuse background. The otherwise smooth intensity profile exhibits a "knot" at ∼5'', the nature of which is further examined in Section 4. For the three individual data sets (ACIS-I, HETG, ACIS-S) and the combined data set, we find 440/382/504/1326 net counts out of a total (source plus background) of 1049/935/1469/3453 counts, giving a 13.6/12.5/13.1/22.6σ significance to G359.944.

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In the lower row of Figure 2, we present the hardness ratio (HR) profile, where HR $\equiv \,({I}_{4-8\mathrm{keV}}-{I}_{2-4\mathrm{keV}})/({I}_{4-8\mathrm{keV}}+{I}_{2-4\mathrm{keV}})$, and I denotes the intensity of a given band. The three data sets again agree with each other, showing an overall trend of softening toward the far side of the filament (a flat HR profile is rejected at 78%/61%/92% confidence level for the ACIS-I/HETG/ACIS-S profiles). As suggested by LMB13, this trend can be understood as synchrotron cooling of the relativistic electrons moving along the jet path. We can estimate a synchrotron cooling timescale ${\tau }_{\mathrm{syn}}\,\sim 0.3{({\gamma }_{e}{m}_{e}{c}^{2}/50\mathrm{TeV})}^{-1}{(B/1\mathrm{mG})}^{-2}$ yr (see Section 6 for details), which is comparable to the light-crossing time of ∼1.3 yr. In the meantime, the consistency of the HR profile among the three data sets suggests a stable supply of relativistic electrons at least over the past two decades. This, however, does not preclude flux and spectral variability on smaller timescales, which will be examined in the following sections.

We first probe flux variation in G359.944 by examining the mean 2–8 keV photon flux in all 122 observations (individual values are listed in Table 4). The source and background regions are outlined by the two rectangles in the insert of Figure 1. We utilize the CIAO tool aprates, which applies a Bayesian approach for Poisson statistics in the low-count regime, to compute the photon flux and bounds for each observation, corrected for the local effective exposure. For those observations with limited net counts, we derive the 3σ upper limit. The resultant long-term light curve, as shown in Figure 3, exhibits no significant inter-observation variability. This is supported by the normalized excess variance (Nandra et al. 1997; Turner et al. 1999), ${\sigma }_{\mathrm{rms}}^{2}\,\equiv {\sum }_{i=1}^{N}[{({f}_{i}-\overline{f})}^{2}{\sigma }_{f,i}^{2}]/(N{\overline{f}}^{2})\approx -0.049$, with 68% error equaling 0.033, which indicates that the apparent deviations from the mean photon flux, $\overline{f}\approx 1.5\times {10}^{-6}\,\mathrm{ph}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$, arise predominantly from statistical fluctuations.

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Since the filament has a length of more than one light year, we do not expect to detect intra-observation variability across the whole filament. On the other hand, short-term variability might be seen in the "knot," which is essentially unresolved in the X-ray image of Figure 1. Therefore, we search for its variability, employing the CIAO tool glvary on each of the 122 observations. This tool uses the Gregory–Loredo variability test algorithm (Gregory & Loredo 1992) on the unbinned X-ray data. We have run the dither_region tool to produce a normalized effective area file, to be fed to glvary, which accounts for the dead time due to bad pixels or chip gaps. This step ensures that any measured time variation is intrinsic and not caused by the telescope dithering. The output of glvary assigns a variability index that takes values from 0 to 10, with values ≥6 indicating a definitely variable source. Probable intra-observation variability is only found in 1 out of the 122 observations, as indicated by its variability index of 6. This strongly suggests that the knot maintained a rather stable flux over the past two decades, thus it is unlikely a stellar object.

We now turn to examine the spatially resolved and time-dependent spectral properties of G359.944. The spectra are extracted from each ObsID using the CIAO tool specextract. For the whole filament, the source and background regions are again defined by the two rectangles in Figure 1. The tool also generates the ancillary response files (ARFs) and redistribution matrix files (RMFs), weighted over the source region. We then produce an average spectrum of ACIS-I, HETG, or ACIS-S, by combining ObsIDs taken with the same instrument and weighting the ARFs and RMFs by the effective exposure. We note that although the instrumental response of Chandra has degraded over the years of its operation, the effective area of a given instrument above ∼2 keV (i.e., the energy range of interest) has undergone no significant change, which justifies the analysis of the combined spectra. Throughout this section we report errors at the 90% confidence level unless otherwise noted.

