Issue |
A&A
Volume 515, June 2010
|
|
---|---|---|
Article Number | A20 | |
Number of page(s) | 8 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361/200913615 | |
Published online | 02 June 2010 |
Multiband emission from pulsar wind nebulae: a possible injection spectrum
J. Fang - L. Zhang
Department of Physics, Yunnan University, Kunming, PR China
Received 6 November 2009 / Accepted 11 February 2010
Abstract
Aims. Recent research shows that particles with a spectrum
of a relativistic Maxwellian plus a high-energy tail can be accelerated
by relativistic collisionless shocks. We investigate the possibility of
the high-energy particles with this new spectrum injected into pulsar
wind nebulae (PWNe) from the terminate shock based on the study of
multiwavelength emission from PWNe.
Methods. The dynamics of a supernova remnant (SNR) and multiband
nonthermal emission from the PWN inside the remnant are investigated
using a dynamical model with electrons/positrons injected with the new
spectrum. In this model, the dynamical and radiative evolution of a
pulsar wind nebula in a nonradiative supernova remnant can be described
self-consistently.
Results. This model is applied to the three composite SNRs,
G0.9+0.1, MSH 15-52, G338.3-0.0, and the multiband observed emission
from the three PWNe is reproduced.
Conclusions. Our studies on the three remnants provide evidence
of a new spectrum of the particles, which are accelerated by the
terminate shock and injected into a PWN.
Key words: gamma rays: ISM - ISM: individual objects: G0.9+0.1 - ISM: individual objects: MSH 15-52 - ISM: individual objects: G338.3-0.0 - acceleration of praticles - radiation mechanisms: non-thermal
1 Introduction
PWNe are prominent sites of high-energy emission in the Galaxy that
are powered by the pulsars associated with them. A pulsar inside a
PWN loses its rotational energy through a pulsar wind composed of
magnetic flux and high-energy particles
(Goldreich & Julian 1969; Gelfand et al. 2007,2009). The ultra-relativistic wind flows
relativistically into a nonrelativistic ejecta of the ambient
supernova remnant (SNR), which results in the PWN and a termination
shock (TS), where the plasma is decelerated and heated
(Volpi et al. 2008; Reynolds & Chevalier 1984). High-energy particles are injected into the
nebula from the TS, and multiband nonthermal photons with energies
ranging from radio, X-ray, to -ray bands are emitted during
the evolution of the PWN.
Usually, multiwavelength observational results of a PWN cannot be
reproduced well by the radiation of particles injected with a single
power-law spectrum, and a broken power-law must be employed to
explain the observations better (e.g., Atoyan & Aharonian 1996; Zhang et al. 2008; Aharonian et al. 2005a).
However, the physics behind the broken power law is unclear. For a
typical PWN, the wind from the pulsar can flow relativistically with
a Lorentz factor of 106. The resulting TS can accelerate
particles to relativistic energy. On the other hand, based on the
long-term, two-dimensional particle-in-cell simulations,
Spitkovsky (2008) finds that the particle spectrum downstream of a
relativistic shock consists of two components: a relativistic
Maxwellian and a high-energy power-law tail with an index of
.
Based on this finding and with the assumption that the
high-energy particles in a PWN are injected with a spectrum of a
relativistic Maxellian plus a power-law high-energy tail, we
investigate the multiwavelength emission from PWNe to test the
possibility of particles with the new spectrum injected into the
PWNe.
The dynamical evolution of the PWN is calculated basically according
to the model in Gelfand et al. (2009), which can self-consistently
describe the dynamical and radiative evolution of a pulsar wind
nebula in a nonradiative supernova remnant. Different from
Gelfand et al. (2009), in which a single power-law injection spectrum for
the electrons/positrons is employed to discuss the radiative
properties during different phase of the PWN, we argue in this paper
that the high-energy particles are injected with the new spectrum of
a relativistic Maxellian plus a power-law, high-energy tail during
the evolution in this paper, and a kinetic equation is used to
obtain the energy distribution of the particles. We apply the model
to the PWNe in the composite SNRs, G0.9+0.1, MSH 15-52, and
G338.3-0.0, which have been observed in radio, X-rays and very
high-energy (VHE) -rays.
