Aspen, April 26, 2005 Tom Gaisser The cosmic-ray spectrum From the knee to the ankle
Aspen, April 26, 2005 Tom Gaisser
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.
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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)
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
Dec 04: 4 stations, 8 tanks
Serap will present IceCube/IceTop on Saturday
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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?
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
Solar flare shock acceleration
Coronal mass ejectionCoronal mass ejection 09 Mar 200009 Mar 2000
Aspen, April 26, 2005 Tom Gaisser
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
Aspen, April 26, 2005 Tom Gaisser
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?