All fitted spectra are adaptively binned to achieve S/Ns better than 3 per bin over the range of 1–9 keV. As shown in Figure 4(a), all three spectra appear featureless (i.e., consistent with non-thermal emission) and can be well-fitted with an absorbed power-law model, tbabs*powerlaw in XSPEC v12.9.1 (Wilms et al. 2000). It is reasonable to assume that the absorption column density toward the inner 30'' around Sgr A* does not significantly vary on a timescale of two decades, thus we apply a joint fit to the three spectra, linking the column density but allowing the photon index to vary. This yields ${N}_{{\rm{H}}}={17.6}_{-4.2}^{+5.1}\times {10}^{22}\,{\mathrm{cm}}^{-2}$, consistent with the typical value derived from X-ray point sources in this region (Zhu et al. 2018). The best-fit photon index (Γ₁) is largest (${1.40}_{-0.50}^{+0.50}$) in the ACIS-I spectrum and smallest (${0.62}_{-0.60}^{+0.58}$) in the ACIS-S spectrum, suggesting the two values differ at 90% significance. In the meantime, a possible small increase in the unabsorbed 2–10 keV luminosity is found in the ACIS-S spectrum, by ∼(30 ± 20)% as compared to the ACIS-I spectrum (Column 6 of Table 2). The observed spectrum might have been manipulated by foreground dust scattering, which results in spectral hardening due to an E⁻² dependence in the scattering cross section (Predehl & Schmitt 1995). We assess this effect under extreme case that the dust scattering is concentrated in a thin plane, obtaining a column density ${N}_{{\rm{H}}}={13.1}_{-4.8}^{+6.8}\times {10}^{22}\,{\mathrm{cm}}^{-2}$. The corresponding best-fit photon indices (Γ₂; Column 8 of Table 2) become slightly larger as expected. However, even under this extreme case, it holds true that the ACIS-S spectrum is rather flat (${{\rm{\Gamma }}}_{2}={0.83}_{-0.61}^{+0.58}$). Below, we shall neglect the effect of dust scattering.

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Table 2.  Spectral Fit Results

Region	Instrument	NH,1	Γ1	χ2/dof	L2–10	NH,2	Γ2
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
All	ACIS-I	${17.6}_{-4.20}^{+5.14}$	${1.40}_{-0.50}^{+0.50}$	12.4/16	${1.96}_{-0.25}^{+0.25}$	${13.1}_{-4.84}^{+6.75}$	${1.62}_{-0.51}^{+0.50}$
All	HETG	⋯	${1.18}_{-0.64}^{+0.62}$	10.6/13	${1.99}_{-0.28}^{+0.37}$	⋯	${1.40}_{-0.64}^{+0.62}$
All	ACIS-S	⋯	${0.62}_{-0.60}^{+0.58}$	9.7/17	${2.56}_{-0.32}^{+0.33}$	⋯	${0.83}_{-0.61}^{+0.58}$
Near	ACIS-I	⋯	${0.92}_{-0.53}^{+0.53}$	20.6/18	${1.24}_{-0.18}^{+0.17}$	⋯	${1.14}_{-0.52}^{+0.53}$
Far	ACIS-I	⋯	${2.61}_{-0.95}^{+0.92}$	8.7/11	${0.74}_{-0.17}^{+0.16}$	⋯	${2.83}_{-0.95}^{+0.92}$
Near	HETG	⋯	${0.20}_{-0.68}^{+0.66}$	9.0/9	${1.38}_{-0.21}^{+0.24}$	⋯	${0.43}_{-0.68}^{+0.66}$
Far	HETG	⋯	${3.09}_{-1.03}^{+0.96}$	4.1/9	${0.83}_{-0.20}^{+0.19}$	⋯	${3.30}_{-1.03}^{+0.96}$
Near	ACIS-S	⋯	$-{0.10}_{-0.66}^{+0.63}$	10.3/20	${1.89}_{-0.26}^{+0.26}$	⋯	${0.11}_{-0.66}^{+0.63}$
Far	ACIS-S	⋯	${1.92}_{-1.13}^{+1.09}$	8.3/9	${0.74}_{-0.18}^{+0.03}$	⋯	${2.13}_{-1.13}^{+1.09}$

