パルサー星雲における高エネルギー粒子の空間分布
田中 周太
宇宙線研 学振PD
共同研究者: 山崎

了 (青学), 大平

豊 (青学)

3, Sep., 2013, 高エネルギーガンマ線でみる極限宇宙@宇宙線研

13年9月3日火曜日

ANRV352-AA46-05

ARI

15 July 2008

10:36

Introduction to
Total spectrum

Figure 3

Annu. Rev. Astro. Astrophys. 2008.46:127-155. Downloaded from arjournals.annualreviews.org
by KOKURITSU-TENMONDAI LIBRARY on 11/28/08. For personal use only.

PWN (Pulsar wind nebula)
Color composite of
the Crab synchrotron
nebula showing a
Chandra X-ray image
in blue, a visible lightmosaic taken with
HST in green, and a
VLA radio image in
red. The pulsar is seenas the bright blue
point source at thecenter of the image.
Note the axisymmetryof the nebula, which ismost apparent fromthe X-ray torus andjets. Emission fromhigh-energy electrons
is brightest near thecenter of the nebula,close to where they are
injected. Moving
outward through thenebula, the spectrum
becomes softer owing
to adiabatic andradiative losses. For
the most part, only
low-energy
radio-emitting
electrons survive to theedge of the nebula.

      

Crab
(HST)

Line emission(SN ejecta)

Crab(radio - X-ray)

Non-thermal(Pulsar wind)

Synchrotron

We reproduced    ・Total spectrum @ 1kyr
・Flux decrease rate ~0.2%/year @ radiofor features seen in thermal emission from ejecta.) High spatial resolution (∼0”.5) ground-based
optical imaging showed that the prominent wisps are only the most obvious of the fine structure
present in the Crab (van den Bergh & Pritchet 1989). The resolution of HST images (Hester et al.
1995) nears the scale of the Larmor radius of the most energetic electrons present.
Serious efforts to model the Crab synchrotron nebula go back to the work of Rees & Gunn
(1974). The standard set of models for the Crab to which subsequent work is typically referred
is the work of Kennel & Coroniti (1984a,b), who calculate spherically symmetrical models of the
expansion of a pulsar wind that is confined by a surrounding thermal shell. These models areconstrained by the need to match the outer boundary condition set by the observed expansion
Crab
G21.5-0.9
speed of the surrounding thermal ejecta, as well as the inferred
location of the wind shock. The
adjustableparameter in these models is the ratio immediately(X-ray)
upstream of the shock of the magnetic(X-ray)energy flux to the energy flux carried by particles, generally written as σ . As demonstrated in
Kennel & Coroniti’s models, σ must be relatively low in order for the wind to shock close to thepulsar. Theory suggests that pulsar winds are born as magnetically dominated high σ flows. The
conversion of a high σ flow to a low σ flow is referred to as the “σ problem” and remains a fieldof active research. The general problem of pulsar winds and PWN has been discussed recently

We obtain
・mean B-field inside PWN.
・particle energy & number inside PWN.
・magnetization at injection.
・particle injection spectrum (broken PL).

Confined by SNR
13年9月3日火曜日

Powered by PSR・spin evolution of the central PSR.

InverseComptonVirtue of

Crab は 点源なのでBright and extended object
・Brightness map in different frequencies of the Crab.
BIETENHOLZ ET AL.

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20

HESS J1825-137

Vol. 615

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40

Bietenholz+04ApJ (radio)

Temim+06ApJ (IR)MORI ET AL.
Mori+04ApJ (X-ray)Vol. 609

F. Aharonian et al.: Energy dependent γ-ray morphology in HESS J1825–137

Dec (deg.)

22 05

188

04

160

-13

140

3EG J1826-1302

03
DECLINATION (J2000)

367

120

PSR J1826-1334

-13.5

100

02

80
tic
lac
Ga

-14

01

ne
Pla

-14.5

00

-20

18h30m20

Aharonian+06A&A (γ-ray)

