Cosmic (Particle) Accelerators II - Sources & Mechanisms - Frank - PowerPoint PPT Presentation

Cosmic (Particle) Accelerators II - Sources & Mechanisms - Frank M. Rieger ISAPP School Heidelberg, May 28, 2019 Max Planck Institut 
 ITA Univ. Heidelberg für Kernphysik Heidelberg, Germany

Outline radio (VLA) • Particle Acceleration Mechanisms • Gap-type particle acceleration (pulsars, black holes) optical (HST) ‣ concept & relevance • Fermi-type particle acceleration ‣ stochastic 2nd order Fermi ‣ shock acceleration - 1st order Fermi (SNR) ‣ shear acceleration (AGN) • Conclusions 2

Possible Acceleration Processes & Sites ( not exhaustive ) radio (VLA) “Fermi-type” “one-shot” wave-particle interactions optical (HST) stochastic shock “vacuum” gap reconnection shear (1st order) (2nd order) AGN & Pulsars… AGN, PWN… AGN, SNRs, PWN.. AGN… AGN… charge density? efficiency efficiency? efficiency? limited in size? ( Γ s , σ )? topology? spectral energetic efficiency? transparency? localized? shape? seeds? spectral shape? 3

⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ The Occurrence of Gaps in Pulsar Magnetospheres I • in vacuum: e E II >> F grav at surface Goldreich & Julian 1969 ‣ vacuum conditions cannot exist • if enough charges, force-free conditions possible: optical (HST) E = − ( v × B ) / c = − ([ Ω × ⃗ r ] × B ) / c • Goldreich-Julian charge density: ∇ ⋅ Ω ⋅ E B ≃ − ρ GJ = 4 π 2 π c • co-rotating dipole magnetic field defines null charge surface e θ ) / r 3 B ∝ (2 cos θ e r + sin θ ⇒ ρ GJ ( r ) ∝ (sin 2 θ − 2 cos 2 θ ) / r 3 R LC =c/ Ω • no particle acceleration (E || =0) 4

⃗ ⃗ ⃗ ⃗ ⃗ ⃗ The Occurrence of Gaps in Pulsar Magnetospheres II Possible sites of particle acceleration • ideal MHD in most of magneto- sphere: E ⋅ B = 0 optical (HST) • deficient charge supply: E ⋅ B ≠ 0 ⇒ particle acceleration • Solve Gauss’ law: ∇ ⋅ E = 4 π ( ρ − ρ GJ ) (Credits: A. Harding) (e.g., Ruderman & Sutherland 1975; Cheng et al. 1985; Muslimov & Harding 2003) 5

The Occurrence of Gaps in BH Magnetospheres ‣ Null surface in Kerr Geometry (r ~ r g ≣ GM/c 2 ) for force-free magnetosphere, vanishing of poloidal electric field E p ∝ ( Ω F - ω ) ∇Ψ = 0, ω =Lense-Thirring optical (HST) ⇒ 𝜍 GJ changes sign, “gap” may easily develop ‣ Stagnation surface (r ~ few r g ) Inward flow of plasma below due to gravitation field, outward motion above ⇒ charges need to be continuously replenished Levinson & Segev 2017 (e.g., Blandford & Znajek 1977; Beskin et al. 1992, Hirotani & Okamoto 1998) 6

The Conceptual Relevance of BH Gaps • BH-driven jets (Blandford-Znajek) ‣ Self-consistency: Plasma source needed to ensure force-free MHD optical (HST) • Non-thermal Particle Acceleration ‣ Implication: efficient (direct) acceleration of electrons & positrons • Radiation & Pair Cascade….. ‣ Features: expect ɣ -ray production, ‣ ɣɣ -absorption triggers pair cascade ‣ generating charge multiplicity ‣ ensuring electric field screening (closure) Koide+ 7