G0.9+0.1 has a 2' PWN inside a 8' shell in the radio band
(Helfand & Becker 1987). The PWN is powered by an energetic pulsar PSR
J1747-2809, which has recently been discovered in G0.9+0.1 with the
NRAO Green Bank Telescope at 2 GHz (Camilo et al. 2009). A jet-like
feature of the nebula was revealed in the high-resolution
observation with Chandra (Gaensler et al. 2001). The observation in
the TeV band with HESS indicates that the PWN is a weak emitter in
VHE -rays (Aharonian et al. 2005a).
MSH 15-52 is a complex SNR with a ragged shell in the radio
observations (Caswell et al. 1981). An elongated PWN powered by an
energetic pulsar was found in the remnant in the X-ray observations
with ROSAT (Trussoni et al. 1996), BeppoSAX (Mineo et al. 2001) and Chandra
(Gaensler et al. 2002). The remnant has also been well detected in VHE
-rays with HESS (Aharonian et al. 2005b) and CANGAROO
(Nakamori et al. 2008), and the significant VHE
-rays are
identified as produced by the PWN.
A VHE -ray source HESS J1640-465 was discovered by HESS in
the survey of the inner Galaxy (Aharonian et al. 2006), and it is spatially
coincident with the composite SNR G338.3-0.0. An extended X-ray
source was found to be located at the center of the VHE
-ray
source with XMM-Newton (Funk et al. 2007). Lemiere et al. (2009) presents
the high resolution X-ray observations on the PWN, and a point-like
source as a putative pulsar appears in the X-ray observations.
In this paper, we investigate the possibility of particles with the new spectrum injected in PWNe based on applications with the spectrum to the three composite SNRs. In Sect. 2, the model is simply described, and the results from the applications to the three SNRs G0.9+0.1, MSH 15-52, and G338.3-0.0, are presented. The main conclusions and discussion are given in Sect. 3.
2 Model and results
A PWN is powered by the its pulsar which dissipates the rotational
energy into the nebula. The spin-down luminosity of a neutron star
with a rotation period of P evolves with time as
(e.g., Slane 2008; Gaensler & Slane 2006)
where


Magnetic field and high-energy particles are injected at the TS
located where the ram pressure of the unshocked wind is equal to
that of the PWN. In this paper, we assume the spin-down power is
distributed between electrons and positions (
)
and magnetic fields (
(e.g., Gelfand et al. 2009). Gelfand et al. (2009),
use a single power-law injection spectrum for the
electrons/positrons to discuss the radiative properties during
different phases of the PWN evolution. However, a broken power-law
spectrum is usually needed to reproduce the nonthermal emission of a
PWN with multiband observations
(e.g., Atoyan & Aharonian 1996; Slane et al. 2008; Zhang et al. 2008; Venter & de Jager 2006). Recently, based on the
long-term, two-dimensional particle-in-cell simulations,
Spitkovsky (2008) has found that the particle spectrum downstream of
a relativistic shock can be fitted as a Maxwellian plus a power-law
tail. The form is
,
where
is the Lorentz factor
of the particles,
is close to
,
is the Lorentz factor of the upstream flow, C2=0 for
,
is about seven times
of
(Spitkovsky 2008). In this paper, we investigate
the possibility of particles with this spectrum injected in PWNe by
multiwavelength studies.
We argue that high-energy particles injected in a PWN are
accelerated by the TS, for which the upstream pulsar wind typically
can have a Lorentz factor 106. Therefore, we assume the
spectrum of the high-energy particles injected in the PWN has the
form
where,








Assuming the particles are homogeneously distributed in space in the PWN, and the distribution in the emission region is given by
where

The dynamics of the PWN in the supernova shell is calculated
basically following the model presented in Gelfand et al. (2009). The
model assumes that the progenitor supernova ejects material with
mass
and energy
into the ambient matter
with a constant density
.
Assuming the PWN has no
influence on the dynamics of the forward shock and the reverse
shock, the velocity and the radius of the forward shock and the
reverse shock of the surrounding SNR are calculated with the
equations in Truelove & McKee (1999). The pulsar dissipates energy into the
PWN, which sweeps up the supernova ejecta into a thin shell
surrounding the nebula, and new particles are injected into the PWN
at each time step.
