Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap
A gamma radiation from pulsars due to inverse Compton scattering of coherent low-frequency radiation on relativistic electrons in a polar gap have been considered. The radio emission in the gap arises due to sub relativistic electron acceleration. The gamma radiation spectrum and luminosity estimate...
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nasplib_isofts_kiev_ua-123456789-1070102025-02-09T15:13:56Z Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap Гамма-излучение пульсаров как результат комптоновского рассеяния при ускорении электронов в полярном зазоре Гамма-випромінювання пульсарів як результат комптонівського розсіювання при прискоренні електронів у полярному зазорі Flanchik, A.B. Kontorovich, V.M. Section B. QED Processes at High Energies A gamma radiation from pulsars due to inverse Compton scattering of coherent low-frequency radiation on relativistic electrons in a polar gap have been considered. The radio emission in the gap arises due to sub relativistic electron acceleration. The gamma radiation spectrum and luminosity estimates have been obtained and connection between gamma radiation and radio emission spectra has been found. Obtained results are in a good agreement with the discovered by Fermi LAT correlation of gamma radiation and radio emission giant pulses in the Crab pulsar. Рассмотрено формирование гамма-излучения пульсаров при обратном комптоновском рассеянии когерентного низкочастотного излучения релятивистских электронов в полярном зазоре. Радиоизлучение в зазоре возникает при ускорении субрелятивистских электронов. Получены спектр и оценки мощности гамма-излучения, а также найдена связь между радиоизлучением и гамма-излучением. Полученные результаты находятся в хорошем согласии с открытой с помощью Fermi LAT корреляцией гамма-излучения и гигантских импульсов радиоизлучения пульсара в Крабовидной туманности. Розглянуто формування гамма-випромінювання пульсарів завдяки зворотному комптонівському розсіюванню когерентного низькочастотного випромінювання релятивістських електронів у полярному зазорі. Радіовипромінювання у зазорі виникає при прискоренні субрелятивістських електронів. Отримано спектр і оцінки потужності гамма-випромінювання, а також знайдено зв'язок між радіовипромінюванням та гамма-випромінюванням. Отримані результати узгоджуються з відкритою за допомогою Fermi LAT кореляцією гамма-випромінювання і гігантських імпульсів радіовипромінювання пульсару у Крабовидної туманності. 2012 Article Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap / A.B. Flanchik, V.M. Kontorovich // Вопросы атомной науки и техники. — 2012. — № 1. — С. 125-129. — Бібліогр.: 26 назв. — англ. 1562-6016 PACS: 97.60.Gb, 98.70.Rz, 12.20.-m https://nasplib.isofts.kiev.ua/handle/123456789/107010 en Вопросы атомной науки и техники application/pdf Institute of Radio Astronomy of NASU |
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Section B. QED Processes at High Energies Section B. QED Processes at High Energies |
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Section B. QED Processes at High Energies Section B. QED Processes at High Energies Flanchik, A.B. Kontorovich, V.M. Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap Вопросы атомной науки и техники |
| description |
A gamma radiation from pulsars due to inverse Compton scattering of coherent low-frequency radiation on relativistic electrons in a polar gap have been considered. The radio emission in the gap arises due to sub relativistic electron acceleration. The gamma radiation spectrum and luminosity estimates have been obtained and connection between gamma radiation and radio emission spectra has been found. Obtained results are in a good agreement with the discovered by Fermi LAT correlation of gamma radiation and radio emission giant pulses in the Crab pulsar. |
| format |
Article |
| author |
Flanchik, A.B. Kontorovich, V.M. |
| author_facet |
Flanchik, A.B. Kontorovich, V.M. |
| author_sort |
Flanchik, A.B. |
| title |
Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap |
| title_short |
Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap |
| title_full |
Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap |
| title_fullStr |
Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap |
| title_full_unstemmed |
Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap |
| title_sort |
gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap |
| publisher |
