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Astropar(clePhysics
AlessandroDeAngelisMárioPimentaAsiago,June2017
CosmicraysGammaraysNeutrinosGravita(onalwaves???
Asiago2017
I-Introduc(on
Asiago2017
MessengersfromtheUniverse
1911/12:DomenicoPaciniandVictorHessperformtwocomplementaryexperiments:Pacinidiscoversthationizingradia(ondecreasesunderwater,andHessthatitincreasesathighal(tudes
– 20%ofthenaturalradia(onatgroundisduetocosmicradia(on!!!Canweusethese“cosmicrays”forscience?
!"
#"
Asiago2017
YES(thebirthofPar(clePhysics)
Positron (Anderson 1932)
µ (Anderson1937)
e+
Rossi,1940:Muonlife(me.Timedila(on!
An(ma]er!(Dirac)γ→e+e-(Einstein)
K, Λ, ... (LeprinceRinguet1944,Rochester,Bu]er1947,…)
π (La]es,Powell1947)Stronginterac(ons(Yukawa)
K+-
Strangeness
Asiago2017
nuclear reactor
Cosmicraysbombardtheatmosphere:thehighestenergieswecanaccess Detectedprotons108
(mesmoreenerge(cthanLHCDetectedgamma-rays10000(mesmoreenerge(cthanhuman-madeDetectedneutrinos105(mesmoreenerge(cthanhuman-made
YES,anditallowsaccessingthehighestenergies
nuclear reactor
YES,anditallowsunderstandinghigh-energyastrophysics(physicsunderextremecondi(ons)
CosmicRays(“astropar(cles”)
• Oncepersecondpercm2ahigh-energypar(clefromtheskyhitstheEarth– Mostly(~89%)protons– He(~9%)nucleiandheavier
(~1%);– Electronsare~1%– 0.01%-1%aregammarays
• Thefluxfallsas~E-2.7asenergyincreases– 1021eVoncepersecondonEarth
• Thehighestenergies
Knee
Ankle
LHC:1beam LHC:2beams
Mostlyfrom
Sun
MainlyGa
lac(c
Extragalac(c?
Asiago2017
Astropar(clephysics Amul&messengerscience1. HEgammas2. HEneutrinos3. HEprotons/nuclei4. Gravita&onalwaves
Severalpossiblefundamentalphysicsobjec&ves
1. Extremelyhighenergycollisions
2. DarkmaGer/energy3. Axions,ALPs4. Neutrinomass5. Neutrinomixing6. CMB
Andofcourse,astrophysics1. Behaviorofphysics
near(SM)BHs2. Accelera&on
mechanisms
Asiago2017
II-Produc(on
Asiago2017
?
Tevatron(p-p) LHC(p-p)13TeV
Origin!?
Asiago2017
PossibleUHECRSources:2scenarios
Top–DownDecay(PhysicsBeyondtheStandardModel)
DecayoftopologicaldefectsMonopolesRelicsSupersymmetricpar(clesStronglyinterac(ngneutrinosDecayofmassivenewlonglivedpar(clesEtc.
ü anisotropyinarrivaldirec(onsü Photons<≈1%
ü isotropyinarrivaldirec(onsü Photons>≈10%
BoCom-UpAccelera(on(AstrophysicalAccelera6onMechanisms)
UHECR’s are accelerated in extended objectsor catastrophic events (supernova remnants,rota(ngneutronstars,AGNs,radiogalaxies)
Asiago2017
IIa-Chargedpar(cleaccelera(on
Asiago2017
Energydensity(cosmicrays)
3
312
eV1~
erg10~~
cm
cmdEdEdNEE
−∫ρ
P ~ρEVgalaxyτ esc
~ 5.1040erg /s
E~1053erg
Origin(E~<1015eV)?
Forexample,powerdissipatedbyaSupernova(theremnantofacollapsedstar)of10Msun.
1SN~30Years~10-9s-1SupernovaeinourGalaxy
Asiago2017
WherecanbetheseacceleratorsintheUniverse?
Hillas-plot
R∼10km,B∼10TE∼10TeV
LargeHadronCollider
E∝∝BR
Pulsar SNR
AGN
RadioGalaxyLobe
Emax~bZBLconfinement!
