We investigate the consequences of the acceleration of heavy nuclei (e.g.
iron nuclei) by the Crab pulsar. Accelerated nuclei can photodisintegrate in
collisions with soft photons produced in the pulsar's outer gap, injecting
energetic neutrons which decay either inside or outside the Crab Nebula. The
protons from neutron decay inside the nebula are trapped by the Crab Nebula
magnetic field, and accumulate inside the nebula producing gamma-rays and
neutrinos in collisions with the matter in the nebula. Neutrons decaying
outside the Crab Nebula contribute to the Galactic cosmic rays. We compute the
expected fluxes of gamma-rays and neutrinos, and find that our model could
account for the observed emission at high energies and may be tested by
searching for high energy neutrinos with future neutrino telescopes currently
in the design stage.Comment: 8 pages, 4 figures, LaTeX uses revtex.sty, submitted to Phys. Rev.
  Let

A. D. Erlykin

A. H. Hillas

A. M. Atoyan

C. Ho

D. A. Lewis

F. Aharonian

F. W. Stecker

G. H. Rieke

G. Vacanti

J. E. Grindlay

J. J. Hester

K. Davidson

K. S. Cheng

M. Amenomori

M. Hoshino

M. J. Chodorowski

O. C. de Jager

P. Goldreich

P. L. Nolan

P. Lipari

R. J. Gould

R. J. Protheroe

R. N. Manchester

R. P. Much

S. Karakuła

S. L. Shapiro

T. C. Weekes

W. Bednarek

W. Kundt

W. M. Cheung

W. M. Kwok

Y. A. Gallant

Physical Review Letters

English

arXiv

Crossref

Gamma Rays and Neutrinos from the Crab Nebula Produced by Pulsar Accelerated Nuclei

We investigate the consequences of the acceleration of heavy nuclei (e.g., iron nuclei) by the Crab pulsar. Accelerated nuclei can photodisintegrate in collisions with soft photons produced in the pulsar's outer gap, injecting energetic neutrons which decay either inside or outside the Crab nebula. The protons from neutron decay inside the nebula accumulate, producing gamma rays and neutrinos in collisions with the matter in the nebula. Neutrons decaying outside contribute to the galactic cosmic rays. We compute the expected fluxes of gamma rays and neutrinos, and find that our model could account for the observed emission at high energies and may be tested by searching for high energy neutrinos with future neutrino telescopes currently in the design stage.W. Bednarek and R. J. Prothero

Bednarek, W.

Protheroe, R.

