1. Model of TeV Gamma-Ray Emission from Geminga Pulsar Wind Nebula and Implication for Cosmic-Ray Electrons/Positrons
Norita Kawanaka (Hakubi Center, Kyoto Univ.)
Kazumi Kashiyama (Univ. of Tokyo)
Kohta Murase (Penn State Univ.)
CTA Japan Workshop　12/15-16/2016

2. “positron excess”
Observed CR e+ flux seems to exceed that expected from the standard secondary production model, and rises with the energy.
Some primary positron sources are needed!
PAMELA (~1-100GeV)
(Adriani et al. 2008)
AMS-02 (~1-500GeV)
 Drop above ~200 GeV?

3. Electron+Positron Flux
H.E.S.S.
ATIC/PPB-BETS
(Chang et al. 2008)
(Aharonian et al. 2008)
Excess from the conventional model
 Primary CR e± sources?
Bumpy structure and sharp cutoff at ~500 GeV?
drop above ~TeV
Fermi-LAT
(Abdo et al )

4. Positron flux (AMS-02)
Peak & Cutoff at 300GeV?

5. Astrophysical Origin Pulsars Supernova Remnant
Aharonian+ 95; Atoyan et al. 95; Chi+ 96; Zhang & Cheng 01; Grimani 07; Yuksel+ 08; Buesching+ 08; Hooper+ 08; Profumo 08; Malyshev+09; Grasso+ 09; NK, Ioka & Nojiri 10; NK, Ioka, Ohira & Kashiyama 11; Kisaka & NK 12; NK, Kashiyama & Murase in prep.
　Supernova Remnant
Pohl & Esposito 98; Kobayashi+ 04; Shaviv+ 09; Hu+ 09; Fujita, Kohri, Yamazaki & Ioka 09; Blasi 09; Blasi & Serpico 09; Mertsch&Sarkar 09; Biermann+ 09; Ahlers, Mertsch & Sarkar 09; NK 12
　Microquasar (Galactic BH)
Heinz & Sunyaev 02
　Gamma-Ray Burst Ioka 10
White Dwarfs Kashiyama, Ioka & NK 11

6. CR e± source = Pulsar wind nebula?
Crab nebula

7. Previous Studies (1) Single source
(a) E=0.9x1050erg, age=2x105yr, a=2.5
(b) E=0.8x1050erg, age=5.6x105yr, a=1.8
(c) E=3x1050erg, age=3x106yr, a=1.8
e+ fraction
e±spectrum
cooling cutoff energy ⇔ Age of the source
Ioka 2010

8. Previous Studies (2) Multiple sources Ee+=Ee-~ 1048erg a ~ 1.9
e+ fraction
solid lines： fave(ee) (average)
dashed lines： fave(ee) ±Dfave
Pulsar birth rate ~ 0.7x10-5/yr/kpc2
Ee+=Ee-~ 1048erg
a ~ 1.9
Average spectra are consistent with PAMELA, Fermi & H.E.S.S.
Large dispersion in the TeV range due to the small N(ee)  possible explanation for the cutoff inferred by H.E.S.S.
e±spectrum
NK et al. 2010

9. Geminga PWN g-ray SED one of the brightest g-ray sources
age: 3.42 x 105 yr
distance: pc
Are we observing the emission from escaping e±?
g-ray SED
(MAGIC; Ahnen+ 2016)
Milagro observation (Abdo+ 2009)

10. e± Transport inside the PWN
e± acceleration at the termination shock
diffusive/convective transport in the nebula
diffusive escape from the nebula into the ISM

11. Transport equation inside the PWN
(one-dimensional)
fint: distribution function
DPWN: diffusion coefficient inside the PWN
V: convection velocity inside the PWN
P: cooling rate (synch./IC/adiabatic)
Q: injection spectrum
Assumptions
nebula radius: rout = 30 pc
inner radius: rTS = pc
contact discontinuity: rCD = 0.01 pc
V = V0 r -1/2, B = B0 r 3/2 : inside the CD
V = 0, B = BISM = 3 mG : outside the CD

