RESONANT COMPTON SCATTERING RESONANT COMPTON SCATTERING AND CONNECTION BETWEEN GAMMA AND CONNECTION BETWEEN GAMMA

EMISSION AND RADIO EMISSION IN EMISSION AND RADIO EMISSION IN MILLISECOND PULSARSMILLISECOND 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. INTRODUCTION. POLAR GAP IN PULSAR MAGNETOSPHEREPOLAR 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 MAGNETOSPHEREBASIC PROCESSES IN A PULSAR MAGNETOSPHERE

Acceleration of electrons in a polar gap

Hard -photon

emission

e-e+pair production

by high energy -photons

Synchrotron emission by

produced electrons & positrons

Next generation pair production by synchrophotons

Observed pulsar -emission formation

Electromagnetic cascade of e-e+ plasma production:

Filling the pulsar

magnetosphere with the

plasma

Arising of instabilities in the plasma, excitation of plasma waves

Observed pulsar radio

emission formation

Electromagnetic cascades in pulsars – Harding & Daugherty, 1982

MILLISECOND PULSARSMILLISECOND PULSARS

Periods: P =1.1 ms – 30 ms,Periods: P =1.1 ms – 30 ms, dP/dt = 10dP/dt = 10-21 -21 –– 1010-19 -19 s/ss/s Surface magnetic fields: B Surface magnetic fields: B 10 1088 – 10 – 1099 G G Rotation total energy: ERotation total energy: Err = MR = MR2222/2 ~ 10/2 ~ 105151 – 10 – 105252 erg erg

Rotation energy losses -dERotation energy losses -dErr/dt = MR/dt = MR22 d d/dt ~10/dt ~103434 – 10 – 103636 erg/s 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 EMISSIONPULSAR 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)

• Radio emission frequency range: 10 MHz 10 GHz

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)

Example of pulsar radio spectrum (Malofeev, Malov, 1994)

PSR B0531+21

= 9.25 GHz

)(RI

PROPERTIES OF MILLESECOND PULSAR X-RAY & GAMMA PROPERTIES OF MILLESECOND PULSAR X-RAY & GAMMA EMISSIONEMISSION

• With help of Fermi LAT With help of Fermi LAT 2727 mPSRs with mPSRs with --emissionemission were discovered (Abdo et al., 2010) were discovered (Abdo et al., 2010)

•Gamma luminosities of mPSRs lie in a range Gamma luminosities of mPSRs lie in a range 10103232 erg/s ≤ I erg/s ≤ I ≤ 10 ≤ 103434 erg/s erg/s

• Photon energy range for mPSR Photon energy range for mPSR -emission-emission

GeVMeV 101

Friere et al., 2011

• Many millisecond pulsars are sources Many millisecond pulsars are sources of X-rays. of X-rays.

• Their X-ray emission usually has both Their X-ray emission usually has both a thermal and a non-thermal a thermal and a non-thermal components.components.

• Thermal X-ray emission is just Thermal X-ray emission is just emission from heated polar cap with T emission from heated polar cap with T = 10= 1066 K. K.

• The total X-ray luminosities are The total X-ray luminosities are 10102929 erg/s ≤ Ierg/s ≤ IXX ≤ 10 ≤ 103232 erg/s, and photon erg/s, and photon energies from a few keV (Kaspi et al., energies from a few keV (Kaspi et al., 2004)2004)

RADIO, X-RAY AND GAMMA EMISSION OF MILLISECOND RADIO, X-RAY AND GAMMA EMISSION OF MILLISECOND PULSARS – WHAT IS AN ORIGIN?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, 2011Kontorovich, 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 -emission

e- e-

Non-resonant ICSHard -emission with photon energies

up to several GeV

Resonant ICSHard X-ray and soft -emission with

photon energies up to 100 MeV

RADIO EMISSION FORMATION IN A POLAR GAPRADIO EMISSION FORMATION IN A POLAR GAP

Accelerating electric field in a mPSR polar gap is cos1

1046.1)(

2/3

12

P

s

G

BzE

(E(z) in Gausses)(Rudak, Dyks, 2000)

)(zw

zmz

The acceleration maximum at low altitudes z << h

The particle acceleration along magnetic force line is

)(

)()(

3 zm

zeEzw

(z) = (1- v2/c2)-1/2 is a Lorentz factor. Total power emitted by a single particle has a form

32

24

3

2

cm

EeI

The electrons in the gap must emit coherently to provide very high brightness temperatures TR 1031 K.

sergc

RBIR /1010~ 3029

2

3322*

where * 102 cm, B 108-109 G, = 2/P.

