arXiv:1410.7553v1 [astro-ph.HE] 28 Oct 2014 ∗ hi eua n uenv enns nfc,u to up fact, In remnants. TeV and supernova now pulsars and such binaries, objects nebulae massive compact their compact type , early concentra- massive also large as and of matter presence of the tion to due processes energy etrud1-Armwk ta.21a.As GeV Also and 2012a). 2007, al. Aharonian al. - et et 2 Abramowski Aharonian γ OB - - Cyg 2 1 Westerlund Westerlund (i.e. 2002, clusters al. open et 3 of rection a iaysse a o endtce pt o nthe in now to up detected Cari- been Eta be TeV not to itself. has has system system binary binary it Wal- nae the Therefore, from & far 2012). evidence (Farnier not al. shows produced period et emission binary Reitberger GeV 2011, the et this ter Farnier with of 2009a, modulation part al. of A et Abdo 2011). 2009a, com- al. al. et (Tavani the within plex Carinae bi- Eta supermassive the system of nary direction the from reported cently ltdGeV ulated ai ae bevdfo hssse.TeGeV The major the system. before this appears just from and state observed transient radio flares is quenched radio emission the This to Bulgar- close 2012). 2010, al. al. et et Abdo elli 2009b, Fermi-LAT al. and et (Tavani AGILE the telescopes by detected recently been has em olbrto nti ieto aebe identified been the have the within by direction with reported this 20a sources in new WR collaboration Two Fermi system Fermi- 2. Westerlund binary the cluster in the open now from to up data identified LAT been not has emission lcrncades [email protected] address: Electronic ryeiso,etnigu to up extending emission, -ray pncutr aebe upce sstsfrtehigh the for sites as suspected been have clusters Open am-asadnurnsfo es niomn fmassive of environment dense from neutrinos and Gamma-rays γ ryrne(baosie l 02) h mod- The 2012b). al. et (Abramowski range -ray γ γ ryplas(boe l 09,SzParkinson Saz 2009b, al. et (Abdo pulsars -ray ryeiso a endtce rmtedi- the from detected been has emission -ray eateto srpyis h nvriyo L´od´z, of University 90- The Astrophysics, of Department γ atr ihnteselrwn aiyadwti h pncl open the within Protons and cavity system. γ wind binary stellar in the within companions matter, massive collisio in the We nuclei from these winds. winds of stellar fragmentation the from of from neutrons region nuclei, and occ collision that processes the assuming by at energy environment accelerated high dense the their consider in We and stars. massive ing ASnmes 97.80Jp,98.20Ej,96.40Qr,98.60Ce,98.70Rz clus numbers: PACS open f fluxes the neutrino within the IceCube. on and of limits systems calcsensitivity upper also binary ANTARES We C with the cluster. Eta confronted open around systems 2 binary protons Westerlund two the by within of 20a, case WR the and for telescopes Cherenkov ryeiso rmbnr ytmCgX-3 Cyg system binary from emission -ray ry n etio.W ics h eetblt fsuch of detectability the discuss We neutrinos. and -rays e am-a msinhsbe eetyosre rmdire from observed recently been has emission gamma-ray TeV .INTRODUCTION I. oe Bednarek, W lodek ∼ 0 e,hsbe re- been has GeV, 100 Dtd coe 5 2018) 15, October (Dated: ∗ pnclusters open ez aih n oazSobczak Tomasz and Pabich, Jerzy γ -ray ta.19,Tre ta.20,Bdae 2007). Bednarek 2004, al. et Torres Giovannelli 1996, 1983, al. V¨olk Montmerle & et & (e.g. cluster the Cesarsky open of 1982, the accelerate Forman collisions of to matter during dense able formed with are produced waves winds clusters winds shock open strong at in that particles clus- stars proposed open massive been the by from has emission It energy ters. high the of nations 2010). al. et cnro rvd uko h ihenergy those high of the which present of at bulk clear & a not is provide Bartko It scenarios 2013, 2003, 2014). al. et al. (Bednarek Ohm et 2011, Aliu al. cluster et inter- Abramowski open dense 2008, the Bednarek with an of PWNe of result within a matter accelerated as particles or of PWNe action within produced also iheeg aito Aaoin&Aoa 96.A 1996). Atoyan & of produce (Aharonian to part radiation able energy are also can that high cluster particles open relativistic the accelerate within shock clouds SNRs dense and of with Interaction (SNRs) waves (PWNe). remnants nebulae supernova wind relatively pulsar a producing at life time their end Mas- short clusters 2011). open Pabich within & stars sive Pit- Bednarek 2006, 2006, al. Dougherty et Benaglia & Reimer 1995, tard 2005a, Chen Bednarek & 2003, White Romero 1993, & systems Usov binary & massive acceler- Eichler within particles (e.g. formed by shocks the produced at also ated be can neutrinos and atce ihcmaal oe,ie fteodro 10 of order the relativistic of inject erg. i.e. (mas- might power, processes objects comparable PWNe) few with of SNRs, particles a types winds, cluster different open since sive specific important in be above. that can mentioned likely clusters is open few It a from observed sion n rudtemsiebnr ytm uruddby surrounded systems binary within massive processes the hadronic around in and expected radiation energy e cnro aebe osdrda osbeexpla- possible as considered been have scenarios few A ntepeetpprw netgt ndti h high the detail in investigate we paper present the In 3 Lo´ ,u.Pmrk 4/5,Poland 149/153, Pomorska L´od´z,236 ul. swt tla aito n atro the of matter and radiation stellar with ns aclt h ae fijcino protons of injection of rates the calculate γ se,pouigposwihdcyinto decay which pions producing uster, ryeiso ytepeetadfuture and present the by emission -ray γ rigwti asv iaysystems binary massive within urring h tla id fmsiesas are stars, massive of winds stellar the ryeiso rmteoe lsescnbe can clusters open the from emission -ray to fafwoe lsescontain- clusters open few a of ction n etoscnitrc ihthe with interact can neutrons and rne ihnteCrn Nebula, Carina the within arinae, lt h etioflxsproduced fluxes neutrino the ulate o iceesucsadwt the with and sources discrete rom es hsnurn msinis emission neutrino This ters. iayssesin systems binary γ ryemis- -ray γ -rays 50 2 the large concentration of matter. It is assumed that nu- Note, that the at first accelerate from the clei are accelerated in the region of colliding winds within stellar surface reaching the asymptotic velocity (see Wa- the binary stars (e.g. see Bednarek 2005b). These nuclei ters et al. 1988). After initial acceleration, due to the can severely disintegrate, in the interaction with the ra- gas pressure, the wind decelerates due to the gravi- diation field of massive stars and with the matter of the tational attraction of the massive star. The velocity stellar winds, injecting neutrons and protons. Charged of the wind drops with a distance from the star ac- 2 2 protons diffuse through the producing γ- cording to, vw(R) = vo − 2GMwr(1/RWR − 1/R) ≈ 16 2 15 2 2 rays and neutrinos in collisions with the matter of the 10 v3 − 2.7 × 10 (M10/R12)(1 − 1/r) cm /s , where stellar wind cavity and dense environment of the open MWR = 10M⊙M10 is the of the star and G is the cluster. On the other hand, neutrons move balistically gravitational constant. For the parameters of the stars through the wind cavity and decay into protons at some considered in this paper, the deceleration effect of the distance from the binary system which can be still within wind can be neglected. The radii of the wind cavities the wind cavity or already within the open cluster. Pro- around WR type binary systems within the open clus- tons from their decay can also contribute to the high ters are typically of the order of a few for the energy γ-ray and neutrino spectrum. As an example, density of surrounding matter of the order of ∼ 10 cm−3 4 we perform calculations of the γ-ray and neutrino fluxes and its temperature Toc ∼ 10 K. In fact, the scenario produced in the clusters surrounding the Eta Carina su- discussed above is a simplification of the real situation permassive binary system and WR 20a binary system in in which the interaction of the stellar winds with open open cluster. This emission is confronted cluster matter can result in a complicated double shock with the present measurements of the GeV-TeV γ-ray structure. Additionally the cavity does not have to be emission from these clusters, sensitivities of the future isotropic due to anisotropies of the environment. We ex- Cherenkov Telescope Array (CTA) and the IceCube neu- pect that the above estimated radius of the wind cavity trino telescope. is approximately correct since the amount of the mass overtaken by the expanding stellar wind (with the radius of the order of a few pc) is much smaller than the total II. A MASSIVE BINARY SYSTEM WITHIN mass of the open cluster (with the radius of several pc). THE OPEN CLUSTER Therefore, the environment in which the binary system is immersed does not change significantly with time. We consider a massive binary system in which one or We consider consequences of acceleration of nuclei both companion stars belongs to the class of the Wolf- within the binary system located in the open cluster. Nu- Rayet (WR) stars. WR type star produces fast and dense clei (from the stellar winds) can be accelerated within the wind, due to the huge mass loss rate, which can be of the collision region of the winds (e.g. Eichler & Usov 1992). ˙ −5 ˙ −1 order of MWR = 10 M5 M⊙ yr . The winds propagate The recconnection of the magnetic field and the diffu- with the characteristic velocities of the order of vw = sive shock acceleration process can play important role 3 −1 10 v3 km s . The density of the wind drops with the in this place. The details of the acceleration process, distance from the star according to, propagation of hadrons and their subsequent interaction within the binary system and its surrounding are dis- ≈ × 11 ˙ 2 2 −3 nw(r) 3.2 10 M−5/v3R12r cm , (1) cussed in the next section. We show that nuclei can ef- ficiently disintegrate in the dense radiation and matter where R = 1012R cm is the radius of the star, and WR 12 of the winds from massive stars. As a result, neutrons r = R/R is the distance from the star in units of the WR are injected. They decay at the distance from the bi- stellar radius. Note that at the distance of the order of a nary system which is determined by their Lorentz fac- , density of the wind becomes very low, e.g. for 1 − tors. Protons, extracted from nuclei, lose energy on in- pc the wind density becomes ∼ 0.03 cm 3. So then, the teraction with the dense wind close to the binary system. outer regions of the wind cavity are filled with very rare They also suffer adiabatic energy losses in the expanding but high velocity gas. wind within the wind cavity. We consider high energy The massive binary systems are usually immersed itself processes in which γ-rays and neutrinos are produced in within a relatively dense open clusters (OCs). Typical hadronic collisions in the above described scenario. The densities of the OCs are of the order of noc = 10n10 −3 schematic representation of the processes around the bi- cm and temperatures of the gas of the order of Toc = 4 nary system is shown in Fig. 1. 10 T4 K. At certain distance from the binary system, the pressure of the stellar wind is balanced by the pressure of Note that hadrons might be also accelerated in such thermal gas within the OC. We estimate the dimension scenario at the shock structure formed in the collision of such stellar wind cavity, in the case of a constant wind of the stellar wind with the circumstellar gas. We ex- velocity, by comparing the energy density of the wind pect that this acceleration process is less efficient than with the energy density of the medium within the OC. the acceleration process occurring within the binary sys- This allows us to estimate the radius of the wind cavity, tem. The product of the magnetic field strength and the characteristic dimension of the shock, determining the 19 1/2 Rcav ≈ 1.1 × 10 [M˙ −5v3/(n10T4)] cm. (2) maximum energies of accelerated particles, is expected 3

