Constraining the fraction of primary gamma rays at ultra-high energies from the muon data of the Yakutsk extensive-air-shower array

0.13 MB·English

by  A. V. Glushkov

Pis’ma v ZhETF
Constraining the fraction of primary gamma rays at ultra-high
energies from the muon data of the Yakutsk extensive-air-shower array
A.V.Glushkova,D.S.Gorbunovb, I.T.Makarova, M.I.Pravdina,G.I.Rubtsovb,c,I.E.Sleptsova andS.V.Troitskyb
a TheYakutskEASArrayCollaboration,Yu.G.ShaferInstituteofCosmophysicalResearchandAeronomy,Yakutsk677980, Russia
b InstituteforNuclearResearchoftheRussianAcademyofSciences, 60thOctoberAnniversaryprospect7a,Moscow117312, Russia
c FacultyofPhysics,M.V.LomonosovMoscowState University,Moscow119992, Russia
SubmittedDecember 26,2006
7
0 By making use of the data on the total signal and on the muon component of the air showers detected
0 by the Yakutsk array, we analyze, in the frameworks of the recently suggested event-by-eventapproach, how
2 largethefraction ofprimarygamma-raysatultra-highenergiescanbe. Wederiveupperlimitsonthephoton

n fraction in the integral flux of primary cosmic rays. At the 95% confidence level (CL), these limits are 22%
a for primary energies E >4·1019 eV and 12% for E >2·1019 eV. Despitethe presence of muonless events,
0 0
J
the data are consistent with complete absence of photons at least at 95% CL. The sensitivity of the results

9 to systematic uncertainties, in particular to those of the energy determination for non-photon primaries, is

discussed.
1
v
5PACS:98.70.Sa, 96.50.sd
4
2
1 1 INTRODUCTION composition estimators, respectively. Among the fifty
0 showersin the sample, two are muonless (that is, muon
7 detectors were operating in the showerimpact areabut
0 With the increase of statistics of ultra-high-energy
didnordetectanysignal). Theseeventsarecompatible
/(UHE) cosmic-ray (CR) events the study of the chemi-
h withbeing initiated byprimarygammaraysofenergies
pcalcompositionattheveryendofthespectrum(beyond
2·1019 eV< E < 4·1019 eV, even though the recon-
-1019 eV) is becoming quite realistic. This issue is of 0
o structedenergyexceeds4·1019eVforoneofthem. One
rprimary interest today, in view of a systematic discrep-
muon-poor shower is consistent with a photon primary
stancy between energy spectra measured by different de- ofenergyabove4·1019 eV withprobability about10%.
atectors[1,2,3,4]andofindicationstowardsafractionof
: For the rest of the showers, the hypothesis of a photon
vneutralparticles amongthe UHECR primaries[5]. The
primary is rejected at the 95% CL for each event. We
Xichemical composition is also a starting point in stud- derive upper limits on the fraction ǫ of photons in the
γ
ies of: (i) extragalactic magnetic fields and radiation
r integralfluxofprimarycosmicrayswithactual energies
abackgrounds;(ii) accelarationmechanismsoperatingin
E > 2·1019 eV and E > 4·1019 eV (the difference
astrophysicalsources;(iii) possible top-downscenarios 0 0
between actual (E ) and reconstructed (E ) energies
emerging in various extensions of the Standard Model 0 est
is discussed in Sec. 2).
of particle physics. In particular, the photon fraction
The rest of the paper is organized as follows. In
in the CR flux is of crucial importance; the aim of this
Sec. 2 we discuss the experimental data set used in our
work is to derive stringent limits on this fraction in the
study. In Sec. 3 we briefly review the approach we use
integral CR flux above the energy 2·1019 eV.
and present our main results. We discuss how robust
We make use of a recently suggestedapproach[6, 7]
theseresultsarewithrespecttochangesinassumptions
andperformcase-by-caseanalysisof 50 eventsdetected
andintheanalysisprocedureanddiscusstheuncertain-
by the Yakutsk extensive-air-showerarray(Yakutsk ar-
ties associated with possible systematics in energy de-
ray in what follows) [1] with reconstructed energies
terminationofobservedUHECReventsinSec.4. Sec.5
above 2·1019 eV chosen according to quality cuts de-
contains our conclusions.