Asiago2017
Afewnewterms• Stellar end-products. A star heavier than the
Sun collapses at the end of its life into a neutron star (R ~ few km, which can be pulsating – a pulsar) or into a BH, and ejects material in an explosion (SuperNova Remnant). – Very large B fields are in the pulsar; magnetic
fields also in the SNR
• The centres of galaxies host black holes, often supermassive (millions or even billion solar masses). They might accrete at the expense of the surrounfing matter, and accelerate particles in the process. When they are active, they are called Active Galactic Nuclei.
Asiago2017
Theysurpasshuman-madeaccelerators
Yearofcomple(on
Energy(G
eV) The Large Hadron Collider (LHC)
~1930
~ 10 MeV
HighLuminositySophis(cateddetectorsCentralregionEnergylimited
14TeV
Asiago2017
Howtogeneratebo]om-upenergiesmuchhigherthanthermal?
Asiago2017
Accelera(onmechanismFermi2ndorder(1949)
par(clesacceleratedinstochas(ccollisionswithmassiveinterstellarclouds(collisionstoamovingdiffusivewall!)Inthecloudreferenceframe
BacktotheLabreferenceframe
Then:
But:Probability
Asiago2017
Accelera(onmechanismFermi1storder
Par(clesgainenergybyconsecu(vecrossingsoftheshockfront!
Now(planeshockfront):
Solar coronal mass ejection 9 Mar 2000
Shockforma(on:• SuddenreleaseofEnergy(CMEs,SNRs,GRBs,…)• Supersonicflowhitsanobstacle(AGNsjets,pulsarwinds,…)
Crossingprobabilityαcos(θ)
Asiago2017
Thepowerlaw γ−∝ EdEdN
( ) 1+−∝> γEENIneachcycle thepar(clegainsa small frac(onofenergyε.Ayerncycles:
En=E0(1+ε)n
Orthenumberofcyclestoa]ainanenergyEis:
n=ln(E/E0)/ln(1+ε)
The par(cle may escape from the shock region with some probability Pi .Then theprobabilitytoescapewithE>Enis:
and
7.2)(. −∝⎟⎠
⎞⎜⎝
⎛∝⎟⎠
⎞⎜⎝
⎛ EEdEdN
dEdN
escSourceEarth
τ
2−≈⎟⎠
⎞⎜⎝
⎛ EdEdN
Source
γ=α+1
Asiago2017
Zwickyconjectures(1933)1. Heavyenoughstarscollapseattheendof
theirlivesintosuper-novae2. Implosionsproduceexplosionsofcosmic
rays3. Theyleavebehindneutronstars
(Zwickyin1930)
Asiago2017
Oneshouldconsideralsoenergylossesatthesource
Wheredotheycomefrom?
rLmustbesmallerthanthedimensionofthesourceLtoremainconfined.
Whateveristheaccelera(onmechanism…
ThemaximumenergypossibleonEarthis~5000TeV
R∼1015km,B∼10-10T⇒E∼1000TeV
R∼10km,B∼10T⇒E∼10TeV
LargeHadronCollider
TychoSuperNovaRemnant
E = k BR
Asiago2017
IIb-Produc(onofhighenergyphotons(andneutrinos)
Asiago2017
Theobservedphotonspectrumextendsover30decades(measurementsupto1TeV)
CMB:~400photons/cm3
EBL:~410-3photons/cm3
log(λ/cm)
Thermalradia(on:BlackbodySpectra
A Galactic gas cloud 60 K Dim star in the Orion Nebula: 600 K
The Sun: 6000 K
Clusterofverybrightstars,OmegaCentauri:60000K
CMB: 2.7 K
Accre(onnearBHs:~thekeVAsiago2017
γ rays:non-thermalUniverse• Par(clesacceleratedinextremeenvironmentsinteractwithmedium
– Gasanddust;Radia(onfields–Radio,IR,Op(cal,…;Intergalac(cMagne(cFields,…
• Gammaraystravelingtous!