surrounding medium are expected to be mainly composed from nuclei heavier γ than hydrogen such as helium to oxygen. P ν Massive stars are frequently found within the massive γ γ binary systems in which strong winds collide providing ν conditions for acceleration of nuclei to large energies. Be- P ν low, we generally consider the process of acceleration of P N nuclei at the shocks or the reconnection regions created N by these colliding winds. The propagation and interac- R tion of nuclei with the stellar radiation field results in cav BS their photo-disintegration to neutrons, protons and sec- vw ondary nuclei. We perform numerical simulations of nu- clei in the radiation field of the massive stars in order to dense wind determine the rate of injection of different nuclei. Note that density of stellar photons in the vicinity of massive 16 −3 5 wind cavity star, nph ≈ 2 × 10 T5 ph. cm (where T = 10 T5 K is the surface temperature of the massive star), is a rare wind few orders of magnitude larger than density of matter in the stellar wind (see Eq. 1). Therefore, it is expected that nuclei with sufficiently large energies interact at first FIG. 1: Schematic representation of the massive binary sys- in collisions with stellar photons rather than with the tem. Powerful stellar wind creates a cavity in the medium of matter of the stellar wind. After that, nuclei can suf- the open cluster. A cavity has the radius Rcav. It is filled fer significant fragmentation in collisions with the matter with dense wind, close to the binary system, and a rare wind of the stellar wind. This second process is independent at large distances. The wind is expanding with the velocity on energy of nuclei. Therefore, lower energy nuclei can vw. Relativistic nuclei are accelerated in the region of col- also suffer strong disintegration process in collisions with liding winds of the massive stars. These nuclei disintegrate dense matter of the stellar winds in the case of stars with in collisions with the stellar radiation and the matter of the wind, injecting relativistic protons and neutrons. Protons (P) exceptionally strong winds such as considered in this pa- are captured in the expanding wind suffering huge adiabatic per (i.e. WR and O type stars which mass loss rate is −5 −1 energy losses. They can also lose a part of their energy on above ∼ 10 M⊙ yr ). Neutrons released from nuclei collisions with the matter of the wind. High energy γ-rays in collisions with the matter have the spectrum similar and neutrinos are produced in these hadronic collisions. Neu- to the spectrum of primary nuclei. Therefore, neutrons trons (N), from fragmentation of nuclei, propagate along the with low energies can decay relatively close to the binary straight lines and decay at some distance from the binary sys- system where the density of matter is still high. On the tem. Protons, from decaying neutrons, are captured by the other hand, high energy neutrons can even reach dense local magnetic field. They can interact efficiently with the regions outside the wind cavity of the massive binary sys- surrounding matter producing γ-rays and neutrinos. Since tem. In this paper we calculate γ-ray and neutrino spec- the adiabatic energy losses of these protons, from decaying tra produced by protons extracted from nuclei and also neutrons, are relatively low, produced by them γ-rays and neutrinos have larger energies than those produced by pro- from protons from neutrons decaying at some distance tons from direct fragmentation of primary nuclei. from the binary system. These neutrons decay within the wind cavity and also within the dense open cluster in which binary system is immersed. to be lower at the shock produced by the wind in sur- We estimate the maximum energies of hadrons ac- rounding gas due to the mainly radial of the magnetic celerated in the shock region of colliding winds fol- field within the binary system and its toroidal structure lowing the conditions considered e.g. in Bednarek & far away from the binary. Pabich (2011) and Bednarek (2005b). The maximum energies of hadrons are determined by comparing their acceleration time scale and their escape time scale from III. INJECTION OF NUCLEI FROM THE the acceleration region or collision time scale with the BINARY SYSTEM matter of the stellar wind. The acceleration time scale is given by,

