ALFVÉN WAVE AMPLIFICATION AND SELF-CONTAINMENT OF COSMIC-RAYS ESCAPING FROM A SUPERNOVA REMNANT

Yutaka Fujita (Osaka U.)

Fuijta, Takahara, Ohira, & Iwasaki, 2011, MNRAS, in press (arXiv:1105.0683)

Tokyo

Osaka

200 km

Fukushima

Epicenter

Tsunami

Fukushima nuclear power plants

11 March 2011

CRISM 2011 Yutaka Fujita

Origin of Cosmic-Rays Expanding supernova remnants (SNRs)

are believed to be the main source of cosmic-rays (CRs) in the Galaxy CRs are accelerated at the shock of SNRs

Shock

SNR

CR particle

CRISM 2011 Yutaka Fujita

Gamma-Rays from Molecular Clouds around SNRs

Gamma-rays have been observed from molecular clouds around SNRs Molecular clouds may be illuminated by protons escaped

from the SNRs (pp-interaction) CR escape (e.g. Ptuskin & Zirakashvili 2005; Lee et al. 2008; Gabici et al.

2009; Reville et al. 2009 ; Caprioli et al. 2010; Ohira et al. 2010; Drury 2010; Casanova et al. 2010; Ellison & Bykov 2011)

Aharonian et al. (2008)

SNR

W 28

Gamma-ray emission from the SNR W28

MolecularClouds

Gamma-ray Map

Comparison with Observations

Typical diffusion coefficient for CRs in the Galaxy D(E ~ 1 TeV) ~ 1029 cm2 s-1

Diffusion time for E~1 TeV Lc

2/(6 D) ~ 100 yr Cloud size: Lc ~ 15 pc

Much smaller than the time since active CR acceleration stopped (~104 yr)

W 28 (Fujita et al. 2009)

Gamma-rays are mainly produced through pp-interaction and pion decay (blue)Cloud

SNR

CRISM 2011 Yutaka Fujita

Diffusion Coefficient Gamma-rays appear to have been

emitted for a long time (~104 yr) Diffusion coefficient in and/or around

clouds must be much smaller than the typical value in the Galaxy (~1%; Torres et al. 2008; Fujita et al. 2009) If not, gamma-rays should have

disappeared in 100 yrs. In the following, it is assumed that the

diffusion coefficient around clouds is small We consider protons as CRs

CRISM 2011 Yutaka Fujita

What makes the diffusion coefficient small? Generation of plasma waves by CRs

(e.g. Wentzel 1974) Waves scatter CRs Decrease of the diffusion coefficient

Wave amplification rate (Skilling 1975) Waves interact with CRs with E

f : CR distribution function

CRISM 2011 Yutaka Fujita

Simple Model Fujita, Ohira, & Takahara (2010) We put CRs at the shock of a model SNR

CR spectrum is given by a simple model We calculated the diffusion of the CRs

around the SNR and the amplification of Alfvén waves at the same time For diffusion, we performed Monte Carlo

simulations We treated the motion of CR particles as

random walks

CRISM 2011 Yutaka Fujita

Simple Model Distribution of CRs with

E = 1 TeV around an SNR Black: t = 103 yr Blue: t = 2.2103 yr Red: t = 104 yr

Marks: CRs Circles: Size of the SNR

Most CRs do not escape from the periphery of the SNR for at least 104 yrs Wave amplification delays

diffusion

CRISM 2011 Yutaka Fujita

This Study In Fujita et al. (2010), CR acceleration at the

shock and their diffusion into the interstellar space were treated separately.

However, both of the processes follow the same transport equation. They should be treated seamlessly.

In this study, we treat CR acceleration (very close to the shock front) and their propagation into the interstellar space (far away from the shock front) at the same time. CRISM 2011 Yutaka

Fujita

Equations We cannot assume a plane geometry

We assume spherical symmetry CR particles

: diffusion coefficientw : velocity of the background gasQ : source term

CRISM 2011 Yutaka Fujita

Equations Background gas

We solved these equations using the model of Berezhko et al. (1994)

CRISM 2011 Yutaka Fujita

Equations Wave amplification (Skilling 1975, Bell

1978)

: wave energy density Diffusion coefficient for CRs

0 : background gas density

B0 : background magnetic field CRISM 2011 Yutaka Fujita

Initial Conditions Fully ionized, uniform interstellar medium

(ISM) 0 = 710-27 g cm-3, T = 106 K, B0 = 3 G Neutral damping of the waves is not considered

Initial diffusion coefficient (initial wave energy) Away from the shock front

Typical value in the Galaxy Close to the shock front

Bohm diffusion It is required to accelerate particles to high energies

We interpolate the two diffusion coefficientsCRISM 2011 Yutaka Fujita

Results Amplification of

waves Waves grow even at r ~

2 Rs (for waves resonant with CRs with pc ~ 20 TeV)

However, the way they grow is somewhat different between pc = 1 TeV and 20 TeV : wave energy

Rs : shock radiust0 : end time of free expansion

Dashed: initial (t = 0.55 t0)Solid: t = 10 t0

Shin

Instep

Wave energy density

2 Rs

CRISM 2011 Yutaka Fujita

Results Evolution of particle

distribution CRs with pc ~ 1 TeV

escape into the “instep”, but those with pc ~ 20 TeV are confined in the “shin”

The difference affects the growth of the wave energy For 0.55t0 < t < t0

(t0 : end time of free expansion)

t

CRISM 2011 Yutaka Fujita

What makes the difference of the particle distribution?

It depends on the initial diffusion coefficient The initial diffusion coefficient away from

the shock front is the one in the interstellar space in the Galaxy

Wave energy density is ISM E /ISM E0.5

ISM is smaller for CRs with smaller E

Smaller energy CRs tend to go further away from the shock front if the distance is represented in the units of Bohm / Vs

They can escape into the “instep”

(Gabici et al. 2009)

CRISM 2011 Yutaka Fujita

Spectra of CRs away from the shock front Spectra at t = 10 t0 (t0: end time

of free expansion) If diffusion is always Bohm

everywhere (dotted), low energy CRs cannot go away from the shock front

If waves do not grow (dashed), low energy CRs can escape from the shock front

If waves grow (solid), the results are between the two

Wave growth significantly affects CR spectra away from the shock front

Solid: wave growthDotted: always BohmDashed: no wave growth (initial values are kept)

CRISM 2011 Yutaka Fujita

Summary We have investigated the escape of CR protons

accelerated at an SNR and their diffusion in the surrounding ISM. We solved a transport equation from the vicinity of the

shock front to the region far away from the front. We also considered the amplifications of Alfvén waves.

We found that the amplification of the waves reduces the diffusion coefficient on a scale of the SNR. The initial (=ISM) value of diffusion coefficient is

important. Gamma-ray emission form escaped CRs could be

significantly affected by wave amplification.CRISM 2011 Yutaka Fujita