Searching for Faint X-ray Emission from Galactic Stellar Wind Bow Shocks

TL;DR

This study uses archival Chandra data to set upper limits on X-ray emissions from stellar wind bow shocks, compares properties of bow shock stars to other OB stars, and evaluates Lynx observatory's detection prospects.

Contribution

It provides the most stringent X-ray luminosity upper limits for bow shocks and assesses future detection capabilities with Lynx.

Findings

Upper limit on X-ray luminosity of bow shocks is <2×10^{29} erg/s.

No high L_X/L_bol ratios indicative of magnetic stars in the sample.

Lynx could detect the nearest bow shocks with ~100 ks exposure.

Abstract

We present a stacking analysis of 2.61 Msec of archival Chandra observations of stellar wind bow shocks. We place an upper limit on the X-ray luminosity of IR-detected bow shocks of $<2\times10^{29}$ erg s$^{-1}$, a more stringent constraint than has been found in previous archival studies and dedicated observing campaigns of nearby bow shocks. We compare the X-ray luminosities and $L_X/L_{\rm bol}$ ratios of bow shock driving stars to those of other OB stars within the Chandra field of view. Driving stars are, on average, of later spectral type than the "field of view" OB stars, and we do not observe any unambiguously high $L_X/L_{\rm bol}$ ratios indicative of magnetic stars in our sample. We additionally asses the feasibility of detecting X-rays from stellar wind bow shocks with the proposed Lynx X-ray Observatory. If the X-ray flux originating from the bow shocks is just below our Chandra detection limit, the nearest bow shock in our sample (at $\sim$0.4 kpc with an absorbing column of $\sim10^{21}$ cm$^{-2}$) should be observable with Lynx in exposure times on the order of $\sim$100 kiloseconds.

Figures

Tables

Table 1. Table 1: Chandra Observations Containing Stellar Bow Shocks

	Obs. Date		Nominal Aim Point (J2000)		Effective Exp.	# Bow
Obs. ID	(YYYY-MM-DD)	ACIS-	R.A.	Decl.	Time (ks)	Shocks
748	2000-10-15	S	18:46:24.7	-02:58:34.0	34.0	1
972	2002-03-02	I	18:20:29.9	-16:10:45.5	39.4	3
1985	2001-07-26	I	14:12:08.0	-61:45:29.0	9.3	1
2298	2001-05-20	I	18:43:32.1	-03:54:44.8	88.7	2
3501	2003-08-23	I	10:24:02.5	-57:45:23.0	34.7	3
3811	2003-10-04	S	12:26:52.8	-62:49:07.0	3.0	1
3854	2003-07-15	S	19:13:20.3	+10:11:23.0	19.6	1
4495	2004-09-21	I	10:43:57.5	-59:32:53.0	57.1	1
4550	2004-07-03	S	17:54:28.3	-26:20:35.0	16.8	1
4600	2004-07-09	I	18:25:27.0	-14:48:38.0	11.0	1

