We present a complete set of diagnostic tools aimed at reproducing synthetic
non-thermal (synchrotron and/or Inverse Compton, IC) emissivity, integrated
flux energy, polarization and spectral index simulated maps in comparison to
observations. The time dependent relativistic magnetohydrodynamic (RMHD)
equations are solved with a shock capturing code together with the evolution of
the maximum particles energy. Applications to Pulsar Wind Nebulae (PWNe) are
shown.Comment: 3 pages, 7 figures, proceeding of the conference "40 Years of Pulsars
  ", 12-17 August 2007, Montreal, Canada, submitted to AI

A. Cumming

C. Bassa

Delia Volpi

Elena Amato

Luca Del Zanna

Niccoló Bucciantini

V. M. Kaspi

Z. Wang

English

arXiv

Crossref

Simulated synchrotron and Inverse Compton emission from Pulsar Wind Nebulae

Volpi, Delia

Del Zanna, Luca

Amato, Elena

Bucciantini, Niccolo

DI-fusion

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Simulated synchrotron and Inverse Compton emission from
Pulsar Wind Nebulae
Delia Volpi∗, Luca Del Zanna∗, Elena Amato† and Niccoló Bucciantini∗∗
∗Dipartimento di Astronomia e Scienza dello Spazio-Largo Fermi 2-50125 Firenze-Italy
†INAF-Osservatorio Astrofisico di Arcetri-Largo Fermi 5-50125 Firenze-Italy
∗∗Astronomy Department-University of California at Berkeley-601 Campbell Hall-Berkeley-CA
94720-3411-USA
Abstract. We present a complete set of diagnostic tools aimed at reproducing synthetic non-thermal (synchrotron and/or
Inverse Compton, IC) emissivity, integrated flux energy, polarization and spectral index simulated maps in comparisonto
observations. The time dependent relativistic magnetohydrodynamic (RMHD) equations are solved with a shock capturing
code together with the evolution of the maximum particles energy. Applications to Pulsar Wind Nebulae (PWNe) are shown.
Keywords: Synchrotron radiation; Relativistic plasmas; Magnetohydrodynamic and fluid equation; Supernova remnants
PACS: 41.60.Ap; 52.27.Ny; 52.65.Kj; 98.38.Mz
Pulsar Wind Nebulae (e.g. Vela and Crab Nebula) are
a class of Supernova Remnants (SNR), which originates
from the interaction of the pulsar wind with the surround-
ing ejecta. They are characterized by non-thermal radia-
tion at all wavelengths, mostly synchrotron (from radio
to X-ray bands) and Inverse Compton (gamma-ray band),
due to the presence of high energy pairs embedded in a
strong magnetic field. In the optical and X-ray ranges ob-
servations from space (HST and Chandra) show typical
axisymmetric features known as “jet-torus structure”.
The theoretical interpretation of the jet-torus morphol-
ogy [3], [10] is based on the idea of a stronger equa-
torial energy flux. This creates the torus and an oblate
termination shock (TS) with cusps at the poles. Post-
shock flows first converge toward the equator and then
are diverted along the symmetry axis by magnetic hoop-
stresses to form the jets. Thanks to the development of
RMHD codes (i.e. [5]), we can now investigate this pic-
ture in detail.
Our scheme [6] evolves the ideal axisymmetric
RMHD equations together with the local maximum
particle energy (in unit of mc2) ε∞, taking in account of
adiabatic and synchrotron losses:
d lnε∞
dt
′ =
dlnn1/3
dt
′ +
1
ε∞
(
dε∞
dt
′
)
sync
(1)
where the first term represents the adiabatic losses, the
second one represents the synchrotron losses averaged
with pitch angles,
(
dε∞
dt
′
)
sync
= − 4e
4
9m3c5
B
′2ε2∞, n is the
fluid proper density, m and e are respectively the particle
mass and charge, c is the velocity of light, t
′
is the time
and B
′
is the amplitude of the magnetic field in the
comoving frame.
We employ the ECHO (Eulerian Conservative High
Order Scheme) code developed by Del Zanna’s code [5]
(recently extended to GRMHD [8]) assuming a purely
toroidal magnetic field and poloidal velocity. A descrip-
tion of the initial and boundary conditions can be found
in [6] and [7].
Emitting particles are continuously injected at TS with
a distribution function which is a power-law in energy
and isotropic in momentum:
f(εTS) =
Aw
4π
ε−(2α+1)TS , (2)
where AW is proportional to the thermal pressure of the
post-shock fluid (the electron thermal energy),εTS is the
particle energy at TS andα = 0.7 is the spectral index.
The particles are then advected by the nebular mildly
relativistic flow and the post-shock distribution function
is obtained from conservation of particles’number along
streamlines as in [7].
Under the assumption of quasi-stationarity and of neg-
ligible synchrotron losses, the emission coefficient in ob-
server’s fixed frame is:
jν(ν,~n) ∝ Dα+2 ·p · |~B′×~n′ |α+1 ·ν−α (3)
if ν∞ ≥ ν and 0 elsewhere. D is the Doppler factor,~n′ is
the direction of the observer in the comoving frame,ν is
the optical or X-ray observation frequency,ν∞ is the cut-
off frequency (used to obtain the synchrotron burn-off):
ν∞ = D
3e
4πmc
|~B′×~n′|ε2∞. (4)
Integrating the emission coefficient along the line of
sight one can obtain surface brightness, optical polariza-
tion [4] and spectral index maps [7].
Simulated flux maps reproduce the two polar jets and
the equatorial flows with the correct ranges of velocity.
Brightness maps show, as expected, an equatorial torus,
