Transcript The Puzzle of the cosmic ray "knee"

Arunava bhadra
High Energy & Cosmic ray research centre,
University of North Bengal
Siliguri, India
Collaborators: Biplab Bijay, Prabir Banik
The knee in the Energy spectrum
 Energy spectrum of all particle cosmic rays exhibits a
power law behavior.
 There are few features in the spectrum out of which
the knee and the ankle are prominent features.
 A slight bend of the spectrum at about 3 PeV, is known
as the so called knee of the spectrum, where the power
law spectral index changes from about -2.7 to nearly 3.0.
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Energy spectrum
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Knee
s
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140 GeV
2.5 TeV
2nd knee? Dip/Ankle
GZK?
20 TeV 100 TeV 450 TeV
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Origin of the knee
 The knee is an important imprint of the true model of
origin of cosmic rays
 Several mechanisms have been proposed so far to
explain the knee.
 an effect of the reduced efficiency of galactic
magnetic field to confine the cosmic ray particles with
energies above the knee within galaxy [Ginzburg and
Syrovatskii, 1964, The Origin of Cosmic Rays,
Macmillan, NewYork]
 the observed knee is the proton knee as per this model
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Contd.
 Due to acceleration mechanism [Fichtel and
Linsley(1986),
Jokipii(1986),
Biermann(1993),
Berezhko(1999), Stanev et al(1993) etc,]
 Among the galactic sources supernova remnants
(SNRs) satisfy the energy budget of cosmic rays.
 cosmic rays are most probably energized by
diffusive shock acceleration.
 The maximum energy that a charged particle can
gain by diffusive shock acceleration is proportional
to Z.
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Contd.
 The knee corresponds to the maximum energy that
protons can have under diffusive shock acceleration in
SNRs.
 The knee is very sharp, the spectral slop changes rather
abruptly at the knee position [Erlykin and Wolfendale,
J.G (1997)]
 Single source of the knee (EW 1997, Bhadra, (2005),
Erlykin et al (2011), Ter-Antonyan, PRD (2014)]
 a variety of supernovae [Sveshnikova Astron Lett
(2004), Sveshnikova AA(2003)]
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Cont.
 Nuclear photo-disintegration at the sources [Hillas
Ann. Rev. Astron. Astrophys. (1979), Karakula and
Tkaczyk(1993), Candia et al(2002) etc].
 Cannonball model [Dar and Plaga(1999), Plaga(2002),
Dar(2005), De Rujula(2005)]
 masses
of baryonic plasma (cannonballs),
ejected ultra-relativistically in bipolar supernova
explosions, are considered as universal sources
of hadronic galactic cosmic rays.
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Contd.
 a change in the characteristics of high energy
interactions [Nikolsky and Romachin, Physics of
Atomic Nuclei (2000)]
 producing a new type of a heavy particle unseen by air
shower experiments,
 or an abrupt increase in the multiplicity of produced
particles
 Ruled out by the LHC
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 Mass distribution of progenitor of cosmic ray sources
(Biplab Bijay and Bhadra, RAA, 2015)
 Particles are accelerated by expanding shock waves up
to a maximum energy Emax. Emax is not the same for all
the sources but differs depending on the explosion
energy.
 The explosion energy in NS formation process is more
or less constant (since the maximum mass of white
dwarf/neutron star is restricted to ~1.4 MΘ.
 In the case of BH formation process the explosion
energy may differ considerably depending on final BH
mass.
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 In
the gravitational collapse of a spherical mass
distribution of rest mass M leading to formation of black
hole, the maximum energy of extraction out of the collapse
will be [Ruffini and Vitagliano(2003), Christodoulou and
Ruffini(1971)].
 Instead of collapse and resulting explosion, large amount
of energy also can be released through accretion process.
The Eddington luminosity limit, the maximum steadystate luminosity that can be produced is proportional to
mass (M) of the central black hole.
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 the zero age main sequence (ZAMS) stars mass spectrum
also exhibits power law behavior [Salpeter. APJ, 1955]
 Using the expression for explosion energy as function of
progenitor mass, we convolve the resulting explosion
energy-progenitor mass relation with the initial mass
function of the progenitors to obtain explosion energy
distribution.

