Possible Association of Two Stellar Bowshocks with Unidentified Fermi Sources

There is an important, significant number of unidentified sources of high- and very-high-energy photons. Even with the improved capabilities of the Fermi Large Area Telescope (LAT; see Atwood et al. 2009), the latest release of its 3FGL catalog (Acero et al. 2015) contains 1059 gigaelectronvolt sources without a counterpart at lower energies. This represents about 35% of the total. The situation is not much better at very high energies, where the latest edition of the TeVCat catalog (Wakely & Horan 2008) includes 27% of unidentified sources. Many of these unassociated sources are located in our Galaxy. However, the search for counterparts among well-known gamma-ray emitters in the Milky Way (objects such as pulsars, supernova remnants, molecular clouds, or compact binaries) is not always successful.

Among the more exotic gamma-ray emitters proposed in the literature, we can find the bowshocks of runaway massive stars. del Valle & Romero (2012, 2014) provided theoretical arguments for these objects to be high-energy sources. In these models, the bowshocks of luminous runaway stars act as the acceleration sites of relativistic particles. Gamma rays result from inverse Compton (IC) interactions of relativistic electrons with background thermal photons and, to a lesser extent, from pp collisions. The expected luminosities are relatively modest in the gigaelectronvolt domain (∼10³¹–10³³ erg s⁻¹), and the detection of such bowshocks in gamma rays is only plausible if they are nearby. So far, only two candidates have been proposed: ζ Ophiuchi, which might be detected by the ground-based detector Cherenkov Telescope Array in the future as well as by the Fermi satellite, and HD 195592, which was proposed to be associated with the Fermi gamma-ray source 2FGL J2030.7+4417 (see del Valle & Romero 2012; del Valle et al. 2013, respectively). This latter source, however, was recently claimed to be associated with a pulsar. Therefore, there is currently no bowshock clearly associated with an unidentified Fermi source.

At radio, nonthermal radiation has been found in the bowshock of BD+43°3654 with the Very Large Array (VLA; see Benaglia et al. 2010). This indicates the presence of relativistic particles and motivates further efforts in the search for high-energy counterparts.

Schulz et al. (2014) performed the first systematic search in the megaelectronvolt and gigaelectronvolt emission from the 27 bowshocks listed in the E-BOSS catalog (Peri et al. 2012). They analyzed 57 months of Fermi-LAT data and found no significant detection. They reported upper limits for all sources, ruling out the most optimistic model predictions for ζ Ophiuchi by a factor of 5. In addition, the High Energy Stereoscopic System (H.E.S.S.) Collaboration (Abdalla et al. 2018) performed a similar analysis of 32 sources listed in the second E-BOSS catalog (Peri et al. 2015). None of these sources showed detectable emission at E > 100 GeV. Despite the efforts made to find high-energy radiation from the bowshocks of massive runaway stars, a reliable detection still remains elusive.

Similar searches were carried out in X-rays using data from XMM-Newton (Toalá et al. 2016, 2017; de Becker et al. 2017), with no positive identification. On the basis of energy considerations for all sources in the E-BOSS catalog, de Becker et al. (2017) anticipate that the detection of IC emission from the bowshocks of massive runaways is very unlikely with current X-ray facilities.

In this work, we report two runaway stars whose bowshocks are firm candidates for being responsible for the gamma-ray emission in two respective unidentified Fermi sources. One of them is a massive runaway that was not previously known and is reported here for the first time.

In a first step, we cross-matched the luminous star catalogs by Hardorp et al. (1959) and Stephenson & Sanduleak (1971) with unidentified gamma-ray sources from the latest release of the Fermi 3FGL catalog. This was done for low galactic latitudes $| b|$ < 5° because we are interested in galactic sources in the Milky Way. In a second step, positional matches were further investigated by examining the presence of arc-shaped bowshocks that could trace the possible runaway nature of the stars. This kind of structure is easily revealed by the far-infrared (IR) emission from the heated dust accumulated as the star sweeps the interstellar medium (ISM). This cross-check was often facilitated by the different releases of the E-BOSS catalog in Peri et al. (2015) and references therein.

