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High Energy Emission From
Pulsar Wind Nebulae
Wlodek Bednarek
Department of Experimental Physics, University of Lódź, Poland
• What’s new in respect to old ?
• Hybrid (hadronic-leptonic) model for PWNe.
• Gamma-ray production in H-model.
• Possible neutrino emission from PWNe ?
• PWNe in high density regions ?
• Cosmic Rays from PWNe:
Contribution to galactic cosmic rays
Early phase Pulsar Wind Nebulae
Leptonic model for γ-rays from PWNe
leptons + B→ ε; leptons + ε → γ-rays; SSC model
synch. spectrum and its distribution → lepton spectrum and ....
ε = syn, MBR, IF, Opt, .... ?
de Jager & Harding (1992) prescription:
• Apply the model for B distribution inside the nebula
(Kennel & Coroniti (1984) →
• invert the synchrotron spectrum → get electron spectrum
and distribution inside the nebula,
• calculate the TeV γ-ray spectrum from IC scattering
and its distribution.
Leptonic model for the γ-ray emission from the Crab Nebula [from
Hillas et al. 1998].
Figure 1:
Figure 2:
[from Harding & de Jager (1992), Atoyan & Aharonian (1996)].
• SSC model other applications:
MSH 15-52 [du Plessis et al. 1995],
Vela Nebula [de Jager et al. 1996].
• Investigation of basic features of the time dependent SSC model
[Aharonian, Atoyan & Kifune 1997]:
electrons injected continuously with the power law spectrum,
evolve in a constant magnetic field.
⇓
IC γ-ray and synchrotron spectra - application to PSR 1706-44
Observations: MSH 15-52 [Aharonian et al. 2006].
• spectrum power law with index 2.27 between 280 GeV up to 40 TeV,
• 150 ms pulsar at ∼ 5 kpc, age: ∼ 1700 yrs,
• extended asymmetric TeV γ-ray emission →
Doppler boosted jet emission, interaction with RCW 89 nebula ?
Vela region [Aharonian et al. 2006].
• 89 ms pulsar at ∼ 300 pc, age ∼ 11300 yrs,
• TeV γ-ray emission displaced from the pulsar location by ∼ 0.5 degree
Interaction with the surrounding medium ?
required movement of the pulsar with ∼ 250 km/s ?
(measured 65 km/s, Caraveo et al. 2001).
Spectrum from the Vela PWNa between 550 GeV and 65 TeV →
power law with index 1.45 with the cut-off at ∼ 14 TeV [from Aharonian
et al. 2006].
Figure 3:
⇓
Hybrid (hadronic-leptonic) model for HE in PWNe
Possible importance of hadronic processes in PWNe:
Cheng et al. (1990), Atoyan & Aharonian (1996), Bednarek & Protheroe (1997),
Amato, Guetta & Blasi (2003), Bednarek & Bartosik (2003).
Model for acceleration of particles
• We apply the model for acceleration of leptons in resonant interactions
with the iron nuclei injected by the pulsar (see e.g. Hoshino et al. 1992;
Gallant & Arons 1994).
• From normalization to the observations of the Crab pulsar, Arons (1998)
postulates that the Lorentz factors of iron nuclei in the pulsar’s wind
should be
γ1 ≈ 0.3ZeΦopen/mic2
(1)
where mirand Ze are the mass and charge of the iron nuclei, and
Φopen = Lem /c is the total electric potential drop across the open
magnetosphere. These nuclei take a part, χ, of the total pulsar energy
loss rate.
• The spectrum of positrons accelerated by ions is close to a power
law with spectral index δ1 ≈ 2 between Emin ≈ m±
e γ1 and Emax ≈
γ1mi c2/Z. The conversion efficiency of energy of ions into energy of
positrons is ξ.
• Low energy leptons are also injected into the nebula from the inner
pulsar magnetosphere with the power law spectrum between ∼ 0.1
GeV and Emin and index δ2 ≈ 1.2 (Hibshman & Arons 2002).
A simple model for expansion of PWNe
• Evolution of the nebula.
The expansion velocity of the nebula at any time, t, is estimated by
taking into account the energy supplied into the nebula by the pulsar
2
2
Z t
MSN (t)VSN
(t) M0,SNV0,SN
=
+ 0 Lpul(t0)dt0
2
2
(2)
2
−4
Lpul(t) = Bs2Rs6Ω4/6c3 ≈ 3 × 1043B12
Pms
erg s−1,
(3)
where
is the pulsar energy loss, Ω = 2π/P , and P = 10−3Pms s changes with
2
2
2
time according to Pms
(t) = P0,ms
+ 2 × 10−9tB12
.