• Nodeflec(onfrommagne(cfields,gammaspoint~tothesources– Magne(cfieldinthegalaxy:~3µGGammarayscantracecosmicraysatenergies~10x
• Largemeanfreepath– RegionsotherwiseopaquecanbetransparenttoX/γ
StudyingGammaRaysallowsustoseedifferentaspectsoftheUniverse
Asiago2017
Examplesofknownextremeenvironments
~ parsecs
Accretion Disk 3- 10 rs Black Hole Diameter = 2rs ~ 4 AU
GRB SuperNovaRemnantsPulsars
Ac(veGalac(cNuclei
Asiago2017
Energiesabovethethermalregions
• (LE)orMeV:0.1(0.03)-100(30)MeV• HEorGeV:0.1(0.03)-100(30)GeV• VHEorTeV:0.1(0.03)-100(30)TeV• UHEorPeV:0.1(0.03)-100(30)PeV
• LE,HEdomainofspace-basedastronomy• VHE+domainofground-basedastronomy
• Whennoambiguity,wecall“HE”alltheHEandVHE+
Asiago2017
>3kHEand>200VHEphotonemi]ers
Asiago2017
(1)Bo]om-up:Interac(onofacceleratedpar(cleswithradia(onandma]erfields
• Gamma-rayproduc(onandabsorp(onprocesses:severalbutwellstudied
• Thesephenomenagenerallyproceedunderextremephysicalcondi(onsinenvironmentscharacterizedby– hugegravita(onal,magne(candelectricfields,– verydensebackgroundradia(on,– rela(vis(cbulkmo(ons(black-holejetsandpulsarwinds)– shockwaves,highlyexcited(turbulent)media,etc.
• Theyarerelatedto,andtheirunderstandingrequiresknowledgeof,– nuclearandpar(clephysics,– quantumandclassicalelectrodynamics,– specialandgeneralrela(vity,– plasmaphysics,(magneto)hydrodynamics,etc.– astronomy&astrophysics
Asiago2017
Leptonicandhadronicproduc(onofgammarays
E2 d
N/d
E
energy E
IC
e- (TeV) Synchrotron γ (eV-keV)
γ (TeV) Inverse Compton γ (eV)
B
e.m. processes
π0decay
π-
π0
π+
γγ (TeV)
p+ (>>TeV)
matter
hadronic cascades
VHE
In the VHE region, dN/dE ~ E-ΓΓ (ΓΓ: spectral index)
To distinguish between hadron/leptonic origin study Spectral Energy Distribution (SED): (differential flux) . E2 Asiago2017
50TeVgamma-rayshadronicallyproducedtrackapupula(onofprotonsofenergy~1PeV
Thehadronicmechanismisatworkalsoforneutrinos…
Asiago2017
Inahadronicprocess(isospinsymmetry)• N(π+)~N(π-)~N(π0)Sameenergies!
π+->µ+vπ-->µ-vπ0->γγ
A“typical”(V)HEγsource:CrabNebula• TheCrabNebulaisanearby(~2kpcaway)PWNandthefirstsourcedetectedinVHEgamma-rays[Weekes1989].
• ItisthebrighteststeadyVHEgamma-raysource,thereforeithasbecometheso-called“standardcandle”inVHEastronomy.– Recentobserva(onofflaresintheGeVrangehavehowevershownthatoccasionallytheCrabfluxcanvary.
Asiago2017
(E/GeV)10
Log1 2 3 4 5 6
)-1 s-1
(GeV
2 m4
in 1
0pa
rticl
esN
15−10
13−10
11−10
9−10
7−10
5−10
3−10
1−10
10
310
510
o x 1oCosmic rays in 1
Crab
(E/GeV)10
Log1 2 3 4 5 6
o x
1o
CR
in 1
/ N
Cra
bN
5−10
4−10
3−10
2−10
1−10
γ-raydetec(on:signalvs.background
• IsCrabNebulaeasytodetect?• Supposetohavea100x100m2detectorwitharesolu(onof1squaredegree:
Conclusion:youneedlargeeffec(vearea,goodangularresolu(on,protonrejec(onAsiago2017
Conceicao,DeAngelis,Tome+2016)
S/B
(2)Top-down:aretherenew(heavy)par(cleswhichcanproduceHEphotons?