N(>) ~ -1.35.
 Finally using the relation of maximum energy that a cosmic
ray particle may attain in shock acceleration process with
explosion energy, the maximum energy distribution for
main cosmic ray sources is derived.
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Problems with the model of the knee
 Standard SNR model/Leakage  There should a Fe knee around 100 PeV.
 Hence a special variety of supernovae or some
other type of galactic or extra-galactic source
has to be invoked as generator of cosmic rays
between 100 PeV and the ankle.
 it requires fine-tuning to match both the flux
and the energy at the point of taking over.
 There are other problems such as lower than
expected observed gamma ray fluxes from SNRs
(Bhadra J. Phys G 2002).
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Contd.
 Other models
 Fine tuning
 Mass composition
 The
dilemma of
continues.
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the knee thus still
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How the knee has been detected
 Detection of cosmic rays at very high energies
 Extensive Air Showers (EAS)
 EAS observables:
 Electron (shower) size, muon size, arrival direction,
slope of lateral (radial) charge density, longitudinal
development profile

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Shower size spectrum
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PRIMARY ENERGY SPECTRUM FROM EAS
SHOWER SIZE SPECTRUM
 The observational charged particle size (often known
as shower size) spectrum in EAS is found to exhibit
power law behaviour
 The energy dependence of total number electrons,
muons and hadrons at shower maximum in EAS
initiated by a nucleus with atomic mass number A and
energy Eo
i stands for electron, muon, hadron
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 For
pure em cascade and under few simple
approximations such as the all electrons have the same
energy (which is the critical energy (85 MeV in air), at
which ionization losses and radiative losses are equal)
e is nearly equal to 1 (Matthews, Astropart. Phys.
(2005), Hoerandel, Mod.Phys.Lett.A (2007).
 If one considers that total primary cosmic ray energy is
distributed between electron and muon component,
e will be slightly higher, about 1.05.
 Similarly when all muons are considered to have the
same energy (which is the energy at which the
probability for a charged pion to decay and to interact
are equal) and taking the charged pion production
multiplicity is 10 (constant), µ ~ 0.85.
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 Two important points to be noted are
 (i) the total number of electrons increases with energy
slightly faster than exactly linear whereas the total
number of muons grows with energy slightly less than
exactly linear.
 (ii) The electron number decreases with increasing
mass number whereas muon number grows with mass
number.
 One can infer the primary cosmic ray spectrum
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 Since a sudden change in e at a size corresponding to
a primary energy of about 3 PeV is observed,
consequently a change in  at 3 PeV is inferred which is
the so called knee of the cosmic ray energy spectrum.
 Muon and hadron size spectra also should exhibit
power law behaviour.
 Since µ < e ,for a change in  one expects µ > e .
 Observationally, however, no significant change in µ
is found !
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 On this ground Stenkin [Mod. Phys Letts. 2004, Nucl Phys
B 2006] refuted the reality of the knee in the primary
cosmic ray energy spectrum.
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Aim of the present work
 We shall examine from a detailed Monte Carlo
simulation study whether the different EAS
observables suggest for consistent spectral indices in
the primary cosmic ray energy spectrum before and
after the knee considering the fact that primary
composition may or may not change across the knee.
 We use CORSIKA simulation code to have the relation
between energy and shower size.
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Simulation procedure adopted
 The HE interaction model: QGSJET 01 (version 1c)




/EPOS (version 2.1)
The Low Energy interaction model UrQMD
The US-standard atmospheric model with planar
approximation
The events are generated at EAS-TOP and KASCADE
locations.
The magnetic fields, observation levels, threshold
energies of particle detection and zenith angles are
provided accordingly.
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Inferring Primary cosmic ray spectrum from
measured EAS size spectra
 Only a few EAS experiments so far measured both e
and µ before and after the knee.
 Here we consider the results of two experiments, the
KASCADE (Antoni et. al, Astropart. Phys. (2002) and
EAS-TOP (Navarra et al, Nucl. Phys. B (1998).
 The KASCADE experiment
 Site - Forschungszentrum Karlsruhe (Germeny)
 altitude 110 m above sea level (49.1o N, 8.4o E),
 energy range ~100 TeV to nearly 100 PeV
 in operation during October 1996 to 2003.
