Chandra Monitoring of the J1809–1917 Pulsar Wind Nebula and Its Field

3.1.1. Proper Motion

In order to measure the pulsar's proper motion, we matched the observations to a common astrometric frame using an external catalog, as outlined in the corresponding CIAO thread. ⁷ The frame was defined by the Gaia DR2 catalog ⁸ (Gaia Collaboration et al. 2018). We cross-correlated the positions of the Gaia DR2 stars with the X-ray sources detected by wavdetect in each of the Chandra observations. ⁹ We excluded the pulsar and any sources within a $30^{\prime\prime}$ radius of it to prevent bright nebular emission from being misidentified as point sources. We also required the selected X-ray sources to be detected with signal-to-noise ratios of ≥3 and be within 5' of the optical axis. After cross-correlation with the Gaia DR2 catalog, we selected X-ray sources with Gaia counterparts within a 1'' radius from the X-ray source position determined by wavdetect. Each observation had at least three cross-correlated reference sources. We then used CIAO's wcs_match to calculate the translation transformation to shift the input (X-ray) sources to the reference (Gaia DR2) source locations in a way that minimizes the differences in their positional offsets. We iterated the transformation calculation process until the largest source-pair position error became less than 05 by iteratively rejecting those Chandra–Gaia pairs that violated this condition. The 05 was the criterion chosen because it is approximately the typical astrometric accuracy of Chandra. For each observation, we then calculated the root mean square of the offsets for the pairs of sources that were used in the final transformation. Following the CIAO thread mentioned above, we then used wcs_update to recalculate the aspect solutions and update the world coordinate system (WCS) parameters in the WCS transformation blocks of the Level 2 event list files.

After the observations were aligned to the common reference frame (based on Gaia DR2), we measured the position of the pulsar centroid by calculating the average R.A. and decl. position of all counts within $1\buildrel{\prime\prime}\over{.} 5$ of the brightest pixel (in the vicinity of the pulsar) in the images binned by a factor of 0.5 and smoothed with an r = 3'' Gaussian kernel. The uncertainties of the pulsar positions were calculated using CIAO's celldetect tool. ¹⁰ The positions and uncertainties are also given in Table 3. (We did not include ObsIDs 20327, 20967, 21098, 21724, and 20332 in the proper motion measurement either because the astrometric correction did not converge to the required precision or because the pulsar image appeared to be distorted.) The total uncertainty of the pulsar position also includes the uncertainty of alignment for each observation to the Gaia DR2 reference frame, reported by wcs_match, ¹¹ which was added in quadrature to the pulsar centroiding uncertainty. The coordinates of the pulsar (in R.A. and decl.) and their uncertainties for each observation epoch are shown in Figure 2. We fitted a linear function to the pulsar coordinates over time (the best fits are shown in the corresponding panels) and found the proper motion μ_α  = −1 ± 9 mas yr⁻¹ and μ_δ  = 24 ± 11 mas yr⁻¹. The net result is that there is an indication of proper motion northward, but only at a 95% confidence level.

Zoom In Zoom Out Reset image size

Table 3. Pulsar Coordinates in 12 Chandra Observations Used for the Proper Motion Measurement

ObsID	Exposure	R.A.	Decl.	σα	σδ
	(s)	(deg)	(deg)	(mas)	(mas)
3853	19702	272.429702	−19.293967	150	150
14820	46746	272.429690	−19.293923	180	180
16489	64864	272.429741	−19.293867	180	180
20328	33604	272.429750	−19.293909	260	260
20329	29661	272.429732	−19.293875	220	220
20330	32617	272.429677	−19.293886	200	200
20331	39531	272.429658	−19.293849	170	170
20962	20926	272.429698	−19.293807	180	190
20963	16334	272.429648	−19.293862	200	210
21067	30643	272.429754	−19.293925	200	200
21126	40008	272.429684	−19.293827	140	150
21874	28667	272.429761	−19.293976	210	210

Note. The coordinates correspond to those after the alignment with the Gaia DR2 catalog was performed. The uncertainties σ_α and σ_δ are 1σ.

Download table as:  ASCIITypeset image

3.1.2. Spectrum

3.2.1. Morphology

3.2.2. Spectrum

We use the same regions and numbering as defined in K+18, with the modification of region 3 (the CN) from a contour into a larger ellipse to better accommodate the morphological variability of the CN across all epochs (see Figure 1). For region 2 we obtained a hard spectrum with Γ₂ = 1.23 ± 0.09, which is consistent with the previously reported result. This spectrum is also consistent with the PL component of the spectrum extracted from the pulsar vicinity (region 1; Γ = 1.28 ± 0.15; see above). This suggests that the PL component seen in the spectrum extracted from the pulsar region may be due to contamination from the surrounding nebula, or that both the emission from the pulsar region and its surrounding vicinity have the same spectrum. We see evidence of spectral softening between this region and the CN's spectrum (region 3), with Γ₃ = 1.52 ± 0.03. These results are similar to those reported by K+18 (${{\rm{\Gamma }}}_{2,\mathrm{old}}=1.20\pm 0.11$ and ${{\rm{\Gamma }}}_{3,\mathrm{old}}=1.53\pm 0.08$). We list all spectral fit results (for these regions and the ones to be discussed subsequently) in Table 4.