As a result, here we found two promising new candidates: the stars λ Cep (HD 210839, HIP 109556) and LS 2355 (HD 99897, HIP 56021). The physical parameters of the stars are shown in Table 1, and the details about their radial velocity, proper motions, and distances are given in Appendix A. We tentatively associate them with the unidentified Fermi sources 3FLG J2210.1+5925 and 3FGL J1128.7–6232, respectively, as no other remarkable object appears inside their error ellipses. While λ Cep is part of the E-BOSS catalog, it is worthwhile to note that the star LS 2355 represents a new addition to the known population of stellar bowshocks. In the following sections, we describe the observational parameters of both objects. This information is used as an input for applying a simple model in order to fit the observed spectral energy distribution (SED; following de Becker et al. 2017), and then to assess the possibility of a physical association with the Fermi high-energy emission.

Table 1.  Physical Parameters for the Stars

Parameter		λ Cep	LS 2355
SpT	Spectral type	O6.5I(n)fp	O6.5IV
Vw [km s−1]	Wind velocity	$2.25\times {10}^{3}$	2 × 103
$\dot{M}$ [ M⊙ yr−1]	Wind mass-loss rate	6.8 × 10−6	10−6
Pw [erg s−1]	Mechanical wind power	$\sim {10}^{37}$	∼1036
R [cm]	Stagnation point	5.06 × 1018	1.79 × 1018
χ ∼ Pw/Pe	Fraction of the wind power	0.6	2.7
${L}_{* }$ [erg s−1]	Bolometric luminosity	∼2 × 1039	∼2 × 1039
B [μG]	Minimum magnetic field	0.06	0.1

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The star λ Cep, with spectral type O6.5I(n)fp (Sota et al. 2011), is one of the most massive runaway stars known to date. It is located at a distance of about 0.6 kpc according to the parallax provided by the Hipparcos satellite (van Leeuwen 2007a; see also Appendix A). Unfortunately, this star is not yet included the latest Gaia data release.

Figure 1 shows the 95% confidence error ellipse of the unidentified gamma-ray source 3FGL J2210.1+5925 over a trichromatic composition that shows the radio, IR, and optical appearance of the field as red, green, and blue layers, respectively. The composition displays the corresponding image at 1.4 GHz from the NRAO VLA Sky Survey (NVSS; Condon et al. 1998) in red, the Wide-field Infrared Survey Explorer (WISE) emission at 22 μm in green, and the Digitized Sky Survey optical emission of the red plate in blue (Lasker et al. 1990; Mauch et al. 2003; Wright et al. 2010). The bowshock around λ Cep appears as the most peculiar object compatible with the Fermi ellipse position (see Figure 1). Historically, this extended feature around λ Cep was first detected in IRAS images (see van Buren & McCray 1988). The volume of the paraboloid limited by the star and the bowshock vertex amounts to (1.3 ± 0.5) × 10⁵⁶ cm³. The estimated velocity relative to the star Regional Standard of Rest (RSR) gives 70 ± 6 km s⁻¹ (see Appendix B). After applying the correction for Galactic rotation, the position angle (PA) of the RSR velocity changes by a few degrees, improving the expected alignment with the bowshock vertex. From the image, we can estimate the distance R from the star to the midpoint of the bowshock. Correcting from the angle between the peculiar RSR velocity and the observer, estimated to be ∼30° ± 5°, we obtain R ∼ 1.6 pc.

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This star has a high bolometric luminosity and a powerful wind. The wind properties quoted in Table 1 have been taken from Mokiem et al. (2007). They combine to provide a mechanical power ${P}_{{\rm{w}}}=0.5\dot{M}{V}_{{\rm{w}}}^{2}\sim {10}^{37}$ erg s⁻¹.

3.1. SED of the λ Cep Bowshock

In Figure 2, we display the SED of the λ Cep bowshock together with the Fermi-LAT spectrum of 3FLG J2210.1+5925. Axes are logarithmically distributed. The energy E is in eV, and the vertical axis shows the monochromatic luminosity times the energy, EL(E) in erg s⁻¹. In addition to the IR flux density, taken from IRAS and completed by performing aperture photometry on the WISE 22 μm image, an upper limit to the extended X-ray emission is also included.

