Transcript Flanchik, Alexander: Compton scattering... in millisecond pulsars

RESONANT COMPTON SCATTERING
AND CONNECTION BETWEEN GAMMA
EMISSION AND RADIO EMISSION IN
MILLISECOND PULSARS
A.B. Flanchik
Institute of Radio Astronomy of NASU, Kharkov
New Trends in High-Energy Physics, Alushta, September 3 – 10, 2011
THE REPORT PLAN
1. Introduction. Millisecond pulsars (mPSRs) as rapidly rotating neutron
stars and sources of radio and gamma emission.
• Magnetosphere structure, pulsar polar gap above star magnetic pole.
• Radio emission of mPSRs.
• Gamma emission from mPSRs.
2. Formation of pulsar radio emission in a polar gap.
• Low-frequency emission due to electron acceleration near star surface.
• Spectrum & high frequency cutoff. Total luminosity estimation.
3.
•
•
•
•
Inverse Compton scattering in magnetic field.
Scattering kinematics & cross section.
Electron energy losses due to resonant inverse Compton scattering.
Angular distribution of scattered photons.
Resonant ICS spectrum & total luminosity estimate.
4. Conclusions.
INTRODUCTION.
POLAR GAP IN PULSAR MAGNETOSPHERE
P = 1.2 ms – 10 s,
B = 108 1013 G,
M  MSun , R  106 cm
The polar gap is considered as a region of particle
acceleration, radio emission and -rays formation. In
this region there is a strong electric field E directed
along pulsar magnetic field B.
BASIC PROCESSES IN A PULSAR MAGNETOSPHERE
Electromagnetic cascade of e-e+ plasma production:
Acceleration
of electrons in
a polar gap
Hard -photon
emission
e-e+pair
production by
high energy
-photons
Observed
pulsar
-emission
formation
Observed
pulsar radio
emission
formation
Synchrotron emission
by produced electrons
& positrons
Next generation pair
production by
synchrophotons
Arising of
instabilities in the
plasma, excitation of
plasma waves
Electromagnetic cascades in pulsars – Harding & Daugherty, 1982
Filling the pulsar
magnetosphere
with the plasma
MILLISECOND PULSARS





Periods: P =1.1 ms – 30 ms,
dP/dt = 10-21 – 10-19 s/s
Surface magnetic fields: B  108 – 109 G
Rotation total energy: Er = MR22/2 ~ 1051 – 1052 erg
Rotation energy losses -dEr/dt = MR2 d/dt ~1034 – 1036 erg/s
Millisecond pulsars – old pulsars
(age 106 -107 years) predominantly
in binary systems with usual stars
Millisecond pulsars differ from usual
pulsars due to sufficiently lower surface
magnetic fields.
It is a very important circumstance
for mechanisms of pulsar emission in
various spectral ranges.
PULSAR RADIO EMISSION
• Today about 100 millisecond pulsars are known, most of them are radio sources.
• Typical mPSRs radio luminosities are
IR  1029 – 1031 erg/s (Malov, 2004)
I R ( )   
Example of pulsar radio spectrum
(Malofeev, Malov, 1994)
Some of mPRSs have giant pulses
(GP) – very short pulses in which
the luminosity may increase by
several orders.
Giant pulse of the Crab pulsar
(Hankins, Eilek, 2007)
• Radio emission frequency range:
10 MHz    10 GHz
PSR B0531+21
 = 9.25 GHz
PROPERTIES OF MILLESECOND PULSAR X-RAY & GAMMA
EMISSION
• With help of Fermi LAT 27 mPSRs with emission were discovered (Abdo et al., 2010)
•Gamma luminosities of mPSRs lie in a range
1032 erg/s ≤ I ≤ 1034 erg/s
• Photon energy range for mPSR -emission
1 MeV    10 GeV
• Many millisecond pulsars are sources of Xrays.
• Their X-ray emission usually has both a
thermal and a non-thermal components.
• Thermal X-ray emission is just emission
from heated polar cap with T = 106 K.
• The total X-ray luminosities are 1029 erg/s
≤ IX ≤ 1032 erg/s, and photon energies from
a few keV (Kaspi et al., 2004)
Friere et al., 2011
RADIO, X-RAY AND GAMMA EMISSION OF MILLISECOND
PULSARS – WHAT IS AN ORIGIN?
• We proposed a model in which radio emission arises due to acceleration of electrons by
an electric field in a polar gap (Kontorovich, Flanchik, 2011).
• Inverse Compton scattering of the radio emission by ultrarelativistic electrons in the gap
leads to formation of X-ray and -emission of millisecond pulsars.
radio emission
e-
Non-resonant ICS
Resonant ICS
-emission
e-
Hard -emission with photon energies
up to several GeV
Hard X-ray and soft -emission with
photon energies up to 100 MeV
RADIO EMISSION FORMATION IN A POLAR GAP
Accelerating electric field in a mPSR polar gap is
 B  1 s 
E ( z )  1.46 12    
 10 G   P 
(Rudak, Dyks, 2000)
3/ 2
cos 
(E(z) in Gausses)
w(z )
The particle acceleration along magnetic force line is
w( z ) 
eE ( z )
m 3 ( z )
(z) = (1- v2/c2)-1/2 is a Lorentz factor. Total power
emitted by a single particle has a form
z
zm
The acceleration maximum at
low altitudes z << h
2e 4 E 2
I
3m 2 c 3
The electrons in the gap must emit coherently to
provide very high brightness temperatures TR 1031 K.
Taking into account contributions of all electrons over all polar gap we estimate the total
radio emission power
Typical radio
*2 B 23 R 3
luminosities
IR 
~ 1029  1030 erg / s
2
c
of mPSRs
where *  102 cm, B  108-109 G,  = 2/P.
INVERSE COMPTON SCATTERING IN A POLAR GAP
r
e