Table 2. Table 2: Bow Shocks in Sample

	RA	Decl.	$R_0$	P.A.	X-ray Exp.	Off-Axis
Name	(J2000)	(J2000)	(′′)	(∘)	Time (ks)	Angleaafootnotemark: (′)
(1)	(2)	(3)	(4)	(5)	(6)	(7)
G015.0749-00.6461	18:20:22.8	-16:08:34	2.5	140	325.9	2.2
G015.0812-00.6570	18:20:25.9	-16:08:32	14.5	135	325.9	2.2
G015.1032-00.6489	18:20:26.7	-16:07:09	6.1	150	325.9	3.6
G338.2791-00.01416	16:40:33.3	-46:33:20	18.4	110	205.6	1.8
G029.7810-00.2176	18:46:27.1	-02:54:12	6.7	145	183.7	4.4
G172.0813-02.2592	05:16:18.2	34:18:44	9.9	350	140.5	0.1
G284.2999-00.3359	10:24:11.5	-57:46:47	3.9	295	135.0	1.4
G284.3011-00.3712	10:24:03.1	-57:48:36	2.9	135	135.0	3.2
G327.2741-00.14811	15:51:10.3	-54:17:46	15.8	100	106.1	0.7
G028.4787-00.0056	18:43:19.0	-03:57:54	8.2	305	98.7	3.2
G028.5028-00.0343	18:43:28.0	-03:57:24	3.1	25	98.7	2.7
G359.0835-00.4367	17:45:08.2	-29:56:45	26.9	160	89.4	0.5
G041.5496+00.0975	19:06:54.0	07:42:30	6.5	115	87.9	4.1
G348.2233+00.46284	17:12:20.8	-38:29:31	40.0	160	76.8	0.1
G006.2812+23.5877	16:37:09.5	-10:34:02	29.0	30	72.1	2.8
G014.4703-00.6427	18:19:10.6	-16:40:27	14.7	210	66.0	2.5
G287.1148-01.0236	10:40:12.4	-59:48:10	15.8	285	59.6	1.4
G288.1505-00.5059	10:49:25.0	-59:49:44	4.2	220	59.5	4.3
G287.4389-00.6132	10:44:00.9	-59:35:46	4.0	325	57.3	2.9
G287.6736-01.0093	10:44:11.1	-60:03:21	3.7	5	56.5	0.9
G080.3667+00.4209	20:35:16.1	41:12:34	17.6	125	56.3	4.9
G287.4071-00.3593	10:44:43.9	-59:21:25	7.8	110	55.3	0.1
G333.3639-00.3327	16:21:37.7	-50:21:17	5.3	30	54.3	3.0
G333.3665-00.4112	16:21:59.3	-50:24:31	40.6	160	54.3	0.5
G353.0649+01.2985	17:22:50.0	-34:03:22	10.2	25	39.5	1.3
G012.8263-00.1278	18:14:0.3	-17:52:32	7.5	355	38.2	3.2
G012.8724-00.23427	18:14:29.4	-17:53:10	31.0	130	38.2	2.6
G026.1437-00.0420	18:39:09.1	-06:03:28	22.1	50	37.5	1.7
G284.3400-00.2827	10:24:39.2	-57:45:21	4.1	285	36.2	0.6
G045.2527-00.4751	19:15:54.0	10:43:36	5.4	14	29.6	2.4
G016.8993-01.1152	18:25:38.9	-14:45:06	24.0	120	29.0	3.5
G026.6435-00.0209	18:40:06.1	-05:37:03	6.8	305	20.1	3.4
G044.5388-00.2303	19:13:40.0	10:12:30	4.5	225	19.6	1.2
G337.1246-00.1209	16:36:29.9	-47:29:11	6.6	225	19.5	4.3
G003.2532-00.2836	17:54:15.6	-26:17:24	25.3	290	19.1	3.2
G337.2776-00.2660	16:37:44.5	-47:28:13	10.9	30	19.0	3.7
G336.9225+00.05767	16:34:54.6	-47:30:54	11.0	270	19.0	3.3
G022.4119-00.2010	18:32:48.0	-9:26:40	10.1	55	18.2	4.8
G021.6949+00.24498	18:29:51.0	-09:52:26	26.5	265	15.2	1.0
G000.1169-00.5703	17:48:07.0	-29:07:56	26.4	27	14.1	2.4
G033.8783+00.2033	18:52:26.0	00:56:06	14.0	155	11.9	4.3
G028.8142+00.1922	18:43:13.1	-03:34:34	3.9	230	10.9	2.8
G347.8625-00.1941	17:13:59.4	-39:10:11	4.4	240	10.7	2.1
G046.7943-00.2716	19:18:06.0	12:11:06	19.6	130	9.9	1.6
G319.9407+00.2825	15:05:28.1	-58:04:54	2.5	240	9.9	0.6
G312.2963-00.42721	14:12:03.9	-61:49:27	17.5	90	9.3	4.0
G003.5118-00.0470	17:53:56.0	-25:56:50	8.6	135	6.8	3.6
G332.9033+00.11195	16:17:36.9	-50:21:41	16.4	50	5.0	1.5
G031.9308+00.2676	18:48:39.1	00:46:08	15.5	10	4.7	0.6
G031.9747+00.3348	18:48:30.0	00:41:57	6.9	230	4.7	3.6
G356.6602+00.9209	17:33:47.9	-31:16:27	15.8	105	4.6	4.0
G028.6268-00.16592	18:44:09.9	-03:54:24	13.3	335	3.1	1.2
G300.1020-00.1371	12:26:34.4	-62:52:20	1.5	100	3.0	3.2
G021.6408-00.18419	18:31:17.6	-10:07:18	27.7	105	2.8	1.3
G345.3932-00.0552	17:05:45.7	-41:04:17	31.0	210	2.4	0.7
G352.4288-00.0241	17:26:24.9	-35:19:34	11.9	220	2.3	2.8
G352.4634+00.0358	17:26:16.0	-35:15:50	7.4	130	2.3	1.0
G003.7391+00.1425	17:53:43.0	-25:39:19	3.9	20	2.0	0.7
G341.3576+00.1490	16:51:14.4	-44:06:37	5.0	225	1.8	3.1
G343.9419-00.1440	17:01:22.1	-42:16:40	4.2	210	1.3	4.5
G060.9223-00.1176	19:46:22.7	24:37:48	4.9	195	1.3	1.0

