Fermi Bubbles as a Scaledup Version of Supernova Remnants and Predictions in the TeV Band Yutaka Fujita Osaka Ryo Yamazaki Aoyama Yutaka Ohira Aoyama ApJ L in press arXiv13085228 ID: 386260
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Slide1
The Fermi Bubbles as a Scaled-up Version of Supernova Remnantsand Predictions in the TeV Band
Yutaka Fujita (Osaka)Ryo Yamazaki (Aoyama)Yutaka Ohira (Aoyama)
ApJ
L
in press (
arXiv:1308.5228
)Slide2
IntroductionSlide3
Fermi BubblesHuge gamma-ray bubbles discovered with Fermi SatelliteApparent size is ~50°If they are at the Galactic center (GC), the size is ~10 kpcSu et al. (2010)Slide4
Interesting Features Flat distributionSharp edgesHard spectrumSurface brightness Spectrum
Su et al. (2010)Slide5
Interesting FeaturesFlat distributionCosmic-rays (CRs) are distributed neither uniformly nor at the shellsSharp edgesCRs do not much diffuse out of the bubbles Hard spectrum (∝E -2)Short electron cooling time (tcool, e ~10
6 yr) compared with the age of the bubbles (tage ~10
7
yr)
Ongoing acceleration? hadronic?
Standard diffusion (higher
energy CRs escape
faster)
Even if the spectrum is hard when CRs are accelerated, it becomes softer as time goes bySlide6
Proposed ModelsHadronic + starburst (Aharonian & Crocker 2011)Leptonic + acceleration inside the bubbles (Cheng et al. 2011, Mertsch & Sarkar 2011)
CR protons
CR electrons
Inverse
Compton
pion decaySlide7
Our ModelCRs are accelerated at the forward shock like a SNRActivities of central BH or starburst at the GCGamma-rays come from protons (hadronic)CR proton - gas proton interaction
SN 1006(Chandra)
?
Fermi bubbles (Su et at. 2010)Slide8
ModelsSlide9
EquationsCRsDiffusion-advection equation (spherically symmetric)f : distribution function, κ : diffusion coefficientw : gas velocity, Q : CR source (at the shock surface)CRs escape from the shock surface (r =R
sh) pmax ∝
(
eB
/
c
2
)
V
sh
2
t
Q
(r,
p, t ) ∝ p -
q
δ
(
r
-
R
sh
) for
p
< pmaxB : Magnetic
fieldVsh: Shock velocity
p
max
p
-q
QSlide10
EquationsDiffusion coefficientCRs are scattered by magnetic fluctuations (Alfvén waves)Wave growth rate∂ψ/∂t ∝ |∇f | (streaming instability; Skilling 1975)ψ : wave energy densityDiffusion coefficientκ
∝ 1/ψGas Sedov solutionBack reaction from CRs is ignored
CR
Wave
ResonanceSlide11
Parameters (Fiducial Model)EnergyInjection from Galactic Center (GC)Etot = 2.5×1057 ergInjected at 0 < t t0
= 1×106 yr (instantaneous)CR energyE
cr,tot
= 0.2
E
tot
CRs are accelerated for
t
0
<
t
<
t
stop
= 3×1
06 yr
CR acceleration stops because of low Mach number of the shock (
M
~ 4)
Accelerated CR spectrum at the shock
∝
p
-4.1
Current time is
t
obs
=1×1
07 yrHalo gasInitial halo gas profile is
∝ r -1.5Temperature: T
=2.4×106 KSlide12
ResultsSlide13
Surface Brightnessγ -ray surface brightness profileFairly flatHalo gas remains inside the bubbleInteract with CR protonsSharp edgeGas density is high at the shockDecrease of diffusion coefficient just outside the shock (CRs amplify waves)CRs cannot much diffuse out of the shock
Surface brightness
ρ
gas
R
shSlide14
Amplification of Magnetic FluctuationsBecause of CR streaming, magnetic fluctuations increaseCRs are more scatteredDiffusion coefficient decreasesMost CRs cannot escape from the bubbleSince tstop < tobs, Most CRs are left far behind the shock front at t = tobs
At
t
=
t
obs
,
r
=
R
sh
+
Shock
CRsSlide15
SpectrumGamma-ray spectrumHard spectrumCR energy spectrum is not much deferent from the original one (∝E -2)Decrease of diffusion coefficient just outside the shockconsistent with observationsTeV flux depends on pmaxFor Bohm diffusion, pmax ~10
15 eVNeutrino spectrum is also calculated
Bohm diff.
(large
p
max
)
Small
p
maxSlide16
Other parametersNo wave growth (NG)Larger diffusion coefficient
Brighter at 2 GeVLow energy CRs reach high gas density region just behind the shockDimmer at 1 TeVHigh energy CRs escape from the bubbleγ
-ray spectrum does not follow observed spectrum (
∝
E
-2
)
1 TeV
Surface brightness profile
Fiducial
Shock
CRs
CRs
Shock
2 GeVSlide17
Other ParametersLate acceleration (LA)CRs are accelerated at 4×106 yr < t < 107 yr = tobsLater than fiducial (FD) model (
106 yr <
t
<
3×1
0
6
yr)
Bubble limb becomes brighter
CRs have not diffused much
CRs must be accelerated
at the early stage
of bubble evolution
Surface brightness profileSlide18
Other ParametersContinuous energy injection (CI) from GCEnegy is injected for 0< t < tobsLonger than fiducial (FD) model (0
t 1×106 yr)Bubble limb becomes sharp
Gas is concentrated around the shock
Energy injection from GC must be
instantaneous
Surface brightness profileSlide19
SummaryWe treated the Fermi bubbles as a scaled-up version of a supernova remnantCRs are accelerated at the forward shock of the bubbleWe solved a diffusion-advection equationWe considered the amplification of Alfvén wavesComparison with observationsWave growth is requiredCRs are accelerated at the early stage of bubble evolutionEnergy injection from GC must be instantatious