Massive stars produce fast and dense winds which can τacc = Eh/P˙acc ≈ 0.02γh/(χ−5B3) s, (3) extract significant amount of original mass from the star during its lifetime. In fact, the intensive mass loss rates where Eh and γh are the energy and the Lorentz fac- −6 −4 −1 of the order of a few 10 − 10 M⊙ yr are charac- tor of particles, P˙acc = χcEh/RL is the acceleration −5 teristic for the Wolf-Rayet (WR) and O type stars. Dur- rate, χ = 10 χ−5 is the acceleration coefficient, RL = ing the stage, the outer parts of stars are Acγh/ZeBsh is the Larmor radius of hadron in the mag- completely lost and only inner parts, composed of heavy netic field at the shock Bsh, c is the velocity of light, e nuclei, are left. Therefore, the winds of early type stars is the elemental charge, and A and Z are the mass and 4 charge numbers of nuclei. We apply A/Z = 2. Bsh, is massive star, Lh = ηLw (see Table 1 for specific binaries). related to the surface magnetic field of the massive star In Table 1 we also report other basic parameters of these by assuming its dipolar structure close to the surface up three binary systems. Their orbital periods are equal to to ∼ 1.2R⋆ and radial structure at larger distances (Usov 4.8 hrs for Cyg X-3 binary system (Becklin et al. 1973), & Melrose 1992)). For the distance of the collision region 3.675 days for WR 20a (Rauw et al. 2004) and 2027.7 from the star equal to Rsh =2R⋆, Bsh drops to ∼ 0.25B⋆. days for (Damineli et al. 2008)). The advection time scale of hadrons from the collision region is estimated from,

4 IV. DISINTEGRATION OF HADRONS WITHIN τadv ≈ Rsh/vw ≈ 10 R12/v3 s, (4) BINARY SYSTEM

12 where Rsh = 10 R12rsh cm is the distance of the colli- The process of disintegration of nuclei has been ex- sion region from the star and rsh = Rsh/RWR. We es- timate the diffusion time scale of hadrons (in the Bohm tensively studied in the past in the context of the origin and propagation of the highest energy cosmic rays (e.g. approximation) in the acceleration region τdif ≈ 1.5 × 4 2 6 Stecker 1969, Tkaczyk et al. 1975, Puget et al. 1976). 10 R12B3/γ6 s, where γ = 10 γ6 is the Lorentz factor of 3 This process has been also proposed to be important hadrons and Bsh = 10 B3 G. This diffusion time is larger than the above estimated advection time scale even for in compact sources in which dense soft radiation field the most energetic hadrons considered in this scenario. is expected, i.e. in supernova remnants (e.g. Pollack & Then, the maximum energy of hadrons accelerated at Shen 1969), binary systems (e.g. Karakulaet al. 1994), the region of colliding stellar winds is obtained from com- dense stellar clusters (e.g. Anchordoqui et al. 2007a,b), parison of Eq. 3 and Eq. 4. It is then given by, or the Galactic Center (e.g. Kusenko et al. 2006). γ-ray emission from de-excitation of fragments of nuclei, which adv 5 γmax ≈ 5 × 10 B3v3R12rsh GeV, (5) survived disintegration, has been calculated in some of these works following the prescription emphasized by where the acceleration coefficient is estimated to be χ = Balashov et al. (1990). This γ-ray production process 2 −5 2 (vw/c) ≈ 10 v3. is generally relatively inefficient since only a small part On the other hand, hadrons lose also energy on colli- of the initial energy of hadrons is converted into radia- sions with the matter of the stellar wind. The hadron- tion. However, it may play a role in the case of sources hadron energy loss time scale can be estimated from, with strong soft radiation field but without large amount of matter. Here we consider production of γ-rays and −1 3 2 2 ˙ τhh = (cnw(r)kσpp) ≈ 3.5 × 10 R12r v3/M−5 s, (6) neutrinos by secondary products of disintegrated nuclei in their interaction with dense matter surrounding the × −26 2 where σpp =3 10 cm is the cross section for proton- source of relativistic nuclei. We neglect possible direct proton collision, and k = 0.5 is the in-elasticity coeffi- production of neutral high energy radiation in the inter- cient. action of hadrons with the stellar radiation (p + γ → π) The maximum energies of hadrons allowed by colli- since, as we have shown above, nuclei are not accelerated sional energy losses are, to large enough energies to reach the threshold for this hh 5 2 2 3 process in the environment of the binary systems. γ ≈ 3.5 × 10 R r v B3/M˙ −5. (7) max 12 3 In order to have an impression about the role of the We have calculated the maximum energies of hadrons due fragmentation process of nuclei in the radiation field of to these two processes for three example massive stars massive stars we consider a simple case of their injection within the binary systems. The results are shown in Ta- from a point-like source not far from the stellar surface, ble 1. In the case of the parameters of the WR type star e.g. at the distance of two stellar radii. We calculate as observed in Cyg X-3 binary system, the maximum the optical depths for fragmentation of nuclei injected at energies of accelerated hadrons are limited by advection different initial directions, as a function of their energy process. In the case of the binary system containing WR and two mass numbers corresponding to the helium and 20a stars, the maximum energies of hadrons are compara- the oxygen nuclei (see Fig. 2). The approximation of the ble in the case of advection process and collisional energy cross section for photo-disintegration process of nuclei is losses. But, in the case of Eta Carinae the maximum en- applied as described in Karakula& Tkaczyk (1993). Nu- ergies of hadrons are limited by collisional energy losses. clei are considered to propagate in the vicinity of three In all considered cases hadrons can reach energies of the representative massive stars with different parameters: order of ∼106 GeV. WR type star as observed in the Cyg X-3 binary system, In all calculations of the γ-ray and neutrino spectra WR star in the WR 20a binary system and supermas- (presented below), it is assumed that nuclei are injected sive star in the Eta Carinae binary system (see Fig. 2). with the power law spectrum (spectral index equal to 2), Note that only nuclei with Lorentz factors above γmin can extending up to the lower value between those given by be efficiently disintegrated. This critical Lorentz factor th 4 Eqs. 5 and 7. The power in these hadrons is normalized to can be estimated from γmin = Eγ /3kBT ∼ 4 × 10 /T5, th a part, η, of the power provided by the stellar wind of the where Eγ = 2 MeV is the minimum energy of stellar 5

TABLE I: Parameters of massive stars in binary systems, maximum Lorentz factors of accelerated nuclei and the optical depths for protons in the matter of the stellar wind

adv col Name B RWR vw Rsh TWR MWR M˙ WR Lw τhp γmax γmax −1 unit G cm km/s RWR K M⊙ M⊙/yr erg s

WR 3 × 103 1011 3 × 103 2 1.4 × 105 5 3 × 10−6 1037 ∼0.3 9 × 105 3.8 × 106

WR 20a 103 1.4 × 1012 103 2 4 × 104 30 3 × 10−5 1037 ∼2.4 1.4 × 106 106

Eta Car 200 1.2 × 1013 700 1.4 4 × 104 80 2.5 × 10−4 4 × 1037 ∼4.1 1.2 × 106 2.7 × 105

) 1.5 ) 2

photon in the nuclei rest frame which is able to effec- τ τ 5 tively photo-disintegrate the nuclei, T = 10 T5 K is the log( 1 Helium log( 1.5 Oxygen surface temperature of the star, and kB is the Boltzmann 0.5 1 constant. In this figure we also determine the number of nucleons dissolved from the primary nuclei in the photo- 0 0.5 disintegration process. The investigation of the results -0.5 0 presented in Fig. 2, in the context of the maximum ener- -1 -0.5 gies of nuclei expected in our model (see Table. 1), allows -1.5 -1 us to conclude that in the case of WR 20a binary system -2 -1.5 the process of photo-disintegration of nuclei can be ne- -2.5 -2 4 4.5 5 5.5 6 6.5 7 4 4.5 5 5.5 6 6.5 7 glected. In the case of WR star with parameters observed log(E / GeV) log(E / GeV) 5 in Cyg X-3 binary system and Eta Carinae, significant 1.2 number of nuclei with energies in the range ∼ 10(5−6) Oxygen Helium 4 will lose nucleons in collisions with stellar radiation. 1

0.8 In order to conclude whether nuclei can be efficiently 3 disintegrated in collisions with the matter of the stel- 0.6 lar wind, we estimate the optical depth for relativistic 2 hadrons on collisions with the matter of the wind. This 0.4 1 optical depth can be estimated from, 0.2

