Hα >%0 
4/?5-#; 3(Cf.) Shimoda & Laming 2019a, MNRAS, 485
Shimoda & Laming 2019b, MNRAS, 489

èćÂŋ1,2Collaborators:
J. M. Laming3; S. Katsuda4
1. Nagoya Univ.; 2. Tohoku Univ.; 3. Naval Research Lab.; 4. Saitama Univ.

ŃŌ³Kg]LA_, 2019, 12/26

SummaryppúäĭüÑĖSNR*È·.
);,÷:$
pSNR(0DI=F)ª¯)¯ÄT)ËÉ2ºÂ'1+'.
'pHα/Ĭªİ­>¢<1判別可能4/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9/Ĉ½0î¸); KgHfSfgį
É8: (e.g. Warren & Hughes 04).

Ha:
mĝ.ÑĖı*ª');
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4/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®;?!
ġÐą-CRzíKTdD
017eVĖSNR?!E>10ðīĽŐĮŔĕ

17eVĖSNR?!E>1017eVĖ®;?!
CR/Ĝ¹ľ«|.8:SNR)s·{Ä¥E<10-, p, He, …
¹è­@,
e0+ļ¦→§«i*'=T,PQ,HñB
Ç, 2012

=T,PQ,HñB Ç, 2012ÀýĠ100Uþ¯ĎCosmic-Ray Modified Shock (CRMS)
no CR

Velocitypúä- /
ŅðŉąÑĖ

p: protons inbackground plasma

CRW

up

down
shock (z=0)

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

CRYcN^ĖČ>Ŋ ÓŅ0Wµ<;

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

precursor

down
shock (z=0)

zCosmic-Ray Modified Shock (CRMS)
Velocityno CR

CRhŉc_h.Ŏ® ÓŅ/YcN^£í>Ì;shocká¿ 

pwith CRCR

up

precursor

down
shock (z=0)

zCosmic-Ray Modified Shock (CRMS)
no CR

VelocitypCRhŉc_h.Ŏ® ÓŅ/YcN^£í>Ì;shocká¿ p

zĒ 0photoionization-,*5
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 thisaresimulationĦĩĈńYcN^ù>Ćĕ";SNRÑĖ/
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 Ä´<; £í 0 ¶ā§<>Æī";ĠĿ;

SNR jÏkpc (0DI=F)ĦĩĈńYcN^ù>Ćĕ";SNRÑĖ/)¯ÄT2ºÂ!-hybrid simulation (Ohira16)

Challenging!

Supernova Remnant (SNR)
X-ray:~TeV9/Ĉ½0î¸); KgHfSfgį
É8: (e.g. Warren & Hughes 04).

Ha:
mĝ.ÑĖı*ª');
From Chandra archival image(e.g. Hovey+15).
SNR 0509-67.5 (Chandra & HST)
Ha0ÑĖÍĮ/YcN^Öó>Ĝs
Blue: 1.5 – 7.0 keV)ª;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LEE ET AL.
Hα emission fromupstream

Hα Surface Brightness

Tycho’s SNR (Lee+2010)precursor

postshockPhotoionization?

Shock Direction

The Astrophysical Journal Letters, 715:L146–L149, 2010 June 1

doi:10.1088/2041-8205/715/2/L146⃝
C 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

RESOLVED SHOCK STRUCTURE OF THE BALMER-DOMINATED FILAMENTS IN TYCHO’S SUPERNOVAREMNANT: COSMIC-RAY PRECURSOR?
Jae-Joon Lee1 , John C. Raymond2 , Sangwook Park1 , William P. Blair3 , Parviz Ghavamian4 , P. F. Winkler5 ,and Kelly Korreck2
1 Astronomy and Astrophysics Department, Pennsylvania State University, University Park, PA 16802, USA; lee@astro.psu.edu
2 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

3 Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
4 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
5 Department of Physics, Middlebury College, Middlebury, VT 05753, USA−8−6 Received 2010
−4February 24; accepted−2 2010 April 28;
0 published 20102May 1246Distancefrom the peak [′′ ]ABSTRACTWe report on the results from Hα imaging observations of the eastern limb of Tycho’s supernova remnant (SN1572)

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+2016)

Katsuda et al.
Hα emission fromupstream

Shock Direction
The Astrophysical Journal Letters, 819:L32 (6pp), 2016 March 10

SNR Cygnus Loop
(Katsuda+2016)
doi:10.3847/2041-8205/819/2/L32© 2016. The American Astronomical Society. All rights reserved.

