Theoriginofthecosmic-rayknee

YutakaOhira,ShotaKisaka,RyoYamazaki(AoyamaGakuin University)

Outline1) Problem for the cosmic-ray knee2) Pulsar wind nebulae (PWNe) inside an SNR3) Particle acceleration by the PWN-SNR system4) Monte Carlo simulation5) Summary

Cosmic-ray spectrum

Ohira et al., 2012

Eknee ~3 PeV,

Energy

Energyflux

1particle/m2/sec

Knee1particle/m2/yr

Cosmic-ray spectrum

EFe,knee =ZEp,knee~100PeV,

Energy

Energyflux

1particle/m2/sec

Knee1particle/m2/yr

Fe

C,N,O

P

Ep,knee ~3 PeV,

ProtonandHeliumspectra(E<0.2PeV)

Ahn etal.ApJL 2010

CRHeliumdominatesat~0.1PeV!?

CREAM NUCLEON

Atkin etal.arXiv:1702.02352

ThespectrumofCRHeisharderthanthatofprotons.

P+He spectrum(E~1PeV)Montini etal.arXiv:1608.01251

ARGO-YBJ

Thetotalspectrumbreaksat~3PeV.Thep+He spectrumbreaksat~1PeV.

IfCRHedominatesoverCRpat1PeV,theprotonspectrumbreaksat0.5PeV(<3PeV).

P+He spectrum(E>1PeV)

D.KangarXiv:1702.08743

KASKADE+KASKADE-Grande

HeavyCRsdominateovertheCRp+He above10PeV.

TheP+He spectrumdoesnotfalloffexponentially.

TotalCRspectrum(IceTop)

Rawlinsetal.2016Breaksat~3PeVand~100PeV

Dipstructureat10PeV

TotalCRspectrum(Tale)

FromslideofTareq AbuZayy

Breaksat~3PeVand~100PeVDipstructureat10PeV

TotalCRspectrum(Tunka-HiSCORE,Tunka-133)

Breaksat~3PeVand~100PeV

Dipstructureat10PeV Ironsdonotdominateat100PeV.

LOFAR(E=100PeV-300PeV)

thetotalfractionofp+He at100PeVisintherange[0.38,0.98]ata99%confidencelevel,withabest-fitvalueof0.8.

Ironsdonotdominateat100PeV.

Buitink etal.Nature2016

a=(<Xproton>- Xmax )/(<Xproton>- Xiron )ThecumulativeXmax distributionshowsthat

SummaryofCRobservations

CRHedominatesat~0.1PeV.(CREAM,NUCLEON)

Thep+He spectrumbreaksat~1PeV<3PeV.(ARGO-YBG)

Therearesomeunexpectedresultsandtensions.

Thep+He spectrumdoesnotfalloffexponentiallyabove3PeV.(KASKADE+KASKADE-Grande)

HeavyCRsdominateovertheCRp+He at~100PeV.(KASKADE+KASKADE-Grande)

ThetotalCRspectrumbreaksat3PeVand100PeV,anddipsat10PeV.(IceTop,TALE,Tunka-133)

CRp+He dominatesoverheavyCRsat~100PeV.(LOFAR)

Energy spectrum of total cosmic rays

EFe,knee =ZEp,knee~100PeV,

Energy

Energyflux

1particle/m2/sec

Knee1particle/m2/yr

Fe

C,N,O

P

Ep,knee ~3 PeV,

Scholer

Axford1977,Krymsky1977,Blandford&Ostriker1978,Bell1978

Diffusive Shock Acceleration(DSA)

CRs are scattered by MHD waves.

