A&A 407, 1–6 (2003) Astronomy DOI: 10.1051/0004-6361:20030929 & c ESO 2003 Astrophysics Neutrinos from the pulsar wind nebulae W. Bednarek Department of Experimental Physics, University of Ł´od´z, ul. Pomorska 149/153, 90-236 Ł´od´z, Poland Received 13 February 2003 / Accepted 20 May 2003 Abstract. In a recent paper we calculated the γ-ray spectra from pulsar wind nebulae (PWNe), assuming that a significant amount of the pulsar rotational energy is converted into relativistic nuclei. These nuclei accelerate leptons which are responsible for most of the observed electromagnetic emission from PWNe. A small part of nuclei also interact with the matter of the supernova producing γ-rays, which can also contribute to the observed spectra of young nebulae. Here we calculate the spectra of neutrinos from the interaction of nuclei inside the nebula and the expected neutrino event rates in the 1 km2 neutrino detector from the Crab Nebula (PSR 0531+21), the Vela SNR (PSR 0833-45), G 343.1-2.3 (PSR 1706-44), MSH15-52 (PSR 1509-58), 3C 58 (PSR J0205+6449), and CTB80 (PSR 1951+32). It is shown that only the Crab Nebula can produce neutrino event rate above the sensitivity limit of the 1 km2 neutrino detector, provided that nuclei take most of the rotational energy lost by the pulsar. The neutrino event rate expected from the Vela SNR is comparable to that of the Crab Nebula but these neutrinos are less energetic and are emitted from a much larger region on the sky. Therefore it may be difficult to subtract the Vela SNR signal from the higher background of atmospheric neutrinos. Key words. ISM: supernova remnants – stars: pulsars: general – radiation mechanisms: non-thermal 1. Introduction Recently we have considered a more general model for the hadronic and leptonic processes inside the PWNe, which are The possibility that hadronic processes can contribute to the based on the proposition that a significant part of the pulsar ro- γ observed -ray emission from the PWNe has been considered tational energy is taken up by relativistic nuclei (Arons and col- in recent years by e.g. Cheng et al. (1990) and Aharonian & laborators, e.g. Arons 1998). Our purpose was to calculate the Atoyan (1996). Following these works and earlier results (e.g. γ-ray spectra from well-known PWNe. From the comparison Berezinsky & Prilutsky 1978), we discussed a model for the of the calculations with the observations of these γ-ray nebu- production of radiation in hadronic processes with the appli- lae, we derived some free parametrs of the considered model in cation to the very young PWNe (Protheroe et al. 1998; Beall order to predict the γ-ray and neutrino fluxes from other neb- γ / & Bednarek 2002). In these papers, the -ray and or neutrino ulae, which may become potential targets for the next genera- fluxes were estimated from the interaction of nuclei, injected tion of γ-ray and neutrino telescopes. The calculations of the γ- by the pulsar, with the matter and soft radiation of the super- ray spectra from leptonic and hadronic processes were reported nova remnant during its early phase of development, i.e. within in the accompanying paper by Bednarek & Bartosik (2003, the first few years. A general model like this has recently be- BB03). The neutrino spectra are calculated in the present pa- come very popular, finding its application in the estimation of per. Most of the earlier calculations of the γ-ray fluxes from the γ neutrino fluxes from the -ray bursts in terms of the supra- PWNe, which refer mainly to the Crab Nebula (e.g. De Jager & nova model (e.g. Guetta & Granot 2002; Razzaque et al. 2002; Harding 1992; Aharonian & Atoyan 1995; De Jager et al. 1996; Dermer & Atoyan 2003), which postulates the formation of a Hillas et al. 1998), were done based only on the leptonic ori- very fast pulsar during supernova explosion (Vietri & Stella gin for this emission. The calculations of the γ-ray fluxes from 1998). In another paper the contribution of nuclei from the pul- other nebulae are available only for a few objects, e.g. nebu- γ sar to the -ray (and neutrino) spectrum was also calculated lae around PSR 1706-44 (Aharonian et al. 1997), PSR 1509-58 for the best known example of an older supernova remnant, i.e. (Du Plessis et al. 1995), Vela pulsar (De Jager et al. 1996). the Crab Nebula (Bednarek & Protheroe 1997). Recently, the neutrino flux from the Crab Nebula has been independently es- The neutrino fluxes from a few PWNe have recently been