e
Frequencies of radio emission in the gap satisfy a
condition ħ << mc2, and we consider ICS in the
Thompson limit. The energy of scattered photon  is
given by
1  Vc cos 
   V
1  c cos  
Here we consider a resonant Compton scattering, and a differential cross
section has a form in electron rest frame (Herold, 1979, Dermer, 1990)
z
323 mc2
 d 
 T  (  B ) (   )

 
 dd   R 4 
k
where prime denotes a scattered photon, T – Thompson cross section
Using the Lorentz transformations, we obtain for the cross section in a
relativistic case

 
1  Vc cos  
B
      V

   
2
V
(1  c cos  )  
1  c cos   
d
323 mc  T 

dd  4

 3 (1  Vc cos  )(1  Vc cos  ) 2
V
k


RESONANT ICS IN THE POLAR GAP
We have a resonance condition
(1  Vc cos  )   B
This condition is not
been satisfied for
usual pulsars, only
for mPSRs
 
B

V
(1  Vc cos  )
Due to relativistic aberration 1-(V/c) cos  1/2 << 1 and

k
z
from we obtain the scattered photon frequency
   B 



k
For energy emitted per second by single particle we have
 3
 
d
V
dq  d  3  (1  c cos  )
 N (k )d k d
4
dd 
where N(k) is a photon distribution of low frequency emission
  2c3
 1 ( 3 )
N (k ) 
(  1)U min


 2d 3 k
I
  N (k ) (2 )3  U  cR
I R ( )   
SPECTRUM AND TOTAL ELECTRON ENERGY LOSSES IN
RESONANT ICS
For a power-law initial photon distribution we have for a spectrum of ICS
 1
2 (  1) mc2min

 1
dq  d 
c

U

T
2 
B2
dq
d 
where eff = 323T, U is an energy density of low frequency emission

Frequencies of resonant ICS photons lie in a range B/ ≤ ≤ B
Total energy losses of electron due to resonant ICS is found to be
 mc
2 (  1)
 d 
q()   

c eff U  1 
 dt  RICS 2(2   )
 min

2
  min
  
  B




The resonant ICS energy losses strongly depend on low-frequency emission spectrum
INFLUENCE OF RESONANT ICS ENERGY LOSSES ON
ELECTRON ACCELERATION IN THE GAP
Electron acceleration process is described by an equation
 eff U
d eE ( z )
 1


g

dz
mc 2
mc 2
g

2 (  1) mc
2(2   ) min
2

  min
 B




where eff = 323T,  is a spectral index of low frequency radiation luminosity.
Further estimation will be for an acceleration field form
 B  1 s 
E ( z )  1.46 12    
 10 G   P 
3/ 2
cos 
Very
high
energy
losses
Acceleration
P = 2 ms, B = 109 G
FREQUENCIES OF ICS PHOTONS AND TOTAL LUMINOSITY
ESTIMATION
 ≤ max = B m
(m is a maximal Lorentz factor)
 B   m 
 6 
9
10
G

  10 
 max  1.6  10 22 s 1 
soft -spectral range
Discussed mechanism is a source of hard X-ray and soft -photons
Total luminosity is given by
I    PC  q() f (, z )ddz
where PC is a polar cap area, q() is ICS energy losses of single electron, f(,z) is an
electron distribution
2
2 (  1)
 1  mc
q ( ) 
c eff U  
2(2   )
 min
f e (, z )  ne (  ( z ))
  min
  
  B
ne  nGJ 




(z)

