The cannonball model of GRBs is very overt (and, thus, falsifiable) in its
hypothesis and results: all the considerations I review are based on explicit
analytical expressions derived, in fair approximations, from first principles.
The model provides a good description of all the data on all GRBs of known
redshift, has made correct predictions, and is unprecedentedly self-consintent,
simple and successful.Comment: 8 pages, 7 figures in text. To appear in the Proceedings of the 4th
  Microquasar Workshop, 2002, eds. Durouchoux, Fuchs & Rodriguez, published by
  the Center for Space Physics: Kolkata. Slightly longer versio

De Rujula, A.

English

arXiv

The cannonball model of GRBs is very overt (and, thus, falsifiable) in its hypothesis and results: all the considerations I review are based on explicit analytical expressions derived, in fair approximations, from first principles. The model provides a good description of all the data on all GRBs of known redshift, has made correct predictions, and is unprecedentedly self-consintent, simple and successful

De Rujula, Alvaro

CERN Document Server

pGRBs in the Cannonball model: an overviewA. De Ru´jula11CERN, 1211 Geneva 23, SwitzerlandAbstract :The cannonball model of GRBs is very overt (and, thus, falsiable) in its hypothesis and results: all theconsiderations I review are based on explicit analytical expressions derived, in fair approximations, fromrst principles. The model provides a good description of all the data on all GRBs of known redshift,has made correct predictions, and is unprecedentedly self-consintent, simple and successful.The cannonball (CB) model of GRBs [8, 9,2, 5] is based on our ignorance, for we (its au-thors) do not understand, e.g.: how the GRBengine works, how core-collapse supernovae(SNe) eject their ejecta, the transport of angu-lar momentum in processes of collapse and/oraccretion, relativistic magnetohydrodynamics,the relativistic ejections in quasars and micro-quasars... Thus, we base our starting hypothe-sis on analogy with the observations of quasarsand -quasars, overlooking current numericalsimulations of these phenomena1. Quasars and-quasars appear to expell relativistic plas-moids when matter accretes abruptly from adisk or torus orbiting them. We assume theGRB engine to be similar: relativistic CBs areemitted axially from the recently made com-pact object in a core-collapse SN, as mat-ter that has not been expelled as a SN shell(SNS) falls back [12] to constitute an unsta-ble disk. Most indications are that the plas-moids are made of ordinary matter, not somefancier substance such as e+ e− pairs withsome nely-tuned \baryon-load", as assumedin the conventional GRB scenarios: reballs ortheir progeny (hereinafter \the standard model(SM)"; for a balanced review, see [13]).Crossing the SNS with a large Lorentz factorγ, the surface of a CB is collisionally heated tokeV temperatures and the radiation it emitswhen it reaches the transparent outskirts ofthe shell |boosted and collimated by the CB’smotion| is a single γ-ray pulse in a GRB. Thecadence of pulses reflects the chaotic accre-1 The denition #1.a of \simulation" in the OEDis: \The action or practice of simulating, with in-tent to deceive; false pretence, deceitful profession".tion processes and is not predictable, but theindividual-pulse temporal and spectral prop-erties are. One example of γ-ray light-curve isgiven in Figure 1, for the single pulse of GRB980425, the closest-by GRB on known redshiftz. An example of spectrum is given in Fig-85008000750070006500600055005000counts s–1100806040200-20-40seconds since triggerGRB 980425 BATSE50–300 keVR.M. Kippen  UAH/MSFC  1998Figure 1 : Temporal shape of GRB 980425GRB 99012310-810-710-6E2N E  (erg · cm–2 · s–1 )0.01 0.1 1 10 100Photon Energy (MeV)Figure 2 : E2 dnγ=dE spectrum of GRB 990123ure 2, for the most energetic recorded GRB ofknown z. The high-energy tail is not well repro-duced by our simplied quasi-thermal model[9]; it should be flatter. This is not