Institute of Radio Astronomy of NASU |
| publishDate |
2012 |
| topic_facet |
Section B. QED Processes at High Energies |
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https://nasplib.isofts.kiev.ua/handle/123456789/107010 |
| citation_txt |
Gamma radiation of pulsars as result of inverse compton scattering at acceleration of electrons in a pulsar polar gap / A.B. Flanchik, V.M. Kontorovich // Вопросы атомной науки и техники. — 2012. — № 1. — С. 125-129. — Бібліогр.: 26 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-11-27T05:39:44Z |
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2025-11-27T05:39:44Z |
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1849920835611000832 |
| fulltext |
GAMMA RADIATION OF PULSARS AS RESULT OF
INVERSE COMPTON SCATTERING AT ACCELERATION OF
ELECTRONS IN A PULSAR POLAR GAP
A.B. Flanchik 1∗and V.M. Kontorovich 1,2
1Institute of Radio Astronomy of NASU, 61002, Kharkov, Ukraine
2Karazin Kharkov National University, 61077, Kharkov, Ukraine
(Received November 3, 2011)
A gamma radiation from pulsars due to inverse Compton scattering of coherent low-frequency radiation on relativistic
electrons in a polar gap have been considered. The radio emission in the gap arises due to sub relativistic electron
acceleration. The gamma radiation spectrum and luminosity estimates have been obtained and connection between
gamma radiation and radio emission spectra has been found. Obtained results are in a good agreement with the
discovered by Fermi LAT correlation of gamma radiation and radio emission giant pulses in the Crab pulsar.
PACS: 97.60.Gb, 98.70.Rz, 12.20.-m
1. INTRODUCTION
Pulsars are rapidly rotating neutron stars with
very strong magnetic fields [1–3], which have mag-
netosphere filled with relativistic electron-positron
plasma. This plasma is produced by high energy pho-
tons in strong magnetic field above the star magnetic
poles [2].
Fig. 1. A scheme of the polar gap in pulsars
Pulsars are the pulse sources of radio waves and
some of them emit high energy gamma radiation.
The pulsar gamma radiation arises in an inner gap [4]
above a polar cap under magnetosphere of open mag-
netic field lines (Fig. 1), which plays a role of an ac-
celerator for electrons from the star surface. In pulsar
classical models [4,5] the gamma radiation are gener-
ated due to curvature radiation (CR) mechanism [6].
We showed [7] that the powerful radio band radia-
tion in the gap changes the gamma emission mecha-
nism from the curvature radiation to inverse Comp-
ton scattering (ICS) of low-frequency radiation. It
leads to connection between pulsar gamma ray ra-
diation and radio emission. The correlations (both
in luminosities and spectra) of pulsar radio emis-
sion and gamma ray radiation was predicted in [7].
In that work we considered the polar gap as a res-
onator cavity accumulating powerful low-frequency
radiation generated by the sparks [4] in the strong
electric field of the gap. The formation of the res-
onator and accumulation of high energy density have
some difficulties. In [8, 9] we have shown that the
high energy density of low-frequency radiation may
arise because of continuous energy pumping due to
emission in electron acceleration process in the gap
electric field. The free exit of electrons from the star
surface due to low electron work function [10] leads to
vanishing the electric field on the surface. This field
increases from zero with distance from the star sur-
face and emission of electrons falls within the radio
spectral range. The Fermi LAT data obtained af-
ter our work [7] showed that there is a correlation in
phase (Fig. 2) between radio giant pulses and gamma
ray radiation [11]. The authors of [11] related this
correlation with a reconnection of magnetic force lines
near light cylinder [12]. In the Lyutikov model [12] of
pulsar giant pulses (Fig. 3) there is a reconnection of
magnetic force lines at the periphery of pulsar mag-
netosphere near the light cylinder where there is a
region of dense hot plasma. Occasional reconnec-
tion jets produce high Lorentz factor beams prop-
agating along magnetic force lines and emitting co-
herent cyclotron-Cherenkov radiation at anomalous
Doppler resonance. Due to curvature radiation high
∗Corresponding author E-mail address: alex.svs.fl@gmail.com
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1.
Series: Nuclear Physics Investigations (57), p. 125-129.
125
energy beams emit also the hard gamma ray photons
correlated with radio giant pulses.