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Given the absence of diffuse X-ray radiation associated with the bowshock, we proceeded to calculate a 4σ upper limit from XMM-Newton archival data (Obs. ID 0720090501). A power-law spectrum with Γ = 2 and a hydrogen column density of N_H ∼ 5.3 × 10²² cm⁻² have been assumed for the fitting. This value is consistent with the observed color excess for λ Cep $E(B-V)\simeq 0.56$ mag, equivalent to an interstellar extinction of A_V ≃ 5.3 × 10⁻²²N_H ≃ 1.7 mag. Concerning radio emission, we preferred not to include an upper limit in this SED plot because it could not be physically meaningful given the lack of sensitivity of the NVSS data to angular scales as large as those of the bowshock ($\sim 20^{\prime}$). Numerical values for the SED data points are given in the appendix (Table 2).

Following the approach by de Becker et al. (2017), we use a simple model to fit the observed gamma emission with the aim of establishing whether it is physically possible for the bowshock of λ Cep to generate the Fermi source.

3.2. Model and Fitting

LS 2355 is an early spectral type O6.5IV runaway star (see Sota et al. 2014) toward the constellation of Centaurus. Based on its sky location, LS 2355 has been associated with the open cluster Cru OB1 (see Kaltcheva & Georgiev 1994). In this work, we adopt a distance of 2.1 ± 1.1 kpc derived from the parallax information furnished by the first data release of the Gaia Collaboration (2016). To better estimate proper motions, we have combined the Gaia data with other available sources of information in order to take advantage of nearly a century-old time baseline (see Appendix A for details).

Figure 3 shows the 95% confidence error ellipse of the unidentified gamma-ray source 3FGL J1128.7–6232, taken from Acero et al. (2015), on a trichromatic composition. The same surveys mentioned above have been used here except for the radio layer, for which we display the Sydney University Molonglo Sky Survey (SUMSS) radio emission at 843 MHz in red. In this case also, the bowshock appears as the most peculiar object at all wavelengths compatible with the Fermi position ellipse. This bowshock is just at the southern edge of the H ii region named GAL 293.60–01.28, whose nebulosity has been studied by several authors (Georgelin et al. 2000; Cersosimo et al. 2009; Lee et al. 2012).

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The bowshock has an angular size of ∼111 × 74 arcsec² on the plane of the sky (see Figure 3). The volume of the paraboloid limited by the star and the bowshock vertex is about (3.0 ± 0.5) × 10⁵⁵ cm³. We derive an RSR velocity of 23 ± 5 km s⁻¹ for LS 2355, whose PA, once corrected for Galactic rotation, clearly points toward the bowshock vertex (see Appendix B). The modulus of the RSR velocity found has a moderately low value for a runaway star. The prominent presence of the bowshock is then likely to be further enhanced by an overdense environment as the star motion impinges into the H ii region. From the image we also estimate an R that gives ∼0.6 pc; in this case, the velocity is almost in the plane of the sky, and no angle correction is needed.

4.1. SED of the LS 2355 Bowshock

This SED has been compiled from different sources and is plotted in Figure 4. The horizontal axis gives the logarithmically spaced photon energy, E in eV, and the vertical axis gives the monochromatic luminosity times the energy, EL(E) in erg s⁻¹. The value of the distance quoted above has been used. Radio and IR emission are estimated based on SUMSS and WISE images, respectively. We also searched for diffuse X-ray emission associated with the bowshock. If present, it must be below the detection limits of the XMM-Newton archive data. Thus, a 4σ upper limit for the X-ray flux has been estimated from XMM-Newton archival data (Obs. ID 0672320101) by assuming a power-law spectrum with Γ = 2 and a hydrogen column density of N_H ∼ 2.5 × 10²¹ cm⁻². This latter value is derived from the star color excess E(B − V) ≃ 0.43 mag, which translates into a visual extinction value of A_V ≃ 5.3 × 10⁻²²N_H ≃ 1.3 mag. The Fermi-LAT spectrum of 3FGL J1128.7–6232 is also included in Figure 4. The numerical values of the data are given in the appendix (Table 3).