Rc 0 0 σppnwc M˙ −5 1 1 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 τ = dR ≈ 2.9 × 1012 ( − ),(8) log(E / GeV) log(E / GeV) hp Z 2 RBS vw v3 RBS Rc FIG. 2: Upper panel: The optical depths for nuclei, as a function of their energy (per nucleon), for two injection an- where RBS (in cm) is the radius of the binary system at o o which hadrons are injected within the wind. It is assumed gles α = 45 (thick curves) and 135 (thin curves) (measured to be equal to the shock radius. The optical depths for from the direction towards the star) for the helium and oxygen protons on the interaction with the matter of the wind nuclei and for three considered massive stars: WR in Cyg X-3 binary system (dotted), WR 20a binary system (dot-dashed) are shown in Table 1 for three example parameters of and Eta Carinae (solid). Lower panel: The average number the massive stars. Note that the optical depth for nuclei of neutrons extracted from relativistic nuclei (as a function with specific mass number A1 in collisions with nuclei of their energy per nucleon) with different initial mass num- β with the mass number A2 scales as, τA1A2 ∝ (A1A2) , bers, He (left figures), O (right) as a result of their photo- where β is between 2/3 to 1 (see DPMJET calculations disintegration in the stellar radiation field for three considered given in Mori 2009). For the case of the helium nuclei example massive stars: WR type star as observed in Cyg X-3 (A1 = A2 = 4), the optical depths will be a factor of (dotted curve), WR 20a (dot-dashed) and Eta Carinae (solid). ∼ 14 larger (β = 0.94) and for the oxygen nuclei a fac- Nuclei are injected isotropically at the distance of the shock tor of ∼ 43 larger (β = 0.68, see Mori 2009). There- from the star (see Table 1). fore, we conclude that in the case of considered binary system relativistic nuclei should be completely disinte- grated. Large values of the optical depths for collisions binary system within the wind cavity or, in the case of the of protons with the matter of the stellar winds indicate most energetic neutrons, directly in the region of the open that these relativistic hadrons should efficiently lose en- cluster. Protons, from decay of these neutrons, can also ergy on production of high energy γ-rays and neutrinos produce high energy radiation at large distances from the in the close vicinity of the massive binary system. On the binary systems, i.e in the region with low level of the soft other hand, neutrons, released from these nuclei, should radiation field and low density of matter in respect to the move rectilinearly and decay at large distances from the density of the wind within the binary system. 6

V. HADRONS ESCAPING FROM THE BINARY dial at distances below ∼ 10RWR, i.e. in this region 2 SYSTEM B ∝ B⋆(10RWR/R) . At larger distances the magnetic field becomes toroidal. Then, for distances greater than Accelerated nuclei initiate a sequence of processes ∼ 10RWR, the magnetic field strength can be approxi- 3 within the binary system and its surrounding. As we mated by B(R) ≈ 100B3(RWR/R) G, where B = 10 B3 have shown above nuclei suffer complete disintegration if G is the surface magnetic field of the WR type star. Ap- injected within massive binary systems containing lumi- plying this simple scaling, the condition for capturing of 6 nous stars characterized by dense stellar winds (WR type protons, RL < R, is fulfilled for γn < 3 × 10 . Protons stars). Unstable neutrons, from photo-disintegration of with energies fulfilling this condition are captured in the these nuclei, decay at some distance from the binary sys- stellar wind. They are expected to suffer strong adia- tem. Depending on their energy, they can decay within batic energy losses during gradual expansion of the wind the stellar wind region (the wind cavity) or outside the from the star. On the other hand, hadrons with larger stellar wind shock, i.e. within the open cluster. Protons, energies can leave the stellar wind region (and the wind from neutrons decaying within the stellar wind, are ex- cavity) without significant energy losses. They also prop- pected to suffer adiabatic energy losses during the fast agate almost along the straight lines without significant expansion of the wind. These protons are also partially collisions with the matter of the wind. However, hadrons advected with the wind to the open cluster. Neutrons with such large energies are not expected to be acceler- with large enough energies can also decay outside the ated at the collision region within the binary system (see wind cavity in the volume of the open cluster. Protons Table 1). from their decay diffuse gradually through the open clus- Hadrons captured in the stellar wind lose energy on the ter suffering some collisions with the distributed matter. adiabatic process. We can determine the Lorentz factor On the other hand, primary nuclei, accelerated within of hadrons at a specific distance from the binary system the binary system, and also protons from their fragmen- by taking into account adiabatic and collisional energy tation are captured by the magnetic field in the dense losses, stellar wind. These hadrons can interact with the matter γ (R)= γ (R )R kτhp /R, (9) of the wind. As a result of these interactions, an addi- h h BS BS tional population of neutrons is produced not far from where τhp is given by Eq. 8, and k ≈ 0.5 is the in-elasticity the vicinity of the binary system where the matter in the coefficient in proton-proton collisions. Depending on the stellar wind is still relatively dense. These neutrons decay parameters of the considered scenario, either adiabatic within or outside the wind cavity as described above. losses or collision losses determine the Lorentz factors of We conclude that the simple scenario which postulates hadrons at a specific distance of the wind from the bi- acceleration of hadrons within the massive binary system nary system. The Lorentz factors of hadrons at a specific immersed in the open cluster provides variety of condi- distance from the binary system, in the case of only col- tions for production of high energy radiation in different lisional and also collisional and adiabatic energy losses, parts of open cluster characterized by different condi- for three example stars within the binary systems η Car, tions, e.g the wind cavity of the binary system and dense WR 20a and WR star in Cyg X-3, are shown in Fig. 3. medium of the open cluster. We are interested in the There are huge differences in the values of these Lorentz γ-ray and neutrino emission produced in such scenario factors with and without adiabatic energy losses. There- in the context of recent observations of the TeV γ-ray fore, adiabatic energy losses play an important role in emission from open clusters (e.g. Westerlund 2 and the the process of production of high energy radiation in the Carina Complex). open clusters. Let us at first estimate whether charged hadrons (ac- celerated within the binary system and products of their fragmentation) can be captured in the stellar wind. We VI. GAMMA-RAYS FROM PROTONS IN THE compare the Larmor radius of charged hadrons with WIND CAVITY a specific energy with the characteristic distance scale which is the distance at which hadrons are located from In this section we calculate the spectra of γ-rays and the binary system, R. The Larmor radius of hadrons neutrinos produced within the wind cavity. As shown with the Lorentz factor γn is given through the expres- above, primary nuclei are completely fragmented on sep- 6 sion RL = 3 × 10 γn/BG cm, where B = 1BG G is the arate nucleons (protons and neutrons) in collisions with magnetic field strength in the wind at the distance R the matter and radiation already within the binary sys- from the binary system. The magnetic field in the stel- tems. These nucleons are accelerated with the power law lar wind is expected to have complicated structure as a spectrum. Protons from disintegration of nuclei are cap- function of the distance from the star (dipolar, radial tured by the magnetic field of the stellar winds. They and at farther distances toroidal). This structure be- are advected from the binary system with the velocity comes even more complicated in the case of stars within of the wind. They produce high energy radiation in col- the compact binary system when both stars have large lisions with the matter of the stellar wind during their velocities. We assume that the magnetic field is ra- propagation within the wind cavity. These γ-rays are 7

possible propagation angles in respect to the direction 0 )) towards the star. We calculate the reduction factors for BS

