the cosmic-ray spectrum

Aspen, April 26, 2005 Tom Gaisser

The cosmic-ray spectrum

From the knee to the ankle


Spectrometers (A = 1 resolution, good E resolution)

Calorimeters (less good resolution)

Direct measurements

Air showers

Air-shower arrays on the ground to overcome low flux.Don’t see primaries directly.


Theme of this talk

• SNR shock model of cosmic-ray origin based on– Energy content– Composition– Spectrum

• Full spectrum: three energy regions– < PeV (up to the knee)– PeV – EeV (knee – ankle)– > EeV (UHECR)

• Where is transition from galactic to extra-galactic cosmic rays? – Use spectrum, composition, energy content also to

answer questions at high energy


Energetics of cosmic rays

• Total local energy density: – (4/c) ∫ E(E) dE ~ 10-12 erg/cm3 ~ B2 / 8

• Power needed:(4/c) ∫ E(E) / esc(E) dEgalacticesc ~ 107 E-0.6 yrsPower ~ 10-26 erg/cm3s

• Supernova power:1051 erg per SN~3 SN per century in disk~ 10-25 erg/cm3s

• SN model of galactic CRPower spectrum from shock

acceleration, propagation

Spectral Energy Distribution (linear plot shows most E < 100 GeV) (4/c) E(E) = local differential CR energy density


30

Rigidity-dependence• Acceleration, propagation

– depend on B: rgyro = R/B– Rigidity, R = E/Ze– Ec(Z) ~ Z Rc

• rSNR ~ parsec Emax ~ Z * 1015 eV– 1 < Z < 30 (p to Fe)

• Slope change should occur within factor of 30 in energy

• With characteristic pattern of increasing A

• Problem: continuation of smooth spectrum to EeV


B. Peters on the knee and ankle

B. Peters, Nuovo Cimento 22 (1961) 800

Peters cyclePeters cycle: systematic increase of < A > : systematic increase of < A > approaching Eapproaching Emaxmax

<A> should begin to decrease again<A> should begin to decrease again for E > 30 x Efor E > 30 x Ekneeknee


Direct measurements to high energyshow no strong features below PeV

R. Battiston, Rapporteur talk, Tsukuba, 2003

RUNJOB: thanks to T. ShibataATIC: thanks to E-S Seo & J. Wefel

/nucleon)


All-particle spectrum:Knee ~3 PeV

Tibet EE/1.23

x 0.1

x 0.01


Recent Kascade data show increasing fraction of heavy nuclei with expected cutoff

sequence starting at ~3 PeV

K-H Kampert et al., astro-ph/0204205 ICRC 2001 (Hamburg)

M. Roth et al., Proc ICRC 2003 (Tsukuba) vol 1, p 139No information > 1017 eV

from original Kascade


Models of galactic particles, E >> knee

• Fine-tuning problem:– continuity of spectrum over factor

300 of energy implies relation between acceleration mechanisms

• Axford:– reacceleration by multiple SNR

• Jokipii & Morfill, Völk:– reacceleration by shocks in

galactic wind (termination shock or CIRs)

• Erlykin & Wolfendale:– Local source at knee on top of

smooth galactic spectrum– (bending of “background” could

reflect change in diffusion • What happens for E > 1017 eV?

– Hillas: component B

Völk & Zirakashvili, 28th ICRC p. 2031

Erlykin & Wolfendale, J Phys G27 (2001) 1005


Speculation on the knee

Total

protons

helium

CNOMg…

Fe

1 component: = 2.7, Emax = Z x 30 TeV; (Lagage & Cesarsky)

or Emax = Z x 1 PeV

3 components


Power needed for knee B-component

• Integrate to E > 1018 eV assuming – esc ~ 2 x 107 yrs x E-1/3

– Vgalaxy ~ (15 kpc)2 x 200 pc ~ 3 x 1066 cm3

– Total power for “B” component ~2 x 1039 erg/s

• Possible sources– Sources may be nearby – e.g. -quasar SS433 at 3 kpc has Ljet 1039 erg/s– Eddington limited accretion ~ 2 x 1038 erg/s– Neutron source at GC ~ 1038 erg/s


Where is transition to extragalactic CR?

G. Archbold, P. Sokolsky, et al.,Proc. 28th ICRC, Tsukuba, 2003

HiRes new composition result: transition occurs before ankle

Original Fly’s Eye (1993): transition coincides with ankle

3 EeV

0.3 EeV


Composition with air showers• Cascade of nucleus

– mass A, total energy E0 – X = depth in atmosphere along shower axis– N(X) ~ A exp(X/), number of subshowers– EN ~ E0 / N(X), energy/subshower at X– Shower maximum when EN = Ecritical

– N(Xmax) ~ E0 / Ecritical

– Xmax ~ ln { (E0/A) / Ecritical }– Most particles are electrons/positrons

• from -decay a distinct component– decay vs interaction depends on depth– N ~ (A/E)*(E0/AE)0.78 ~ A0.22