We now apply the model to investigate the three composite SNRs,
G0.9+0.1, MSH 15-52, and G338.3-0.0. First, if the distance, the
age, and the radii of the SNR shell and the PWN are known, the
parameters such as the supernova energy (
), the ejecta
mass (
), the ambient density (
), and the
initial spin-down energy (
)
can be constrained by making
the results consistent with the known values. In our calculation, a
typical spin-down time scale (
)
is set to 500 yr for
the three remnants, and
is also constrained by the
current spin-down power of the pulsar if it is available. Finally,
to obtain a consistent nonthermal emmission with the multiband
observational fluxes for the SNR, the other parameters can be
constrained. Uncertainties for some parameters still exist owing to
both their insensitivities in the final results and the
uncertainties of the key properties of the system, such as the
distance, the age, and the properties of the pulsar.
2.1 G0.9+0.1
Table 1: Input parameters for the three PWNe.
The composite SNR G0.9+0.1 consists of a bright 2' PWN hosted by a
8' shell in the radio band (Helfand & Becker 1987; La Rosa et al. 2000). A recent
high-resolution radio study of the PWN indicates that the radio
emission of the nebula has a spectral index of
,
and
the fluxes are 1.35, 1.45, and 1.75 Jy for the wavelengths 3.6, 6,
and 20 cm, respectively (Dubner et al. 2008). Furthermore, an energetic
pulsar PSR J1747-2809 with a period of 52 ms has recently been
discovered in G0.9+0.1 with the NRAO Green Bank Telescope at 2 GHz
(Camilo et al. 2009).
The PWN in G0.9+0.1 was detected in X-rays with BeppoSAX, and the
result shows that the X-ray emission from the source has a power-law
spectrum with a photon index of
(Sidoli et al. 2000; Mereghetti et al. 1998).
High-resolution observation with Chandra indicates that the nebula
is axisymmetric with a jet-like feature, which is evidence of a
torus of emission in the pulsar's equatorial plane and a jet
directed along the pulsar spin axis (Gaensler et al. 2001).
Proquet et al. (2003) studied G0.9+0.1 using observations by XMM-Newton. The X-ray spectrum softens with distance from the core,
and the spectrum in the energy range 2-10 keV has a power law
form with a photon index of
1.9.
Very high-energy (VHE) emission from G0.9+0.1 has been detected with
HESS (Aharonian et al. 2005a). The photon flux above 0.2 TeV is
cm-2 s-1, and the spectrum can be
fitted with a power law with a photon index
.
The source
is a weak TeV emitter, and the VHE
-rays appear to originate
in the core rather than the shell (Aharonian et al. 2005a).
The dynamical and radiative properties of the composite SNR G0.9+0.1
are investigated with the parameters in Table 1 for this
source. Although the pulsar PSR J1747-2809 has a characteristic age
of 5.3 kyr, Camilo et al. (2009) argue that G0.9+0.1 has a young age of
no more than 2-3 kyr either from PWN evolution models of
Blondin et al. (2001) for the observed ratio
or from the PWN energetics (Dubner et al. 2008). The distance of
the pulsar is likely in the range of 8 kpc to 16 kpc due to the
uncertainty of the electron density model toward the distant inner
Galactic regions (Dubner et al. 2008). We assume the distance is 8.5 kpc in the calculation, then the radii of the PWN and the shell are
2.55 pc and 10.2 pc, respectively. Moreover, with
erg and
,
an age of 1900 yr and
a relatively low density
cm-3 are needed to
reproduce the structure of the system correctly, i.e., the radius of
the shell and the ratio
.
A pulsar's
velocity of 120 km s-1 similar to the Crab pulsar (Kaplan et al. 2008)
is
used to illustrate the evolution of the PWN, which has no influence
on the final results for G0.9+0.1 since it is a young remnant, and
now the pulsar is safely inside the nebula. With these parameters,
the resulting radii of the PWN and the SNR shell are 2.6 and
10.2 pc, respectively, consistent with the observational results
(upper
panel Fig. 1). The influence of the ejecta mass
on the radius of the nebula is shown in the upper panel of
Fig. 1. With a lower
,
both the nebula and the
SNR shell expand more quickly, and the nebula collides with the
reverse shock at a later time. As a result, the magnetic field in
the PWN is weaker for a lower
because of the bigger
volume of the nebula (lower panel Fig. 1).
