Particle Acceleration in Astrophysics

Transcription

1 Particle Acceleration in Astrophysics Don Ellison, North Carolina State University Lecture 3: 1) Stochastic Acceleration (i.e., second-order Fermi) 2) Turbulence 3) Magnetic Field Amplification (MFA) in diffusive shock acceleration

2 Second-order Fermi ç è First-order Fermi First-order Fermi (DSA) is, in fact, a second-order process see, Jones, F.C. 1994, ApJS For shocks, momentum gain on crossing the shock is first-order in (u/v p ) (shock speed) / (particle speed) But, a particle must make many scatterings upstream and downstream from the shock for each crossing DSA is not faster because it is first-order and stochastic acceleration is second-order. It is faster because shock speeds are generally larger than scattering center speeds (clouds for E. Fermi, turbulence now) Need high B-fields for stochastic to dominate. Do not typically have this in IGM, ISM or interplanetary medium Do have conditions for stochastic to dominate in solar flares and most likely in GRB fireballs and pulsar winds

3 Equation of continuity for stochastic acceleration (Jones 1994): Solution : p&= α p is rate of momentum gain T is mean time particles stay in the accelerator, i.e., escape time This is only a power law if (αt esc ) is independent of momentum For TP DSA get f( p) p p 0 σ σ = r 3 1 Power law with index determined solely by shock compression ratio, r Note: here, f(p) is scalar distribution, not phase space distribution as used in previous slides

4 Stochastic è αt will depend on details of turbulence. è No simple physical reason why αt should be independent of momentum è No basic power law prediction from SA è Expect αt to vary with ion species (one success of stochastic model is explanation of 3 He/ 4 He ratios in solar flare events) è Expect αt to be quite different for ions and electrons First-order Fermi shock acceleration f( p) p p è In TP limit, spectral index does NOT depend on details of turbulence. è In TP limit, DSA predicts same power law shape for electrons, protons, and heavy ions. To good approximation, this is what is seen for CRs : 0 σ σ = 3 r 1

5 Cosmic rays measured at Earth Spectral shape of cosmic ray electron spectrum is similar when radiation losses are considered. Note: recent work shows small, but important, difference in shapes of H and He spectral measured at Earth p / He Δq = q p q He 0.1 Figure from P. Boyle & D. Muller via Nakamura et a Rigidity (GV), R = pc/(ez) PAMELA (Adriani et al. 2011) Stochastic acceleration cannot reproduce such similar spectral shapes. Stochastic acceleration is NOT acceleration mechanism for galactic CRs

6 Stochastic acceleration rate v A For stochastic acceleration, mean momentum gain per collision is second-order in (u A /v) The rate of momentum gain is this times collision frequency, ν Stochastic acceleration rate Here, v A is speed of scattering centers moving through plasma. v A called Alfven speed but turbulence is always more complex than simple Alfven waves

7 For First-order Fermi: Mean momentum gain per shock crossing : First order in u/v. But : When take into account the scattering upstream and downstream from the shock needed for each shock crossing, find crossing frequency is f cros u ν v So, rate of momentum gain is: = ν is collision frequency Acceleration rate for first-order Fermi: Identical form as stochastic: both have second-order term.

8 Second-order Fermi First-order Fermi Here, v A is speed of scattering centers within plasma and u is shock speed.

9 Second-order Fermi First-order Fermi Here, v A is speed of scattering centers within plasma and u is shock speed. Even in TP case, can have different scattering center speeds interacting with different energy particles and/or difference ion species For DSA, u is shock speed : Same for all particle species and momenta in test-particle case è TP approximation assumes scattering centers are frozen in fluid (or same for all momenta)

10 Typical values: v A B = Alfven speed 4πρ è ISM: B ~ 3 µg, n ~ 0.1 cm -3 è v A ~ 20 km/s. Shock speeds ~ 1000 km/s è SNR shocks with MFA: B ~ 300 µg, n ~ 1 cm -3 è v A ~ 650 km/s Shock speed ~ 1000 km/s è Solar wind: B ~ 10-4 G, n ~ 5 cm -3 è v A ~ 100 km/s Solar wind speed ~ 400 km/s. Interplanetary traveling shocks slower ~ 150 km/s è Solar corona: B ~ 100 G, n ~ 5 x 10 9 cm -3 è v A ~ 3 x 10 5 km/s Here stochastic acceleration highly likely Stochastic acceleration likely to be important wherever B-fields have substantial energy density è e.g., solar flares, GRBs, pulsar winds