(R -0.5

γ γ-rays injected isotropically at the distance R from the

(R)/ -1 massive star from, γ

log( -1.5 1 −τγγ (R,µ) -2 P =0.5 e dµ, (10) Z−1 -2.5

-3 where τγγ(R,µ) is the angle dependent optical depth for the γ-ray photon injected at the distance R, µ = cos θ, -3.5 and at the angle θ in respect to the direction defined by -4 the injection place and the center of the star (see e.g. -4.5 Bednarek 1997, B¨ottcher & Dermer 2005, Dubus 2006, -5 Zdziarski et al. 2014). These optical depths can be eas- 0 1 2 3 4 5 6 log(R/R ) BS ily re-scaled for stars with different parameters follow- ing simple prescription given by Eq. 2 in Bednarek & FIG. 3: The change of the Lorentz factor of a charged hadron Pabich (2010). The absorption process concerns mainly as a function of distance from the binary system caused by min γ-rays with energies above Eγ = me/3kBT ∼ 20/T5 only collisional energy losses (thin curves) and by both colli- GeV. We calculate the optical depths for γ-rays as a func- sional and adiabatic energy losses (thick) for different param- tion of their energies and the distance from the massive eters of the winds produced by the massive stars: classical WR type star (dot-dashed), η Carinae type star (solid) and star. As we noted above, the exact values of the opti- WR star in WR 20a binary system (dashed). The dotted line cal depths depend on the propagation angle of γ-rays in shows the adiabatic energy losses of hadrons without their respect to the direction towards the star. Therefore, we collisional energy losses. show the reduction factor values averaged over the injec- tion angles assuming isotropic injection of γ-rays from a point source at a specific distance from the star. The produced isotropically since the production mechanism results of these example calculations are shown in Fig. 4 (hadronic collisions) is independent on the radiation field for the WR 20a and Eta Carinae massive stars. It is of the massive star. On the other hand, neutrons, ex- clear that γ-rays with energies above several GeV are ef- tracted from nuclei, move rectilinearly through the wind ficiently absorbed even if they are produced at relatively cavity. They decay at distances from the binary system large distances from the binary system. which depend on their Lorentz factors. Secondary pro- tons, from decaying neutrons, are also captured in the stellar wind. All these secondary protons suffer colli- B. Protons from disintegrated nuclei sional and adiabatic energy loses due to the expansion of the wind. In order to obtain the γ-ray spectra, es- We consider the production of radiation by protons caping from the wind cavity region to the observer, we from nuclei accelerated within the binary system. These have to consider possible absorption of γ-rays produced protons are advected outside the binary system with the in hadronic collisions in the radiation field of the mas- velocity of the stellar wind. The number of hadrons sive stars. Therefore, we calculate the optical depths for which interact during the advection process with the γ-rays. These absorption effects has to be taken into ac- stellar wind, on the range of distances from the binary count when calculating the γ-ray spectra produced by system between RBS (considered as the injection place) hadrons not far from the binary system. and R, is determined by the factor [1 − exp(−τpp)], where τpp = A(1/RBS − 1/R) (see Eq. 8), and A = ˙ 2 12 ˙ 2 Mcσpp/(4πvw) ≈ 2.9 × 10 M−5/v3 cm. The spectrum A. Absorption of γ-rays close to the massive star of hadrons, which interact at the distance R from the binary system, is Significant amount of γ-rays produced in hadronic col- dNh(γh, R) A lisions (as described above) originate close enough to the ˙ A(1/R−1/RBS) Nh = = NhJ 2 e , (11) massive star that their absorption in the stellar radiation dγhdRdt R can play important role. The details of the absorption process are determined by the geometry of the binary where N˙ h = dN(γh)/dγhdt is the injection rate of system (production place of γ-rays in respect to the star) hadrons with the Lorentz factors γh from the binary sys- τ and the parameters of the massive star. Its importance tem, J = dγh(RBS)/dγh(R)= R/(RBSK hp ) is the Jaco- in the case of binary systems without precise orbital pa- bian of transformation of hadron energy (see Eq. 9). rameters can be approximately evaluated by calculating In order to calculate the γ-ray and neutrino spectra the average reduction factors for γ-ray photons, i.e. the produced by protons, we have to integrate the above in- probability of escape averaged over the whole range of jection rate of protons (Eq. 11) over the whole dimension 8

1 1 P P

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3

0.2 0.2

0.1 0.1

0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 log(E / GeV) log(E / GeV)

FIG. 4: The average γ-ray reduction factors, P (see Eq. 10), due to absorption of γ-rays in the stellar radiation (γ + γ → e±), as a function of the energy of γ-ray photon. The results are shown for the massive star in WR 20a (on the left) and Eta Carinae (on the right) binary systems. The reduction factors are calculated assuming isotropic injection of γ-rays at a specific distance from the massive star in units of the stellar radius equal to r = 3 (dashed), 10 (solid), 30 (dotted), 100 (dot-dashed), 300 (dot-dot-dashed), and 103 (thin dashed). of the wind cavity and over the spectrum protons (given produced within the wind cavity. by Eq. 11), The optical depth for neutrons, which move along straight lines through the wind cavity, on the interac- Rc γmax dNγ,ν dNγ,ν(γh) −τγγ tion with the matter of the wind is equal to τnp = = Nh e dγhdR (12) Rc dEγ,ν dt ZR Zγ dEγ,ν σppnwdR, where nw is defined by Eq. 1. It is a BS min RBS factorR of c/vw smaller than the optical depth for pro- The spectra of γ-rays and neutrinos are calculated by tons given in Table 1. Therefore, the interaction rate applying the scaling break model for hadronic collisions of neutrons moving along the straight lines through the developed by Wdowczyk & Wolfendale (1987), which is wind cavity can be neglected for the considered range of suitable in the considered energy range of relativistic the parameters characterizing the binary systems. The hadrons. The distribution of protons within the wind neutron decay rate at the distance, R′, from the binary cavity, Nh, is given by Eq. 11. The spectra are calcu- system (equal to the rate of creation of protons from their lated for the range of energies of hadrons γmin = 10 and decay) is given by, γmax as reported in Table 1. Eγ and Eν are the energies ′ of γ-ray photons and neutrinos, respectively. The exam- dNp(γp, R ) N˙ n ′ = e−R /(cγnτn), (13) ple spectra of γ-rays, calculated for two binary systems dγ dR′dt cγ τ (WR 20a and Eta Carinae), are shown in Fig. 5. We show p n n the γ-ray spectra with (thick curves) and without (thin where N˙ n = dN/dγndt is the neutron injection rate from curves) absorption effects in the radiation of the massive the binary system (equal to the acceleration rate of nu- stars. As expected, the absorption of γ-rays produced by clei), τn = 900 s is the neutron decay time, and the protons, extracted from nuclei within the inner part of Lorentz factor of secondary protons (γp) is assumed to the wind cavity, is very strong. be equal to the Lorentz factor of neutrons (γn). Protons, from decaying neutrons, are confined by the magnetic field of the stellar wind. Therefore, they suffer adiabatic C. Protons from decaying neutrons and collisional energy losses as considered for protons from fragmentation of nuclei in the previous section. The Neutrons, extracted from nuclei within the binary sys- collision rate of protons at the distance, R > R′, from the tem, propagate along the straight lines and gradually de- binary system, is given by the formula similar to that cay into protons in the dense medium surrounding the given by Eq. 11, binary system. Depending on the Lorentz factors of neu- ′ ′ trons, these protons appear within the wind cavity or dNp(γp, R , R) dNp A A(1/R −1/R) ′ = ′ 2 Je , (14) outside the wind cavity (i.e. within the open cluster). In dγpdR dRdt dγpdR dt R this subsection, we calculate the spectra of protons from ′ ′ τpp neutrons decaying within the wind cavity. These spectra where J = dγp(R )/dγp(R) = R/(R k ), and τpp ≈ 12 ˙ 2 ′ ′ are used for the calculation of γ-ray and neutrino spectra 2.9 × 10 (M−5/v3)(1/R − 1/R)= A(1/R − 1/R). 9

34.5 34.5 wind cavity wind cavity 34 (WR 20a) 34 (Eta Car) 33.5 33.5

dN/dE/dt / erg/s) 33 dN/dE/dt / erg/s) 33 2 2

32.5 32.5 log(E log(E 32 32

31.5 31.5

31 31

30.5 30.5

30 30

29.5 29.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 log(E / GeV) log(E / GeV)

FIG. 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 products 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 γ-ray absorption. The γ-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 η = 10−2.