Note. (1) Spectral extraction region: "All" for the whole filament; "Near" for the half of the filament closer to Sgr A*, defined by a 375 × 15 box; "Far" for the far half. (3) and (7) The fixed column density, in units of 10²² cm⁻². (4) The best-fit photon index of the absorbed power-law model. (6) The unabsorbed 2–10 keV luminosity given a distance of 8 kpc, in units of 10³² erg s⁻¹. (8) The best-fit photon index of the absorbed power-law model, with the foreground dust scattering considered. Quoted errors are at the 90% confidence level.

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As evident in Figure 2, the filament exhibits gradual softening toward the far side. To quantify this softening, we divide the source rectangle into two equal halves and extract a spectrum for each half (Figures 4(b)–(d)). We tie the absorption column densities of both halves to the best-fit value, ${N}_{{\rm{H}}}=17.6\,\times {10}^{22}\,{\mathrm{cm}}^{-2}$, found for the whole filament. This is justified by the fact that K-band foreground extinction across this region varies by less than 10% (Schödel et al. 2010). We note that fixing the absorption column density effectively eliminates its degeneracy with the photon index and thus artificially reduces the estimated uncertainty of the latter. However, it is the relative change in the photon index, spatially or temporally, that we are most interested in here. The best-fit photon indices, listed in rows 4–9 of Table 2 for the three instruments, are different between the near half and the far half at more than the 95% confidence level. In particular, the near half exhibits a very flat spectrum (Γ₁ < 1) in both HETG and ACIS-S. It is noteworthy that the knot does not dominate the flux of the near half, nor does it show a distinct HR (Figure 2). The far half, in contrast, shows a steep spectrum consistent with the softening trend seen in the HR profile. The unabsorbed 2–10 keV luminosity of the near half is about two times that of the far half.

As discussed in Section 4, the statistical uncertainty and the finite light-crossing time may smear any moderate intrinsic variability in G359.944. In order to reduce the statistical errors, we divide the 18 yr of observations into several epochs, requiring at least 300 ks exposure and a minimum baseline of 2 yr in each epoch. We also ensure that observations from different instruments are not brought into the same epoch. As summarized in Table 3, we eventually choose 6 epochs and group the ObsIDs assigned to each epoch to extract a combined spectrum for the whole filament. 5% of the total exposure from 23 observations are excluded. The fitted results of the combined spectra are shown in Figure 5. G359.944 reached the softest state (${\rm{\Gamma }}={1.94}_{-0.67}^{+0.64}$) in epoch 2002.2–2002.6, and became harder (${\rm{\Gamma }}={0.08}_{-1.23}^{+1.12}$) in epoch 2008.5–2010.5, at ∼95% significance. To see whether this apparent difference can be attributed to pure statistical fluctuations about a constant power-law spectrum, we employ multifake in XSPEC to simulate 1000 spectra for each epoch, feeding the tool with the corresponding ARFs and RMFs and assuming a fixed photon index of Γ = 1.15 and unabsorbed 2–10 keV luminosity L_2–10 = 2.0 × 10³² erg s⁻¹, which represent the long-term mean of the observed spectra. The fake spectra are then fitted to derive the 90% percentile of the best-fit parameters, which are taken as the range of statistical fluctuations (the gray strips in Figure 5(a)). The results suggest that there is intrinsic variation in the photon index of both epochs 2002.2–2002.6 and 2008.5–2010.5. The apparent variation in L_2–10, however, can be accounted for by statistical fluctuations. Furthermore, as illustrated in Figure 5(b), there is no significant correlation between L_2–10 and Γ, according to the Spearman's rank correlation coefficient r = 0.31, with a p-value of 0.54 for random correlation.

