HαF-#8E
;6G=4*C.7
Cf.) Shimoda et al. 2018, MNRAS, 473
Shimoda & Laming 2019a, MNRAS, 485
Shimoda & Laming 2019b, MNRAS, 489

äą½Ň1,2Collaborators for today’s talk:
J. M. Laming3; S. Katsuda4
1. Nagoya Univ., 2. Tohoku Univ., 3. Naval Research Lab., 4. Saitama Univ.

¬BS`Fj÷ĦĿy, 2019, 12/5

0'+% &<!I
pSNR).HαĪ¥-7:j÷àté.Í
Shimoda & Laming (2019 a,b)
pSNR).ĆĔJbGaQabĭÄ-7:ľŁ¾ÏKXGQ
`.ÍShimoda, Akahori, Lazarian, Inoue & Fujita (2018)pčęăìAT2018cow.ĆĔĪ¥è.zÅ
Huang, Shimoda, Urata, Toma, Yamaoka, Asada, Nagai, Takahashi,
Pettipas, & Tashiro (2019)
pGRB·¥.ĆĔĪ¥]P`.©õ
Shimoda & Toma in prep.
pMilky Way Gas Hallo.Ü¯
Shimoda, Inutsuka on going0'+% &<!I
pSNR).HαĪ¥-7:j÷àté.Í
Shimoda & Laming (2019 a,b)
pSNR).ĆĔJbGaQabĭÄ-7:ľŁ¾ÏKXGQ`.Í
Shimoda, Akahori, Lazarian, Inoue & Fujita (2018)pčęăìAT2018cow.ĆĔĪ¥è.zÅ
Huang, Shimoda, Urata, Toma, Yamaoka, Asada, Nagai, Takahashi, Pettipas, &Tashiro (2019)
pGRB·¥.ĆĔĪ¥]P`.©õ
Shimoda & Toma in prep.
pMilky Way Gas Hallo.Ü¯
Shimoda, Inutsuka on goingSummarypj÷àīùÌĔSNR)Ã²-(:+ó9$
pkpc)jË(0DI=F)
§¬)¬ÀT)ÇÅ2¶¾'1+'.'pHα.Ī¥Į§=;0判別可能

;6Cosmic Rays
CE²ĕīĽŐĮŔĶńįĻŐThe energy spectrum of CRs

CE²ĕīĽŐĮŔĶńį
ĽŐĮŔĕOhira, Yamazaki & Terasawa (2012)­@, e-, p, He, …

dF/dE∝E-2.7

ðīĽŐĮŔĕ
-, p, He, …ýĠ100Uþ¯Ď¹è­@, e15.5

< 10

eV

> 1015.5 eV

SNROriginÀýĠ100Uþ¯Ď

17eVĖ®;?!
017eVĖSNR?!E>10ðīĽŐĮŔĕ

17eVĖSNR?!E>1017eVĖ®;?!
E<10¹è­@, e-, p, He, …
=T,PQ,HñB Ç, 2012

=T,PQ,HñB Ç, 2012ÀýĠ100Uþ¯ĎSupernova Remnant (SNR)
X-ray:~TeV8.Ć¸/ê³(: JbGaQabĭ
Ä79 (e.g. Warren & Hughes 04).

Ha:
hě-ÌĔį)¥'(:
From Chandra archival image(e.g. Hovey+15).
SNR 0509-67.5 (Chandra & HST)
Blue: 1.5 – 7.0 keVGreen: 0.2 – 1.5 keV
Red: Ha05J
9$.
∗(X1 )P (X2 )⟩X(4)– 5 –(Diffusive Shock Acceleration; DSA)
1

λ = X2 − X 1U¦upstream
上流(5)
DSAの模式図Ō ÌĔ/ ĲÌčÌ(A)! # ):""Ĕ
"#2磁気擾乱−1 $%∆p
Alfven
wave
−1
ln
Λ
n
T
ō
AlfvenĔ,+-µľ
exp k
p0 1 cm−3
30.9
1 keV
;ÎŁ*qŁ=nĤ
!
"
4u2
dNCR
":ł¸ê³":
p −k
∝ p−s
c

dp
3u2
dNk
−s
s=1+
≈2
∝p
u0 − u2dp
3u2
τCR ∼ 107 yr≈2
WE¹Ö/cÊĜ)1u0 − u2
D(E) ∼ ξB rg c
1:*ó8;
3
" #−2
(:
δB

(C)

downstream
下流

(46)
(6)