CRs excite the MHD waves.

dN/dE∝ E-s s = = 2 u1/u2 + 2u1/u2 - 1

Emax ofDSA

c ,p u Δp =2 p

Forashock,cu

3c4(u1- u2)

Momentumchangebyparticlescattering,Δp

Δp = p = p

Afterscattering,

u1 u2shock Dp peronecycleis

Timeofonecycle,Δt =(lmfp,1/u1 +lmfp,2/u2)~Tgyro,1(c/u1)+Tgyro,2(c/u2)

tacc =pΔt/Δp ~Tgyro,1(c/ush)2 +4Tgyro,2(c/ush)2 (Krymsky etal.1979,Drury1983)

tacc =tSedov ~200yr,andTgyro,1 >>Tgyro,2à Emax ~0.03PeV Bup,1µG(lmfp/rg)(ush/3000km/s)2

ToaccelerateCRsto3PeV,B>~100µGintheupstreamregion,butnosimulationsdemonstratethesufficientmagneticfieldamplification.

cu1

RXJ1713.7-3946

Ifg-raysareduetoIC,wecanmeasureBdown.

Ifg-raysareduetothepiondecay,wecanestimateEp,max.Eg,max ~0.01PeVà Ep,max ~0.1PeV

nFnsyn/nFnIC ~16à Bdown ~12µG

Abdalla+2017

Ohira&Yamazaki17

SN1006

Ifg-raysareduetoIC,wecanmeasureBdown.

Ifg-raysareduetothepiondecay,wecanestimateEp,max.Eg,max ~0.008PeVà Ep,max ~0.08PeV

nFnsyn/nFnIC ~100à Bdown ~30µG

Xing+2016Acero+2010

RCW86

Ifg-raysareduetoIC,wecanmeasureBdown.

Ifg-raysareduetothepiondecay,wecanestimateEp,max.Eg,max ~0.0035PeVà Ep,max ~0.035PeV

nFnsyn/nFnIC ~50à Bdown ~22µG

Abramowski+2016

RXJ0852.0-4622(VelaJunior)

Ifg-raysareduetoIC,wecanmeasureBdown.

Ifg-raysareduetothepiondecay,wecanestimateEp,max.Eg,max ~0.0055PeVà Ep,max ~0.055PeV

nFnsyn/nFnIC ~4à Bdown ~7µG

Abdalla+2016

Cas A

Eg,c =3.5TeV

Ep,c =12TeV

UCR ~1050 erg

Ahnen etal.2017

dN/dE∝E-2.4

PulsarwindnebulaeinsideSNRsWatters&Romani,ApJ,2012

B0 =1012.66 G,Lsd,0 ~1038 erg/s,Erot,0 ~1049 erg,Tsd ~3kyràPulsarbirthrate~1per59yr,Initialspinperiod,P0 ~50ms

Mostcore-collapseSNRshavepulsarwindnebulae(PWNe).

Fermiobservedmanygammaraypulsars.

ThePWNregionhasstrongmagneticfields,B>~100µG

ShockedregionsofSNRsarealsoexpectedtohavestrongmagneticfield,B>~100µG

TheshockedregionofSNRsandPWNregionreaccelerateCRstothekneeenergyfrom0.1PeV.ThePWN-SNRsystemcouldbetheoriginofheavyCRnuclei.

Inthistalk,weproposethefollowingtwothings.

0

3

6

9

12

15

0 2000 4000 6000

Rad

ius

( pc

)

Time ( yr )

tc tend

PWN

Shocked SNR

RSNR,fs

RSNR,rs

RPWN

EvolutionofaPWNinsidetheSNR

Mej =3M◉ ,ESN =1051 erg,nISM =0.1cm-3 ,Lsd =3x1038 erg/s

vanderSwaluw etal.(2001)

McKee&Trulove (1995)RSNR,fs

RSNR,rs

RPWN

RSNR,fs andRSNR,rs

RPWN (t<tc )

RPWN (t>tc )

VPWN =- VPWN(tc)/2

rej andrISM =uniform,andLsd =constant.

tc

0

3

6

9

12

15

0 2000 4000 6000

Radiu

s (

pc

)

Time ( yr )

tc tend

PWN

Shocked SNR

RSNR,fs

RSNR,rs

RPWN

Particleacceleration(t<tc )

BeforethePWNinteractswiththereverseshockoftheSNR(t<tc ), thePWN-SNRsystemcanbeinterpretedastwowallsapproachingeachother.