Fig. 2. Phase correlation between gamma pulses
(triangles) and radio giant pulses (circles)
observed by Fermi LAT (from the paper of
A.Belous et al [11])
The observed phase correlation may be considered
also as confirmation of idea of our model that there
is a powerful radio emission in the gap and pulsar
giant pulses are direct emissions through waveguides
in the magnetospheric plasma [13, 14]. The gamma
ray radiation leaves the gap through the waveguide
too, therefore the phase correlation between the ra-
dio giant pulses and gamma ray pulses arises. In the
Crab pulsar B0531+21 the waveguide is close to the
magnetic axis.
Fig. 3. Generation of the Crab pulsar giant
pulses in the Lyutikov model [12]
Below it is shown that the total luminosity of
gamma rays produced by ICS of the low-frequency
radiation [7,15] in the gap is sufficient to explain the
gamma emission from pulsars if the gamma radiation
goes out from the all surface of the polar cap (Fig. 1).
2. HARD GAMMA RAY RADIATION
DUE TO INVERSE COMPTON
SCATTERING IN THE GAP
Because of the high energy density of the low-
frequency radiation there are a lot of soft photons in
the gap which are scattered by the relativistic elec-
trons. As is shown [8] that in this case the spectrum
of the coherent radio emission is the power-law
I (ω) ∝ ω−α, (1)
where α is a spectral index, which has the values from
the range 1 ≤ α ≤ 3. The frequencies of initial pho-
tons obey a condition h̄ωΓ << mc2, so we can con-
sider the ICS in the Thomson limit. In the electron
rest frame the differential cross section of the ICS in
the strong pulsar magnetic field has the form [16–18]
dσ =
r2
e
4
ω2
ω2
B
(
1 + cos2 θ
) (
1 + cos2 θ′
)
dΩ′, (2)
where re is the electron classical radius, ωB =
eB/mc, B is the star surface magnetic field, θ and
θ′ are the angles between magnetic field and mo-
menta of the initial and final photons (Fig. 4), dΩ′ =
2π sin θ′dθ′. The cross section dependence on the
magnetic field describes the suppression of soft pho-
ton Compton scattering in strong magnetic fields [17].
Using Eq. (4) and the Lorentz transformations for
angles θ, θ′ we obtain the scattering cross section for
the case of the ultrarelativistic electrons
dσ = r2
e
ω2
ω2
B
(
1 − V
c cos θ
)2
(
1 − V
c cos θ′
)2 dΩ′. (3)
From Eq. (5) it is seen that the scattered radia-
tion is quite anisotropic due to relativistic aberration
and is concentrated within a narrow cone along the
open magnetic field lines.
Fig. 4. ICS (left) and its kinematics (right)
With help of Eq. (3) we write the scattering proba-
bility as [19]
w (q,k, Γ) d3q = c
(
1 − V
c cos θ
)
dσ,
where q is the scattered photon wave vector, and
126
w (q,k, Γ) = c4 r2
e
ω2
B
(
1 − V
c cos θ
)
× δ
(
ωγ − ω
1 − V
c cos θ
1 − V
c cos θ′
)
, (4)
ωγ is a frequency of gamma ray photon. The spec-
trum I (ωγ) dωγof the radiation is given by
I (ωγ) =
h̄ω3
γ
4π2c3
∫
w (q,k, Γ)fe (Γ, z) n (k)
× dΩ′dΓdΣdz, (5)
where fe (Γ, z) and n (k) are the distribution func-
tions of electrons and low-frequency photons, which
are normalized as
∞∫
1
fe (Γ, z)dΓ = ne,
∫
h̄ω · n (k)
2d3k
(2π)3
= U,
ne ≈ nGJ = ΩB/2πce is the average electron concen-
tration in the gap (nGJ is the Goldreich-Julian par-
ticle density [20]), Ω is the pulsar rotation frequency,
and U is the total energy density of the radio emission
in the gap. Since the low-frequency radiation spec-
trum is power-law we have for the distribution of the
low-frequency photons
n (k) =
π2c3
h̄
(α − 1)Uωα−1
minω−(3+α), (6)
and ωmin ∼ 107s−1 is a minimal frequency of low-
frequency radiation in the gap. The electron distrib-
ution function is given by
fe (Γ, z) = neδ (Γ − Γ (z)) . (7)
Then the scattered radiation spectral distribution
takes a form [7]
I (ωγ) =
3
8
22α
α + 2
cσT neUΣPC
ω2
B
ωα−1
min
× ω2−α
γ
h∫
0
Γ2α−2 (z)dz, (8)
with σT being the Thomson cross section. We see
from Eq. (8) that in case of power-law radio emis-
sion spectrum (1) the gamma ray spectrum is also a
power-law with the index connected with the radio
spectral index αby the relation [7]
αγ = α − 2. (9)
This relation appears due to dependence of the
scattering cross section on the initial photon fre-
quency (see Eq. (2)). According to the Fermi LAT
observation data [21] several gamma ray pulsars such
as PSR B0531+21 (Crab) and PSR B0833-45 (Vela)
obey to this index relation (9).