The nebula increases its mass according to
4
3
(t),
(4)
MSN(t) = M0,SN + πρsur RNeb
3
where ρsur is the density of surrounding medium and RNeb is the radius
of the expanding envelope at the time ’t’
RNeb =
Z
t
0
VSN (t0)dt0.
(5)
• The average density of matter inside nebula
3
ρNeb = 3MSN(t)/4πRNeb
(t),
Solve numerically the above set of Eqs.
(6)
• Location of the shock in the PWNa.
The pulsar wind pressure is balanced by the pressure of expanding
nebula at (Rees & Gunn 1974)
Lpul(t)
2 c ≈
4πRsh
Rt
0
σLpul(t0)dt0
,
4
3
πR
Neb
3
(7)
where σ is the ratio of the magnetic energy flux to the total energy flux
lost by the pulsar at the location of the pulsar wind shock at radius
Rsh.
• Magnetic field at the shock region.
We estimate the strength of the magnetic field at the shock region from
3
√
R
Rlc
pul

Bsh = σBpul 
,
Rlc Rsh


(8)
where Rpul and Bpul are the radius and surface magnetic field of the
pulsar.
• Propagation of particles inside the nebula.
• Nuclei injected into the nebula at a specific time tinj, escape from it at
the time tesc , if their diffusion distance in the turbulent magnetic field
of the nebula, Rdiff , is equal to the dimension of the nebula, RNeb , at
the time tesc .
Rdiff =
Z
v
u
tesc u
u
t
tinj
3D 0
dt ,
2t0
(9)
where the diffusion coefficient is taken to be D = RLc/3, and RL is
the Larmor radius of nuclei.
• Due to the adiabatic losses of nuclei during the period of their propagation inside the nebula the energy of a nucleus at a time, t, is
E(t) = E(tinj)
tinj + t
2tinjK τ
(10)
where E(tinj) is its energy at the time tinj, K is the inelasticity coefficient
for collisions of nuclei with the matter, and τ is the optical depth.
Figure 4: (A) The radius of the nebula RNeb (thick curves), the pulsar wind shock Rsh
(thin curves), for B = 5 × 1012 G and three initial periods: 1 ms (dotted curves),
5 ms (dashed curves) and 20 ms (full curves). The initial expansion velocity of
the nebula is 2 × 108 cm s−1 and its mass is 4 M and the density of surrounding
medium is 0.3 cm−3. (B) The expansion velocity of the nebula (thick curves) and
the strength of the magnetic field at the shock region (thin curves) as a function of
time.
Equilibrium spectra of particles inside the nebula
• Spectra of hadrons.
The pulsar with specific parameters injects iron nuclei with the fixed
Lorentz factor.
Nuclei lose energy due to adiabatic expansion and collisions with the
matter inside the nebula.
Some of them diffuse through the nebula and escape.
⇓
Take these processes to obtain the equilibrium spectrum of nuclei
inside nebula at specific time ’t’.
Figure 5: Equilibrium spectra of nuclei inside the nebula at different time after the
supernova explosion (pulsar formation): t = 3 × 102 yr (full curve), 103 yr (dashed),
3 × 103 yr (dot-dashed), and 104 yr (dotted) for the pulsar with P0 = 15 ms, and
B = 4 × 1012 G.
• Spectra of leptons.
Leptons injected into the nebula lose energy on adiabatic expansion and
radiation processes (bremsstrahlung, synchrotron and inverse Compton
scattering) which are described by
dE
= (α1 + α2)E + (β1 + β2)E 2 GeV s−1,
(11)
dt
where: bremsstrahlung losses are described by α1 ; adiabatic losses
by α2; synchrotron losses by β1 ; and inverse Compton losses on the
radiation field inside the nebula by β2.
⇓
−
We obtain the equilibrium spectrum of leptons at an arbitrary time
after supernova explosion.
Figure 6: Equilibrium spectra of positrons at the time t = 3 × 10 2 , 103, 3 × 103, and
104 years for the pulsar with P0 = 15 ms, and B = 4 × 1012 G. Leptons are injected
into the nebula with the spectrum normalized to the pulsar energy loss rate with
χ = 0.8 and ξ = 0.5, and the spectral index δ1 = 2.5. It is assumed that e± pairs
and nuclei are injected from the pulsar within the angle of 20 o.