Adelaide Research & Scholarship

PUBLISHED VERSION     Bednarek, W.; Protheroe, Raymond John  Gamma rays and neutrinos from the crab nebula produced by pulsar accelerated nuclei Physical Review Letters, 1997; 79(14):2616-2619  ©1997 American Physical Society  http://link.aps.org/doi/10.1103/PhysRevLett.79.2616             http://link.aps.org/doi/10.1103/PhysRevD.62.093023                         http://hdl.handle.net/2440/12772    PERMISSIONS http://publish.aps.org/authors/transfer-of-copyright-agreement   “The author(s), and in the case of a Work Made For Hire, as defined in the U.S. Copyright Act, 17 U.S.C. §101, the employer named [below], shall have the following rights (the “Author Rights”): [...] 3. The right to use all or part of the Article, including the APS-prepared version without revision or modification, on the author(s)’ web home page or employer’s website and to make copies of all or part of the Article, including the APS-prepared version without revision or modification, for the author(s)’ and/or the employer’s use for educational or research purposes.”    13th May 2013  VOLUME 79, NUMBER 14 P HY S I CA L REV I EW LE T T ER S 6 OCTOBER 199726Gamma Rays and Neutrinos from the Crab Nebula Produced by Pulsar Accelerated NucleiW. Bednarek* and R. J. ProtheroeDepartment of Physics and Mathematical Physics, University of Adelaide, Adelaide, SA 5005, Australia(Received 7 April 1997)We investigate the consequences of the acceleration of heavy nuclei (e.g., iron nuclei) by the Crabpulsar. Accelerated nuclei can photodisintegrate in collisions with soft photons produced in the pulsar’souter gap, injecting energetic neutrons which decay either inside or outside the Crab nebula. Theprotons from neutron decay inside the nebula accumulate, producing gamma rays and neutrinos incollisions with the matter in the nebula. Neutrons decaying outside contribute to the galactic cosmicrays. We compute the expected fluxes of gamma rays and neutrinos, and find that our model couldaccount for the observed emission at high energies and may be tested by searching for high energyneutrinos with future neutrino telescopes currently in the design stage. [S0031-9007(97)04179-3]PACS numbers: 98.70.Sa, 95.85.Ry, 97.60.Gb, 98.70.RzThe Crab nebula is a well established g-ray sourcewith a spectrum extending up to at least TeV energies[1]. Its emission below a few tens of MeV is interpretedas synchrotron emission by ,1015 16 eV electrons in theCrab nebula magnetic field of strength ,3 3 1024 G [2].These models interpret the emission at higher energies asbeing due this same population of electrons by inverseCompton scattering (ICS) of synchrotron photons (SSCmodels). The TeV g rays might also originate near thelight cylinder as a result of ICS of infrared photonsfrom another outer gap [3]. The possibility of hadronicprocesses has also been considered by Cheng et al. [4] whoassumed that relativistic protons accelerated in the Crabpulsar outer gap interact with the matter inside the nebula,and noted that this may result in TeV g rays.In this Letter, we analyze the consequences of accel-eration of heavy nuclei in the pulsar magnetosphere as apossible mechanism of energetic radiation from the Crabnebula. The importance of photodisintegration of nucleiis determined by the reciprocal mean free path which wecalculate using cross sections of Karakuła and Tkaczyk [5]and show in Fig. 1 for nuclei during propagation in the ra-diation field supposed to be present in the outer gap of theCrab pulsar. Ho [6] has shown that the total luminosityand spectrum of the outer gap radiation is not strongly de-pendent on P. For P ­ 33 ms we adopt the photon num-ber density given by Eq. 7.1 in Paper II of Cheng et al.