surpris-ing: we did not take into account that a CBin its rest system is bombarded by SNS par-ticles of high γ, which cannot be instanta-neously thermalized. The low-energy part ofthe spectrum, in this and other GRBs, behavesas E2 dnγ=dE  E1, in agreement with theCB-model’s prediction (the standard reballscenario inescapably predicts a slope disagre-ing with observation by  1=2 unit [14]). Along list of general properties of GRB pulses(e.g., that they are narrower at high than atlow energy) is reproduced in the CB-model, inwhich, unlike in the SM, the GRB’s γs are ofthermal (as opposed to synchrotron) origin [9].From our analysis of GRBs we deduced thatthe observed γ-ray fluences and individual-γenergies imply that CBs have typical Lorentzfactors γ  103 and are only observable forangles  (between the jet axis and the observer)of O(10−3). For such a small viewing angle,the universal rate of GRBs and that of core-collapse SNe are comparable: we are defendingthe extreme view that a good fraction of suchSNe emit GRBs. The mass and baryon number(NCB) of a CB are typically a fraction of thoseof our planet: peanuts, by stellar standards.In GRS 1915+105 the observations are com-patible with the ejecta expanding laterallywith a transverse velocity (in their rest system)comparable to c=p3. In many quasars, suchas Pictor A, the ejecta appear to travel longdistances without expanding laterally. In theanalysis of the radiation from these sources, asin the CB model which they inspire, γ and (plus the total energy in the ejecta) are the pa-rameters needed to describe the observations.In the old reball model of GRBs the ejectawere spherical. Dar and collaborators have in-sisted for a long time that this implied toolarge a total energy, and that GRBs shouldbe \jetted" emissions from SNe [19]. Fireballadvocates have slowly let reballs become re-cones [17] or, more properly, retrumpets: jetsof material funneled in a cone of initial open-ing angle (also called) , that increases asthe ejecta encounter the interstellar medium(ISM), see Figure 3. For years the modellersplaced the observer precisely on-axis, so thatall detected GRBs would point to us: an an-thropoaxial view. More recently, the SM viewis evolving towards the realization that the ob-serving angle also matters [18], a step in whatI believe to be the right direction: the observa-tion angle is the only one that matters.We assume CBs, like the observed ejectain quasars and -quasars, to contain a tan-gled magnetic eld. In that case, as they plowthrough the ISM, they gather and re-scatterits constituent protons. The re-emitted pro-tons exert an inwards pressure on a CB whichcounters its expansion. In the approximation ofisotropic reemission in the CB’s rest frame andconstant ISM density np, we explicitely ndthat, in a matter of observer’s minutes, a CB|faithfull to its name| reaches an asymptoticradius R of O(1014) cm. In the same approx-θθISMISMSNSSHOCKCBFigure 3 : Standard and CB-model geometry.imation we may compute the magnetic eldthat sustains the inwards pressure of the out-going protons (B  O(a few) Gauss) and de-rive the explicit law of CB deceleration in theISM, that depends on the initial γ = γ0 asthey exit the SNS and a \deceleration" param-eter x1 = NCB=( R2 np). CBs decelerate toγ(t) = γ0=2 in a journey of x1=γ0 length, typ-ically of O(1) kpc.A CB exiting a SNS soon becomes trans-parent to its own enclosed radiation. At thatpoint, it is still expanding and cooling adia-batically and by bremsstrahlung. The bremssspectrum is hard and dominates the early X-ray AG, with a fluence of predictable magni-tude decreasing with time as t−5. An exampleof how well this describes early X-ray AGs isshown in Figure 4. All X-ray AGs are compat-ible in magnitude and shape with this predic-tion. In the \internal-external shock" SM bothTime After Burst (days) erg cm-2  s-110-1510-1410-1310-1210-1110-1010-910-810-710 -4 10 -3 10 -2 10 -1 1 10 10 21/t5Quasi-achromaticregimeFigure 4 : The Xray AG of GRB 010222 [2]the GRB proper and its AG are due to syn-chrotron radiation, internal collisions betweenshells result in the GRB, the external collisionof all shells with the ISM begets the AG. In-ternal shocks are inecient at creating internalenergy, e.g.: two shells of mass m and Lorentzfactors γ and γ=2 coalesce to produce and ob-ject of mass  2m (1 + 1=16)  1:06 (2m),so that, in e-p-B energy equipartition,  2%of the energy would end up in synchrotron-radiating electrons. The external shock (a col-lision of a composite object of mass M andLorentz factor Γ with the ISM at rest) is over-whelmingly more ecient: a third of all the en-ergy M Γ c2 is available! It is dicult to under-stand why the integrated energy in a GRB ismuch larger than in the AG [13], why the X-raylight curves initially descend the way they do,and how the discovery of such patently misbe-having AGs could be hailed as a great successof the SM (the real diculty lies in imaginingany GRB model without an AG; try!).The optical AGs of all GRBs of known zare also well described in the CB model. They,and the late X-ray AGs, are due to synchrotronradiation by the electrons that the CB gathersin its voyage through the ISM.The optical AGs for which the data startvery early after the GRB are particularly inter-esting. The AG of GRB 990123, in Figure 5, isan example. In these early AGs we detect |inthe CB model, in which the observer’s \clock"runs at 10−6 to 10−5 the rate of a CB’s travel-time| the CBs plowing through the  r−2density-prole of the \wind" ejected by theassociated SN. This implies an early decline/ t−2, whose normalization can also be esti-mated, also agreeing with the data. In the SMTime After Burst (days)µ Jansky10-310-210-111010 210 310 410 510 610 -4 10 -3 10 -2 10 -1 1 10 10 2Galaxy1998bw-like SNTotal1/t QuasiAchromaticRegime2Figure 5 : The R-band AG of GRB 990123 [2]the absence of \windy" signatures is a prob-lem, to the extreme that, after quoting some20 earlier failures: \Unfortunately, until nowthere has been no clear evidence for a wind-fed circumburst medium" (CBM), these SM-devotee authors [16] thus continue to reporttheir personal feelings about GRB 011121: \toour delight [we] have found a good case for awind-fed CBM"; see [11] for comment.In the CB model, all long-duration GRBs areassociated with SNe compatible with a (prop-erly transported) SN 1998bw [7], the one as-sociated with the very close-by GRB 980425.Naturally, \standard candles" do not exist, butthis one, so far, is doing a good job. Half of thescore of GRBs of known z are too far to seetheir associated SN and, when the SN shouldnot be seen, it was not seen. Analized in theCB model, the other half have either indica-tions or (as z decreases) incontrovertible ev-idence for such a SN: when the SN could beseen, it was seen. This gave us condence topredict how the associated SN would appear inthe case of GRB 011121. We used in [3] the rst2 days of R-band data to t the parameters de-scribing the CBs’ contribution to the AG. Ex-trapolating it in time, we predicted explicitelyhow the AG would evolve, and we concluded:the SN will tower in all bands over the CB’sdeclining light curve at day  30 after burst.The comparison with the data [4], gatheredlater, is shown in Figure 6. The SN spectrumis slightly bluer than that of 1998bw, but notsignicantly so. In the SM, it is not possibleto reproduce the previous exercise because theAGs (unlike the smoothly-vaying data) have\breaks". The early data on GRB 011121 donot tell you where the break \is": they cannotbe extrapolated. That may help explain whythe same SM-abiding observers rst concludedthat this GRB had no associated SN [1], theday after that it did [15], to compromise nallyinto half of a SN1998bw-like signal [16].Time After Burst (days)µ Jansky10-310-210-111010 210 310 -1 1 10 10 2CBs’ contributionTransportedSN1998bwTotalFigure 6 : R band AG of GRB 011121 with thegalaxy contribution subtracted [4].In the CB model [5] the spectrum of elec-trons in the CB, accelerated