The Crab PWNa
Interpretation of the Crab Nebula high energy emission in terms of
hybrid hadronic-leptonic model. [Bednarek 2005]
Figure 7:
The Vela PWNa
(TeV γ-ray source (H.E.S.S. collab., Aharonian et al. 2006)
Figure 8:
The spectrum of the Vela PWNa [from Aharonian et al. 2006].
Figure 9: The γ-ray spectrum from Vela modeled with hybrid hadronic-leptonic
model. γ-rays from π o decay are created in hadronic collisions (dot-dashed curve)
and from ICS of leptons (full curves). The acceleration mechanism of leptons operates through all the lifetime of the pulsar (the thinnest full curve), during the
first 5000 yrs, 3000 yrs, and 2000 yrs (the thickest full curve). The acceleration of
hadrons is continuous.[Bednarek & Bartosik 2003]
Neutrinos from PWNe ?
• Neutrinos from the Crab PWNa:
Bednarek & Protheroe (1997):
nuclei from NS accelerated in the outer gap + radiation outer gap
→ neutrons + matter → ν
(neutrinos might be detected by km2 detector).
• Hybrid model (see e.g. Arons 1998):
Amato, Guetta & Blasi (2003):
Bednarek & Bartosik (2003) from several PWNe
(1-2 ν events/km2/yr from the Crab PWNa).
• Horns et al. (2006) estimate neutrino flux from the Vela PWNa
based on the scaling from the observed γ-ray flux
(not example event rate calculated so not clear if can be detected)
Figure 10: Neutrino spectra (νµ ) expected from: Crab Nebula - PSR 0531+21 (thick
full curve), Vela Nebula - PSR 0833-45 (thick dashed), MSH15-52 - PSR 1509-58
(thin dotted) with close high density medium with 300 cm−3 (thick dotted), CTB80
- PSR 1951+32 (thin dashed) [from Bednarek 2003].
Figure 11: The muon neutrino event rate in 1 km2 detector from the pulsar wind
nebula (distance of 2 kpc) as a function of the time. Initial parameters of the
pulsar: initial period 15 ms and surface magnetic field B = 4 × 1012 G (full curve),
5 ms and B = 4 × 1012 G (dashed curve), and 15 ms and B = 2 × 1013 G (dotted
curve) [from Bednarek 2003].
Middle aged pulsar in young open cluster ?
(Cygnus OB2 - TeV J2032+4130)
• Largest massive galactic association, distance ∼ 1.7 kpc, diameter ∼ 60 pc,
core ∼ 14 ± 2 pc, mass ∼ 3.3 × 105 M , contains OB type (∼ 2600 ± 400) and
O type (∼ 120 ± 20) stars.
• The EGRET sources towards the Cyg OB2: 2EG J2033+4112 (Mori et al. 1997),
GeV J2035+4214 (Lamb & Macomb 1997), GRO J2034+4203 (Reimer, Dingus
& Nolan 1997),
3EG J2033+4118 (Hartman et al. 1999), non-variable (Butt et al. 2003), a
simple power law with a break (Bertsch et al. 2000, Reimer & Bertsch 2001). .
• Steady, extended TeV source (Aharonian et al. 2002): differential spectrum
−1.9 ± 0.3stat ± 0.3sys, flux two orders below that from 3EG J2033+4118.
• Cosmic rays: AGASA shows excess, 3.9 σ between 1018 − 1018.4 eV (Hayashida
et al. 1999).
• A very energetic pulsar formed in a core collapse of the Wolf-Rayet star in the
Cyg OB2 association.
• The pulsar accelerate heavy nuclei (see e.g. Arons 1998), with the Goldreich &
Julian efficiency.
• The equilibrium spectra of nuclei and leptons inside the nebula determined as
discussed for the PWNe (Bednarek & Bartosik 2003).
• Let’s assume that the pulsar was born in the Cyg OB2 with the initial period
P0 = 2 ms and the surface magnetic field B = 6 × 1012 at about t = 2 × 104 yrs
ago (present period ∼ 210 ms). The initial velocity of the supernova envelope
is 2000 km s−1 and its mass is 4 M (as for the Crab Nebula, Davidson &
Fesen 1985).
The broad band spectrum of the Cyg OB2 association: the diffuse
X-ray emission (Chandra - Butt et al. 2003), the GeV γ-ray emission from
the EGRET source 3EG J2033+4118 (Hartman et al. 1999, Lamb & Macomb 1997)), the TeV emission from the HEGRA source (Aharonian et al.