2ce
ne average electron number density in the gap
z
NUMERICAL ESTIMATES
Estimate of total ICS luminosity
2
2 (  1)
 1  mc
I 
c PC nGJ  eff hU m 
2(2   )
 min

  min
  
  B




 is a spectral index of radio emission, U is the radio emission energy density, h is the gap
height, min is a minimal frequency of initial photons
For B = 109 G, P = 2 ms, IR = 1029 erg/s and  = 2.5 we have
I  2 1033 erg/s,
max  4 1022 s-1
mPSR
J0030+0451
J0218+4232
J0613-0200
J0751+1807
I, erg/s
0.57  1033
2.7  1034
0.89  1033
0.47  1033
From 1-st Fermi LAT pulsar
catalogue (Abdo et al., 2010)
Resonant ICS luminosities are
comparable with observed
-luminosities of mPSRs
CONCLUSIONS
• We have considered a resonant inverse Compton scattering of the
radio emission in a polar gap of a millisecond pulsar. Radio emission
is supposed to arise due to coherent emission of electrons
accelerated in a strong electric field.
• The total energy losses due to resonant ICS have been obtained
and the electron acceleration process has been studied with taking
into account resonant ICS.
• Resonant ICS of low frequency photons in the gap was found to be
an effective source of hard X-ray and soft -radiation of millisecond
pulsars.
•The total power emitted due to ICS has been estimated. These
estimates are in good agreement with the Fermi LAT observation
data on -radiation from millisecond pulsars.
REFERENCES
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V.S. Beskin, MHD Flows in Compact Astrophysical Objects, Springer (2010).
A.V. Bilous, V.I. Kondratiev, M.V. Popov et al., astro-ph/0711.4140 (2007).
A.V. Bilous, V.I. Kondratiev, M.A. McLaughlin et al., ApJ., 728, 110, (2011) .
T.H. Hankins, J.A. Eilek, Astrophys. J., 670, 693 (2007).
V.A. Izvekova, A.D. Kuzmin, V.M. Malofeev,et al., Ap.Space Sci., 78, 45 (1981).
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V.M. Kontorovich, ВАНТ, №4 (68), 143 (2010) (In Russian); astro-ph/0911.3272 (2009).
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V.M. Kontorovich, A.B. Flanchik, International Conference “Physics of Neutron Stars -2011” Abstract
book, p. 75 (2011).
L.D. Landau, E.M. Lifshitz, Classical Theory of Fields, Butterworth, 1987, 438 p.
V.M. Malofeev, J.A. Gil, A. Jessner et al., Astron. Astrophys. 285, 201 (1994).
V.M. Malofeev, I.F. Malov, Astron. Zh., 57, 90 (1980).
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THANK YOU FOR ATTENTION!
Institute of Radio Astronomy
Nat. Acad. of Science of Ukraine, Kharkov, Ukraine (RI NANU)
Decametric wave radio telescope
UTR-2 of RI NANU, Kharkov
AVERAGE SPECTRA OF ELECTRON RADIATION IN THE
INNER
GAP


r2 
 R*
B

E0 (r )  Emax 1 
RPC  R*


2 
RPC

c
Power emitted by single particle is
2e 2 w2 (r ) 2e3 E0 (r )
I (r ) 

3
3mc h
3c
The emission spectrum and frequency
range are
2eE0 (r )
I (r )
I (r ,  )d 
d , c (r ) 
c ( r )
mh
r
dr
I (r ,  )

d
c (r )

2
 c2 (r )
eEmax 
r2 
1  2 

2mh  RPC 
The pulsar radio emission mechanism
must be coherent to provide very
high brightness temperatures which
may reach up 1031 K
COHERENT EMISSION SPECTRUM
Average spectrum is given by (Kontorovich, Flanchik, 2011)
RPC 1
I ( )  2

2
 m2
2
I (r ,  ) N block (r ) N coh
(r ,  ) rdr
0
N block 
N block
2
 PC
 PC
2
2
,  PC  RPC
RPC
N
coh
rdr  N e
0
Ne  nePCL is the total number of electrons
determined by average current <j>  jGJ  B/2
Nblock is the number of
coherent blocks with a
cross section  2, ( is a
wavelength)
Ncoh is the number of
electrons in a coherent
block
L is the maximal height of
the radiation formation
region
N coh  2 Lne
ne  nGJ 
B
2ce
POWER-LAW ASYMPTOTIC OF AVERAGE SPECTRA
We obtain for average spectrum
I ( )  2 22 ne2
b ( )

L2 (r )I (r ,  ) rdr
0
where b()  Rpc(1 - 2/m2)1/2 , and L = L(r) is a height of single coherent emission region,
I(r, ) is a spectrum of single particle.
Assuming L  zc(r), we have for the average spectrum (Kontorovich, Flanchik, 2011)
const 
 
2eB
1 
 , m  
I ( ) 
2 
  m 
mc
Spectral index   2 is close to average
spectral index of pulsars <>  1.8 ± 0.3
(Malofeev, 1994). There are a lot of radio
pulsars with such spectrum.
log I()

 

I ( )   2 1 

m


log 