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Non-thermal radiation from a runaway massive star

We present a study of the radio emission from a massive runaway star. The star forms a bow shock that is clearly observed in the infrared. We have performed VLA observations under the assumption that the reverse shock in the stellar wind might accelerate charged particles up to relativistic energies. Non-thermal radio emission of synchrotron origin has been detected, confirming the hypothesis. We have then modeled the system and we predict a spectral energy distribution that extends up to gamma-rays. Under some simplifying assumptions, we find that the intensity at high energies is too low to be detected by current instruments, but the future Cherenkov Telescope Array might detect the source.


Introduction
Runaway OB stars (Gies and Bolton 1986) can produce so-called stellar bow shocks on the surrounding interstellar medium. Bow shocks develop as arc-shaped structures, with bows pointing in the same direction of the stellar velocity, while the star moves supersonically through the interstellar medium (ISM). The stellar and shock-excited radiation heat the dust and gas swept by the bow shock. The dust, in turn, re-radiates the energy as mid to far IR flux. Van Buren & McCray (1988) looked for bow-shaped features near high-velocity O stars and found an IR candidate close to the O supergiant BD+43 • 3654 (α, δ[J2000] = 20 h 33 m 36.077 s , +43 • 59 07.40 ; l, b = 82.41 • , +2.33 • ). Comerón & Pasquali (2007) related the star BD+43 • 3654 to a bow shock detected with the Midcourse Space eXperiment (MSX) at D and E bands. Also, data from the NRAO-VLA 1 NVSS Survey (Condon et al. 1998) revealed a coma-shaped source of ∼ 7 arcmin spatially coincident with the MSX feature ( Figure 1).
A radio study of the bow shock can shed light on the physical processes that give rise to highenergy emission from a stellar source, regardless of the history of the runaway star. The shock can accelerate particles up to relativistic energies by Fermi mechanism. Energetic electrons will cool through synchrotron radiation, producing a non-thermal radio source. We carried out radio observations at two frequencies to study the nature of the emission from the bow shock of BD+43 • 3654.  5,8,11,15,19,24,29,50,70, and 90 mJy beam −1 .

Observations and results
Our continuum observations were carried out with the Very Lare Array (VLA) at 1.42 GHz (C config.) and at 4.86 GHz (D config.). Figure 2 presents the resulting images after primary beam correction, re-gridded with the same synthesized beam of 12". There is emission at both frequencies along the extension of the MSX source. The hypothesis of a physical association between the star and the radio/IR features is supported by the very good agreement of the residual proper motion of the star and the direction from the star to the apsis of the bow shock (Fig. 2). We used the continuum images at 1.42 and 4.86 GHz to build a spectral index distribution map. We only considered input pixels with a signal-to-noise ratio ≥ 4. Besides, the spectral index map was masked for a signal-to-noise ratio ≥ 10. Figures 3 and 4 show the spectral index distribution and corresponding noise maps.

Bow-shock emission
Most of the area shows a source of non-thermal radiation with index < α >= −0.5 (S ν ∝ ν α ), as obtained from the VLA data. We adopted a distance to the bow-shock of 1.4 kpc (Hanson 2003). The distance from the star to the bow-shock is R = 5 , or 2 pc. The volume occupied by the bowshock is ∼ 4.6 pc 3 . We took a particle density of the ISM in the bow shock region of 100 cm −3 (see Kobulnicky et al. 2010).
The non-thermal radiation is expected from synchrotron emission generated by relativistic electrons accelerated either at the forward shock in the ISM or in the reverse shock in the stellar wind. We estimated the particle energy distribution (n) using the observed flux density and spectral slope, and assumed equipartition between magnetic and relativistic particles energy density.
We considered that the energy density of relativistic particles has three contributions: where e 1 , p, and e 2 stand for relativistic primary electrons, protons, and secondary electron-positron pairs (i.e. pairs coming from charged pion decays), respectively. The relation between primary electrons and protons energy density is u p = au e 1 , with a ≥ 0. Three cases were considered: a = 0 (just electrons), a = 1 (equal energy density in both species), and a = 100 (proton-dominated case, as observed in the galactic cosmic rays). The magnetic field resulted B ∼ 5 × 10 −5 G.
The maximum energy of the particles was determined by balancing energy gains and losses. The loss mechanisms considered were (i) synchrotron radiation, (ii) relativistic Bremsstrahlung, (iii) particle escape from the radiation region due to convection by the stellar wind, and (iv) inverse Compton (IC) scattering of IR, stellar and cosmic microwave background photons. In the case of protons, the only relevant losses are proton-proton (pp) inelastic collisions and convective escape. Diffusion is negligible in comparison to convection in this situation (the respective timescales are t conv ∼ 6×10 6 s and t diff ∼ 10 13 /(E/erg) s). Both primary electrons and protons reach energies up to ∼ 10 13 eV, which is imposed by non-radiative losses, except for a = 100, where synchrotron losses dominate for electrons. Figure 5 shows the losses for electrons and protons in the case a = 1.

Discussion and perspectives
The presence of highly relativistic particles in a dense medium with high photon density can result in the efficient generation of γ-rays. The corresponding γ-ray emissivity can be calculated using the delta-functional approximation (e.g. Aharonian & Atoyan 2000, Kelner et al. 2006). In Fig. 6 we show the spectral energy distribution obtained for the case a = 1, with all contributions included (synchrotron self-Compton losses are negligible). The total luminosity from pp interactions is similar to that obtained from relativistic Bremsstrahlung of electrons. The IC upscattering of IR photons is the major contribution at high energies, with a peak around 100 GeV. The detectability of the source by the Fermi LAT 2 γ-ray observatory will depend on the actual particle density and the contribution related to the secondary electrons at large a. The pp contribution extends well into the TeV regime, but its weaker and will be difficult to detect with the current ground-based Cherenkov telescope arrays.
For the case a = 100, the relativistic particle contain is proton-dominated and γ-rays from pp process dominate the high energy spectrum. The CTA 3 North observatory might detect the source yielding information on the high enery cutoff.
Observations of the spectral slope at high energies can be used to identified the proton content through the luminosity level, and the proton spectral index. Radio polarization data will provide additional information of B. X-ray observations will allow to determine the cutoff of the synchrotron spectrum, directly related to the maximum energy of the electrons 4 . This, in turn, would yield valuable information on the actual value of B and the correctness of the equipartition hypothesis.  Figure 6: Spectral energy distribution for the case a = 1. Acronyms as in Figure 5. Measured radio fluxes from VLA observations ('VLA Obs') and MSX luminosity at D band are also represented. The contribution from secondary pairs is negligible in this case, so is not shown here.