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4.2. Model and Fitting

We fitted the observed emission with the bowshock model as done in Section 3.2. The wind parameters of this star are not well determined. However, since LS 2355 shares the same spectral type as λ Cep, we have assumed similar values for the wind and identical bolometric luminosity. For a wind mass-loss rate of $\dot{M}={10}^{-6}$ M_⊙ yr⁻¹ and wind velocity V_w ∼ 2 × 10³ km s⁻¹, P_w is ∼10³⁶ erg s⁻¹. We also adopted the same IR photon field for the IC scattering.

The Fermi position ellipse of the source 3FGL J1128.7–6232 also contains the H ii region. Then there is the possibility that the gamma emission detected by Fermi, or at least part of it, might be produced by the background cosmic rays (CRs)—protons mainly—through pp inelastic collisions with the protons of the H ii region. In order to investigate this possibility, we estimate the pp emission considering a proton CR flux in the Galaxy ${J}_{\mathrm{CR}}^{{\rm{p}}}(E)=2.2{\left(\tfrac{E}{\mathrm{GeV}}\right)}^{-2.75}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}\,{\mathrm{sr}}^{-1}\,{\mathrm{GeV}}^{-1}$ (Aharonian & Atoyan 1996). The density of the region can be estimated from the interaction between the stellar wind and the ambient material. The distance R can be thought as the stand-off point of the bowshock, where the ram pressure of the wind is balanced with that from the incoming ISM (in the star reference frame); then

$$\begin{eqnarray}&&R=\sqrt{\displaystyle \frac{{V}_{{\rm{w}}}\dot{M}}{4\pi {\rho }_{{\rm{a}}}{V}_{\star }^{2}}},\end{eqnarray} \tag{ 1 }$$

where ρ_a is the ambient density. Using the parameters for the wind given above and the measured value of R, together with an assumed mean ISM gas with μ = 2.3 × 10⁻²⁴ g, we estimate n_a ∼ 1.5 × 10³ cm⁻³, which is reasonable for a H ii region (e.g., Cox 2000). With this density and the proton CR flux, assuming a cloud with the semimajor axis of the Fermi ellipse of 8.4 pc, we calculate this expected background component. This component alone cannot explain the Fermi source; higher radiation levels are needed. Therefore, to fit the emission, we consider the sum of this background component plus the IC produced by the electrons accelerated locally.

The result is shown in Figure 4. The fitting is done with the data points of the lowest energies (see the appendix, Table 3). This produces a better fit; besides, the error bars are smaller at these energies. From this fit we obtain α ∼ 1.8, E_max ∼ 90 GeV, and χ ∼ 2.7 with D = 3 × 10⁻¹. This high value of χ may seem unrealistic. It actually might reflect our ignorance of the true parameters of the system. It could be lower if, for instance, convection of relativistic particles is not effective, something that might occur if Kelvin–Helmholtz instabilities affect the streams (e.g., Comeron & Kaper 1998). A more elaborate model would easily produce a better fit. The minimum magnetic field required to accelerate an electron up to 90 GeV is relatively small, as in the previous case: about 0.1 μG. With this value, the synchrotron emission lies well below the radio data point. In any case, the SUMSS flux density contains a significant contribution of unrelated thermal emission from GAL 293.60–01.28.

Although it is not possible to get rid of the background component, we analyze the case in which this is absent. This also produces a good fit, as can be seen in Figure 4, green line. For this fit, we get α = 1.8, E_max ∼ 125 GeV, χ ∼ 5, and D = 6.5 × 10⁻¹.

The lack of detected radio emission from the bowshocks of the stars under study does not allow us to obtain a value for the magnetic field directly from observations. Instead, we can estimate the magnetic field needed to achieve the inferred maximum energies with a DSA process, taking into account that the actual magnetic field can be higher. The electrons are more likely accelerated at the reverse shock, in the wind, because this shock is faster and adiabatic. Hence, the magnetic field in the acceleration region is that of the stellar wind, which depends on the stellar magnetic field. This field might also be shock-compressed, depending on its geometry.