11 log spectral density [ m -3 ] Interstellar turbulence Lazarian et al log wavenumber [ m -1 ] Sources of turbulence: Injection of turbulence by large-scale motions, cascading to shorter wavelengths, dissipation at shortest λ Turbulence, at some level, exists in all diffuse astrophysical environments For second-order Fermi acceleration to be important, there must be an external source of strong turbulence. Magnetic reconnection in solar flares and GRBs can turn magnetic energy stored in large B-fields into turbulence that can then acceleration particles. During second-order acceleration, the turbulence is damped as energy is transferred to non-thermal particle distributions. Note Kolmogorov spectrum

12 Solar Flares: Ideal location for magnetic reconnection and SA Image: NASA s Solar Dynamics Observatory captured this image of an M6.5 class flare at 3:16 EDT on April 11, This image shows a combination of light in wavelengths of 131 and 171 Angstroms. Credit: NASA/SDO 12

13 Petrosian 2012 Magnetic reconnection site in solar flare. Energy in B-field explosively turned into turbulence Can match observations : See Petrosian (2012) for references

14 Hoshino 2012: Reconnection PIC simulations PIC simulation showing SA as particle scatters between multiple magnetic islands created by reconnection Particle interacting with reconnection outflows

15 Sironi & Spitkovsky 2011 Sironi & Spitkovsky 2011 PIC simulation of Stripped Pulsar Wind Obliquely rotating relativistic pulsar wind sets up alternating B-fields: è reconnection è particle acceleration.

16 Sironi & Spitkovsky 2011 Energization of positrons interacting with current sheet Downstream spectra for different magnetizations Sironi & Spitkovsky 2011

17 Both first- and second-order acceleration require turbulence. But, shocks have an important advantage over stochastic acceleration in this regard: Shocks can, and do, produce their own turbulence. No independent, external source of turbulence is necessary for DSA to take place. When a supersonic plasma, even one with zero B-field, encounters a barrier : è currents will be generated by particles reflecting off barrier, è small-scale B-fields result (call this the Weibel instability if you like), è fresh, unshocked particles now gyrate in these fields and become randomized, è a shock quickly forms, è particles start to be accelerated by the shock and the streaming instability generates more magnetic field, etc.

18 Particle-in-cell (PIC) simulations (for example, Spitkovsky 2008) Here, relativistic, electron-positron shock this is a 2-D simulation But, good example of state-of-art Also, DS Shock upstream Mass density En. density in B Density B generated at shock B-field Start with NO B-field, Field is generated self-consistently (Weibel instability), Shock forms, see start of Fermi acceleration

19 Self-generated turbulence at weak Interplanetary shock ΔB/B ΔB/B ΔB/B Baring et al ApJ 1997 Indirect evidence for strong turbulence produced by CRs at strong SNR shocks Tycho s SNR Sharp X-ray synch edges

20 Evidence for High (amplified) B-fields in SNRs Sharp synch. X-ray edges Cassam-Chenai et al magnetically limited rim Radial cuts synch loss limited rim magnetically limited rim synch loss limited rim radio X-ray Chandra observations of Tycho s SNR (Warren et al. 2005) If emission drops from B-field decay instead of radiation losses, expect synch radio and synch X-rays to fall off together. Thin structures: evidence for radiation losses and, therefore, large, amplified B-fields. On order of 10 times higher than expected

21 Table from Caprioli et al 2009 Estimated shocked B-fields are considerably higher than compressed ISM B-field.

22 Magnetic Field Amplification (MFA): How do you start with B ISM 3 µg and end up with B 300 µg at the shock? Efficient diffusive shock acceleration (DSA) not only places a large fraction of shock energy into relativistic particles, but also amplifies magnetic field by large factors MFA is connected to efficient CR production, so nonlinear effects essential Bell & Lucek 2001 à apply Q-linear theory when ΔB/B >> 1; Bell 2004 à non-resonant streaming instabilities Amato & Blasi 2006; Blasi, Amato & Caprioli 2006; Vladimirov, Ellison & Bykov 2006, 2008 } calculations coupled to nonlinear particle accel.

