32nd Rironkon Symposium @NAOJ
December 26, 2019⼭崎 翔太郎 (東⼤理・天⽂)
磁気共鳴散乱で解き明かす
マグネターフレアの放射機構
with Y. Lyubarski (Ben-Gurion U.),
J. Granot (OUI) & E. Gogus (Sabanci U.)

Introduction

MAGNETAR = HIGHLY MAGNETISED NEUTRON STAR

Rea+13Magnetars
BC =4.4 x
10 13 (bursting in X- & γ-ray)
Critical field strengt
hRadio pulsars(radio pulsation)

High-BLow-B

̇ 1/2 Gauss
B = 3.2x1019 (PP)(assuming rotational energy loss = dipole radiation)BURSTS/FLARES FROM MAGNETARS

Typical light curves
Counts/s [x104]

Note: quiescent luminosity is ~1035 erg/s
Short bursts
l t ~ 0.1 – 1 sl L ~ 1039 – 1041 erg/sl thermal spectra (<10 keV)

Giant flares

Counts/s

l t ~ 1 – 40 s
l L ~ 1041 – 1043 erg/sl thermal spectra

large and rare

Intermediate flaresTime [s]Time [s]events ever (SGR 1806-20)
l L ~ 1044 – 1047 erg/sl initial spike (~ 0.1s) +pulsating tail (~ a few 100 s)

Counts/sl the brightest gamma-ray

SGR 1806-20

Time [s]HISTORICAL GIANT FLARESHurley+98; Israel+05; Enoto, Kisaka & Shibata 19”initial spike”“Pulsating tail” (pulsating@ stellar rotation period)

MODELS FOR FLARES
Magnetic reconnection
generates an opticallythick plasma of photons& e± pairs (= fireball)

Thompson & Duncun 95; Lyubarsky 02

Flares?

Spin axiskT~10-100 keV
Fireball is magneticallyconfined to the stellar
surface and evaporates,
radiating thermal X-ray
emission
Whether a trapped
fireball is formed insmaller flares isunclear…

NS“Trapped fireball”
Prad < Pmag

EMISSION SPECTRA FROM FIREBALL?

!

N (ϵ) ∝ ϵ2 exp"2$ϵ#−1222Teﬀ ϵ + (3π /5)Teﬀ

dN/dE

Superposition of BB= flat spectrum at low-E%−1,

Lyubarsky 02

Energy transfer inside FB
must consider two photonpolarization states
Extraordinary (E-) modecross-section is suppressed! ϵ "2 # B $−2σE∼ 10−4σO
10 keV1014 GEmission fromE-mode photospheres
E/kBTeff

Lyubarsky 02→ we “see” deeper layers
at lower energies
Emergent spectrum is NOT
a pure Planckian

DISCREPANCY: OBSERVATION VS THEORY

Olive+06; Israel+08

An intermediate flare from
SGR 1900+14 on 2001 July
Model: a thermal radiationfrom a trapped fireballduring flares (Lyubarsky 02)

WXM + FREGATE(2-150 keV)

Observed spectrum: muchharder at high-E than model
Obs.

Original spectrum shouldhave been altered by someprocesses?

Theo.

→ Resonant scattering?
Olive+06

Formulation

RESONANT INVERSE COMPTON SCATTERING
Resonant scattering cross section is energy dependent:
σres (ω) = π 2 re c δ(ω − ωB )(1 + cos2 θi )(in rest frame of e±)

Electron cyclotron energy:

𝜖# = 0e−ℏ𝜔+𝑣⃗
𝜖# = 0 → ℏ𝜔+ (absorption)

B-field line

𝜖# = ℏ𝜔+ → 0 (re-emission)ℏ𝜔+Rapid synchrotron cooling: 10-20-10-16 s

RESONANT INVERSE COMPTON SCATTERING
Resonant scattering cross section is energy dependent:
σres (ω) = π 2 re c δ(ω − ωB )(1 + cos2 θi )(in rest frame of e±)

Electron cyclotron energy:

Resonant (magnetic) scattering is dominant:

"−1!
!ω
σresB
∼ 105
σT
1 keV

Photons are efficiently scattered by magnetospheric particles
if a photon satisfies the resonance condition:

photon energy in rest frame of e± = cyclotron energy of e±

VELOCITY DISTRIBUTION OF PARTICLES DURING FLARES
Need to consider a realistic particle velocity distribution
During the flare, particles feel strong radiation force, which issignificantly different from the quiescent state
Frad∼ 107Fgrav!

Bp1014 G

"−1 !

r
RNS

"3 !

L
1040 erg s−1"≫1Observer
Electron DISTRIBUTION OF PARTICLESVELOCITY
frame
rest-frame
Need to consider a realistic velocity distribution−
During the flare, particles feel strong radiation eforce
from the−efireball (significantly different from quiescent state)e−radiationforce
In the electron’s rest-frame, the radiation force acts on aparticle in perpendicular direction to the local magnetic fieldso that electrons do not gain or lose the kinetic energy

v-distribution as a function of angle (radius)

TOY MODEL
Fireball = point-like source with
Initial spectrum (Lyubarsky 02)

Observerframe!

N (ϵ) ∝ ϵ2 exp

e−"2$ϵ#−12
Teﬀ ϵ2 + (3π 2/5)Teﬀ%−1(Teff : effective FB temperature)
Dipole field geometry
Aligned rotator (spin axis =magnetic pole = z-axis)
Single scattering + 100%
scattering probability
3D Monte Carlo Simulation,

Result

REPROCESSED SPECTRA (single-energy case)

SY, Lyubarsky, Granot& Gogus in prep.

injected photons(10 keV)scattered photons(angle-integrated)

up-scattering(x2)

θv=90°
θv=60°
θv=30°
θv=15°REPROCESSED SPECTRA (full energy range)

viewed fromdifferent angles

SY, Lyubarsky, Granot& Gogus in prep.

reprocessed spectrum(angle-integrated)

softening
initial fireball spectrum
initial fireball spectrumwith Tb =10 keVwith Teff =10 keV
hardeningApplication

APPLICATION: 2006 FOREST OF SGR 1900+14

Burst 1Burst 3

Burst 2Israel+08

Bp=7x1014 G
P=5.20 s
D~10 kpc

Flares from SGR 1900+14
in April 2006
Three intermediate flares
Data taken from Swift/BAT(15-150 keV)RESULTS: INTERMEDIATE FLARES

Δt = 1.2 s
L = 1.5×1041 erg s-1

SY, Lyubarsky, Granot & Gogus in prep.

RESULTS: INTERMEDIATE FLARES

Δt = 1.2 s
L = 1.0×1041 erg s-1

SY, Lyubarsky, Granot & Gogus in prep.

RESULTS: INTERMEDIATE FLARESΔtΔt== 1.20.34ss
LL== 1.0e41
41 erg s-1
1.1×10erg/s

SY, Lyubarsky, Granot & Gogus in prep.

CONCLUDING REMARKS

Energetic flare spectra (~1041 erg/s) from SGR 1900+14
can be explained by the reprocess of fireball emission
by resonant scatteringl Single scattering by mildly-relativistic particles is sufficient,suggesting optical depth ~ O(1)l Fireball temperatures: Teff = 6-7 keVl Size of fireball at D=10kpc :!
"1/2 !
"−2LTeﬀrFB∼ 2.5RNS1041 erg s−1
6 keV

Fitting result is surprisingly good; this could be a newtheoretical foundation
Application to many other flares from different sources
is needed; future (ongoing) work