Chapter 9Cosmic Rays

9.1 Composition and energy distributionCosmic rays can be broadly defined as the massive particles, photons (γ rays, X-rays, ultra-violet and infrared radiation, ...), neutrinos, and exotics (WIMPS, axions,...) striking theearth. The primary cosmic rays are those entering the upper atmosphere, the cosmic raysof the interstellar medium. Secondary cosmic rays are those produced by the interactions ofthe primary rays in the atmosphere or in the earth. Also products of cosmic ray interactionsin the interstellar medium (e.g., spallation products from cosmic ray - cosmic ray collisions)are also labeled as secondary cosmic rays. Cosmic rays can be of either galactic (includingsolar) or extragalactic origin.

If we confine ourselves to the particle constituents (protons, nuclei, leptons), their motion inthe galaxy has been roughly randomized by the galactic magnetic field. (We will mentionsome exceptions to this below.) Thus they provide very little information about the directionof the source. The peak of the distribution in energy is in the range of 100 MeV - 1 GeV.The intensity of cosmic rays of energy 1 Gev/ nucleon or greater is about 1/cm2sec sr. Anapproximate formula is

IN(E) ∼ 1.8(

E

GeV

)αnucleons/cm2 sec sr (1)

where E is the energy per nucleon (rest and kinetc) and α ∼ -2.7. The energy density cor-responding to this is thus about 1 ev/cm3. This can be compared to the energy density ofstellar light of 0.3 eV/cm3.

The principal components of the (primary) cosmic rays are shown Figure 1. This abundancedistribution is approximately independent of energy, at least over the dominant energy rangeof 10 MeV/nucleon through several GeV/nucleon. By mass about 79% of nucleons in cosmicrays are free protons, and about 80% of the remaining nucleons are bound in helium. Thecomposition has been measured by instruments mounted on balloons, satellites, and space-craft. Figure 2 shows the chemical distribution of the elements in our solar system differsfrom that of the cosmic rays in some remarkable ways. The most dramatic difference is anenormous enrichment in the cosmic ray abundances for the elements Li/Be/B. Note also thatthere is enrichment is even Z elements relative to odd Z, when normalized to solar systemabundances. Finally the cosmic rays are enriched in the heaviest elements relative to H andHe.

As can be seen from Figure 2, many elements heavier than the iron group have been mea-sured with typical abundances of 10−5 relative to iron. Much of this information was gainedfrom satellite and spacecraft measurements over the last decade. Some of the conclusions:1) Abundances of even Z elements with 30 ∼< Z ∼< 60 are in reasonable agreement with solarsystem abundances.

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20. Cosmic rays 3

Dif

fere

nti

al fl

ux

(m2

sr s

MeV

/nu

cleo

n)−

1

Kinetic energy (MeV/nucleon)

H

He

C

Fe

105 10610410310210 107

10−5

10−6

10−7

10−8

10−9

10−4

10−3

10−2

0.1

10

1

Figure 20.1: Major components of the primary cosmic radiation (from Ref. 1).

Most measurements are made at ground level or near the top of the atmosphere,but there are also measurements of muons and electrons from airplanes and balloons.Fig. 20.3 includes recent measurements of negative muons [3,13,14,15]. Since µ+(µ−) areproduced in association with νµ(νµ), the measurement of muons near the maximum ofthe intensity curve for the parent pions serves to calibrate the atmospheric νµ beam [16].

June 14, 2000 10:39

Figure 1: Major components of the primary cosmic rays (from Simpson).

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2.1. COMPOSITION 11

Figure 2.1: Relative abundance of elements in cosmic rays and in the solarsystem.

Figure 2: The abundances of cosmic rays are compared with solar abundances.

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Z Element Relative Abundance1 H 4852 He 263-5 Li-B 0.406-8 C-O 2.209-10 F-Ne 0.3011-12 Na-Mg 0.2213-14 Al-Si 0.1915-16 P-S 0.0317-18 Cl-Ar 0.0119-10 K-Ca 0.0221-25 Sc-Mn 0.0526-28 Fe-Ni 0.12

Table 1: Relative abundances of cosmic ray nuclei at 10.6 GeV/nucleon normalized to oxy-gen (=1). The oxygen flux at kinetic energy 10.6 GeV/nucleon is 3.26 × 10−6/cm2 sec sr(GeV/nucleon)−1. From Boezio et al. and Engelmann et al., as quoted by Gaisser andStanev.

2) In the region 62 ∼< Z ∼< 80, which includes the platinum-lead region, abundances are en-hanced relative to solar by about a factor of two. This suggests an enhancement in r-processelements, which dominate this mass region. This is consistent with r-process scenarios wehave discussed (e.g., if the r-process site is core-collapse supernovae, then one would expectenrichment in r-process nuclei as supernovae are also believed to be the primary accelera-tion mechanism for lower energy cosmic rays). However, one also needs to consider whetherheavier nuclei with larger charges might be confined in the galaxy for a longer time, anothereffect that could differentiate heavy from light nuclei.

Galactic cosmic rays are fully ionized: the acceleration mechanisms fully strip the ions. Cos-mic rays also have an antimatter component, as measured in the Space Shuttle DiscoveryAMS (Alpha Magnetic Spectrometer) experiment. The AMS detected about 200 antipro-tons above 1 GeV, generally attributed to nuclear collisions of CR particles with interstellarmatter.

The energy distribution of cosmic rays from about 1010eV to about 1015eV is smooth, witha power-law distribution

particles/cm2 sec MeV/n ∝ Es (2)

with s between -1.6 and -1.7. However there is a break or “knee” in the curve at about 1015

eV. The slope sharpens above this knee (see Figure 3), falling with s ranging from -2.0 to-2.2, eventually steeping to an exponent of above -2.7. The knee is generally is attributedto the fact that supernova acceleration of cosmic rays is limited to about this energy. Thiswould argue that the cosmic rays above this energy either have a different origin, or were

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cr-knee.gif (GIF Image, 468x333 pixels) http://imagine.gsfc.nasa.gov/docs/features/topics/snr_group/images...

1 of 1 03/10/2004 10:17 AM

Figure 3: Energy spectrum of cosmic rays, showing a kink or ”knee” near 1015 eV.

further accelerated after production. While this break is commonly attributed to the inabil-ity of supernova shocks to accelerate particles to energies beyond the knee, the sharpness ofthe knee has troubled many of the experts: in is difficult to find natural models that producesuch a defined break.

There is an additional, somewhat less distinct feature at an energy of about 1019 eV, termedthe ankle. Characteristics of this high-energy feature will be discussed later.

9.2 Propagation and originThe most commonly used toy model for galactic cosmic rays is called the ”leaky box” model.It assumes that the cosmic rays are confined within the galactic disk, where the mass densityis high, but with some gradual leaking out of the disk. The confining force is the galacticmagnetic field, which is on the order of 10−7 Gauss. A relativistic particle moving in amagnetic field executes a helical path. Using the relation between the momentum p, field B,and magnetic radius R,

p⊥(MeV/c) = 3× 10−4BR(gauss cm) (3)

one sees that a 1014 eV proton would have a radius of 3 × 1018 cm, or 1pc, which is much

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less than the distance to the Crab nebulae, a potential accelerator for cosmic rays relativelynear earth. Thus cosmic rays from the knee and below will have no memory of their originwhen they reach earth. A 1018 eV proton corresponds to 10 kpc, about the galactic radius.Clearly any cosmic ray much above this energy could be presumed to be extragalactic, unlessit can be associated with a local source, which would be possible as the direction of suchcosmic rays would point back to their origin. For example, a cosmic ray of energy 1020 eVwould be minimally perturbed by the galactic magnetic field and thus would ”point back”to the extragalactic source from which the cosmic ray originated.

The leaky box models cosmic ray production in the galaxy, cosmic ray trapping by magneticfields and eventual escape, and cosmic ray interactions in the intragalactic medium. Thismodel does a good job in explaining the energy-dependence of the life of cosmic rays (moreon this later). But others have argued for other models, including closed models wherecosmic rays are fully confined, then explaining isotope lifetimes (see below) through devicessuch as a combination of a few nearby and many distant cosmic ray sources.

