PHYSICAL REVIEW D, VOLUME 61, 087302

Cosmic dust grains strike again

Luis A. AnchordoquiDepartment of Physics, Northeastern University, Boston, Massachusetts 02115

~Received 7 September 1999; published 14 March 2000!

A detailed simulation of air showers produced by dust grains has been performed by means of theAIRES

Monte Carlo code with the aim of comparing with experimental data. Our analysis indicates that extensive dustgrain air showers must yet be regarded as highly speculative but they cannot be completely ruled out.

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It has long been known that small solid particles~or dustgrains! may be accelerated effectively at strong collisionleshock waves~popular in supernovae! @1#. In addition, it wassuggested years later that, even upon destruction, a subtial fraction of the superthermal debris~those created in thepre-shock region! might re-enter the shock waves to underadditional acceleration@2#. These ideas have been recenstrengthened by astronomical observations@3# and by theanalysis of primitive meteorites@4#.

Despite some still open questions concerning the tscale for grain destruction in the source environment alater on, during the trip to Earth, from time to time dugrains have been considered as possible progenitors ofair showers. The earliest significant contribution we aaware of is due to Herlofson@5#. He argued that relativisticdust grains could indeed produce extensive air showers,vided that in the first interaction each constituent nuclecontributes with an energy above 1014 eV. The field then layfallow for eighteen years until Hayakawa@6# tried to explainthe exceptional event reported by Sugaet al. @7#. Promptedby this proposal several plausible suggestions came outhe 1970s@8#.

Unfortunately, the values of the depth of shower mamum registered by Haverah Park and Volcano Ranch expments do not provide an exact picture of showers initiateddust grains@9#. Nonetheless, in view of the low statisticsthe end of the spectrum and the wide variety of uncertainin these experiments, one may be excused for reservingjudgment. In order to increase the statistics significantly,Southern Auger Observatory is currently under constructa surface array~that will record the lateral and temporal ditribution of shower particles! and an optical air fluorescencdetector~which will observe the air shower developmentthe atmosphere! @10#. A major advantage of the optical device is precisely its capability of measuring the depth formaximum shower development.

Whatever the source~s! of the highest energy cosmic raythe end of the spectrum remains unexplained by a uniconsistent model@11#. This may be due to the present lackprecision of our knowledge of these rare events or, perhmay imply that the origin and nature of ultrahigh enercosmic rays have more than one explanation. If one assuthe latter hypothesis, relativistic specks of dust are likelygenerate some of the events.

The above considerations have motivated us toexamine the effects of giant dust grain air showers. Befproceeding to discuss in detail how these extensive show

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evolve, it is useful to review some key characteristics ofmechanisms that could lead to the destruction of dust graNotice that the opacity of the interstellar medium will impose lower and upper limits on the value of the Lorenfactor g for the primaries impacting on the Earth’s atmsphere.

An early investigation by Berezinsky and Prilutsky indcates that the grains turn out to be unstable with respecthe development of a fracture@12#. On the one hand, subrelativistic dust grains disintegrate in collisions with heavy nclei of the interstellar gas. On the other hand, electrical strinduced by the photoelectric effect in the light field of thSun results in the mechanical disruption and subdivisionrelativistic grains. Doubts have also been expressed abouprospects of surviving against heating arising from photoiization within the solar radiation field@13#. The evaporationof the surface atoms@14# and even the capture of electronfrom the interstellar medium have been suggested as posways to reduce the accumulation of charges.

All in all, the path length up to the first break-up in favoof these figures (logg'2 and initial radii between 300–60Å! turns out to be of a few parsecs@15#, i.e., much less thanthe characteristic size of the Milky Way. This entails thonly RX J0852.0-4622, the closest young supernova remnto Earth~distance'200 pc! @16#, could scarcely be considered far away.

Let us now turn to the discussion of dust grain air show~DGASs!. Relativistic dust grains encountering the atmsphere will produce a composite nuclear cascade. Strispeaking, each grain evaporates at an altitude of aboutkm and forms a shower of nuclei which in turn producmany small showers spreading over a radius of severalof meters, whose superposition is observed as an extenair shower. Forg@1, the internal forces between the atomwill be negligible. What is more, the nucleons in each indent nucleus will interact almost independently. Conquently, a shower produced by a dust grain containingnnucleons may be modeled by the collection ofn nucleonshowers, each with 1/nth of the grain energy. Thus, recallinthat muon production in proton showers increases withergy asE0.85 @17#, the total number of muons produced bthe superposition ofn individual nucleons showers isNm

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BRIEF REPORTS PHYSICAL REVIEW D 61 087302

ively select the event recorded at the Yakutsk array~May 7,1989! as the best giant DGAS candidate in the whole cosray data sample@18,19#.