Table 4. Spectral Fit Results for PWN Regions

Region	Name	Area	Counts	${ \mathcal B }$	Γ	${{ \mathcal N }}_{-5}$	${\chi }_{\nu }^{2}$	F−13	${F}_{-13}^{\mathrm{unabs}}$
2	Pulsar Vicinity	9.44	1019 ± 32	15	1.23 ± 0.09	0.55 ± 0.05	1.06 (51)	0.39 ± 0.09	0.50 ± 0.03
3	Compact Nebula	464	5206 ± 75	25	1.52 ± 0.03	3.36 ± 0.13	1.29 (192)	1.62 ± 0.03	2.25 ± 0.04
4	CN Vicinity	2623	1879 ± 66	25	1.72 ± 0.08	1.48 ± 0.12	0.92 (140)	0.55 ± 0.03	0.82 ± 0.03
5	Extended Nebula	42671	9138 ± 302	200	1.74 ± 0.05	7.98–10.35	1.31 (211)	2.6–4.9	3.9–7.3
6	Outflow	42659	4031 ± 321	200	1.74 ± 0.12	2.25–5.45	1.15 (123)	0.8–1.8	1.2–2.7

Note. Spectral fit results for the different regions of the PWN. Listed are the region number (following the numbering of K+18), region name, area (in arcsec²), net counts, minimum number of counts per energy bin ${ \mathcal B }$, photon index Γ, PL normalization ${{ \mathcal N }}_{-5}$ in units of 10⁻⁵ photons s⁻¹ cm⁻² keV⁻¹ at 1 keV, reduced ${\chi }_{\nu }^{2}$ (ν dof), and absorbed and unabsorbed 0.5–8 keV fluxes F₋₁₃ and ${F}_{-13}^{\mathrm{unabs}}$ in units of 10⁻¹³ erg cm⁻² s⁻¹. The chip gap crossed through regions 5 and 6 (at varying positions due to varying roll angles), so we left the normalizations (and fluxes) as free parameters and list the range of values they spanned. In all fits we set N_H = 0.7 × 10²² cm⁻².

Download table as:  ASCIITypeset image

3.2.3. Variability

In Figure 3 we present images of the CN from the six new epochs (in addition to the three archival images, for comparison). The new images of J1809 show that the CN continues to exhibit changes over timescales of months. Across epochs 1–3, the variability was best described as a tail-wagging motion (as was previously reported in K+18). However, in epochs 4–9, the CN emission appears to be dominated by a blob-like structure, appearing to be 2''–4'' in size and positioned 4''–5'' NE of the pulsar, but whose position, shape, and orientation vary between the epochs.

Zoom In Zoom Out Reset image size

In Figure 4 we present contours of the CN across the six new epochs to compare the morphological changes over short-term timescales (intervals of 6–8 weeks). In epochs 4 and 5, the blob appears elongated in the SE–NW direction, that is, perpendicular to the CN's (and EN's) axis of symmetry. In epochs 5 and 8, the blob appears round, and in epochs 7 and 9, the blob appears elongated in the NE–SW direction. When overlaying the contours of the blob from epochs 4–9 in the same frame (as shown in the right panel of Figure 4), there appears to be no evidence of steady motion, either away from or toward the pulsar.

Zoom In Zoom Out Reset image size

In some epochs, the blob appears comparable in brightness to the pulsar itself (see Figures 3 and 4). To investigate possible spectral variability in the blob, we used an r = 25 extraction radius to obtain the spectra from each of the "new" epochs (i.e., epochs 4–9). We list the results in Table 5; the fit results for epochs 1–3 are not listed as the blob is not present in those observations. Since the individual observations that comprise epochs 4–9 were adjacent in time (i.e., observations within an epoch were taken within 2 days of each other) and were taken at the same roll and off-axis angles, we combined the spectra and corresponding response files from multiple observations (within the same epoch) using combine_spec. We found no evidence of any significant spectral variability across the epochs, although the count rates varied significantly. We then simultaneously fitted the spectra from epochs 4–9 with the PL slopes tied, but with the normalization for each epoch left as free parameters. For the best-fit Γ = 1.34 ± 0.06 (with ${\chi }_{\nu }^{2}=0.99$ for ν = 87 degrees of freedom), we found that the blob's flux varied significantly by up to a factor of 3 across epochs, ranging from $({12.4}_{-0.7}^{+0.4})$ to $(4.2\pm 0.4)\times {10}^{-14}$ erg cm⁻² s⁻¹ (in the 0.5–8 keV band).

Table 5. Blob Spectral Analysis

Epoch	Count Rate	Γ	${{ \mathcal N }}_{-5}$	${\chi }_{\nu }^{2}$	${F}_{-14,{\rm{\Gamma }}=1.34}$
	(counts ks−1)			(dof)
4	6.20 ± 0.30	1.33 ± 0.11	2.01 ± 0.25	0.55 (17)	${12.4}_{-0.7}^{+0.4}$
5	4.89 ± 0.28	1.46 ± 0.14	1.73 ± 0.26	1.37 (17)	9.3 ± 0.6
6	1.85 ± 0.16	1.48 ± 0.24	0.80 ± 0.21	0.96 (10)	4.2 ± 0.4
7	3.75 ± 0.23	1.14 ± 0.16	0.95 ± 0.17	1.35 (14)	${7.1}_{-0.4}^{+0.5}$
8	3.39 ± 0.23	1.34 ± 0.16	1.09 ± 0.20	0.87 (15)	${6.9}_{-0.6}^{+0.5}$
9	3.18 ± 0.22	1.41 ± 0.16	1.09 ± 0.20	0.81 (14)	6.2 ± 0.4

Note. For each epoch, we fitted the blob spectra extracted from an r = 25 circular aperture. We list the count rate, photon index Γ, normalization ${{ \mathcal N }}_{-5}$ (in units of 10⁻⁵ photon s⁻¹ cm⁻² keV⁻¹, at 1 keV), and the reduced χ² for ν degrees of freedom. F_{−14, Γ = 1.34} represents the absorbed flux (in units of 10⁻¹⁴ erg cm⁻² s⁻¹) when the blobs were simultaneously fitted to the same PL slope (Γ = 1.34, the average value), but with their normalizations left as free parameters. We used N_H = 0.7 × 10²² cm² for all fits.

