Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022
In this paper, an alternative theoretical interpretation to the generally assumed thermal emission models of the observed X-ray spectrum of isolated pulsar RX J0420.0-5022 is presented. It is well-known that at a pulsar surface, the distribution function of relativistic particles is one-dimensional....
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| Cite this: | Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 / N. Chkheidze, Iu. Babyk // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 1. — С. 32-37. — Бібліогр.: 24 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1194222025-02-09T17:19:38Z Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 Chkheidze, N. Babyk, Iu. In this paper, an alternative theoretical interpretation to the generally assumed thermal emission models of the observed X-ray spectrum of isolated pulsar RX J0420.0-5022 is presented. It is well-known that at a pulsar surface, the distribution function of relativistic particles is one-dimensional. However, cyclotron instability causes an appearance of transverse momenta of relativistic electrons, which as a result start to radiate in the synchrotron regime. On the basis of the Vlasov kinetic equation we study the process of quasi-linear difusion (QLD) developed by means of the cyclotron instability. This mechanism enables the generation optical and X-ray emissions on the light cylinder lengthscales. An analysis of the three archival XMM-Newton observations of RX J0420.0-5022, is performed. Considering a different approach to synchrotron emission theory, a spectral energy distribution was obtained, which was in a good agreement with the observational data. A fit to the X-ray spectrum was conducted using both the present synchrotron emission model spectrum absorbed by cold interstellar matter, as well as the generally assumed black-body absorption model. The authors are grateful to Prof. George Machabeli for valuable discussions. The HEASARC online data archive at NASA/GSFC has been used extensively in this research. This research was supported by the Shota Rustaveli National Science Foundation grant (12/31). 2013 Article Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 / N. Chkheidze, Iu. Babyk // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 1. — С. 32-37. — Бібліогр.: 24 назв. — англ. 2227-1481 https://nasplib.isofts.kiev.ua/handle/123456789/119422 en Advances in Astronomy and Space Physics application/pdf Головна астрономічна обсерваторія НАН України |
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In this paper, an alternative theoretical interpretation to the generally assumed thermal emission models of the observed X-ray spectrum of isolated pulsar RX J0420.0-5022 is presented. It is well-known that at a pulsar surface, the distribution function of relativistic particles is one-dimensional. However, cyclotron instability causes an appearance of transverse momenta of relativistic electrons, which as a result start to radiate in the synchrotron regime. On the basis of the Vlasov kinetic equation we study the process of quasi-linear difusion (QLD) developed by means of the cyclotron instability. This mechanism enables the generation optical and X-ray emissions on the light cylinder lengthscales. An analysis of the three archival XMM-Newton observations of RX J0420.0-5022, is performed. Considering a different approach to synchrotron emission theory, a spectral energy distribution was obtained, which was in a good agreement with the observational data. A fit to the X-ray spectrum was conducted using both the present synchrotron emission model spectrum absorbed by cold interstellar matter, as well as the generally assumed black-body absorption model. |
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Chkheidze, N. Babyk, Iu. |
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Chkheidze, N. Babyk, Iu. Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 Advances in Astronomy and Space Physics |
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Chkheidze, N. Babyk, Iu. |
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Chkheidze, N. |
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Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 |
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Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 |
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Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 |
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Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 |
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Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 |
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nonthermal emission model of isolated x-ray pulsar rx j0420.0-5022 |