a system of rings, with brighter arches and a central knot
due to Doppler boosting (Fig.1). The optical and X-ray
spectral index maps (Fig.1) agree with observations [12],
[11].
We found that, by changing the width of the equato-
rial striped region b and the magnetization of the wind
σ (with σeffective> 0.1 to have supersonic polar jets), the
emission pattern changes so that it is, in principle, possi-
ble to use the observed morphology of the jet-torus struc-
ture to infer the conditions in the wind and to reproduce
different Pulsar Wind Nebulae.
High energy gamma-ray emission (COMPTEL,
EGRET, HEGRA and HESS observations) is primarily
due to IC scattering of high energy electrons on tar-
get photons from CMB, dust (far infra-red emission,
FIR), starlight, and from the PWN itself (synchrotron
emission, SSC).
We consider here two different post-shock distribution
functions [1]: one describing the primordial radio emit-
ting electrons (born at the supernova outburst) and the
other the high energy tail accelerated at the TS. Our aim
is to reproduce the observed spectrum in Crab.
The low energy distribution function is:
fr(ε) = Arε−(2αr+1)e−ε/ε∗ (5)
with Ar a constant chosen to fit data at 1Ghz,αr = 0.26
the spectral index andε∗ the radio particle energy cut-off.
The high energy distribution function at TS is:
fTS(εTS) = Aw(εTS+ ε0)−(2αw+1)e−εTS/εc (6)
where Aw is a constant proportional to the thermal pres-
sure of the post-shock fluid,ε0 is the lowest wind parti-
cle energy chosen to fit radio-optical data,αw = 0.7 is
the spectral index andεc is the gamma particle energy
cut-off at MeV frequencies.
The incident photon density per unit of frequency is
obtained either from a black body formula (CMB or
FIR target) or from integrated synchrotron flux (SSC)
assumed to be homogeneous and isotropic.
Integrating distribution function and power per unit of
frequency over the particle energy and incident photon
frequencies for every energy regime [2], energy spectra
and brightness maps are produced.
The emission recipes has been successfully tested by
comparing the broadband spectrum obtained with the
Kennel and Coroniti spherical flow [9], [1] against the
Crab Nebula observations (fig. 2). However, when ap-
plied to the flow structure from RMHD simulations, re-
sults at synchrotron high energies are not satisfactory yet
and further tuning of the emission model would be re-
quired to fit all data (Fig.2). Gamma-ray surface bright-
ness maps are shown in Fig.3 for various sources of target
photons. The strongest IC emission is due to SSC.
The present work confirms jet-launching mechanism
due to magnetic hoop stresses with the best agreement
between simulations and Crab Nebula data given by the
wind magnetization parameterσeffective≈ 0.02.
Further work is required to refine our model in order to
compare with future Glast observations (paper in prepa-
ration).
This complete set for calculating simulated syn-
chrotron emission, polarization and spectral index maps
accounting for synchrotron losses can be used for other
classes of objects (eg. AGN jets), in any scheme for
RMHD (e.g. non-conservative, in full 3-D).
ACKNOWLEDGMENTS
N.B. was supported by NASA through Hubble Fellow-
ship grantHST-HF-01193.01-A, awarded by the Space
Telescope Science Institute,which is operated by the As-
sociation of Universities for Research inAstronomy, Inc.,
for NASA, under contract NAS 5-26555.
REFERENCES
1. A. M. Atoyan, and F. A. Aharonian,MNRAS278, pp.
525–541 (1996).
2. G. R. Blumenthal, and R. J. Gould,Review of Modern
Physics42, pp. 237–270 (1970).
3. S. V. Bogovalov, and D. V. Khangoulian,MNRAS336, pp.
L53–L55 (2002).
4. N. Bucciantini, et al.,Astronomy and Astrophysics443, pp.
519–524 (2005).
5. L. Del Zanna, et al.,Astronomy and Astrophysics400, pp.
397–413 (2003).
6. L. Del Zanna, et al.,Astronomy and Astrophysics421, pp.
1063–1073 (2004).
7. L. Del Zanna, et al.,Astronomy and Astrophysics453, pp.
621–633 (2006).
8. L. Del Zanna, et al.,Astronomy and Astrophysics473,
pp.11–30 (2007).
9. C. F. Kennel, and F. V. Coroniti,Astrophysical Journal283,
pp. 710–730 (1984).
10. Y. E. Lyubarsky,MNRAS329, pp. L34–L36 (2002).
11. K. Mori, et al.,Astrophysical Journal, 609, pp. 186–193
(2004).
12. M. P. Véron-Cetty, and L. Woltjer,Astronomy and
Astrophysics270, pp. 370–378 (1993).
FIGURE 1. On the left: runA (b= 10 andσ = 0.025) simulated brightness map in X-ray band, in logarithmicscale and
normalized to the maximum value. On the right: runA simulated spectral index map in X-ray band. Distances from the central
pulsar are reported on the axes, expressed in light year (ly)units.
FIGURE 2. On the left: Kennel and Coroniti 2-D spectra. On the right: runA spectra. Crab observed data are also plotted.
FIGURE 3. Simulated brightness maps (in units of erg/(sr cm2s Hz) in logarithmic scale) at 350GeV. On the left: IC from CMB
target. In the middle: IC from FIR target. On the right: IC from synchrotron target.


Simulated synchrotron and Inverse Compton emission from Pulsar Wind
  Nebulae

Simulated synchrotron and Inverse Compton emission from Pulsar Wind Nebulae

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