Download table as:  ASCIITypeset image

3.3.1. Morphology

In Figure 5 we present the merged exposure-map-corrected images of the CN's vicinity (left panel) and also of the large-scale PWN (right panel). The deep 536 ks exposure image reveals two interesting features. The first is that the EN is confined within a dome-like boundary, with its axis coincident with that of the CN. The EN extends approximately 15 NE of the pulsar and 21 SW of the pulsar, after which the brightness drops abruptly to background levels. At its SW boundary (i.e., the widest part), the EN spans 5' across. The EN's average net surface brightness is 0.214 ± 0.007 counts arcsec⁻² in the 536 ks exposure.

Zoom In Zoom Out Reset image size

The second interesting feature is a very elongated and slightly curved outflow extending eastward from the EN. The outflow maintains an average width of roughly 1' as it extends at least 75 away from the EN's edge, while curving slightly to the north over its extent. It is unclear if the outflow's length exceeds 75, or if is just no longer detected beyond that point because of the decreased sensitivity at the considerable off-axis angle or extending beyond the detector's field of view. The outflow's average net surface brightness is less than half that of the EN, at 0.094 ± 0.007 counts arcsec⁻².

3.3.2. Spectrum

Although the pulsar's proper motion was only marginally detected, the morphology of the EN may be caused by the (transverse) pulsar motion toward the northeast. The alignment of the PWN's symmetry axis (i.e., both the CN and EN) with the direction toward the peak of the TeV source HESS J1809–193 (which is located about 7' to the SW ¹² ) suggests that HESS J1809 is the relic PWN and TeV counterpart of PSR J1809–1917, as was suggested by Aharonian et al. (2007), Kargaltsev & Pavlov (2007), H.E.S.S. Collaboration et al. (2018), and K+18 (see Figure 6). The center of the extended HAWC source eHWC J1809–193 (HAWC Collaboration et al. 2020; Malone & HAWC Collaboration Team 2019) coincides well with both the J1809 PWN and the center of HESS J1809–193, suggesting that eHWC J1809 and HESS J1809 are the same source, and that it is the counterpart to the J1809 PWN. In Figure 6 we present a multiwavelength (MW) image of the J1809 field.

Zoom In Zoom Out Reset image size

Although the dome-like shape of EN resembles the compact heads of SPWNe (see, e.g., Kargaltsev et al. 2017), it can hardly be attributed to a bow shock, since the standoff distance (r ≈ 15) is far too large for reasonable values of ISM sound speed or density. In supersonic pulsars, the bow shock standoff distance r_BS can be crudely estimated by balancing the isotropic pulsar wind pressure ¹³ with the ram pressure of the ambient medium: $\mu {m}_{{\rm{H}}}{{nv}}_{\mathrm{psr}}^{2}=\dot{E}/(4\pi {{cr}}_{{\rm{s}}}^{2})$ (where m_H is the mass of the hydrogen atom, n is the ISM number density, and μ = 1.3 is used to convert H density to total density of the ambient medium). With the distance to the apex of the dome of ${r}_{{\rm{s}}}=4.4\times {10}^{18}\,\mathrm{cm}$ (15 at 3.3 kpc), we get an implausibly low $n\sim {10}^{-3}{({v}_{\mathrm{psr}}/100\mathrm{km}{{\rm{s}}}^{-1})}^{-2}$ cm⁻³ (for a typical pulsar speed). Thus, the observed size of the EN cannot be reconciled with supersonic pulsar motion in a normal ambient medium. In the case of transonic motion, the above approximation is no longer applicable, and therefore, an implausibly low ambient-medium density is not required. Given the size of the EN at its estimated distance, the pulsar is likely moving transonically through the ISM (i.e., Mach number ${ \mathcal M }\approx 1$). In the absence of any evidence suggesting that the pulsar resides in the hot interior of an SNR, it is reasonable to assume that the ambient medium (i.e., ISM) sound speeds c_ISM are on the order of a few or a few tens of km s⁻¹ for the "cold" and "warm" phases of the ISM (see p. 525 of Cox 2000). A transonic pulsar velocity does not contradict our marginal proper motion detection given its large uncertainties.

The large distance between the pulsar and the northeastern edge of the EN (r ≈ 1.4 pc) is comparable to those of two other known transonic PWNe produced by PSRs B1706–44 (r ≈ 1.7 pc; d = 3 kpc; Romani et al. 2005; M. de Vries et al. 2020, in preparation) and J2021+3651 (r ≈ 1.0 pc; the Dragonfly PWN; d ∼ 3–4 kpc; van Etten et al. 2008); see Figure 7. In all three of these PWNe, the pulsar jets are not destroyed by the ram pressure and remain within the extent of the paraboloid-shaped PWN head (as opposed to tracing the boundaries of the bow shock, as is seen in some supersonic PWNe; see, e.g., the J1509–5850 PWN, Klingler et al. 2016a).

