Transcript Nature of the cosmic ray power law exponents

Nature of the cosmic ray power law
exponents
A. Widom, J. Swain (Boston, MASS USA)
Y. Srivastava (Perugia, Italy)
Presented by YS
@
17th Lomonosov Conference on Elementary Particles
Session 21.08 C
21st August 2015
Moscow State University, Moscow, Russia
Plan of the Talk
1. Two major unresolved issues with cosmic ray particle
energy spectrum: isotropy & stable critical indices
2. Basic hypothesis for isotropy: Thermal production
basic tool for critical indices: thermal field theory
3. Evaporation: Landau and Fermi
4. Classical and quantum critical indices
5. Bosonic and Fermionic indices
6. Quantum phase transition
7. AMS data for (e-e+) & cosmic ray data on nuclei
8. Development of the knee
9. Energy loss estimates
10. Conclusions and work in progress
Cosmic Ray particle spectrum:
Isotropy & power law indices
The experimental differential energy flux of cosmic
ray nuclei obeys a scaling law with index alpha:
with
Our theoretical result
Problems with the “usual” explanation
1. First order Fermi acceleration mechanism does
produce a power law behavior but with index = 1
2. Second order produces an incorrect index 2.
3. Since multiple sources contribute to what is seen,
one has to explain:
• A: why the observed spectrum is as smooth as it is
(i.e. why each source has, within observed errors,
the same exponent)
• B: why various sources should be distributed in such
a way and with such intensities that there would, even
with the same slopes, be no jumps in the spectrum.
Our references: By A. Widom, J. Swain, Y. Srivastava
1. Entropy and the Cosmic Ray Particle Energy
Distribution Power Law Exponent: arXiv:1410.1766 v1
[hep-ph] (2014)
2. Concerning the Nature of the Cosmic Ray Power Law
Exponents: arXiv:1410.6498 [hep-ph] (2014)
3. A Quantum Phase Transition in the Cosmic Ray Energy
Distribution: arXiv:1501.07809v2[hep-ph](2015)
4. The Theoretical Power Law Exponent for Electron and
Positron Cosmic Rays, A Comment on the Recent
Letter of the AMS Collaboration: arXiv:1501.07810v2
[hep-ph] (2015)
5. Bremsstrahlung Energy Losses for Cosmic Ray
Electrons and Positrons
Statistical Thermodynamical Model
We apply entropy computations in a form originally
due to Landau for the Landau-Fermi liquid drop model
of a heavy nucleus.
The energy distribution of some of the decay products
are thought to be evaporating nucleons from the bulk
liquid drops excited by a heavy nuclear collision.
We propose as the sources of cosmic rays, the
evaporating stellar winds from (say) neutron star
surfaces.
Possible high energy cosmic ray sources
Unknown: Neutron stars, Supernovae, AGN….?
Cosmic Ray Evaporation I
• The structure of neutron stars consists of a big nuclear
droplet facing a very dilute gas, i.e. the “vacuum”.
• Neutron stars differ from being simply very large nuclei in
that most of their binding is gravitational rather than nuclear,
• But, the droplet model of the nucleus should still offer a good
description of nuclear matter near the surface where it can
evaporate.
• The evaporation is from the effective fields in the form of
• Note that from neutron stars we will be at high temperatures
where the heat capacity goes to a constant.
Cosmic Ray Evaporation II
1. What evaporates from the neutron star via scalar and
vector fields are then energetic protons and alpha
particles along with other nuclei to a much lesser extent.
2. Deuterons are only weakly bound and would be
expected to photo-dissociate on background photons
present throughout space rapidly to produce protons and
neutrons which in turn would produce protons when they
decay.
3. The energy distribution comes directly from the
entropy of scalar (spin zero) and vector (spin 1)
combinations of baryons.
Power Law Index I: Bosons
Classical and Quantum Critical Indices
Cosmic Quantum Phase Transition I: The Knee
• There is a break at an energy Ec about 1 PeV [The Knee]
• For energies of nuclei lower than the knee, the index
α = 2.7 (Boson value)
• For energies of nuclei higher than the knee, the index
α = 3.1 (Fermion value)
• The energy distribution depends on the heat and thereby
entropy of evaporation from the cosmic ray source. There
exists a quantum phase transition of cosmic proportions at
the crossing energy.
• It is evidently a quantum phase transition since the order
parameter involves the difference between Bose and Fermi
statistical phases.
• In virtue of the experimental continuity of the energy
distribution and thereby the entropy, the phase transition is
higher than first order.
Cosmic Quantum Phase Transition II
• The boson phase arises from those evaporation nuclei described
by the conventional collective Boson models of nuclear physics.
• There exist pairing correlations in odd-odd nuclei made up of
deuterons. Correlations between two spin one deuterons lead to
spin zero alpha particles and so forth all within the pairing
condensate.
