supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (bell...
TRANSCRIPT
![Page 1: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/1.jpg)
Supernova remnantsas cosmic ray laboratories
Tony BellUniversity of Oxford
SN1006: A supernova remnant 7,000 light years from EarthX-ray (blue): NASA/CXC/Rutgers/G.Cassam-Chenai, J.Hughes et al; Radio (red): NRAO/AUI/GBT/VLA/Dyer, Maddalena & Cornwell;Optical (yellow/orange): Middlebury College/F.Winkler. NOAO/AURA/NSF/CTIO Schmidt & DSS
1
![Page 2: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/2.jpg)
gr
!
1) Spatial confinement Larmor radius less than size of accelerating plasma
"# =%&'
CR energy in eV ( < *+,
2) All acceleration comes from electric field - = −/×+
velocity of thermal plasma
Maximum energy gain: maximum electric field!× ( < /+,
- = −/×+
Physics behind Hillas energy
CR
Please note: I use T for CR energy (E is electric field)
2
![Page 3: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/3.jpg)
To get to maximum (Hillas) energy: optimally correlated
Where is the electric field in shock acceleration?
shoc
kupstream
Scattering on random magnetic field
downstream
!" = −%"×' !( = −%(×'%" %(
Random E due to turbulent B
+,+- = v. 0 ⇒ + ,
+- = 2. v×3CR energy gain:
v , 3
3
![Page 4: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/4.jpg)
Hillas: necessary but not sufficient
The case of diffusive shock acceleration
shoc
kupstream!"
diffusion coefficient#"=
downstream!$
diffusion coefficient#$=
Lagage & Cesarsky (1983): %&''() = 4 #"!"$
+ #$!$$
%&''() =-!" #./01 = 234
3 !$ =!"4
#$!$$
≪ #"!"$
(debatable)
7 = 34
898:;<=
>`9!"@- equivalent to 7 = 1
4BCD
>`9!"@-
Assuming that
Maximum CR energy is
To reach Hillas energy: need scattering length equal to Larmor radius B~CD
This is Bohm diffusion
CD
Bohm diffusion
4
![Page 5: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/5.jpg)
A disordered field needs some structure on Larmor scaleof every particle being accelerated (GeV to PeV/EeV).
OK for shocks (Fourier components of delta function)OK for broad spectrum turbulenceProblematic for magnetic reconnection, shear acceleration
Hillas: necessary but not sufficient
General considerations: getting to Hillas energy
! = −$×& depends on frame
CR to need to move relative to u= 0 frame
) = *+,CR to need to move distance L parallel to −$×& electric field
) = ∫ v. ! dl
In disordered field need correlation between v and E.Makes Fermi1 better than Fermi2 (usually)
) = ∫ v. ! dl
Needs Plasma Physics! 5
![Page 6: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/6.jpg)
Bohm diffusion indicated by synchrotron spectrum turnover
Cas A, Stage et al 2006
(ℎ#)%&= 3×10, -.
/ 012
34
RXJ1737-3946 Uchiyama et al 2007Cut-off frequencies
Observed cut-off requires close to Bohm diffusion
Turnover frequency is
6
![Page 7: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/7.jpg)
Need amplified magnetic field
Magnetic field amplification increases to near equipartition (100s µG in SNR)
PCRCR current in rest frame of upstream (moving) plasma
forces drive non-resonant instability (Bell 2004,2005)
produces turbulence
amplifies magnetic field
$%&
$%&×(
)
shoc
k
7
![Page 8: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/8.jpg)
j x Bj x B
B
Cosmic ray Electric current
Matthews et al (2017)
Magnetic field amplification
Instability grows until1) Tension in field lines opposes jxB2) CR get tied to field lines: Loop size = rg
Automatically saturates with
and
&~()
3
0
2
vcv~ scrssat UB r
µµ
8
![Page 9: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/9.jpg)
Historical shell supernova remnants(interpretation: Vink & Laming, 2003; Völk, Berezhko, Ksenofontov, 2005)
Kepler 1604ADTycho 1572AD
SN1006 Cas A 1680ADChandra observations
NASA/CXC/NCSU/S.Reynolds et al.
NASA/CXC/Rutgers/J.Warren & J.Hughes et al.
NASA/CXC/MIT/UMass Amherst/M.D.Stage et al.
NASA/CXC/Rutgers/J.Hughes et al.
9
![Page 10: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/10.jpg)
B2/(8pr) (cgs)
velocity
Magnetic field grows to near equipartition: limited by magnetic tension
Data for RCW86, SN1006, Tycho, Kepler, Cas A, SN1993J
Fit to obs (Vink): Gcmskm10
7002/1
3
2/3
14 µ÷øö
çèæ
÷÷ø
öççè
æ» --
enuB
G1.0cmskm10
4002/12/1
3
2/3
14 µh÷øö
çèæ
÷øö
çèæ
÷÷ø
öççè
æ» --
enuBTheory:
Vink (2008)
See alsoVölk, Berezhko, Ksenofontov, 2005
10
![Page 11: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/11.jpg)
Difficulty: need time to amplify magnetic field
PCR
L
%&
Need about 5 e-foldings in time
TeV200 pc27
2/101.0 RunE eh»Max CR energy
radius in parsecin 10,000 km s-1in cm-3
Zirakashvili & Ptuskin (2008), Bell et al (2013)
acceleration efficiencyFor SNR parameters
⁄( %&
≈ *. ,×./0012 343567
11
![Page 12: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/12.jpg)
Non-resonant instability is best can do
! = #$%&
Invert #'( = %$& !