timated by Amato et al. (2003). The authors predict a few to re-scaled from the observed TeV γ-ray fluxes by Guetta & several neutrino events in a 1 km2 detector per year from this Amato (2002), based on the simple assumption that in all these source. nebulae the γ-rays above 2 TeV are produced in the decay of π ◦, which originate in hadronic processes. This assumption is in e-mail: [email protected] contradiction to the popular opinion on the relative importance Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20030929 2 W. Bednarek: Neutrinos from the pulsar wind nebulae of the leptonic and hadronic processes in PWNe and also with The assumption that the pulsar wind ram pressure is balanced the results presented in this paper. by the total pressure inside the nebula is different from that made in the previous paper (BB03) in which the wind pres- sure is balanced only by the magnetic field pressure. In fact 2. The model for high energy processes this modification changes the location of the pulsar wind shock in the pulsar wind nebula for very young nebulae but does not influence the calculated The details of the model for high energy processes in the PWNe neutrino fluxes from them since the escape conditions of heavy are described in our first paper (BB03). For consistency we nuclei from the nebula do not change significantly. repeat here its main features. The evolution of the supernova Knowing how the magnetic field depends on the distance remnant, containing an energetic pulsar, is described following from the pulsar in the pulsar wind zone, we can estimate the the main points of the picture considered soon after the discov- strength of the magnetic field in the shock region from ery of pulsars by Ostriker & Gunn (1971) and Rees & Gunn √ 3 Rpul Rlc (1974). Let us assume that when the explosion occurs, the ex- Bsh = σBpul , (7) Rlc Rsh pansion velocity of the nebula at its inner radius is V 0,SN and its initial mass is M0,SN. However, this expansion velocity can where σ is the ratio of the magnetic energy flux to the particle increase due to the additional supply of energy to the nebula by energy flux from the pulsar at the location of the pulsar wind the pulsar and can also decrease due to the accumulation of the shock, Rpul and Bpul are the radius and the surface magnetic surrounding matter. We take these processes into account when field of the pulsar, respectively. The evolution of σ with the pa- determining the radius of the nebula at the specific time, t,by rameters of the pulsar is found by interpolating between the val- using the energy conservation, ues estimated for the Crab pulsar, ∼0.003, and for the Vela pul- ∼ 2 sar, 1 (see Eq. (16) and below in Bednarek & Protheroe 2002 M t V2 t M , V t SN( ) SN( ) 0 SN 0,SN for details). = + Lem(t )dt , (1) 2 2 0 It is likely that a significant part of the rotational energy where of the pulsar, transfered through the shock radius R sh,isinthe form of relativistic heavy nuclei. In fact, such an assumption = 2 6Ω4/ 3 ≈ . × 45 2 −4 −1, Lem(t) Bs Rs 6c 1 3 10 B12 Pms erg s (2) can explain morphological features of the Crab Nebula and also the appearance of extremely energetic leptons inside the nebula is the pulsar energy loss on emission of dipole electromag- accelerated as a result of the resonant scattering of positrons netic radiation, Ω=2π/P, and the period of the pulsar P = and electrons by heavy nuclei (Hoshino et al. 1992; Gallant 10−3P s changes with time according to ms & Arons 1994). From the normalization to the observations of 2 = 2 + × −9 2 , the Crab pulsar, Arons and collaborators (see e.g. Arons 1998) Pms(t) P0,ms 2 10 tB12 (3) postulate that the Lorenz factors of iron nuclei in the pulsar’s 12 where P0,ms is the initial period of the pulsar and B = 10 B12 G wind should be the strength of its surface magnetic field. The expanding nebula γ ≈ . Φ / 2, increases the mass from the surrounding medium according to 1 0 3Ze open mic (8) where mi and Ze are the mass and charge of√ the iron nu- 4 3 MSN(t) = M0,SN + πρsurR (t), (4) clei, c is the velocity of light, and Φ = E /c is the 3 Neb open em total electric potential drop across the open magnetosphere. ρ where sur is the density of the surrounding medium and R Neb Equation (8) postulates that a pulsar with a specific period is the outer radius of expanding envelope at the time, t, which and a surface magnetic field accelerates nuclei monoenerget- depends on the expansion history of the nebula, ically.