Table 3. Table 3: X-ray Detected OB Stars

R.A.	Decl.	Stellar	Spectral	Distancebbfootnotemark:	Net Cts/Exp. Time	Off-Axis	log$L_X$	Driving
(X-ray source; J2000)		Counterpart	Typeaafootnotemark:	(kpc)	(0.5-7 keV)/(ks)	Angle (′)ccfootnotemark:	(erg s-1)	Star?	Notesddfootnotemark:
05:16:18.1	+34:18:44.3	HD 34078	O9.5V	0.41$\pm$0.01	3004/140.5	0.1	31.1	Y	M
17:12:20.9	-38:29:30.4	CD-38 11636	O8	0.72$\pm$0.25	974/78.8	0.1	31.3	Y	M
10:27:58.0	-57:45:49.0	V* V712 Car	O3If*/WN6+O3If*/WN6	5.3$\pm$1.4	660/34.7	1.4	33.2	N
10:24:01.2	-57:45:31.0	Wd 2 MSP 188	O5.5, O3V+O5.5	5.3$\pm$1.4	527/34.7	0.6	33.1	N	C
10:24:18.4	-57:48:29.5	WR 20b	WN6ha	3.6$\pm$0.8	408/34.7	4.9	32.7	N
10:24:02.4	-57:44:35.9	Wd 2 5	O5/5.5V/III(f)	5.3$\pm$1.4	337/34.7	0.8	32.9	N
10:24:01.9	-57:45:27.7	Wd 2 MSP 167	O8V, O8V	4.2$\pm$0.5	264/34.7	0.4	32.6	N	C
10:44:43.9	-59:21:25.1	HD 93249	O9III	3.4$\pm$0.4	209/55.3	0.1	32.1	Y	PM
10:40:31.7	-59:46:43.9	HD 92644	B0V	2.6$\pm$0.4	139/59.1	2.8	31.7	N	M
10:44:11.1	-60:03:21.5	HD 305536	O9.5V	2.4$\pm$0.2	126/56.5	4.9	31.6	Y
10:24:02.2	-57:45:31.3	[RSN2011] C, D, E	O7V, O9.5, O6-7	3.1$\pm$0.8	112/34.7	0.3	32.0	N	C
18:31:16.5	-10:09:24.8	UCAC 160-180469	WR8	9.9	82/2.8	0.8	$\cdots$	N
10:24:00.2	-57:45:32.4	2MASS J10240020-5745327	O8.5V	5.7$\pm$2.4	68/34.7	0.8	32.3	N
10:24:00.7	-57:49:25.2	2MASS J10240073-5745253	O8V, O6.5V	6.7$\pm$1.3	68/34.7	0.7	32.4	N	C
10:23:55.1	-57:49:26.6	Wd 2 MSP 165	O4V	6.0$\pm$1.7	63/34.7	2.1	32.3	N
10:24:16.2	-57:43:43.7	Wd 2 NRM 2	O8.5III	5.9$\pm$1.5	57/34.7	3.6	32.3	N
10:4405.9	-59.9948782	HD 305520	B1Ib	2.3$\pm$0.2	45/56.5	1.7	31.1	N
10:44:42.1	-59:22:30.6	CPD-58 2655	B1V	2.6$\pm$0.2	42/55.3	1.2	31.2	N
18:13:58.2	-17:56:25.4	[MCF2015] 6, 7	B0-5, O4-6	4.0$\pm$1.8	39/38.2	3.9	31.7	N	C
10:44:35.9	-59:23:35.6	Tr 15 C28	O9V	2.6$\pm$0.2	28/55.3	3.0	31.0	N
10:23:56.1	-57:45:29.9	Wd 2 MSP 182	O4III	5.7$\pm$1.2	27/34.7	1.8	31.9	N
10:24:01.5	-57:45:56.9	Wd 2 MSP 263	O6V	10.2	25/34.7	0.7	$\cdots$	N
10:24:04.8	-57:45:28.1	Wd 2 MSP 171	O5V	4.0$\pm$0.6	22/34.7	0.4	31.5	N
10:44:43.7	-59:21:17.3	Tr 15 2	O9/9.5III	3.0$\pm$0.3	19/55.3	0.1	31.0	N
10:48:58.9	-59:41:09.2	HD 303413	B1Ib	2.8$\pm$0.2	15/50.0	5.0	30.9	N
10:44:42.3	-59:23:03.8	CPD-58 2656	B0.5IV/V	3.1$\pm$0.3	15/55.3	1.7	30.9	N
10:24:02.4	-57:45:46.8	Wd 2 MSP 235	O9.5V	3.8$\pm$0.8	15/34.7	0.5	31.3	N
10:24:00.9	-57:45:05.0	Wd 2 MSP 96	B1+B1	4.1$\pm$0.7	14/34.7	0.7	31.3	N
10:24:01.3	-57:45:29.5	Wd 2 MSP 175	O4V	4.2$\pm$0.5	13/34.7	0.5	31.3	N
10:24:00.4	-57:44:44.2	Wd 2 MSP 44	B1V+PMS	7.0$\pm$2.0	13/34.7	1.0	31.8	N
17:05:45.6	-41:04:17.3	TYC 7873-1475-1	OB+	4.2$\pm$2.2	12/2.4	2.6	32.4	Y
18:13:59.7	-17:57:41.2	[MCF2015] 8	O4-6	$\cdots$	11.38.2	4.0	$\cdots$	N
12:26:36.7	-62:47:52.0	CD-62 653	B7e	1.2$\pm$0.1	10/3.0	4.0	31.2	N
10:24:00.3	-57:45:42.5	2MASS J10240034-5745426	O8V	0.69$\pm$0.22	9/34.7	0.8	29.6	N	C
18:14:20.5	-17:56:11.2	[MCF2015] 23	O6-7	$\cdots$	9/38.2	1.8	$\cdots$	N
10:49:04.4	-59:48:00.2	LS 1940	OB	2.3$\pm$0.2	7/50.0	2.9	30.4	N
10:44:46.5	-59:21:53.9	CPD-58 2662	B2V	3.2$\pm$0.3	7/55.3	0.8	30.6	N
10:40:23.4	-59:50:39.0	[AHP2016] OBc 3	O7V	11.7$\pm$4.9	7/26.8	2.9	32.1	N
10:24:06.6	-57:47:15.7	Wd 2 NRM 3	O9.5V	5.1$\pm$1.4	6/34.7	2.0	31.2	N
10:23:57.7	-57:45:34.2	Wd 2 MSP 201	OB	8.0$\pm$3.2	5/34.7	1.4	31.5	N