Typical radio luminosities

of mPSRs

Taking into account contributions of all electrons over all polar gap we estimate the total radio emission power

INVERSE COMPTON SCATTERING IN A POLAR GAPINVERSE COMPTON SCATTERING IN A POLAR GAP

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

cos1

cos1

cV

cV

r

e e

Here we consider a resonant Compton scattering, and a differential cross section has a form in electron rest frame (Herold, 1979, Dermer, 1990)

)()(4

323 2

BTR

mc

dd

d

z

V

k

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

23

2

)cos1)(cos1(

cos1

cos1

)cos1(

4

323

c

VcV

cVcV

cV

B

Tmc

dd

d

RESONANT ICS IN THE POLAR GAPRESONANT ICS IN THE POLAR GAPWe have a resonance condition

BcV )cos1(

from we obtain the scattered photon frequency

)cos1(

cV

B

This condition is not been satisfied for usual pulsars, only for mPSRs

Due to relativistic aberration 1-(V/c) cos 1/2 << 1 and B

For energy emitted per second by single particle we have

dkdkNdd

dddq c

V 33

)()cos1(4

z

V

k

k

where N(k) is a photon distribution of low frequency emission

)3(1min

32

)1()( Uc

kN

)(

)2(

2)(

3

3

R

R

I

c

IU

kdkN

SPECTRUM AND TOTAL ELECTRON ENERGY LOSSES IN SPECTRUM AND TOTAL ELECTRON ENERGY LOSSES IN RESONANT ICSRESONANT ICS

For a power-law initial photon distribution we have for a spectrum of ICS

12

1min

2

2

)1(2

Ucmc

ddq TB

d

dq

Frequencies of resonant ICS photons lie in a range B/ ≤ ≤ B

Total energy losses of electron due to resonant ICS is found to be

where eff = 323T, U is an energy density of low frequency emission

Beff

RICS

mcUc

dt

dq min

min

21

)2(2

)1(2)(

The resonant ICS energy losses strongly depend on low-frequency emission spectrum

INFLUENCE OF RESONANT ICS ENERGY LOSSES ON INFLUENCE OF RESONANT ICS ENERGY LOSSES ON ELECTRON ACCELERATION IN THE GAPELECTRON ACCELERATION IN THE GAP

Electron acceleration process is described by an equation

122

)(

mc

Ug

mc

zeE

dz

d eff

B

mcg min

min

2

)2(2

)1(2

where eff = 323T, is a spectral index of low frequency radiation luminosity.

Further estimation will be for an acceleration field form cos1

1046.1)(

2/3

12

P

s

G

BzE

P = 2 ms, B = 109 G

Acceleration

Very high energy losses

FREQUENCIES OF ICS PHOTONS AND TOTAL LUMINOSITY ESTIMATION

≤ max = B m (m is a maximal Lorentz factor)

69122

max 1010106.1 m

G

Bs soft -spectral range

Discussed mechanism is a source of hard X-ray and soft -photons

Total luminosity is given by dzdzfqI PC ),()(

where PC is a polar cap area, q() is ICS energy losses of single electron, f(,z) is an electron distribution

Beff

mcUcq min

min

21

)2(2

)1(2)(

))((),( znzf ee ce

nn GJe 2

ne average electron number density in the gap

(z)

z

NUMERICAL ESTIMATESNUMERICAL ESTIMATES

BmeffGJPC

mchUncI min

min

21

)2(2

)1(2

Estimate of total ICS luminosity

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

CONCLUSIONSCONCLUSIONS• 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.

REFERENCESREFERENCES

A. A. Abdo, M. Ackermann, M. Ajello et al., Ap J. Suppl. Series, 187, 460 (2010).

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).

V.M. Kontorovich, A.B. Flanchik, Journal Exper. & Theor. Physics, 106, 869 (2008).

V.M. Kontorovich, ВАНТ, №4 (68), 143 (2010) (In Russian); astro-ph/0911.3272 (2009).

V.M. Kontorovich, Journal Exper. & Theor. Physics, 137, 1107 (2010).

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).

I. F. Malov, Radio Pulsars. Moscow: Nauka, 2004 (In Russian).

D. Moffett, T.H. Hankins. Astrophys.J., 468, 779 (1996).

THANK YOU FOR ATTENTION!

Decametric wave radio telescopeUTR-2 of RI NANU, Kharkov

Institute of Radio AstronomyNat. Acad. of Science of Ukraine, Kharkov, Ukraine (RI NANU)

AVERAGE SPECTRA OF AVERAGE SPECTRA OF ELECTRONELECTRON RADIATION IN THE RADIATION IN THE INNER GAPINNER GAP

dr r

2

2

max0 1)(PCR

rErE

c

RRRPC

**

hmc

rEe

c

rwerI

3

)(2

3

)(2)( 0

3

3

22

mh

reErd

r

rIdrI c

c

)(2)(,

)(

)(),( 0

Power emitted by single particle is

The emission spectrum and frequency range are

2

2max22 1

2)(

PCc

R

r

mh

eEr

),( rI

)(rc

dThe pulsar radio emission mechanism must be coherent to provide very high brightness temperatures which may reach up 1031 K

B

COHERENT EMISSION SPECTRUMCOHERENT EMISSION SPECTRUM

rdrrNrNrII coh

R

block

mPC

),()(),(2)( 2

1

0

2

2

Average spectrum is given by (Kontorovich, Flanchik, 2011)

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

22

, PCPCPC

block RN

e

R

cohPC

block NrdrNNPC

0

2

Ne nePCL is the total number of electrons determined by average current <j> jGJ B/2

ecoh nLN 2

ce

Bnn GJe 2

POWER-LAW ASYMPTOTIC OF AVERAGE SPECTRAPOWER-LAW ASYMPTOTIC OF AVERAGE SPECTRA

We obtain for average spectrum

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)

mc

BeconstI m

m

2,1)(

2

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()

log

m

I 1)( 2

rdrrIrLnIb

e ),()(2)()(

0

2222