Zoom In Zoom Out Reset image size

The best-fit value for the proper motion implies that the projected pulsar velocity is 370 (±170) km s⁻¹ at the DM distance d = 3.3 kpc, which is at odds with the interpretation of the PWN's morphology (which suggests a much lower transonic pulsar speed). At such a high velocity, the CN should have been crushed by the ram pressure for any reasonable ISM sound speed (i.e., less than a few tens of km s⁻¹). Of course, the pulsar velocity could be smaller if the pulsar is closer than its DM distance of 3.3 kpc, but the large N_H does not support a significantly smaller distance. Using the Parkes radio telescope and a baseline (in time) of 10 yr, Parthasarathy et al. (2019) measured a proper motion for J1809 of μ_α  = −19 ± 6 and μ_δ  = 50 ± 90 mas yr⁻¹ (95% CL). Although their measurement appears somewhat discrepant from ours in that they only detect proper motion in the westward direction, it is still consistent within 2σ of our measurement. The transverse velocity in R.A. computed from their measurement, v_α  = −300 ± 100 km s⁻¹, is reasonable with respect to the transverse velocities of the general pulsar population (Verbunt et al. 2017). K+18 previously reported a velocity of μ_δ  = 39.6 ± 8.8 mas yr⁻¹ (using the first three epochs of Chandra data). Although also consistent within 2σ of our measurement, it is possible that they underestimated the systematic uncertainties in the Chandra WCS.

The lack of steady motion of the "blob" suggests that the blob is not an actual (isolated) clump of plasma moving away from the pulsar, such as those produced by PSRs J1509–5850 (Klingler et al. 2016a) or B1259–63 (Pavlov et al. 2015; Hare et al. 2019). Instead, it could be a Doppler-boosted region of a bent pulsar jet. We present a qualitative illustration of the geometry of this scenario in Figure 8. In this scenario, the leading jet (ahead of the pulsar) is initially launched along the spin axis, whose direction is offset from the line of sight. As the leading jet experiences the ram pressure produced by the pulsar's motion through the ISM, it will be deformed and bent backward. At some point along the jet's curved path, the jet flow is directed toward the observer. When projected onto the sky, this part of the jet looks brighter because of Doppler boosting, which could explain the bright clump a few arcseconds NE of the pulsar. The changing position of the Doppler-boosted region seen in epochs 4–9 and the "wagging-tail" motion seen in epochs 1–3 (reported by K+18) can be due to pressure nonuniformities in the region ahead of the pulsar, varying jet flow pressure, kink instabilities within the jet, jet precession, or some combination of the above. This geometrical interpretation also explains why the CN is extended in the direction ahead of the pulsar, as the trailing jet is initially oriented away from our line of sight and therefore Doppler deboosted (making the CN appear brighter NE of the pulsar). This picture and interpretation are broadly in agreement with those for the jets of the Vela pulsar (Pavlov et al. 2003; Durant et al. 2013).

Zoom In Zoom Out Reset image size

The blob's spectrum (Γ = 1.34 ± 0.06) is marginally softer than the spectrum in the pulsar vicinity (Γ = 1.23 ± 0.09), but distinctly harder than the CN's spectrum (region 3; Γ = 1.52 ± 0.03). A similar spectral behavior is seen in the Vela PWN (which is much closer and whose structure is well resolved; Durant et al. 2013). These support the idea that the blob is a part of the pulsar's jet.

The interpretation of the J1809 PWN and magnetospheric geometry implies that J1809 may be a rather rare instance of a jet-dominated PWN (similar to the PWN of J1811–1925 in SNR G11.2–0.3; Roberts et al. 2003). Note that both pulsars are γ-ray quiet, which is expected for the case when the spin and magnetic dipole axes are more or less aligned. This may be the reason that some PWNe are jet-dominated (e.g., Bühler & Giomi 2016). The J1809 torus, if present, would then be underluminous compared to other PWNe produced by pulsars with similar ages and spin-down luminosities.

Extending ≥7' from the eastern edge of the EN is a faint collimated structure revealed by the merged image (536 ks). Although the collimated structure is fainter than the EN (0.094 ± 0.008 versus 0.214 ± 0.007 net cts arcsec⁻²), both the EN and the structure exhibit identical spectral indices, Γ = 1.74 (±0.05 and ± 0.12, respectively), indicating that they are composed of electron populations with the same spectral energy distribution (SED). The lack of spectral changes could suggest either that there is no noticeable synchrotron cooling occurring as particles travel along the outflow, or that there is a reacceleration mechanism occurring along the outflow preventing any noticeable spectral changes from synchrotron losses (see, e.g., Xu et al. 2019). The outflow's spectrum is also consistent with the spectra exhibited by the outflows produced by the fast-moving pulsars mentioned in Section 1, of which almost all exhibit a photon index in the 1.6–1.7 range.