Fig. 1. Acceptance-corrected smoothed excess map (smoothing radius 2.5! ) of the 2.7◦ × 2.7◦ field of view surrounding HESS J1825–137. The!
linearcolouris in units
of integrated
countsatwithin
the smoothing
Fig. 1.—Left: Chandra ACIS-S combined image of the 2nd–8th observations. The center
ofscalethe white
circle(R ¼ 50 00 )excess
is locatedthe pulsar
position.radius
The of 2.5 . The excess has been derived from a model of thesystem acceptance as described in the text. The inset in the bottom left corner shows the PSF of the dataset (smoothed in the same way as the‘‘hole’’ at the pulsar position is caused by severe event pileup resulting in the rejectionof mosteventsatdashed
this position.
Narrow
through
the Thepulsarare black and white contours are linearly spaced and denote
excess map
with theblack
circle etdenoting
the lines
smoothingradius).
dashedF. Aharonianal.:Energydependent
γ-raymorphology in HESS J1825–137
instrumental artifacts due to trailing events. Right: Photon index map of the Crab Nebula
after
correctionforpileupeffects.
White
regionsaroundtheeastern,the 5σ, 10σ and 15σ significance levels (the 5σ contour being the outermost one), determined with a θ = 0.1◦ radius cut. The best fit position
western, and southern edges were excluded from analysis because of the dominance ofoftrailing
eventsandscatteredphotons.
The
pulsarpositionisalso
white,
since
HESS J1825–137 is marked with a black square, the best extension and position angle by a black ellipse (see text). The dotted white contour
MORI
AL.index could be derived there because of severe pileup.
Vol. 609 shows the 95% positional confidence contour of the unidentified EGRET source 3EG
no ET
photonJ1826–1302. The position of the pulsar PSR J1826–1334 is180
marked2.8
by a white triangle. The bright point-source to the south of HESS J1825–137 is the microquasar
LS 5039
J1826–148)
Using
BG(HESSestimatefrom (Aharoniansame FoV
Temim et al.
et al. 2005d). The colour scale for this source is truncated in this Figure. The Galactic plane is shown as a white dashed line. Some indication for160
an additional emission region to the north of the pulsar is seen.
Using BG estimate from off Data

BIETENHOLZ ET AL.

, and thus-200
from considerably-100
earlier multidata. This larger-scale structure is thus not dible to that in the optical and X-ray observations.
we argued above and in Paper I, there is little
ct rapid variations on these scales. Our chief
paper is 22
in the03 smaller-scale structure. On spatial
than !2000 our u-v coverage is excellent, andt our images reliably indicate the structure ofd in particular changes from one epoch to anr ensure the02reliability of the images we present,
he remainder of this paper only with spatially
red radio images. We conservatively filteredn of full width
01 at half-maximum (FWHM) 1400 ,isolate those spatial features for which we haverage and thus reliable imaging. The high-passsure that our images at each epoch contain only00
ly determined by the data and not derived fromVol. 490

188
Temim+12ApJ
The Astrophysical Journal, 753:72 (9pp), 2012 July 1(IR)Mori+04ApJ (X-ray)al. 1997)
and the &PSU
ACIS1993).
Monte Carloand exceedsMARX
α = 1.0(Wisein theetNW(Veron-Cetty
Woltjer
CCDuncertainty
simulator on(Townsley
The calibration
the ratioetofal.
the2002),
fluxesrespectively.
in the two Since
LYNX
takes into accountpossiblethe resulting
IRAC channels
is approximately
4% the(Reachet al.overlap2005),ofwhichchargecloudswithineach
CCD
exposureframe,
spectra aftranslates into a ±0.18 uncertainty in the synchrotron spectral
fectedbypileupcanbesimulated
for
both
point
sourcesandindex. This large uncertainty in the spectral index is systematic
diffusesources.
We
simulatedtheobserved
Crabspectrumforacross the nebula and does not affect the spatial variations in theseveral different values of true surface brightness and for true
in index.
photon indices of 1.5, 2.0, and 2.5. The results are superposed
In order to investigate the morphology of the dust and line
emission in the Crab Nebula, we subtracted the synchrotron contribution from the IRAC 5.8 and 8.0 µm images and the MIPS
24 and 70 µm images. We produced a synchrotron-subtracted
image for each wavelength by subtracting the synchrotron contribution extrapolated from the IRAC 3.6 µm image using theequationFi,residual = Fi − F3.6 (3.550/λi )−α .
(2)the0 support, and will 100
reduce any spurious 200
differences between
the images due to possible deconvolution errors.
The optical observations were carried out with the HST
Wide Field Planetary Camera 2 (WFPC2) using a relatively
line-free filter centered near 5500 8 (F547M). They consistedof 24 visits between 2000 August and 2001 April at 11 day
intervals. The radio observations occurred during the period
between HST visits 19 and 24. The X-ray observations werecarried out using the Chandra Advanced CCD Imaging Spectrometer (ACIS). The optical and X-ray observations are more
fully described in Mori et al. (2002) and Hester et al. (2002).
3. RESULTSIn Figure 1, we show our latest radio image of the Crab
Nebula, taken on 2001 April 16. The size of the restoring beam
was 1B4 FWHM, which was conservatively chosen as acommon size for all seven epochs. The peak brightness was