SPATIALLY RESOLVED SPECTROSCOPY OF A BALMER-DOMINATED SHOCK IN THE CYGNUS LOOP:
AN EXTREMELY THIN COSMIC-RAY PRECURSOR?
Satoru Katsuda1, Keiichi Maeda2,3, Yutaka Ohira4, Yoichi Yatsu5, Koji Mori6, Wako Aoki7, Kumiko Morihana8,
John C. Raymond9, Parviz Ghavamian10, Jae-Joon Lee11, Jiro Shimoda4, and Ryo Yamazaki4
1

Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), 3-1-1 Yoshinodai,
Chuo, Sagamihara, Kanagawa 252-5210, Japan; katsuda@astro.isas.jaxa.jp
2
Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
3
Kavli Institute for the Physics and Mathematics of the universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
4
Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara 252-5258, Japan
5
Department of Physics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro, Tokyo 152-8551, Japan
6
Department of Applied Physics and Electronic Engineering, Faculty of Engineering, University of Miyazaki,
1-1 Gakuen Kibanadai-Nishi, Miyazaki 889-2192, Japan
7
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
8
Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo, 407-2 Nichigaichi, Sayo-cho, Sayo, Hyogo 679-5313, Japan
9
Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
10
Department of Physics, Astronomy and Geosciences, Towson University, Towson, MD 21252, USA
11
Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea
Received 2016 January 28; accepted 2016 February 20; published 2016 March 7

ABSTRACTKatsuda et al.
Hα emission fromupstream

Shock Direction
The Astrophysical Journal Letters, 819:L32 (6pp), 2016 March 10

SNR Cygnus Loop
(Katsuda+2016)
doi:10.3847/2041-8205/819/2/L32© 2016. The American Astronomical Society. All rights reserved.

SPATIALLY RESOLVED SPECTROSCOPY OF A BALMER-DOMINATED SHOCK IN THE CYGNUS LOOP:
AN EXTREMELY THIN COSMIC-RAY PRECURSOR?

p Ha0ÓŅ*ª');+đ<);
p CRË-Ŀo0 Ō()-£í ;+ĩ<1CR+¦;
p Hα/ŃŌą-Ê0
Satoru Katsuda1, Keiichi Maeda2,3, Yutaka Ohira4, Yoichi Yatsu5, Koji Mori6, Wako Aoki7, Kumiko Morihana8,
John C. Raymond9, Parviz Ghavamian10, Jae-Joon Lee11, Jiro Shimoda4, and Ryo Yamazaki4
1

Institute of Space and Astronautical Science (ISAS), Japan Aerospace Exploration Agency (JAXA), 3-1-1 Yoshinodai,
Chuo, Sagamihara, Kanagawa 252-5210, Japan; katsuda@astro.isas.jaxa.jp
2
Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
3
Kavli Institute for the Physics and Mathematics of the universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan
4
Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara 252-5258, Japan
5
Department of Physics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro, Tokyo 152-8551, Japan
6
Department of Applied Physics and Electronic Engineering, Faculty of Engineering, University of Miyazaki,
1-1 Gakuen Kibanadai-Nishi, Miyazaki 889-2192, Japan
7
National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
8
Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo, 407-2 Nichigaichi, Sayo-cho, Sayo, Hyogo 679-5313, Japan
9
Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
10
Department of Physics, Astronomy and Geosciences, Towson University, Towson, MD 21252, USA
11
Korea Astronomy and Space Science Institute, Daejeon 305-348, Korea
Received 2016 January 28; accepted 2016 February 20; published 2016 March 7

ABSTRACTHα emission from upstream
H

no CR

Velocityp

H 0shockĶ>æĀ
:";
H + p/e → H* + p/eemits Lyβp/e 0shock»n>
Ì;

up

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocityp

Lyβ

H 0shockĶ>æĀ
:";
H + p/e → H* + p/eemits Lyβp/e 0shock»n>
Ì;

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 0shock»n>
Ì;

Lyβ

precursor

H 0shockĶ>æĀ
:";