2002). The cosmic ray flux at EeV energies is marked by the filled circles
(CR). The spectra of Vela type pulsars i.e., the Vela pulsar (V) and PSR
1706-44 (P), are shown by the thin dotted curves. The synchrotron and
IC spectrum from the nebula around the pulsar are shown by the full and
dashed curves, respectively. These spectra are reported for two targets of
soft photons inside the nebula: (1) only the MBR and synchrotron photons (thin dashed curve); (2) additional infrared photons from the nebula
(thick dashed). The spectrum of γ-rays from collisions of hadrons with the
matter inside the nebula is shown by the dot-dashed curve. The spectra
of neutrons (included their decay during propagation from the distance of
1.7 kpc) and γ-rays, produced in hadronic collisions by nuclei captured in
dense regions of the Cyg OB2, are shown by the dot-dot-dot-dashed and
thick dotted curves, respectively [Bednarek 2003].
Figure 12:
The spectrum of muon neutrinos, produced by hadrons captured
in the high density regions of the Cyg Ob2 association (full curve) and
produced by hadrons inside the PWNa (dot-dashed curve), are compared
with the atmospheric neutrino background (dashed curves) within 1 o of
the source for the zenith and azimuth directions (Lipari 1993). The 3-yr
sensitivity of the IceCube detector is marked by the dotted line (Hill 2001)
[Bednarek 2003].
Figure 13:
Very fast pulsar in GC?
(TeV γ-rays: CANGAROO, HESS, MAGIC, Whipple)
(Diffuse TeV γ-rays from the GC ridge, Aharonian et al. 2006)
(EeV cosmic rays: AGASA - SUGAR; AUGER ???)
• Pulsar close to the GC: Pinit = 2 ms, Bsur = 6 × 1012 G,
• Dense inner GC region: e.g. R = 50pc, B = 3 × 10−5G,
R = 10pc, B = 3 × 10−5G.
• Several neutrinos per 1 km2 yr (normalization to neutron excess).
Figure 14: Spectra of muon neutrinos produced in hadronic interactions of iron nuclei
from the pulsar with the matter at the Galactic Center. The dashed curves indicate
the atmospheric neutrino background, ANB, (Lipari 1993) within a 1 o of the source,
the dotted line - the 3 yr sensitivity of the IceCube detector (Hill 2001). [Bednarek
2002]
Galactic cosmic rays from PWNe ?
• Hadrons accelerated by large amplitude electromagnetic waves (Ostriker &
Gunn 1969, Karakula et al. 1974),
• Nuclei accelerated in the pulsar outer gaps (Cheng et al. 1986); contribution to
the GCRs (Bednarek & Protheroe 2002),
• Neutron star quakes -origin of the knee (Cheng & Chi 1996),
• Hadrons from the pulsar (no energy losses, Giller & Lipski 2002),
• Heavy nuclei present in the pulsar winds (Hoshino et al. 1992, Gallant &
Arons 1994); contribution of nuclei from PWNe to GCRs (Bednarek & Bartosik 2004).
• Heavy nuclei from early PWNe → HECRs (Blasi et al. 2000, Arons 2003).
• Calculate the spectrum of nuclei which are injected by pulsar and escape from
the PWNa for arbitrary initial parameters (Bednarek 2004),
• Take pulsar population within the Galaxy: Model B of Lorimer et al. (1993) the Gaussian distributions of log B, with < logB[G] >= 12.3 and σlogB = 0.35,
and for log P0 , with < logP0 [ms] >= 2.6 and σlogB = 0.35 above 2 ms,
• Consider a model for propagation of nuclei inside the Galaxy (Berezinsky et
al. 1990).
Figure 15: The comparison of the spectrum of particles accelerated by pulsars with the
parameters described by the model (i) (dot-dot-dot-dashed curve in (a)), model (ii)
(dashed curve in (a)), model (iii) (dot-dot-dot-dashed curve in (b)), and model (iv)
(dashed curve in (b)), with the observed cosmic ray spectrum (thin full curve). It
is assumed that at low energies the supernova remnants (SNR) accelerate CRs with
the spectrum dN/dE ∝ E −2.7exp(−E/107GeV ) (dot-dashed curve). At extremely
high energies (EG), the spectrum has the form dN/dE ∝ E −2.7 (dotted line).