![]() |
Figure 1:
Upper panel: radius of PWN (
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![]() |
Figure 2: Left panels: particle spectra of electrons and positrons at different times during the evolution of the PWN. Right panels: the resulting spectral energy distribution at different ages with the other parameters listed in Table.1. |
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The dynamical properties of the SNR during the evolution is similar
to those for the Crab remnant in Gelfand et al. (2009) although the new
spectrum of the particles is used in this paper. Initially, the
pressure of the PWN is much greater than for the surrounding
supernova ejecta, so the PWN expands adiabatically into the cold
supernova ejecta. The ejecta surrounding the PWN is swept up to a
thin shell, which is decelerated by ram pressure since its velocity
is higher than the local sound speed (Gelfand et al. 2007). The mass of
the PWN
increases continuously since the shell expands
faster than the ambient ejecta. This expansion phase ends when the
PWN collides with the reverse shock of the SNR. After the collision,
the pressure of the nebula
is much less than that of
the supernova ejecta around the nebula
.
The velocity of the PWN decreases a lot, and finally the PWN is
compressed when the shell moves inward. During this process of
compression, the magnetic field strength in the nebula increases
significantly (lower panel in Fig. 1), and, as a result,
the synchrotron luminosity has a rapid rise (lower right panel in
Fig. 2). Furthermore, the radius of the PWN decreases
significantly, and the PWN will expand again when the pressure in it
eventually becomes greater than that of the surrounding ejecta. The
nebula enjoys a series of contractions and re-expansions until the
SNR enters the radiative phase of its evolution. The pulsar with a
velocity moving in space will leave the PWN if the velocity is high
enough in the compression process, and it can re-enter the nebula
when the nebula expands again.
Particles with a spectrum of a Maxwellian plus a power-law tail
(
)
are injected in the PWN when the pulsar is
inside it. The particles lose energy through synchrotron radiation,
inverse Compton scattering, and adiabatic loss. Nonthermal emission
from the PWN from the radio to X-ray band is produced via
synchrotron radiation, whereas
-rays are produced through
inverse Compton scattering on the seed photons, i.e., cosmic
microwave background (CMB), infrared (IR), and optical (opt)
photons. For the soft seed photons, the energy density of the
infrared radiation is 0.23 eV cm-3 as used for the GALPROP code
(Porter et al. 2006; Strong et al. 2000) and a density of 5.7 eV cm-3 for the
optical component, which is 50% lower than the value used in
GALPROP, are used in Aharonian et al. (2005a) to discuss the origins of the
VHE
-rays. We find densities of 0.5 eV cm-3 for the
infrared component (
eV), and 20 eV cm-3 for the optical soft photons (
eV) can
reproduce the observed spectrum in the VHE
-ray band, so
these densities are used in this paper. The resulting energy
distribution of the particles in the PWN and the multiwavelength,
nonthermal emission during the evolution are presented in
Fig. 2. The particles with energies below
are
mainly from the high-energy particles with energies >
experienced energy losses, and the energy distributions in the range
<
at different ages in the evolution all show a power-law
form with an index of
1 (
). On the other
hand, the energy distribution in the higher-energy band (>
)
becomes steady between 1000 yr and 20 000 yr, and the
distribution can also be represented as a power law but with an
index
2.5.
The expansion and compression of the PWN cause the magnetic field
strength in the nebula
to decrease and increase,
respectively. The synchrotron emissivity diminishes before 10 000 yr
as the PWN expands into the cold supernova ejecta, when the magnetic
field strength in the nebula decreases gradually. However,
synchrotron radiation can gain significance again when the PWN is
compressed, because the magnetic field strength rises greatly during
the compression. In this case, the energy of the particles in the
nebula can show a rise caused by the adiabatic compression, then the
emissivity of inverse Compton scattering can also show a rise (see
the emission in Fig. 2 for 30 000 yr). During the whole
evolution process, the PWN is an important emitter of the GeV
-rays, although the emission from the radio to the X-ray
band is insignificant sometimes.
![]() |
Figure 3: The energy contained in the PWN at different ages of the system with the parameters same as in Fig. 2. |
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Figure 3 shows the evolution of the energy contained in the
PWN (
)
during the evolution of the system, and the
spin-down power of the pulsar and the adiabatic loss rate of the
PWN, which can be obtained with
,
are indicated in Fig. 4. Here
and
are the velocity and radius of the PWN. At
first, the energy of PWN increases continuously since the pulsar
injects the spin-down power into the nebula, and this stage ends
after
1000 yr (Fig. 3) when the adiabatic loss rate is
considerably more than the spin-down power of the pulsar
(Fig. 4). After this phase, the energy of the nebula
decreases or increases because of the competition between the
spin-down power of the pulsar adiabatic loss.
