Gamma rays and neutrinos from dense environment of massive binary systems in open clusters

TeV gamma-ray emission has been recently observed from the direction of a few open clusters containing massive stars. We consider the high energy processes occurring within massive binary systems and in their dense environment by assuming that nuclei, from the stellar winds of massive stars, are accelerated at the collision region of the stellar winds. We calculate the rates of injection of protons and neutrons from fragmentation of these nuclei in collisions with stellar radiation and matter of the winds from the massive companions in a binary system. Protons and neutrons can interact with the matter, within the stellar wind cavity, and within the open cluster, producing pions which decay into $\gamma$ rays and neutrinos. We discuss the detectability of such $\gamma$-ray emission by the present and future Cherenkov telescopes for the case of two binary systems Eta Carinae, within the Carina Nebula, and WR 20a, within the Westerlund 2 open cluster. We also calculate the neutrino fluxes produced by protons around the binary systems and within the open clusters. This neutrino emission is confronted with ANTARES upper limits on the neutrino fluxes from discrete sources and with the sensitivity of IceCube.

Figure 1

Schematic representation of the massive binary system. Powerful stellar wind creates a cavity in the medium of the open cluster. A cavity has the radius $R_{\text{cav}}$. It is filled with dense wind, close to the binary system, and a rare wind at large distances. The wind is expanding with the velocity $v_{\mathrm{w}}$. Relativistic nuclei are accelerated in the region of colliding winds of the massive stars. These nuclei disintegrate in collisions with the stellar radiation and the matter of the wind, injecting relativistic protons and neutrons. Protons ($P$) are captured in the expanding wind suffering huge adiabatic energy losses. They can also lose a part of their energy on collisions with the matter of the wind. High energy $\gamma$ rays and neutrinos are produced in these hadronic collisions. Neutrons ($N$), from fragmentation of nuclei, propagate along the straight lines and decay at some distance from the binary system. Protons, from decaying neutrons, are captured by the local magnetic field. They can interact efficiently with the surrounding matter producing $\gamma$ rays and neutrinos. Since the adiabatic energy losses of these protons, from decaying neutrons, are relatively low, $\gamma$ rays and neutrinos produced by them have larger energies than those produced by protons from direct fragmentation of primary nuclei.

Figure 2

Upper panel: The optical depths for nuclei, as a function of their energy (per nucleon), for two injection angles $\alpha =45°$ (thick curves) and 135° (thin curves) (measured from the direction towards the star) for the helium and oxygen nuclei and for three considered massive stars: WR in the Cyg X-3 binary system (dotted line), the WR 20a binary system (dot-dashed line), and Eta Carinae (solid). Lower panel: The average number of neutrons extracted from relativistic nuclei (as a function of their energy per nucleon) with different initial mass numbers He (left figures) and O (right) as a result of their photodisintegration in the stellar radiation field for three considered example massive stars: a WR-type star as observed in Cyg X-3 (dotted curve), WR 20a (dot-dashed), and Eta Carinae (solid). Nuclei are injected isotropically at the distance of the shock from the star (see Table 1).

Figure 3

The change of the Lorentz factor of a charged hadron as a function of distance from the binary system caused by only collisional energy losses (thin curves) and by both collisional and adiabatic energy losses (thick curve) for different parameters of the winds produced by the massive stars: a classical WR-type star (dot-dashed line), a $\eta$ Carinae-type star (solid line), and a WR star in the WR 20a binary system (dashed line). The dotted line shows the adiabatic energy losses of hadrons without their collisional energy losses.

Figure 4

The average $\gamma$-ray reduction factors $P$ [see Eq. (10)], due to absorption of $\gamma$ rays in the stellar radiation ($\gamma +\gamma \to e^{\pm }$), as a function of the energy of a $\gamma$-ray photon. The results are shown for the massive star in the WR 20a (on the left) and Eta Carinae (on the right) binary systems. The reduction factors are calculated by assuming isotropic injection of $\gamma$ rays at a specific distance from the massive star in units of the stellar radius equal to $r=3$ (dashed line), 10 (solid line), 30 (dotted line), 100 (dot-dashed line), 300 (dot-dot-dashed line), and ${10}^3$ (thin dashed line).