[7], and for other periods we scale this by r23LC. We as-sume this radiation is produced by cascading due to elec-trons and positrons accelerated in the gap, and so is highlyanisotropic and directed across the gap (in both directions).The dimension of the outer gap is of the order of the ra-dius of the light cylinder, lgap ø rLC ­ cyV. For thecase of the Crab pulsar, rLC ø 1.5 3 108 cm, and it is evi-dent from Fig. 1 that multiple photodisintegrations of pri-mary Fe nuclei will occur provided they can be acceleratedto Lorentz factors above ,103. We have also computedthe mean interaction length for pion photoproduction us-ing the cross section given by Stecker [8], and the energyloss length for pair production using the approximations16 0031-9007y97y79(14)y2616(4)$10.00given by Chodorowski et al. [9]. The results are shown inFig. 1, and it is clear that these latter processes are not im-portant loss mechanisms compared to photodisintegration.We assume that Fe nuclei can escape from the polarcap surface of the Crab pulsar, and move along magneticfield lines to enter the outer gap where they can beaccelerated in the outer gap potential as in the model ofCheng et al. [7] and Ho [6]. The nuclei accelerated inthe outer gap will interact with photons either producingsecondary e6 pairs (with negligible loss of energy) orextracting a nucleon. The pairs could eventually saturatethe electric field of the gap, although this is far fromcertain. We shall assume that for some reason the fieldis not shorted. Possibilities include: (a) Nuclei, havingmuch larger Larmor radii and much lower synchrotron andcurvature losses than electrons, more easily drift across themagnetic field lines away from the region of the gap wherethey had produced pairs; (b) the secondary e6 pairs mayFIG. 1. Reciprocal mean free paths for photodisintegration ofnuclei with mass numbers, A ­ 56, 40, 32, 24, 16, 8, and 4(full curves from the top) in the radiation field of the Crabpulsar’s outer gap as a function of the Lorentz factor of thenuclei. The reciprocal mean free path for pion photoproduction(dotted curve) and the energy loss length for e6 pair production(dashed curve) by iron nuclei are also shown.© 1997 The American Physical SocietyVOLUME 79, NUMBER 14 P HY S I CA L REV I EW LE T T ER S 6 OCTOBER 1997not be able to saturate the electric field in the outer gapwhich is close to the light cylinder since the Goldreichand Julian [10] density tends to infinity where the gapapproaches the light cylinder.In order to obtain the energy spectrum of neutrons ex-tracted from Fe nuclei, Nnsgnd, we simulate their accelera-tion and propagation through the outer gap using a MonteCarlo method. To obtain the rate of injection of neutronsper unit energy we multiply Nnsgnd by the number of Fenuclei injected per unit time, ÙNFe, which can be simply re-lated to the total power output of the pulsar LCrabsB, Pd[11],ÙNFe ­ jLCrabsB, PdyZFsB, Pd , (1)where j is the parameter describing the fraction of the totalpower taken by relativistic nuclei accelerated in the outergap, Z ­ 26 is the atomic number of Fe, B is the surfacemagnetic field, P is the pulsar’s period, andFsB, Pd ø 5 3 1016µB4 3 1012 G¶ µP1 s¶4y3V (2)is the potential difference across the outer gap [4]. Weassume B ­ 4 3 1012 G.Soon after the supernova explosion, when the nebulawas relatively small, nearly all energetic neutrons wouldbe expected to decay outside the nebula. However, at earlytimes we must take account of collisions with matter. Theoptical depth may be estimated from tnH ø sppnHr ø8.6 3 1014M1y228 t22, where M ­ M1Mfl is the massejected during the Crab supernova explosion in unitsof solar masses, r ­ yt, nH ­ Mys4y3pr3mpd is thenumber density of target nuclei, and y ­ 108y8 cm s21 isthe expansion velocity of the nebula. Note that tnH ­ 1at t ø 0.93M1y21 y218 yr, and that in this paper we consideronly interactions in the ejecta and have neglected swept-upinterstellar matter.We estimate the evolution of the Crab pulsar’s periodfrom birth to the present time taking account of magneticdipole radiation energy losses and gravitational energylosses for an ellipticity of 3 3 1024 [12]. Magnetic dipolelosses determine the pulsar period at present, but the initialperiod is determined largely by gravitational losses and isprobably