Table 4. Table 4: X-ray Luminosities of Selected Massive Stars Compared to the Literature

	$L_X$ (erg s-1)
Star	This Work	Literatureaafootnotemark:	Reference
(1)	(2)	(3)	(4)
V* V712 Car	1.6$\times {10}^{33}$	4.0$\times {10}^{33}$	Tsujimoto et al. (2007)
WR 20b	5.0$\times {10}^{32}$	7.3$\times {10}^{32}$	Tsujimoto et al. (2007)
Wd 2 5	7.9$\times {10}^{32}$	1.3$\times {10}^{33}$	Tsujimoto et al. (2007)
HD 305536	4.0$\times {10}^{31}$	1.4$\times {10}^{31}$	Broos et al. (2011)

Equations

$$S(r)=S_0{\left[1+\frac{r}{r_{\mathrm{c}}}\right]}^{-3\beta +1/2},$$

Full text

Stars: massive — Stars: winds, outflows — circumstellar matter — X-rays: ISM

††journal: AAS Journals††facilities: Chandra (ACIS)††software: CIAO (v4.10; Fruscione et al., 2006), SOXS

1 Introduction

Stellar wind bow shocks produced by runaway OB stars ($M>$ 8 M*⊙*) are believed to be a major source of high-energy emission in the Milky Way (Mohamed et al., 2012; del Valle et al., 2015; Toalá et al., 2016; del Valle & Pohl, 2018). Non-thermal emission arises from relativistic particles (mainly electrons) being accelerated by a magnetic field at the shock front (del Valle & Romero, 2012; Meyer et al., 2017) via first-order Fermi acceleration; models of this process typically use the magnetic field strength of the ambient ISM ($\sim$few $\mu$G; Meyer et al., 2017) or equipartition arguments with respect to the kinetic power from the driving star’s stellar wind ($\sim$tens of $\mu$G; del Valle & Romero, 2012). The electrons then participate in inverse Compton scattering with IR photons emitted by swept-up dust in the bow shock, scattering the IR photons up to X-ray and gamma ray energies (Peri et al., 2012; del Valle & Pohl, 2018).

These models, however, predict only faint X-ray luminosities, $\sim(1-10)\times 10^{29}$ erg s*-1* (e.g., Pereira et al., 2016; Meyer et al., 2017; De Becker et al., 2017; del Valle & Pohl, 2018), making direct X-ray observations of bow shocks difficult. Although López-Santiago et al. (2012) reported the first high energy detection of the AE Aurigae bow shock, it was later shown by Toalá et al. (2017) that the X-ray emission was not spatially coincident with the IR bow shock. Toalá et al. (2016) report a detection of diffuse, thermal X-ray emission surrounding $\zeta$ Oph using Chandra, although pile-up during the observation makes direct interpretation of the X-ray spectrum difficult. Non-thermal radio emission has been observed in BD +43*∘3654 (Benaglia et al., 2010), although observations with Suzaku and XMM-Newton have only yielded upper limits on the X-ray luminosity (3$\sigma$ upper limit of 1.1$\times$1032* erg s*-1*; Terada et al., 2012; Toalá et al., 2016). Recent 2D hydrodynamical models by del Valle & Pohl (2018) suggest that only a very small fraction of the total stellar wind kinetic power ($\sim 10^{-5}$) is converted into nonthermal emission, and that such emission is more likely to be detected at radio wavelengths. At these faint luminosities, any hope of directly observing X-rays from bow shocks $>$0.5 kpc from the Sun requires prohibitively long exposure times.