The conventional explanation for the most dramatic isotopic anomaly in the cosmic rays,the enrichment in Li/Be/B by about six orders of magnitude, is that these isotopes areproduced in the interstellar medium when accelerated protons collide with C, N, and O.We mentioned this process earlier. The enrichment of odd-A nuclei (these also tend to berelatively rare in their solar distribution since stellar processes tend to favor production ofmore stable even A nuclei) is also often attributed to spallation reactions off more abundanteven-A nuclei. These associations immediately lead to some interesting physics conclusionsbecause, from the known density of cosmic rays (at least in the earth’s vicinity) and fromknown spallation cross sections, one can estimate the amount of material through which atypical cosmic ray propagates. Although the estimates are model dependent - and probablynot sufficiently interesting to go through in detail - the resulting values for the effectivethickness are typically 4 - 6 g/cm2. Now the mass density within intragalactic space isabout 1 proton/cm3, or about 1.7· 10−24 g/cm3. Thus taking a velocity of c, we can crudelyestimate the cosmic ray lifetime

1.7× 10−24g/cm3 × (3 · 1010cm/sec)× t = (4− 6)g/cm2 (4)

So this givest ∼ 3 · 106y (5)

This calculation assumes an average galactic mass density that is not known by direct mea-surement. Thus it is nice that a more direct estimate of the galactic cosmic ray lifetime isprovided by cosmic ray radioactive isotopes. The right chronometer is one that has a lifetimein the ballpark of the estimate above. 10Be, with a lifetime of 1.51 ×106 y, is thus quitesuitable. It is a cosmic ray spallation product: this guarantees that it is born as a cosmicray. Its abundance can be normalized to those of the other, stable Li/Be/B isotopes: thespallation cross sections are known. Thus the absence of 10Be in the cosmic ray spectrumwould indicate that the typical cosmic ray lifetime is much larger than 1.51 · 106 y. The

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survival probability should also depend on the 10Be energy, due to time dilation effects. Oneobserves a reduction in 10Be to about (0.2-0.3) of its expected instantaneous production,relative to other Li/Be/B isotopes. From this one concludes

t ∼ (2− 3) · 107years

This suggests that the mass density estimate used above (in our first calculation) may havebeen too high by a factor of 5-10.

In modeling the origin of cosmic rays, the first conclusion, given their richness in metals, isthat must come from highly evolved stars such as those that undergo supernovae. We havealready noted the abundance of r-process nuclei, which could be taken as a “smoking gun”of supernova dominance, for those who accept that supernovae are the r-process site.However this is clearly not the full picture. Studies of the isotopic composition as the kneeis approached shows that the composition changes: the spectrum of protons becomes notice-ably steeper in energy, while the iron group elements do not show such a dramatic change.This is qualitatively consistent with the notion that the galactic ”accelerator” producingcosmic rays tops out at some maximum confining field strength. Because the accelerationlikely scales as ZB, where Z is the charge, the very highest energies should be dominatedby the largest Zs, the nuclei.

Above the knee - at energies above 1016 eV the galactic magnetic field is too weak to ap-preciably trap particles. Thus it is probable that at these high energies the character of thecosmic rays changes from primarily galactic to primarily extragalactic: the trapping thatenhances the abundances of lower-energy galactic cosmic rays would not enhance very highenergy ones.

The cosmic rays appear to be approximately isotropic – once one gets above about 50 GeVto escape local magnetic effects. One exception is a small anisotropy measured by AGASA,excess events at about 1018 eV pointing back to the galactic center - which generated thespeculation that these are neutrons, which because of time dilation can reach the solar systemonce they reach 1018 eV. If this speculation were true, it would argue for a central galacticaccelerator that (most likely) is capable of accelerating ions up to 1018 eV per nucleon. Re-cent results from Pierre Auger find no evidence for the AGASA anomaly.

9.3 Energetics and origin of galactic cosmic raysWe now have the basic information needed to calculate the energetics of galactic cosmic rays.If we take the galactic radius as 10 kpc, we have a volume of 1068 cm3. We noted that theenergy density of cosmic rays is about 1 eV/cm3. Thus the cosmic ray energy content of thegalaxy is about 1068 eV. We have argued above that the lifetime of cosmic rays might beabout 107 years. Thus the energy production in cosmic rays must be about

1068eV/107y ∼ 3× 1054eV/sec ∼ 5× 1042ergs/sec. (6)

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We mentioned in passing above that there are cosmic ray models that, unlike the leaky box,confine cosmic rays longer – and thus need to contrive localize sources to account for Be,etc. Thus our energetics calculation could be modified, replacing the leaky box model withone where the cosmic rays were effectively confined over times up to the age of the galaxy.This would extend the dwell times by up to three orders of magnitude, and thus reduce theenergetics requirement proportionally. So that in principle would lower the galactic energeticrequirement to about 1040 ergs/sec. The result is a very generous range for the necessaryenergetics, requiring sources capable of generating between 1040 and 5 · 1042 ergs/sec.

One can quickly show that stellar winds – e.g., the flares our sun produces – are insufficientenergetically to produce energy at this rate, even if integrated over the 1011 potential sourcesin the galaxy – the integrated energy in stellar flares falls short of the lower bound above byat least one and perhaps two orders of magnitude. But an interesting source is supernovae –they eject large quantities of material, that material includes both protons and nuclei, andthe shock wave and associated fields are an acceleration mechanism.

We have seen that the explosion energy of a supernova is about 1051 ergs, and the estimatedrate of Type II supernovae is 1/30 years. Additional contributions would come from rarerclasses of core-collapse supernovae, SNIb SNIc. Thus the energy production rate is about1042 ergs/sec – close to that estimated above. There are many arguments based on the chem-ical patterns of cosmic rays that support core-collapse supernovae as a principal mechanismfor generating and accelerating cosmic rays. Novae are powered by the accretion onto awhite dwarf. The matter is sucked from a large companion star, perhaps a red giant or mainsequence star, under conditions that allow periodic thermonuclear runaway reactions on thewhite dwarf surface. Novae are another plausible contributor. Novae outbursts within ourgalaxy occur with a frequency of about 100/year with an energy output about 10−4 that ofthe ejecta from a core-collapse supernova. Thus the integrated nova output is similar to thatof galactic supernovae.

9.4 Solar-system, terrestrial, and atmospheric environmental effectsCosmic rays measured on earth reflect not only the galactic inventory of cosmic rays, butalso the effect of the local environment of our solar system, the earth, and the atmosphere.The sun’s heliosphere – the region of space altered by the solar wind – extends to about 200AU. The magnetic structure of the heliosphere shields the region against energetic chargedparticles. This is apparent experimentally from the correlations between induced cosmic rayactivity measured on earth and the 11-year solar cycle, as shown in Fig. 4. This correla-tion is reflected in changes in the chemistry of the atmosphere, such as 14C production, animportant radio-isotope for dating. 14C is a product of cosmic ray interactions with O inthe atmosphere, and the production is anticorrelated with the shielding, and thus with theintensity of solar activity. Interesting, 14C production also appears to correlate with variouslong-term climate anomalies of the past 1000 years, such as the Maunder Minimum (14Chigh) and the 12th-Century Maximum (low), leading to some interesting speculations about

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Figure 4: The top curve is the cosmic ray flux from the neutron monitor in Climax, Colorado(1953 – 1996). The middle curve is the annual mean variation in the cosmic ray flux asmeasured by ionization chambers (1937 – 1994). The bottom curve is the relative sunspotnumber. While there is a clear solar cycle modulation of the cosmic ray flux, the amplitudesare not well correlated. From Svensnak.

the solar role in climate change.

There are also more localized effects due to the earth’s magnetic field, a dipolar field thatextends from the magnetic poles and thus is roughly parallel to the earth surface at theequator (Fig. 5). If we envision a cosmic ray proton come into the earth at the equationand use 1000 km as a rough trapping radius, then our previous formula

p⊥(MeV/c) = 3× 10−4BR(gauss cm)

for B=0.3 Gauss would give a p ∼ E ∼ 10 GeV as the energy of the trapped proton. Thusthis defines an energy below which charged cosmic rays would not penetrate to the surface,but instead be sharply deflected. This is the reason that so many cosmic ray balloon exper-iments are done at the poles, where the magnetic fields are weaker away from the earth andmore perpendicular to the surface: one can then more easily sample cosmic rays character-istic of the environment away from the immediate terrestrial neighborhood.

The trapping of lower-energy cosmic rays by the earth’s magnetic field in also part of the

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Figure 5: Rough representation of the earth’s magnetic field, which has an average valuenear the surface of about 0.3 Gauss.

third effect of the local environment, interactions of the cosmic rays with the atmosphere.The trapping leads to a larger time in the vicinity of upper atmosphere and thus enhancesnuclear interactions than can produce all sorts of cosmic ray secondaries. Such secondariesare also produced by higher energy cosmic rays that are not perturbed significantly by themagnetic field, but do interact in the upper atmosphere. The secondaries include pions,muons, new nuclei created by spallation, electrons and positrons, neutrinos, and the high-energy showers produced by very energetic cosmic ray interactions.

The density profile of the atmosphere is approximately exponential with a scale height ofabout 7.6 km,

ρ(r) = 1.205× e−r/7600mkg/m3. (7)

Thus the total amount of matter that a cosmic ray encounters on approaching the earthgrows exponentially with decreasing altitude.

9.5 Muons and neutrinos at the earth’s surface and below.The muons and neutrinos, the most penetrating components of the cosmic ray secondaries,result from strong interaction mechanisms that produce pions and kaons through decaychains such as

π+ → µ+ + νµ

µ+ → e+ + νe + νµ (8)

as we have discussed before. Figure 6 illustrates some important features of these and othercosmic ray secondaries. The figure was generated by cascade code calculations that begin

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4 20. Cosmic rays

5070

100

200

300

500electrons + positrons

10 100 1000E [GeV]

E3 d

N/d

E

[m–2

s–1

sr–

1 G

eV2 ]

Figure 20.2: Differential spectrum of electrons plus positrons multiplied by E3

(data summary from Ref. 7). The dashed line shows the proton spectrum multipliedby 0.01.