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Nonthermal emission model of isolated X-ray pulsar RX J0420.0-5022 / N. Chkheidze, Iu. Babyk // Advances in Astronomy and Space Physics. — 2013. — Т. 3., вип. 1. — С. 32-37. — Бібліогр.: 24 назв. — англ. |
| series |
Advances in Astronomy and Space Physics |
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AT chkheidzen nonthermalemissionmodelofisolatedxraypulsarrxj042005022 AT babykiu nonthermalemissionmodelofisolatedxraypulsarrxj042005022 |
| first_indexed |
2025-11-28T13:37:57Z |
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Nonthermal emission model
of isolated X-ray pulsar RX J0420.0-5022
N.Chkheidze1∗, Iu. Babyk2,3,4†
Advances in Astronomy and Space Physics, 3, 32-37 (2013)
© N.Chkheidze, Iu. Babyk, 2013
1Center for Theoretical Astrophysics, ITP, Ilia State University, 0162, Tbilisi, Georgia
2Main Astronomical Observatory of NAS of Ukraine, 27 Akademika Zabolotnoho St., 03680 Kyiv, Ukraine
3Dublin Institute for Advanced Studies, Fitzwilliam Place, 31, Dublin 2, Ireland
4Dublin City University, Dublin 9, Ireland
In this paper, an alternative theoretical interpretation to the generally assumed thermal emission models of
the observed X-ray spectrum of isolated pulsar RX J0420.0-5022 is presented. It is well-known that at a pulsar
surface, the distribution function of relativistic particles is one-dimensional. However, cyclotron instability causes
an appearance of transverse momenta of relativistic electrons, which as a result start to radiate in the synchrotron
regime. On the basis of the Vlasov kinetic equation we study the process of quasi-linear di�usion (QLD) developed
by means of the cyclotron instability. This mechanism enables the generation optical and X-ray emissions on the
light cylinder lengthscales. An analysis of the three archival XMM-Newton observations of RX J0420.0-5022, is
performed. Considering a di�erent approach to synchrotron emission theory, a spectral energy distribution was
obtained, which was in a good agreement with the observational data. A �t to the X-ray spectrum was conducted
using both the present synchrotron emission model spectrum absorbed by cold interstellar matter, as well as the
generally assumed black-body absorption model.
Key words: pulsars: individual RX J0420.0-5022, stars: magnetic �elds, radiation mechanisms: non-thermal
introduction
The soft X-ray source RXJ0420.0-5022 (hereafter
RXJ0420) belongs to the group of seven radio-quiet,
isolated neutron stars discovered in the ROSAT all-
sky survey data, often referred to as the X-ray Dim
Isolated Neutron Stars (XDINSs, see [10] for review).
In the optical domain, only a few XDINSs have coun-
terparts certi�ed by their proper motion measure-
ments. However several additional likely candidates
remain, based on their coincidence with the X-ray
positions [17]. The X-ray spectra of XDINSs are
well-represented by an absorbed black-body model
(kT ≈ 45 − 100 eV), emission which originates in
the hotter parts of the neutron star surface [10].
Whereas the cooler part of the XDINSs surface is
assumed to be emitting in the optical domain [20].
The formation of a non-uniform surface temperature
distribution is still under debate; it is most likely ar-
ti�cial and therefore needs to be examined through
convincing theory. The optical emission is also ex-
plained in terms of hydrogen layers of �nely-tuned
thickness superposed on a condensed matter surface,
reprocessing surface radiation [11], or in terms of
non-thermal emission from particles in the star mag-
netosphere [18].
In contrast to somewhat contrived thermal emis-
sion models, the observed properties of the faintest
object in X-rays among the XDINSs RXJ0420 can
be explained in the framework of the plasma emis-
sion model. This model has already been applied to
explain the observed spectra of two other XDINSs
(RXJ1856.5-3754 and RBS1774, see [4, 5] for more
details). The plasma emission model is based on the
well-developed theory of pulsars [14, 15] and suggests
successful interpretation of the observational data.
According to these works, in the electron-positron
plasma of a pulsar magnetosphere, the low frequency
cyclotron modes, during the quasi-linear evolution
stage, create conditions for generation of high energy
synchrotron emission. Generally speaking, at the
pulsar surface, relativistic particles e�ciently lose
their perpendicular momenta via synchrotron emis-
sion in very strong magnetic �elds, therefore they
transit to their ground Landau state very rapidly
(pitch angles are vanishing). However, cyclotron in-
stability causes the appearance of transverse mo-
menta of relativistic particles in the outer parts of
the pulsar magnetosphere. Therefore, the resonant
electrons start to radiate in the synchrotron regime.