(B)

(47)
(7)
(8)
(48)

u0

(9)
(49)
衝撃波面
shock
(10)

u2

– 13 –
M:P"> 4*C
ρ u = ρ u0 0

u0: velocity
p0: pressure
r0: density

Transition layer

upstream

2 2

ρ0 u0 2 + P0 = ρ2 u2 2 + P2
downstream3
ρ0 u 0
ρ2 u2 3+ h0 =jump condition
+ h2
Shock
2
2

ρ0 u0 = ρ2 u2

u2
p2
r2

ρ0 u0 2 + P0 = ρ2 u2 2 + P2
u0F3m = ρ2 u2 ρ2 u2 3
ρ0 uρ00−+ h0 = 2+ h2
2
ρ0 u0 + P0 2− Fp = ρ2 u2 + 2P2

ρ0 u0 3+ h0 − FE2=

ρ2 u2 3+ h2
2

ρ0 u0 −10
Fm15 cm= ρ2 u2ĨÀĹ«Ā 1/nσ

ρ0 u0 2 + P0 −!FpkT̄ =" 32 ρ2 u2 2 + P2
12ŁìŅĂ,ÌĔ.Ï­_bEb^IRC
sec np −1
ln Λ 33Gabŉ¼ τpp ∼ ρ10
u
ρ
1
keV
0 0
2 u2
+ h0 − FE =+ h28cÊĜ<:ZOTÖð*
22

H4A4*C

u0: velocity
p0: pressure
r0: density

downstream
Transition layer

upstream

ρ0 u0 2 + P0 = ρ2 u2 2 + P2
ρ0 u 0 3
ρ2 u2 3+ h0 =+ h2
2
2

Shock jump condition
ρ0 u0 − Fm = ρ2 u2

u2
p2
r2

ρ0 u0 2 + P0 − Fp = ρ2 u2 2 + P2
ρ0 u0 3
ρ2 u2 3+ h0 − FE =
+ h2
2
2

CR,+.ĝĐĂł¸»&ĉ":ÂŃkĊŃ
BS`FŁç=3,*N\ýÐ.ŁìŅ-/¡;,ł¸$&.ĺ

H4A4*C
upstream

ρ0 u0 2 + P0 = ρ2 u2 2 + P2
ρ0 u 0 3
ρ2 u2 3+ h0 =+ h2
22

downstream
Transition layer

Shock jump conditionp ĲÌčÌĔ)/ ł¸ Ìč-7:kĊŃ¤ρ0 u0 − Fm = ρ2 u2ĠÉħ,$3 ZGK@A`ħĢ8iñ
ρ0 u0 2 + P0 − Fp = ρ2 u2 2 + P2
$ł¸ê³:→j÷à4(OK!
33
u : velocity
u

ρ0 u0
ρ2 u2
+ h0 − FE =+ h2: pressure
p222
pp0Shockjump condition/+;%.ĝĐĂł¸
0

2

r0=ÛÙ
: density $ * r#;8.ł¸.kĊŃKXG
2
Q`. -eê":

CR,+.ĝĐĂł¸»&ĉ":ÂŃkĊŃpDSA)té":j÷à.kĊŃKXGQ` BS`
BS`FŁç=3,*N\FKXGQ` /shock jump condition)1ýÐ.ŁìŅ-/¡;,ł¸$&.ĺ:cÊĜ-79Čøġ8;:

H4A4*C

ρ0 u0 2 + P0 = ρ2 u2 2 + P2
ρ0 u 0 3
ρ2 u2 3+ h0 =+ h2
2
2

Transition layer

upstream
downstreamØ ;1).Ŀň j÷à.cŅ
ÎŁ._
Shock jump conditionp ĲÌčÌĔ)/ł¸ Ìč-7:kĊŃ¤[c *Ñî;($ρ0 u0 − Fm = ρ2 u2ĠÉħ,$3 F:<45J¼º.N
2
2
ρ
u
+
P
−
F
=
ρ
u
0 0
0
p
2 2 + P2Ø "Íê³
DbZà*Xà.è=ċ¼-ßĳ":*):→j÷à4(OK!
33
u0:,'$
velocity
u
ρ
u
ρ
u
2
0
0
2
2
e.g. Abdo+11 →Ŀň.ĕİ+ h0 − FE =+ h2: pressure
p222
pp0Shockjump condition/+;%.ĝĐĂł¸
ÈĬėÂ.ĿzĠÉħ%'$3DbZàè.zr0=ÛÙ
: density $ * r#;8.ł¸.kĊŃKXG2Å=f($uĒØ¹ā;(:
e.g.
Q`.
-eê":
Inoue+12, Inoue 19 
CR,+.ĝĐĂł¸»&ĉ":ÂŃkĊŃpDSA)té":j÷à.kĊŃKXGQ` BS`Ø
#4#4 j÷àcŅ.èĂ,ü
BS`FŁç=3,*N\FKXGQ`/shock_[cjump condition)1ÞÍ/, ¿®/'$ ýÐ.ŁìŅ-/¡;,ł¸$&.ĺ:cÊĜ-79Čøġ8;:

Cosmic-Ray Modified Shock (CRMS)
no CR

Velocityj÷à, .
ŁìŅĂ,
ÌĔ

p: protons inbackground plasma

CRW

up

down
shock (z=0)

z0&Cosmic-Ray Modified Shock (CRMS)
Velocityno CR

CRV_LZĔĊ=ņ ÎŁ/tĐ;:

p-/)CRW1$0&CR
heated/turbulent
up

precursor

down
shock (z=0)

zCosmic-Ray Modified Shock (CRMS)
Velocityno CRCRcŅ_[c-Ŋ¨ ÎŁ.V_L
Zé=Ç:shockÝº pwith CRCR

up

precursor

down
shock (z=0)

zCosmic-Ray Modified Shock (CRMS)
no CR

VelocitypCRcŅ_[c-Ŋ¨ ÎŁ.V_L
Zé=Ç:shockÝº ptĐ /photoionization,+)4
with CRMedina+14).
CR Ghavamian+00,: (e.g.
p t 2]±$CRMS)i2"up

precursor

down

shock (z=0)

zCosmic-Ray Modified Shock (CRMS)

The Astrophysical Journal, 817:137 (5pp), 2016 February 1

Ohira

Ohi

ampliﬁed by the turbulence, which was suggested by Ohira(2013b). In this paper, we ﬁrst demonstrated via hybrid
simulations that even though shocks propagate partially ionizedplasmas, magnetic ﬁelds are ampliﬁed up to near theequipartition level by the downstream turbulence. Figure 1
shows that downstream magnetic ﬁelds are locally ampliﬁed
over 30B0 and the spatially averaged value is about 15B0 at
x = 58, 400 c wpp , that is, a signiﬁcant fraction of the
upstream kinetic energy is converted to the magnetic ﬁeld
energy. After the magnetic ﬁeld strength reaches a saturationlevel, it gradually decays as the turbulence decays. The decay
length scale is about 300 c wpp , which is much smaller than theobservable length scale. However, once particles are accelerated by DSA, density ﬂuctuations with larger length scales
would be generated by the accelerated particles (Caprioli &The AstrophysicalJournal,817:137
1
Spitkovsky 2013).
If so, thedecay (5pp),
length 2016
scale Februaryof magnetic
Figure 2. Shock structures averaged over the y direction at t = 2000 W-cp1. T
ﬁelds would be larger. Although simulations in this paper are ared, blue, and black lines show the ﬂuid velocity normalized by the-1 threetwo-dimensional
system,ithas
been
demonstratedby
theand normalized
the energy
by 10 spectru
times thevalue, uacceleration
x vd , the proton density
Figure 1. Two-dimensional shock structures at t = 2000 Wcp . From top upstream
to
upstream value, 0.1rp rp,0 , and the ionization fraction, fi , respectively.
dimensional magnetohydrodynamic simulation that the turbuin the previous simulation for vd =bottom,lence
the panels
show proton density, rp , magnetic
ﬁeld strength, ∣B∣, eachdoes amplify magnetic ﬁelds up
to near the equipartition
hand, the energy spectrum has a
Bx , By , Bactual
component
the magnetic
ﬁeld,Therefore,
ﬂuid velocity
of protons inz , andhigher
levelof(Inoueet al. 2010).
Alfvén Machsimulation for vd = 1000 km s-1
c wpp ) are
he downstream
rest frame,
leftamplify
regions magnetic(x < 57600
number shocks
can beﬁelds
ux , expectedu y . The tomorestrongly.
upstreamregions.
particle can experience the second
The amplitude of the magnetic ﬁeld ﬂuctuations is
The maximum velocity of leaking
dB B0 » 3 in the upstream region. The coherent length scale
3000 km s-1 in the downstream resof magnetic ﬁeld structures is of the order of the gyroradius ofwith themagnetic
ﬁeld
strengthin theions
upstreamregion and the
upstream
pickupions.
The pickup
are preferentiallythe upstream region, they are picke
acceleratedbychargeexchange
andpickupprocesses(Ohirawave vector is highly oblique to the magnetic ﬁeld direction,and their velocity becomes about 4
2013b). Therefore, the observed magnetic turbulence isthat is,importantthe fastformagnetosonicmodes
are excited(Ohirarest frame. The picked up particles
injection into DSA.
Simulationsin thispaper 2014).
-1, particle
performed infor
the vtwo-dimensional
system,km
so sthat
are heated to v » 8000 km s-1, t= 30 v = 1000
the correlaIn thisaresimulation