Gamma-Ray Emission from AGN Magnetospheres ‣ Direct electric field acceleration: Rate of energy gain for electron: d ɣ /dt ∝ e Δϕ gap · (c/h) optical (HST) ‣ Curvature & Inverse Compton: HE ɣ -rays via curvature: 𝓦 ~(0.2c) ( ɣ 3 /R c ) VHE ɣ -rays via IC: h 𝓦 ≲ ɣ m e c 2 ‣ Accretion environment (RIAF): Radiatively inefficient needed to facilitate escape of VHE photons ‣ Maximum Gap luminosity: L gap ∝ n GJ (Volume) (d ɣ /dt) 8

Characterizing the Magnetospheric Potential dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) Possible boundary conditions in the pulsar case : optical (HST) • “ non-free escape” (Ruderman): E II (h=0) ≠ 0, E || (h=H)=0, ρ e << ρ GJ : • “ free escape” ( Arons ): E II (h=0)=0, E || (h=H)=0, ρ e ~ ρ GJ ( ρ e ≠ ρ GJ ≡ Ω B cos θ b ) : 9

Characterizing the Magnetospheric Potential dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) Possible boundary conditions in the pulsar case : optical (HST) • “ non-free escape” (Ruderman): E II (h=0) ≠ 0, E || (h=H)=0, ρ e << ρ GJ : E II h H • “ free escape” ( Arons ): E II (h=0)=0, E || (h=H)=0, ρ e ~ ρ GJ ( ρ e ≠ ρ GJ ≡ Ω B cos θ b ) : 9

Characterizing the Magnetospheric Potential dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) Possible boundary conditions in the pulsar case : optical (HST) • “ non-free escape” (Ruderman): E II (h=0) ≠ 0, E || (h=H)=0, ρ e << ρ GJ : dE || E II dh ' � 4 π ρ GJ ) E || ( h ) = � 4 π ρ GJ h + const E || ( h = H ) = 0 ) const = 4 πρ GJ H ( H � h ) Thus : E || ( h ) = E 0 , where E 0 = 4 πρ GJ H h H H • “ free escape” ( Arons ): E II (h=0)=0, E || (h=H)=0, ρ e ~ ρ GJ ( ρ e ≠ ρ GJ ≡ Ω B cos θ b ) : 9

Characterizing the Magnetospheric Potential dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) Possible boundary conditions in the pulsar case : optical (HST) • “ non-free escape” (Ruderman): E II (h=0) ≠ 0, E || (h=H)=0, ρ e << ρ GJ : dE || E II dh ' � 4 π ρ GJ ) E || ( h ) = � 4 π ρ GJ h + const E || ( h = H ) = 0 ) const = 4 πρ GJ H ( H � h ) Thus : E || ( h ) = E 0 , where E 0 = 4 πρ GJ H h H H • “ free escape” ( Arons ): E II (h=0)=0, E || (h=H)=0, ρ e ~ ρ GJ ( ρ e ≠ ρ GJ ≡ Ω B cos θ b ) : 9

Characterizing the Magnetospheric Potential dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) Possible boundary conditions in the pulsar case : optical (HST) • “ non-free escape” (Ruderman): E II (h=0) ≠ 0, E || (h=H)=0, ρ e << ρ GJ : dE || E II dh ' � 4 π ρ GJ ) E || ( h ) = � 4 π ρ GJ h + const E || ( h = H ) = 0 ) const = 4 πρ GJ H ( H � h ) Thus : E || ( h ) = E 0 , where E 0 = 4 πρ GJ H h H H • “ free escape” ( Arons ): E II (h=0)=0, E || (h=H)=0, ρ e ~ ρ GJ ( ρ e ≠ ρ GJ ≡ Ω B cos θ b ) : dE || dh ' 4 π d ( ρ � ρ GJ ) | h = H/ 2 ( h � H/ 2) dh h ( H � h ) E A =2 π d ( ρ � ρ GJ ) H 2 ) E || ( h ) = � E A with 9 H 2 dh