21 59

58

57

0.3

56

55
05 31 50

45

0.5

0.6

0.7

0.8

0.9

1

on the data in Figure 2 (left). The expected reduction of ap2.6 photon index in regions of higher surface brightness
parent140
above
1 TeV. The
peak of HESS
is locatedcamera images(Aharonian et al. 2004a). The shower geometryis evident.
However,
it isJ1825–137
also clearthat justtheoutvariations
inside the 95% confidence limits on the position of the unidenti- was reconstructed based on the intersection of the image axes,
120
observed
indices
greatly
expected
fromfied
EGRETphoton
source 3EG
J1826–1302.
As exceed
shown bythose
Aharonianprovidingan angular resolution of ∼0.1◦ for individual γ-rays.
2.4
pileup,
and
there
are
certainly
real
spectralvariations
acrosset al. (2005c), the HESS energy spectrum can be connected to Cuts on scaled width and length of the image (optimised on γ-ray
100 and off-source data) are applied to select γ-ray canthe
spectrumas
bydescribed
extrapolation.
despitethe (2000).
simulations
theEGRET
Crab Nebula
byTherefore,
Weisskopf
et al.
somewhatmarginal
spatialcoincidence,anassociation
betweendidatesand
We used the LYNX simulation results to correct the data suppress the hadronic background (Aharonian et al.
these 2.2
two objects was considered.
2004b). The
80 energy of the γ-ray is estimated from the total image
points in Figure 2 (left) for the photon index andintensity
surfacetaking into account the shower geometry. The resulting

HESS J1825–137 was revisited in 2005 for ∼7 h in pointedis ∼15%. As previously described (Aharonian
observations between June and July and was additionally in energy resolution
60
et
al.
2005b,
2006d),
two sets of quality cuts are applied. For
the field of view of a large part of the pointed observations on
2studies of a source a rather tight image size cut of
the nearby(distance ∼1◦ ) γ-ray emitting microquasar LS 5039 morphological
40(HESS J1826–146), adding another 50.9 h between April and 200 photo-electrons (p.e.) is applied (along with a slightly tighter
cut
on
the
mean scaled width), yielding a maximum signal-toSeptember (Aharonian et al. 2005d). Here we report on the tonoise
ratio
for a hard-spectrum source. For spectral studies the20
tal available
dataset (i.e. 2004 and 2005 data) that includes now
1.8∼67 h of observations with HESS J1825–137 within 2.0◦ of the image size cut is loosened to 80 p.e. to extend the energy specpointing position of the telescopes. The exposure adds up to tra to lower0 energies. Different methods are applied to derive a
0
0.2
0.4
0.6
0.8
1
1.2
0
0.2
0.4
0.6
0.8
1
1.2
a total dead-time corrected lifetime of 52.1 h after quality se- background estimate as described by Hinton et al. (2005). For
morphologicalstudiesthebackground
at
each
test
positioninDistancefrom
Pulsar(°)
Distancefrom
Pulsar(°)
lection of runs according to hardware and weather conditions,from a ring surrounding this test pothereby increasing the observation time by more than a factor the sky is either derived(with radius 1.0◦, an area 7 times that of the on-source
Here, the subscript i refers to the wavelength of the imageof 6 comparedearlierLeft:publications.
The meanzenithangle asof a sition
Fig. 5. Energy spectrain radialtobins.
power-law
photonindex
functionof the radius of the region (with respect to the pulsar
the dataset presented here is 20.1◦, the mean offset of the peak area, taking into account the changing acceptance on the ring),from which the extrapolated synchrotron emission is being
the regions given in
Fig.
4.
The
closedpointsareobtainedbyderiving
thebackgroundfromregionsderived
with the
or
from
a
model
ofestimate
the system
acceptance,
fromsame
off- offset as
position of HESS J1825–137 from the pointing direction of thesubtracted. In each case, the 3.6 µm image was convolved
to the same fielddata (datawithno γ-ray γ-ray
source in
the field inof view)
with similar
withinofisview.
(data
without
sourcesthe fieldof view) for thesystem1.2◦ . The open points are derived using off-data
zenith angle. In all background methods, known γ-ray emitting
the resolution of λi (Gordon et al. 2008), and each ofestimate.
theA constant fit
the filledyields a χ2 schemeof 58 wasfor applied
11 degrees
of freedom, clearly showing the dependence of the photon
Thetostandard
HESSpoints
event reconstruction
regions are excluded from the background regions to avoid γ-ray −12
images was extinction corrected using the extinction curve
of
to
the
raw
data
after
calibration
andtail-cuts
cleaningofthedistance from the pulsar position. Right: surface brightness between 0.25 and 10 TeV per integration region area in units of 10 erg cFigure 2. Synchrotron index map calculated from the synchrotron-dominated
IRAC 3.6 and 4.5 µm images.Fig.
The1.—Left:
spectralChandra
index αACIS-S
steepens
from 0.3image
in theof the 2nd–8th
Chiarobservations.
& Tielens The(2006).
surfacecorrection
aspulsara function
the distance to the pulsar position. Error bars denote ±1σ statistical errors.
combined
centerTheof theIRAC
white circle(R ¼brightness
50 00 ) is locatedat theposition.ofThetorus and jet structures to 0.7
(1.0)
in
the
outer
SE
(NW)
parts
of
the
nebula.
factors
wereappliedtoofallmost
IRAC
imagesof the‘‘hole’’ at the pulsar position is caused by severe event pileup
resultingin therejection
eventsat this (Table
position. 4.9
NarrowlinesIRAC
through the pulsar are