We suppose that the observed X-ray emission of
RXJ 0420 is generated by the synchrotron mecha-
nism at the light cylinder length-scales. In general
∗nino.chkheidze@iliauni.edu.ge
†babikyura@gmail.com
32
Advances in Astronomy and Space Physics N.Chkheidze, Iu. Babyk
the synchrotron radiation spectrum is considered to
be a power-law, which is not consistent with the
observational data from RXJ0420. The standard
theory of the synchrotron radiation [2, 7] typically
provides the power-law spectral energy distribution.
Contrary to the standard scenario, by taking into ac-
count the speci�cations produced due to the present
emission model we obtain di�erent spectral distribu-
tion, which can be successfully �tted with the mea-
sured X-ray spectrum of RXJ0420.
In this paper, we describe the plasma emission
model and derive the synchrotron radiation spec-
trum based on our scenario, present the results
of spectral analysis of re-processed XMM-Newton
archival data from RXJ0420, and present our con-
clusions.
emission model
Any well-known theory of pulsar emission sug-
gests that the observed radiation is generated due
to processes taking place in an electron-positron
plasma. It is generally assumed that the pulsar
magnetosphere consists of dense relativistic electron-
positron plasma with an anisotropic one-dimensional
distribution function (see Fig. 1 from [1]) and is com-
prised of the following components: a plasma bulk
with an average Lorentz-factor of γp ' 102, a tail on
the distribution function with γt ' 105, and the pri-
mary beam with γb ' 107. The distribution function
is one-dimensional and anisotropic, hence the plasma
becomes unstable, which may cause excitation of the
plasma eigen-modes. Assuming the eigen-modes of
the electron-positron plasma to have small inclina-
tion angles with respect to the magnetic �eld, one
is left with three branches, two of which are mixed
longitudinal-transversal waves (lt1,2). The high fre-
quency branch on the diagram ω(k‖) begins with
the Langmuir frequency and for longitudinal waves
(k⊥ = 0), lt1 reduces to the pure longitudinal Lang-
muir mode. The low frequency branch, lt2, is similar
to the Alfvén wave. The third t mode is the pure
transversal wave, the electric component of which
Et is perpendicular to the plane of the wave vector
and the magnetic �eld, (k,B0). The vector of the
electric �eld Elt1,lt2 is located in the plane (k,B0).
When k⊥ = 0, the t-mode merges with the lt waves
and the corresponding spectra are given by [12]:
ωt ≈ kc (1− δ) , δ =
ω2
p
4ω2
Bγ
3
p
, (1)
where k is the modulus of the wave vector, c is
the speed of light, ωp ≡
√
4πnpe2/m is the plasma
frequency, e and m are the electron's charge and
rest mass, respectively, np is the plasma density,
ωB ≡ eB/mc is the cyclotron frequency, and B is
the magnetic �eld induction.
The main mechanism of wave generation in plas-
mas of the pulsar magnetosphere is cyclotron insta-
bility. The cyclotron resonance condition can be
written as [12]:
ω − k‖V‖ − kxux +
ωB
γr
= 0, (2)
where ux = cVϕγr/ρωB is the drift velocity of the
particles due to curvature of the �eld lines with a
curvature radius ρ. During the wave generation pro-
cess, one also has a simultaneous feedback of these
waves on the resonant electrons [24]. This mecha-
nism is described by the QLD, leading to a di�usion
of particles along as well as across the magnetic �eld
lines. Therefore, resonant particles acquire trans-
verse momenta (pitch angles) and, as a result, start
to radiate through the synchrotron mechanism.