Asiago2017
• Rota(oncurvesofspiralgalaxies
– flatatlargeradii:iflighttracedmasswewouldexpectthemtobeKeplerianatlargeradii,v∝ r−1/2,becausethelightisconcentratedinthecentralbulge
• anddisclightfallsoffexponen(ally• Zwickyhadalreadynotedin1933thatthe
veloci(esofgalaxiesintheComaclusterweretoohightobeconsistentwithaboundsystem
• Observedformanygalaxies,includingtheMilkyWay
ToassumethatinandaroundtheGalaxiesthereis
DarkMaCersubjecttogravita(onalinterac(onbutnoelectromagne(cinterac(on– Mustbe“cold”,i.e.,non-rela(vis(c(itistrappedbythegravita(onalfield),and“weakly”interac(ng:WIMP
– Thehypothesisisnotodd:rememberthattheexistenceofNeptunewassuggestedonthebasisoftheirregularmo(onsofUranus
– HowmuchDMdoweneed?resultstobe5(mesmorethanluminousma]er(astrophysics,evolu(onoftheUniverse)
Thecurrentlyfavoredsolu(on
M (r)∝ r⇒ vrot =GM (r)r
= const.
Asiago2017
HowdoWIMPsproducephotons?• Theenergy“blob”fromχχannihila(onmight
decay:– Directlyinto2γ,orintoZγifkinema(cally
allowed.Clearexperimentalsignature(photonline),butnotverylikely(requiresoneloop).InSUSY,theBRdependsonwhatisthelightestneutralinocomposi(on.
– Intoagenericf-áarpair,thengenera(ngahadroniccascadewithπ0decayingintophotonsinthefinalstate.Remindthatflavorsareley-handedandan(-flavorsareright-handedwithamplitude[1+|p|/(E+mf)]/2~v/c,andinthiscaseforans-waveyouneedto“force”oneofthedecayproductstohavethe“wrong”elicity.
Asiago2017
=>Theχχpairwillprefertodecayintotheheaviestavailablepair–i.e.,if20GeV<mχ<80GeV,intob-bbar
ff_
=
M fi ∝121−
pE +mf
⎛
⎝⎜⎜
⎞
⎠⎟⎟=
mf
2mχ +mf
III-Propaga(on
Asiago2017
Propaga(onofchargedCRintheUniverse
!!
r1!pc
≅
E1!PeVB
1!µG
• GyroradiusBintheGalaxy:afewµG;outsidetheGalaxy:1nG>B>1fG• IfyouwanttolookattheGC(d~8kpc)youneedE>21019eV– Butonly1par(cle/km2/year– Andnogalac6cemi:ersexpectedatthisenergy
• Butinprincipleonecouldlookoutsidethegalaxy,wereBissmallerandthereareSMBHs…• No:theresonantinterac6onwiththeCMB(GZKeffect)
providesacutoffatE~1019eV
• Conclusion:extremelydifficulttousechargedCRforastrophysics
Neutralmessengersmustbeusedforastronomy&astrophysics
• Neutrinos:verydifficulttodetectduetothesmallinterac(oncrosssec(on(despiteakm3detectorinAntarc(ca,theonlycosmicsourceslocalizeduptonowareSN1987A,theSun,andtheEarth)– <10neutrinosperyearfromastrophysicalsourcesiden(fiedbyIceCube(1km3)!
• Gravita(onalwaves:juststarted• Photons:theyhavealongtradi(oninastronomysincemillennia…Andtheyarethe“starrymessangers”bydefaultsince1610atlatest...
Asiago2017
IIIa-Propaga(onofphotons
Asiago2017
• γ-raysareeffec(velyproducedinEMandhadronicinterac(ons– EnergyspectrumatsourcesE-2
• areeffec(velydetectedbyspace-andground-basedinstruments
• effec(velyinteractwithma]er,radia(on(γγàe+e-)andB-fields
• Theinterac(onwithbackgroundphotonsintheUniversea]enuatesthefluxofgammarays
• The“enemies”ofVHEphotonsarephotonsneartheop(calregion(Extragalac(cBackgroundLight,EBL)
A]enua(onofγ-rays
γHEγbckàe+e-
Asiago2017
Galac(cCentre(9kpc)
DeAngelis,Galan(,Roncadelli2011withFranceschiniEBLmodeling
30GeV100GeV
redshiyz
γrayenergy(TeV)
τ=1(GRH)
τ >1regionofopacity
),(emobs )(),( zEeEzE τ−×Φ≡Φ
γVHEγbck → e+e-
Maxfor:
σ(β)~
CenA(3.5Mpc)
1/nσ
Asiago2017
• Thediffuseextragalac(cbackgroundlight(EBL)isalltheaccumulatedradia(onintheUniversedueessen(allytostarforma(onprocesses
• Thisradia(oncoversawavelengthrangebetween~0.1and600µm(considertheredshiyandthereprocessing)
• AyertheCMB,theEBListhesecond-mostenerge(cdiffusebackground
• TheunderstandingoftheEBLisfundamental• Toknowthehistoryofstarforma(on• TomodelVHEphotonpropaga(onforextragalac(cVHE
astronomy.VHEphotonscomingfromcosmologicaldistancesarea]enuatedbypairproduc(onwithEBLphotons.Thisinterac(onisdependentontheSEDoftheEBL.