PWN emission reﬂects B-ﬁeld & particle distribution of PWN

40

35
30
25
RIGHT ASCENSION

20

15

FIG. 2aÈThe relative radio spectral index between 327 MHz and 1.5 GHz (*a1.5) in units of 0.001. These maps show the di†erence of the spectral index to
0.3contours are the 0.5%, 1%, and 2% contours in total intensity of the 327
pectral index of the Nebula. The FWHM of restoring beam is 16A. Thee. (a) The careful version, made by deconvolving with a default and using only data at u-v distances [1.6 kj. It contains little information ones [2@.7 but is not corrupted by correlator nonlinearity. (b) The standard version, which was made without a default and contains information onscales but may be slightly biased.

13年9月3日火曜日

0.4

-2

Bietenholz+97ApJ (radio)

Photon Index

・Spectral index map in different frequencies of the Crab.

ebula at 5 GHz on 2001 April 17. The FWHM size of the restoring beam was 1B4. Peak brightness is 48.5 mJy beam"1, and the image has been
rimary beam response of the VLA antennas. The rms background was 48 !Jy beam"1 before primary beam correction. Contours are drawn at
nd 8% of the peak, and gray scale is labeled in mJy beam"1. Maximum entropy deconvolution was used with a support to recover the low spatiale (see text, x 2 for details). The accompanying animation shows a 61 00 ; 70 00 region near the center of the nebula between 1998 August 10 and
Table 1). The mpeg timescale is nonlinear, being compressed between 1998 and 2000. The individual frames have been high-pass filtered with asian filter to enhance the mobile features. [This figure is also available as an mpeg animation in the electronic edition of the Astrophysicalerg cm-2 s-1 deg )

35
30
25
RIGHT ASCENSION (J2000)

RA J2000 (hours)

-12

40

18h25mSurface brightness (1005 34 45DECLINATION

0

-15

58

40
20

LS 5039

21 59

60

instrumental artifacts due to trailing events. Right: Photon index
map of the Handbook).
Crab Nebula after
correction
for pileup
effects. White regions around the eastern,
Instrument
The
resultingsynchrotron-subtracted
Table
2. white,
Spectralwestern, and southern edges were excluded from analysis because of the dominance of trailing events and scattered photons. The pulsar positionis alsosinceparameters for the radial bins surrounding PSR J1826–1334. PSF denotes a HESS point-source analysis at the pu
images are shown in Figure 3 and will be discussed in Section 4.
a break in the power-law
spectrumoccurssomewhere
in oftheno photon
index could
be derived
there because
severe pileup.
The background estimate for the numbers in the table have been derived from reflected positions within the same field of view. Th