In contrast, the massive stars driving the bow shocks may appear as X-ray point sources that are detectable in modest exposure times. Roughly 10% of OB stars exhibit strong (often dipolar) magnetic fields (Petit et al., 2013; ud-Doula & Nazé, 2016). In these systems, charged particles from the stellar wind become trapped and channeled along magnetic field lines, leading to magnetically confined wind shocks (Babel & Montmerle, 1997a, b). These stars have systematically higher X-ray luminosities and $L_{\rm X}/L_{\rm bol}$ ratios than non-magnetic OB stars. The prototypical example is $\theta^{1}$ Ori C (Gagné et al., 2005), and magnetic fields have also been detected in Tr 16-22 and Tr 16-13 in the Carina Nebula (Nazé et al., 2012). Stellar wind bow shock nebulae formation, however, is likely not affected by the magnetic surface properties of driving stars, as the radial dipolar component of the stellar $B$-field falls off as $\sim 1/r^{2}$. The stellar $B$-field is thus negligible at the standoff radius $R_{0}$ (typically at $\sim 0.1-1$ pc).

We have leveraged 91 archival Chandra X-ray observations (with a total exposure time of 2.61 Msec) containing 60 IR-bright Galactic stellar-wind bow shocks. The majority ($\sim$70%) of these bow shocks are located in apparently isolated environments, making them good candidate runaway stars. By stacking the X-ray images, we have created the deepest X-ray exposure of IR stellar wind bow shocks to date. We additionally performed a comparison of the X-ray properties of bow shock driving stars to other massive stars detected within the Chandra field of view. In Section 2 we describe the IR bow shock sample, the Chandra archival observations we use, and describe our data reduction and processing procedures (including X-ray point source detection). In Section 3 we describe our bow shock stacking analysis, and Section 4 presents a comparison of the X-ray properties of driving stars to other OB stars. We discuss our results in Section 5 and prospects for observations with future X-ray facilities, and summarize our findings in Section 6.

2 Sample Selection

The largest published catalog of mid-IR stellar bow shocks contains 709 sources identified in Spitzer and WISE images of the Galactic Plane (Kobulnicky et al., 2016), and the latest data release from the citizen science initiative the Milky Way Project (MWP; Jayasinghe et al. in prep) has found an additional 282 IR stellar wind bow shocks that we include in our initial Galactic bow shocks sample.

The massive OB driving stars of these stellar wind bow shocks may also appear as X-ray point sources. The superior angular resolution of the Chandra X-ray Observatory is therefore necessary to separate potential X-ray emission from the bow shock driving star from the bow shock itself. We searched the Chandra archive for ACIS observations containing the position of at least one IR-identified bow shock within 5*′* of the nominal aim point. This radius was chosen to ensure reasonably small (${\lesssim}2\arcsec$) and symmetric PSFs at the position of the bow shock. The search returned 91 archival observations (containing 60 unique bow shocks) with a total of 2.61 Msec exposure time. In Table 1, we summarize the observation identification numbers (hereafter referred to as “ObsIDs”), the date of the observation, which ACIS instrument was used (S or I), the nominal aim-point, the effective exposure time (see next section), and the number of bow shocks contained within 5*′* of the nominal aim point. Most archival observations were originally used to study massive stars, star clusters, and young stellar objects in H II regions, such as the Carina Nebula and M17. Other observations targeted pulsars and their resulting wind nebulae, supernova remnants, or follow-up observations of Swift or Fermi sources.

2.1 Data Reduction and Reprocessing

We used CIAO v4.10 and CALDB 4.7.8 to reprocess all the observations using the chandra_repro task using standard reduction procedures111See http://asc.harvard.edu/ciao/threads/index.html.. Point source detection was performed using the CIAO task wavdetect (Freeman et al., 2002) with scales of 1*′′, 2′′, and 4′′* on the 0.5-7 keV image. The absolute astrometric accuracy of Chandra observations222See http://cxc.harvard.edu/cal/ASPECT/celmon/ is typically $\sim$0.8*′′*. We compare the X-ray point source positions to 2MASS positions and use CIAO task reproject_aspect to refine the positional accuracy of our X-ray images. Figure 1 shows the positional difference between Chandra and 2MASS sources as a function of off-axis angle for Obs ID 3501, a particularly crowded field; only sources within the dashed-line box (defined as off-axis angles $<5^{\prime}$ and positional difference $<2^{\prime\prime}$) are retained in our analysis.

All X-ray sources in our preliminary list were then masked out of the X-ray images. We inspected each observation for background flares using the lc_clean script; background light curves were clipped at 5$\sigma$ to create good-time intervals. Each observation was then filtered using the new good time intervals (e.g., the “effective” exposure time listed in Table 1), and we restricted the energy range for each observation to 0.5-7 keV. We then use the CIAO task fluximage to create exposure maps and exposure-corrected images of each IR bow shock region. The cleaned, energy-restricted event files were used for the remainder of our analysis.