-10 -10 wind cavity Fermi wind cavity -10.5 (WR 20a) -10.5 (Eta Car) HESS -11 -11

-11.5 -11.5 HESS

-12 -12

log(E^2dN/dE / erg/cm^2/s) log(E^2dN/dE / erg/cm^2/s) CTA CTA -12.5 -12.5

-13 -13

-13.5 -13.5

-14 -14 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0 1 2 3 4 5 6 log(E / GeV) log(E / GeV)

FIG. 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 γ-rays in the stellar radiation are included. The γ-ray spectrum observed by HESS from the direction of WR 20a binary system is shown by the dot-dashed line (Abramowski et al. 2011). In the case of Eta Carinae binary system, the Fermi-LAT spectrum is shown by triangles (Abdo et al. 2009) and the HESS upper limits (Abramowski et al. 2012b) are shown by the thin dot-dashed line. The γ-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 η = 3 × 10−3, in order to be consistent with the γ-ray flux reported by HESS from the open cluster Westerlund 2 (see thin dot-dashed line), and η = 10−2, in order to be consistent with the Fermi observations of Eta Carinae below 10 GeV. The broken thin dotted line show the level of sensitivity of the CTA (Bernl¨ohr et al. 2012).

The γ-ray and neutrino spectra, produced by these sec- binary system, R′, and their interaction distance R, ondary protons in the wind cavity, can be calculated by integrating the above formula over the spectrum of pro- Rc Rc γmax tons, their creation distance in the cavity measured from dNγ,ν ′ = dR dR dγ Z Z Z p dEγ,ν dt RBS R γmin dNp dNγ,ν(γp(R)) ′ , (15) dγpdRdR dt dEγ,ν 10

′ where dNp/dRdR dγpdt is given by Eq. 14, and the spec- and the second one extending up to ∼ 100 GeV (Farnier tra of γ-rays and neutrinos are calculated as described et al. 2011). The highest energy component show evi- below Eq. 12. dences of variability with the of the binary We have performed calculations of the γ-ray spectra system (Walter & Farnier 2011, Reitberger et al. 2012). produced by protons from neutrons decaying within the This component is expected to be produced within the wind cavity for the parameters of two considered binary binary system. On the other hand, the lower component systems (see thick solid curves in Fig. 5). These spectra seems to be steady. We compare the γ-ray spectrum ex- are clearly below the γ-ray spectra produced by protons pected in terms of our model from the wind cavity around directly extracted from nuclei. This effect is due to the the binary system in Fig. 6. The spectrum is normalized appearance of protons (from decaying neutrons) at a rel- to the observed lower energy component extending to a atively large distances from the binary system where the few GeV. Since the γ-ray emission produced within the density of the stellar wind is already low. On the other wind cavity is strongly absorbed in the stellar radiation, hand, these γ-ray spectra show much smaller absorption the γ-ray spectrum expected in our model in the TeV en- effects in the stellar radiation due to their production at ergy range is steep (spectral index close to -4, see Fig. 6). larger distances from the massive star. Therefore, this emission is clearly below the present up- per limit reported by the HESS Collaboration in the TeV energy range (Abramowski et al. 2012b). Moreover, due D. Confrontation with observations of specific to the steepness of this spectrum, future detection of this binary systems emission component by the CTA is rather problematic (Fig. 6). The γ-ray spectra produced in the wind cavity by two considered above populations of protons are compared VII. GAMMA-RAYS FROM PROTONS IN THE with the available observations of the two considered bi- OPEN CLUSTER nary systems in the GeV-TeV energy range and with the sensitivity of the planned CTA. As mentioned in the In- troduction, the TeV γ-ray source has been reported in In this section we calculate the γ-ray (and neutrino) the direction of the open cluster Westerlund 2 which spectra produced by protons which originate as a decay contains binary system WR 20a (Aharonian et al. 2007, products of neutrons within the wind cavity, but they Abramowski et al. 2011). The γ-ray spectrum of the are advected with the stellar wind into the surrounding source in the direction of this open cluster has the spec- open cluster. We also calculate the γ-ray emission from tral index 2.58 in the energy range ∼1-10 TeV. The na- relativistic protons which originate from the most ener- ture of this source is at present unknown. It is supposed getic neutrons decaying directly outside the wind cavity, that this emission can be related to the binary system i.e. within the open cluster. It is assumed that the open WR 20a, the (PWNe) around PSR cluster has the basic parameters of the order of, the den- −3 −4 J1022-5746 or maybe also to the dense molecular clouds sity of matter 10 cm , the magnetic field strength 10 present in this open cluster. We compare the γ-ray spec- G, and the radius 20 pc. As we show below, the com- trum expected from the wind cavity around the binary bination of these parameters determines the escape of system WR 20a with the above mentioned observations. protons from the open cluster and, as a consequence the The results are shown in Fig. 6. In order to be consis- γ-ray production rate and their spectra in collisions with tent with the TeV observations, reasonable value for the the matter of the open cluster. energy conversion efficiency from the stellar wind to rela- tivistic nuclei is required (∼ 5 × 10−3). According to our calculations, γ-rays produced in the wind cavity should A. Protons advected outside the wind cavity be mainly responsible for a part of this emission at the highest observed energies, i.e. ∼ 10 TeV. As we show A part of protons, which is advected with the stellar below, the lower energy part of the γ-ray emission from wind, can arrive up to the wind cavity border. They Westerlund 2 could be either produced by protons which can be injected into the dense open cluster surrounding escape from the wind cavity into dense regions of the the binary system. However, only protons from decaying open cluster, as considered in Sect. 7, or it comes from neutrons can still have large energies allowing them to the other sources present within the Westerlund 2 (e.g. produce the TeV γ-rays and neutrinos. Protons, from other massive binary systems or PWNe). direct disintegration of nuclei, appear close to the binary We also compare our calculations with the observations system and therefore suffer huge adiabatic energy losses. of the binary system Eta Carinae and the surrounding The spectrum of protons injected from the wind cavity dense complex . The source in this di- (with the radius Rc) into the open cluster can be calcu- rection has been detected in the GeV energies by the lated from, Agile (Tavani et al. 2009) and Fermi telescopes (Abdo Rc et al. 2009). γ-ray emission from this source shows two dNp(γp) dNp ′ = JdR , (16) components spectrum, first one extending to a few GeV Z ′ dγpdt RBS dγpdR dt 11

35 35

34.5 34.5

dN/dE / erg/s) 34 dN/dE / erg/s) 34 2 2

log(E 33.5 log(E 33.5

33 33

32.5 32.5

32 32

31.5 31.5

31 31 2.5 3 3.5 4 4.5 5 5.5 6 6.5 2.5 3 3.5 4 4.5 5 5.5 6 6.5 log(E / GeV) log(E / GeV)

FIG. 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). 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 WR 20a binary system (on the left) and Eta Carinae binary system (on the right). Density of matter in the open cluster determines the radius of the wind cavity (see −3 −3 Eq. 2), noc = 10 cm (thick curves) and noc = 100 cm (thin). The power in relativistic nuclei is normalized to 1% of the stellar wind power (given in Table 1).