The wave excitation leads to redistribution pro-
cess of the resonant particles via the QLD. The ki-
netic equation for the distribution function of the
resonant electrons can be written as [4]:
∂f0
∂t
+
∂
∂p‖
{
F‖f
0
}
+
1
p⊥
∂
∂p⊥
{
p⊥F⊥f
0
}
=
=
1
p⊥
∂
∂p⊥
{
p⊥D⊥,⊥
∂
∂p⊥
f0 (p)
}
, (3)
where
F⊥ = −αs
p⊥
p‖
(
1 +
p2⊥
m2c2
)
, F‖ = − αs
m2c2
p2⊥ (4)
are the transverse and longitudinal components of
the synchrotron radiation reaction force and αs =
2e2ω2
B/3c
2.
Here D⊥,⊥ is the perpendicular di�usion coe�-
cient, which can be de�ned as follows [4]:
D⊥,⊥ =
e2
8c
δ |Ek|2 , (5)
where |Ek|2 is the density of electric energy in the
waves. Its value can be estimated from the expres-
sion |Ek|2 ≈ mc2nbγbc/2ω, where ω is the frequency
of the cyclotron waves.
The transversal QLD increases the pitch-angle,
whereas force F⊥ resists this process, leading to a
stationary state (∂f/∂t = 0). The pitch-angles ac-
quired by resonant electrons during the process of
the QLD satis�es ψ = p⊥/p‖ � 1. Thus, one can
assume that ∂/∂p⊥ >> ∂/∂p‖. In this case the solu-
tion of Eq. (3) gives the distribution function of the
resonant particles by their perpendicular momenta
[4]:
f(p⊥) = C exp
(∫
F⊥
D⊥,⊥
dp⊥
)
= Ce
−
(
p⊥
p⊥0
)4
, (6)
33
Advances in Astronomy and Space Physics N.Chkheidze, Iu. Babyk
where
p⊥0
≈ π1/2
Bγ2p
(
3m9c11γ5b
32e6P 3
)1/4
. (7)
And for the mean value of the pitch angle we �nd
ψ0 ≈ p⊥0
/p‖ ' 10−3. Synchrotron emission is gener-
ated as the result of the presence of pitch angles.
synchrotron radiation spectrum
To explain the observed X-ray emission of
RXJ0420, let us assume that the resonant parti-
cles are the primary beam electrons with γb ∼ 107,
placing the synchrotron radiation in the soft X-ray
spectrum. According to our emission scenario, the
synchrotron radiation is generated as the result of
acquirement of pitch angles by resonant particles,
during the QLD stage of cyclotron instability. As
was shown in [16], the cyclotron resonance condi-
tion (see Eq. (2)) is ful�lled at light cylinder length-
scales. Consequently, the observed X-ray emission
comes from the region near the light cylinder, where
the geometry of the �eld lines is determined by the
curvature drift instability excited at the same length-
scales [19]. The curvature drift instability e�ectively
recti�es the magnetic �eld lines (the curvature ra-
dius tends to in�nity). Therefore, in the synchrotron
emission generation region the �eld lines are practi-
cally straight and parallel to each other, and one can
assume that electrons with ψ ≈ ψ0 e�ciently emit
in the observer's direction.
The synchrotron emission �ux of the set of elec-
trons in this case is given by (see [4]):
Fε ∝
∫
f‖(p‖)Bψ0
ε
εm
∞∫
ε/εm
K5/3(z)dz
dp‖. (8)
Here f‖(p‖) is the distribution function of the res-
onant electrons by their parallel momenta, εm ≈
5 · 10−12Bψγ2 keV is a photon energy of maximum
of the synchrotron spectrum of a single electron and
K5/3(z) is the Macdonald function.
In order to �nd the synchrotron emission spec-
trum, one needs to know the behaviour of the dis-
tribution function, f‖(p‖). For solving this problem,
we consider the equation governing the evolution of
f‖(p‖) [4]:
∂f‖
∂t
=
∂
∂p‖
(
αs
m2c2π1/2
p2⊥0
f‖
)
. (9)
Considering the quasi-stationary case from Eq. (9),
we can �nd the redistributed distribution function
of the resonant particles by their parallel momenta:
f‖ ∝
1
p
1/2
‖ |Ek|
. (10)
On the other hand, the cyclotron noise is described
by the equation
∂|Ek|2
∂t
= 2Γc|Ek|2, (11)
where
Γc =
π2e2
k‖
f‖(pr) (12)
is the growth rate of the instability, and from the res-
onance condition (2) it follows that k‖ ≈ ωB/cδγr.