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Table 3.  Spectral Fit Results of Various Epochs

No.	Epoch	Instrument	Exposure (ks)	Net Counts	Γ	χ2/dof	L2–10
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
1	2002.2–2002.6	ACIS-I	5.39 × 102	230	${1.94}_{-0.67}^{+0.64}$	5.43/9	${2.46}_{-0.40}^{+0.40}$
2	2004.7–2005.8	ACIS-I	3.05 × 102	90	${0.74}_{-1.57}^{+1.64}$	5.02/5	${1.79}_{-0.60}^{+0.59}$
3	2008.5–2010.5	ACIS-I	3.57 × 102	84	${0.08}_{-1.23}^{+1.12}$	1.32/4	${2.09}_{-0.58}^{+0.58}$
4	2012.2–2012.10	HETG	2.83 × 103	381	${1.19}_{-0.64}^{+0.62}$	9.57/13	${1.99}_{-0.28}^{+0.27}$
5	2013.5–2014.10	ACIS-S	7.68 × 102	290	${0.79}_{-0.43}^{+0.42}$	11.50/17	${2.35}_{-0.24}^{+0.23}$
6	2015.5–2017.4	ACIS-S	5.45 × 102	217	${0.77}_{-0.67}^{+0.63}$	8.32/7	${2.53}_{-0.32}^{+0.33}$

Note. (5) Net counts in the 1–9 keV band. (6) The best-fit photon index of the absorbed power-law model. (8) The intrinsic 2–10 keV luminosity, given a distance of 8 kpc, in units of 10³² erg s⁻¹. Quoted errors are at the 90% confidence level.

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It was anticipated that the periapsis passage of G2, occurring at T₀ ∼ 2014.2 (marked by a vertical dashed line in Figure 3; Witzel et al. 2017), might boost accretion onto Sgr A* due to its partial disruption under the strong tidal force of the SMBH. However, there seems to be no observational evidence for a dramatic change in the accretion rate, which is presumably manifested by Sgr A*'s broadband radiation, in particular, its quiescent X-ray flux within the Bondi radius (Yuan & Wang 2016; Ahnen et al. 2017; Witzel et al. 2018). On the other hand, Ponti et al. (2015) and Mossoux & Grosso (2017) claimed evidence of an enhanced incidence rate of bright X-ray flares a few months after G2's periapsis passage. We note that this time delay is comparable to the freefall time at the periapsis distance of G2 (∼200 au; Witzel et al. 2017). If the passage of G2 also had an effect on the putative jet traced by G359.944, we would expect to probe the associated variations after a time delay of ≳2 yr, given the distance of G359.944 from Sgr A*. Thanks to the high-cadence ACIS-S observations since 2013, such an effect can be readily probed. However, no significant flux variation can be seen when comparing the epochs 2013.5–2014.10 and 2015.5–2017.4 (blue and magenta points in Figures 3 and 5(b)), assuming that the former epoch represents the normal state of the jet. We also examine the light curve near the periapsis passage of G1 at T₀ ∼ 2001.3. G1 has similar observational properties with G2 in the near-infrared and shows signs of tidal expansion after periapsis passage (Witzel et al. 2017). Interestingly, at epoch 2002.2–2002.6, G359.944 exhibits ∼2 times flux increase (∼2σ significance) compared to the mean flux before the G1 passage. We caution that a real physical connection is highly uncertain due to the sparse Chandra observations before and after this epoch.

In the proposed jet scenario, relativistic electrons, accelerated at the shock front and streaming down the jet path, are responsible for the observed non-thermal X-ray emission from G359.944. LMB13 showed that inverse Compton radiation can be ruled out, due to the lack of sufficient seed photons at lower frequencies (e.g., constrained by the upper limits in the radio band as illustrated in Figure 6), which left synchrotron as the most viable radiation mechanism. Here, we argue that the observed flat spectra, in particular those from the near half, place strong constraints even on the synchrotron scenario.