Figure 16: The comparison of the mass composition of the cosmic rays, < lnA >,
obtained in terms of the model (iv) for the case of the light extragalactic component
extending to low energies (thick dashed curve) and breaking at 10 18 eV (thin dashed
curve), with the measurements reported by different experiments (JACEE - Shibata
et al. (1999), RUNJOB - Apanasenko et al. (2001), CASA-MIA - Glasmacher et
al. (1999), KASCADE (e/m) - Ulrich et al. (2001), KASCADE (p/m) - Engler et
al. (1999), EAS-TOP - Alessandro et al. (2001), FLY’S-EYE - Dawson et al. (1998),
Akeno A1 - Hayashida et al. (1995), Akeno A100 - Hayashida et al. (1997), Haverah
Park - Ave et al. (2003), Volcano Ranch - Dova et al. (2003)). The region between
the thin full curves shows < lnA > obtained from many experiments and derived
by Hörandel (2004). < lnA > equal to 1.5 is taken for the SNR contribution to
cosmic ray spectrum as measured at low energies by direct experiments. Similar
composition is also applied for the extragalactic (EG) component of CRs at the
highest energies.
EHE cosmic rays from early phase PWNe ?
• Heavy nuclei accelerated in pulsar winds just after pulsar formation
(Blasi et al. 2000).
• Magnetars accelerate hadrons in their winds above ∼ 1021 eV (Arons 2003)
Neutrinos from early phase PWNe
(Pulsar inside the SNa)
• Detectable fluxes of γ-rays, ν, (but not cosmic rays?) from the pulsar
inside SNa (Berezinsky & Prilutsky 1978, Sato 1977).
• SN 1987A - hadrons from the PW shock: e.g. Gaisser, Harding &
Stanev (1987), Berezinsky & Ginzburg (1987), Yamada et al. (1988),
Harding et al. (1991).
• Nuclei accelerated in the pulsar slop gap: Protheroe et al. (1998)
(prompt, pulsed ν emission and delayed, steady ν emission)
• Heavy nuclei accelerated in pulsar winds interact with the radiation
and matter from SNa (Beall & Bednarek 2002).
Figure 17: Maximum energies of accelerated iron nuclei, temperature of thermal radi-
ation in the acceleration region (dotted curve), and column density of matter in the
envelope (thick dot-dashed curve) are shown as a function of time which is measured
from the supernova explosion. Iron nuclei are accelerated by the pulsars with initial
parameters: B12 = 4, Pms = 3 (thin full curve) and B12 = 100, Pms = 10 (thick
full curve). The vertical lines mark the times: after which the envelope becomes
transparent to thermal radiation (dot-dot-dot-dashed), and at which the envelope
becomes transparent to hadronic collisions and the parameters of the neutron star
may change drastically due to the gravitational energy losses (long dashed).
• Neutrino event rate normalized to the observed CR flux.
Table 1: Expected number of detected νµ per km2 per SNa at 10kpc (normalized to Gal. CR flux)
N-γ → νµ (H)
Fe-M→ νµ (H)
N-γ → νµ (N)
Fe-M→ νµ (N)
Pms = 3, B12 = 4 Pms = 10, B12 = 100 Pms = 20, B12 = 4
classical
magnetar
Crab SNa (2kpc)
1
100
3
9
720
11
0.2
20
1
3
260
9
Figure 18: Spectra of muon neutrinos and antineutrinos produced in interactions of nucleons from
photodesintegration of iron nuclei with the thermal radiation field inside the supernova envelope
(N − γ → π → νµ ) and from interactions of iron nuclei with the matter of the envelope (F e − M →
π → νµ ). The density factor is η = 1, and the initial periods and the surface magnetic fields of the
pulsars are: Pms = 10 and B12 = 100 (full histograms), Pms = 3 and B12 = 4 (dashed), and Pms = 20
and B12 = 4 (dotted).
Multi-messenger VHE Approach to the PWNe
• Recent obs. results =⇒
work on time dependent, two-three-dimensional model
for the PWNe.
⇓
Search for more TeV γ-ray PWNe =⇒
morphology, spectra (H.E.S.S., MAGIC, VERITAS, ...., CTA)
↓
Why some of them are observed but not others ?
• PWNe might be also sites of acceleration of hadrons =⇒
hybrid: hadronic-leptonic models
⇓
Search for neutrinos, neutrons from the PWNe
(IceCube - NEMO, AUGER)
Testing the hypothesis of the PWNe contribution to the Gal. CRs.
(CR anisotropies from the nearby PWNe (due to local B structure ?):
Geminga, Vela, ... ?