ģħĆŀV_LZö=Ąē":SNRÌĔ.
hybrid simulation (Ohira16)

Cosmic-Ray Modified Shock (CRMS)

The Astrophysical Journal, 817:137 (5pp), 2016 February 1

Ohira

Ohi

ampliﬁed by the turbulence, which was suggested by Ohira(2013b). In this paper, we ﬁrst demonstrated via hybrid
simulations that even though shocks propagate partially ionizedplasmas, magnetic ﬁelds are ampliﬁed up to near theequipartition level by the downstream turbulence. Figure 1
shows that downstream magnetic ﬁelds are locally ampliﬁed
over 30B0 and the spatially averaged value is about 15B0 at
x = 58, 400 c wpp , that is, a signiﬁcant fraction of the
upstream kinetic energy is converted to the magnetic ﬁeld
energy. After the magnetic ﬁeld strength reaches a saturationlevel, it gradually decays as the turbulence decays. The decay
length scale is about 300 c wpp , which is much smaller than theobservable length scale. However, once particles are accelerated by DSA, density ﬂuctuations with larger length scales
would be generated by the accelerated particles (Caprioli &The AstrophysicalJournal,817:137
1
Spitkovsky 2013).
If so, thedecay (5pp),
length 2016
scale Februaryof magnetic
Figure 2. Shock structures averaged over the y direction at t = 2000 W-cp1. T
ﬁelds would be larger. Although simulations in this paper are ared, blue, and black lines show the ﬂuid velocity normalized by the-1 threetwo-dimensional
system,ithas
been
demonstratedby
theand normalized
the energy
by 10 spectru
times thevalue, uacceleration
x vd , the proton density
Figure 1. Two-dimensional shock structures at t = 2000 Wcp . From top upstream
to
upstream value, 0.1rp rp,0 , and the ionization fraction, fi , respectively.
dimensional magnetohydrodynamic simulation that the turbuin the previous simulation for vd =bottom,lence
the panels
show proton density, rp , magnetic
ﬁeld strength, ∣B∣, eachdoes amplify magnetic ﬁelds up
to near the equipartition
hand, the energy spectrum has a
Bx , By , Bactual
component
the magnetic
ﬁeld,Therefore,
ﬂuid velocity
of protons inz , andhigher
levelof(Inoueet al. 2010).
Alfvén Machsimulation for vd = 1000 km s-1
c wpp ) are
he downstream
rest frame,
leftamplify
regions magnetic(x < 57600
number shocks
can beﬁelds
ux , expectedu y . The tomorestrongly.
upstreamregions.
particle can experience the second
The amplitude of the magnetic ﬁeld ﬂuctuations is
The maximum velocity of leaking
dB B0 » 3 in the upstream region. The coherent length scale
3000 km s-1 in the downstream resof magnetic ﬁeld structures is of the order of the gyroradius ofwith themagnetic
ﬁeld
strengthin theions
upstreamregion and the
upstream
pickupions.
The pickup
are preferentiallythe upstream region, they are picke
acceleratedbychargeexchange
andpickupprocesses(Ohirawave vector is highly oblique to the magnetic ﬁeld direction,and their velocity becomes about 4
2013b). Therefore, the observed magnetic turbulence isthat is,importantthe fastformagnetosonicmodes
are excited(Ohirarest frame. The picked up particles
injection into DSA.
Simulationsin thispaper 2014).
-1, particle
performed infor
the vtwo-dimensional
system,km
so sthat
are heated to v » 8000 km s-1, t= 30 v = 1000
the correlaIn thisaresimulationp ¿®;: é / ±þ¢;=Áĩ":ĞĻ:

ģħĆŀV_LZö=kpc(0DI=F))Ąē":SNRÌĔ.
¬ÀT2¶¾!-
hybrid simulation (Ohira16)

Challenging!