We can estimate the synchrotron radiation expected from the same electron population that produces the gamma rays when they interact with the ISM magnetic field of ∼5 μG, as electrons eventually escape into it. This radiation can be considered as a lower limit. We obtain for both λ Cep and LS 2355 at E ∼ 6 × 10⁻⁶ eV (1.4 GHz) an intrinsic radio luminosity of L_synchr ∼ 10²⁹ erg s⁻¹. This value is lower than the SUMSS data for LS 2355, but it is of the same order as, or higher than, the VLA radio upper limits for the sources studied in de Becker et al. (2017).

We can compare our predictions with estimates made for similar sources. First, our results are in agreement with the upper limit obtained for bowshocks in the H.E.S.S. Collaboration (Abdalla et al. 2018), simply because there is almost no emission at E > 100 GeV. The sources studied in de Becker et al. (2017) are not as powerful as those studied here. The mechanical power in the wind of λ Cep and LS 2355 is very high, and hence there is more power available to be converted into relativistic electrons. The maximum energies fitted for four out of the sample of five by De Becker et al. are also of the order of hundreds of gigaelectronvolts, like the ones obtained here. The gamma emission for those sources at Fermi energies is between 10³⁰ and 10³² erg s⁻¹. This latter value is of the order of the value of 3FLG J2210.1+5925. However, the computed Fermi upper levels for these sources in Schulz et al. (2014) are almost two orders of magnitude higher.

In the case of the star BD+43°3654, modeled by Benaglia et al. (2010) to fit the detected radio emission, the electrons are cooled mainly by synchrotron radiation and not by IC scattering as assumed here; the best-fitting magnetic field found by Benaglia et al. (2010) is ∼50 μG. Although the expected gamma emission is ∼10³² erg s⁻¹, of the same order as that estimated here for λ Cep, the spectrum is shifted toward higher energies, peaking around 1 TeV.

The evidence presented so far is consistent with the bowshocks being the true emitters of Fermi gamma rays. However, to be cautious, we need to better assess the chances of alternative counterpart candidates. To do so, we also carried out an additional cross-match between Fermi (Acero et al. 2015), XMM-DR6 (Rosen et al. 2016), and NVSS (Condon et al. 1998) catalogs, and we found several point-like objects with X-ray counterparts in the field covered by the Fermi error ellipses for both sources considered in this paper. At most, only one compact X-ray source (3XMM J221043.5+592239), which could have a very weak NVSS radio counterpart (NVSS 221043+592236) located at α = 22^h10^m439, δ = +59°22'361, J2000, could provide an alternative identification to the Fermi gamma-ray source 3FLG J2210.1+5925. However, the object is very faint in X-ray and radio, and we could not obtain any further evidence of its possible association. We did not find any alternative counterpart candidate to the Fermi gamma-ray source 3FGL J1128.7–6232.

In addition, the possibility of a pure chance association for both associations presented here should also be analyzed. In order to estimate the a priori probability of random coincidence of the stars under study with a Fermi source, we carried out a series of Monte Carlo simulations following the approach outlined in Romero et al. (1999). With 1° binning and running up to 10⁶ Fermi synthetic populations, we found a total 4820 and 11921 coincidences at the positions of λ Cep and LS 2355, respectively. Thus, the corresponding probabilities are estimated at the level of about 0.5% and 1.2%. Running the simulations with 2° binning does not significantly change these numbers. Therefore, the idea of a physical association with the 3FGL sources is feasible and worthy of further consideration.

Finally, we comment briefly on why there are so few gamma-ray candidates among the relatively large population of massive runaways. It is a well-known fact that isolated, massive stars are not efficient at producing relativistic particles. This is likely related to the absence of strong terminal shocks in their wind. In the case of runaway stars, the mass swept by the bowshock accumulates in front of the star, so the wind impacts on this material and a strong reverse shock is generated with a velocity of ∼10³ km s⁻¹. Such velocity can result in efficient particle acceleration. Nonthermal radiation will then be produced by either synchrotron or IC losses. In the case of high magnetic fields, synchrotron cooling might dominate, but then the gamma-ray counterparts will be weak or absent (as in the case of BD+43°3654 ). In order for IC cooling to dominate, the magnetic field should be low, but in addition an external photon field is necessary. This field is provided by the material swept by the star, whose density depends both on the ambient conditions and the proper velocity of the star. Hence, only fast stars moving in a dense medium of low magnetization are favored. It is not surprising that just a few stars satisfy such a stringent criterion. In addition, the expected luminosities are not very high, as we have seen in this work and the previous papers by del Valle & Romero (2012, 2014), so only nearby sources can be detected with the current sensitivities. All these conditions are fulfilled by the two candidates presented here, which seem to be exceptional.