• Therefore,itisnecessarytoknowtheSEDoftheEBLinordertostudyintrinsicproper(esoftheemissionintheVHEsources.
Asiago2017
Mea
n Fr
ee P
ath
The γ horizon: nuisance and resource
100 TeV 10 TeV 1 TeV 100 GeV 10 GeV 1 EeV 100 PeV 10 PeV 1 PeV 10 EeV 100 EeV
1 Mpc 100 kpc 10 kpc
10 Mpc
1 Gpc 100 Mpc Mrk 421
Cen A M 31 GC
z=5 z=1
CMB
UV NIR
FIR
Radio
3C 279
Can be used to measure: - EBL - EG magnetic fields - vacuum energy (search for axions) - Cosmological parameters… Data from existing detectors give many hints but are not conclusive Ground
-based detectors
γ + γ à e++ e-
(AdA,Roncadelli&Galan(2013)
EBL
TheEBLaffectsinpar(cularthesignalfromextragalac(csources
Asiago2017
Fermi2FHLandgammahorizon
Asiago2017
Areminder:EBLratherwellconstrained,andSEDextrapola(onfromFermiispossible PKS1424
Ifz=0.6
PKS1424Ifz=0.8
Padova2017
SpectralindexofAGN
Asiago2017
IIIb-Propaga(onofchargedpar(cles
Asiago2017
Thepropaga(oninourgalac(c
52
Propaga(on by:T.Gaisser
Charged cosmic rays diffuse and interact inthe Galac(c randomly magne(zed ISM .Confinement (mes are quite long (τ~107years) and direc(ons become basicallyisotropic.
Transportequa(on:
Sources
Diffusion
Convec(on
Energygainsandlosses
Spalla(ongains
Spalla(onanddecaylosses
( ) ( )( ) ∑>
+−∂∂
+−∇⋅∇+=∂∂
ij j
jji
i
iiiii
i NPNNEbE
NVNDQtN
ττ
!!!
53
Leaky-Box
A box where charged cosmic rays freelypropagates having however some probability toescape by the walls. The sources are uniformelydistributed.
⎭⎬⎫
⎩⎨⎧
++−⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
++= ∑>
esci
decayi
spallii
ijdecayji
spalljiji cNcNQ
τγτσρβ
γτσρβ
1110
Simplifiedsta(onaryequa(on:
Sources Spalla(onanddecaysgains
Spalla(on,decaysandescapelosses
54
Constraining propagation models
Secondary/primaryra(os
10Be/9BeB/C
Unstable/stableisotopos
Radioac(veclocksBoxsize,Diffusioncoef.,escape(me,...
55
D(E)∝Eδ
δ =1/ 3
δ = 0.7
Primary/Primary
CREAM2008
Energy dependence (𝜏𝜏sc) sc) CREAM2008
56
Confinementandcomposi(on
Galac(c~1-3µGIntergala(c1nG>B>1fG
LarmorRadius:
ZeBER =
Magne(cField:
Severalknees?
57
T.Stanev
Galactic Magnetic Field deflection (p)
Above1019:Astronomy!
Anuniqueopportunitytomeasurethegalac(cmagne(cfield?
58
The Greisen-Zatsepin-Kuzmin (GZK) cutoff
protons
p
γ2.7K
Δ N
π
N
Mpc6≈
1=CMBp ρσ
λγ
eV10E 20p ≈
p Δ N
π
N
Energyatsource
Propaga(ondistance(Mpc)
59
GZK is model dependent
Sourcestypeanddistribu(on
Magne(cfields
Primarycomposi(on
Notatruecutoff!
PileupRecoveryofthespectrumathigherenergies?
GZKcutoffEnergy–SteckerandScullyGZKandmagne(cfields(protons)Deligny,Parizot,Letessier-Selvon
1+z Energy(inEeV)
60
Par(cleshowers
Pierre Auger, 1938
d
#
Firstshowerenergyes(mates!