Combining Eqs. (9) and (11) it is easy to �nd that
[4]:
|Ek|2 ∝ p3−2n
‖ , (13)
here n denotes the index of the initial distribution
function of the resonant electrons (f‖0
∝ p−n
‖ ). From
Eqs. (10) and (13) it follows that f‖(p‖) ∝ pn−2
‖ . As
the emitting particles in our case are the primary
beam electrons, nothing can be told about their ini-
tial distribution. We only know the scenario of cre-
ation of the primary beam electrons [8, 3] which are
extracted from the pulsar's surface via the electric
�eld induced by the star's rotation. To our knowl-
edge there is no convincing theory that would pre-
dict the initial form of the distribution function of
the beam electrons, which must be drastically de-
pendent on the neutron star's surface properties and
temperature.
The frequency of the original waves, excited dur-
ing the cyclotron resonance can be estimated from
Eq. (2) as follows
ν ≈ 2π
ωB
δγb
∼ 1014Hz. (14)
As we can see, the frequency of the cyclotron modes
comes in the same domain as the measured optical
emission of XDINSs with the certi�ed optical coun-
terparts. Their spectra mostly follow the Rayleigh-
Jeans tail Fν ∝ ν2. On the other hand, the spec-
tral distribution of the cyclotron modes is given by
expression (13) and combining this equation with
Eq. (14) we �nd
Fν ∝ |Ek|2 ∝ ν2n−3. (15)
From Eq. (15) it follows that when n = 5/2 the spec-
tral distribution of the cyclotron modes is coincident
with the Rayleigh-Jeans function. And for the ini-
tial distribution of the beam electrons, as well as
for their �nal distribution, we �nd f‖0
∝ p
−5/2
‖ and
34
Advances in Astronomy and Space Physics N.Chkheidze, Iu. Babyk
f‖ ∝ p
1/2
‖ . We have used this distribution for the
beam electrons to de�ne the theoretical X-ray spec-
trum of RXJ1856.5-3754, which �tted the measured
one well [5]. Although for RXJ0420 the detection of
the optical counterpart has not yet been con�rmed,
based on similarities between XDINSs, we assume
that the initial distribution function of the beam
electrons must be the same for all XDINSs. Thus, in
place of integral (8) as for two other XDINSs inves-
tigated in previous works [4, 5], we get:
Fε ∝ ε0.3 exp
[
− (ε/εm)b
]
. (16)
To �nd the values of the parameters b and εm, one
should perform a spectral analysis by �tting the
model spectrum absorbed by cold interstellar mat-
ter with the observed X-ray spectrum of RXJ0420.
spectral analysis
To obtain the X-ray spectra of RXJ0420 with the
highest statistical quality, we used the EPIC-pn data
collected from three XMM-Newton observations be-
tween December 2002 and January 2003. The
archival XMM-Newton data were processed with the
Science Analysis Software (SAS) version 11.0.
The X-ray spectra were grouped in spectral bins
containing at least 30 photons. Subsequent spec-
tral analysis was performed with XSPEC V12.7.0.
The three EPIC-pn spectra �ts of RXJ0420 were
performed simultaneously, and spectral analysis was
limited to energies between 0.15 and 1.0 keV. Along
with the plasma emission model proposed in the
present work, we also examined the black-body
model to compare the �t results.
the black-body model
For the spectral analysis of EPIC-pn data for
RXJ0420 �rst we used an absorbed black-body
model. We allowed only the black-body normaliza-
tion to vary between the spectra of the individual ob-
servations, and �tted the temperature and amount of
interstellar matter as common parameters. We found
that the black-body model provided a reasonable �t,
but with NH ∼ 1018 cm−2, which is not perfect.