23 A lot of work by many people on nonlinear Diffusive Shock Acceleration (DSA) and Magnetic Field Amplification (MFA) Some current work (in no particular order): 1)Amato, Blasi, Caprioli, Morlino, Vietri: Semi-analytic 2)Bell: Semi-analytic and PIC simulations 3)Berezhko, Volk, Ksenofontov: Semi-analytic 4)Malkov: Semi-analytic 5)Niemiec & Pohl: PIC 6)Pelletier and co-workers: MHD, relativistic shocks 7)Reville, Kirk & co-workers: MHD, PIC 8)Spitkovsky and co-workers; Hoshino and co-workers; other PIC simulators: Particle-In-Cell simulations, so far, mainly rel. shocks 9)Caprioli & Spitkovsky; Giacalone et al.: hybrid simulations 10)Vladimirov, Ellison, Bykov: Monte Carlo 11)Zirakashvili & Ptuskin: Semi-analytic, MHD 12)Bykov et al 13)Apologies to people I missed

24 Magnetic Field Amplification in DSA is a hard problem 1) DSA is intrinsically efficient ( ~50% ) è test-particle analysis not good approximation è must treat back reaction of CRs on shock structure 2) Magnetic field generation intrinsic part of particle acceleration è cannot treat DSA and MFA separately 3) Strong turbulence means Quasi-Linear Theory (QLT) not good approximation è But QLT is our main analytic tool (QLT assumes ΔB/B << 1) 4) Heliospheric shocks, where in situ observations can be made, are manly small and low Mach number (M Sonic < ~10) è don t see production of relativistic particles or strong MFA 5) Length and momentum scales are currently well beyond reach of 3D particle-in-cell (PIC) simulations if wish to see full nonlinear effects è Particularly true for non-relativistic shocks a) Problem difficult because TeV protons influence injection of kev protons and electrons 6) To cover full dynamic range, must use approximate methods: e.g., Monte Carlo, Semi-analytic, MHD

25 Phenomenological approach: Growth of magnetic turbulence driven by cosmic ray pressure gradient (socalled streaming instability) e.g., McKenzie & Völk 1982 growth of magnetic turbulence energy density, U(x,k), as a function of position, x, and wavevector, k energetic particle pressure gradient as function of position, x, and momentum, p V G (x,k) contains all of the complicated plasma physics that we don t understand Make approximations for V G and proceed Determine diffusion coefficient, D(x,p), from U(x,k)

26 Phenomenological approach assuming resonant wave generation (turbulence produced with wavelengths ~ particle gyro-radius): Growth of magnetic turbulence driven by cosmic ray pressure gradient (so-called streaming instability) e.g., Skilling 1975, McKenzie & Völk 1982 growth of magnetic turbulence energy density, W(x,k). (x position; k wavevector) energetic particle pressure gradient. (p is momentum) d dt W ( x, k) stream = V G P CR ( x, p) x p= p res ( k ) V G parameterizes the complicated plasma physics we don t understand dp dk Also, can produce turbulence non-resonantly (current instability): Bell s non-resonant instability (2004): Cosmic ray current produces turbulence with wavelengths shorter than particle gyro-radius Cosmic ray current produces turbulence with wavelengths longer than particle gyro-radius: e.g., Malkov & Drury 2001; Reville et al. 2007; Bykov, Osipov & Toptygin 2009 Produce turbulence resonantly assuming QLT Different instabilities will dominate in different parameter regimes of same shock

27 Using approximate plasma physics (quasi-linear theory, Bohm diffusion, etc.) Monte Carlo code iteratively solves nonlinear DSA problem with MFA (work with Andrei Bykov, Andrey Vladimirov & Sergei Osipov) Thermal leakage Injection Acceleration Efficiency iterate Shock structure magnetic turbulence, ΔB/ B, dissipation, & cascading If acceleration is efficient, all elements feedback on all others Iterative, Monte Carlo model of Nonlinear Diffusive Shock Acceleration (i.e., Vladimirov, Ellison & Bykov 2006,2008; Ellison & Vladimirov 2008) Similar semi-analytic results: Amato & Blasi (2006); Blasi, Amato & Caprioli (2006)