![]() |
Figure 4: The spin-down power of the pulsar (solid line) and the adiabatic loss rate of the PWN (dotted line) during the evolution of the system. The others are the same as in Fig. 3. |
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With the parameters in Table 1, the dynamical structure and
the multiband radiative properties of G0.9+0.1 are reproduced at
1900 yr. At this age, the magnetic field strength in the PWN is 8.1 G, and the current spin-down power of the pulsar is
erg s-1, which is still consistent with the
measured one
erg s-1 (Camilo et al. 2009)
thanks to the uncertainty of the moment of inertia; moreover, the
observational radii of the nebula and the SNR shell are reproduced
in this scenario. The resulting multiband emission of the PWN from
the model is shown in the lower panel in Fig. 5. The
radio and the X-ray observations can be well explained as
synchrotron radiation of the particles injected in the PWN. The VHE
-rays from the nebula are mainly produced by inverse Compton
scattering on the optical light and the cosmic microwave background.
With a higher ejecta mass (
), the radius of the PWN is
smaller due to the deceleration of the ejecta matter before the
collision between the reverse shock and the nebula. As a result, the
resulting synchrotron radiation is stronger for a bigger
(the upper panel in Fig. 5). Moreover, the influence
of the break energy
on the resulting multiband
nonthermal emission is indicated in Fig. 6 for
,
,
and
MeV. With a higher
,
the resulting fluxes
in X-rays and
-rays are higher. The multiband observational
results in the radio, X-rays, and VHE
-rays can be
reproduced with
.
In such a case, the
Lorentz factor of the pulsar wind upstream of the TS can be
estimated as
.
![]() |
Figure 5:
Upper panel: the multiband spectral
distribution of the nonthermal emission for
|
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![]() |
Figure 6:
The resulting spectral energy
distributions for
|
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2.2 MSH 15-52
MSH 15-52 (G320.4-1.2) is a complex object located at a distance of
kpc based on the HI absorption measurement, consistent
with the value of
kpc from the pulsar dispersion measure
(Taylor & Cordes 1993). It is a rough circular SNR with a diameter of
30' from the radio observations (Caswell et al. 1981), and a PWN
powered by an energetic pulsar PSR B1509-58 (e.g., Gaensler et al. 2002) was
discovered in the remnant. Livingstone et al. (2005) presented an updated
timing solution for the young energetic pulsar PSR B1509-58 based on
the 21.3 yr of radio data and the 7.6 yr of X-ray timing data. The
results show that the pulsar has a period of about 150 ms with a
braking index of
,
and a characteristic age of
1700 yr. In the radio band, the source appears as a
shell-like SNR with bright spots in the NW and SE region
(Mineo et al. 2001), and the NW region coincides with the IR and optical
nebula RSW 89 (Seward et al. 1982). The PWN around the pulsar is
comparatively faint in radio bands, and Gaensler et al. (2002) estimated a
flux density of
Jy at both 0.8 and 1.4 GHz using the data of
Whiteoak & Green (1996) and Gaensler et al. (1999) for the PWN. In the X-ray band,
diffuse emission is detected from the shell-like remnant with a
bright spot coincident with the NW zone. The PWN has an elongated
structure roughly centered on the pulsar with two arms extending
several arcminutes along the NW and SE directions in the X-ray
observations with ROSAT (Trussoni et al. 1996) and Chandra
(Gaensler et al. 2002). The hard X-ray spectrum for the PWN was measured by
BeppoSAX, and the power-law fit of the unpulsed high-energy flux
gave a photon index
and a flux of
erg cm-2 s-1 in the 20-200 keV energy range
(Mineo et al. 2001). At VHE
-ray energies, the SNR MSH 15-52 has
been observed with the HESS (Aharonian et al. 2005b) and CANGAROO
(Nakamori et al. 2008). The TeV
-rays are from an elliptically
shaped region, and the jet extends more prominently to the
south/southeast. This morphology coincides with the diffuse PWN as
observed in the X-ray bands (Aharonian et al. 2005b). The overall energy
spectrum can be fitted by a power law with photon index
in the energy
range 280 GeV to 40 TeV in the HESS result, and a compatible result
has been obtained with the CANGAROO telescope.