scribed in Sec. 2. To place the limit on the photon
fraction, we compare the reported information on sig-
nals measuredby scintillation andmuon detectors with 2 EXPERIMENTAL DATA
thatexpectedfromair-showersimulations. Wefocuson
thesurfacedetectorsignaldensityat600metersS(600) Yakutsk array is observing UHECR events since
and the muon density at 1000 meters, ρ (1000), which 1973, with detectors in various configurations. Since
µ
areusedinexperimentsas primaryenergyandprimary 1979, muon detectors with areas up to 36 m2 (cur-
1
2 A.V. Glushkov et al.
rently,fivedetectorsof20m2eachwiththresholdenergy CORSIKA v6.5011 [10], choosing QGSJET II-03 [11]
1 GeV for vertical muons) supplement ground-based as high-energy and FLUKA 2005.6 [12] as low-energy
scintillator stations. At present, it is the only installa- hadronic interaction model. Electromagnetic shower-
tion equipped with muon detectors capable of studying ing was implemented with EGS4 [13] incorporated into
ultra-high-energy cosmic rays. CORSIKA. Possible interactions of the primary pho-
The energy of a primary particle is estimated from tonswiththegeomagneticfieldweresimulatedwiththe
S(600) and zenith angle with the help of the procedure PRESHOWER option of CORSIKA [14]. As suggested
describedinRef.[8],calibratedexperimentallybymak- in Ref. [15], all simulations were performed with thin-
ing use of the atmospheric Cherenkov light. This re- ning level 10−5, maximal weight 106 for electrons and
constructed energy E differs from the true primary photons, and 104 for hadrons.
est
energy E both due to natural fluctuations and due to For each simulated shower, we determined S(600)
0
possible systematic effects. These latter effects depend and ρ (1000) by making use of the detector response
µ
on the primary particle type; in particular, the differ- functions from Ref. [16]. For a given arrival direction,
encebetweenphotonsandhadronsis significant. More- there is one-to-one correspondencebetween S(600)and
over,for photons,the effects ofgeomagneticfield [9] re- the estimated energy as determined by the standard
sultin directionaldependence ofthe energyreconstruc- analysisprocedurefortheYakutskexperiment[8]. This
tion. Thus,theeventenergyreportedbytheexperiment enables us to select simulated showers compatible with
should be treated with care when we allow the primary the observed ones by the signal density, which follows
to be a photon. Because of possible energy underesti- the Gaussian distribution in log(energy); the standard
mationfor high-energyphoton-inducedshowers,we use deviation of E has been determined event-by-event
est
events with E ≥2×1019 eV even when deriving the and is typically 17% [17]. Namely, to each simulated
est
limit for E > 4·1019 eV; they contribute to the final shower, we assigned a weight w proportional to this
0 1
limit with different weights [7]. GaussianprobabilitydistributioninlogE centeredat
est
For our study, we selected a subset of events with theobservedenergy. Additionalweightw wasassigned
2
E ≥ 2×1019 eV satisfying the following cuts aimed to each simulated shower to reproduce the thrown en-
est
at the most precise determination of both S(600) and ergy spectrum ∝E−2 (see Sec. 4.3 for the discussion of
0
ρ (1000): the variationof the spectral index). For eachofthe ob-
µ
(i) shower core inside the array; servedeventsfromourdataset,wecalculatedthedistri-
(ii) zenith angle θ ≤60◦; butionofmuondensities ρµ(1000)representingphoton-
(iii) three or more muon detectors between 400 m induced showers compatible with the observed ones by
and 2000 m from the shower axis, operational at the S(600)andarrivaldirections. Tothisend,wecalculated
moment of the shower arrival. ρµ(1000)foreachsimulatedshowerbymakinguseofthe
Our sample consists of 50 air showers; the cuts se- same muon lateral distribution function as used in the
lect approximately one third of the events used for the analysis of real data [18]. To take into account possible
determination of the spectrum. experimental errors in the determination of the muon
density,wereplacedeachsimulatedρ (1000)byadistri-
µ
butionrepresentingpossiblestatisticalerrors(Gaussian
3 SIMULATIONS AND RESULTS with 25% standard deviation [6]). The distribution of
the simulated muon densities is the sum of these Gaus-
Theapproachweusewasdescribedanddiscussedin sians weighted by w1w2.
detail in Refs. [6, 7] and has already been applied to a Foreacheventwecalculate,bymakinguseoftheob-
similar study of the photon fraction at energies above tained distributions, two numbers: the probability that
1020 eV [6]. Here, we summarise the main steps of this it could be initiated by a photon with true energy in
approach. the range of interest (that is, above E = 4·1019 eV
0
For each of the events in our sample, we generated or above E0 = 2·1019 eV) and the probability that it
a libraryof simulatedshowersinduced by primarypho- could be initiated by any other primary (whose energy
tons. ThrownenergiesE ofthesimulatedshowerswere is assumed to be determined correctly by the experi-
0
randomly selected within a relevant energy interval in ment; see Sec. 4.1 for relaxing this assumption) with
order to take into account possible deviations of Eest energy above this E0. For most of the events, the mea-
from E , see below. The arrival directions of the simu- suredmuondensities aretoo highascomparedtothose
0
latedshowerswerethe sameasthoseofthecorrespond- obtained from simulations of photon induced showers.