IR, between 10 and 1000 µm (Marsden et al. 1984). The most2
recent estimate for this break frequency is (7.0+6.5−3.4 ) × 10 GHz,

Next, we subtracted the synchrotron contribution from theand surface brightness are given for the energy range between 0.25 and 10 TeV.
SL and LL spectra for each spatial position. We created fourMotivation
What do we learn from observations of the Crab Nebula?
PSR & PWN properties
・Magnetization of pulsar wind. → σ-problem
・Injection spectrum of particles. → κ-problem & particle acceleration・e± escaping process from PWN. → PAMELA anomaly
Physics
・Particle transport mechanism inside PWN. → advection? diffusion?
・Particle acceleration process inside PWN. → second-order acceleration?
・Expansion of PWN. → Interaction between PWN & SNR at outer boundary.
13年9月3日火曜日

Past Studies

13年9月3日火曜日

Amato+00, advection onlyRadio brightness map

Tang & Chevalier12, diffusion
optical spectral index map

Reynolds03, advection only
X-ray spectral index map

Vorstar & Moraal13,
diffusion & advection
particle spectrum

1D - Model
Dynamics
・radial expansion

・toroidal B-field・induction equation (MHD condition)・parameters
inner radius: r0
inner velocity: v0vel. profile index: αv
injection B-field: Binj
13年9月3日火曜日

1D - Model
Particle Spectrum
・diffusion & convection transport+ adiabatic & radiative cooling@f=@tr · [(v

1 @Kr)f ] + 2
p @p

✓

1
r · v + ( syn +
3

IC

◆

p3 f + Qinj

・diffusion coefficient・injection spectrum

・parameters
diffusion coefficient: ξ
injection paramters: p1, p2, γmin, γmax, γb

13年9月3日火曜日

Mimicking the Crab Nebula
We consider that the particles and the magnetic field
are injected at the inner radius r = r0 at a time t = tinj.
Main parameters are
1. gyro-factor ξ,
2. inner radius r0 or velocity profile index αv,
RPWN = 2.0pc, VPWN = 1.500km/s @ tage = 1kyr
(r0 = 0.1pc & v0 = c/3 are too much.)
3. injected B-field or magnetization σ
B0 = 300μG
4. broken power-law injection with2
69p1 = 1.5, p2 = 2.5, γmin =10 , γ =10 , γmax =10
13年9月3日火曜日

Results: Particleœ

r0 = 0.007pc

without diffusion

13年9月3日火曜日

with diffusion(ξ=1)

1. strong adiabatic cooling forr0 = 0.007pc.
2. When ξ is non-zero, e± canescape from PWN (r >> RPWN).
3. Escaped high energy e± arecooled slowly.
4. For r0 = 0.007pc, because
r0 is smaller than diffusion
length for high energy e±,more particles can escapethan for r0 = 0.2pc, mostly inan early phase of evolution.

Results: Spectral Index Profile[r0 = 0.007pc, i.e., RPWN ~ 300r0]

without diffusion
with diffusion (ξ=1)
p1 = 1.5 & p2 = 2.5 corresponds α = 0.25 & 0.75
1. Without diffusion, we find synchrotron cooling effectincreases spectral index at1016Hz > 10 at 100r0 ~ 0.7pc.
2. Diffusion effect smooths spectral index profile and we do
not find synchrotron cooling hardening of the spectrum for B0= 100μG. We need to select appropriate parameter set of (ξ,B0) to fit the spectral index distribution.
3. α=-1/3 corresponds to low freq. side of synchrotron
spectra and is appeared at r > RPWN @ < 1016Hz.
13年9月3日火曜日

Conclusion
・Convection-Diffusion transport equation is considered to study thebroadband emission structure of PWNe.
・For the escaping of e± from PWNe, we should compare diffusion length & r0.
・γ-ray distribution almost traces the particle distribution for inverse
Compton scattering off CMB.
・Synchrotron Self-Compton process is considered to be dominated in the
Crab Nebula in γ-rays and should be considered the future work.
・We need larger value of B-field at injection point, to obtain softer spectra
observed for many PWNe in X-rays (α > 2).

13年9月3日火曜日