A.M. Hillas, in a review of the origins of cosmic rays, has recently
criticized the "cannonball" (CB) model of cosmic rays and gamma-ray bursts. We
respond to this critique and take the occasion to discuss the crucial question
of particle acceleration in the CB model and in the generally accepted models.
We also summarize our claims concerning the CB model.Comment: 3.3 pages, no figure

Dar, Arnon

De Rujula, A.

English

arXiv

A.M. Hillas, in a review of the origins of cosmic rays, has recently criticized the cannonball (CB) model of cosmic rays and gamma-ray bursts. We respond to this critique and take the occasion to discuss the crucial question of particle acceleration in the CB model and in the generally accepted models. We also summarize our claims concerning the CB model

Dar, Aron

CERN Document Server

arXiv:hep-ph/0611369 v1   29 Nov 2006The vicissitudes of “cannonballs”: a response to criticisms by A.M. Hillasand a brief review of our claimsArnon DarDepartment of Physics and Space Research Institute, Technion, Haifa 32000, IsraelA. De Ru´julaTheory Unit, CERN, 1211 Geneva 23, Switzerland; Physics Department, Boston University, USA(Dated: November 30, 2006)A.M. Hillas, in a review of the origins of cosmic rays, has recently criticized the “cannonball” (CB)model of cosmic rays and gamma-ray bursts. We respond to this critique and take the occasion todiscuss the crucial question of particle acceleration in the CB model and in the generally acceptedmodels. We also summarize our claims concerning the CB model.PACS numbers: PACS NumbersI. MOTIVATIONThe ‘cannonball’ (CB) model is based on the hypoth-esis that a good fraction of core-collapse SNe biaxiallyemit a few plasmoids of ordinary matter, initially ex-panding (in their rest system) at the speed of soundin a relativistic plasma. The CBs have a typical ini-tial Lorentz factor of O(103) and a baryon number ofO(1050), roughly corresponding to half the mass of Mer-cury. We contend that this model provides a good, sim-ple, few-parameter description of the properties of cosmicrays (CRs), long-duration gamma-ray bursts (GRBs), X-ray flashes, the gamma background radiation, the natalkicks of neutron stars, the magnetic fields of galaxy clus-ters, and the ‘cooling flows’ of rich clusters.The CB model is no doubt a considerable simplifica-tion, and may of course be false. One way to expressour claims —undeniable, in our opinion— is the follow-ing. The model is an excellent mnemotechnic pedagogicaltool: practically every single property of the mentionedphenomena can be derived, in the proverbial extent ofthe back of an envelope, from the stated hypothesis, afew auxiliary observations (e.g. the density of the inter-stellar medium) and elementary physics considerations.In an a-posteriori addition to a contribution to a con-ference [1], A.M. Hillas has made criticisms of the CBmodel. We are very grateful to receive an open critiquesince, up to now, written comments on this model wereconfined to the asymmetric environment of anonymousreferee’s reports.In criticizing the CB model, Hillas gives a brief outlineof it. We will quote large portions of Hillas’ article, sincehis outsider’s explanations are also useful here, and areconcordant in style with his critical comments. Quotesfrom Hillas will be in italics, e.g. The authors have goneon to estimate (most fully in Dar and de Ru´jula [2]) thatthese objects [CBs] would also naturally account for thegeneration of virtually all cosmic rays as a consequenceof their motion through the interstellar gas. However, Ican give no credence to this model.II. ON THE EXPANSION OF CANNONBALLSThe vital properties of the cannonball are its Lorentzfactor, Γ, which determines the energy of the particlesit emits, and its transverse radius, R, which determinesthe rate at which particles are swept up and the CB slowsdown. A quite false effect is employed in calculating thatthe expansion of R is quickly slowed down... The swept-up particles, which have a very high individual energyΓmpc2 in the CB reference frame, and which are sup-posed to diffuse out of the CB, are said to exert an inwardpressure, opposing lateral expansion, supposedly becauseof momentum reaction when they leave, whereas the oppo-site is true: near the edges, where the net particle