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Contd.
 detectors
 an array of electron spread over 700 m × 700 m.
 Muon detector
 a central hadron calorimeter
 The EAS-TOP experiment
 Location - Campo Imperatore, National Gran Sasso
Laboratories in Italy,
 Altitude - 2005 m a.s.l.
 Detectors - electromagnetic, muon, hadron and
atmospheric Cherenkov light
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Energy dependence of
total charged particles at
KASCADE location from the Monte Carlo simulation data for p
primary
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Energy dependence of truncated muon number for p
primary
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Electron and muon spectra for astrophysical
knee
 We shall follow a reverse process, we shall estimate the
expected spectral slopes in charged particle and muon
spectra for different primary composition scenario
assuming that the primary energy spectrum has a
knee.
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Expected electron size spectrum for unchanged
proton primary
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Expected electron size spectrum for unchanged
Fe primary
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Muon size spectrum for unchanged p primary
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Muon size spectrum for unchanged Fe primary
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Electron size spectrum when primary changes
from p to Fe across the knee
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Muon size spectrum when primary changes from
p to Fe across the knee
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2-dimensional electron size muon size spectrum
for unchanged p primary
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Conclusion
 The EAS-TOP observations on total charged particle
and muon spectra consistently infer a knee in the
primary energy spectrum provided the primary is pure
unchanging iron.
 No consistent primary spectrum emerges from
simultaneous use of the KASCADE observed total
charged particle and muon spectra.
 For pure unchanging proton or iron primaries the
difference in spectral slopes below and above the knee
of the size spectrum is larger for muon spectrum than
the electron spectrum.
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 The prominent knee in the electron size spectrum but




not in the muon size spectrum is really puzzling.
When mass composition changes across the knee the
situation becomes quite complex.
In such a situation estimation of spectral index
properly is challenging, particularly for total charged
particle spectrum.
the position of the knee depend on primary
composition both below and above the knee of the
primary energy spectrum
the points close to the knee in the size spectra may
change the overall slope considerably.
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 The simultaneous use of the measured EAS total
charged particle and muon size spectra to infer the
primary energy spectrum is certainly a desirable
approach but it requires a careful and experiment
specific analysis.
 The two-dimensional differential spectrum contents
substantially higher information than those of two
one-dimensional ones but one dimensional spectra
also carry important and exclusive signatures about
primary energy spectrum and composition.
 Independent measurement of muon size spectrum is
also very important . Looking for GRAPES
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Thank you
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Origin of cosmic rays
 “The problem of cosmic ray origin”
 Where they come from –
one of the most enduring mysteries in
physics
 Being charged particles Cosmic Rays are deflected
by the galactic magnetic field and as a result their
direction does not point towards their origin
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Power requirement of Cosmic Ray
sources
 If cosmic rays with the same energy density are also
spread over the extra-galactic space, it will be too high
for sources to meet such a huge power requirement.
 the power required to supply all the galactic cosmic
rays is ~ 5  1040 erg /sec.
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 An associated and relevant question :How they are
produced or more specifically how they are accelerated
to such high energies
(the energy of the observed cosmic ray particles at the
upper end of the energy spectrum is nearly 100,000,000
times higher than the maximum energy achieved in
human made accelerators)
“The so called problem of acceleration mechanism”
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Some Important characteristics of
cosmic rays
 Isotropy
 Energy density
 Power law Energy spectrum
 Nuclear composition
 Isotropy - upper limit of amplitude of anisotropy upto
the knee region is around 10-3 or even less
 isotropized by the galactic magnetic fields
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Energy density
 Energy density ~1 eV/cm3
(of the same order of the interstellar magnetic field
and CMBR)
 the total cosmic ray energy density in the galaxy is
~ 4  1054 erg.
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Nuclear abundance
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Propagation
Li, Be or B
Cosmic ray
(proton or α)
C, N, or O
(He in early universe)
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Resident time of cosmic rays in the
galaxy
 The abundances of few nuclei like Li, Be, B, Mn, Sc are
many order of magnitude higher in cosmic rays in
compare to solar system material.