This structure could be interpreted as another instance of a "misaligned outflow" (also known as a "kinetic jet"; see Bykov et al. 2017; Kargaltsev et al. 2017; Reynolds et al. 2017; Barkov et al. 2019; and Olmi & Bucciantini 2019). As most of the known misaligned outflows are associated with supersonic pulsars, one might assume that a high Mach number is required to produce such a structure. However, since J1809 is unlikely to have a high Mach number, the existence of a "kinetic jet" in this PWN (and also in the transonic Dragonfly PWN; see the right panel of Figure 7) would imply that supersonic velocities are not required to produce such outflows. Alternatively, the elongated feature could be analogous to the X-ray filament near the Vela pulsar that is sometimes referred to as Vela X, which is also misaligned with respect to the Vela pulsar's direction of motion and believed to be formed by the interaction between the pulsar wind and the reverse shock in the Vela SNR (though Vela X is much larger than this X-ray filament; see Abramowski et al. 2012). However, J1809 is likely to be older than the Vela pulsar, and no evidence of an SNR associated with J1809 has been found so far (Castelletti et al. 2016).

In the case of J1809 (and also PSR J2021+3651; see Figure 7), the particle leakage cannot be the result of large gyroradii (Bandiera 2008), since the gyroradii of X-ray emitting particles here are orders of magnitude smaller than the size of the EN. For X-ray synchrotron-emitting electrons, the gyroradius r_g can be estimated as ${r}_{g}\sim {10}^{14}{(E/1\mathrm{keV})}^{1/2}{(B/20\mu G)}^{-3/2}\,\mathrm{cm}$. For an 8 keV emitting electron in a 5 μG magnetic field, ¹⁴ r_g  ≈ 2.3 × 10¹⁵ cm. At the distance of J1809 (d ∼ 3.3 kpc), this corresponds to ≈005. Thus, this case can be interpreted as observational evidence that PWN and ISM magnetic fields can reconnect in the nebulae of transonic pulsars as well as supersonic pulsars. If this structure is produced by PWN/ISM magnetic field reconnection, the point of reconnection is not necessarily at the interface between regions 5 and 6 as shown in Figure 5, since that is a 2D projection of a 3D structure, but could be at a point "inside" (in projection) region 5. However, in the MHD simulations that demonstrated this reconnection scenario (Barkov et al. 2019; Olmi & Bucciantini 2019), the pulsars had Mach numbers ${ \mathcal M }\gg 1$, so further simulations for the transonic case are needed.

We analyzed 15 Chandra observations covering the J1809 field and listed in Table 2. We excluded ObsIDs 20332 and 20967 because the astrometric correction did not converge to the required precision. The 2σ statistical positional uncertainties (PUs) were calculated using the empirical relation between PU, off-axis angle, and source counts from Kim et al. (2007). The 2σ astrometric uncertainty was then added in quadrature to the statistical PU to calculate the overall 2σ PU.

We ran the CIAO tool ¹⁵ srcflux on each observation, using the source coordinates found by wavdetect from the astrometrically corrected images. The sources detected with a ≥6σ significance were then selected and cross-matched (within 25) between observations. After excluding sources located within 10 of the pulsar/PWN region (to avoid PWN emission clumps being interpreted as point sources), 90 unique sources remained, with many of them detected (at ≥6σ) in multiple observations. Another cut was then applied to keep only those sources that are detected at a >10σ confidence level in at least one observation. The more demanding 10σ cut is needed to ensure that the source is detected significantly enough that the fluxes in the individual bands and corresponding hardness ratios can be reliably calculated in at least one observation. On the other hand, the >6σ detections in other observations are sufficient for comparisons of broadband fluxes to probe each source's variability. After the above cuts were applied, we were left with 35 sources (with 199 total detections across all 15 observations).

We then found weighted averages of the positions and fluxes of each source, using the inverse square uncertainties as weights. To identify variable sources, we fitted a constant-flux model to the broadband (0.7–7.0 keV) fluxes measured from multiple observations and calculated the minimum reduced chi-squares, ${\chi }_{\nu }^{2}$. The X-ray fluxes ${F}_{s},{F}_{m},{F}_{h}$ and their uncertainties are measured in three energy bands (s = 0.7–1.2, m = 1.2–2, h = 2.0–7 keV) for each source. The broadband flux F_b (b = 0.7–7.0 keV) is calculated by coadding the fluxes at soft, medium, and hard bands together. The uncertainty of F_b is calculated from the flux uncertainties in each of the three bands added in quadrature. These energy bands are chosen because they overlap with the energy bands used in the 3XMM-DR8 catalog, ¹⁶ which we use to construct our training data set (see the Appendix). Due to the increasing buildup of a contaminating layer on the ACIS detector (see, e.g., Plucinsky et al. 2018) and uncertainties in the ACIS quantum efficiency contamination model near the O–K edge at 0.535 keV and F–K edge at 0.688 keV, ¹⁷ we chose to use 0.7–1.2 keV for the soft energy band. From these fluxes, we calculated two hardness ratios HR2 = (F_m  − F_s )/(F_m  + F_s ) and HR4 = (F_h  − F_m )/(F_h  + F_m ). The plot of hardness ratios of all 35 sources is shown in Figure 10 together with the sources from the training data set (see the Appendix). These and other X-ray parameters for each source are also listed in Table 6.