The age of the SNR MSH 15-52 has been estimated as 6-20 kyr with
the standard parameters for the interstellar medium and for the
supernova explosion (Seward et al. 1983), which is significantly older
than the characteristic age (1700 yr) of pulsar. However, it is very
likely that the system is young with an age of 1700 yr since
the SNR has expanded rapidly into a low-density cavity
(Seward et al. 1983), which is supported by the observation of HI
emission in this region (Dubner et al. 2002).
The resulting multiband nonthermal emission from MSH 15-52 is shown
in Fig. 7, and the parameters are listed in
Table1. With an initial spin-down power of
erg s-1 and
yr, the spin-down
power of the pulsar is
erg s-1 at an age of
1900 yr, consistent with the measured one,
erg s-1 (Livingstone et al. 2005). An energy density of 1.5 eV cm-3for the optical soft photons is used in the calculation, which is
consistent with the value from the GALPROP code
(Porter et al. 2006; Strong et al. 2000). For the infrared component, we find a
density of 1.5 eV cm-3 is needed to reproduce the observation
in VHE
-rays, so this value is employed in the calculation.
With the parameters in Table1 for MSH 15-52, the radii of
the PWN and the SNR shell are 3.6 pc and 14.8 pc, respectively, and
the resulting magnetic field strength inside the PWN is 19.3
G
now. The observed emission from the radio (Gaensler et al. 2002) to the
X-ray bands detected with BeppoSAX (Mineo et al. 2001) can be explained
as the synchrotron radiation of the high-energy electrons/positrons
injected in the nebula; moreover, the resulting emission from 100
MeV to 10 TeV is mainly produced via inverse Compton scattering off
the soft infrared photons, and the HESS flux points can be
reproduced fully.
![]() |
Figure 7:
Comparison of the resulting photon emission
of synchrotron (dashed line), inverse Compton scattering on the CMB
(dotted line), IR(dash-dotted line), starlight (short-dashed line),
and synchrotron photons (close-dotted line) with the radio
(Gaensler et al. 2002), X-ray (Mineo et al. 2001), and VHE |
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2.3 G338.3-0.0
HESS J1640-465 was discovered in the survey of the inner Galaxy with
HESS as a center-filled VHE -ray source with a differential
energy spectrum fitted as a power law with an index of
above 0.2 TeV (Aharonian et al. 2006). This source is spatially coincident
with the SNR G338.3-0.0, which has a broken shell with a diameter of
8' indicated in the 843 MHz radio survey using the Molonglo
Observatory Synthesis Telescope (Whiteoak & Green 1996). A highly absorbed
source inside the shell was indicated in the X-ray observations with
ASCA (Sugizaki et al. 2001) and Swift (Landi et al. 2006). Extended X-ray
emission centered on the VHE
-rays was detected with a
dedicated XMM-Newton observation in 2006 (Funk et al. 2007).
Recently, Lemiere et al. (2009) present the high-resolution X-ray
observations with Chandra on the extended source. The observed
morphology shows a PWN and a point source presented as a potential
pulsar. The spectrum of the putative pulsar and the PWN can be
fitted with a power law with indices of 1.1 and 2.5, respectively
(Lemiere et al. 2009). They argue that the pulsar's spin power is
erg s-1 based on the X-ray luminosities of
the putative pulsar and nebula between 2 to 10 keV. The distance of
the source is less certain, and it can be from 8 kpc to 13 kpc based
on the H I absorption features observed along the line of sight
(Lemiere et al. 2009).
