Acceleration and radiation mechanisms in extragalactic gamma ray - PowerPoint PPT Presentation

Acceleration and radiation mechanisms in extragalactic gamma ray sources E.V. Derishev Institute of Applied Physics, Nizhny Novgorod, Russia

Are jets efficient emitters? ? Prompt emission Cyg A Afterglow AGNs: GRBs: AGN jet luminosity GRB (prompt) energetics 10 48 erg/s few × 10 54 erg up to up to radio lobe luminosity afterglow energetics 10 44 erg/s few × 10 52 erg of the order of up to Not too much room for inefficient sources

Timescales in a relativistic jet variability timescale, t v R θ dinamical timescale, t d light-crossing time, t l In the comoving frame: t v ≃ t d t d = R/ (Γ c ) t l = min [ R/ (Γ c ) , θR/c ] For a wide jet ( θ ≥ Γ − 1 ): t v ≃ t d ≃ t l

Are the jets wide? AGNs: you can see it GRBs: check observed correlations Narrow jets imply a correlation between peak energy ε p and energetics E GRB : E GRB ∝ ε 3 p Observed correlation: E GRB ∝ ε 2 Amati, 2006 p M 87

Radiation mechanisms electrons 3 γ 2 σ T cB 2 L sy = 4 ε sy ∼ γ 2 � eB • Synchrotron radiation 8 π m e c undulator radiation • Inverse Compton radiation When coupled to diffusive shock acceleration, ε sy � m e c 2 /α f ∼ 70 MeV • Bremsstrahlung due to radiative losses, that limit acceleration protons • Synchrotron radiation • Inelastic nucleon collisions • Coulomb losses

Radiation mechanisms Toptygin & Fleishman 1987, Medvedev 2000 electrons 3 γ 2 σ T cB 2 L und = 4 ε und ∼ γ 2 � c • Synchrotron radiation 8 π d undulator radiation d < m e c 2 / ( eB ) differs from synchrotron if • Inverse Compton radiation • Bremsstrahlung ν F ν synchrotron ν 4/3 undulator protons ν • Synchrotron radiation ν 2 • Inelastic nucleon collisions • Coulomb losses d B

Radiation mechanisms electrons ( ε ph ≪ m e c 2 /γ ): Thomson regime • Synchrotron radiation L IC = 4 3 γ 2 σ T cw ph ε IC ∼ γ 2 ε ph undulator radiation • Inverse Compton radiation • Bremsstrahlung ( ε ph � m e c 2 /γ ): Klein-Nishina regime L IC < 4 3 γ 2 σ T cw ph ε IC ∼ γm e c 2 protons • Synchrotron radiation ε ph – background photons’ energy • Inelastic nucleon collisions w ph – background radiation energy density • Coulomb losses

Interlude: Two-photon absorption ε γ ≫ m e c 2 In the limit we have σ γγ ≈ 2 σ eγ

Two-photon absorption Optical depth for two-photon absorption τ γγ ( ω ) ≃ σ γγ N ph ( ω ∗ ) R Inverse Compton energy losses per particle ε ≃ 1 ˙ 2 ε σ eγ N ph ( ω ∗ ) c ( ˙ ε > ε/t v ) Under assumption of high radiation efficiency R ≃ ct v the optical depth of a source with size is τ γγ > 2 σ γγ ( ε/ 2) ≫ 1 σ eγ ( ε ) N ph ( ω ∗ ) – number density of photons with frequency ∼ ω ∗

2nd interlude: SSC vs ERC m e c w ′ Efficient cooling means that ph > • ) 2 Γ t v e 2 ( 32 π γ ′ m e c 2 9 2 π 2 ( � c ) 3 K ≃ w ′ Photons’ occupation number • ph ε 4 ∗ Comptonization in the Thomson regime, i.e. • Γ γ ′ > ε/m e c 2 ε ∗ < m e c 2 /γ ′ and ) 3 K > 9 π ε λ c ( (for SSC) α 2 Γ 4 ct v m e c 2 16 Hence, ) 3 K > 9 π ε λ c ( (for ERC) α 2 Γ 2 ct v m e c 2 16 ε ∗ – the energy of comptonized photon in the comoving frame α – the fine-structure constant – the electron Compton wavelength λ c

SSC vs ERC Assume: the photons’ occupation number does not exceed its magnitude at the peak of black-body spectrum, i.e. K < 0 . 02 obtain: independent lower limit to the Lorentz factor For synchrotron self Compton • ) 3 / 4 ( λ c ≃ 2 ε 3 / 4 ) 1 / 4 3 ε ( 12 Γ > m e c 2 α 1 / 2 t 1 / 4 c t v 3 For external radiation Compton • ) 3 / 2 ( λ c ≃ 4 ε 3 / 2 ) 1 / 2 Γ > 9 ε ( 12 m e c 2 t 1 / 2 α c t v 3

Radiation mechanisms electrons emission power density: • Synchrotron radiation w ff = 2 √ Tm e c 2 G ( n e , T ) πα f σ T c n 2 undulator radiation ˙ e • Inverse Compton radiation At an optical depth τ • Bremsstrahlung each electron on average radiates w ff = 2 Tm e c 2 G ( n e , T ) √ π α f τ protons n e • Synchrotron radiation f m e c 2 ∼ 25 eV T � α 2 inefficient unless • Inelastic nucleon collisions • Coulomb losses