15 10 5 3 2 1 0

0 200 400 600 800 10000.01

0.1

1

10

100

1000

10000

Atmospheric depth [g cm–2]

Ver

tica

l flu

x

[m–2

s–1

sr–

1 ]Altitude (km)

µ+ + µ−

π+ + π−

e+ + e−

p + n

νµ + νµ_

Figure 20.3: Vertical fluxes of cosmic rays in the atmosphere with E > 1 GeVestimated from the nucleon flux of Eq. (20.2). The points show measurements ofnegative muons with Eµ > 1 GeV [3,13,14,15].

Because muons typically lose almost two GeV in passing through the atmosphere, the

June 14, 2000 10:39

Figure 6: The solid lines show vertical fluxes of cosmic rays in the atmosphere with energyabove 1 GeV, as estimated from parameterized initial nucleon primary fluxes. The pointsare from measurements of µ−. From Gaisser and Stanev.

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6 20. Cosmic rays

1 10 100 1000

0.01

0.02

0.05

0.002

0.005

0.1

0.2

pµ (GeV/c)

p µ2.

7 dN

/d

p µ [

cm–2

s–1

sr–

1 (

GeV

/c)1

.7]

Figure 20.4: Spectrum of muons at θ = 0◦ (� [18], � [20], H [21], N [22], X,+ [23]),and θ = 75◦ � [24]).

Figure 20.4 shows the muon energy spectrum at sea level for two angles. At large angleslow energy muons decay before reaching the surface and high energy pions decay beforethey interact, thus the average muon energy increases. An approximate extrapolationformula valid when muon decay is negligible (Eµ > 100/ cos θ GeV) and the curvature ofthe Earth can be neglected (θ < 70◦) is

dNµdEµ

≈0.14E−2.7

µ

cm2 s sr GeV

×

1

1 +1.1Eµ cos θ

115 GeV

+0.054

1 +1.1Eµ cos θ

850 GeV

, (20.5)

where the two terms give the contribution of pions and charged kaons. Eq. (20.5) neglectsa small contribution from charm and heavier flavors which is negligible except at veryhigh energy [27].

The muon charge ratio reflects the excess of π+ over π− in the forward fragmentationregion of proton initiated interactions together with the fact that there are more protonsthan neutrons in the primary spectrum. The charge ratio is between 1.1 and 1.4 from1 GeV to 100 GeV [18,23]. Below 1 GeV there is a systematic dependence on location dueto geomagnetic effects. [23]

June 14, 2000 10:39

Figure 7: The spectrum of muons at the earth’s surface at θ = 0 degrees (solid points) and75 degrees (open diamonds). From Gaisser and Stanev.

with the primary cosmic ray spectrum at the top of the atmosphere, then propagate thatspectrum and the associated secondaries through the atmosphere, taking into account thevarious reactions that produce new particles and degrade their energies. In contrast to thevery large flux/energy losses encountered for other secondaries, the muons and neutrinosgenerally penetrate the atmosphere well. The atmosphere (and earth) are transparent toneutrinos, while muons typically lose 2 GeV in ionization energy while transiting the atmo-sphere.

Consequently muons dominate the charged-particle spectrum at the earth’s surface. Theyare the most easily measured component of the cosmic rays and also the primary backgroundin a lot of neutrino experiments – the reason such neutrino experiments must go deep un-derground. The effects of energy loss are illustrated in Figure 7, where the vertical flux ofmuons at the earth’s surface is compared with the much harder spectrum that results formuons impinging the earth at 75 degrees from vertical. The latter must penetrate muchmore matter, which then hardens the spectrum.

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Muons lose energy by ionization, bremsstrahlung, production of e+e− pairs, photonuclearreactions like Compton production, etc. Their range R in standard rock (Z ∼ 11, ρ ∼ 2.65g/cm3) is given in the table. R is given in meters-of-water-equivalent (mwe), or 102 g/cm2.The energy loss is given in terms of α,

−dEµdx

= α. (9)

The table shows that the energy loss per g/cm2 increases sharply between 100 GeV and 1TeV, a result of direct bremsstrahlung, pair production, and nuclear reactions taking overfrom ionization losses, which dominate at lower energy. The former grow linearly with themuon energy. Consistent with the table, a rough rule of thumb is that the net flux of muonsunderground decreases by an order of magnitude for every 1500 mwe, or about 500m ofstandard rock.

Some of you may know that there has been great interest in establishing underground lab-oratories in the U.S. for sensitive dark matter, neutrino, and nucleon decay experiments.While Europe has facilities like Gran Sasso and Frejus, Russia has Baksan, and Japan hasKamioka, the deepest current site in the US is the Soudan Laboratory, operated by theUniversity of Minnesota, at a depth of 710 m. Access underground at Soudan is challengingbecause of the small lift that provides vertical access to that site.

One wonderful development for North America, however, is SNOLab, an expansion of theSNO experimental area in the Sudbury Mine, including both additional underground roomsand a significant surface support facility. This is the world’s deepest underground laboratory,two kilometers underground and providing 6010 mwe in overburden (more than two kilome-ters of rock overburden). Furthermore, as the nickel deposits that interest the mine’s ownerhave so far continued to be increasingly rich at depth, it quite conceivable that the minecould some days reach depths of three kilometers or more. As discussed below, this wouldapproach the ultimate depth for an underground laboratory, the point at which atmosphericneutrinos become an irreducible background.

Some next-generation experiments could require 5000 mwe or more of overburden. Examplesinclude certain next-generation dark matter, solar neutrino, and double beta decay efforts.Overburden is often important in experiments focused on measuring low-energy events: pen-etrating muons themselves can often be vetoed by ”turning off” the detector after a muonis detected. (Kamiokande, for example, has about a 10% deadtime due to this techniquefor background suppression.) But muons, in addition to producing prompt secondaries likeknock-out neutrons, can also activate nuclei in the detector that, some time later, decay toproduce a signal. In cases where there is a long delay before the induced activity is detected,conventional vetoing techniques can lead to an unacceptable deadtime. In such cases thereis no alternative but great depth to remove the initiating muon events.

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Eµ (GeV) R (1000 mwe) α (10−6 MeV cm2/g)

10 50 2.19100 410 2.741000 2450 6.6010000 6090 46.43

Table 2: From Gaisser and Stanev: the calculated ranges R and energy losses (per gm/cm2)α are both sharply dependent on the muon energy, and lead to a systematic hardening ofthe muon spectrum as one goes underground.

In other cases, backgrounds may be controllable at moderate depth, making great depthless important than other factors, such as the economies that come from ease of access: theability to ”drive-in” large equipment and efficiently operate large experiments may be thepriority. Both Gran Sasso and Kamioka, the world’s premier underground laboratories, aredrive-in facilities at moderate depth.

While Europe has established several underground laboratories (Gran Sasso, Canfranc, Fre-jus,...) and while Japan has steadily developed Kamioka, the US has lacked a comparablefacility. Experiments were done at Homestake before the mine’s closing ten years ago, andthe Soudan Mine (Minnesota) and WIPP (New Mexico) both currently host experiments.But a site offering good and frequently experimental access and depth comparable to ourbetter than Gran Sasso has been lacking. The NSF headed a ten-year effort o create a DeepUnderground Science and Engineering Laboratory in the US, settling early on Homestake asthe preferred site, but very recently (and oddly) decided the operation of such a facility wasnot in its mandate. A DOE-appointed committee is now trying to sort things out, thoughthe cost of developing Homestake is a major obstacle, given how tight science budgets areexpected to be in 2012 and beyond, and given DOE obligations to existing as well as new,previously approved projects.

The relevance to the present discussion is the importance of being able to calculate the muonflux at depth, folding the energy and angular spectrum at the surface with the site topog-raphy. An example shown here were the investigations of University of Washington physicsgrad student Kregg Philpott to determine the effective depth of a tunnel in the Cascades,which several years ago was a DUSEL candidate. The resulting contours of the muon fluxunder the Steven Pass’s Cowboy and Big Chief Mountains is shown in Fig. 8, for a horizontalslice at the Pioneer tunnel’s elevation. This tunnel proves to be at just the right place forconvenient access to the point of greatest overburden, under Cowboy Mt. The resulting flux,2.07 × 10−7/cm2sec, is about 90% that at Kamioka (2.28 × 10−7/cm2sec). .

While we have discussed going deep underground to find an environment sufficiently cleanto do neutrino physics, there are some absolute limits to what can be achieved. Atmospheric

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Figure 8: The cosmic ray muon flux under Cowboy Mt., Stevens Pass, at the 743 m elevationof the Pioneer Tunnel. Calculation done by Kregg Philpott.

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neutrinos provide a underground source of high-energy muons and electrons that does notattenuate: these are the muons that the energetic atmospheric neutrinos produce as secon-daries. As Figure 9 shows, at a depth of about 10 km mwe (3.5 km of rock) these become aconstant background that is not reducible by going further underground. It also follows thatupward going muons (or electrons, though they have a shorter range) in deep detectors thuscan be used as a signal of neutrino reactions in the rock below. Figure 10 is a reminder ofour earlier discussion describing how these neutrino fluxes were exploited to probe neutrinooscillations, through the muons and electrons they produce in underground detectors.