Table 6. Chandra Sources Detected in the J1809 Field

# a	R.A.	Decl.	PU b	S/N c	χ2/νd	Fb e	HR2 f	HR4 f	Gmag g	Jmag h	5.8 mag i	Class(%) j
1	272.38184	−19.26356	0.57	54.03	58.9/13	1.35 ± 0.32	${0.59}_{-0.25}^{+0.21}$	${0.47}_{-0.21}^{+0.17}$	16.31	12.51	10.71	STAR(?)
2	272.52743	−19.28941	0.75	52.40	57.2/6	0.85 ± 0.22	${0.22}_{-0.32}^{+0.32}$	${0.29}_{-0.29}^{+0.24}$	17.89	14.21	10.12	STAR(?)
3	272.63647	−19.29869	1.67	46.26	⋯	24.39 ± 1.58	−${0.10}_{-0.07}^{+0.08}$	${0.37}_{-0.06}^{+0.06}$	12.81	10.87	9.55	STAR(?)
4	272.37050	−19.29553	0.54	44.43	12.1/10	7.02 ± 1.20	−${0.21}_{-0.48}^{+0.54}$	${0.99}_{-0.01}^{+0.00}$	⋯	⋯	⋯	AGN(?)
5	272.36630	−19.16929	0.77	40.29	51.4/11	2.56 ± 0.57	−${0.22}_{-0.20}^{+0.24}$	${0.15}_{-0.30}^{+0.23}$	14.25	12.63	11.68	STAR(98)
6	272.40015	−19.33660	0.54	39.74	21.7/13	4.93 ± 0.94	${0.58}_{-0.43}^{+0.25}$	${0.94}_{-0.04}^{+0.03}$	⋯	⋯	⋯	AGN(?)
7	272.47389	−19.26788	0.62	35.83	20.8/11	3.08 ± 0.71	${0.33}_{-0.63}^{+0.39}$	${0.97}_{-0.02}^{+0.01}$	⋯	⋯	⋯	AGN(86)
8	272.41968	−19.42886	0.81	31.26	10.8/4	9.62 ± 1.40	${0.86}_{-0.12}^{+0.08}$	${0.86}_{-0.04}^{+0.04}$	⋯	⋯	⋯	AGN(97)
9	272.33989	−19.25460	0.71	29.29	7.1/9	5.60 ± 1.13	−${0.71}_{-0.19}^{+0.47}$	${1.00}_{-0.01}^{+0.00}$	⋯	⋯	⋯	AGN(?)
10	272.40211	−19.31132	0.59	25.70	18.5/7	0.63 ± 0.20	−${0.02}_{-0.30}^{+0.33}$	−${0.21}_{-0.37}^{+0.38}$	12.24	11.37	10.95	STAR(96)
11	272.30315	−19.33844	0.87	24.68	19.7/4	3.54 ± 0.77	${0.88}_{-0.10}^{+0.07}$	${0.68}_{-0.13}^{+0.11}$	19.90	⋯	⋯	CV(?)
12 k	272.32227	−19.25281	1.07	23.42	⋯	6.88 ± 1.25	⋯	${0.95}_{-0.04}^{+0.03}$	⋯	⋯	⋯	AGN(?)
13	272.41819	−19.20079	0.76	23.40	9.4/7	4.17 ± 0.93	−${0.18}_{-0.55}^{+0.57}$	${1.00}_{-0.01}^{+0.00}$	⋯	⋯	⋯	AGN(?)
14	272.25864	−19.23210	1.47	20.96	⋯	16.67 ± 2.06	−${0.08}_{-0.50}^{+0.52}$	${0.98}_{-0.01}^{+0.01}$	⋯	⋯	⋯	AGN(?)
15	272.55197	−19.34022	1.45	19.68	17.0/4	2.71 ± 0.52	${0.79}_{-0.21}^{+0.12}$	${0.66}_{-0.12}^{+0.11}$	19.35	14.87	⋯	YSO(73)
16	272.52225	−19.34824	0.99	17.75	38.5/13	4.11 ± 0.80	−${0.42}_{-0.37}^{+0.55}$	${0.99}_{-0.01}^{+0.01}$	⋯	⋯	⋯	AGN(?)
17 k	272.39803	−19.31851	0.73	16.23	⋯	1.82 ± 0.57	${0.41}_{-0.39}^{+0.31}$	${0.50}_{-0.27}^{+0.21}$	⋯	⋯	⋯	LMXB(?)
18	272.59734	−19.28699	1.39	14.79	⋯	8.15 ± 1.20	⋯	${0.95}_{-0.03}^{+0.02}$	⋯	⋯	⋯	YSO(?)
19	272.46344	−19.28710	0.72	13.78	0.38/4	1.47 ± 0.52	−${0.55}_{-0.30}^{+0.50}$	${0.97}_{-0.05}^{+0.02}$	⋯	⋯	⋯	AGN(?)
20	272.61540	−19.34647	1.95	13.42	⋯	5.52 ± 0.94	${0.35}_{-0.17}^{+0.17}$	${0.62}_{-0.11}^{+0.09}$	15.11	12.58	11.28	YSO(?)
21	272.42610	−19.27109	0.65	13.38	3.3/1	0.32 ± 0.16	${0.08}_{-0.45}^{+0.43}$	${0.56}_{-0.39}^{+0.24}$	19.13	⋯	⋯	YSO(?)
22	272.54439	−19.31711	1.41	12.92	3.5/4	2.21 ± 0.60	${0.52}_{-0.50}^{+0.28}$	${0.78}_{-0.14}^{+0.11}$	19.68	14.20	11.20	YSO(?)
23	272.34743	−19.20938	1.15	12.67	⋯	0.75 ± 0.23	${0.83}_{-0.22}^{+0.11}$	${0.10}_{-0.34}^{+0.26}$	⋯	⋯	⋯	AGN(74)
24	272.47246	−19.21609	1.01	12.34	4.1/7	1.11 ± 0.38	${0.76}_{-0.33}^{+0.15}$	${0.70}_{-0.19}^{+0.14}$	⋯	⋯	⋯	AGN(97)
25	272.38873	−19.38628	1.34	11.98	3.2/1	1.72 ± 0.45	−${0.15}_{-0.25}^{+0.28}$	${0.59}_{-0.21}^{+0.15}$	14.45	12.98	12.29	STAR(95)
26	272.46664	−19.20017	1.26	11.43	5.4/3	2.19 ± 0.69	⋯	${0.98}_{-0.03}^{+0.01}$	⋯	⋯	⋯	AGN(79)
27 k	272.39593	−19.29765	0.65	11.31	⋯	1.33 ± 0.53	${0.41}_{-0.48}^{+0.32}$	${0.66}_{-0.27}^{+0.18}$	⋯	⋯	⋯	NS(?)
28	272.37751	−19.30023	0.78	10.99	⋯	1.04 ± 0.33	⋯	${0.95}_{-0.07}^{+0.03}$	⋯	⋯	⋯	AGN(76)
29	272.41503	−19.27108	0.61	10.81	⋯	0.37 ± 0.21	${0.23}_{-0.41}^{+0.37}$	${0.34}_{-0.49}^{+0.33}$	18.19	⋯	⋯	YSO(?)
30	272.34974	−19.26876	0.97	10.61	⋯	0.57 ± 0.22	${0.94}_{-0.15}^{+0.04}$	${0.37}_{-0.34}^{+0.25}$	⋯	⋯	⋯	AGN(99)
31	272.51118	−19.15637	2.10	10.48	9.2/3	1.48 ± 0.32	−${0.28}_{-0.19}^{+0.20}$	${0.09}_{-0.34}^{+0.26}$	15.45	13.64	⋯	STAR(90)
32	272.37483	−19.21707	1.35	10.12	⋯	1.83 ± 0.55	${0.05}_{-0.51}^{+0.47}$	${0.93}_{-0.08}^{+0.05}$	⋯	⋯	⋯	AGN(?)
33	272.45647	−19.26167	0.82	10.11	3.3/1	0.30 ± 0.15	−${0.13}_{-0.39}^{+0.46}$	${0.52}_{-0.42}^{+0.26}$	18.19	⋯	⋯	YSO(?)
34	272.41733	−19.21707	1.21	10.09	⋯	1.10 ± 0.53	−${0.12}_{-0.33}^{+0.33}$	${0.36}_{-0.48}^{+0.33}$	17.43	14.05	10.69	STAR(?)
35	272.50596	−19.27867	0.98	10.00	4.2/8	1.78 ± 0.55	−${0.11}_{-0.53}^{+0.56}$	${0.97}_{-0.05}^{+0.02}$	⋯	⋯	12.00	YSO(?)