Assuming the SNR has a distance of 10 kpc, the radius of the radio
shell is 12 pc (4') (Whiteoak & Green 1996), and that of the PWN is
3.5 pc (1.2') in the X-rays according to the high-resolution
observations with Chandra (Lemiere et al. 2009). Firstly, G338.3-0.0 is
assumed to be a young SNR expanding into a tenuous medium with a
density of 0.1 cm-3. The age of the remnant should not be too
young since the PWN must contain enough energetic particles to
produce the observational VHE
-rays through inverse Compton
scattering. As a result, the supernova explosion energy
and the initial spin-down power of the pulsar are chosen to be
1051 erg and 1040 erg s-1, respectively; moreover,
E
is constrained to 500 TeV to make the resulting
emission consist with the observations in X-rays, and relatively
high densities are needed to reproduce the VHE
-ray fluxes
detected with HESS, i.e., 5.0 eV cm-3 and 25.0 eV cm-3for the infrared and the optical soft photons, respectively. At an
age of 4500 yr, with the other parameters listed in Table1
for the SNR G338.3-0.0 (CASE 1), the radii of the shell, the reverse
shock and the PWN are 11.1, 8.8 and 6.9 pc, respectively, and the
magnetic field strength in the nebula is 3.7
G. In such a case,
the pulsar is energetic with a spin-down power of
erg s-1 now. Furthermore, the observed spectra in the X-rays
with Chandra (Lemiere et al. 2009) and in the VHE
-rays with
HESS (Aharonian et al. 2006) can be reproduced (Fig. 8).
Inverse Compton scattering on the optical light dominates the
resulting emission at 0.1 TeV, whereas the emission above 1 TeV is
mainly produced via inverse Compton scattering off the IR photons.
![]() |
Figure 8:
Comparison of the resulting photon
emission of synchrotron (dashed line), inverse Compton scattering on
the CMB (dotted line), IR(dash-dotted line), starlight (short-dashed
line), and synchrotron photons (close-dotted line) with the X-ray
(Lemiere et al. 2009), and VHE |
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![]() |
Figure 9: The resulting spectral energy distribution with the parameters listed in Table1 for the CASE 2 of G338.3-0.0 (CASE 2). Others are the same as in Fig. 8. |
Open with DEXTER |
On the other hand, we investigate the dynamical and radiative
properties of G338.3-0.0 expanding into a medium with a density of
1 cm-3. With
erg, the radius of
the shell of the SNR in radio means that the age of the remnant is
8000 yr. With an initial spin-down power of
erg s-1 and other appropriate parameters
(see Table1 for G338.3-0.0 CASE 2), the current spin-down
power of the pulsar is
erg s-1, and the
resulting radius of the PWN is just 2.45 pc, which is even smaller
than the extension of the X-rays (
3.5 pc) assuming a distance
of 10 kpc (Lemiere et al. 2009). A smaller
,
and the maximum energy of the particles is set
to 500 TeV to reproduce the observational fluxes in the X-rays and
-rays. The resulting multiband nonthermal emission is
indicated in Fig. 9 with low densities of 1.0 eV cm-3 for the infrared and 6.0 eV cm-3 for the optical soft
photons. In this scenario, the PWN has been compressed by the
reverse shock, and the resulting flux with energies below 1 eV is
about two orders of magnitude higher than in the CASE 1.
3 Discussion and conclusions
Motivated by the finding that the spectrum of the particles
downstream of a relativistic shock consists of two components: a
relativistic Maxwellian and a power-law, high-energy tail with an
index of
(Spitkovsky 2008), we investigate the
possibility of particles with this new spectrum injected into PWNe
from the TS based on the studies of multiband emission from PWNe.
Following the dynamical method proposed in Gelfand et al. (2009), we
studied the dynamical and multiband radiative properties of the
three composite SNRs G0.9+0.1, MSH 15-52, and G338.3-0.0. With
appropriate parameters, we find that a typical PWN is a strong
-ray emitter during its evolution although the nonthermal
radiation from the radio to the X-ray band is insignificant
sometimes. The multiband observations of the three PWNe in the
remnants can be reproduced with the new spectrum of the injected
particles. Therefore, our studies of the dynamical and
multiwavelength radiative properties of PWNe provide evidence that
high-energy electrons/positrons can be injected into a PWN with a
Maxwellian plus a power-law, high-energy tail from the TS of the
PWN.
In modeling the multiband nonthermal emission from a PWN detected in
the radio, X-ray, and -ray bands, particles injected with a
spectrum of a broken power law are widely used to reproduce the
observed multiwavelength emission (e.g., Zhang et al. 2008; Slane 2008; Venter & de Jager 2006).