Given that we have discussed so many aspects of the terrestrial neutrino flux, including thechanges induced by neutrino oscillations, it is amusing to display the local neutrino spectrumin its entirety in Figure 11. The atmospheric neutrinos, despite their importance due to theirhigh energies and larger cross sections in matter, do not appear on the graph because theirfluxes are so low. Two sources we have not discussed in detail are the geoneutrinos, producedfrom terrestrial radioactivity and perhaps recently seen in KamLAND, and the thermal flux(∼ keV) of solar neutrinos of all flavors, generated in our sun from neutral current processes,analogous to those we discussed (at higher energies) in the context of supernovae cooling.

9.6 The highest energy cosmic rays, the GZK cutoff, and Pierre AugerSome of the most curious observations in cosmic ray physics have to do with the highestenergy cosmic rays. A number instruments, such as the Fly’s Eye and AGASA detectors,and most recently the Pierre Auger observatory, are designed with sensitivity to ultrahigh-energy cosmic rays. For example, the Fly’s Eye uses air fluorescence to detect UHE cosmicrays. An extensive air shower is generated when a primary cosmic ray interacts with theatmosphere. This is imaged using the fluorescence light produced by excitation of the ni-trogen molecules by the secondaries in the extensive air shower. The shape of the showerallows the experimenters to reconstruct the energy of the primary. It also may provide someinformation on composition. The Fly’s Eye can provide stereo information on the developingshower because of detector arrays located 3.4 km apart.

The rare high energy events show some structure, particularly around 1019eV, where thespectrum flattens from a slope of about -3.0 to one of about -2.6. Some years ago therewere claims that events were been seen above the so-called Greisen-Zatsepin-Kuzmin cutoffof about 1020 eV. At one time there were tens of such events extending up to about 1021

eV )(see Figs. 12 and 13). The GZK cutoff is explained below, the new results from PierreAuger are described.

The cosmic medium is filled by background radiation of relic photons, left over from theback bang and noninteracting since the time electrons and nuclei recombined to form atoms.Their typical energy is about 10−3 eV. We consider the propagation of a high energy protonthrough this medium.

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20. Cosmic rays 9

1 10 100

Ver

tica

l in

ten

sity

(cm

−2sr

−1s−

1)

10−14

10−12

10−10

10−8

10−6

Depth (km water equivalent)

Figure 20.5: Vertical muon intensity vs depth (1 km.w.e. = 105 g cm−2 of standardrock). The experimental data are from: �: the compilations of Crouch [32], �:Baksan [33], f: LVD [34], v: MACRO [35], �: Frejus [36]. The shaded area atlarge depths represents neutrino induced muons of energy above 2 GeV. The upperline is for horizontal neutrino-induced muons, the lower one for vertically upwardmuons.

Contained and semi-contained events reflect neutrinos in the sub-GeV to multi-GeVregion where the product of increasing cross section and decreasing flux is maximum. Inthe GeV region the neutrino flux and its angular distribution depend on the geomagneticlocation of the detector and, to a lesser extent, on the phase of the solar cycle. Naively,we expect νµ/νe = 2 from counting neutrinos of the two flavors coming from the chainof pion and muon decay. This ratio is only slightly modified by the details of the decaykinematics, but the fraction of electron neutrinos gradually decreases above a GeV asparent muons begin to reach the ground before decaying. Experimental measurementshave to account for the ratio of ν/ν, which have cross sections different by a factor of 3 inthis energy range. In addition, detectors generally have different efficiencies for detectingmuon neutrinos and electron neutrinos which need to be accounted for in comparing

June 14, 2000 10:39

Figure 9: Vertical muon intensity as a function of depth (in km.w.e.) The shaded regionat depth represents neutrino-induced muons above 2 GeV. The upper line is for horizontal-induced muons, the lower one for vertically upward muons. From Gaisser and Stanev.

17

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mber

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Figure 1: The SuperKamiokande atmospheric neutrino results showing excel-lent agreement between the predicted (blue lines) and observed electron-likeevents, but a sharp depletion in the muon-like events for neutrinos comingfrom below, through the earth. The results are fit very well by the assump-tion of νµ → ντ oscillations with maximal mixing (red lines).

4

Figure 10: The SuperKamiokande atmospheric neutrino results – which exploited the factthat penetrating neutrinos produce a irreducible flux of electrons and muons at depth.

18

FIG. 4. Natural neutrino sources. The terrestrial νe flux and continuous flux of extragalactic

supernova neutrinos of all flavors are from Krauss et al. [12]. The solar (fusion) νe flux is the

standard solar result of Bahcall et al. [11]. The thermal solar neutrinos are for a single flavor.

spectrum contains a great deal of information on the temperature distribution within thesun.

These remarks are made because the most likely opportunity for measuring the thermalneutrino spectrum is a process that depends on flux density, not on total flux, and whichsamples that flux at a precise energy, the resonant reaction

νe + e− + (A,Z) → (A,Z − 1). (23)

This reaction has been discussed previously in connection with terrestrial νe sources [12].Cross sections can be large in high Z atoms, where the electron overlap with the nucleusis favorable. Because nuclear level widths are very narrow, this process samples the νe fluxdensity at a discrete energy. The are several possible candidate transitions with energiesbetween 2 and 20 keV. (One that has been studied in connection with neutrino mass mea-surements is the decay of long-lived 163Ho to 163Dy, which has a positive q-value of less than3 keV: either a neutrino mass or νe inducement of electron capture alters the atomic orbitsthat participate in the capture.)

The heavy-flavor neutrino flux also contains interesting information: if the existence ofthis flux were established, it would immediately impose kinematic mass limits of ∼ 1 keV onthe νµ and ντ . Unfortunately there is no obvious possibility for measuring these species. Theproblem could well prove as difficult as in the case of the cosmic microwave neutrinos, whereexisting experimental bounds exceed the expected flux by about 15 orders of magnitude [14].

11

Figure 11: The fluence of neutrinos at earth, ranging from cosmic background neutrinos tothose produced by high-energy cosmic ray interactions in the atmosphere. From Haxton andLin.

19

14 20. Cosmic rays

0.1

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E [eV/nucleus]

E2.

7 dN

/d

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cm–2

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sr–

1 G

eV1.

7 ]

Figure 20.9: The all-particle spectrum: � [52], N [54], H [55], O [56], 4 [57],+ [58], X [59], � [60]. References for the high energy portion of the spectrum aregiven in Fig. 20.10.

of the muons (ρµ) is larger and depends on the transverse momenta of the muons atproduction as well as multiple scattering.

There are large fluctuations in development from shower to shower, even for showers ofthe same energy and primary mass—especially for small showers, which are usually wellpast maximum development when observed at the ground. Thus the shower size Ne andprimary energy E0 are only related in an average sense, and even this relation dependson depth in the atmosphere. One estimate of the relation is [52]

E0 ∼ 3.9× 106 GeV (Ne/106)0.9 (20.13)

for vertical showers with 1014 < E < 1017 eV at 920 g cm−2 (965 m above sea level).Because of fluctuations, Ne as a function of E0 is not the inverse of Eq. (20.13). As E0

increases the shower maximum (on average) moves down into the atmosphere and therelation between Ne and E0 changes. At the maximum of shower development, there areapproximately 2/3 particles per GeV of primary energy.

Detailed simulations and cross-calibrations between different types of detectors arenecessary to establish the primary energy spectrum from air-shower experiments [52,53].Figure 20.9 shows the “all-particle” spectrum. In establishing this spectrum, efforts havebeen made to minimize the dependence of the analysis on the primary composition. Inthe energy range above 1017 eV, the Fly’s Eye technique [71] is particularly useful becauseit can establish the primary energy in a model-independent way by observing most of thelongitudinal development of each shower, from which E0 is obtained by integrating theenergy deposition in the atmosphere.

June 14, 2000 10:39

16 20. Cosmic rays

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Figure 20.10: Expanded view of the highest energy portion of the cosmic-rayspectrum: o [71] (stereo), � [71] (monocular) � [72], H [73].

June 14, 2000 10:39

Figure 12: From about ten years ago, when an all-particle cosmic-ray spectrum derived fromexisting detectors showed approximately 20 cosmic ray events with energies between 1019

and 1021 eV. An expanded spectrum is also shown. From Gaisser and Stanev.

20

Figure 13: A comparison of the HIRES and AGASA high-energy cosmic ray events. Thelatter data set tends to show more events at or above 1020 eV.

21

Let pµ = (ε, ~p) be the photon four-momentum. Then |~p| = ε. Let Pµ = (ω, ~P ) be the protonfour-momentum. We evaluate in the center-of-mass

(P µ + pµ)(Pµ + pµ) = (ω + ε)2 = ε2CM (10)

which we recognize as the square of the center-of-mass energy. Note that if εCM exceeds

mπ +MN (11)

then clearly the reactionγ +N → π +N (12)

can occur, degrading the nucleon energy. But the center-of-mass energy is a Lorentz invariantquantity, so it can be evaluated in the laboratory frame

ε2CM = M2N + 2ωε− 2~P · ~p (13)

As the cosmic background photons are moving in all directions, we are free to maximize theRHS by taking cos θ ∼ −1. Noting that the incident nucleon is highly relativitistic

(εmaxCM )2 ∼M2N + 4ωε (14)

Thus the requirement for photoproduction is εmaxCM ∼> mπ +MN ⇒

ω ∼>m2π + 2MNmπ

4ε∼ MNmπ

2ε

∼ 3 · 1020

(2.7K

Eγ

)eV (15)

This results in a mean free path for protons of about 108 light years for protons at ∼ 1020

eV or higher energies, a distance substantially smaller than the horizon. Thus if the originof such cosmic rays is all of extragalactic space, there should be a very sharp cutoff in thecosmic ray flux at about this energy. This is called the Greisen-Zatsepin-Kuzmin cutoff, andis shown in the figure. Yet the very high energy events from AGASA show no evidence forany such cutoff.