Supernova Remnant (SNR)
X-ray:~TeV8.Ć¸/ê³(: JbGaQabĭ
Ä79 (e.g. Warren & Hughes 04).

Ha:
hě-ÌĔį)¥'(:
From Chandra archival image(e.g. Hovey+15).
SNR 0509-67.5 (Chandra & HST)
Ha/ÌĔÈĬ.V_LZÑï=Ěm
Blue: 1.5 – 7.0 keV(¥:Green: 0.2 –(e.g.
1.5 keVRaymond 91 for review).
Red: HaLEE ET AL.
Hα emission fromupstream

Hα Surface Brightness

Tycho’s SNR (Lee+2010)precursor

postshockPhotoionization?

Shock Direction

−8

−6

−4

−2

0

2

4

6

Distance from the peak [′′ ]le across the shock normal extracted from cut 04. The bright narrow peak is believed to correspond toKatsuda et al.
Hα emission fromupstream

Shock Direction

SNR Cygnus Loop
(Katsuda, SJ+2016)

Katsuda et al.
Hα emission fromupstream

Shock Direction

SNR Cygnus Loop
(Katsuda, SJ+2016)

p Ha/ÎŁ)¥'(:*|ď;(:p */ĿňĂ,zÅ=ĺ;0okHα emission from upstream
H

no CR

Velocityp

H /shockĴ=âý
9":
H + p/e → H* + p/eemits Lyβp/e /shockµi=
Ç:

up

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocityp

Lyβ

H /shockĴ=âý
9":
H + p/e → H* + p/eemits Lyβp/e /shockµi=
Ç:

up

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

τLyβ ~ 1pup

Velocity

1s → 3p

Lyβ

H + p/e → H* + p/eemits Lyβp/e /shockµi=
Ç:

Lyβ

precursor

H /shockĴ=âý
9":

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Pol. Hαup

τLyβ ~ 1p

Velocity

1s → 3p → 2s
Lyβ

Lyβ

ÎŁHα . 
1. Raman µľ
Lyβ to Hα 

Hαprecursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Pol. HατLyβ ~ 1p

Velocity

1s → 3p → 2sLyβHαyÁz.a"&¿xÁz*
up

Lyβ

ÎŁHα . 
1. Raman µľ
Lyβ to Hα precursor

0&

down fully ionizedshock (z=0)

zPolarization angle for Lyβ→Hα
ShockÆ(½{ ,üàĪ¥*,:
Lyβ→Hαdownstream
Scattered HaHα emission from upstream
H

no CR

Pol. Hαup

τLyβ ~ 1p

Velocity

1s → 3p → 2s
Lyβ

Lyβ

ÎŁHα . 
1. Raman µľ
Lyβ to Hα 

Hαprecursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

VelocityPol. HατLyβ ~ 1pLyβ

H + e → H* + eÎŁHα . 
1. Raman µľ
Lyβ to Hα 2.
tĐ ;$
Ć¸-7:Ìč
ņ

unPol. Hαupprecursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocity

CR modified shock)|pwith CRup

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocity«Zw_·R=x (ÎŁ.H/p*ċ!éć©å=»&:

p
H+p→p+H
with CRup

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocityp

H /shockĴ=âý
9":
H + p/e → H* + p/eemits Lyβ

with CR

p/e /shockµi=
Ç:

Lyβ
up

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocity

A?DIyX(-/)Áz)Lyβ *e1'pwith CR
Pol. Hαup

precursor

Lyβdown fully ionizedshock (z=0)

zPolarization angle for Lyβ→Hα
ShockÆ(¤,üàĪ¥*,:
Lyβ→Hαdownstream
Scattered Ha
No scatteringin this direction.

Hα emission from upstream
H

Velocityno CR

This Lyβ photon is
not scatteredshockÆ(½{ →¿x¬
because of theshockÆ(¤Doppler→¿x¬
shift.