by its enclosedmagnetic maze and cooled by synchrotron ra-diation, has an injection bend at the energyEb = me c2 γ(t) at which a CB would, inits rest system, see the ISM electrons arrive,with γ(t) the instantaneous CB Lorentz fac-tor, extractable from the t to the AG light-curve. The emitted synchrotron radiation hasa corresponding bend at a frequency (in theCB’s frame) b = 0:2175 γ(t)2 L, with L theLarmor frequency in the CB’s magnetic eld,whose magnitude is also explicit and evolvesas B(t) / γ(t), so that b / γ(t)3. Prior to ab-sorption corrections, the synchrotron fluence ina CB’s rest system is:fsync   dnγd / [=b]−1=2√1 + [=b](p−1)(1)with a predicted p  2:2, in agreement withall the data on relatively late optical AGs,at which time   b and fsync / − with = p=2  1:1 (it is easier to extract this in-dex from ts to the AG light-curve than fromthe spectra, which are beset by absorption cor-rections). The explicit interpolating form ofEq. 1 is a guess, but the existence and explicittime-dependence of the injection bend are boldconclusions, that need to be confronted withdata. Getting a bit ahead of myself, I showin Figure 7 a typical predicted spectrum, inthe observer’s frame. The gure shows howνν-(p-1)/2ν-p/21 102 104 10610102103104µ Jansky300 100 30 10 1RADIO  OPTICALFrequency (GHz)3/2Figure 7 : Typical predictions for the CB model’sGRB spectra, at times from 1 to 300 days. The peakfrequencies correspond to CB self-opacities ofO(1).The black dots are the location of the injection-bend frequency in the synchrotron radiation [5].the predicted location of the spectral bendin frequency diminishes with time. Measuredaround a xed frequency, a spectral slope maybe time-dependent:  = (p − 1)=2  0:6 be-fore the \passage" of the injection bend andFREQUENCY (GHz)µ JANSKY10-410-310-210-111010 210 310 410 510 610 -1 1 10 10 2 10 3Time after burst (days)1000 K100 J10 IRV/10B/100U/1000(a)14.5 14.7 14.9 15.1 15.3 15.5Log ν (1+z) (Hz)2.11.91.71.51.3Log Fν (mJy)-----(b)Figure 8 : GRB 000301c. (a) (Galaxy-subtracted)CB t to optical light curves in all bands. (b) Pre-dicted spectrum at t  3 days [5]. = p=2 1:1 after it. In the 7 cases of GRBswith sucient data to do this test, the agree-ment with expectations is good (the errorsare often large). The complementary test isto look at a narrow-band spectrum when thebend is crossing or is nearby, so that the pre-dicted slope would be neither of the extremes.A good case, with insignicant absorption, isGRB 000301c. From its observed optical lightcurves, t to the CB model as in Figure 8a,we extract the AG parameters (normalization,, γ0 and x1) needed to predict b(t) and thespectral shape at a given time. The results att  3 days are shown in Figure 8b (the nor-malization is borrowed from the data but theslightly curving slope is a prediction).In the radio domain, self-absorption in theCB is important. The dominant mechanism isfree-free attenuation, characterized by a sin-gle parameter a in the opacity, that behavesas  = (a=)2(γ(t)=γ0)2. Absorption is re-sponsible for the turn-around of the spectrain Figure 7. All observed spectra agree well,in spite of the scintillations in the radio, withthis gure, t in each case to the specic GRB.The overall ts to the light-curves and spectrain all bands involve the four parameters men-tioned earlier plus the single \radio" parame-ter a (the situation is in stark contrast withthe SM model ts, that are multiple-choice andinvolve many parameters in the spectral de-scription, sometimes re-t for each particularobservational time). The complete descriptionof the radio AG requires the inclusion of twoeects that introduce no extra parameters: a\cumulation factor" for the electrons that emitthe observed radio frequencies (it takes timefor the ISM electrons gathered by the CB tocool to the radio-emitting energies) and an \il-lumination and limb-darkening" factor takinginto account that the CBs are viewed relativis-tically (an observer would \see" almost all ofthe 4 surface of a spherical