ing real events. The simulations were performed with Given these probabilities for each event, we con-
The fraction of primary gamma rays at ultra-high energies 3
4 ROBUSTNESS OF THE RESULTS
Z-burst
00..88
A The systematic uncertainties of our results are re-
00..66 SHDM lated to the air-shower simulations and to the data in-
HP HP terpretation. They were discussed in detail in Ref. [6]
ΓΓ
ΕΕ
00..44 A AY for a different data set, with the conclusion that the
A TD approach we use to constrain ǫγ results in quite robust
00..22 PA Y limits.
Y
00
1199 1199..55 2200 2200..55 4.1 Systematic uncertainty in the S(600) and
LLooggEE energy determination
Figure1. Limits(95%CL)onthefractionǫγofphotons The systematic uncertainty in the absolute energy
intheintegralCRfluxversusenergy. Theresultsofthe determination by the Yakutsk array is about 30% [1].
presentwork(Y)areshowntogetherwiththelimitspre- It originates from two quite different sources: (a) the
viously given in Refs. [19] (HP), [20] (A),[6] (AY) and measurement of S(600) and (b) the relation between
[21](PA).Alsoshownarepredictionsforthesuperheavy
S(600) and primary energy. The probabilities that a
dark matter model (thick line), the topological-defect
particular event may allow for a gamma-rayinterpreta-
models (necklaces, between dotted lines) [22] and the
tionarenotatallsensitivetotheS(600)-to-energycon-
Z-burst model (shaded area) [23]. Theoretical curves
version because we select simulated events by S(600)
are normalized to the AGASA spectrum [2]. Energy is
and not by energy. These probabilities may only be
measured in eV.
affected by relative systematics between the determina-
tions ofρ (1000)andofS(600). Onthe otherhand,we
µ
struct the likelihood function (see Ref. [7] for details)
assumed that the experimental energy determination is
to estimate, at a given confidence level, the fraction ǫ
γ correct for non-photon primaries; the values of proba-
of primary photons among UHECR with energies in a
bilities that a particular event could be initiated by a
given range. In this way we obtain at 95% CL
non-photon primary with energy above threshold and
ǫ <22% for E >4·1019 eV, (1) hencetheeffectivenumberofeventscontributingtothe
γ 0
limit on ǫ would change if the energies are systemat-
γ
ǫ <12% for E >2·1019 eV. (2) ically shifted. The effect of such a shift would be to
γ 0
change the energy range for which the limit is applica-
These limits include corrections for the “lost photons”
ble and to change, by a few per cent, the limit itself.
(thosewithtrueenergiesE >4·1019eVforthelimit(1)
0 This is illustrated in Fig. 2, which has been obtained
andE >2·1019 eV for the limit (2) but reconstructed
0 in a way similar to that described in Sec. 3, but with
energiesE <2·1019 eV,seeRef.[7]formoredetails).
rec six minimal values of E for each of the three curves
0
In Fig. 1, we present our limits (denoted by Y) to-
corresponding to −30%, 0% and +30% shifts in ener-
gether with previously published limits1) on ǫ . Also,
γ gies of non-photon primaries. We see that the limit at
typical theoretical predictions are shown for the super-
E >2·1019 eVisuncertainbylessthanafew percent
0
heavydarkmatter,topological-defectandZ-burstmod-
while at higher energies, systematic shifts downwards
els. Ourlimitsonǫ arecurrentlythestrongestonesfor
γ reduce statistics considerably, which results in relaxing
theenergyrangeunderdiscussion. Theydisfavorthesu-
the limit. Similar uncertainties are expected for limits
perheavydarkmatterexplanationofthehighestenergy
from other experiments shown in Fig. 1. Note that the
events.
theoretical expectations presented there are also sensi-
tive to the energy scale.
4.2 Interaction models and simulation codes
Our simulations were performed entirely in the
1)A 65% upper limitfor energies above 1.2·1020 eV has been CORSIKA framework, and any change in the interac-
claimed from the study of AGASA data [24]; however, there are
tion models or simulation codes, which affects either
problems inaccounting forthe difference between actual and re-
S(600) or ρ (1000), may affect our limit. As discussed
constructed photon energies in that work (see Ref. [6] for a de- µ
taileddiscussion). in Ref. [6], our method is quite robust with respect to
4 A.V. Glushkov et al.
0.5 • artificial fluctuations in S(600) and ρ (1000) due
µ
to thinning;
0.4
• experimental errors in ρ (1000) determination.