• The condensate resides near the surface of evaporating high
baryon number A ≫ 1 nuclei. For example, a neutron star itself is
merely a nucleus of extremely high baryon number (A ≫ ≫ 1) with
superfluidity (and superconductivity) in the neighborhood of the
nuclear surface.
• The “partons” from the pairing condensate are evidently the
nucleons. The partons then turn into fermions for the phase that
exists above the crossing energy. For energies above the knee, the
cosmic rays must be composed mainly of protons. In order to
comprehend the phase transition, it is necessary to understand
how photons can photo-disintegrate the compound boson
odd-odd nuclei ultimately into its nucleon parts
Cosmic Quantum Phase Transition III
• We can make an estimate of the cross-over energy
using a simple kinetics model for photo
disintegration.
• Consider an initial compound nucleus I that is hit by
a photon leading to a final state F:
Cosmic Quantum Phase Transition IV
• The pressure from the Bose-Einstein gas is slightly
lower than that of a Maxwell Boltzmann gas in that the
quantum statistics describes an attraction.
• The pressure from the Fermi-Dirac gas is slightly higher
than that of a Maxwell Boltzmann gas in that the
quantum statistics describes a Pauli exclusion repulsion.
• Although the value change in alpha due to quantum
statistics is small,
∆α = (αFD − αBE) ≈ 0.450196,
It is entirely responsible for the quantum cosmic ray
second order phase transition and the development of
the knee.
Spectrum of cosmic electrons/positrons:
Theory and AMS data
• For fermions, we had predicted that the critical
power law index would be
• Recently, AMS Collaboration has measured the
energy distribution of combined electrons &
positrons
• Were they classical particles obeying the MaxwellBoltzmann distribution, the index would have been
3
AMS Data
Index changes due to energy losses I
• We have investigated conditions under which
energy losses due to EM radiation would not
change the observed energy power law spectrum
from the critical indices at the source
• Our analysis is of particular relevance for the AMS
electron/positron data as energy losses for these
are (potentially) the largest
• We find that for E < 1 TeV, the measured index
remains the same and reflects the index at the
source.
• Hence, AMS data are quite robust and of
fundamental importance.
Energy losses II: Bremsstrahlung
• We have computed energy losses for ultrarelativistic electrons and/or positrons due to
classical electro-dynamic bremsstrahlung.
• The energy losses considered are (i) due to
Thompson scattering from fluctuating
electromagnetic fields in the background cosmic
thermal black body radiation and (ii) due to the
synchrotron radiation losses from quasi-static
domains of cosmic magnetic fields.
• For distances to sources of galactic length
proportions, the lepton cosmic ray energy must be
less than about a TeV for negligible losses.
Conclusions
• Thermal origin (from neutron stars, supernoave,..) can
explain the observed isotropy and smoothness in the
cosmic ray energy spectrum
• Using quantum relativistic thermal field theory, we
have computed power law indices for bosons and
fermions in very good agreement with data.
• A second order phase transition is shown to occur
leading to the observed knee in the spectrum and the
estimate of the cross-over energy is satisfactory.
• Our prediction of the critical index for electron/fermion
index is in excellent agreement with the AMS data.
• Our computations of the EM energy losses –largest for
electrons and positrons- confirm that the AMS data for
E < 1 TeV, reflect the critical index at the source.
Work in progress I
• Ultra-relativistic cosmic ray particles should have
tiny deviations from our computed critical indices
due to asymptotic freedom that anchors the quasifree parton model, leading to an ideal gas of bosons
and fermions (IBM). We hope to present –albeit
small- one-loop corrections soon.
• Quantum EM energy losses need to be performed
to confirm our classical energy loss estimates.
Particularly relevant would be computation of
changes in the critical indices for
electrons/positrons with energies > 1 TeV.
Work in progress II
• For cosmic energies far beyond the knee, we expect
a dramatic change in the composition of the nuclei
so much so that at asymptotic energies we expect
to observe essentially only protons. This statement
needs to be quantified and details of the spectrum
need to be computed.
• An important problem that concerns future work is
into the nature of the very high energy spectrum of
the photon and the neutrino.
Thank you for your patience
and
We would like to thank the
organizers for inviting us
to present our results
at such an interesting conference
спасибо
Further Notes for the curious
Our references: By A. Widom, J. Swain, Y. Seivastava
1. Entropy and the Cosmic Ray Particle Energy
Distribution Power Law Exponent: arXiv:1410.1766 v1
[hep-ph] (2014)
2. Concerning the Nature of the Cosmic Ray Power Law
Exponents: arXiv:1410.6498 [hep-ph] (2014)
3. A Quantum Phase Transition in the Cosmic Ray Energy
Distribution: arXiv:1501.07809v2[hep-ph](2015)
4. The Theoretical Power Law Exponent for Electron and
Positron Cosmic Rays, A Comment on the Recent
Letter of the AMS Collaboration: arXiv:1501.07810v2
[hep-ph] (2015)
5. Bremsstrahlung Energy Losses for Cosmic Ray
Electrons and Positrons