The AGASA events created a lot of controversy. Fairly mundane solutions were offered, suchthat these high energy events are exclusively nuclear (CNO elements and then iron), whichcan achieve higher energies at lower velocities. It has been suggested that the events aresecondaries from the collisions of still higher energy neutrinos. However this requires newphysics in that the Standard Model predicts a declining neutrino cross section above the Zmass that would not be sufficient to produce the needed event rate, it is thought. It waspointed out that ultrahigh energy cosmic rays both above and below the GZK cutoff couldbe of relatively local origin, thus evading the cutoff – but also raising new questions of whatconfines the cosmic rays if they are extragalactic but somehow produced primarily in a local

22

region about us. Perhaps we are somehow near some remarkable local source or sources: ourposition in the cosmos is special.

In fact the expect GZK cutoff involves a lot of physics. Pion production may be the key issuefor protons, but in nuclei additional processes have to be considered. At a center-of-massenergy considerably below pion production theshold, nuclei can absorb (in their rest frame)a photon of energy ∼ 20 MeV, resulting in photodistintegration. This leads to a GZK cutofffor iron nuclei of ∼ 5 · 1020eV.

Very high energy cosmic ray interactions with atmospheric nuclei lead to an extensive airshower of secondary particles that, by the time the shower reaches the earth’s surface, maynumber in the billions and cover an area as large as 25 square kilometers. The event rateof very high energy collisions, above 1019 eV, is about 1 per 100 square kilometers per year.Because of this daunting number, the recent construction of the Pierre Auger Observatorywas a major step forward for the field. This detector is sited in western Argentina and itssurface sites are spread over an area of about 4000 square kilometers. The detector is ahybrid, with two detection schemes. One scheme uses 1600 water-tank detectors that forma grid with spacings of about 1.5 km. Energetic particles scattering in the detector produceCerenkov light that is recorded by phototubes mounted on the tanks. So a shower coveringup to 25 square kilometers might be recording simultaneously in 5-10 tanks. The energy ofthe incident particles can be estimated from the amount of light produce in the tanks, andthen this energy can be extrapolated over the entire detection area (that is, one corrects forthe small fraction of the surface that is covered by tanks) to determine the total shower en-ergy. The second scheme uses the upper atmosphere as the detection medium. The chargedparticles in the shower interact with atmospheric nitrogen, leading to atomic excitation andsubsequent emission of ultraviolet light. The resulting N fluorescence is recorded in PierreAuger’s optical detectors – a grid of focusing mirrors to collect light and cameras that canthen view the light at distances up to 15 km. The cameras can follow the path of highenergy cosmic ray showers as the shower progresses through the atmosphere. Since all of theshower is viewed, a more accurate estimate of total shower energy can be made – providedatmospheric conditions allow the shower to be seen.

The Pierre Auger Observatory began operations in 2004. It has gathered significant in-formation on events with energies in the vicinity of the GZK cutoff. Shower developmentdepends on the nature of the collision, with the depth to which the shower develops sensitiveto whether the incident cosmic ray was a proton or a nucleus like Fe. Variations in observedshowers are compared to simulations – a tricky business because the most energetic cosmicray collisions correspond to center-of-mass energies two orders of magnitude beyond thosedirectly probed at the LHC/FermiLab and RHIC. Because one has the shower energy and atest of composition, one may be able to tell whether cosmic ray composition is changing withenergy. Cross checks are possible. For example, shower-to-shower variations are predictedto decrease as the typical mass of the incident nucleus increases.

23

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FIGURE 3. 〈Xmax〉 and RMS(Xmax) compared with air shower simulations [22] using different hadronic interaction models [23].

range. For this purpose the effective upper and lower fieldof view limits are calculated for each event and〈Xmax〉 ismeasured as a function of these limits. An example ofthe〈Xmax〉 dependence on the lower FOV limit is shownin Fig. 2 for data and simulated events. As can be seen,the 〈Xmax〉 is asymptotically unbiased for events with asufficiently deep FOV limit, but it is systematically tooshallow when the FOV boundary starts cutting into thetails of theXmax distribution. Obviously, the unbiased re-gion depends on the distribution itself and can thus notbe determined by simulations. Instead, we fit the datawith the mean of a one-sided truncated normal distribu-tion (shown as solid lines in Fig. 2) and reject all eventsthat have a FOV limit for which the measured〈Xmax〉 de-parts by more than 5 g/cm2 from its asymptotic value.

After all cuts, 3754 events are selected for theXmaxanalysis. TheXmax resolution as a function of energy forthese events is estimated using a detailed simulation ofthe FD and the atmosphere. The resolution, defined bythe full standard deviation, is at the 20 g/cm2 level abovea few EeV. The difference between the reconstructedXmax values in events that had a sufficiently high energyto be detected independently by two or more FD stationsis used to cross-check these findings and as it was shownin [13], the simulations reproduce the data well.

RESULTS

The measured〈Xmax〉 and RMS(Xmax) are measured inenergy bins of∆ lgE = 0.1 below 10 EeV and∆ lgE =0.2 above that energy. The last bin starts at 1019.4 eV,integrating up to the highest energy event (E = (59±8) EeV). The systematic uncertainty of the FD energyscale is 22% [24]. Uncertainties of the calibration, at-mospheric conditions, reconstruction and event selectiongive rise to a systematic uncertainty of≤13 g/cm2 for〈Xmax〉 and ≤6 g/cm2 for the RMS. The results werefound to be independent of zenith angle, time periods and

FD stations within the quoted uncertainties.The measured values are displayed in Fig. 3. A fit of

〈Xmax〉 data with a constant elongation rate does not de-scribe our data (χ2/Ndf=34.9/11), but using two slopesyields a satisfactory fit (χ2/Ndf=9.7/9) with an elonga-tion rate of (106+35

−21) g/cm2/decade below 1018.24±0.05eVand (24±3) g/cm2/decade above this energy. If the prop-erties of hadronic interactions do not change significantlyover less than two orders of magnitude in primary energy(< factor 10 in center of mass energy), this change of∆D10 =(82+35

−21) g/cm2/decade would imply a change inthe energy dependence of the composition around the an-kle, supporting the hypothesis of a transition from galac-tic to extragalactic cosmic rays in this region.

The shower-to-shower fluctuations, RMS(Xmax), areobtained by subtracting the detector resolution in quadra-ture from the width of the observedXmax distributionsresulting in a correction of≤6 g/cm2. As can be seen inthe right panel of Fig. 3, we observe a decrease in thefluctuations with energy from about 55 to 26 g/cm2 asthe energy increases. Assuming again that the hadronicinteraction properties do not change much within the ob-served energy range, these decreasing fluctuations are anindependent signature of an increasing average mass ofthe primary particles.

For the interpretation of the absolute values of〈Xmax〉and RMS(Xmax) a comparison to air shower simulationsis needed. As can be seen in Fig. 3, there are considerabledifferences between the results of calculations using dif-ferent hadronic interaction models. These differences arenot necessarily exhaustive, since the hadronic interactionmodels do not cover the full range of possible extrapo-lations of low energy accelerator data. If, however, takenat face value, the comparison of the data and simulationsleads to the same conclusions as above, namely a gradualincrease of the average mass of cosmic rays with energyup to 59 EeV.

It is illustrative to compare the data with predictionsfor a simple two-component proton/iron model using

Figure 14: Pierre Auger data for shower depth (in g/cm2, left panel) and in the RMSvariation in shower depth (right panel) both show trends that suggest the primary cosmicray spectrum is trending away from primarily protons at energies around 1018 eV to nuclei atenergies near the GZK cutoff. From M. Unger and the PA Collaboration, arXiv:1103.5857.

The Pierre Auger data of Fig. 14 show a trend from protons to nuclei as one approachesthe GZK cutoff. This is reminiscent of the similar trend that was seen near the “knee” thatis usually attributed to the cutoff for galactic supernova cosmic ray acceleration, with SN-associated acceleration mechanisms like shock waves able to accelerate nuclei to somewhathigher energies than protons. Thus nuclei tend to dominate at the very end of the energyspectrum. Thus something similar might be happening in the extragalactic accelerators re-sponsible for the highest energy cosmic rays.