In order to go a step further and test these qualitaconsiderations, we have performed several atmosphericcade development simulations by means of theAIRES MonteCarlo code@20#. Several sets of showers were generateach one for different specks of metallic nature, i.e., wdifferent Lorentz factors. The sample was distributed inenergy range of 1018 eV up to 1020 eV and was equallyspread in the interval of 0° to 60° zenith angle at the topthe atmosphere. All shower particles with energies abovefollowing thresholds were tracked: 750 keV for gammas, 9keV for electrons and positrons, 10 MeV for muons, 60 Mfor mesons, and 120 MeV for nucleons and nuclei. The pticles were injected at the top of the atmosphere~100km.a.s.l!, and the surface detector array was put beneathferent atmospheric densities selected from the altitude ofmic ray observatories~see Table I!. SIBYLL routines @21#were used to generate hadronic interactions above 200 GNotice that while around 14 TeV c.m. energies the kinemics and particle production of minijets might need furthattention, for DGASs the energy of the first interactionreduced to levels where the algorithms ofSIBYLL accuratelymatch experimental data@22#. Results of these simulationwere processed with the help ofAIRES analysis program.Secondary particles of different types and all charged pticles in individual showers were sorted according to thdistanceR from the shower axis.

In an attempt to examine our qualitative consideratiowe first restrict the attention to the highest event reportedthe group at Yakutsk. Next, details of the most relevantservables of the showers are given from the analysis of bthe particles at ground and those generated during thelution of the cascade.

The Yakutsk experiment determines the shower energyinterpolating and/or extrapolating the measurements ofr600~charged particle density at 600 m from the shower core!, asingle quantity which is known from the shower simulatioto correlate well with the total energy for all primary partictypes. In the case of the event detected on May 1989,trigger of 50 ground-based scintillation detectors at 202000 m from the shower core allowed us to estimate a rable value ofr600554 m22 and a declination axis given bcos u50.52 @19#. Examining the lateral distribution of ousimulation sample, we note that showers initiated by relaistic particles ~log g5423.8) of energies in the rang

TABLE I. Sites of giant air shower arrays.

Experiment Longitude Latitude Altitude

Volcano Ranch 35°098N 106°478W 834 g/cm2

SUGAR 30°328S 149°438E 1020 g/cm2

Haverah Park 53°588N 1°388W 1020 g/cm2

Yakutsk 61°428N 129°248E 1020 g/cm2

Fly’s Eye 40°8N 113°8W 860 g/cm2

AGASA 38°478N 138°308E 920 g/cm2

Auger 35°128S 69°128W 875 g/cm2

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36–38 EeV and with orientationu559° are compatible withsuch a value ofr600 @23#. It is important to stress that thlower and upper energy bounds are compatible withevent of interest within 2s; however, for these high Lorentfactors the interstellar medium is extremely opaque to dgrains~again the reader is referred to Ref.@15#!. In Fig. 1 weshow the lateral distributions of muons and charged particIt is easily seen that the predicted fluxes at ground levelpartially consistent with those detected at the giant array~seeFig. 2!.

In what follows we shall discuss the main propertiesDGASs. The atmospheric depthXmax at which the showerreaches its maximum number of secondary particles isstandard observable to describe the speed of the showevelopment. In view of the superposition principle this quatity is practically independent ofn, depending only upong.For this reason the altitude of theXmax is generally used tofind the most likely mass for each primary. The behaviorthe Xmax with increasingg in vertical showers has been aready discussed in detail elsewhere@9#. Here we shall extendLinsley’s analyses studying the dependence of the shoevolution with the incident angle. In the last panel of Fig.we show the numerical results from 1019 eV cascades initi-ated by nucleons with logg53 and different primary zenithangles. It can be observed that, at the same total energyair shower induced by particles with an oblique incidendevelops faster than a vertical shower. Since muons are tcally leading particles in the cascade, the position ofXmax isalso related to the relative portion of muons in the showTo illustrate this last point, the resulting fluxes at groulevel from the same events are shown in the first two panof Fig. 3. As it is expected, the radial distribution of thshower particles of inclined primaries~mainly dominated by

FIG. 1. From left to right:~a! Lateral distributions of chargedparticles and muons fromAIRES simulations of a 36 EeV, logg54 DGAS. The error bars indicate the RMS fluctuation of tmeans.~b! Id. with E538 EeV and logg53.8.

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BRIEF REPORTS PHYSICAL REVIEW D 61 087302

muons! is flatter than the distribution of a vertical showeThe opposite behavior points to the supremacy of electrand positrons near the core. The density of these chaparticles, however, falls off rapidly with increasing core dtance, dimming the electromagnetic cascade.

FIG. 3. From left to right:~a! Lateral distribution of chargedparticles of DGASs of 10 EeV. The primaries with logg53 wereinjected vertically and with 60 degree zenith angle. The figure ashows the fluctuations measured in terms of RMS.~b! Idem for thecase of muons.~c! Longitudinal evolution of the shower profilesThe error bars indicate the standard fluctuations.