Ī¥Į§*Ī¥ć.¦d:
p
t'

→

t/

→

with CR
Pol. Hαup

precursor

Lyβdown fully ionizedshock (z=0)

zHα emission from upstream
Velocityno CR
pHLine.ŋÄĸã*atomic
population (rate-eq.)
This Lyβ photon isĪ¥Į§*Ī¥ć.¦d:=Ī¥*ċ¼-z→ 3(ĥ´not scatteredppt'
`T$¿x¬2¸V0:→ shockÆ(½{ →¿x¬
because of the
1. t/atomic population/Ī¥,(SJ &→ shockÆ(¤)z→¿x¬
Doppler shift.
Laming 19a). Stokes I/&5>*¶):
with CR

2. Lyβ /á-ĲĪ¥):*":
Lyβ
3. Stokes Q-í (ÎŁ.3pÑï/Lyβ
toPol. HαHα ._Zbµľ (i.e. radiative excitation)%
precursor(ğs":.
up -ĹĽ":*down fully ionizedzSee, SJ & Laming
19b
for details
shock
(z=0)

Cosmic ray modified shock polarimetry

Model set up for the shock

2727

Downloaded from https://academic

ShockSÌ*`)",¥)IK8KH;B7
Figure 3. Schematic illustration of the shock models considered in thisco%ÈT
0.1 Tpof2U¦
paper.
The vertical axis showsethe velocitieshydrogen atoms0.
and protons
measured in the shock rest frame. The horizontal axis is the z-axis. The
shock (or sub-shock for the modified shock case) is located at z = 0. The

Cosmic ray modified shock polarimetry

Model set up for the shock

2727

We solve 3 cases:
1. No precursor
Downloaded from https://academic

2. Ć¸tĐ 9, é, (electron heating precursor)
3. Ć¸tĐ 9, é9 (Cosmic-Ray Modified Shock)

ShockSÌ*`)",¥)IK8KH;B7
Figure 3. Schematic illustration of the shock models considered in thisco%ÈT
0.1 Tpof2U¦
paper.
The vertical axis showsethe velocitieshydrogen atoms0.
and protons
measured in the shock rest frame. The horizontal axis is the z-axis. The
shock (or sub-shock for the modified shock case) is located at z = 0. The

Line Transfer ModelLine transfer at SNR shock: 2s-state hydr

librium for the upstream plasma and fix theas T0 = 6000 K for simplicity.
Parameters:
Firstly, we describe the ionization structu
N be the number density of ’narrow’ hLet nH,jŌ ÌĔéć
Vshhave not experienced the charge-exchangeō ÎŁ.£Öıć
ntot,0be the number densityof ’broad’ hydrogencharge-exchange reactions. Obviously, we haŎ Ćŀć
fraction χ0
N +nBproton
nH,
.
Fig.
1b
is
schematic illustration ofH, jjŏ qŁ.ļ¸pć
Tdown
of particles. We consider
that the partially ioni
the far upstream region (z < zout ) and presumŐ qŁ.Ć¸pć
Te=βT
ionization equilibrium.
Hence,
we set the bo
down
N
N
B
nH,1s (z < 0) = nH,1s (zout ), nH,1s (z < 0) =np (zout ), where np is the number density of(z = 0), we assume the jump conditions as

Pure hydrogen plasma.
np (0) = 4np (zout ),ņËd/4f1)z;(:
Vsh
u
=
,
2

kBTp

=

Te

=

4
3 ′
µ mpVsh16
βTp

where Vsh is the shock velocity, kB is the Bo

2728

J. Shimoda and J. M. Laming

Results: Ionization Structure of H

Decelerated H

Results: Radiative vs. Collisional
ÎŁ.3pÑï/Lyβ to Hα ._Zbµľ (i.e. radiative excitation)%-Ĺ
Ľ":*":. →%$okResults:
Polarizationof Ha
Cosmicray modified
shock polarimetry2729

The sign of degree indicates the polarization angle (Stokes Q).

Results: Polarization of Ha

Cosmic ray modified shock polarimetry

Polarization degreet

Downloaded from https://academic.oup.com/mnras/article

p ¿xÁz%2729 2730

J. Shimoda and J. M. Laming

Surface brightness)ÇÅ¼0

Figure 6. The polarization degree of H α. The blue, red, and black lines Figure 7. The surface brightness profile of H α. The blue, red, and black
indicate the cases of no precursor (i), only an electron heating precursor lines indicate the cases of no precursor (i), only the electron heating(ii), and the electron heating precursor with decelerated protons (iii), precursor (ii), and the electron heating precursor with decelerated protons
respectively. The vertical thin lines at n tot, 0 z ≃ −27 × 1015 cm−2 and (iii), respectively. The vertical thin lines at ntot, 0 z ≃ −27 × 1015 cm−2 andn tot, 0 z ≃ 0 cm−2 indicate the locations of the precursor front and the shock ntot, 0 z ≃ 0 cm−2 indicate the locations of the precursor front and the shock
front, respectively. Positive values correspond to polarization along the z- front, respectively.
axis, while negative values correspond to polarization along the x-axis. Notethat these results includes all of atomic levels and processes unlike the result
is positive with a degree of ≃ 5 per cent. The degree of attenuation
shown in Fig. 2.