What about super-GZK events? Pierre Auger finds a suppression of the event rate setting inabove 3 · 1019 eV, consistent with the GZK cutoff. It does not find evidence for super-GZKevents – suggesting that perhaps earlier first-generation experiments may not have fully un-derstood their energy calibrations (see Fig. 15). At energies above 5.5 · 1019 eV a correlationwith the distribution of nearby extragalactic objects is found, including an excess in thedirection of Centaurus A, the nearest radio-loud active galaxy. Centaurus A is about 15million light years from earth, and has a prominent relativistic jet that is thought to extractenergy from the vicinity of a supermassive black hole at the galaxy’s center.

9.7 High energy neutrinos, GZK Neutrinos, and Beyond GZK NeutrinosThe field of very high energy neutrino astronomy is in its infancy. The Amanda neutrinotelescope was a prototype south Pole detector, and now a much larger second-generation de-tector, IceCube, is operating. Neutrinos penetrating the ice can be detected via the muonsthey produce. The muons produce Cherenkov light in the ice, which can be detected byphotomultipliers place on detector “strings” placed in the deep ice from the surface. Deepice - ice a mile below the surface - is exceptional pure and transparent, with light attentua-tion lengths of 100 meters or more. Thus a relatively spare array of photomultiplier strings,

24

Latest results from the Auger Observatory Esteban Roulet

Energy [eV]

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power laws

power laws + smooth function

Figure 1: Spectrum measured above 1 EeV (solid dots) and power law fits with breaks (dotted line). Forcomparison also the HiRes measurements are displayed (opendots).

The physical origin of the ankle is still uncertain, being the main candidate scenarios to explainthis feature those relating it to the transition from a dyinggalactic component to a harder extragalac-tic component becoming dominant, or alternatively the so-called dip-scenario [3], in which cosmicrays are assumed to be extragalactic protons down to energies below 1 EeV and the concave shapeobserved arises from the effect of energy losses by pair creation with cosmic microwave back-ground (CMB) photons. To properly fit the observed spectral shape this last scenario requires softspectra at the sources (α at the source being typicallyαg ≃ 2.4-2.7) and/or strong evolution ofthe sources with redshift, what makes the distant sources intrinsically brighter (or more abundant)so that a larger fraction of the observed protons come from far away and are hence more affectedby interactions with CMB photons. Also an upward shift of theenergy scale of Auger by∼ 40%would be required in this scenario to fit the location of the dip in the spectrum.

Anisotropy measurements will help to distinguish among thetwo scenarios, because the galac-tic/extragalactic transition may lead to measurable dipole type patterns in the arrival direction dis-tribution resulting from the diffusive escape of the galactic cosmic rays, and already significantconstraints have been obtained by Auger at EeV energies [4].Also composition measurements areimportant because galactic cosmic rays at EeV energies are expected to be dominated by heavynuclei, since their confinement by galactic magnetic fields is a rigidity dependent effect. Enhance-ments of the Auger observatory to improve the sensitivity down to energies of 1017 eV, such as theHEAT fluorescence detectors or the AMIGA infill and muon detectors, will help to shed light onthese issues in the near future.

The second feature mentioned, i.e. the suppression observed at the highest energies, is similarto the expectations from the so called GZK effect associatedto the attenuation of extragalacticprotons by photo-pion production off CMB photons (this suppression was predicted by Greisenand Zatsepin and Kuz’min just after the discovery of the CMB). Also the photodisintegration ofnuclei as heavy as iron would lead to similar features, whilelighter nuclei would instead show asuppression down to a lower energy threshold, in approximate proportion to their masses. Notethat a change in the injection spectrum at the sources may also contribute in part to the observed

3

Figure 15: The solid dots are the Pierre Auger measurements at the GZK cutoff. Alsoshown are data from a second observatory, HiRes. From Roulet and the PA Collaboration,arXiv:1101.1825.

25

placed in the ice by using hot water to drill very deep holes in the ice, can view vast massesof ice efficiently. IceCube is the world’s largest high energy neutrino detector, viewing onecubic kilometer of deep South Pole ice at depths of 1.4-2.4 kilometers via detectors placed on86 strings. LBNL played an important role in the design of the detectors and the associateddata acquisition system. IceCube construction was completed at the end of 2010. Whilemany muons penetrate the ice, almost all of these come from above the detector, the sec-ondaries from cosmic ray interactions. But because only neutrinos can penetrate the earth,upward going muons must be the daughters of upward going neutrinos that interact in ornear the detector. Thus by studying upward going muons, the experimenters can determinethe rate of neutrinos penetrating the earth from below.

The IceCube mass is sufficient to detect neutrinos up to about 1016 eV. Beyond this point,the event rate is too low: the km3 volume is insufficient. One of IceCube’s important scien-tific justifications is using neutrinos to located possible specific point sources – so that wecan connect very energetic events with candidate astrophysical accelerators. Since neutrinosare unaffected by the CMB or by magnetic field, they point back to their sources.

But neutrino astronomy with still higher energy neutrinos is clearly important. One of theimportant consequences of the Pierre Auger observation of the GZK cutoff is the associ-ated prediction that very high energy neutrinos, produced for example by π+ → µ+νµ →νµ+e+ + νµ+νe. In addition, it is quite plausible that the astrophysical accelerators produc-ing cosmic rays in the vicinity of 1019 − 1020 eV are in fact capable of accelerating protonsor nuclei to still higher energies – though we would not see such energetic primary cosmicrays because they cannot penetrate the CMB. Nevertheless, in the vicinity of the accelera-tor, these cosmic rays would be converted to neutrinos, which would reach earth. The fluxof GZK neutrinos and the flux of those neutrinos associated with cosmic rays acceleratedbeyond the GZK cutoff can be estimated, if one assumes a spectrum of primary cosmic rays(say a proton flux declining as E−α); a maximum proton energy (1023 eV was chosen forone of the calculations used in defining the band in Fig. 16), and a cosmological model(effectively the z at which the typical neutrino was produced, so that redshift effects can beaccounted for). In this way, reasonable assumptions yield curves within the band of Fig. 16.The bulk of these neutrinos are beyond the reach of IceCube: the low flux of the highestenergy neutrinos requires detection volumes of 100 km3 or more, not 1 km3.

Yet these neutrinos are important: they may be our only tool for investigating the universeat asymptotically high energies and large distances. How can they be detected? First, plau-sible estimates of fluxes quickly lead to the conclusion that the detector must be huge, onthe order of 100 km3 or more. Clearly such a detector cannot be a conventional one. Second,one needs some kind of neutrino interaction that can be detected in such a large volume, atreasonable cost.

There is an attractive possibility, based on the Askaryan effect, proposed by Gurgen Askaryan

26

arX

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v1 [

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IceRay: An IceCube-centered Radio-Cerenkov GZK Neutrino Detector

P. Allisona, J. Beattyb, P. Chenc, A. Connollyd, M. DuVernoisa, P. Gorhama, F. Halzene, K. Hansone, K. Hoffmanf,A. Karlee, J. Kelley∗,e, H. Landsmane, J. Learneda, C. Mikia, R. Morsea, R. Nichold, C. Rottb, L. Ruckmana,

D. Seckelg, G. Varnera, D. Williamsh

aDept. of Physics and Astronomy, Univ. of Hawaii, Manoa, HI 96822, USAbDept. of Physics, Ohio State University, Columbus, OH 43210, USA

cDept. of Physics, National Taiwan Univ., Taipei 106, TaiwandDept. of Physics & Astronomy, Univ. College London, London WC1E 6BT, UK

eDept. of Physics, Univ. of Wisconsin, Madison, WI 53703, USAfDept. of Physics, Univ. of Maryland, College Park, MD 20742, USA

gDept. of Physics and Astronomy, Univ. of Delaware, Newark, DE 19716, USAhDept. of Physics and Astronomy, Univ. of Alabama, Tuscaloosa, AL 35487, USA

Abstract

We discuss design considerations and simulation results for IceRay, a proposed large-scale ultra-high energy (UHE)neutrino detector at the South Pole. The array is designed to detect the coherent Askaryan radio emission from UHEneutrino interactions in the ice, with the goal of detecting the cosmogenic neutrino flux with reasonable event rates.Operating in coincidence with the IceCube neutrino detector would allow complete calorimetry of a subset of the events.We also report on the status of a testbed IceRay station which incorporates both ANITA and IceCube technology andwill provide year-round monitoring of the radio environment at the South Pole.

Key words: neutrino detection, Askaryan effect, radio frequencyPACS: 14.60Lm, 95.55.Vj, 98.70.Sa, 84.40.-x

1. Introduction

Continued progress in the determination of the ultra-high energy cosmic ray (UHECR) spectrum above 1017

eV has established the presence of the Greisen-Zatsepin-Kuzmin (GZK) suppression [1], resulting from the interac-tion of UHECRs with the cosmic microwave background(see Fig. 1). Such interactions lead to a “guaranteed” fluxof UHE neutrinos, although the characteristics of the fluxdepend on the details of the source distribution, UHECRcomposition, and other currently unknown factors. Mea-surement of the GZK neutrino flux would not only shedlight on these issues, but also could indicate the UHECRsources themselves via the direction of the individual neu-trinos.