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According to the standard diffusive shock acceleration (DSA) theory (e.g., Drury 1983), post-shock electrons acquire a power-law energy distribution, which can be expressed as $N({\gamma }_{e})\,=K{\gamma }_{e}^{-p}$, where γ_e is the Lorentz factor and K is the normalization factor. The slope p is determined by the shock compression ratio χ as p = (χ + 2)/(χ − 1), while χ itself can be written as χ =(γ + 1)/(γ − 1 + M⁻²) via the adiabatic index γ and Mach number M. Therefore, in the case of a strong shock in a non-relativistic plasma, γ = 5/3 and $M\to \infty$, we obtain the canonical value of p = 2, and the corresponding photon index Γ = (p + 1)/2 = 1.5. The broadband spectral energy distribution (SED)⁹ of such a case is shown as the solid line in Figure 6. We have assumed an empirical magnetic field strength B ≈ 1 mG at the central parsec (Plante et al. 1995; Eatough et al. 2013), and the minimum/maximum Lorentz factors γ_e,min = 1 and γ_e,max = 10⁸. Evidently, this canonical synchrotron cannot account for the flatness of the near half spectra obtained with ACIS-I, HETG, and ACIS-S, with Γ = ${0.92}_{-0.53}^{+0.53}$, ${0.20}_{-0.68}^{+0.66}$ and $-{0.10}_{-0.66}^{+0.63}$, respectively (see solid lines in Figure 6). If we further take into account the fact that the strong shock is propagating in the relativistic plasma of the jet, i.e., γ = 4/3, we can obtain a harder slope of p = 1.5 and Γ = 1.25. This latter value, however, still cannot account for the HETG and ACIS-S spectra.

The flat spectrum motivates us to consider synchrotron from monoenergetic electrons, i.e., represented by a δ-function distribution: N(γ_e) = N₀δ (γ_e − γ_e,0) (Pacholczyk 1970). When ${\gamma }_{e,0}\to \infty$, the corresponding SED asymptotically approaches ${EdN}/{dE}\propto {E}^{0.3}$, that is, a photon index Γ = 0.7, which in principle is the flattest possible synchrotron spectrum. This value barely falls within the uncertainties of the photon indices of the HETG and ACIS-S near half spectra (Table 2). In Figure 6, we plot the synchrotron spectrum of monoenergetic electrons with an energy of ${\gamma }_{e,0}{m}_{e}{c}^{2}=50$ TeV (dashed curve) and ${\gamma }_{e,0}{m}_{e}{c}^{2}=5$ TeV (dotted curve), the former approximately matching the observed near half spectra and the latter consistent with the far half spectra. We note that these SEDs are fully compatible with the non-detections in radio as well as the 3σ upper limit on the 10–40 keV flux as constrained by NuSTAR.

In reality, a population of quasi-monoenergetic electrons may be generated from rapid synchrotron cooling of an initial population having a power-law energy distribution (Rybicki & Lightman 1986):

$$\begin{eqnarray}&&N({\gamma }_{e})d{\gamma }_{e}={N}_{i}({\gamma }_{e,i})d{\gamma }_{e,i}\propto {\gamma }_{e,i}^{-p}d{\gamma }_{e,i},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&\displaystyle \frac{d{\gamma }_{e}}{{dt}}=-\displaystyle \frac{1}{{m}_{e}{c}^{2}}\displaystyle \frac{4}{3}{\sigma }_{{\rm{T}}}c{\beta }_{e}^{2}\displaystyle \frac{{B}^{2}}{8\pi }{\gamma }_{e}^{2}\equiv -A{\gamma }_{e}^{2},\end{eqnarray} \tag{ 2 }$$

where p > 1 is the initial power-law slope, σ_T is the Thomson scattering cross section, β_e ≈ 1 is the electron velocity relative to the speed of light (c). We have $A\,\approx \,1.3\,\times {10}^{-15}{(B/1\mathrm{mG})}^{2}\,{{\rm{s}}}^{-1}$. From Equations (1) and (2) we can derive the time-dependent electron energy distribution:

$$\begin{eqnarray}&&N({\gamma }_{e})\propto {\gamma }_{e}^{-p}{\left(1-{At}{\gamma }_{e}\right)}^{p-2},\end{eqnarray} \tag{ 3 }$$