To create our final X-ray source lists, only sources with $>$5 counts within 5*′* of the nominal aim point were preserved. The sources were then visually examined for possible false detections. The positions of the detected X-ray sources were checked against the position of the bow shock driving stars and other known OB stars using SIMBAD. We derived distances to the bow shock driving stars and other known OB stars in the field of view (hereafter referred to as “FOV stars”) using Gaia DR2 parallaxes (Gaia Collaboration et al., 2018). Figure 2 shows the distribution of distances for driving stars and FOV stars with reasonably small distance uncertainties (i.e., $d/\sigma>3$). We find that bow shock driving stars are systematically closer (2.3$\pm$0.5 kpc) than FOV stars (4.5$\pm$1.0 kpc). Table 3 provides a summary of all the X-ray detected OB stars in our study, in order of decreasing 0.5-7 keV counts; our procedure for estimating the star’s X-ray luminosity is described in Section 4. Only 5 out of the 65 unique bow shocks ($\sim$8%) contained within a Chandra observation had their driving star detected with $>$5 counts.

2.2 Bow Shock “Postage Stamps”

We created “postage stamp” Chandra images for each of the 60 unique bow shocks from the exposure-corrected “fluxed” images. We masked the location of the driving star for each bow shock with a circular region that was approximately twice the radius of the PSF full width at half maximum at the detector location, so that our resulting stacked image did not contain low-level X-ray emission from the driving stars. Generally, the size of the Chandra PSF is less than the stand-off radius $R_{0}$ between the driving star and the bow shock (see, e.g., Primini et al., 2011, their Appendix A for details on modeling the Chandra PSF), so inadvertent masking of X-ray counts that are genuinely associated with the IR bow shock location is unlikely. The size of the box was set to three times the stand-off radius ($R_{0}$) of the bow shock. Bow shocks in the Kobulnicky et al. (2016) catalog have measured position angles giving the orientation of the IR bow shock relative to Galactic north; we use the same methodology to measure the position angles of the bow shocks in the Milky Way Project using the 24 µm images.

For each image, we define a vector located at the coordinates of the driving star, with a magnitude (length) $R_{0}$ (the standoff radius) that is pointed at the position angle of the IR bow shock. Figure 3 show two example IR bow shocks from the Milky Way Project with deep ($>$100 ks) corresponding X-ray image and bow shock vectors.

3 Bow Shock Stacking Analysis

To create the final stacked X-ray image of the bow shocks, we used the CIAO task dmregrid to rotate and resize each image vector so that the IR bow shock is located at an ($x,y$) position (0.5$n$,0.67$n$), where $n$ is the size of the rescaled image. We tested several final image sizes (50, 70, and 100 pixels on a side) but our choice of final image size did not affect our results.

Our stacked X-ray image reveals an average photon flux at the location of the IR bow shock of $\sim$1.1$\times 10^{-7}$ ph s*-1*. We use the CIAO task modelflux to convert this photon flux to an energy flux, assuming an absorbed power law spectral model ($\Gamma=2$) and a typical Milky Way absorbing column of $\sim 6\times 10^{21}$ cm*-1*. The predicted 0.5-7 keV energy flux is 4.4$\times 10^{-16}$ erg s*-1* cm*-2* (unabsorbed). Assuming an average distance to a Galactic bow shock of $\sim$2 kpc, this flux corresponds to a total unabsorbed 0.5-7 keV luminosity of $\sim$2.2$\times 10^{29}$ erg s*-1*. For comparison, the predicted “background” flux for this image (selected from a region in the stacked image that is not expected to contain any X-ray sources) is 3.9$\times 10^{-16}$ erg s*-1* cm*-2* (corresponding to a flux of 1.9$\times 10^{29}$ erg s*-1* at a distance of 2 kpc).

Although $\sim$70% of the IR bow shocks in the Kobulnicky et al. (2016) catalog are in “isolated” environments, $\sim$34% of the total X-ray exposure time in our sample was targeted at star-forming regions that likely contain significant diffuse X-ray emission. Spectral fitting of Chandra observations of five massive star-forming regions (Townsley et al., 2011) found the diffuse emission to be dominated by at least two thermal components, one at $kT\sim$0.2-0.6 keV and one with $kT\sim$0.5-0.9 keV, with an integrated surface brightness of $\sim(3-500)\times 10^{30}$ erg s*-1* pc*-2*. The physical size of a “postage stamp” that is 70 pixels on a side (with a plate scale of 0.492*′′* per pixel) at an average distance of 2 kpc is $\sim$0.32 pc on a side ($\sim$0.10 pc2). The total X-ray luminosity in each “postage stamp” is therefore expected to be (0.3–50)$\times 10^{29}$ erg s*-1*, in agreement with our background estimate above. We therefore do not find any evidence of excess X-ray emission in our stacked image that can be attributed to stellar wind bow shocks.