Summarizing, in this work we propose to identify two Fermi sources with the bowshocks of the massive runaway stars λ Cep and LS 2355. These objects are the most promising candidates lying inside the 95% error ellipses of the gamma-ray data. Using a simple model, we fit the observed emission for reasonable parameters, concluding that both systems are in principle capable of producing the gamma radiation detected by Fermi and in agreement with the existing multiwavelength data. We showed that a chance association is not very likely. In the case of 3FGL J1128.7–6232, we have considered a possible additional contribution from the irradiation of a nearby H ii region by ambient CRs. We conclude that both bowshocks might be true gamma-ray emitters and deserve further investigation.

This work was supported by the Agencia Estatal de Investigación grant AYA 2016-76012-C3-3-P from the Spanish Ministerio de Economía y Competitividad (MINECO), and the Consejería de Economía, Innovación, Ciencia y Empleo of Junta de Andalucía under research group FQM-322, as well as FEDER funds. M.V.dV. acknowledges support from the Alexander von Humboldt Foundation. G.E.R. acknowledges support from PIP 0338 (CONICET) and AYA 2016-76012-C3-1-P.

Proper motions and radial velocities are required in order to correctly understand the kinematics of runaway stars. In the case of λ Cep and LS 2355, estimates of their heliocentric radial velocities (−75.1 ± 0.9 km s⁻¹ and −3.0 ± 4.5, respectively) are available from the Pulkovo compilation (Gontcharov 2006). Concerning proper motions, these parameters are harder to accurately measure given the need for multiepoch observations.

λ Cep is a very bright star not yet available in the Gaia DR1. Given its brightness, it is also easily saturated in historic photographic plates, rendering difficult the measurement of accurate positions. Therefore, we directly adopted the Hipparcos proper motions available in the literature: ${\mu }_{{\alpha }_{\mathrm{ICRS}}}\cos {\delta }_{\mathrm{ICRS}}\,=-7.2\pm 1.6$ mas yr⁻¹ and ${\mu }_{{\delta }_{\mathrm{ICRS}}}=-11.06\pm 0.44$ mas yr⁻¹ (van Leeuwen 2007b).

With respect to the LS 2355 star, its astrometric positions are available in the literature, and we have compiled them as shown in Table 2. When the catalog positions were not directly expressed in the International Celestial Reference System (ICRS), we transformed them for appropriate comparison using the rotation matrices in Aoki et al. (1983) from B1950.0 to J2000.0, or in Hilton & Hohenkerk (2004) from J2000.0 to ICRS. The fit results are displayed in Figure 5, yielding values of ${\mu }_{{\alpha }_{\mathrm{ICRS}}}\cos {\delta }_{\mathrm{ICRS}}=-7.8\pm 0.5$ mas yr⁻¹ and ${\mu }_{{\delta }_{\mathrm{ICRS}}}=+3.5\pm 0.3$ mas yr⁻¹ in ICRS R.A. and decl., respectively. The least squares fit was carried out giving equal weight to all points in order to avoid an excessive bias toward the still-preliminary Gaia Collaboration et al. (2016) data. The Gaia point apparently does not follow the general trend in decl. (see Figure 5).

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Concerning distances, we adopt for both stars the values corresponding to their latest trigonometric parallax available from Gaia and Hipparcos (van Leeuwen 2007b; Gaia Collaboration et al. 2016). The values used in the SED calculations are thus 0.6 ± 0.1 and 2.1 ± 1.1 kpc for λ Cep and LS 2355, respectively.