An array to detect UHE neutrinos via their coherent ra-dio emission in a dense medium was originally describedby Gusev and Zhelezhykh [2], based on theoretical workby Askaryan. Since then, significant experimental workby the RICE collaboration [3] has established many of thefundamental characteristics of radio transmission in thepolar ice, and the ANITA balloon experiment [4] has cur-rently set the best limits on UHE neutrino fluxes. Directobservation of coherent radio emission using an ice target

∗Presenter.Email address: jkelley@icecube.wisc.edu (J. Kelley)

Figure 1: World ultra-high energy cosmic ray and predicted cos-mogenic neutrino spectrum as of early 2007, including data fromthe Yakutsk [5], Haverah Park [6], the Fly’s Eye [7], AGASA [8],HiRes [1], and Auger [9], collaborations. Data points represent dif-ferential flux dI(E)/dE, multiplied by E2. Error bars are statisticalonly. GZK neutrino models are from Protheroe & Johnson [10] andKalashev et al. [11].

Preprint submitted to Elsevier April 8, 2009

Figure 16: The hashed band is the predicted spectrum of high energy neutrinos resultingfrom the interaction of primary cosmic rays with the CMB. The data points are variousmeasurements of the hadronic cosmic ray spectrum, including data from Pierre Auger. Graphfrom Allison et al.

in 1962. A very energetic particle traveling through matter can produce a shower of sec-ondary particles that carry a net charge and that emit a cone of coherent Cherenkov radiationat radio or microwave frequencies. Indeed, high energy neutrino reactions in matter producean electron/γ shower containing perhaps 20% more electrons than positrons: positrons andelectrons annihilate into γs, but γs can Compton scatter off electrons in the matter to pro-duce high energy electrons. The charges move faster than the local speed of light in matter,c/n where n is the index of refraction. At long wavelengths – radio or microwaves – themoving front of charges – which may have a thickness on the order of 10cm – can produceCherenkov microwave or radio waves coherently. (The wavelength is large compared to thethickness of the charge wave.) The Askaryan effect has been observed in several materials,such as silica, salt, and ice: several of the key experiments were done at SLAC. There areseveral detector ideas being developed around this idea, most based on instrumenting a verylarge volume of South Pole ice with surface radio detectors.

27

9.8 Gamma rays: general issues, GROThe properties of the earth’s atmosphere divides gamma ray astronomy into two halves.From the ultraviolet to gamma rays of energy ∼ 20 GeV the atmosphere is opaque. Thusobservations in this energy range must be done with instruments mounted in satellites orcarried by balloons. The ease of detecting the radiation generally goes up with energy, butthe strengths of typical astrophysical sources go down. The net result is that one can do alot over this range: this motivated the design of the four instruments on board the GammaRay Observatory. For gamma rays above 20 GeV, interactions in the atmosphere produceshowers that can be observed either by the Cerenkov light produced by the secondaries or,at high altitude, by direct detection of the secondaries. Of course, observations can also be(and are) made by space-bound detectors, too.

Many of the concerns of this field are driven by instrumental issues. Some of the centralissues are clear:• Producing detectors with greater sensitivity. The dynamic range of existing detectors -the gap between the brightest nearby sources such as the Crab and the faintest detectablesources - is typically about a factor of 100. Thus the situation is equivalent to being able tosee no stars fainter than the 5th magnitude. Improvements in sensitivity can thus greatlyextend the horizon of our observations, while also allowing much more detailed spectral stud-ies of known bright sources. Greater sensitivity can be achieved with great collection areasand by reducing ambient backgrounds. The push towards greater size is clearly an expensivechallenge given the necessity for observing outside the atmosphere.• Enhancing spectral resolution. This includes both enhanced spectral resolution and en-hanced spatial resolution, the latter required to better identify sources.• Enhanced temporal and spatial coverage and resolution.

The technology in the field has advanced greatly over he past 20 years. The second ofNASA’s Great Observatory projects (following the Hubble Space Telescope) was the Comp-ton Gamma Ray Observatory. Launched in 1991 from the shuttle Atlantis, the GRO oper-ated for over nine years. Its instruments included BATSE, OSSE, COMPTEL, and EGRET.BATSE - the Burst and Transient Source Experiment - was an all-sky monitor with sharptiming capability: its NaI detectors were designed to detect gamma rays with energies be-tween 20 and about 600 keV. This proved decisive in demonstrating that gamma ray burstsare distributed approximately isotropically. This detector also led to the discovery of newpulsars, x-ray novae, and the identification of one soft gamma ray repeater. OSSE - theOriented Scintillation Spectrometer Experiment - employed NaI and CsI detectors to lookfor gammas between 50 keV and 10 MeV, and could point to sources. COMPTEL - theImagining Compton Telescope – detected gamma between 0.75 and 30 MeV, with an angu-lar resolution of 1 degree. EGRET - the Energetic Gamma Ray Experiment - was able tocorrelate high energy gammas (20 MeV-30 GeV) with the lower energy bursts detected byBATSE. It also measured high energy gammas from active galaxies.

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9.9 Nuclear Gamma RaysWe have touched on this theme before, but here I’d like to gather together several examplesof what is becoming possible. One of these examples is 26Al, which 720,000 y lifetime fordecay to 26Mg. The decay of the 5+ ground state populates the first two excited states of26Mg, which are 2+ states with energies of 2.938 and 1.809 MeV. The latter state is populated97% of the time, so the primary signature is a 1.809 MeV γ. The 2.938 MeV state decaysto the 1.809 MeV level, so a small number of 1.129 MeV γs are also produced.

The primary site for producing 26Al is thought to be Type II and IIb supernovae. Addi-tional aluminum may come from the winds of very massive stars. COMPTEL has produceda galactic map of the 1.809 MeV γs. That map differs from higher energy (∼ 100 MeV) mapsin that there is marked clumpiness to the production, including intense sources associatedwith Cygnus, Vela, etc. This map is interpreted as an indicator of recent supernova activity.The conclusions drawn from such a map are clearly model dependent because one obtainsan angular distribution but no spatial depth information. But under the assumption thatthe entire galaxy is contributing in the expected way, one deduces a recent supernova rateof 3.4 ± 2.8/century. The model dependence also includes the uncertainty in the aluminumproduction per event. The attribution of the total flux to the Al injection rate of massivestars yields an upper bound on the recent star formation rate of 5 ± 4 M� per year. Thiscalculation, of course, requires not only a model of the Al production per supernova, butalso a model of the range of stellar masses that undergo core collapse and a model for thedistribution of stars with mass (populations roughly decline exponentially with an exponentof about -2.35).

In a similar way, 44Ti decay proceeds with a ∼ 60 year half life to the ground state of 44Sc,which in turn electron captures to 44Ca. The order of the states in Sc is 2+ (gs), 1− (68keV), and 0− (146 keV). The decay feeds the second excited state 98% of the time, whichthen decays through the 1− state to the ground state, producing γs of 78 and 68 keV. Thesubsequent decay to 44Ca has a 4 hour lifetime and produces a 1.157 MeV γ, as the 2+ firstexcited state of 44Ca is populated 99% of the time. The ∼ 100 keV line for the the sourceCas A is within the detection abilities of OSSE, while the 1.157 MeV line can be seen byCOMPTEL.

Various types of supernovae are thought to produce 44Ti, including both types I and II. Asin the case of the 26Al line, the galaxy is effectively transparent to the produced γ ray, sothe detection provides a measure of the very recent supernova rate free from worries aboutobscuration. With COMPTEL one had an instrument sensitive to nrearby supernovae occur-ring within the past 1000 years, or 15 half lives. Given a supernova rate of some several percentury, it is clear that the distribution should be from quite localized sources, representingrecent events. Typical productions of 44Ti from supernovae are, according to modelers, onthe order of 10−4 M� per event.

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Figure 17: COMPEL’s map of the galactic plane in the 1.809 MeV gamma ray emittedby 26Al. The distribution is not uniform. It is thought to represent over 100,000 events,supernovae or novae, producing something on the order of 1-3 solar masses of 26Al.

The youngest known galactic supernova remnant is Cas A, noted optically by John Flam-steed in 1680. COMPTEL reported the observation of 44Ti γs from Cas A in 1994. Theresults of a survey extending over a six-year period beginning in 1991 found only one ad-ditional source, identified with a young supernova remnant not observed either optically orin the radio. The source is located in the direction of the Vela constellation. Constraintson the doppler broadening of the 1.16 MeV line limits the velocity of the ejecta to no morethan 19000 km/sec. The COMPTEL results are confirmed by ROSAT x-ray data of thevela region, which found a shell-type supernova remnant at the same location. The shelltemperature is on the order of several keV, which also indicates a young remnant. Finally,COMPTEL previously saw 26Al in this region, attributing this to the known Vela supernovaremnant. However the centroid of that distribution has been argued to better fit the newsupernova remnant. Modelers are currently engaged in arguments about the nature of theprogenitor, using both the ejection velocity bound and the 44Ti yield to bound models. Onepossibility is a core-collapse supernova of a massive star that had previously lost its hydrogenenvelope. It has been claimed that a supernova at this distance (100-300 pc, derived fromthe Ti γ flux and age estimates of 600-1100 years based on the expansion velocity) could havebeen as bright as the moon, leaving an interesting question as to why it was not observed.

