TeV Neutrinos and Gamma rays from Pulsars/Magnetars. Arunava Bhadra High Energy & Cosmic Ray Research Ctr. North Bengal University. Introduction. The energy spectrum of cosmic rays extends to extremely high energies, values exceeding 10 20 eV .
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High Energy & Cosmic Ray Research Ctr.
North Bengal University
The recent success of satellite/ground-based very-high-energy γ -ray telescopes has opened a new window on the most powerful and violent objects of the Universe.
Link and Burgio (PRL 2005, MNRAS 2006) estimated the neutrino event rate to be observed by a neutrino telescope alike to ICECUBE from pulsars, if cosmic rays are accelerated up to PeV energies in pulsar environment .
Presence of a hadronic component in the flux of pulsar accelerated particles should result in the emission of high-energy neutrinos and gamma-rays simultaneously.
electron may be accelerated
or may lead acceleration of positive ions
The maximum potential drop that may be induced across the magnetic field lines between the magnetic pole and the last field lines that opens to infinity
BS is the strength of magnetic field at neutron star surface
RS is the radius of the neutron star
is the angular velocity
~ 7 1018 B12Pms-2
BS=B12 1012 G, Pms is the pulsar period in millisecond.
Let us conjectured that protons or heavier ions are accelerated near the surface of a pulsar by the polar caps to PeV energies (correspond to small screening) when
μ · Ω < 0
(such a condition is expected to hold for half of the total pulsars).
The threshold condition for the production of -resonance state in pγ interaction is
p(1-cosp) 0.3 GeV2
p Proton energy, photon energy
p angle between proton and photon in the Lab frame.
2.8 kTS (1+zg)
TS is the surface temperature of Neutron star
B12 Pms-2T0.1keV 3 10-4
T0.1keV (kTS/0.1 keV),
typical surface temperature of neutron star is 0.1 keV
q = eZnGJ
where nGJ BsR3/(4Zecr3) is the Goldreich–Julian density at distance r
gap = fd(1-fd)nGJ
is the ratio of the polar cap area to the neutron star surface area.
n(RS) = (/2.8k)[(1+zg)TS]3
being the Stefan–Boltzmann constant.
n(r) = n(RS) (RS/r)2
PC =1 -rRSP(r)dr
dP/P =- n(r)Pdr
Requiring conversion to take place in the range RS ≤ r ≤ 1.2RS , PC has been found to be ~ 0.02 T30.1keV.
L/PC = 2cgapAPCPC
= 4/3 for photon
= 2/3 for mu-neutrino
fb is the duty cycle of the gamma-ray/neutrino beam (typically fb ∼ 0.1– 0.3)
(the decays of pions and their muon daughters result in initial ﬂavour ratios φνe : φνμ : φντ of nearly 1:2:0 but at large distance from the source the ﬂavour ratio is expected to become 1:1:1 due to maximal mixing of νμ and ντ .).
P ~ 1.3 10-6 (/1 TeV)
If m is the mean multiplicity of charged particles in proton–ion interaction, then the flux of gamma-rays at a distance d from the source would roughly be
β represents the fraction of pulsar-accelerated protons trapped in the nebula and t is the age of the pulsar.
The neutrino fluxes from the nebulae would be of nearly the same to those of gamma-rays. Incorporating the neutrino oscillation effect, the expected event rates in a neutrino telescope due to
The energy spectrum of cosmic rays extends to extremely high energies, values exceeding 1020eV.
the recent success of ground-based very-high-energy γ -ray telescopes has opened a new window on the most powerful and violent objects of the Universe, giving a new insight into the physical processes at work in such sources.