Different proper-motion vectors are displayed in the trichromatic Figures 1 and 3 for λ Cep and LS 2355, respectively. The thin white arrows indicate the magnitude and direction of the proper motions as observed from a heliocentric reference frame. We can estimate the actual velocity of the two runaway stars with respect to their RSR by combining the proper motion data, the heliocentric radial velocities in the literature, and the distances assumed in this paper (see Appendix A). In this process, we also need to adopt a plausible rotation curve of the Milky Way Galaxy and velocity components of the Sun in its Local Standard of Rest (LSR). The resulting RSR velocities relative to the stellar environments, when projected onto the celestial sphere, correspond to the thick white arrows in Figures 1 and 3. To apply the correction for Galactic rotation, we assumed the analytic Milky Way rotation curve by Fich et al. (1989) and the Sun LSR velocity components by Schönrich et al. (2010).

For λ Cep, the PA of the corrected proper motion measured from north to east is found to be 223° ± 17°, while the modulus of its RSR velocity amounts to 70 ± 6 km s⁻¹. Similarly, for LS 2355, we obtain a PA value of −24° ± 21° and an RSR velocity of 23 ± 5 km s⁻¹.

In both cases, it is remarkable how the PA of the corrected proper motions aligns well with the directions of the bowshock cusps, as evidenced in the 22 μm data from WISE. The velocity estimate for λ Cep is certainly high, consistent with being a well-known runaway star identified for a long time. In contrast, LS 2355 exhibits a not-so-high RSR velocity as compared to λ Cep. However, as this object seems to be impinging a dense ISM, as suggested by Figure 3, the bowshock around it becomes noticeably enhanced.

The distances quoted in Appendix A (0.6 kpc for λ Cep and 2.1 kpc for LS 2355) have been used to estimate the luminosities in Tables 3 and 4 of this appendix.

Table 3.  SED Values for λ Cep Bowshock

Telescope	WISE	XMM-Newton	Fermi-LAT
E [eV]	${5.64}_{-0.56}^{+0.56}\times {10}^{-2}$	${4.02}_{-2.02}^{+5.98}\times {10}^{3}$	${1.54}_{-0.54}^{+1.46}\times {10}^{8}$	${4.76}_{-1.76}^{+5.23}\times {10}^{8}$	${1.54}_{-0.54}^{+1.46}\times {10}^{9}$	4.76 ${}_{-1.76}^{+5.23}\times {10}^{9}$	1.98 ${}_{-0.98}^{+8.02}\times {10}^{10}$
EL(E) [erg s−1]	9.39${}_{-1.17}^{+1.17}\times {10}^{35}$	3.37 × 1030	2.65${}_{-0.55}^{+0.65}\times {10}^{32}$	2.08${}_{-0.27}^{+0.27}\times {10}^{32}$	8.91${}_{-1.80}^{+1.88}\times {10}^{31}$	9.38${}_{-9.38}^{+10.72}\times {10}^{30}$	3.00${}_{-3.00}^{+66.03}\times {10}^{29}$

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Table 4.  SED Values for LS 2355 Bowshock

Telescope	SUMSS	WISE	XMM-Newton	Fermi-LAT
E [eV]	${3.44}_{-0.01}^{+0.01}\times {10}^{-6}$	${5.64}_{-0.56}^{+0.56}\times {10}^{-2}$	${4.02}_{-2.02}^{+5.98}\times {10}^{3}$	${1.54}_{-0.54}^{+1.46}\times {10}^{8}$	${4.76}_{-1.76}^{+5.23}\times {10}^{8}$	${1.54}_{-0.54}^{+1.46}\times {10}^{9}$	${4.76}_{-1.76}^{+5.23}\times {10}^{9}$	${1.98}_{-0.98}^{+8.02}\times {10}^{10}$
EL(E) [erg s−1]	1.32${}_{-0.44}^{+0.44}\times {10}^{30}$	${1.79}_{-0.14}^{+0.14}\times {10}^{36}$	5.87 × 1031	2.40 × 1033	${3.20}_{-0.46}^{+0.46}\times {10}^{33}$	1.61${}_{-0.38}^{+0.39}\times {10}^{33}$	4.24${}_{-2.30}^{+2.54}\times {10}^{32}$	1.07${}_{-0.84}^{+1.03}\times {10}^{32}$

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