Finally, there have been recent papers suggesting that future generations of gamma ray de-tectors might see γs in the energy range of 100-700 keV associated with elements specific tothe r-process. Establishing a correlation between such γs and known supernova remnantscould thus establish the r-process site and, potential, constrain the total r-process productionper site. One of the candidates, 126Sb, has a 144,000 year lifetime, easily long enough toallow a galaxy survey. It produces lines at 415, 666, and 695 keV. The proposed detectorATHENA possibly could detect 126Sb lines from Vela.

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9.10 Astrophysics of Intermediate Energy GammasEGRET conducted the first all-sky search for gamma sources above 100 MeV, succeedingin identifying 271 high-energy gamma ray sources, most of which are associated with activegalaxies and characterized by nonthermal spectra. 170 these were unknown prior to thesurvey. Such ”blazars” are highly variable and are bright radio sources. The radio structureconsists of knotty jets moving outward at high velocities. The luminosity in gamma rayscan exceed that from other wavelengths by up to two orders of magnitude. The variabilityof the emission can be fast, less than a week. The density of high energy gammas at thesource are sufficient that photon-photon pair production would keep them trapped, unlessthe gammas are highly beamed, as in a relativistic jet. Thus the hope is that the gammaray spectrum can yield information on the nature of the jet and of the acceleration processesoccurring there. It is thought that the gamma rays may originate from a region of the jetcloser to the central engine, than in the case of the radio emission.

A few blazars have been observed producing very high energy gamma rays, up to TeV scales,which then can be readily observed from earth. One, Markarian 421, was measured in theTeV range by the Whipple Observatory, which detects Cerenkov radiation from air showers.It was not seen at GeV energies by EGRET. The high energy flare had a rise time of abouttwo days. One day after the flare began this source was seen in the X-ray. Both of thesesignals differ from typical blazars in their higher energies: most blazars have lower energygamma and low-energy radiation that does not extend into the x-ray. The interpretation isthat blazars accelerate electrons to high energies, which then radiate soft synchrotron radi-ation and hard gammas by inverse Compton scattering. Markarian 421 is thus exceptionalin the energies to which it accelerates electrons, accounting for the higher energy of its x-ray/gamma emission.

Markarian 421, which was first observed in May, 1994, is not unique. The second closestblazar of this type, Markarian 501 (z=0.034), was seen in 1997. It flared to become thebrightest TeV source in the sky, outshining the Crab Nebulae by an order of magnitude.The periods of flaring lasted a few days. The elevated activity spanned a period from aboutMarch through June. The high energy spectrum (observed by Whipple) was flat from belowa TeV to at least 10 TeV. The x-ray cutoff in Markarian 421 is about 1 keV; in Markarian501 it is above 100 keV. As in 421, it is assumed that this spectrum comes from relativisticacceleration of electrons along a jet closely aligned with our line of sight.

What does this tell us about the electron energies? First, the plasma in the jet is movingtowards us, boosting the energy of the emitted gammas, relative to the jet rest frame. TheDoppler factor is

D =

√(1− v2/c2)

(1 + z)(1− v cos θ/c)(16)

where θ is the observation angle relative to the jet axis. This is the standard relativistic

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Doppler shift corrected by the redshift. The observed energy of the gamma rays is

Emax ∼ Dγmec2 (17)

where γmec2 is the maximum energy of the electrons in the jet rest frame. The Doppler

factor also appears in the calculation of the photon density in the blob, and thus of the blobsopacity to high energy γs. The argument goes as follows: if ∆tobs is the fastest observed TeVgamma ray flare variability, then the radius of the blob emitting the photons must be lessthan ∼ cD∆tobs. Thus a larger D means a lower photon density. From this one concludesD ∼> 30. Since the highest energy gammas from Markarian 501 is about 20 TeV, one derivesfor the maximum energy of electrons in the jet frame

γmc2 ∼ 0.65TeV (18)

Since the maximum electron velocity is now known, one can deduce the magnetic field in thejet required to produce synchrontron radiation with a maximum energy of 200 keV. Thatyields

Emax ∝ DBγ2 ⇒ B ∼ 0.7G (19)

where B is the field in the jet rest frame. Other aspects of the blazar dynamics - such as thephysics responsible for the short timescale of the flares - is less clear.

Another exciting result involving high energy γs are the gamma ray burst observations ofEGRET. While the vast majority of the bursts are seen by BATSE, on the order of 10%of the events produce spectra that extend into EGRET’s range of above 30 MeV, typicallyproducing about five counts. A great deal more about such events is now known because ofthe Fermi Telescope.

These high energy tails place a lot of constraints on gamma ray burst models. Since highenergy gammas were also seen early in the burst, there must be high-energy particle accel-eration simultaneous to the keV emission. The lack of attenuation of high energy γs fromγ−γ pair production off lower energy γs place a particularly strong constraint on the sourceand on models involving beaming.

Finally, a third interesting source of high energy γs are both isolated and binary pulsars.Gamma ray emission can be very strong, representing 10% or more of the spin-down energyof some pulsars. There is relatively little consensus on the mechanism or even the precisesite of the gamma ray production (neutron star surface? accretion disk? etc?)

Centaurus X-3 is a well-studied high-mass accreting X-ray binary. EGRET measured asmoothly declining spectrum that extended from 100 MeV to its detection limit. Resultshave been reported from the Durham Mark 6 gamma ray telescope in the vicinity of a TeV:the flux is consistent with a linear extrapolation of the EGRET flux. Centaurus X-3 containsa 4.8s pulsar in a 2.1 day orbit about an O-type supergiant V779 Centaurus. The pulsar

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period has been shortening since its discovery almost 30 years ago, which is attributed tospin-up from matter accreting on the neutron star from the more rapidly rotating inner edgeof its accretion disk. The EGRET GeV burst observations were pulsed in agreement with theX-ray period. Initial TeV gamma ray observations also indicated pulsation near the pulsarperiod and localized in But later measurements at high energy indicated unpulsed emissionthat one would then associated with radiation over an extended volume encompassing theorbit.

9.11 Fermi TelescopeA new high-energy gamma ray telescope – the Fermi Telescope, or the telescope-formerly-known-as-GLAST – was launched into space in June of 2008. Its purpose is to probe in-termediate energy gamma ray sources, such as active galactic nuclei, supernova remnants,and pulsars, in order to catalog these sources and determine the nature of these accelerators.The telescopes can detect gammas with energies between 20 MeV and 300 GeV – so it canbe viewed as somewhat of a successor to EGRET. The telescope looks for transient eventsas well as exotic phenomena, such as dark matter annihilation into high energy γs. Oneinstrument, the Gamma Ray Burst Monitor, is designed to view the entire sky not occultedby earth, to look for and identify the location of gamma ray bursts. It is sensitive to gam-mas between 8 keV and 40 MeV. The second instrument, the Large Area Telescope, has anaperture that can view 20% of the sky at one time. It can detect gammas from 20 MeVto 300 GeV. In its first year, Fermi extended the EGRET catalogue of 271 point sources to1451 sources. Among Fermi discoveries to date are the observation of a gamma-ray-emittingpulsar but emits in no other band; the observation of the most energetic gamma-ray burstyet recorded; and the observation of very energetic cosmic rays from the vicinity of supernovaremnants. It has also placed important constraints on the diffuse gamma ray background,an isotropic gamma ray component of unknown origin, and on gamma-ray decay channelsof dark matter candidates.

9.12 Gamma ray burstsGamma ray burst have been mentioned several times. Gamma ray bursts are short-livedburst lasting from a few milliseconds to several minutes. They are detected roughly onceper day, from all directions in the sky. They represent tremendous energy, several hundredtimes brighter than a typical supernova (were they radiated in 4π). They were originallydetected in the 1960s by military satellites monitoring nuclear testing. They are not local,but originate at cosmological distances. In the past few years it has become clear they areassociated (at least some of the time) with certain supernovae.

Recently fast-response telescopes - like NASA’s High-Energy Transient Explorer or theJapanese Automated Response Telescope - have been able to view the gamma-ray burstarea within a couple of minutes of the burst. The ”afterglows” have been observed for onthe order of an hour to a day after the burst – representing a lot of additional energy.

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Figure 18: The Fermi Telescope, prior to launch.

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Figure 19: The Fermi Telescope’s map of gamma rays and gamma-ray point sources in theplane of the galaxy. Compare to Figure 17.

General ideas exist that gamma ray bursts are associated with fireball phenomena wheretremendous energy and high velocities are produced in a region relatively free of baryons –to keep the gamma rays from thermalizing. The motion leads to a beaming of the burst,reducing the energy requirements but increasing the frequency of events (many of which arenot beamed at earth and thus are not observed).

A specific idea is the hypernova. A massive star’s core collapses into a black hole. The blackhole’s spin or magnetic fields may act like a slingshot, flinging material outward as a beamedblast wave or jet. The gamma rays are created when the blast wave collides with stellarmaterial still inside the star. The gamma rays burst out of the star just in front of the blastwave. Behind the gamma rays, the blast wave pushes the stellar material outward.

The blast wave then sweeps through space, colliding with gas and dust, producing additionalradiation – progressing from less energetic gammas, to x-rays, to visible light, and to radio.This forms the afterglow, lasting perhaps up to days.

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Figure 20: A long-duration gamma ray burst event.

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