′ where dNp/dγpdR dt is given by Eq. 13 and the Jacobian The time scale for collisions of protons with the matter ′ −1 14 is J = dγp(R )/dγp(Rc). is, τpp = (cσppncl) ≈ 10 /n10 s. We calculate the spectra of protons advected into the By comparing the diffusion time scale with collision open cluster for two considered binary systems (WR 20a time scale, we estimate critical energy of relativistic pro- and Eta Carinae). Two different values for the density tons, of matter within the open cluster, which determine the outer radius of the wind cavity, are assumed. The results int × 4 2 are shown in Fig. 7 (see dashed curves). As expected, γp <γp =7 10 R20B−4n10 (17) for denser matter within the open cluster (corresponding to smaller radius of the wind cavity) the spectra have below which they can interact efficiently within the open larger intensities and the maximum in the spectra are cluster. We assume that protons with such energies shifted to lower energies. These effects are due to the reaches steady state equilibrium in which the rate of pro- lower adiabatic energy losses in the case of wind cavities ton injection equals the rate of proton interaction. We with smaller radii. calculate the γ-ray and neutrino spectra produced by pro- In order to calculate the γ-ray and neutrino spectra tons with the spectra shown in Fig. 7 in the range limited produced by these protons in the open cluster, we have by Eq. 17. to estimate their residence time within the open clus- Note that the winds from the massive stars in the bi- ter, due to the diffusion process, and compare it with nary system do not change significantly the distribution the collisional time scale. We assume that protons dif- of the matter within the open cluster since the mass fuse in the turbulent medium of the open cluster with 3 swept-up by the stellar wind is Msur = 4Rcnoc/3 ≈ the rate well determined by the Bohm diffusion coeffi- ˙ 1/2 26 2 −1 90(M−5v3n10/T4) M⊙. This is only a small amount cient, D = R c/3 ≈ 3 × 10 γ /B− cm s , where B L 6 4 of the total mass of the open cluster which is typically the magnetic field strength within the open cluster is 3 4 −4 expected in the range 10 M⊙ to a few 10 M⊙. Boc = 10 B−4 G. Then, the average diffusion time scale of protons within the open cluster, with the char- The γ-ray and neutrino spectra produced by protons, acteristic dimension Roc = 20R20 pc, is estimated on, advected from the wind cavity, are calculated by integra- 2 12 2 tion of the above derived proton spectrum, τdif = Roc/2DB ≈ 7 × 10 R20B−4/γ6 s. The collision time of these protons can be estimated out −1 6 int from tp = (cnocσpp) ≈ 10 /n30 yrs, where the den- γp − dNγ,ν dNp(γp) dNγ,ν (γh) sity of surrounding matter is n = 30n cm 3. The in- = dγp (18) oc 30 dE dt Z dγ dt dE teraction process of these protons within the open cluster γ,ν γmin p γ,ν depends on the lifetime of the massive binary system and the diffusion time scale of protons from the open cluster. where dNp(γp)/dγpdt is given by Eq. (16). 12

B. Protons from neutrons decaying outside the open cluster Westerlund 2 is consistent with the positive wind cavity detection of this open cluster by the HESS Collaboration (Abramowski et al. 2011), provided that the parameter 2 The most energetic neutrons, extracted from nuclei R20B−4n10 ≤ 1.5 (see Fig. 8). Note that γ-rays pro- within the binary system, can decay directly outside the duced in this case are expected to contribute mainly to ∼ wind cavity, since their propagation distance Ln = γnτnc the energy range around 1 TeV. This is clearly below becomes comparable to the radius of the wind cavity. the energy range at which the γ-ray emission from the The spectrum of protons from decay of these neutrons is wind cavity is expected. γ-rays, expected from the open given by, cluster in terms of our model for Westerlund 2, are pre- dicted to be still detected by the CTA provided that the 2 dN (γ ) dN (γ ) −Rc parameter R B− n ≥ 0.15. p,cl p n,cl n γ τ c 20 4 10 = = N˙ ne ( n n ) , (19) dγpdt dγndt We have also compared the predictions of our model with the observations of the Carina Complex contain- where N˙ n = dN(γn)/dγndt is the spectrum of neutrons ing the Eta Carinae binary system. HESS Collabora- extracted from nuclei, Rcav is the radius of the wind cav- tion has derived an upper limit on the γ-ray flux from ity (see Eq. 2). This neutron spectrum has exactly the the extended source from this direction (Abramowski et same shape as the spectrum of accelerated nuclei, i.e. the al. 2012b), which is about a factor of five higher than the power law type with the spectral index equal to 2 (see upper limit on the point source towards the Eta Carinae Section. 3). It is assumed that Lorentz factors of neutrons itself. We have compared the calculated γ-ray spectra are equal to Lorentz factors of parent nuclei. Proton spec- with the HESS upper limit in Fig. 8. These spectra are tra, from neutrons decaying inside the open cluster (i.e. still consistent with the upper limit provided that the 2 outside the wind cavity), are shown for both considered value of the parameter R20B−4n10 ≤ 0.2. γ-rays pro- binary systems in Fig. 7 (dotted curves). Relative con- duced in terms of our model should contribute only to tribution of protons from these neutrons, in respect to the sub-TeV energy range. We conclude that the γ-ray protons advected from the wind cavity, depends on the emission, produced by relativistic protons in the Carina parameters defining the acceleration scenario, the wind Complex, is expected to be still detectable by the CTA of the companion stars and the parameters of the open provided that the open cluster is characterized by the 2 cluster. The largest contribution is expected in the case parameter R20B−4n10 ≥ 0.04. However, this γ-ray com- of binary systems containing massive stars with strong ponent is expected to extend only through the low energy surface magnetic field (large Lorentz factors of nuclei) range of the CTA sensitivity, i.e. at ∼100 GeV. and relatively weaker stellar winds (smaller radius of the wind cavity). Therefore, more neutrons should decay di- rectly within the open cluster (outside the wind cavity) VIII. NEUTRINOS FROM THE VICINITY OF in the case of the WR type stars than in the case of the BINARY SYSTEM most massive stars of the Eta Carinae type which have very large mass loss rates but weaker surface magnetic Detection of neutrinos, produced in hadronic interac- fields. tions between relativistic protons and the matter of the The γ-ray and neutrino spectra, produced by these stellar wind and/or open cluster, could provide additional protons, are calculated by integrating formula given by constraints on the high energy processes in the consid- Eq. 18. ered scenario. Therefore, we calculate the neutrino spec- tra from the wind cavity and the open cluster applying derived above spectra of relativistic protons in these re- C. Confrontation with observations of specific open gions. clusters The neutrino spectra from the wind cavity (on the left) and the open cluster (on the right) are shown in Fig. 9 We calculate the γ-ray spectra produced by protons for the WR 20a binary system (solid) and Eta Carinae in hadronic collisions with the matter of the open clus- binary system (dashed). They are obtained for the pa- ter, applying their diffusion and interaction model as de- rameters of the model as used for the corresponding γ-ray scribed above. As before, we consider the open clusters spectra shown above, i.e. for the energy conversion in- which contain the WR 20a and Eta Carinae binary sys- efficiencies as described in Fig. 6 and the distances to tems. The calculations of the γ-ray spectra are performed these binary systems equal to ∼ 2 kpc. These spectra for the same parameters of the acceleration scenario as are compared with the atmospheric neutrino background discussed for the γ-ray production in the wind cavity re- (ANB) and the upper limit on the neutrino flux from gions of these two binaries. The results are shown for discrete sources reported by the ANTARES Collabora- 2 two different values of the parameter R20B−4n10 which tion (Adrian-Martinez et al. 2012) and the 5 yr sensitiv- determines the conditions within the open cluster. ity of the IceTop + IceCube (Aartsen et al. 2013). The In the case of the open cluster containing the binary neutrino spectra, expected from these two binary sys- system WR 20a, the γ-ray spectrum expected from the tems immersed within the open clusters, are on the level 13

-10.5 -10.5 HESS open cluster open cluster -11 -11 (WR 20a) (Eta Carinae)

-11.5 -11.5 HESS -12 -12 log(E^2dN/dE / erg/cm^2/s) CTA log(E^2dN/dE / erg/cm^2/s) CTA -12.5 -12.5