Thus, we set a lower limit for this parameter, which
did not alter the �t quality drastically. The resulting
χ2 = 1.47 for 97 degrees of freedom, and for the col-
umn density we got NH = (1.01±0.19)×1020 cm−2.
The best �t black-body temperature kT∞
bb = 43 eV
appears to be the lowest value derived for any of the
known XDINSs (see parameters in Table 1).
the synchrotron emission model
The plasma emission model proposed in the
present paper was recently applied to explain the
X-ray spectra of RXJ1856.5-3754 and RBS1774, re-
vealing good �t quality in both cases [4, 5]. We per-
formed �tting of the model spectrum Eq. (16) ab-
sorbed by cold interstellar matter with the EPIC-pn
spectra of RXJ0420. The best-�t results were b =
1.27 and εm = 0.1keV, corresponding to χ2 = 1.51
for 96 degrees of freedom. The column density NH ,
εm and b were treated as free parameters common to
all three spectra. Only normalization was allowed to
vary freely for di�erent spectra independently, as was
done in previous cases when the black-body model
was applied. The �t results are listed in Table 1.
discussion
The spectral analysis of the pulse phase-averaged
X-ray spectra of RXJ0420 shows that the quality of
the �ts in the cases of both models (black-body and
plasma emission models) is not very good. When
looking at Fig. 1, one might consider the residuals
around 0.3 keV as an absorption feature. This fea-
ture, described as a broad (σ = 70 eV) Gaussian ab-
sorption line, was noted and discussed by [9]. We
added the absorption line at ∼ 0.3 keV to both mod-
els considered in the present work and re-�t the data.
The �t quality improved in both cases, provided an
absorption edge model was used. The best-�tting
energy of the edge is Eedge ≈ 0.3 keV, and the op-
tical depth τedge ≈ 0.7 (see Table 1). The resulting
value of χ2 reduces to 1.1 for both models.
The nature of the spectral features discovered
in X-ray spectra of XDINSs is not fully clari�ed
as of yet. According to the thermal emission sce-
narios, the most likely interpretation of the absorp-
tion lines is that they appear as a result of proton
cyclotron resonance. The proton cyclotron absorp-
tion line at ∼ 0.3 keV implies the magnetic �eld of
Bcyc = 6.6 × 1013G, which di�ers from the value of
the dipolar magnetic �eld inferred from the timing
measurements Bdip = 1.0× 1013G [10].
We suppose that existence of the absorption fea-
ture in X-ray spectra of RXJ0420 might be caused by
wave damping at photon energies ∼ 0.3 keV, which
takes place near the light cylinder. During the far-
ther motion in the pulsar magnetosphere, the X-ray
emission might come in the cyclotron damping range.
If we assume that damping happens on the left
slope of the distribution function of primary beam
electrons (see Fig. 1 from [1]), the photon energy
of damped waves will be ε0 = (h/2π)2ωB/γbψ
2 '
0.3 keV [4]. Taking into account the shape of the
distribution function of beam electrons, we interpret
the large residuals around ∼ 0.3 keV as an absorption
edge.
Despite the fact that �t quality considerably im-
proves when including the absorption edge at 0.3 keV
for both emission models, the physical interpretation
of this feature is still uncertain. It might be caused
by calibration uncertainties. A feature of possibly
similar origin was detected in EPIC-pn spectra of the
much brighter prototypical object RXJ1856.4-3754
and classi�ed as a remaining calibration problem by
[10]. Thus, we agree that more data are necessary
35
Advances in Astronomy and Space Physics N.Chkheidze, Iu. Babyk
to de�nitely prove or disprove the existence of this
feature.