28 Once turbulence, W(x,k), is determined from CR pressure gradient or CR current, must determine diffusion coefficient, D(x,p) from W(x,k). Must make approximaaons here: 1) Bohm diffusion approximaaon: Find effecave B eff by integraang over turbulence spectrum (e.g., Vladimirov, Ellison & Bykov 2006) 2 ( x) 1 eff = W( x, k ) B 8π 2 0 dk cp λ ( x, p) =, D( x, p) = eb eff 1 3 vλ( x, p) 2) Resonant diffusion approximaaon (QLT) (e.g., Skilling 75; Bell 1978; Amato & Blasi 2006): 1 λ ( x, p) = 2 π p 2 e c W ( x, k res ) pc kres rg ( B0 ) = kres = 1 eb 3) Hybrid model for strong turbulence: Different diffusion models in different momentum ranges applicable to strong turbulence (Vladimirov, Bykov & Ellison 2009) 0 Work underway to include three instabiliaes (resonant, short λ, long λ) in fully non- linear Monte Carlo model : Bykov, Vladimirov, Osipov

29 Once turbulence, W(x,k), is determined from CR pressure gradient or CR current, must determine diffusion coefficient, D(x,p) from W(x,k). Must make approximaaons here: 1) Bohm diffusion approximaaon: Find effecave B eff by integraang over turbulence spectrum (e.g., Vladimirov, Ellison & Bykov 2006) 2 ( x) 1 eff = W( x, k ) B 8π 2 0 dk cp λ ( x, p) =, D( x, p) = eb eff 1 3 vλ( x, p) 2) Resonant diffusion approximaaon (QLT) (e.g., Skilling 75; Bell 1978; Amato & Blasi 2006): 1 λ ( x, p) = 2 π p 2 e c W ( x, k res ) pc kres rg ( B0 ) = kres = 1 eb 3) Hybrid model for strong turbulence: Different diffusion models in different momentum ranges applicable to strong turbulence (Vladimirov, Bykov & Ellison 2009) a) Low paracle momentum, p; λ part ~ constant (set by turbulence correlaaon length) b) Mid- range p; λ part gyro- radius in some effecave B- field c) Maximum p; λ part p σ (criacal for E max ) ç sall highly uncertain, depends on escaping CRs 0

30 Example with just resonant instability using Monte Carlo techniques: Calculate shock structure, particle distributions & amplified magnetic field Assume resonant, streaming instabilities for magnetic turbulence generation Assume Bohm approximation for diffusion coefficient

31 Nonlinear Shock structure, i.e., Flow speed vs. position DS Particle distributions and wave spectra at various positions relative to subshock for resonant wave production upstream FEB Position relative to subshock at x = 0 [ units of convective gyroradius] subshock

32 Bohm approx. for D(x,p) 2 ( x) 1 eff = W( x, k ) B 8π 2 0 dk cp λ ( x, p) =, D( x, p) = eb eff 1 vλ( x, p) 3 DS p 4 f(p) k W(k,p) D(x,p)/p Iterate until Energy & mom. fluxes conserved u(x) f(x,p) W(k,p) D(x,p) upstream DS Nonlinear Shock structure

33 Red: Bohm diffusion approximation upstream DS subshock Flow speed B eff Amplified B-field B 0 x 70 More complete examples will include: Combined resonant & non-resonant wave generation; more realistic diffusion calculations; dissipation of wave energy to background plasma; cascading of turbulence; etc.

34 plasma flow speed, u(x)/u sk unshocked precursor ux ( ) u sk Subshock Shock structure smoothed by backpressure of accelerated particles, compression ratio r > 4 feedback B amp /B 0 B amp B 0 Magnetic field structure across shock B amp is 30 times the far upstream field for this example Magnetic field varies strongly across precursor un-amplified B x-scale in units of gyroradius Vladimirov, Ellison & Bykov 2006

35 plasma flow speed, u(x)/u sk B amp /B 0 unshocked B 0 =30 µg B 0 =0.3 µg B amp B 0 Keep physical size of shock the same, but reduce ambient B-field to B 0 = 0.3 µg Subshock Now, magnetic field DS is 400 times upstream field (high Alfvén Mach # case, B 0 =0.3 µg) Weak fields are amplified more than strong fields Magnetic field varies strongly across precursor un-amplified B x-scale in units of gyroradius These two shocks have same physical size Work in progress by Bykov, Osipov & Vladimirov will include: Combined resonant & non-resonant wave generation; more realistic diffusion coefficient; dissipation of wave energy to background plasma; cascading of turbulence; etc.