Coincidences
d
61
The events: Cosmic rays “rain”
62
The events: Cosmic rays “rain”
67
Theevents:firstinterac(on
68
Theevents:showerdevelopment
69
Theevents:showerdevelopment
70
Theevents:showerhitsEarthsurface
71
P(Fe)Air➝Baryons(leading,net-baryon≠0)➝π0(π0➝𝛾𝛾𝛾𝛾➝e+e-e+e-➝…)➝π±(π±➝𝜇𝜇±ifLdecay<Lint) ➝K±,D.…
Theevents:showerhitsEarthsurface
72
Particle interactions
-wellknown!
-forwardregion,smallpt,veryhigh
hadronicintera(ons-largeuncertain(es!
s-mainparameters:σin,kin,<n>,(frac(onπ0,NbofBaryons,…)
e.m.andweakintera(ons
Nuclearfragmenta(on
MissingEnergy-Nucleiarenotjustasuperposi(onofnucleons!
-5%to10%…
P(Fe)Air➝Baryons(leading,net-baryon≠0)➝π0(π0➝𝛾𝛾𝛾𝛾➝e+e-e+e-➝…)➝π±(π±➝𝜇𝜇±ifLdecay<Lint) ➝K±,D.…
73
Electromagne(cinterac(ons J. Knapp
74
Hardandsoyhadronicinterac(onsJ.Knapp
Perturba(veQCD
PomeronexchangeGRT
75
Stringfragmenta(on
u
d
u
d
d
u
u
u
π0
π-
Κ-
Κ+
Hadrons!
d
u
s
u
s
u
d
d
u
d
Inthisway,youcanseethatquarksarealwaysconfinedinsidehadrons
(that’sCONFINEMENT)!
Thinkofthegluonsbeingexchangedasaspring…whichifstretchedtoofar,willsnap!Storedenergyinspringàmass!
76
“Standard”Hadronicmodels(lowpt)
SIBYLL
QGSJET
EPOS
Minimum string configuration Ralph Engel
77
Hadronicmodelsparameters P.Tanguy
p air
78
Crosssec(onsextrapola(ons(beforeLHC)
79
Crosssec(onsextrapola(ons(ayerLHC) (P
roto
n-Pr
oton
) [
mb]
inel
σ
30
40
50
60
70
80
90
100
110
[GeV]s310 410 510
Auger 2012 (Glauber)ATLAS 2011CMS 2011ALICE 2011TOTEM 2011UA5CDF/E710TOTEM 2013This work
QGSJETII.3SIBYLL2.1EPOS1.99EPOS-LHCQGSJETII-04
80
LHC Kinematics (14 TeV)
pseudo-rapidity;η=-ln(tan(θ/2))
MulSplicity EnergyFlux
Allpar(cles
neutral
Mostoftheenergyflowsintoveryforwardregion
TakashiSAKO
81
The µs
82
Muon production
83
Muon spectrum at Earth Surface
J.Beringeretal(PDG)PRD86010001(2012)84
J.Beringeretal(PDG)PRD86010001(2012)
Fluxes in the atmosphere
85
UnderEarth
AttheEarthsurface:~70m-2s-1sr-1
~1cm-2min-1(Ω∼π)
1~7.2~Kamiokande2~5.3~GranSasso3~5~Blanc.Mt
)TeV(Threshold)KmWater(DepthPlace
86
Extensive Air Showers (EAS) 1019eV
87
EAStransverseprofiles
5.4s0
2s0
20e )r/r1()r/r(r/N)s(c)r( −− +=ρ
NKG(Nishimura,Kamata,Greisen)
r0:Moliéreradius
s:showerage
Ptdistribu(onsMul(pleCoulombsca]ering
88
EAS longitudinal profiles
⎟⎠
⎞⎜⎝
⎛ −−
−
⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−= λ
λλ
λ
1max
max
1maxXX
X
ee eX
XXNN
Gaisser
Nemax∝E
Xmax∝lnE
Iron~56nucl(E/56)Smallerfluctuac(ons
SmallerXmax
89
ΔX
Xmax=X1+ΔX
Shower development
X1 Xmax
emprofilemuonic
profile
∫ dXdXdNe
E∝Ne∝
dXdXdN∫ µNμ ∝
90