12. e± Transport outside the PWN
time dependent diffusion equation in the ISM
Q: injection luminosity at the PWN outer boundary
= 4 p rout2 ・(outgoing flux at the boundary)
solution
r = 30 – 100 pc (around the PWN) & 250 pc (observed CR e±)

13. Result: observed CR spectrum
e± spectrum
total e± energy:
Etot ~ 1047 erg
injection spectrum:
broken power-law
a1=1.9, a2=3.0, gb=6x105
e+ spectrum
very difficult to reproduce both of the spectra with a single source…
different origins?
softer spectrum?
no cutoff?

14. Results: emission around the PWN
synchrotron and IC scattering
SED: inconsistent with MAGIC/Milagro data
harder e± spectrum? higher break energy?
brightness distribution: extending outside the nebula
10-12 erg cm-2 s-1 (250pc)
Spectral energy distribution
~7°
MAGIC/Milagro
brightness distribution

15. A young PSR/PWN is surrounded by a SNR.
 CR e± from a PWN should go through the SNR shock without trapped by the magnetic field around the shock
Kennel & Coroniti 93 r
shock front
Escape condition:
Lesc
eesc (t): given by models
LE CR
HE CR
e± spectrum from a young pulsar should have a low energy cutoff
 Probe of the energy-dependent escape scenario (Ohira+ 2010; Ohira, Yamazaki, NK & Ioka 2012; Ohira, NK & Ioka 2016)
Models of eesc(t) x

16. TeV e± spectrum can prove the CR escape!
Without energy-dependent escape
Electron spectrum from Vela SNR/PSR (d=290pc, tage~104yr, Etot=1048erg)
Only e± s with ee>eesc(tage) can run away from the SNR.
 Low Energy Cutoff
5yr obs. by CALET (SWT=220m2sr days; see next slide) may detect it.
eesc(t) from Ptuskin & Zirakashvili 03
NK+ 2011
Direct Evidence of Escape-Limited Model for CR accelerators (=SNR)!

17. TeV Gamma-Ray Sky HESS sources ~40 … e± emitting PWN?
CTA: larger number of sources with better statistics
e± ~ 1048erg
TeV emission ~

18. Summary pulsar wind nebulae = cosmic-ray e± sources?
e± escaping the PWN … spatially extended emission from e± is expected
We solve the transport of high energy e± inside/outside the PWN (e.g. Geminga), and compare the CR electron/positron spectra with those observed by Fermi/AMS-02, and compare the g-ray emission feature around the nebula with that observed by Milagro and MAGIC (in prep.)
High energy (>~ TeV) e± spectral feature may tell us the properties of CR sources.
PWNe might account for the significant fraction of un-identified TeV sources.

19. Backup Slides

20. Why are the PAMELA/AMS-02 results “anomaly”?
Positrons are generated from CR protons (secondary origin)
Higher energy protons can escape the Galaxy earlier
Higher energy positrons are less produced: ①
Observed positron spectrum becomes softer because of the escape and energy loss: ②
Electrons: primary origin
 Spectral change should be only from ②
primary ①
secondary ②
Observed e+ spectrum
CR e+ spectrum should be softer than that of e-

21. CR escape from SNRs (Ptuskin & Zirakashvili 05; Caprioli+ 09; Gabici+ 09; Ohira+ 10 etc.)
Lesc r
shock front
e>eesc(t)
e<eesc(t)
The particles with highest energy can escape the SNR shock at the beginning of the Sedov phase
As the shock decelerates, lower energy particles become able to escape the shock x
Nesc
observed CR spectrum
If the CR injection rate increases with time, the observed CR spectrum would become softer
 consistent with observations (CR spectrum ∝ e-2.7)
eesc(t)
g-ray spectra of SNRs (Ohira+ 10), CR helium hardening (Ohira, NK+ 16) e

22. Constraints on pulsar-type decay time
* A significant fraction of observed electrons are emitted recently.
pulsar type: t0=105yr
H.E.S.S.
pulsar type: t0=104yr