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A.B. Flanchik

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.

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A.B. Flanchik

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  1. 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

  2. THE REPORT PLAN • 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. • 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. • 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.

  3. INTRODUCTION. POLAR GAP IN PULSAR MAGNETOSPHERE The polar gapis 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. P = 1.2 ms – 10 s, B = 108 1013 G, M  MSun , R  106 cm

  4. BASIC PROCESSES IN A PULSAR MAGNETOSPHERE Electromagnetic cascade of e-e+plasma production: e-e+pair production by high energy -photons Synchrotron emission by produced electrons & positrons Acceleration of electrons in a polar gap Hard -photon emission Observed pulsar -emission formation Next generation pair production by synchrophotons Observed pulsar radio emission formation Arising of instabilities in the plasma, excitation of plasma waves Filling the pulsar magnetosphere with the plasma Electromagnetic cascades in pulsars – Harding & Daugherty, 1982

  5. 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.

  6. 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) • Radio emission frequency range: • 10MHz  10 GHz PSR B0531+21 Example of pulsar radio spectrum (Malofeev, Malov, 1994)  = 9.25 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)

  7. PROPERTIES OF MILLESECOND PULSAR X-RAY & GAMMA EMISSION • With help of Fermi LAT 27 mPSRs with -emissionwere 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 • Many millisecond pulsars are sources of X-rays. • 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

  8. 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 -emission e- e- Hard -emission with photon energies up to several GeV Non-resonant ICS Hard X-ray and soft -emissionwith photon energies up to 100 MeV Resonant ICS

  9. RADIO EMISSION FORMATION IN A POLAR GAP Accelerating electric field in a mPSR polar gap is (Rudak, Dyks, 2000) (E(z) in Gausses) The particle acceleration along magnetic force line is (z) = (1- v2/c2)-1/2 is a Lorentz factor. Total power emitted by a single particle has a form The acceleration maximum at low altitudes z << h 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 luminosities of mPSRs where *  102 cm, B  108-109 G,  = 2/P.

  10. INVERSE COMPTON SCATTERING IN A POLAR GAP r 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  Here we consider a resonant Compton scattering, and a differential cross section has a form in electron rest frame (Herold, 1979, Dermer, 1990) z 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 V k  

  11. RESONANT ICS IN THE POLAR GAP We have a resonance condition This condition is not been satisfied for usual pulsars, only for mPSRs from we obtain the scattered photon frequency Due to relativistic aberration 1-(V/c) cos  1/2 << 1 and For energy emitted per second by single particle we have where N(k) is a photon distribution of low frequency emission

  12. SPECTRUM AND TOTAL ELECTRON ENERGY LOSSES IN RESONANT ICS For a power-law initial photon distribution we have for a spectrum of ICS 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 The resonant ICS energy losses strongly depend on low-frequency emission spectrum

  13. INFLUENCE OF RESONANT ICS ENERGY LOSSES ON ELECTRON ACCELERATION IN THE GAP Electron acceleration process is described by an equation where eff = 323T,  is a spectral index of low frequency radiation luminosity. Further estimation will be for an acceleration field form Very high energy losses Acceleration P = 2 ms, B = 109 G

  14. FREQUENCIES OF ICS PHOTONS AND TOTAL LUMINOSITY ESTIMATION  ≤ max =B m (m is a maximal Lorentz factor) soft -spectral range Discussed mechanism is a source of hard X-ray and soft -photons Total luminosity is given by where PC is a polar cap area, q() is ICS energy losses of single electron, f(,z) is an electron distribution (z) z ne average electron number density in the gap

  15. NUMERICAL ESTIMATES 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 Resonant ICS luminosities are comparable with observed -luminosities of mPSRs From 1-st Fermi LAT pulsar catalogue (Abdo et al., 2010)

  16. 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 -radiationfrom millisecond pulsars.

  17. REFERENCES 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).

  18. 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

  19. AVERAGE SPECTRA OF ELECTRONRADIATION IN THE INNER GAP Power emitted by single particle is The emission spectrum and frequency range are The pulsar radio emission mechanism must be coherent to provide very high brightness temperatures which may reach up 1031 K

  20. COHERENT EMISSION SPECTRUM 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 numberof electronsin a coherent block L is the maximal height of the radiation formation region Ne nePCL is the total number of electrons determined by average current <j>  jGJ  B/2

  21. POWER-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) log I() 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 

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