shorter than ,10 ms. Hence, we consider twoinitial periods, 5 and 10 ms.The spectrum of protons from neutron decay outsidethe Crab nebula is given byNoutp sgp , tCNd ­Z tCN0dt ÙNFestdNnsgp , td3 e2tnH stde2ytCNycgptn , (3)where tn ø 900 s is the neutron decay time, and we makethe approximation that the Lorentz factor of protons isequal to that of parent neutrons, gp ø gn.For the spectrum of protons injected inside the Crabnebula we must take account of proton-proton collisionsand adiabatic energy losses due to the expansion of thenebula. The Lorentz factor of these protons at time t afterthe explosion such that their present Lorentz factor is gpis given bygpstd ø gpst 1 tCNd2tKtppstd, (4)where tppstd is the optical depth for collision of protonswith matter between t and tCN, and is given by tppstd ø1.3 3 1017M1y238 st22 2 t22CNd, and K ø 0.5 is the inelas-ticity coefficient in proton-proton collisions.Since we are interested in protons interacting inside thenebula at the present time, we must also include thoseneutrons which decayed at locations outside the nebulaat time t but which will be inside the nebula at timetCN. Taking account of all these effects, we arrive at theformula below for the proton spectrum inside the nebula attime tCN,Ninp sgp , tCNd ­ g21pZ tCN0dt ÙNFestde2tnH std(Nnfgpstd, tggpstd h1 2 expf2ytycgpstdtngj1Z tCNtdt0 Nnfgpst0d, tggpst0dy expf2yt0ycgpst0dtngcgpst0dtn). (5)The first term gives the contribution from neutrons decay-ing initially inside the nebula while the second term givesthe contribution from neutrons decaying at points initiallyoutside the nebula which will be inside the nebula at timetCN. Using the minimum diffusion coefficient we esti-mate the typical diffusion distance during time tCN forprotons with gp ­ 105 in a magnetic field of the orderof B ­ 5 3 1026 G to be comparable to the radius of theCrab nebula. Hence, in Eq. (5) we have assumed that pro-tons from neutrons decaying inside the nebula will remaininside the nebula.The diffusion distances discussed above also suggestthat even protons from neutrons decaying initially outsidethe nebula may eventually be captured by the nebula asit expands, and this is what we have assumed in Eq. (5)(second term). However, it is possible that energetic pro-tons from neutrons decaying outside the nebula may haveexerted sufficient pressure on the surrounding gas suchthat it expanded rapidly together with the energetic protongas, reducing the probability of capture of energetic pro-tons by the nebula. If this occurred, it would have had theeffect of reducing the g-ray and neutrino fluxes, and we2617VOLUME 79, NUMBER 14 P HY S I CA L REV I EW LE T T ER S 6 OCTOBER 1997FIG. 2. Spectra of protons from the decay of neutrons injectedby the Crab pulsar inside and outside the Crab nebula assumingM1 ­ 3 for the following parameters: P0 ­ 10 ms, and Crabnebula radius rCN ­ 1 pc (dot-dashed curve) and 2 pc (dashedcurve), and for P0 ­ 5 ms and rCN ­ 1 pc (full curve). Thedotted curve shows the effect for P0 ­ 5 ms and rCN ­ 1 pcof no capture by the nebula of p’s from n’s decaying outside it.shall investigate this possibility in an approximate way byneglecting the second term in Eq. (5).We compute separately the spectra of protons fromneutrons decaying inside and outside the Crab nebula. InFig. 2 proton spectra are shown for two initial periods, 5and 10 ms, and present nebula radii of 1 and 2 pc. Protonsfrom neutrons decaying outside the present nebula radiuswill typically have high energies and diffuse rapidly, thusescaping to become galactic cosmic rays. In the case ofrCN ­ 1 pc and P0 ­ 5 ms we also show the result forprotons inside the nebula for the case where there is nocapture of energetic protons during nebula expansion [i.e.,neglecting the second term in Eq. (5)].The protons which have accumulated inside the Crabnebula since the pulsar was formed (i.e., with spectra la-beled “inside” in Fig. 2) can produce observable fluxesof g rays and neutrinos. We compute the expected g-ray