p ÎŁ/ĳ:p Ī¥ć Ö/è): (Sparks+ 15).

degree of H α, finally, is written as%# 1 (i) $ 3
9 2
N
dµ
I
−
µ
Q(s)
R
ν,µ
−1
16
16
ν
=

of Ly β photons radiated in the direction µ ≈ 1 depends on whether
the decelerated/non-decelerated atoms emit/absorb them, while thephotons radiated in the direction µ ≈ 0 are attenuated by the both
populations of atoms. Thus, the photons with µ ≈ 0 are efficiently
attenuated resulting in positive polarization.

The Astrophysical Journal Letters, 815:L9 (4pp), 2015 Decemb

Discovery of polarized Hα emission@ bright filament of SN 1006 (Sparks+ 15)
Figure 2. Upper, co-added spectra showing total intensity after basic reductions, and lower, same after subtraction of sky background showing strong Balmer
dominated shock spectrum. Lines visible are, right to left, Hα, Hβ, and Hγ.

Stokes I

Observed Area

Stokes Q

Stokes U

Ø Linear Polarization
Ø Polarization angle
perpendicular to the shock
Figure 1. Location of 22 arcsec polarization slit segment on the Hubbl
TelescopeØ
(HST)
image of the SN 1006
North
is up, east is toDegree2.0remnant.
± 0.4%
the SNR ﬁlament is in position angle ≈55°.

The Astrophysical Journal Letters, 815:L9 (4pp), 2015 Decemb

Discovery of polarized Hα emission@ bright filament of SN 1006 (Sparks+ 15)
Figure 2. Upper, co-added spectra showing total intensity after basic reductions, and lower, same after subtraction of sky background showing strong Balmer
dominated shock spectrum. Lines visible are, right to left, Hα, Hβ, and Hγ.

Observed Area

Stokes Iü è*ċĀć.Ī¥ć=Õÿ)$→Ŀň¶/7#ü Sparks+15.è/ ħz;(,.)
é:/1%ħ8,
Stokes Qü ÎŁqŁ= ħz
Stokes U$èĞĻØ Linear Polarization
Ø Polarization angle
perpendicular to the shock
Figure 1. Location of 22 arcsec polarization slit segment on the Hubbl
TelescopeØ
(HST)
image of the SN 1006
North
is up, east is toDegree2.0remnant.
± 0.4%
the SNR ﬁlament is in position angle ≈55°.

Polarization of Ha vs others

Cosmic ray modified shock polarimetry

Polarization degree

Downloaded
Downloaded from https://academic.oup.com/mnras/article

Hβ/Hα2729 2730

J. Shimoda and J. M. Laming

Surface brightness

Figure 6. The polarization degree of H α. The blue, red, and black lines Figure 7. The surface brightness profile of H α. The blue, red, and black
indicate the cases of no precursor (i), only an electron heating precursor lines indicate the cases of no precursor (i), only the electron heating(ii), and the electron heating precursor with decelerated protons (iii), precursor (ii), and the electron heating precursor with decelerated protons
respectively. The vertical thin lines at n tot, 0 z ≃ −27 × 1015 cm−2 and (iii), respectively. The vertical thin lines at ntot, 0 z ≃ −27 × 1015 cm−2 andn tot, 0 z ≃ 0 cm−2 indicate the locations of the precursor front and the shock ntot, 0 z ≃ 0 cm−2 indicate the locations of the precursor front and the shock
front, respectively. Positive values correspond to polarization along the z- front, respectively.
axis, while negative values correspond to polarization along the x-axis. Notethat these results includes all of atomic levels and processes unlike the result
is positive with a degree of ≃ 5 per cent. The degree of attenuation
shown in Fig. 2.

degree of H α, finally, is written as%# 1 (i) $ 3
9 2
N
dµ
I
−
µ
Q(s)
R
ν,µ
−1
16
16
ν
=

ë.èŃ*Ĝ~ (é =æ(:.
/Ī¥è%

of Ly β photons radiated in the direction µ ≈ 1 depends on whether
the decelerated/non-decelerated atoms emit/absorb them, while thephotons radiated in the direction µ ≈ 0 are attenuated by the both
populations of atoms. Thus, the photons with µ ≈ 0 are efficiently
attenuated resulting in positive polarization.