Magnetospheric Potential & Jet Power in AGN - Differences Solving Gauss’ laws depending on different boundaries radio (VLA) dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) highly under-dense: 𝞻 e << 𝞻 GJ weakly under-dense: 𝞻 e ~ 𝞻 GJ optical (HST) ‣ Gap potential: ‣ Gap potential: ‣ Δϕ gap ~ a spin r g B (H/r g ) 2 ‣ Δϕ gap ~ a spin r g B (H/r g ) 3 ‣ Constraining losses: ‣ Constraining losses: ‣ Curvature, IC… ‣ IC, curvature… ‣ Jet power: ‣ Jet power: ‣ L VHE ~ L jet x (H/r g ) 2 … ‣ L VHE ~ L jet x (H/r g ) 4 … e.g., Blandford & Znajek 1982, e.g., Hirotani & Pu 2016 Levinson 2000 Katsoulakos & FR 2018 Levinson & FR 2011 10

Magnetospheric Potential & Jet Power in AGN - Differences Solving Gauss’ laws depending on different boundaries radio (VLA) dE || ”Gauss 0 law” dh = 4 π ( ρ e − ρ GJ ) highly under-dense: 𝞻 e << 𝞻 GJ weakly under-dense: 𝞻 e ~ 𝞻 GJ optical (HST) ‣ Gap potential: ‣ Gap potential: ‣ Δϕ gap ~ a spin r g B (H/r g ) 2 ‣ Δϕ gap ~ a spin r g B (H/r g ) 3 ‣ Constraining losses: ‣ Constraining losses: ‣ Curvature, IC… ‣ IC, curvature… ‣ Jet power: ‣ Jet power: ‣ L VHE ~ L jet x (H/r g ) 2 … ‣ L VHE ~ L jet x (H/r g ) 4 … Jet power constraints can become relevant e.g., Blandford & Znajek 1982, e.g., Hirotani & Pu 2016 Levinson 2000 Katsoulakos & FR 2018 Levinson & FR 2011 10

Timescales (example) 10 Loss time scales: τ cur 𝜐 cur ∝ 1/ ɣ 3 , τ ic 8 τ acc ( η =1.0, ν =1.0) 𝜐 IC ∝ 1/ ɣ 𝛃 ( 𝛃 =1 Thompson, 𝛃 <0 KN) Characteristic time scale, log 10 ( τ ) τ acc ( η =1.0, ν =2.0) 6 τ acc ( η =1/6, ν =3.0) optical (HST) 4 2 0 Energy gain − 2 − 4 − 6 5 6 7 8 9 10 11 12 13 Lorentz Factor, log 10 ( γ e ) Parameters: M 9 =5, ṁ =10 -4 (ADAF), h/r g =0.5 Katsoulakos & FR 2018 11

Timescales (example) 10 Loss time scales: τ cur 𝜐 cur ∝ 1/ ɣ 3 , τ ic 8 τ acc ( η =1.0, ν =1.0) 𝜐 IC ∝ 1/ ɣ 𝛃 ( 𝛃 =1 Thompson, 𝛃 <0 KN) Characteristic time scale, log 10 ( τ ) τ acc ( η =1.0, ν =2.0) 6 τ acc ( η =1/6, ν =3.0) optical (HST) 4 can reach Lorentz 2 factors ɣ ~10 10 0 Energy gain − 2 − 4 − 6 5 6 7 8 9 10 11 12 13 Lorentz Factor, log 10 ( γ e ) Parameters: M 9 =5, ṁ =10 -4 (ADAF), h/r g =0.5 Katsoulakos & FR 2018 11

Example: Phenomenological Relevance of Gaps in AGN ‣ Gamma-Ray Emission from Radio Galaxies: misaligned jets: moderate Doppler boosting of jet emission only ⇒ gap IC & curvature emission may show up at hard HE-VHE gamma-rays ‣ Possibly related to observable AGN features in: optical (HST) • M87 (d ~17 Mpc): day-scale VHE variability, radio-VHE outburst correlation… • Cen A (d ~ 4 Mpc): spectral hardening of core emission above ~5 GeV… • IC 310 (d ~ 80 Mpc): rapid (5 min) VHE variability, huge power (L ɣ ~ 10 44 erg/sec) VHE flare in Nov 2012 � 10 � � � � 11 � � log � E 2 dN � dE � erg cm � 2 s � 1 �� � � � � � � � 12 � � � � � � M87 Cen A IC 310 � 13 � 14 � 1 0 1 2 3 4 log � E � GeV �� 12 (cf. FR & Levinson 2018 for review and references)