Radiation mechanisms electrons • Synchrotron radiation undulator radiation • Inverse Compton radiation • Bremsstrahlung At a given energy protons 4    m e sy ∼ 10 − 13 L ( e ) L ( p ) L ( e ) sy = • Synchrotron radiation sy  m p • Inelastic nucleon collisions very slow mechanism, • Coulomb losses works only in TeV range

Radiation mechanisms electrons • Synchrotron radiation undulator radiation • Inverse Compton radiation • Bremsstrahlung protons • Synchrotron radiation end up with energetic electrons, • Inelastic nucleon collisions which radiate by either of the • Coulomb losses electron mechanisms

Acceleration in shear flows Berezhko & Krymskii 1981 Ostrowski 1990, 1998 Rieger & Duffy 2006 Acceleration rate ) 2 ( ∇ V ε = 3 D ˙ ε c For Bohm diffusion ε = ( ∇ V ) 2 ε = ( ∇ V ) 2 ε 2 ˙ ω B eBc ε – particle’s energy c 2 ω B – gyrofrequency, D = 3 ω B Acceleration fails against losses if R 0 < 3 × 10 30 L 3 / 2 45 cm Γ 4 R 0 – size of the central engine

Diffusive shock acceleration Acceleration rate V 2  η ≃ V 2   ε ≈ 1 r − 1 ˙ D ε  c 2 6 r r = u 1 ≤ 4 – shock compression u 2 ratio V – velocity of the shock D = p c 2 for Bohm diffusion 3 eB Spectrum of accelerated d N d ε ∝ ε − α particles: α = − r + 2 r − 1

Acceleration at relativistic shocks θ ∼ 2/Γ The energy gain factor g = (1 / 2) (Γ θ ) 2 ≃ 2 The probability of particle injection back to upstream must be ∼ 1 to get efficient acceleration. The actual probability depends on the (unknown) magnetic field geometry. d N d ε ∝ ε − 22 Favorable geometry gives, e.g., 9 (Keshet & Waxman, PRL 2005) “Realistic” geometry leads to very soft particle distributions, with energy concentrated near Γ 2 mc 2 (Niemiec & Ostrowski, ApJ 2006; Lemoine, Pelletier & Revenu, ApJ 2006) cf. talk by L. Sironi

Diffusive shock acceleration f�(��) � Γ – Lorentz-factor of the shock, γ – Lorentz-factor of an electron, Maximum�acceleration energy ω B = eB/m e c – gyrofrequency, “Thermal ” particles α – fine structure constant, Accelerated�particles � f ( γ ) – injection function 1 � m p c 2 m e (������) 2 m e � � B h f ( γ ) ∝ γ − s , Diffusive shock acceleration gives where s ≃ 2 . 2 (universal power-law)

Schematic broad-band spectrum ν F ν ε sy ε IC Synchrotron peak IC peak Synchrotron cut−off ν

Standard assignment of spectral features – F – log scale “Thermal” break Cut-off ν ν ν – log scale

... – standard problems • Position of the peak is too sensitive to the shock Lorentz-factor Photon energy at the peak in the comoving frame ) 2 � eB Γ m p ( ε ′ peak ∼ m e m e c ε peak ∝ Γ 4 in the laboratory frame (since B ∝ Γ) • The spectrum well above the peak frequency is universal and too hard N γ ∝ γ − 3 . 2 νF ν ∝ ν − 0 . 1 ⇒

... – standard problems • Low-frequency asymptotics in the fast-cooling regime is too soft The hardest possible injection f ( γ ) = δ ( γ − γ 0 ) gives for γ < γ 0 ; νF ν ∝ γη synchrotron losses νF ν ∝ ν 1 / 2 , if η = total radiative losses = const ⇒ more details on this point were given in the talk by E. Lefa

Another assignment of spectral features – F – log scale Cut-off “Thermal” break ν ν ν – log scale

... – other problems • The synchrotron cut-off frequency is too high At the maximum energy, the scattering length (gyroradius) equals to the radiation length: ) − 1 B 2 = γm e c 2 ( 4 η 3 γσ T 8 π eB m e c ≃ η m e c 2 � eB γ 2 So that σ T – Thomson cross-section max α • Low-frequency asymptotics in the fast-cooling regime is too soft The hardest possible injection f ( γ ) = δ ( γ − γ 0 ) gives νF ν ∝ γη for γ < γ 0 ; νF ν ∝ ν 1 / 2 , if η = const ⇒

A universal acceleration-radiation scheme for relativistic outflows?

What limits acceleration? Particle escape from the accelerator Degradation of particles’ energy Sinchrotron radiation • Inelastic collisions • Inverse Compton losses (for electrons) • Photomeson interactions and creation of e − e + pairs • (for protons and nuclei) The probability of photon-induced reaction is usually small, ≪ 1

How small has to be “small” to become dynamically negligible? For a non-relativistic shock, a probability ≪ 1 is always small For a relativistic flow, the answer is either ≪ 1 or ≪ 1 / Γ 2 , depending on what you are talking about If some energy leaks from downstream to upstream and mixes up with the upstream particles, we feed back to the shock Γ 2 times the initial energy! Γ is the Lorentz factor of the flow