decelerated
atoms emerging from the charge-exchange! 3(np /ntot,0 )Vshhydrogen/CCX , we obtain
ldiff
#
$2
reaction with25 thedecelerated
protons,
Vsh /CCX ("Vsh ), where "Vsh
V
sh
−2 −1
cm s
D(E) ! 1.05 × 10 −1
4000
km s−1
≃
200
km
s
is
the
relative
velocity of collision particles. In
Cosmic ray modified shock polarimetry2729#degree $−1
Polarization% n we&−1show≃ 3(np /ntot, 0 )Vsh /CCX . If
thispaper,
caseof zpre (35)
"Vthe
tot,0
sh
moda and× J. M. Laming,
1 cm−3200 km s−1

Outcome

Downloaded from https://academic.oup.com/mnras/article-abstrac

the modification comes from CRs accelerated at the shock, thelength-scale of modification can be given by their d#$ldiff ∼ D(E)/Vsh , where D and E are the CR diffu
"V
CCX
sh
−8
3 −1
≈ 4.59 × 10 cm s.
and energy, respectively. Thus, from the observat
np
200 km s−1
MNRAS 489, 2723–2731 (2019) ldiff ! 3(np /ntot,0 )Vsh /CCX , we obtain
The diffusion coefficient for the interstellar medium, DISM (1 GeV)#
$2
V
∼ 1028 cm2 s−1 , satisfies this condition. When magnetic distursh
D(E) ! 1.05 × 1025 cm−2 s−1bances are excited around an SNR shock, we cannot currently derive4000 km s−1
the relevant diffusion coefficient. If we suppose the simplest case,#$−1
D(E) ≃ ξ B rg (E)c/3, where rg is the gyro radius of CR and ξ B % ntot,0 &−1"Vsh×,> 1 6.isThethepolarization
gyro factor
byand
theblack
energyFiguredegree characterizedof H α. The blue, red,lines spectrum of
1 cm−3200 km s−1
where we approximate

Downloaded from https://academic.oup.com/mnras/article

D(E)Y[¢.Ï­ío":BS`Fü Ī¥è8éńg.ûħ:

indicatethe casesof no precursorwe(i), obtain
only an electron
heating
precursor
magnetic
disturbances,a lowerbound
for the CR energy(ii), and the electron heating precursor with decelerated protons (iii), where we approximate
E responsible for the velocity modification ofrespectively. The vertical thin lines at n tot, 0 z ≃ −27 × 1015 cm−2 and#$$ precursor#
n tot, 0 z ≃ 0 cm−2 indicate the#locations of thefront and the$shock
2
"V
C
CX
sh
B
Vsh along the z1
front, respectively. Positive
values correspondto polarization≈ 4.59 × 10−8 cm3 s−1
.
×
E
!
33
TeV
−1
axis, while negative values
correspondtopolarization
along
the
x-axis.
Note
−1
n
200
km
s
p
ξB
100 µG
4000 km sthat these results includes all of atomic levels and processes unlike the resulttion
structure
blue, red,shown
in Fig.%2. of the hydrogen# atoms. The$−1
The diffusion coefficient for the interstellar medium
&
−1
"V
n
tot,0
sh
ate the casesof no precursor (i), only the electron×.
cm2 s−1 , satisfies this condition. When m∼ 1028(36)
−3
−1
1 cm
200 km süé =òj÷à.{µÖ<:→té]P`.×¢*,:

degreeH α, finally,is written
asandtheof electron
heating
precursor
with decelerated
bances are excited around an SNR shock, we cannot$ 3 the9number%# 1lines
ely.Note
The
solid
are
densityofhydrogen(i)2
thatat the diffusion coefficient. If we suppose theNdµ E is based on the coefficientIν,µ estimate− 16 µ ofQ(s)R −1thisthe relevant
16ν=
perienced a charge-exchange reaction in the precursor

/,
H

no CR

Velocityp

1. é. ¦Ė
;(2:

=Ď

2. G>J)r20

with CRup

precursor

down fully ionizedshock (z=0)

zSummarypj÷àīùÌĔSNR)Ã²-(:+ó9$
pkpc)jË(0DI=F)
§¬)¬ÀT)ÇÅ2¶¾'1+'.'pHα.Ī¥Į§=;0判別可能Ø Êa(-/\%,$CRMS2
identify 0 with ª3}l