Theenergygainineachcycleis∆E/E∼ ∆V/c~(VSNR,shocked −VPWN)/c.Thetimescaleineachcycleis∆t∼ ∆R/c~(RSNR,rs −RPWN)/c.Theaccelerationtimeistacc =∆t(E/∆E)∼ ∆R/∆v~tcu .

à ThetwowallscanaccelerateCRs.

à E~2E0

RSNR,fs

RPWN

RSNR,rs

0

3

6

9

12

15

0 2000 4000 6000

Radiu

s (

pc

)

Time ( yr )

tc tend

PWN

Shocked SNR

RSNR,fs

RSNR,rs

RPWN

Particleacceleration(t>tc )AfterthePWNinteractswiththereverseshock,thePWNiscompressedbytheSNR.

à E(tend)/E(tc)=RPWN(tc)/RPWN(tend)=5

Emax ~ 1 PeVEInj

0.1 PeV

!

"##

$

%&&RPWN(tc) / RPWN(tend)

5

!

"#

$

%&

dE/dt =-(E/3)divVPWN,in =- (E/RPWN )(dRPWN /dt )

àParticlesinsidethePWNareacceleratedbythecompression.

RSNR,fs

RPWN

RSNR,rs

SizeofPWNe afterthecompression

ThesizeofPWNe isdeterminedbythepressurebalance.

pSNR =pPWN à ESN/RSNR,fs3 =hErot/RPWN

3

ESN =1051 erg,Etot =1049 erg,h =0.1à RPWN(tend)=0.1RSNR,fs(tend)

RSNR,fs(tend)~13pc,RPWN(tc)~6pcà RPWN(tc)/RPWN(tend)~5

Synchrotroncooling

Monte Carlo Simulation

Simulation particles are isotropically and elastically scattered in the local fluid frame.

Velocity fields

ParticlesE0 = 0.1 PeV, tsc= Wc

-1 ∝ E / B (Bohm scattering),

VPWN,in (r,t)=-(VPWN(tc)/2)(r/RPWN(t))

VPWN =dRPWN/dt (r<RPWN)

VSNR,shocked =(RSNR,rs/t- VSNR,rs)/4- VSNR,rs (RSNR,rs <r<RSNR,fs )Fort<tc ,thevelocityfieldisassumedtobeuniform.

Fort>tc ,thevelocityfieldisassumedtobeasfollows.

At tinj = 3 kyr, simulation particles are isotropically injected on the reverse shock sphere, r = RSNR,rs.

B=0 in the freely expanding ejecta, B=300µG in other regions.

10-5

10-4

10-3

10-2

10-1

100

0.1 1

E2 d

N /

dE

E ( PeV )

Simulation result (Energy spectra)Black:RSNR,rs <r<RSNR,fs att=tc

Red:r<RPWNatt=tend

Einj =0.1PeV

Blue:r<RSNR,rs =RPWN att=tc

SummaryTheobservedCRspectrumbreaksatabout1PeV.

Sincetheupstreammagneticfieldamplificationisnotsufficient,asimpleSNRsystemcannotaccelerateprotonsto1PeV.

ReverseshocksofSNRsareexpectedtobetheoriginofheavyCRnuclei,butparticlesacceleratedbythereverseshocklosetheirenergybyadiabaticloss.à ThemaximumrigidityofheavyCRnuclei<1PV?.

Therecentobservationofgamma-raypulsarssuggestthatmostcore-collapseSNRshavepulsarswiththespindown luminosityof1038 erg/s.

ThePWN-SNRsystemcanreaccelerate0.1PeVCRsto1PeV.

ThePWN-SNRsystemisPeVatrons andthesourceofheavyCRnuclei.

Parameterdependence

10-5

10-4

10-3

10-2

10-1

0.1 1

E2 d

N /

dE

E ( PeV )

EvolutionofaPWN-SNRsystemForrej andrISM =uniform,

ForLsd =constant,

( t<tc )

McKee&Truelove(1995)

vanderSwaluw etal.(2001)

WeassumeVPWN (t,r)=- (VPWN(tc)/2)(r/RPWN ) (t>tc )