Notes.

^a #—Source number (sources are ordered by their significance). ^b PU—Maximum 2σ positional uncertainties in units of arcseconds among the observations. ^c S/N—Maximum signal-to-noise ratio among the observations. ^d ${\chi }^{2}/\nu$—Chi-square and number of degrees of freedom (ν = number of observations − 1) for a constant model fitted to the broadband fluxes from all observations. Chi-squared is not calculated for the sources detected only once (transients) or observed only once. ^e F_b —Averaged broadband flux in the 0.7–7 keV range in units of 10⁻¹⁴ erg s⁻¹ cm⁻² by weighting with the inverse of squares of their 90% confidence uncertainties. ^f HR2 and HR4—hardness ratios defined in Section 5.1. ^g Gmag—G-band magnitude taken from the GAIA DR2 catalog. ^h Jmag—J-band magnitude taken from the 2MASS catalog. ⁱ 5.8 mag—5.8 μ band magnitude taken from the GLIMPSE catalog. ^j Class—Predicted classification of each source obtained from the automated classification pipeline with their classification confidence (shown in parentheses). Sources with "?" have a classification confidence <70%. ^k Transient sources detected in only one observation.

Download table as:  ASCIITypeset image

The multiwavelength photometry was taken from the Gaia DR2 catalog (Gaia Collaboration et al. 2018), the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006), and the Galactic Legacy Infrared Midplane Survey Extraordinaire (GLIMPSE; Benjamin et al. 2003). These catalogs were cross-matched with each source's averaged X-ray position and were considered to be a match if the MW counterpart was located within the 2σ X-ray PU. We found that 18 out of 35 X-ray sources had MW counterparts. The chance coincidence probabilities for each catalog were calculated by finding the average field source density, ρ, and calculating the probability, $P=1-\exp (-\rho \pi {r}^{2})$, of having one or more sources within a randomly placed, r = 1'' circle, which is the average 2σ PU of all of the sources. The source densities from the corresponding catalogs are ρ_Gaia = 0.0147 arcsec⁻², ρ_2MASS = 0.0105 arcsec⁻², and ρ_GLIMPSE = 0.0245 arcsec⁻², leading to chance coincidence probabilities of 4.5%, 3.2%, and 7.4%, respectively. The GLIMPSE catalog has the largest chance coincidence probability, which implies that about three GLIMPSE sources may be spurious cross-matches. None of the X-ray sources had more than one Gaia or 2MASS counterpart; however, one X-ray source (Source 26) had two potential GLIMPSE counterparts, so the nearest match was taken as the counterpart.