spectra for five different models, taking various ini-tial pulsar periods, present sizes, and masses of the Crabnebula, and whether or not there is capture of energeticprotons as a result of nebula expansion. The fluxes maypossibly be enhanced if protons are efficiently trapped bythe dense filaments as suggested by Atoyan and Aharo-nian [13]. Filaments with density ,500 cm23 are presentin the Crab nebula [14]. Therefore we introduce an ef-fective density experienced by the protons inside nebula,neffH ­ mnH , where nH is defined above, and the parame-ter m takes into account the possible effects of proton trap-ping by the filaments. The g-ray spectra are computed interms of a scaling model [15], and the photon fluxes ex-pected at the Earth are shown in Fig. 3 for jm ­ 1, andare compared with observations of the Crab nebula above0.2 TeV. Results are shown for models I to V having P0,rCN, and M1 as specified in Table I, and for a distance to2618FIG. 3. Spectra of g rays from interactions of protons withmatter inside the Crab nebula for the different proton spectrashown in Fig. 2 and for the different models of the nebula (I–V) considered in the text. Observations: Whipple Observatory[16] (dotted line and error box); THEMISTOCLE [17] (1);and CANGAROO [18] (solid line and error box). Upper limitsfrom various experiments mentioned in Ref. [19]: T—Tibet,H—HEGRA, C—CYGNUS, and U—CASA-MIA.the Crab nebula of 1830 pc [14]. Model V is the sameas model I except that there is no capture of energetic pro-tons by the nebula as it expands, and as expected the fluxesare lower than for model I. Comparison with the Whippleobservations at 10 TeV allows us to place constraints onthe free parameters of the model, and upper limits on jmwhich are given in Table I as sjmdg . Note that it is usu-ally argued for the standard pulsar model that the rate ofinjection of Fe nuclei into the pulsar magnetosphere shouldnot cause the charge density to exceed the Goldreich andJulian density [10]. In the case of no additional currentsflowing through the magnetosphere, this condition con-strains the value of j to j ø 0.1 for the Crab pulsar withperiod 33 ms. However, in the presence of additional cur-rents the value of j can be higher.The question of the importance of hadronic interactionsin the Crab nebula can be settled by the detection of aneutrino signal from the Crab. In Fig. 4 we show theneutrino spectrum produced in collisions of protons withmatter inside the Crab nebula and compare this with theatmospheric neutrino background flux within 1– of thesource direction [20]. It is clear that neutrino detectorswith good angular resolution should be able to detectTABLE I. Model parameters and limits on jm.Model I II III IV VP0 (ms) 5 10 10 10 5rCN (pc) 1 2 2 1 1M1 3 3 10 3 3Nebula captures p’s yes yes yes yes nosjmdg at 10 TeV 0.63 6.9 2.0 1.0 3.2sjmdn at 10 TeV 0.22 1.8 0.54 0.29 0.87VOLUME 79, NUMBER 14 P HY S I CA L REV I EW LE T T ER S 6 OCTOBER 1997FIG. 4. Spectra of neutrinos (nm 1 n¯m) expected for thedifferent models (I–V) considered in the text. The atmosphericneutrino background [20] within 1– of the source is indicatedby the hatched band which shows the variation with angle:horizontal (upper bound), vertical (lower bound).neutrinos at 10 TeV from the Crab nebula if jm is greaterthan sjmdn given in Table I. Note that in all casessjmdn , sjmdg and so the possibility of n detection isallowed by the existing g-ray observations.In the present paper we have not considered those nu-clei which had survived propagation through the outergap radiation field and were injected into the inner neb-ula region following magnetic field lines. These nuclei(and protons) are expected to accumulate in the inner partof the Crab nebula where the magnetic fields are ,2 31023 G [21]. The diffusion distance during tCN is ,0.3 pcfor gA ­ 106, and so most nuclei will probably be con-fined to the inner part of the Crab nebula where there isno evidence of dense matter [14] (other than the neutronstar). Hence, we