Integrating the spectral distribution (8) over fre-
quencies of scattered photons we obtain the estima-
tion of the total gamma ray luminosity
Iγ =
∫
I (ωγ) dωγ ≈ cgneσT U Γ̄4ΣPCh, (10)
where Γ̄ ∼ 108 is the electron maximal Lorentz factor
in the gap and
g =
24
5
α − 1
ω2
B
ωα−1
min
ωcf∫
ωmin
ω2−αdω. (11)
The ICS predominates over the curvature radia-
tion and becomes a dominant mechanism of energy
losses when the condition satisfies
U > Umin =
2e2
3R2
cgσT
,
where is a curvature radius of magnetic force line.
Below we suppose that this condition satisfies.
Substituting U ≈ IR/cΣPC to Eq. (10), we ob-
tain a relation between radio and gamma ray lumi-
nosities [7]
Iγ ≈ gσT nehΓ̄4IR. (12)
The total radio emission intensity in the gap is
determined by contribution of all electrons of the po-
lar cap in the radiation formation region. The power
emitted by a single electron moving with accelera-
tion w = eE/mΓ3 is 2e4E2/3m2c3 [6,22], where E is
the accelerating field in the gap [23, 24]. Taking into
account the contributions from all emitting electrons
and the coherence [25] of emission we have for the
total radio luminosity estimate
IR ≈ λ2
maxΩ3R3B2
c2
, (13)
where R ∼ 106 cm is the star radius and λmax ∼
102 cm is a wavelength, corresponding to the maxi-
mum in the pulsar radio emission spectrum. With
help of Eq. (12) we have for the gamma ray luminos-
ity
Iγ ≈ λ2
maxΩ3R3B2
c2
gσT nehΓ̄4. (14)
In dependence on the pulsar parameters, this esti-
mate gives 1033 erg/s ≤ Iγ ≤ 1035 erg/s, that agrees
with the Fermi LAT data on luminosities of gamma
ray pulsars [21]. For the pulsar B0531+21 which
is close to orthogonal rotator estimates (13) and
(14) should be multiplied by a factor cos2 χ, where
χ ≈ 87o is an angle between magnetic and rotation
axis of the pulsar B0531+21 then the Eq. (14) gives
a correct estimate Iγ ∼ 1035 erg/s for the Crab pulsar
gamma ray luminosity too.
Earlier [7] we considered the gamma ray radiation
exit only through the waveguide near the magnetic
127
axis. But the observations by Fermi LAT show that
the gamma ray radiation is observed from larger part
of open magnetic force line region. Therefore in esti-
mates (10) and (14) we suppose that the area of hard
gamma ray formation region is of order of the polar
cap area.
3. CONCLUSIONS
Due to inverse Compton scattering of the power
radio emission on the ultrarelativistic electrons in
the gap the gamma-radiation is formed [7]. Giant
pulses of radio waves correspond to the free exit of
radiation through the waveguide near the magnetic
axis [13, 14, 26]. According [11] one can conclude
that the gamma radiation direction diagram has also
the maximum along the magnetic axis. Through the
same break the gamma-radiation goes out from the
gap, which explains the angular correlation of the
gamma-radiation with the giant pulses, including the
case of absence of their simultaneity. The obtained
estimates of pulsar gamma ray luminosities and spec-
tra agree with Fermi LAT data if we take into account
the gamma radiation from the all surface of the polar
cap.
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