Of course, for the three PWNe discussed in this paper, the multiband
observed spectra of them can also be explained if the particles are
injected with a broken power law. However, it is unclear why the
broken power-law spectrum is valid when using it to reproduce the
multiwavlength emission from a PWN. From our calculations, we have
found that the energy distribution of the electrons/positrons in the
nebula can be approximated as a broken power law with an index
1 in the lower energy band and an index of
2.5 in the
higher-energy part before the PWN undergos significant compression,
which is most likely the physical explanation of the broad use of a
broken power law in modeling the multiband nonthermal emission from
PWNe.
In this paper, high-energy electrons/positrons are injected into the
PWN from the TS, and the main energy of the nebula is contained in
these particles, which undergo radiative and adiabatic losses when
the nebula evolves in the host SNR. Our study indicates that, for a
typical PWN with the parameters similar as G0.9+0.1, the adiabatic
loss of the particles in the nebula is significant after an age of
1000 yr (see Figs. 3 and 4). Multiwaveband
nonthermal emission from a PWN has been investigated using a
simplified time-dependent injection model, in which high-energy
electrons/positrons are injected into the PWN
(e.g., Zhang et al. 2008; Slane 2008; Venter & de Jager 2006). The pulsar inside the PWN transfers
a part of its spin-down power to the particles with a spectrum of a
broken power law. In the simplified time-dependent injection model
in Zhang et al. (2008), synchrotron loss of the particles is taken
into account, whereas the adiabatic one is ignored. As a result,
either a relatively weaker initial spin-down power of the pulsar or
a lower efficiency of the power to the kinetic energy of the
accelerated electrons/positrons is employed in the model. Moreover,
in Zhang et al. (2008), an initial spin-down power of
erg s-1 for MSH 15-52 was used to investigate the multiband
emission from the PWN, which is a factor of 15 less than used in
this paper. Besides these reasons, another main one is the
relatively large spin-down time scale of
5000 yr, which is
in the paper, used by Zhang et al. (2008),
whereas in this paper it is adopted to be 500 yr. The energy
released by the pulsar is mainly determined by
,
and the value in this paper is not much greater
than in Zhang et al. (2008). Therefore, the multiband observed spectra
for MSH 15-52 can be reproduced within the two scenarios even the
initial spin-down power of the pulsar is significantly different.
We thank the referee, Dr. P. O. Slane, for his constructive comments. This work is partially supported by the Scientific Research Foundation of Graduate School of Yunnan University, the National Natural Science Foundation of China (NSFC 10778702, 10803005), a 973 Program (2009CB824800), and Yunnan Province under a grant 2009 OC.
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All Tables
Table 1: Input parameters for the three PWNe.
All Figures
![]() |
Figure 1:
Upper panel: radius of PWN (
|
Open with DEXTER | |
In the text |
![]() |
Figure 2: Left panels: particle spectra of electrons and positrons at different times during the evolution of the PWN. Right panels: the resulting spectral energy distribution at different ages with the other parameters listed in Table.1. |
Open with DEXTER | |
In the text |
![]() |
Figure 3: The energy contained in the PWN at different ages of the system with the parameters same as in Fig. 2. |
Open with DEXTER | |
In the text |
![]() |
Figure 4: The spin-down power of the pulsar (solid line) and the adiabatic loss rate of the PWN (dotted line) during the evolution of the system. The others are the same as in Fig. 3. |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Upper panel: the multiband spectral
distribution of the nonthermal emission for
|
Open with DEXTER | |
In the text |
![]() |
Figure 6:
The resulting spectral energy
distributions for
|
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Comparison of the resulting photon emission
of synchrotron (dashed line), inverse Compton scattering on the CMB
(dotted line), IR(dash-dotted line), starlight (short-dashed line),
and synchrotron photons (close-dotted line) with the radio
(Gaensler et al. 2002), X-ray (Mineo et al. 2001), and VHE |
Open with DEXTER | |
In the text |
![]() |
Figure 8:
Comparison of the resulting photon
emission of synchrotron (dashed line), inverse Compton scattering on
the CMB (dotted line), IR(dash-dotted line), starlight (short-dashed
line), and synchrotron photons (close-dotted line) with the X-ray
(Lemiere et al. 2009), and VHE |
Open with DEXTER | |
In the text |
![]() |
Figure 9: The resulting spectral energy distribution with the parameters listed in Table1 for the CASE 2 of G338.3-0.0 (CASE 2). Others are the same as in Fig. 8. |
Open with DEXTER | |
In the text |
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