We perform an additional stacking analysis using only the 42 bow shocks from the Kobulnicky et al. (2016) in “isolated” environments and the 19 bow shocks from the Milky Way Project that were not associated with a Galactic bubble. Using only the “isolated” bow shocks ($\sim$67% of our sample by number) yields a total exposure time of 1.73 Msec. We follow the same stacking analysis as for our full sample; at the location of the IR bow shocks the average photon flux is 1.2$\times 10^{-7}$, yielding an energy flux of 4.9$\times 10^{-16}$ erg s*-1* cm*-2* ($\sim$2.4$\times 10^{29}$ erg s*-1* at 2 kpc). The predicted background flux is consistent with the full bow shock sample; we again find no evidence for excess X-ray emission at the location of the IR bow shock. Figure 4 show the stacked X-ray image of the isolated bow shocks (both in “raw” photon counts, and an image that has been smoothed for display purposes); the full sample images look similar.

4 X-ray Characteristics of Bow Shock Driving Stars

We additionally investigated whether the characteristics of X-ray detected bow shock driving stars differed significantly from X-ray detected FOV stars. The X-ray spectra of many of the massive stars listed in Table 3 have been previously analyzed in the literature; here, we only aim to approximate their X-ray luminosities assuming a simplified X-ray spectral model.

We assume a typical X-ray spectrum composed of an absorbed thermal plasma (tbabsapec in XSPEC), with $N_{\rm H}\sim 6\times 10^{21}$ cm-2* and a plasma temperature of $\sim$0.9 keV (see, e.g. Nazé, 2009, for a detailed study of X-ray spectra of massive stars with XMM-Newton), and use PIMMS333See https://heasarc.gsfc.nasa.gov/docs/software/tools/pimms.html to convert the observed count rate for each source into a 0.5-7 keV flux. This flux is then converted into a luminosity for stars with Gaia distance estimates. In Table 4, we compare our estimated luminosities for four well-studied massive stars to the values available in the literature. The most significant deviations occur where the Gaia distances disagree with those assumed in earlier studies; we therefore scale the literature values to the Gaia distances for a more direct comparison. In general, our approximate luminosities agree with the literature values within a factor of a few. We therefore do not anticipate systematic differences in luminosity across our full massive star sample.

We find no evidence of systematic differences in X-ray luminosity between the FOV stars and the five bow shock driving stars. The average 0.5-7 keV luminosity of stars in our sample is $\sim 5\times 10^{31}$ erg s*-1*, while the average bow shock driving star luminosity is $\sim 3\times 10^{31}$ erg s*-1*. We also investigated whether the stars in our sample follow the well-known $L_{X}\sim 10^{-7}L_{\rm bol}$ relationship (Chlebowski, 1989; Berghoefer et al., 1997; Nazé et al., 2011). We obtain the spectral type of each star from SIMBAD. We adopted model luminosities of massive stars (see Crowther, 2007, their Table 2) to infer $L_{\rm bol}$ for different spectral types of stars in our sample. In cases where SIMBAD lists multiple spectral type for a star, we assume the earliest type. Figure 5 shows the distributions of $L_{X}$ and $L_{X}/L_{\rm bol}$ ratios for our sample. We find an average $L_{X}/L_{\rm bol}\sim 1.1\times 10^{-7}$, in excellent agreement with previous studies. None of the stars in our sample exhibit unusually high $L_{X}/L_{\rm bol}$ ratios expected from magnetic OB stars (Petit et al., 2013; ud-Doula & Nazé, 2016; Gagné et al., 2005; Nazé et al., 2012). We note that all of the X-ray detected bow shocks driving stars are of “late-types” (e.g., later than O6), while the FOV star sample contains both early- (e.g., earlier than O5.5) and evolved Wolf-Rayet stars. The number of X-ray detected Wolf-Rayet and early-O type stars is small, and exhibit $L_{X}/L_{\rm bol}$ ratios that are statistically consistent with our sample average.

5 Discussion

Previous attempts to study the X-ray emission from stellar wind bow shocks have yielded only upper limits on the order of $L_{X}\lesssim 10^{30}$ erg s*-1* using archival XMM-Newton observations (Toalá et al., 2017, 2016) and dedicated observations (De Becker et al., 2017) of individual bow shocks. Our stacking analysis adds a new, more stringent upper limit, $L_{X}\lesssim 2\times 10^{29}$ erg s*-1*.

The non-thermal radiation model developed by De Becker et al. (2017) assumes X-rays are generated via inverse Compton scattering at a magnetically-confined shock front. The swept-up dust in the bow shock is heated by photons from the driving star, and emits the reprocessed energy in the IR. These IR photons then interact with the energetic electrons at the shock front and are scattered into the X-ray and $\gamma$-ray regime. The IR luminosity therefore some fraction $\chi_{\rm IR}$ of the bolometric. luminosity of the dust at the shock front (e.g., van Buren & McCray, 1988). The predicted X-ray luminosity additionally depends on the magnetic field strength $B$ at the shock front and the power in relativistic electrons (expressed as a fraction $\chi_{\rm rel}$ of the total power available in the bow shock). When upper limits of $\chi_{\rm IR}=\chi_{\rm rel}=1$ and $B=10^{-4}$ G are assumed (measurements of the ambient ISM magnetic field are consistent with $\sim 2-6\mu$G, Meyer et al., 2017; Harvey-Smith et al., 2011; Fiedler & Mouschovias, 1993; Troland & Heiles, 1986), their model predicts an integrated X-ray luminosity of $\sim 4\times 10^{29}$ erg s*-1*– a factor of $\sim$2 above our upper limit. Our non-detection indicates that, if X-ray photons are indeed being produced in IR bow shocks, the production mechanism is much less efficient than the models derived by De Becker et al. (2017).