may be justified in neglecting the contri-bution of such nuclei to the g-ray and neutrino productionby hadronic collisions in comparison with the contributionfrom interactions of protons from neutron decay. How-ever, some fraction of the energy of these nuclei could betransferred to very high energy electrons by resonant scat-tering [22]. Such electrons might then produce additionalg rays by the SSC process as in the models discussed inRef. [2]. Hence, we suggest that the complex Crab nebulaspectrum may, in fact, be formed as a result of both pro-cesses, i.e., SSC and as a result of pulsar acceleration ofnuclei discussed here.Another consequence of our model is that particles (nu-clei and protons from neutron decay) will also be injectedby the Crab pulsar and other pulsars into the galactic cos-mic rays; this may affect the cosmic ray spectrum and com-position. It is worth noting that the energy distribution ofthe protons from decay of neutrons outside the Crab neb-ula peaks at ,1015 eV (see Fig. 2), which is close to theenergy of the knee in the cosmic ray spectrum. This isparticularly interesting as the possibility of a single sourceof cosmic rays in the range 1015 to 1016 eV has been dis-cussed recently by Erlykin and Wolfendale [23].W. B. thanks the University of Adelaide for hospitalityduring his visit. This research is supported by a grantfrom the Australian Research Council.*Permanent address: University of Łódz´, 90-236 Łódz´,ul. Pomorska 149/153, Poland.[1] P. L. Nolan et al., Astrophys. J. 409, 697 (1993); R. P.Much et al., Astron. Astrophys. 299, 435 (1995); O.C. deJager et al., Astrophys. J. 457, 253 (1996); T. C. Weekeset al., Astrophys. J. 342, 379 (1989); G. Vacanti et al.,Astrophys. J. 337, 467 (1991).[2] R. J. Gould, Phys. Rev. Lett. 15, 577 (1965); G. H. Riekeand T. C. Weekes, Astrophys. J. 155, 429 (1969); J. E.Grindlay and J. A. Hoffman, Astrophys. Lett. 8, 209(1971); W. Kundt and E. Krotschek, Astron. Astrophys.83, 1 (1980); O.C. de Jager and A.K. Harding, Astro-phys. J. 396, 161 (1992); F. Aharonian and A. Atoyan,Astropart. Phys. 3, 275 (1995).[3] W.M. Kwok, K. S. Cheng, and M.M. Lau, Astrophys.J. 379, 653 (1991); W.M. Cheung and K. S. Cheng,Astrophys. J. 413, 694 (1993).[4] K. S. Cheng, T. Cheung, M.M. Lau, K.N. Yu, and W.M.Kwok, J. Phys. G 16, 1115 (1990).[5] S. Karakuła and W. Tkaczyk, Astropart. Phys. 1, 229(1993).[6] C. Ho, Astrophys. J. 342, 396 (1989).[7] K. S. Cheng, C. Ho, and M. Ruderman, Astrophys. J. 300,500 (1986); 300, 522 (1986).[8] F.W. Stecker, Phys. Rev. Lett. 21, 1016 (1968).[9] M. J. Chodorowski, A.A. Zdziarski, and M. Sikora,Astrophys. J. 400, 181 (1992).[10] P. Goldreich and W.H. Julian, Astrophys. J. 157, 869(1969).[11] R. N. Manchester and J. H. Taylor, Pulsars (Freeman,San Francisco, 1977).[12] S. L. Shapiro and S. L. Teukolsky, Black Holes, WhiteDwarfs and Neutron Stars (Wiley, New York, 1983).[13] A.M. Atoyan and F. A. Aharonian, Mon. Not. R. Astron.Soc. 278, 525 (1996).[14] K. Davidson and R.A. Fesen, Annu. Rev. Astron. Astro-phys. 23, 119 (1985).[15] A. H. Hillas, Proc. 17th ICRC (Paris) 8, 193 (1981).[16] D. A. Lewis et al., Proc. 23rd ICRC (Dublin) 1, 279(1993).[17] THEMISTOCLE Collaboration, Proc. 24th ICRC (Rome)2, 315 (1995).[18] T. Tanimori et al. (to be published).[19] M. Amenomori et al., Proc. 24th ICRC (Rome) 2, 346(1995).[20] P. Lipari, Astropart. Phys. 1, 195 (1993).[21] J. J. Hester et al., Astrophys. J. 448, 240 (1995).[22] M. Hoshino, J. Arons, Y. A. Gallant, and A.B. Langdon,Astrophys. J. 390, 454 (1992); Y.A. Gallant and J. Arons,Astrophys. J. 435, 230 (1994).[23] A. D. Erlykin and A.W. Wolfendale, J. Phys. G 8, 979(1997).2619

Gamma rays and neutrinos from the crab nebula produced by pulsar accelerated nuclei

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Gamma rays and neutrinos from the Crab Nebula produced by pulsar
  accelerated nuclei

Gamma rays and neutrinos from the Crab Nebula produced by pulsar accelerated nuclei

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