36 Particle distribution functions f(p) times p 4 Shocks with and without B-field amplification p 4 f(p) B-amp No B-amp The maximum CR energy a given shock produces increases with B-amp BUT Increase is not as large as downstream B amp /B 0 factor!! Precursor structure of B-field is important for determining p max and for synchrotron losses for electrons All parameters are the same in these cases except one has B-amplification For this example, B amp /B 0 = 450µG/10µG = 45 but increase in p max only ~ x 5

37 p 4 f(p)

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39 Upstream Free escape boundary Determine steady-state, shock structure with iterative, Monte Carlo technique Unmodified shock with r = 4 Flow speed Self-consistent, modified shock with r tot ~ 11 (r sub ~ 3) Momentum Flux conserved (within few %) Energy Flux (only conserved when escaping particles taken into account) Position relative to subshock at x = 0 [ units of convective gyroradius ]

40 Essential features of MFA in diffusive shock acceleration: 1) Production of turbulence, W(x,k) (assuming quasi-linear theory) a) Resonant (CR streaming instability) (e.g., Skilling 75; McKenzie & Volk 82; Amato & Blasi 2006) b) Non-resonant current instabilities (e.g., Bell 2004; Bykov et al. 2009; et al 2007; Malkov & Diamond) Reville i. CR current produces waves with scales short compared to CR gyroradius ii. CR current produces waves with scales long compared to CR gyroradius 2) Calculation of D(x,p) once turbulence is known a) Resonant (QLT): Particles with gyro-radius ~ λ waves gives λ part p b) Non-resonant: Particles with gyro-radius >> λ waves gives λ part p σ 3) Production of turbulence and diffusion must be coupled to NL shock structure including injection of lowest energy particles and escape of highest energy All coupled è (1) Thermal injection; (2) shock structure modified by back reaction of accelerated particles; (3) turbulence generation; (4) diffusion in self-generated turbulence; (5) escape of maximum energy particles ç All coupled

41 Next Lecture 4: Modeling evolving supernova remnants Tycho s Supernova Remnant

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43 Lecture 4: Modeling evolving supernova remnants using the The CR-hydro-NEI code (Cosmic Ray, hydro, Non-Equilibrium-Ionization) Tycho s Supernova Remnant

44 CR-Hydro-NEI code Co-workers: Pat Slane, Herman Lee, Dan Patnaude, Andrei Bykov, Daniel Castro, John Raymond, Hiro Nagataki Approximate method that contains much of the essential physics of NL DSA but is fast enough to be included in a hydrodynamic simulation of an evolving SNR è Model broadband emission from specific SNRs 1)SNR RX J1713 2)Vela Jr. 3) CBT 109 4)Tycho s SNR (in preparation) 5)Evolution of SNRs to ~20,000 years (in preparation)

45 Modeling broad-band emission from SNRs Radio to X-rays to GeV-TeV γ-rays VLA - radio Chandra - X-rays XMM - X-rays Australia Telescope Compact Array

46 Fermi γ-ray Telescope (GLAST) Launched 11 June 2008 Fermi s first light 30 MeV 300 GeV

47 TeV Gamma rays : HESS, MAGIC, Veritas, Air Cherenkov Telescopes H.E.S.S

48 MAGIC atmospheric Cherenkov telescope Canary island of La Palma

49 Shock acceleration is intrinsically efficient and various detailed models of nonlinear diffusion shock acceleration (NL-DSA) exist. But, problem is difficult and all methods lack one or more critical parts. Difficult nonlinear aspects undergoing active research: 1. Thermal particle Injection: also e/p ratio (critical for SNRs, Jets) 2. Nonlinear shock structure back-reaction from CRs 3. Magnetic Field Amplification sets scales & maximum CR energy 4. Particle escape highly anisotropic distributions 5. Nonlinear coupling of all of the above 6. Integration into realistic, evolving shock system (e.g., SNR, radio jet) Techniques for treating DSA (all approximate to some degree): è Monte Carlo methods è Particle-In-Cell (PIC) simulations è Semi-analytic solutions è MHD (or hydro) ç è semi-analytic

50 Why is DSA so hard to figure out? 1) DSA is intrinsically efficient ( ~50% ) è test-particle analysis not good approximation è must treat back reaction of CRs on shock structure 2) Magnetic field generation intrinsic part of particle acceleration è cannot treat DSA and magnetic field amplification (MFA) separately 3) Strong turbulence means Quasi-Linear Theory (QLT) not good approximation è But QLT is our main analytic tool for wave-particle interactions 4) Heliospheric shocks, where in-situ observations can be made and theories tested, are all small, low Mach number (M Sonic < ~10), & generally oblique è don t see production of relativistic particles or strong MFA 5) Length and momentum scales are currently well beyond reach of PIC simulations if wish to see full nonlinear effects è Particularly true for non-relativistic shocks a) Problem difficult because TeV protons influence injection of kev protons and electrons 6) To cover full dynamic range, use approximate methods: e.g., Monte Carlo, Semi-analytic, MHD with highly simplified DSA