')
Compare with * = %×$& ,)
Instability growth rate
1) Makes optimal use of jxB force
2) Grows rapidly on small scale in initially weak B
Matthews et al (2017) 12
![Page 13: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/13.jpg)
Difficulty with perpendicular shocks (applies to high velocity shocks)
B into screen
shock
BuE shock ´-=
CR drift velocity
2vBBE
drift´
=
CR gain energy bydrifting in E field
Without scattering,All CR get same energy gainNo high energy tail
13
![Page 14: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/14.jpg)
CR acceleration at perpendicular shockJokipii 1982,1987
Strongscattering
Weakscattering
Noscattering
Not to scale
Currents located close to shockNeed very rapid magnetic field amplification
Previous discussions:Lemoine & Pelettier (2010), Sironi, Spitkovsky & Arons (2013), Reville & Bell (2014) 14
![Page 15: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/15.jpg)
Observed radio spectral index v. mean expansion velocity(Klara Schure, following Glushak 1985)
ushock = c/3ushock = c/30
ushock = c/300
Expected spectral index
15
![Page 16: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/16.jpg)
Fractional CR energy gain
Fraction of cosmic rays lost
How particles are accelerated: diffusive shock acceleration
Shock velocity: ushock
Cosmic ray density at shock: n
High velocityplasma
Low velocityplasma
B2
B1
shock
Cosmic Ray
At each shock crossing
Krimskii 1977, Axford et al 1977,Bell 1978, Blandford & Ostriker 1978
∆"" = $%&'()
*∆++ = −$%&'()*
Differential energy spectrum
-(") ∝ "12 16
![Page 17: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/17.jpg)
Fractional CR energy gain
Fraction of cosmic rays lost
How particles are accelerated: diffusive shock acceleration
Shock velocity: ushock
Cosmic ray density at shock: n
Differential energy spectrum
High velocityplasma
Low velocityplasma
B2
B1
shock
Cosmic Ray
At each shock crossing
Krimskii 1977, Axford et al 1977,Bell 1978, Blandford & Ostriker 1978
∆"" = $%&'()
* 1 − -./0-12∆33 = −$%&'()*
4(") ∝ "8(98:;<=/:?@)/(A8:;<=/:?@ )
Now add in energy loss toMagnetic field amplification
17
![Page 18: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/18.jpg)
Observed radio spectral index v. mean expansion velocity
ushock = c/3ushock = c/30
ushock = c/300
!"#$/!&'
0.5
0.38
0.29
0.0
((*) ∝ *-(.-/012//34)/(5-/012//34 )
18
![Page 19: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/19.jpg)
One thing I have not mentioned – non-linear feedback
Reynolds & Ellison (1992)
Comment: If the spectrum is steepened by other factors, non-linear curvature confined to low energies/frequencies
(It has to be there, eg Drury & Völk 1981)
From conclusions of Reynolds & Ellison
19
![Page 20: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/20.jpg)
General class ofinteractions producing magnetic field
Three species
• Energetic particles: cosmic rays, fast/hot electrons in laser-plasmas• Thermal electrons• Slowly moving thermal ions
Interacting through
• Electric field (to maintain neutrality)• Collisions (Coulomb, charge-exchange…)• Large scale magnetic field (‘frozen-in’)• (Sub-) Larmor-scale magnetic field (scattering, deflection)
Basic process
• Mutual motion (advection/diffusion/drift)• Electric field secures neutrality • Curl(E) generates B
20
![Page 21: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/21.jpg)
Borghesi et al 1998
Magnetic field generated by Biermann batteryFavoured source of primordial field
! = #$%&
' = ()*
⇒ ,-,. =
#%×#0%
21
![Page 22: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/22.jpg)
Weibel instability at shocks
Chang, Spitkovsky & Arons (2008)
Opposing electron beams: 1) Perturbed beam density 2) Magnetic field 3) Focus currents
Ramakrishna et al (2009)
Kinetic instability on scale c/wp 22
![Page 23: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/23.jpg)
Energetic electron beam focussed by magnetic field
Davies et al, PRE 59, 61032 (1999)
!"!# = %×(()*+,-)
)/+01/2 = − )*+,-
resistivity
23
![Page 24: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/24.jpg)
Fast Ignition
laser laser
Cold compressed DT Drill hole with laser
Heat with very high power laser
Cone targetKodama et al 2001
As first proposed by Tabak et al (1994)
24
![Page 25: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/25.jpg)
Experiment to test non-resonant instability(next summer)
Builds on series of experiments led by Gianluca Gregori
25
![Page 26: Supernova remnants as cosmic ray laboratories · forces drive non-resonant instability (Bell 2004,2005) produces turbulence amplifies magnetic field $%& $%&×() k 7. jxB jxB B Cosmic](https://reader035.vdocuments.mx/reader035/viewer/2022062311/605dcb6381a30b49021f76d0/html5/thumbnails/26.jpg)
Experiment next summer on OMEGA laserExperimental lead: Hui Chen (Livermore), Gianluca Gregori (Oxford)
26