The magnitudes and colors for the MW counterparts, together with the X-ray properties (fluxes in two bands and two hardness ratios), add up to 20 features, which were used to classify these sources with a machine learning (ML) approach (see the Appendix; Hare et al. 2016, 2017). The summary of the MW properties of the sources and their classifications is given in Table 6, with 13 sources (marked in bold) having classification confidence >70% (see the Appendix). At this level of confidence, we do not identify any Galactic objects capable of contributing to the extended TeV emission of HESS/eHWC J1809–193 (e.g., pulsars or HMXBs). It is worth noting that there are several confidently identified active galactic nuclei (AGNs) that could, in principle, produce some TeV emission. However, in X-rays, they are significantly fainter than those AGNs that are known to be TeV sources.

The X-ray image of the J1809 field, constructed by stacking all 15 observations together, is shown in Figure 9. All 35 sources with a detection significance >10 are shown by colored circles. The size of each circle is proportional to each source's detection significance, while the circle's thickness is proportional to the source's classification confidence.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Since our ML classification currently does not take into account temporal properties, and TeV HMXBs could be variable in X-rays, we examined the two brightest, significantly variable (>5σ) and transient (i.e., only significantly detected in a single observation) sources. For sources with an optical/near-infrared (NIR) counterpart, we use MW photometry to fit the SED of each source to obtain a spectral type using the VO SED Analyzer (VOSA; Bayo et al. 2008). The spectral type is then determined by using a chi-squared fit to the NextGen theoretical model spectra (Hauschildt et al. 1999). We also include the Gaia-derived distance estimates in the SED fits when available (Bailer-Jones et al. 2018).

Sources 1 and 2 both show strong X-ray variability across the 17 observations, but neither source is particularly variable within the duration of a single observation. The Gaia distances to these sources are 3 kpc and 2 kpc, respectively, but we caution that both are impacted by large astrometric noise (possibly due to the sources being binaries), which may cause these distance estimates to be unreliable (Bailer-Jones et al. 2018). At these distances, both sources have observed peak X-ray luminosities of ∼8 × 10³¹ erg s⁻¹ and "quiescent" luminosities of 8 × 10³⁰ erg s⁻¹ and 2 × 10³⁰ erg s⁻¹, respectively. Both sources also have similar parameters derived from fits to their NIR–optical SEDs (i.e., T_eff ≈ 4500 K and log g = 3.5), implying cool giants. ¹⁸ Therefore, neither of these two sources are likely to be high-mass X-ray binaries (HMXBs), nor are they likely to be responsible for the TeV emission. The hardness ratios indicate soft spectra with only modest absorption (in agreement with the NIR–optical SED shape), suggesting that these are not quiescent low-mass X-ray binaries (LMXBs), which tend to have hard X-ray spectra. Since the X-ray luminosities are somewhat larger than stellar (for these type of stars), we believe that both sources could be active binaries (ABs), similar to, for example, W Uma and RS CVn (van den Berg et al. 2013), which are known to exhibit flares with luminosities up to 10³⁴ erg s⁻¹ (e.g., Tsuboi et al. 2016).

The two brightest short transient sources detected in the Chandra observations are Sources 12 and 17. Source 12 only shows up in ObsID 21098 and does not exhibit strong variability throughout the duration of the observation. No optical/NIR counterpart was found for this source in the catalogs used for ML classification; however, a faint NIR source is detected in the UKIDSS Galactic plane survey (Lucas et al. 2008). The source is offset by 04 and has magnitudes J = 18.4, H = 16.4, and K = 15.5, suggesting that it is strongly absorbed. At a distance of 4–10 kpc, the source would have an observed X-ray luminosity of ${10}^{32}\mbox{--}{10}^{33}$ erg s⁻¹, which is still consistent with being a flaring AB-type source, or, if the source is more nearby, with a flaring M-dwarf star (see, e.g., Stelzer et al. 2013; Pye et al. 2015). It could also be a flaring AGN, given the hard spectrum. Source 17 is only detected in ObsID 20330 and shows a single flare, which decays over ∼7 ks to a persistent low flux level. The source has no MW counterpart, ¹⁹ and there are too few X-ray photons (38 ± 6 in total with a mean energy of ∼2.4 keV) to constrain the spectrum and nature of this relatively hard source without knowledge of its distance.

Lastly, Source 27 is a short transient only detected in ObsID 21126. This source shows flaring behavior, with the longest duration flare lasting ∼2 ks. The total number of photons is small (32 ± 6 in total), which precludes any meaningful spectral analysis. There is one potential counterpart in the UKIDSS Galactic plane survey that lies just at the edge (∼065) of the source's PU and has magnitudes J = 18.5, H = 17.6, and K = 17.1, and it is classified as a galaxy in the UKIDDS catalog. If this source is the true counterpart, then Source 27 could be an AGN. We note that the ML-based classification of this source, which is not confident (i.e., <70%), as an isolated NS (e.g., pulsar) is unlikely since the source is strongly variable. However, the current training data set does not take into account temporal information. To conclude, none of the transient sources appear to be a good HMXB candidate (which could contribute to the TeV flux), and, although AGN classification is not excluded for some of these sources, the low X-ray flux would imply a low TeV flux in this scenario. Therefore, PSR J1809–1917 remains the most likely counterpart to HESS/eHWC J1809–193.