where t is the cooling time. For 1 < p < 2, the electron energy distribution will evolve into a quasi-δ-function peaking at γ_e =1/(At) (Schlickeiser 1984). We can estimate the time needed for electrons cooling from the near half (e.g., ${\gamma }_{e,n}{m}_{e}{c}^{2}\,\approx 50$ TeV) to the far half (e.g., ${\gamma }_{e,f}{m}_{e}{c}^{2}\,\approx \,5$ TeV) along the jet path: ${\rm{\Delta }}t=1/{(A{\gamma }_{e,f})-1/(A{\gamma }_{e,n})\approx 2.2(B/1\mathrm{mG})}^{-2}\,\mathrm{yr}$. This cooling time is compatible with the half-length of G359.944, ∼0.15 pc, if the bulk motion of the electrons is relativistic, as expected for a jet. We conclude that the above simple model is consistent with the physical picture proposed by LMB13: the putative jet drives a bow-shock in the Eastern Arm and generates ultra-relativistic electrons, which cool by synchrotron radiation and produce the observed X-ray filament downstream the shock along the jet path.

We have utilized ∼5.6 Ms of Chandra observations spanning 18 yr to study the X-ray properties of G359.944, a very promising candidate for a jet from Sgr A*. Our main results are as follows:

• 1.  
  The periapsis passage of G2 in early 2014 does not seem to have caused significant variation in the X-ray spectrum of G359.944. On the other hand, a flux enhancement of ∼2σ significance, might be associated with the periapsis passage of G1 in early 2001.
• 2.  
  Unusually hard spectra are found in the near half of G359.944, showing a photon index as low as $-{0.10}_{-0.66}^{+0.63}$. The spectrum becomes softer and less luminous further down the putative jet path. Such properties can be best understood as rapid synchrotron cooling of the ultra-relativistic electrons.

We conclude that G359.944 remains a viable candidate for the long-sought jet from Sgr A*. A decisive test may come from imaging of the Event Horizon Telescope available in the near future (Psaltis et al. 2015). Regardless of the validity of G359.944 being the jet, its unusually flat spectrum is intriguing. Previous work has identified more than a dozen filamentary X-ray features within the inner parsecs of the GC (Lu et al. 2008; Muno et al. 2008; Johnson et al. 2009). Some of these filaments are identified as magnetic flux tubes (Morris et al. 2014; Zhang et al. 2014), while others might be PWN driven by a fast-moving pulsar (Wang et al. 2006; S. Zhang, et al. 2019, in preparation). It is noteworthy that all known Galactic PWNe show a power-law X-ray spectrum with photon indices of 1.1–2.2 (Kargaltsev et al. 2017). Six out of the 17 X-ray filaments studied by Johnson et al. (2009) showed a flat spectrum with best-fit photon index ≲1.0 with large uncertainties due to the limited counting statistics. It will be an important step to revisit the spectral and temporal properties of these filaments using the updated Chandra data, which will facilitate a comparison with the case of G359.944 and help us understand the behavior of high-energy particles in the unique GC environment.

This work is supported by the National Science Foundation of China under grant 11473010. We acknowledge the PIs of the Chandra programs, in particular Fred Baganoff, for acquiring the data that made this work possible. Z.Z. thanks Xiao Zhang for helpful discussions on the jet model.

For ease of reference, Table 4 lists the 2–8 keV photon flux (or the 3σ upper limit in the case of non-detection) of G359.944 in each observation, just as presented in Figure 3.