flow isoutwards, a net outward force (pressure gradient) wouldbe exerted by the diffusing particles on the CB material.Consider the analogous problem of photons diffusingoutwards in the Sun and finally escaping freely from its“surface”: the photosphere. Their diffusion gradient in-deed corresponds to a volume-distributed upwards force.But the escaping photons do exert an inwards force perunit surface on the photosphere. If Hillas were saying thecontrary, he would not be contradicting us, but Newton.Our arguments concerning expansion apply to the wholeCB or, in the analogy, to the inwards pressure on theSun’s photosphere.We explicitly admit in our papers to not having solvedthe problem of the evolution of a CB from first principles.But we recall how the relativistic plasmoids ejected byquasars appear not to expand laterally as they travel forhundreds of kiloparsecs, before they finally stop and blowup. This is an observation, recognized as a mysteriousfact, that we try to explain. Hillas ignores this fact, aswell as the success of our entirely analogous choice ofCB-radius evolution in the description of the afterglowsof GRBs.III. ON THE RECAPTURE OF COSMIC RAYSThe authors suppose that particles can simply leave the2CB’s surface, without Fermi “bouncing”, whereas Achter-berg et al. [3] show that particles entering a plasma ad-vancing with ultrarelativistic speed, and scattered back outof it, cannot escape: even a small external magnetic fieldretards them sufficiently that they are recaptured, and aFermi acceleration process is set up that dominates thespectrum. (If B were as small as the normal Galacticfield ∼ 2µG they would still be recaptured within the CBradius until their rigidity exceeded ∼ 1017 V.)The calculations that Hillas quotes are not relevant.One reason is that a CB is preceded by the collimatedflux of CRs it has previously produced, and this flux islargely sufficient to wipe out the pre-existing magneticfield. An analogous phenomenon is the effect of the Sun’scoronal mass ejections on interplanetary magnetic fields.A CB of Lorentz factor Γ intercepts the particles atrest in the ISM (mainly protons, of number density np)and, via the dominant ‘elastic’ process, re-emits them ina forward cone of characteristic angular width θ = 1/Γ,with a typical Lorentz factor γ∼Γ2. Let the CB and CRvelocities, in c = 1 units, be βCB≈ 1−1/(2Γ2), and βCR≈1−1/(2γ2). The number of ISM particles intercepted bythe CB in an element of travel distance, dx = βCBc dt,is π R2 np dx. They travel forwards in a layer of fore-shortened depth dx¯ = dx(βCR/βCB− 1) ≈ dx/(2Γ2). Ata later time t, let d = βCRc t be the distance travelledby the CRs of our elemental volume, bigger than thedistance βCBc t travelled by the CB. The energy densityof CRs inside the leading conical shell of radius θ d anddepth dx′ is:ǫCR=2R2 np Γ6 mp c2d2∼ 2×107eVcm3×[Γ103]6 [R1014 cm]2np10−3 cm−3[10 kpcd]2(1)This number is very large, with respect to the energydensity ǫB ∼ 0.16 eV/cm3 of a B = 2µG field. At thebeginning of a CB’s trajectory, d is small and the CR en-ergy density in front of it is enormous. Even a tiny frac-tion of CRs evading recapture would suffice to erase anyprevious magnetic field so that the process underlyingEq. (1) can start. It could be argued that we should haveadiabatically ‘compressed’ the ambient magnetic field bythe ratio dx′/dx. This would not change the conclusion.Moreover, it is no doubt incorrect. The ISM into whichthe CRs are emitted was previously totally ionized bythe GRB’s γ rays, becoming a highly conducting plasma.In such a medium the compressed magnetic fields point-ing in various directions would efficiently ‘reconnect’ and‘annihilate’. The CB-generated CRs travel in a domainwherein there is no magnetic field, long enough for the(decelerating) CB not to catch up with them.IV. ACCELERATION WITHIN A CBThe CB authors do wish to use Fermi acceleration toget particles to 1021 V, however, but seem to misinterpretthe reports of Frederiksen et al. [4, 5], as showing thatrelevant acceleration of ions will occur entirely behind theshock, so they considered motion entirely there.The expression behind the shock may not be the rightone, for the quoted papers contain ‘collisionless shocks’ aspart of their titles, but their results do not show