FIG. 2. Density of muons recorded at Yakutsk by ground aunderground detectors on May 7, 1989 at 13 h 23 min Greenwtime. There is a remarkable contradiction with an extrapolatfrom results of the low energy region~dashed line!. This figure wasoriginally published in Ref.@18#.

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To analyze the sensitivity of ground arrays to the showparameters, the radial variation of different groups of sondary particles~we have considered separatelyg, e1e2,andm1m2) was studied at two observation levels. In Fig.we show the last steps of the evolution of the lateral disbution along the longitudinal shower path. It can be seenthere is practically no change in the radial variation. Thwe conclude that the flux of particles does not have intrinsensitivity to the observation altitude until 1400 m.

Coming back to the general features of the longitudidevelopment, the last exercise is to analyze the dependof the atmospheric shower profile withg. To this end wecarry out numerical simulations of vertical showers inducby primaries with the same mass and different Lorentz ftors, namely logg52.5 to 3.2. The results are shown in thlast panel of Fig. 4. As expected, for the same primary mthe number of secondary particles increases with risingg,but it is interesting to note that both cosmic ray cascapresent similar shapes and peak around the same aspheric depth, i.e.,Xmax;350 647 g/cm2 ~consistent withthe analysis of@9#!.

Putting all this together one can draw the following tetative conclusions.

~i! The Fly’s Eye Collaboration has presented evidenindicating that typical extensive air showers above;1 EeVdevelop at a rate which is consistent with a steep powerspectrum of heavy nuclei that is overtaken at higher enerby a flatter spectrum of protons@24#. The group of the AkenoGiant Air Shower Array has reported 7 events above 1020 eV

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FIG. 4. Lateral distributions of electrons, muons, and gamm~at ground level! from AIRES simulations of 1018 eV vertical show-ers (g5300). The figure also shows the longitudinal cascadevelopment profile of 1018–1019 eV showers as would be seen by thAuger fluorescence detector. The logarithm of the Lorentz facare 2.5 and 3.2, respectively. The error bars indicate the stanfluctuations~the RMS fluctuations of the means are always smathan the symbols!.

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until August 1998@25#. In general, the muon componeagrees with the expectation extrapolated from lower ener@26#. However, the highest energy event recorded at Yaku(E51.160.4 eV! seems to be a rare exception. It canreadily noticed from Fig. 1 that the almost completemuonic nature of particles detected may be explained b36–38 EeV DGAS. In addition, if this speculation is true tlack of obvious candidate sources at close distances lethe origin of this event still as a mystery.

~ii ! The dependence of the DGAS longitudinal profileg in the studied range is rather weak. The shower disccomes slightly flatter and thicker with decreasing primaenergy and/or increasing zenith angle. This is mainly duethe rising content of muons among all charged particlesthe inclined shower.

Dust is a very widespread component of diffuse matte

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the Galaxy with apparently active participation in charparticle acceleration. If such acceleration is possible, dgrains may play an important role in determining the coposition of galactic cosmic rays. The question of whetheropacity of the interstellar medium could prevent relativisdust grains from reaching the Earth is as yet undecided.servation of giant DGASs would give an experimental adefinitive answer to this question. We recommend that Ausearch data be analyzed for evidence of DGASs.

I am grateful to D. Go´mez Dumm for helpful commentson the original manuscript and to F. Zyserman for computional aid. I am also indebted to Yakutsk Collaboration, aparticularly to M. I. Pravdin for permission to reproduce Fi2. This work has been partially supported by CONICET. Tauthor is on leave of absence from UNLP.

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@19# N. N. Efimov, N. N. Efremov, A. V. Glushkov, I. T. Makarovand M. I. Pravdin, inAstrophysical Aspects of the Most Enegetic Cosmic Rays@18#, p. 434.

@20# S. J. Sciutto, in Proceedings of the XXVI International CosmRay Conference, edited by D. Kieda, M. Salamon, and B. Dgus, Salt Lake City, Utah, 1999, Vol. 1, p. 411.

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@23# Very recently, a reanalysis of the Yakutsk data was presenE. E. Antonov et al., Pis’ma Zh. Eksp. Teor. Fiz.69, 614~1999! @JETP Lett.69, 650 ~1999!#. According to the newestimates the best DGAS candidates in our sample are twith E'55 EeV.

@24# D. J. Birdet al., Phys. Rev. Lett.71, 3401~1993!. It should benoted that when data from the variation of shower depth ofmaximum reported by the Yakutsk Collaboration are includthere is no evidence of a change of composition, A. M. HillaNucl. Phys. B~Proc. Suppl.! 52, 29 ~1997!.

@25# M. Takeda et al., Phys. Rev. Lett. 81, 1163 ~1998!;astro-ph/9902239.

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