Table 4.  2–8 keV Photon Flux of G359.944 in Individual Observations

ObsID	Ctot	Cnet	F2−8
(1)	(2)	(3)	(4)
ACIS-I
242	21	5.21	${0.60}_{-0.10}^{+1.11}$
15611	25	9.68	${0.97}_{-0.43}^{+1.52}$
15612	8	3.69	${0.96}_{-0.23}^{+1.72}$
2951	13	8.21	${2.34}_{-1.23}^{+3.46}$
2952	9	6.61	${1.97}_{-1.00}^{+2.92}$
2953	12	8.65	${2.63}_{-1.49}^{+3.76}$
2954	8	2.74	${0.78}_{-0.05}^{+1.53}$
2943	38	23.64	${2.27}_{-1.63}^{+2.91}$
3663	31	14.25	${1.35}_{-0.76}^{+1.94}$
3392	115	56.61	${1.20}_{-0.94}^{+1.45}$
3393	147	75.21	${1.67}_{-1.37}^{+1.97}$
3665	66	32.50	${1.27}_{-0.92}^{+1.63}$
3549	10	1.86	<2.97
4683	36	13.50	${1.21}_{-0.68}^{+1.75}$
4684	37	12.11	${1.14}_{-0.60}^{+1.69}$
6113	2	1.52	${1.11}_{-0.08}^{+2.13}$
5950	42	14.24	${1.32}_{-0.74}^{+1.91}$
5951	31	11.38	${1.15}_{-0.60}^{+1.72}$
5952	33	14.81	${1.40}_{-0.83}^{+1.98}$
5953	28	7.90	${0.86}_{-0.33}^{+1.40}$
5954	16	8.34	${1.89}_{-0.97}^{+2.84}$
6640	5	4.04	${2.82}_{-1.16}^{+4.47}$
6641	2	0.00	<4.54
6642	8	5.13	${5.11}_{-2.34}^{+7.97}$
6363	22	3.33	${0.62}_{-0.06}^{+1.20}$
6643	3	0.13	<6.20
6644	3	0.00	<5.44
6645	2	0.09	<5.64
6646	6	4.56	${3.27}_{-1.40}^{+5.12}$
7554	4	0.00	<5.98
7555	1	0.04	<4.84
7556	6	4.56	${4.03}_{-1.64}^{+6.38}$
7557	5	3.09	${2.22}_{-0.58}^{+3.86}$
7558	3	1.56	<6.22
7559	2	0.56	<5.17
9169	19	12.30	${1.84}_{-1.08}^{+2.59}$
9170	17	5.51	${0.75}_{-0.11}^{+1.40}$
9171	18	10.82	${1.71}_{-0.93}^{+2.50}$
9172	14	5.86	${0.84}_{-0.23}^{+1.47}$
9174	20	8.99	${1.14}_{-0.53}^{+1.77}$
9173	20	12.82	${1.65}_{-1.03}^{+2.28}$
10556	62	27.06	${1.10}_{-0.69}^{+1.51}$
11843	29	0.00	<0.80
13016	13	7.74	${1.56}_{-0.74}^{+2.38}$
13017	13	6.30	${1.28}_{-0.44}^{+2.13}$
ACIS-S/HETG
13850	19	9.43	${1.46}_{-0.73}^{+2.20}$
14392	21	10.95	${1.70}_{-0.92}^{+2.49}$
14394	4	0.00	<4.30
14393	11	1.91	<3.00
13856	13	5.34	${1.23}_{-0.37}^{+2.09}$
13857	13	5.34	${1.24}_{-0.39}^{+2.13}$
13854	11	8.13	${3.24}_{-1.81}^{+4.64}$
14413	2	0.09	<4.40
13855	4	0.00	<3.49
14414	7	4.13	${1.90}_{-0.64}^{+3.18}$
13847	66	36.80	${2.20}_{-1.67}^{+2.74}$
14427	24	6.77	${0.78}_{-0.22}^{+1.36}$
13848	36	16.38	${1.53}_{-0.91}^{+2.17}$
13849	47	18.76	${0.97}_{-0.57}^{+1.37}$
13846	16	8.82	${1.45}_{-0.74}^{+2.17}$
14438	5	1.17	<3.52
13845	45	20.59	${1.40}_{-0.89}^{+1.92}$
14460	6	3.13	${1.21}_{-0.26}^{+2.15}$
13844	2	0.00	<3.16
14461	9	4.69	${0.85}_{-0.28}^{+1.43}$
13853	25	15.91	${2.00}_{-1.32}^{+2.68}$
13841	8	0.00	<2.06
14465	10	1.86	<2.72
14466	13	2.95	<3.10