anythinglike the development of a shock.Frederiksen et al. did note, though, that the magneticfield in the external medium was required for significantenergy gain by ions.This is what the quoted authors actually say: “Fred-eriksen et al. [5] reported evidence for particle accelera-tion with electron γ’s up to ∼ 100, in experiments with anexternal magnetic field present in the upstream plasma.This is indeed a more promising scenario for particle ac-celeration experiments, although in the experiments byNishikawa et al. [6] results with an external magnetic fieldwere similar to those without.” The cited ‘experiments’do not seem to us to refer to ions in this context of ‘ex-ternal’ magnetic fields. Also, the results are not decisive.Acceleration playing a crucial role in theories of CRs andGRBs, we discuss it some more.V. MORE ON ACCELERATION IN THEMERGERS OF PLASMASThe required efficiency of the acceleration mechanismsinvoked in the CB model is orders of magnitude smallerthan that required in the SN remnant (SNR) model ofCR production. To generate the CR fluxes up to the‘knees’ (predicted to occur at E(A) = 2Amp c2 Γ20, withΓ0 ∼ 103) no CR ‘acceleration’ mechanism is invoked inthe CB model. These CRs originate in a single ‘elasticcollision’ of a CB and an ISM particle at rest. In con-trast, the CRs of SNR models must laboriously be ac-celerated by multiple passages through a non-relativisticshock. In the CB model only the CRs above the kneeare accelerated in the relativistic merger of two plasmas.This fraction of the observed CR flux is 10−12 to 10−13of the total. Numerical experiments may not be able to‘measure’ such a small fraction.Similar differences in the required acceleration effi-ciency appear in the comparison of the CB model withthe standard ‘fireball’ model of GRBs and their after-glows. The γ-ray spectrum of a GRB is a broken powerlaw changing fast from E−α to E−β at a ‘peak’ energyEp (typical values, predicted by the CB model, and ob-served, are: α ∼ 1, β ∼ 2.1, (1+z)Ep ∼ 250 keV). Thelargely dominant number of γ rays below Ep is gener-ated in the elastic Compton scattering of ambient pho-tons by (non-accelerated) electrons comoving with theCB, in very close analogy with the generation of CRs be-low the knee. At optical frequencies, the afterglow of aGRB is also a broken power law whose indices and ‘bend’frequency are correctly predicted by the CB model. Onlythe very small fraction of the afterglow light lying abovethe bend frequency is emitted by accelerated electrons.3The broken power-law spectra of CRs, GRBs andtheir afterglows, as we have seen, have a commonexplanation, and do not require, except above their‘knees/peaks/bends’ a population of accelerated ions orelectrons. Naturally, the CBs themselves must have beenaccelerated somehow. The SNR models also require a‘first acceleration’: that of the SN shell; the fireball mod-els require the acceleration of their thin conical shells ofrelativistic e+e− pairs. None of these pre-accelerations isconvincingly understood on fundamental grounds.VI. CONCLUSIONSWe have presented some of the reasons why the critiqueof the CB model by Hillas does not convince us. Moresignificant than the criticisms of Hillas and many a refereeis the general immunity to the evidence in favour of themodel. Some examples of this evidence are:• A few parameters (initial Lorentz factor, typi-cal mass and radio self-absorption frequency of aCB) and their distributions are extracted from themodel’s accurate description of GRB afterglows(AGs). GRB afterglows are understood [7, 8].• The AG description was used to conclude thatlong-duration GRBs are made by super-novae [7] and to predict the date in which GRB-associated SNe would be detectable [9]. One ex-ample is SN2003dh, associated with GRB 030329,which changed the GRB community’s views fromconsidering the GRB/SN association a marginalitem (see, e.g. [10]) to a crucial one (see e.g. [11]).The non-relativistic ejecta of a SN close to its GRBaxis are faster than average: these conventionalSNe appear to be ‘hypernovae’ [11], but theyare not.• At small redshifts the CBs of a GRB ought to bedirectly observable as superluminal sources of theirradio AG [12]. One example is the two-pulse (two-CB) GRB 030329 [9, 13], whose double-source radioAG was indeed observed [14, 15]: GRB cannon-balls have been seen.