• Showers past max at ground (except UHE) large fluctuations poor resolution for E, A– Situation improves at high energy and/or

high altitude– Fluorescence detection > 1017 eV

Schematic view of air shower detection: ground array and Fly’s Eye


New detectors to explore galactic to extra-galactic transition

• Need > km2 to reach EeV

• KASCADE-Grande

• IceCube (including IceTop)

• Tunka – 133

• “Hybrid” Hi-Res, TA, Auger– below nominal threshold

piering

Three new kilometer-scale detectors


New South Pole station with IceTop Station 21 in foreground


Two DOMs: 10” PMTOne high-gain; one low-gain in each tank

To DAQ

IceCubeDrill Hole

10 m

HG HG LGLG

Junction box

25 m

IceTop station

• Two Ice Tanks 2.7 m2 x 0.9 m deep (scaled-down version of Haverah, Auger)• Integrated with IceCube: same hardware, software• Coincidence between tanks = potential air shower• Local coincidence with no hit at neighboring station tags muon in deep detector• Signal in single tank = potential muon• Significant area for horizontal muons• Low Gain/High Gain operation to achieve dynamic range• Two DOMs/tank gives redundancy against failure of any single DOM

because only 1 low-gain detector is needed per station

~ 5-10 TeV


DOMs in tank before freezing


Dec 04: 4 stations, 8 tanks

Serap will present IceCube/IceTop on Saturday


Importance of locating transition to extra-galactic component:

energy content depends on it

• Composition signature: transition back to protons

Uncertainties:• Normalization point:

1018 to 1019.5 usedFactor 10 / decade

• Spectral slope =2.3 for rel. shock =2.0 non-rel.

• Emin ~ mp (shock)2


Power needed for extragalactic cosmic rays (assuming transition at 1019 eV)

• Energy in extra-galactic, CR ~ 2 x 10 erg/cm3

– Includes extrapolation of UHECR to low energy CR = (4/c) E(E) dE = (4/c){E2(E)}E=1019eV x ln{Emax/Emin}– This gives CR ~ 2 x 10 erg/cm3 for differential index = 2, (E)

~ E-2 ; significantly more if > 2,

• Power required ~ CR/1010 yr ~ 1.3 x 1037 erg/Mpc3/s– Estimates depend on cosmology + extragalactic magnetic fields:– 3 x 10-3 galaxies/Mpc3 5 x 1039 erg/s/Galaxy– 3 x 10-6 clusters/Mpc3 4 x 1042 erg/s/Galaxy Cluster– 10-7 AGN/Mpc3 1044 erg/s/AGN– ~1000 GRB/yr 3 x 1052 erg/GRB


Bahcall & Waxman (GRB)

• Galactic extragalactic transition ~ 1019 eV

• Assume E-2 spectrum at source, normalize @ 1019.5

• 1045 erg/Mpc3/yr• ~ 1053 erg/GRB• Evolution ~ star-formation• GZK losses included

Physics Letters B556 (2003) 1

Bahcall & Waxman hep-ph/0206217


Berezinsky et al.: AGN

• G E-G transition < 1018 eV• Assume a cosmological

distribution of sources with:– dN/dE ~ E-2, E < 1018 eV– dN/dE ~ E, 1018< E < 1021

– = 2.7 (no evolution)– = 2.5 (with evolution)

• Need L0 ~ 3 ×1046 erg/Mpc3 yr

• Interpret ankle at 1019 as– p + 2.7p + e+ + e-

Berezinsky, Gazizov, Grigorieva astro-ph/0210095

astro-ph/0410650


Questions to ponder

• How to boost Emax to 100 PeV– perpendicular shocks? – self-generated higher magnetic fields?

• What is the energy-dependence of diffusion?• What is the source spectrum?

– Are there different slopes for different sources?– How to use the characteristic concave shape of non-linear

diffusive shock acceleration?

• How many sources? How are they distributed?


Lessons from the heliosphere

• ACE energetic particle fluences:• Smooth spectrum

– composed of several distinct components:

• Most shock accelerated

• Many events with different shapes contribute at low energy (< 1 MeV)

• Few events produce ~10 MeV

– Knee ~ Emax of a few events– Ankle at transition from

heliospheric to galactic cosmic rays

R.A. Mewaldt et al., A.I.P. Conf. Proc. 598 (2001) 165


Solar flare shock acceleration

Coronal mass ejectionCoronal mass ejection 09 Mar 200009 Mar 2000


SOHO/LASCO

CME of 06-Nov 1997


Heliospheric cosmic rays

• ACE--Integrated fluences:– Many events contribute to

low-energy heliospheric cosmic rays;

– fewer as energy increases.– Highest energy (75 MeV/nuc)

is dominated by low-energy galactic cosmic rays, and this component is again smooth

• Beginning of a pattern?R.A. Mewaldt et al., A.I.P. Conf. Proc. 598 (2001) 165


Questions to ponder

• How to boost Emax to 100 PeV– perpendicular shocks? – self-generated higher magnetic fields?

• What is the energy-dependence of diffusion?• What is the source spectrum?

– Are there different slopes for different sources?– How to use the characteristic concave shape of non-linear

diffusive shock acceleration?

• How many sources? How are they distributed?

the cosmic-ray spectrum

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