µ
0.3
Γ While the first two sources are physical and are fully
Ε
0.2
controlled by the simulation code, the variations of the
last two may affect the results.
0.1
IthasbeennotedinRef.[26]thatthefluctuationsin
ρ (1000)due to thinning may affect strongly the preci-
µ
19.1 19.3 19.5 19.7 sionofthecompositionstudies. Forthethinningparam-
Log E eters we use, the relative size of these fluctuations [27]
is ∼10%for ρ (1000)and ∼5% for S(600). Thus with
Figure2. Sensitivityofthelimitonǫγ tothesystematic µ
moreprecisesimulations,thedistributionsofmuonden-
uncertaintyintheenergydeterminationfornon-photon
sities should become more narrow, which would reduce
primaries. The solid (red) curve represents the limits
assuming the energy scale quoted by Yakutsk experi- the probability of the gamma-ray interpretation of the
mentand normalized totheCherenkovlight (thesame studied events even further.
as points Y in Fig.1). The dashed (blue) and dotted The distributions of ρ (1000) we use accounted for
µ
(black) curves correspond to the shifts of −30% and the error in the experimental determination of this
+30%, respectively, in all energies of non-photon pri- quantity. In principle, this error depends on the event
maries. quality and on the muon number itself, which is sys-
tematically lower for simulated gamma-induced show-
the changes in the interaction models and to reason- ers than for the observed events. Still, we tested the
able variations in the extrapolationof the photonuclear stability of our limit by taking artificially high values
crosssectiontohighenergies(the valuespresentedhere of experimental errors in muon density: 50% instead of
were obtained for the standard parameterization of the 25%. The limit on ǫγ changes by less than one per cent
photonuclear cross section given by the Particle Data in that case.
Group [25] and implemented as default in CORSIKA).
5 CONCLUSIONS
4.3 Primary energy spectrum
To summarize, we have studied the possibility that
Forourlimit,weusedtheprimaryphotonspectrum ultra-highenergyeventsobservedby the Yakutsk array
E−α for α = 2. Change in the value of α affects the wereinitiatedbyprimaryphotons. Theuseoflarge-area
0
final limit on ǫγ through the fraction of “lost” photons, muon detectors, a unique feature of the Yakutsk exper-
but we have found that variations of α in the interval iment, together with the new analysis method [6, 7],
1≤α≤3 result in variations of ǫγ only within 1%. enabled us to put stringent constraints on the gamma-
ray primaries even with a relatively small set of high-
qualitydata. Animportantingredientinourstudy was
4.4 Width of the ρ distribution
µ the careful tracking of differences between the actual
The rare probabilities of high values of ρ (1000) in and reconstructed energies. We obtained upper bounds
µ
the tail of the distribution for primary photons depend (1), (2) on the fraction ǫγ of primary photons, assum-
onthe width ofthis distribution. The followingsources ing an isotropic photon flux and E0−2 spectrum. These
contribute to this width: limits are the strongest ones up to date; they constrain
considerably the superheavy dark matter models.
• variations of the primary energy compatible with WeareindebtedtoL.G.DedenkoandV.A.Rubakov
theobservedS(600)(largerenergycorrespondsto for helpful discussions. This work was supported in
larger muon number and hence ρ (1000)); part by the INTAS grant 03-51-5112, by the Russian
µ
Foundation of Basic Research grants 05-02-17363 (DG
• physical shower-to-shower fluctuations in muon and GR), 05-02-17857 (AG, IM, MP and IS) and 04-
density for a given energy (dominated by fluc- 02-17448 (DG), by the grants of the President of the
tuations in the first few interactions, including Russian Federation NS-7293.2006.2 (government con-
preshowering in the geomagnetic field); tract02.445.11.7370;DG,GRandST),NS-7514.2006.2
The fraction of primary gamma rays at ultra-high energies 5
(AG, IM, MP and IS) and MK-2974.2006.2 (DG), by 26. D. Badagnani and S.J. Sciutto, Proc. 29th ICRC
the fellowships of the ”Dynasty” foundation (awarded (Pune),2005.
by the Scientific Council of ICFPM, DG and GR) and 27. D.S. Gorbunov, G.I. Rubtsov and S.V. Troitsky, to ap-
of the Russian Science Support Foundation (ST). Nu- pear.
mericalpartoftheworkwasperformedatthecomputer
cluster of the Theoretical Division of INR RAS.
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