CB). The mostcomplete broad-band data are perhaps thoseof GRB 991208. In Figure 9 I show its spec-trum between 5 and 10 days after burst.FREQUENCY (GHz)µ JANSKY11010 210 310 410 51 10 10 2 10 3 10 4 10 5 10 6t = 5 dt = 10 dFigure 9 : CB-model t to the broad-band spec-trum of GRB 991208 at t = 5 to 10 days [5].To give an example of radio light curveI choose the most interesting of all GRBs:980425, at a tiny redshift of z = 0:0085; seeFigure 10 [5]. In the CB model, this GRB andits associated SN1998bw are not exceptional.Because it was viewed at an exceptionally largeangle ( 8 mrad), its γ-ray fluence was com-parable to that of more distant GRBs, viewedTIME AFTER BURST (DAYS)µ JANSKY11010 210 310 410 510 610 -1 1 10 10 2 10 3Figure 10 : 4.8 GHz light curve of GRB 980425.at   1 mrad. That is why its optical AG wasdominated by the SN, except for the last mea-sured point [8]. The X-ray AG of its single CB(as in Figure 1) is also of \normal" magnitude,it is not emitted by the SN, and its tted pa-rameters allowed us to predict successfully themagnitude of the cited last optical point [2].The normalization, time and frequency depen-dence of the radio AG of this GRB are also\normal", and due to the CB, not the SN [5].SN1998bw, deprived of its \abnormal" X-rayand radio emissions (which it did not emit!),loses most of its \peculiarity".The analysis of the radio scintillations ofpulsars is one way to measure their sky-projected velocities, in agreement with proper-motion results. For cosmological GRBs, thesky angular velocity of their CBs happens tobe comparable to that of the much slower andcloser-by Galactic pulsars. Perhaps, then, theanalysis of GRB radio oscillations may resultin a measurement of their apparent velocities,which are \hyperluminal": vT = O(102) c! [5].I have not discussed the mounting evidencefor X-ray lines in GRB AGs. The results [6]are quite intriguing: the alleged lines are at thepositions predicted [10] in the CB model.What are the CB-model’s limitations? Wecontend that CBs are emitted at a time tCB=O(1) day after the parent-star’s core-collapse[12]. That is the typical time for not-expelledand not-imploded stellar material to collapseback to the newly made compact object. It ispeculiar that the GRBs typically last a smallfraction of tCB, but the build-up of instabili-ties in the accretion disk may take long, whileits episodes of \fall" may be brief. With tCB =O(1) day, the SNS has moved to a distancethat plays a role in our good description ofthe duration of GRB pulses. Yet, our model ofthe complex CB-SNS collisions may be naive:a better model will result in a smaller impliedtCB. As we move away from this early violentcollision into the AG era, the CB model be-comes simple and its results and success are ro-bust. When we move even further and confrontmuch of the GRB community of this planet...that is when the problems hit the roof.References[1] Bloom J.S., et al. 2002 GCN Circ. 1274[2] Dado, S., Dar, A. & De Rujula, A., 2002, A&A388, 1079[3] Dado, S., Dar, A. & De Rujula, A., astro-ph/0111468[4] Dado, S., Dar, A. & De Rujula, A., 2002, ApJL572, L143[5] Dado, S., Dar, A. & De Rujula, A., submittedto A&A, (astro-ph/0204474)[6] Dado, S., Dar, A. & De Rujula, A., submittedto ApJ, (astro-ph/0207015)[7] Dar A., GCN Circ. 346[8] Dar A. & De Rujula A., astro-ph/0008474[9] Dar A. & De Rujula A., astro-ph/0012227[10] Dar A. & De Rujula A., astro-ph/0102115[11] Dermer, C.D., astro-ph/0204037[12] De Rujula, A., 1987, Phys. Lett. 193, 514[13] Ghisellini, G., astro-ph/0111584[14] Ghisellini, G. et al., MNRAS, 313, L1[15] Kulkarni S., et al. 2002 GCN Circ. 1276[16] Price P.A. et al. astro-ph/0203467[17] Rhoades J.E., ApJ 525, 737[18] Rossi, E. et al. astro-ph/0112083; Zhang, B.& Meszaros astro-ph/0112118; Salmonson J.D.& Galama astro-ph/0112298; Granot J. et al.astro-ph/0201322[19] Shaviv N.J., & Dar, A., 1995, ApJ 447, 863

GRBs in the Cannonball model: an overview

Abstract

Similar works

Full text

Available Versions

CERN Document Server