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Pol. Hαup

τLyβ ~ 1p

Velocity

1s → 3p → 2s
Lyβ

Lyβ

ÓŅHα /¤
1. Raman »ł
Lyβ to Hα 

Hαprecursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Pol. HατLyβ ~ 1p

Velocity

1s → 3p → 2sLyβHαyÅz.a"&ÃxÅz*
up

Lyβ

ÓŅHα /¤
1. Raman »ł
Lyβ to Hα precursor

0&

down fully ionizedshock (z=0)

zPolarization angle for Lyβ→Hα
ShockÊ(Á| ÿäĬª+-;
Lyβ→Hαdownstream
Scattered HaHα emission from upstream
H

no CR

Pol. Hαup

τLyβ ~ 1p

Velocity

1s → 3p → 2s
Lyβ

Lyβ

ÓŅHα /¤
1. Raman »ł
Lyβ to Hα 

Hαprecursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

VelocityPol. HατLyβ ~ 1pLyβ

H + e → H* + eÓŅHα /¤
1. Raman »ł
Lyβ to Hα 
2.
zĒ <$
Ĉ½.8;Ñď
Ŋ

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>~ )ÓŅ/H
0p+č!íĉ¯é>À&;

p
H+p→p+H
with CRup

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocityp

H 0shockĶ>æĀ
:";
H + p/e → H* + p/eemits Lyβ

with CRp/e 0shock»n>
Ì;

Lyβ
up

precursor

down fully ionizedshock (z=0)

zHα emission from upstream
H

no CR

Velocity

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

precursor

Lyβdown fully ionizedshock (z=0)

zPolarization angle for Lyβ→Hα
ShockÊ(§-ÿäĬª+-;
Lyβ→Hαdownstream
Scattered Ha
No scatteringin this direction.

Hα emission from upstream
H

Velocityno CR

This Lyβ photon is
not scatteredshockÊ(Á| →Ãx¯
because of theshockÊ(§Doppler→Ãx¯
shift.

Ĭªİ­+Ĭªĉ/©d:
p
t'

→

t/

→

with CR
Pol. Hαup

precursor

Lyβdown fully ionizedshock (z=0)

zHα emission from upstream
Velocityno CR
pHLine/ŏÉĺç+atomic
population (rate-eq.)
This Lyβ photon isĬªİ­+Ĭªĉ/©d:>Ĭª+čÁ.→ 4)Ĩº
not scatteredppt'`¡T$Ãx¯2¼V0:→ shockÊ(Á| →Ãx¯
because of the
1. t/atomic population0Ĭª(SJ &→ shockÊ(§*→Ãx¯
Doppler shift.
Laming 19a). Stokes I0&6?+¼*;
with CR

2. Lyβ 0å.ĴĬª*;+";
Lyβ
3. Stokes Q.ñ )ÓŅ/3pÖó0Lyβ
toPol. HαHα /c^g»ł (i.e. radiative excitation)%
precursor)Ģy";.
up .ĻŁ";+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

ShockSÐ*`¡)",¨)IK8KH;B7
Figure 3. Schematic illustration of the shock models considered in thisco%Ì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. Ĉ½zĒ :, £í- (electron heating precursor)
3. Ĉ½zĒ :, £í: (Cosmic-Ray Modified Shock)

ShockSÐ*`¡)",¨)IK8KH;B7
Figure 3. Schematic illustration of the shock models considered in thisco%Ì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,jŐ ÑĖíĉ
Vshhave not experienced the charge-exchangeő ÓŅ/¨Ûĳĉ
ntot,0be the number densityof ’broad’ hydrogencharge-exchange reactions. Obviously, we haŒ Ĉńĉ
fraction χ0
N +nBproton
nH,
.
Fig.
1b
is
schematic illustration ofH, jjœ wŅ/ŀ½vĉ
Tdown
of particles. We consider
that the partially ioni
the far upstream region (z < zout ) and presumŔ wŅ/Ĉ½vĉ
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 ),ŊÐi04f2*<);
Vsh
u
=
,
2

(SJ & Laming 19a)k T

B p

=

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
ÓŅ/3pÖó0Lyβ to Hα /c^g»ł (i.e. radiative excitation)%.Ļ
Ł";+";. →%$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 ÃxÅz%2729 2730

J. Shimoda and J. M. Laming

Surface brightness)ËÉÀ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 ÓŅ0ĵ;

p Ĭªĉ Û0ì*; (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 ì+čăĉ/Ĭªĉ>ÚĂ*$→ŃŌ¼08#ü Sparks+15/ì0ĩ<)-/*£í;02%ĩ9-
Stokes Qü ÓŅwŅ>ĩ
Stokes U$ìĠĿ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
=

ï/ìŇ+Ğ )£í >ê);/0Ĭªì%

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.

SummaryppúäĭüÑĖSNR*È·.
);,÷:$
pSNR(0DI=F)ª¯)¯ÄT)ËÉ2ºÂ'1+'.
'pHα/Ĭªİ­>¢<1判別可能Ø Îa(-/\% ,$CRMS2
identify 0 with ­3~l