According to the �t results (see Table 1) the spec-
tral analysis of the measured EPIC-pn X-ray spectra
of RXJ0420 does not seem to be enough to distin-
guish between the black-body and the plasma emis-
sion models. In contrast to the thermal radiation
models, which appear to be somehow arti�cial, our
scenario is based on a self-consistent theory. Ac-
cording to works [21] and [22] due to the cascade
processes of a pair creation the pulsar's magneto-
sphere is �lled with electron-positron plasma with
the anisotropic one-dimensional distribution func-
tion. The beam particles undergo a drift perpen-
dicular to the magnetic �eld due to the curvature
of the �eld lines. Both of these factors (the one-
dimensionality of the distribution function and the
drift of particles) might cause the generation of eigen
modes in the electron-positron plasma, if the condi-
tion of cyclotron resonance is ful�lled. The generated
waves interact with the resonant electrons via the
QLD, which leads to the di�usion of particles along
and across the magnetic �eld lines, and inevitably
causes creation of pitch angles by resonant particles.
Therefore, the resonant electrons start to radiate in
the synchrotron regime.
The estimations show that for the beam electrons
with the average Lorentz-factor γb ∼ 107, the syn-
chrotron radiation comes in the same domain as the
measured X-ray spectrum of RXJ0420. Di�erently
from the standard theory of the synchrotron emis-
sion [7], which only provides the power-law spec-
trum, our approach gives the possibility to obtain
di�erent spectral energy distributions. In the stan-
dard theory of the synchrotron emission, it is sup-
posed that the observed radiation is collected from
a large spacial region in various parts of which, the
magnetic �eld is oriented randomly. Thus, it is sup-
posed that along the line of sight of an observer the
magnetic �eld directions are chaotic. In our case the
emission comes from the region of the pulsar mag-
netosphere where the magnetic �eld lines are prac-
tically straight and parallel to one another. And in
contrast to standard approach, we take into account
the mechanism of creation of the pitch angles, which
inevitably restricts their possible values.
acknowledgement
The authors are grateful to Prof. George Macha-
beli for valuable discussions. The HEASARC online
data archive at NASA/GSFC has been used exten-
sively in this research. This research was supported
by the Shota Rustaveli National Science Foundation
grant (12/31).
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Advances in Astronomy and Space Physics N.Chkheidze, Iu. Babyk
Table 1: Model-Fit spectral parameters of RXJ0420.0-5022 for combined �ts to the EPIC-pn spectra obtained from
individual observations in the energy interval 0.15− 1.0 keV.
Model NH εm b kT∞
bb Eedge τedge χ2(d.o.f.)
(1020 cm−2) (keV) (eV) (keV)
plasma 1.00+0.28
−0.28 0.10± 0.04 1.27± 0.31 1.51(96)
plasma*edge 1.00+0.37
−0.37 0.10± 0.05 1.27± 0.42 0.30+0.01
−0.01 0.68+0.30
−0.30 1.10(94)
bbody 1.01+0.19
−0.19 43.3± 1.2 1.47(97)
bbody*edge 1.01+0.33
−0.33 46.3± 1.8 0.31+0.02
−0.02 0.69+0.21
−0.21 1.10(95)
Energy (keV)
n
o
rm
a
liz
e
d
c
o
u
n
ts
s
k
e
V
-1
-1
n
o
rm
a
liz
e
d
c
o
u
n
ts
s
k
e
V
-1
-1
Energy (keV)
Energy (keV)
n
o
rm
a
liz
e
d
c
o
u
n
ts
s
k
e
V
-1
-1
n
o
rm
a
liz
e
d
c
o
u
n
ts
s
k
e
V
-1
-1
Energy (keV)
Fig. 1: Combined EPIC-pn spectra of RXJ0420.0-5022. Top left: The absorbed black-body model �t. Top right:
The black-body model �t including an absorption edge at ∼ 0.3 keV. Bottom left: The synchrotron emission model �t
absorbed by cold interstellar matter. Bottom right: Model �t including absorption edge at 0.3 keV.
37
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