State-of-the art hydrodynamical codes now include particle acceleration, allowing X-ray production in bow shock nebulae to be self-consistently modeled (van Marle et al., 2018). For example, the detailed, 2D hydrodynamical treatment by del Valle & Pohl (2018), which includes diffusion of particles and advection of energy out of the bow shock region, predicts X-ray luminosities on the order of a few $\times 10^{28}$ erg s*-1*  consistent with our upper limit, with potentially higher luminosities ($\sim 10^{30}$ erg s*-1*) produced in the $\gamma$-ray regime. Although these models predict higher luminosities in the $\gamma$-ray than the X-ray, systematic searches for $\gamma$-ray emission from bow shocks have similarly yielded only upper limits (Schulz et al., 2014; H. E. S. S. Collaboration et al., 2018).

It is unlikely that X-ray emission from stellar wind bow shocks, if it is indeed produced through the mechanisms previously proposed, is detectable by present X-ray telescopes. Even the future Athena X-ray Observatory (Nandra et al., 2013) will not possess the sensitivity and angular resolution required to detect such faint X-ray emission from IR bow shocks.

The proposed NASA X-ray flagship mission Lynx, however, will have 50$\times$ greater sensitivity than Chandra with similar angular resolution over a significantly wider field of view444See https://www.lynxobservatory.com/. We use the Simulated Observations of X-ray Sources555See http://hea-www.cfa.harvard.edu/~jzuhone/soxs/index.html (SOXS) package in Python to determine the feasibility of detecting faint X-ray emission from bow shocks with Lynx.

For consistency with our assumptions in Section 3, we assume the non-thermal bow shock spectrum follows a power law with $\Gamma=2$ over an energy range of 0.1-10 keV, subject to absorption due to intervening gas and dust in the Milky Way. We used the nearest bow shock in our sample: driving star HD 34078, at 0.41 kpc. The bow shock nebula is formed at $R_{0}=9.9^{\prime\prime}$ from its driving star, with a column density along the line of sight $N_{\rm H}=1.2\times 10^{21}$ cm*-2*. The spectrum is then renormalized so that the 0.5-7 keV flux is just below our Chandra detection limit at the distance of HD 34078.

Photons are drawn from the underlying spectrum and spatially distributed according to a $\beta$-model surface brightness profile. The X-ray surface brightness $S$ as a function of radius $r$ is given by

[TABLE]

where $S_{0}$ is the core surface brightness, $r_{\rm C}$ is the core radius, and $\beta$ is the slope parameter. We assume $r_{\rm c}\sim 3^{\prime\prime}$ and $\beta=1$ (with an ellipticity of 0.3) to approximately match the typical appearance of the 24 µm emission.

After the photons are assigned a sky location, our simulated bow shock is then “observed” in the 0.2-7 keV energy range with the Lynx high-definition X-ray imager (HDXI) using the SOXS instrument simulator for a given exposure time. The instrument simulator additionally adds a Galactic foreground and instrument noise to our image; we refer the reader to the SOXS User’s Guide for further details.

Figure 6 shows the results of a 100 ks Lynx exposure of the HD 34078 bow shock just below our Chandra detection limit. An X-ray excess clearly evident in the radial surface brightness profile; the bow shock is detectable with a signal-to-noise ratio of $\sim$10. The same bow shock placed farther away ($\sim$2 kpc) is detectable with a signal-to-noise ratio of $\sim$3 in $\sim$500 ks.

6 Conclusions

We have performed a stacking analysis leveraging 2.61 Msec of archival Chandra observations to search for faint X-ray emission from Galactic stellar wind bow shocks. Our stacked image shows no evidence for excess emission at the expected bow shock location to a flux limit of $\sim 4.4\times 10^{-16}$ erg s*-1* cm*-2*  which corresponds to a luminosity of $\sim 2\times 10^{29}$ erg s*-1* assuming a distance of $\sim$2 kpc (typical of the bow shocks in our sample). This provides the most stringent observational upper limit in the X-ray regime to date.

We assess the plausibility of detecting faint X-ray emission from bow shocks with the proposed future X-ray mission Lynx. If stellar wind bow shocks are indeed producing X-rays at just below our Chandra detection limit, the least obscured cases (e.g., the nearest, or runaways at higher Galactic latitudes) should be detectable by Lynx with modest exposure times.

The authors would like to thank H. A. Kobulnicky, L. K. Townsley, and P. S. Broos for useful discussions and feedback on early versions of this manuscript. Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number AR8-19002X issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060.