• Given the information extracted from their AGs,all the properties of the single γ-ray pulses of GRBsare predicted in the CB model, in agreement withobservations [16]. Long GRBs are understood.• The X-ray AGs of GRBs are predicted to have aspecific complicated structure [7]. This has recentlybeen corroborated in impressive detail by SWIFT[17, 18]. The early evolution of CBs is under-stood.• The geometrical and radiation-beaming propertiesof a CB are trivial: those of an effectively point-likerelativistic source. Consequently, many observableproperties of a GRB (e.g. peak energy and isotropicenergy and luminosity) are related to one anotherby predicted power laws [16, 19], in agreement withobservations [16, 20]. GRB radiation is extremelycollimated: a good fraction of core-collapseSNe emit GRBs.• X-ray flashes are nothing but GRBs ob-served at larger angles, as supported by theirproperties [16, 21], including their origin in SN ex-plosions [21, 22].• The spectral shapes and relative abundances ofCRs up to their knees are predicted, and in agree-ment with observations [2]. The predictions areparameter-free and do not invoke any iterative ac-celeration mechanism. CRs are understood upto the knees and their understanding is trivial.• The tiny fraction of CR flux above the knees re-quires, in the CB model, an iterative accelerationakin to that required at all energies in the standardmodels of CRs and GRBs. With only one param-eter for what this fraction is, the observed fluxesof CRs above the knees (and above the analogousenergies in GRBs and their AGs) are understood.The entire spectra of CRs and GRBs are ex-plained with a single source: cannonballs.• The CB model also offers straightforward expla-nations of the natal kicks of neutron stars [23],the properties of the gamma background radiation[24, 25], of cooling flow clusters [26], and of the in-tensity of magnetic fields in the intergalactic space,including that in galaxy clusters [27]. The CBmodel is a proposed simple description of allhigh-energy astrophysical phenomena gener-ated by relativistic jets.Faced with these items, we conclude that there is achoice between Okcam’s razor and the opposite view:For every complex natural phenomenon there is a simple,elegant, compelling, wrong explanation (Tommy Gold).Acknowledgements. We are indebted to AndyCohen, Shlomo Dado and Shelly Glashow for usefuldiscussions. This research was supported in part bythe Helen Asher Space Research Fund at the TechnionInstitute.4[1] A.M. Hillas, astro-ph/0607109[2] A. Dar and A. De Ru´jula, hep-ph/0606199[3] A. Achterberg et al. MNRAS 328, 393 (2001)[4] J.T. Frederiksen et al., Astrophys. J. 608, L13 (2004)[5] J.T. Frederiksen et al., astro-ph/0303360[6] K.-I. Nishikawa et al., Astrophys. J. 595, 555 (2003)[7] S. Dado, A. Dar and A. De Ru´jula, Astron. Astrophys.388, 1079 (2002)[8] S. Dado, A. Dar and A. De Ru´jula, Astron. Astrophys.401, 243 (2003)[9] S. Dado, A. Dar and A. De Ru´jula, Astrophys. J. 594,L89 (2003)[10] E. Waxman, Lect. Notes Phys. 598, 393 (2003)[11] S. E. Woosley and J. S. Bloom, Annu. Rev. Astron. As-troph. 44, 507 (2006)[12] A. Dar and A. De Ru´jula, astro-ph/0008474[13] S. Dado, A. Dar and A. De Ru´jula, astro-ph/0402374[14] G. B. Taylor, D. A. Frail, E. Berger and S. R. Kulkarni,Astrophys. J. 609, L1 (2004)[15] S. Dado, A. Dar and A. De Ru´jula, astro-ph/0406325[16] A. Dar and A. De Ru´jula, Phys. Rep. 405, 203 (2004)[17] J. A. Nousek et al., Astrophys. J. 642, 389 (2006)[18] S. Dado, A. Dar and A. De Ru´jula, Astrophys. J. 646,L21 (2006)[19] A. Dar and A. De Ru´jula, astro-ph/0012227[20] S. Dado, A. Dar and A. De Ru´jula, astro-ph/0611161[21] S. Dado, A. Dar and A. De Ru´jula, Astron. Astrophys.422, 381 (2004)[22] E. Pian et al., Nature 442, 1011 (2006)[23] A. Dar and R. Plaga, Astron. Astrophys. 349, 259 (1999)[24] A. Dar and A. De Ru´jula, MNRAS 323, 391 (2001)[25] S. Dado, A. Dar and A. De Ru´jula astro-ph/0607479[26] S. Colafrancesco, A. Dar and A. De Ru´jula, Astron. As-trophys. 413, 441 (2004)[27] A. Dar and A. De Ru´jula, Phys. Rev.D72, 123002 (2005)

The vicissitudes of "cannonballs": a response to criticisms by A.M. Hillas and a brief review of our claims

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