-13 -13

-13.5 -13.5

-14 -14 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 log(E / GeV) log(E / GeV)

FIG. 8: Gamma-ray spectra produced by protons (from decaying neutrons) in the dense cluster around WR 20a and Eta Carinae binary systems. The escape of protons from the open cluster is described by assuming the Bohm diffusion prescription 2 and the parameter R20B−4n10 = 1.5 (solid curve) and 0.15 (dashed) for WR 20a binary, and 0.2 (solid) and 0.04 (dashed) for 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 η = 5 × 10−3 for WR 20a and 10−2 for Eta Carinae. of the atmospheric neutrino background. However, they the interaction of the binary system with the matter of are about an order of magnitude below the present upper the open cluster. It is postulated that nuclei (from he- limit of the flux from discrete sources by ANTARES col- lium to oxygen) can be efficiently accelerated within the laboration. It looks that nuclei are not energetic enough binary system. We show that these nuclei are disinte- in order to produce neutrino fluxes which could be po- grated in the dense stellar radiation and the matter of tentially detected by the Ice Cube telescope. We have the stellar wind injecting relativistic protons and neu- also calculated the expected neutrino flux produced by trons. The fate of these secondary particles is followed relativistic protons within the open cluster applying the in detail in the region of the stellar wind cavity and in normalization obtained from the comparison of the γ-ray the surrounding dense open cluster. We calculate the ex- fluxes with observations of these two open clusters (see pected γ-ray and neutrino emission produced in the in- Fig. 8). These neutrino fluxes are predicted on much teraction of these particles with the matter of the stellar lower level than those expected from the wind cavities wind and surrounding open cluster. of these binary systems. We conclude that considered The results of calculations are shown for the case of binary systems are not expected to produce detectable the two well known massive binary systems (WR 20a neutrino fluxes from the directions of the open clusters and Eta Carinae), which have been recently reported as Westerlund 2 and Carina Complex. Note however, that a γ-ray sources in the GeV-TeV energy range. Our calcu- neutrino fluxes should be larger if the specific open clus- lations show that the largest fluxes of γ-rays are produced ter contains many massive binary systems. Therefore, by protons close to the binary system where the density our results do not completely exclude future detection of of stellar wind is the largest. However, the absorption neutrinos from massive stellar clusters at distances of a of gamma-rays in the stellar radiation field has the im- few kpc from the vicinity of the . portant effect on the gamma-ray spectrum, produced by protons extracted directly from the nuclei. Therefore, the γ-ray spectra produced in these regions are clearly IX. CONCLUSIONS steeper than the injection spectra of protons (equal to the spectrum of accelerated nuclei). On the other hand, Star forming regions contain plenty of extreme objects, γ-ray spectra, from hadronic collisions of protons which such as massive binary systems and remnants of their are decay products of neutrons extracted form nuclei, are evolution (supernova remnants, PWNe, X-ray binaries). mainly produced at larger distances from the binary sys- These objects might be responsible for the acceleration tems since neutrons move ballisticaly through the wind of hadrons to TeV-PeV energies. In fact, GeV-TeV γ- cavity and decay at relatively large distances. They in- ray emission has been already detected from a few open teract with the matter of the wind with lower density clusters. In this paper we concentrate on the processes but do not suffer strong absorption in the stellar radia- due to the presence of massive binary systems in dense tion field. In total, these γ-ray spectra have clearly lower regions (open clusters). We have formulated a model for level than spectra produced in previous process. 14

-10 -10 ANB ANB ANTARES ANTARES -10.5 -10.5

-11 -11

-11.5 -11.5 IceCube IceCube -12 -12 log(E^2dN/dE / erg/cm^2/s) log(E^2dN/dE / erg/cm^2/s)

-12.5 -12.5

-13 -13

-13.5 -13.5 wind cavity open cluster

-14 -14 2.5 3 3.5 4 4.5 5 5.5 2.5 3 3.5 4 4.5 5 5.5 log(E / GeV) log(E / GeV)

FIG. 9: Spectra of neutrinos (SED) produced by hadrons in the above discussed scenarios from the wind cavity (left) and from 5 2 the open cluster (right). The minimum energy of escaping protons is equal to 10 GeV, corresponding to R20B−4n10 = 1.5, 4 2 for WR 20a (solid) and 1.5 × 10 GeV, corresponding to R20B−4n10 = 0.2 for Eta Carinae (dashed). The neutrino spectra are produced by protons which are the decay products of neutrons extracted from nuclei in their collisions with stellar wind. The atmospheric background (ANB) in a viewcone of 1◦ radius around the source is shown by the thin dashed curves (Abbasi et al. 2011), the 5 yr sensitivity of the IceTop + IceCube is shown by the thin dotted line (Aartsen et al. 2013), and the ANTARES upper limit on the point sources is shown by dot-dashed line (Adrian-Martinez et al. 2012). The proton spectra are normalized in this same way is described for the γ-ray spectra.

Significant amount of protons, which appeared in the of this model, with the observations of the open clusters wind cavity as a result of decay of neutrons, is advected containing binary systems WR 20a (Westerlund 2) and with the stellar wind to the open cluster. We calculate Eta Carinae (Carina Complex). It is concluded that pro- the spectra of these protons taking into account their tons within the specific open cluster can contribute to the adiabatic and collisional energy losses. Protons, directly observed TeV γ-ray spectrum (mainly at its lower energy extracted from nuclei, cannot be advected to the open part) observed from Westerlund 2. This γ-ray emission cluster with large energies due to the huge adiabatic en- is consistent with the upper limits on the TeV flux from ergy losses. Therefore, the radiation produced by them Carina Complex. We also determine the minimum con- can be safely neglected. Another population of relativis- straints on the parameters of these two clusters for which tic protons is provided by the most energetic neutrons they will be detectable by the planned CTA. which can decay directly into the open cluster, i.e. out- We have also calculated the neutrino spectra expected side the wind cavity. We take these protons into account in this model for these two binary systems. Unfortu- when calculating the radiation produced in the open clus- nately, these neutrino fluxes are about two orders of mag- ter. The fate of relativistic protons in the open cluster nitude below the present upper limit on neutrino emission depends on the cluster parameters. Protons diffuse out- from discrete sources provided by ANTARES Collabora- side the cluster and interact with the cluster matter. We tion (Adrian-Martinez et al. 2012). These neutrinos will show, that in the case of Bohm diffusion approximation, be also difficult to observe with the IceCube telescope the escape/interaction conditions of protons depend on since their fluxes, produced in the wind cavity regions, 2 the parameter R20B−4n10, which is the combination of are comparable to the atmospheric neutrino background. the parameters characterizing the open cluster, its radius, They are clearly below this background in the case of magnetic field strength and density of matter. We show neutrinos produced in the open cluster itself. that for likely parameters of the open cluster, protons with largest expected energies escape from the cluster In fact many massive binary systems can be present at practically without interaction with the matter. Only the same time in a specific open cluster. Therefore, in lower energy protons are captured in the open cluster principle larger γ-ray and neutrino fluxes might be ex- and lose energy on the production of γ-rays and neutri- pected from specific open clusters than calculated here nos. Note that protons escaping from the clusters are fluxes from isolated binary systems. However the envi- expected to have Lorentz factors in the range ∼ 10(4−5). ronment of the open cluster with many massive binary Therefore, we expect that open clusters, containing mas- systems might be very complicated due to likely inter- sive binary systems, might become interesting sources of action between different wind cavities. Therefore, simple relativistic protons in the . re-scaling of the γ-ray and neutrino fluxes by the number of massive binaries in specific open cluster seems to be We confronted the γ-ray emission, expected in terms not adequate. A more complicated scenario should be 15 considered in such a case. ish Narodowe Centrum Nauki through the grant No. 2011/01/B/ST9/00411.

Acknowledgments

We would like to thank the Referee for valuable comments. This work is supported by the Pol-

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