Figure 5

Gamma-ray spectra produced by protons, from disintegrated nuclei, which interact within the matter of the stellar winds within the wind cavity (dashed curves) and from protons, appearing in the wind cavity as a decay product of neutrons (solid curves). Two example binary systems are considered: WR 20a (on the left) and Eta Carinae (on the right). The thick curves show the gamma-ray spectra with included absorption effects in the stellar radiation, and the thin curves show the spectra without any $\gamma$-ray absorption. The $\gamma$-ray spectra have been calculated for the spectra of primary nuclei which have been normalized to the stellar wind powers (see Table 1), with the normalization coefficients equal to $\eta ={10}^{-2}$.

Figure 6

Gamma-ray spectra produced by protons from disintegrated nuclei (dashed curves) and by protons (solid curves) decaying neutrons (solid curves). These protons interact with the matter within the wind cavity in the case of two example binary systems: the WR 20a (on the left) and Eta Carinae (on the right). The absorption effects of $\gamma$ rays in the stellar radiation are included. The $\gamma$-ray spectrum observed by HESS from the direction of the WR 20a binary system is shown by the dot-dashed line [28]. In the case of the Eta Carinae binary system, the Fermi-LAT spectrum is shown by triangles [10], and the HESS upper limits [9] are shown by the thin dot-dashed line. The $\gamma$-ray spectra have been calculated for the spectra of primary nuclei which have been normalized to the stellar wind powers (see Table 1). The normalization coefficients are equal to $\eta =3\times {10}^{-3}$, in order to be consistent with the $\gamma$-ray flux reported by HESS from the open cluster Westerlund 2 (see thin dot-dashed line), and $\eta ={10}^{-2}$, in order to be consistent with the Fermi observations of Eta Carinae below 10 GeV. The broken thin dotted line shows the level of sensitivity of the CTA [56].

Figure 7

Differential spectra of protons [spectral energy distribution (SED)] from neutrons decaying within the wind cavity but advected from it to the open cluster (dashed curves) and from neutrons decaying outside the wind cavity but inside the open cluster (dotted curves). The total spectra of protons within the open cluster are shown by the solid curves. Neutrons are extracted from nuclei in collisions with the matter of the stellar wind in the case of the WR 20a binary system (on the left) and Eta Carinae binary system (on the right). The density of matter in the open cluster determines the radius of the wind cavity [see Eq. (2)], $n_{\text{oc}}=10{\mathrm{cm}}^{-3}$ (thick curves), and $n_{\text{oc}}=100{\mathrm{cm}}^{-3}$ (thin). The power in relativistic nuclei is normalized to 1% of the stellar wind power (given in Table 1).

Figure 8

Gamma-ray spectra produced by protons (from decaying neutrons) in the dense cluster around the WR 20a and Eta Carinae binary systems. The escape of protons from the open cluster is described by assuming the Bohm diffusion prescription and the parameter $R_{20}^2{B}_{-4}{n}_{10}=1.5$ (solid curve) and 0.15 (dashed curve) for the WR 20a binary and 0.2 (solid curve) and 0.04 (dashed curve) for the Eta Carinae binary. The HESS spectrum observed from the direction of the open cluster around WR 20a is marked by the thin dot-dashed line, and the CTA sensitivity is marked by the thin dotted curve. The efficiency of acceleration of nuclei is equal to $\eta =5\times {10}^{-3}$ for WR 20a and ${10}^{-2}$ for Eta Carinae.

Figure 9

Spectra of neutrinos (SED) produced by hadrons in the above discussed scenarios from the wind cavity (left) and from the open cluster (right). The minimum energy of escaping protons is equal to ${10}^5\mathrm{GeV}$, corresponding to $R_{20}^2{B}_{-4}{n}_{10}=1.5$, for WR 20a (solid line) and $1.5\times {10}^4\mathrm{GeV}$, corresponding to $R_{20}^2{B}_{-4}{n}_{10}=0.2$ for Eta Carinae (dashed line). The neutrino spectra are produced by protons which are the decay products of neutrons extracted from nuclei in their collisions with stellar wind. The ANB in a view cone of 1° radius around the source is shown by the thin dashed curves [59], the 5 yr sensitivity of $\mathrm{IceTop}+\mathrm{IceCube}$ is shown by the thin dotted line [58], and the ANTARES upper limit on the point sources is shown by the dot-dashed line [57]. The proton spectra are normalized in the same way as described for the $\gamma$-ray spectra.