13842	37	5.89	${0.28}_{-0.02}^{+0.55}$
13839	47	21.63	${1.13}_{-0.74}^{+1.54}$
13840	43	18.59	${1.06}_{-0.64}^{+1.48}$
14432	19	6.08	${0.76}_{-0.21}^{+1.32}$
13838	40	24.68	${2.30}_{-1.66}^{+2.94}$
13852	43	18.11	${1.07}_{-0.64}^{+1.51}$
14439	35	15.86	${1.31}_{-0.76}^{+1.86}$
14462	36	9.20	${0.64}_{-0.21}^{+1.08}$
14463	14	10.65	${3.21}_{-2.00}^{+4.40}$
13851	31	12.33	${1.07}_{-0.54}^{+1.61}$
15568	12	8.65	${2.22}_{-1.26}^{+3.17}$
13843	42	23.81	${1.82}_{-1.28}^{+2.37}$
15570	20	6.12	${0.82}_{-0.22}^{+1.44}$
14468	38	11.68	${0.74}_{-0.32}^{+1.17}$
ACIS-S/Non-grating
14702	13	5.34	${1.30}_{-0.35}^{+2.27}$
14703	19	7.51	${1.53}_{-0.60}^{+2.49}$
14946	18	7.95	${1.52}_{-0.65}^{+2.41}$
15041	38	8.80	${0.68}_{-0.20}^{+1.17}$
15042	44	17.68	${1.34}_{-0.78}^{+1.91}$
14945	14	3.95	${0.78}_{-0.09}^{+1.49}$
15043	47	7.27	${0.55}_{-0.07}^{+1.04}$
14944	13	5.34	${1.01}_{-0.32}^{+1.73}$
15044	43	12.85	${1.02}_{-0.44}^{+1.60}$
14943	18	8.43	${1.59}_{-0.73}^{+2.48}$
14704	41	18.50	${1.76}_{-1.09}^{+2.46}$
15045	47	24.50	${1.85}_{-1.28}^{+2.43}$
16508	35	9.63	${0.82}_{-0.30}^{+1.36}$
16211	50	27.03	${2.23}_{-1.58}^{+2.87}$
16212	29	0.76	<1.46
16213	35	11.07	${0.79}_{-0.30}^{+1.29}$
16214	39	16.03	${1.23}_{-0.69}^{+1.77}$
16210	26	14.99	${3.03}_{-1.88}^{+4.18}$
16597	20	13.30	${2.78}_{-1.76}^{+3.79}$
16215	37	15.94	${1.33}_{-0.76}^{+1.90}$
16216	44	20.07	${1.62}_{-1.02}^{+2.23}$
16217	25	10.64	${1.08}_{-0.52}^{+1.64}$
16218	29	12.25	${1.14}_{-0.54}^{+1.75}$
16963	18	8.43	${1.34}_{-0.58}^{+2.12}$
16966	21	6.64	${1.00}_{-0.21}^{+1.81}$
16965	20	8.03	${1.23}_{-0.51}^{+1.98}$
16964	29	15.12	${2.30}_{-1.40}^{+3.22}$
18055	100	5.71	<5.62
18056	98	1.80	<5.33
18731	85	28.52	${1.28}_{-0.81}^{+1.76}$
18732	77	36.80	${1.68}_{-1.23}^{+2.14}$
18057	12	1.47	<2.10
18058	20	6.60	${0.96}_{-0.25}^{+1.68}$
19726	17	3.12	<2.11
19727	22	7.64	${0.89}_{-0.26}^{+1.54}$
20041	28	16.51	${1.92}_{-1.21}^{+2.63}$
20040	23	11.99	${1.56}_{-0.82}^{+2.32}$
19703	38	18.38	${1.44}_{-0.91}^{+1.99}$
19704	78	37.80	${1.69}_{-1.25}^{+2.13}$

Note. (1) Observation ID, (2), (3) 2–8 keV total counts and net counts of G359.944. (4) The 2–8 keV photon flux, in units of 10⁻⁶ erg s⁻¹ cm⁻². For the observations with sufficient net counts, the quoted errors are at the 1σ confidence level. For other observations with limited net counts, 3σ upper limits are given (arrows in Figure 3).

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