 Spallation product-
The average total matter traverse by cosmic rays
 The residence time of cosmic rays in the galaxy before
escaping into intergalactic space is ~ 6  106 years.
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Potential sources of cosmic rays
 RATE OF SUPERNOVAE in our galaxy: 1/30 years
 Typically
Ekin ~ 1051 ergs goes to KINETIC ENERGY OF
EJECTA.
 This corresponds to:
LSN = R  ESN ~ 1042 erg/s
 Conversion efficiency required – few %
 (conversion efficiency varies from 7% to 58 % depending
on the energy dependence of diffusion coefficient).
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 Diffusive Shock Acceleration
 Power law spectrum with power index ~ -2.0
 Maximum energy ~ 1014 eV (too low!)
 B-field amplification
 detection of narrow rims in the X-ray emission of several
SNRs
 interpreted as the result of the synchrotron emission
 A simple estimate leads to magnetic fields of the order
∼100−1000µG downstream of the shock
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First detection of amplified
magnetic field in SNR
Chandra
Cassiopeia A
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Chandra
SN 1006
 ISM magnetic field is typically ∼1−10 µG
 the compression at a strong shock is a factor ∼4
 CRs may amplify the magnetic field close to the
shock surface (B/B ~ 50-100)
 Implication – Proton can be accelerated up to the
knee energy.
 2nd knee – Iron knee (3 x 26 PeV) ~ 1017 eV (end of
the galactic cosmic ray spectrum!)
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Observational supports
 Observations of TeV gamma rays from few shell type
SNRs by HESS, CANGAROO, MAGIC and by FERMI at
GeV energy.
 The combined spectrum of SNR RX J1713-3946 by
HESS in TeV regime and by Fermi at lower energies
appears to be flat and probably of hadronic origin.
 Observation of non-thermal X-ray radiation in rims of
SNRs (such as Tycho) (likely to be produced through
synchrotron emission of high energy electrons in the
magnetic field around the shock)
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Problems with SNR paradigm
 “despite the recent encouraging observational and
theoretical results, the SNR paradigm of galactic CRs
is still waiting for the decisive breakthrough.
Currently it remains a likely hypothesis with
attractive features, but not free from ‘nasty
problems
 Galactic to Extra-galactic transition at 1017 eV
 The problem of exact matching of two different
contributions at the transitional energy.
 What is the cause of the “ankle”?
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An alternative proposal for the knee
 Basic philosophy of the model  Whatever may be the sources, there is little doubt that
they are products of stellar evolution process.
 the zero age main sequence (ZAMS) stars mass
spectrum also exhibits power law behavior [Salpeter.
APJ, 1955]
 The feature that ZAMS star mass distribution exhibits
a power law is very intriguing in connection with the
power law behavior of energy spectrum of primary
cosmic rays. It seems unlikely that these two spectra
are totally independent.
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
N(>Emax) ~ Emax-2.6.
 Therefore beyond the knee the spectrum should be
steepen by a factor Emax-0.6. and for acceleration by
relativistic shock by a factor Emax-0.17
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 Composition:
 The model requires not much change in mass
composition across the knee.
 The observational situation of mass composition in
the knee region is quite controversial.
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 the non-detection of X-ray lines at 1 keV from SNR RX
J1713-3946 by Suzaku mission is problematic for a
scenario in which the detected gamma rays are of
hadronic origin (Ellison et al, APJ, 2010).
 it is not enough to just amplify the field on small
length-scales, the field has to be amplified on scales at
least as large as their gyro-radius
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Concluding remarks:
 The progenitor model so far is consistent with the
observations.
 Precise measurement of mass composition in the knee
region can test the validity of the model.
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 Thank you
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 for a power law injection spectrum of CRs ∝ E- , the
spectrum observed at Earth is n(E) ∼E-(+),
 δ >0.5−0.6 leads to excessive anisotropy of the CRs
observed at Earth
 for a Kolmogorov diffusion coefficient D(E) ∝E1/3 the
required injection spectrum must be ∼ E-2.4,
 such steep spectra are not admissible in DSA (even
considering non-linearity) with efficient acceleration
and magnetic field amplification..
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