51 CR-hydro-NEI code (Lee et al. 2012,2013; Ellison et al and earlier papers) Couples: 1) 1-D, spherically symmetric hydro simulation of SNR based on VH-1 2) NL DSA model largely following published, semi-analytic solutions of Blasi, Amato, Caprioli, Gabici & co-workers è some differences and additions 3) Non-equilibrium ionization (NEI) calculation of X-ray line emission 4) Continuum emission from trapped CRs in SNR and forward shock precursor 5) Continuum emission from escaping CRs & secondary particles è Explicit calculation of upstream, cosmic-ray precursor è Momentum and space dependent CR diffusion coefficient è Explicit calculation of resonant, quasi-linear magnetic field amplification (MFA) è Calculation of E max using amplified magnetic field è Finite Alfven speed for CR scattering centers è Line-of-sight projections of individual X-ray lines See poster by Herman Lee

52 Shocked ISM material : Calculate X-ray emission from this region CD Shocked Ejecta material : Work in progress: thermal X-rays from reverse shock and ejecta material 1-D: Model Type Ia or core-collapse SN with Pre-SN wind Reverse Shock Forward Shock Extent of shock precursor Spherically symmetric: We do not model clumpy structure Escaping CRs 1) CR electrons and ions accelerated at FS a) Protons give pion-decay γ-rays b) Electrons give synchrotron, IC, & non-thermal brems. c) High-energy CRs escape from shock precursor & interact with external mass 2) Evolution of shock-heated plasma between FS and contact discontinuity (CD) a) Electron temperature, density, charge states of heavy elements, and X-ray line emission b) Include adiabatic losses & radiation losses 3) Now adding X-ray lines from reverse shock (H. Lee, Dan Patnaude) 52

53 If you want clumpy: Don Warren & John Blondin 2013 No DSA RS-CD-FS positions 3D hydro simulations showing positions of forward shock, reverse shock and contact discontinuity. Includes a phenomenological model of NL DSA Efficient DSA è Efficient DSA causes CD-FS separation to decrease è Rayleigh-Taylor instabilities alone can allow ejecta knots to move ahead of FS RS-CD-FS positions

54 Don Warren & John Blondin 2013 ejecta knot Knots of ejecta material have overtaken forward shock Line-of-sight simulation of thermal X-ray and non-thermal synchrotron emission (crude model for synch.) Compared to Chandra X-ray obs. of Tycho s SNR (J.Warren et al. 2005) Tycho efficient DSA No DSA medium eff. For now, stay with 1-D spherically symmetric model with good NL DSA calculation

55 3D hydro simulation with X-ray lines and efficient DSA (Ferrand et al. 2012) Thermal emission ( kev) from shocked ISM and ejecta material Includes effects from back reaction of CRs on thermal plasma No CR backreaction With CR back-reaction Hydro simulations are important steps forward but not so easy to include NL-DSA in 3D models

56 Shocked ISM material : Calculate X-ray emission from this region 1-D: Model Type Ia or core-collapse SN with Pre-SN wind Forward Shock 1) Calculate CR electrons and ions accelerated at FS with reasonably consistent NL DSA model CD Reverse Shock 2) Self-consistently calculate X- ray line emission from shockheated plasma between FS and CD Shocked Ejecta material : Extent of shock precursor Escaping CRs Spherically symmetric: We do not model clumpy structure

57 Shock wave Diffusive Shock Acceleration: Shocks set up converging flows (Fermi s trap) of ionized plasma SN explosion V DS V sk = u 0 Interstellar medium (ISM), cool with speed V ISM ~ 0 flow speed, u 0 shock frame shock Post-shock gas à Hot, compressed, dragged along with speed V DS < V sk charged particle moving through turbulent B-field Upstream DS u 2 X u 2 = V sk - V DS Particles make nearly elastic collisions with background è gain energy when cross shock è bulk kinetic energy of converging flows put into individual particle energy

58 p 4 f(p) [f(p) is phase space distr.] Temperature p 4 f(p) NL TP: f(p) p -4 If acceleration is efficient, shock becomes smooth from backpressure of CRs Flow speed Concave spectrum test particle shock subshock X Compression ratio, r tot > 4 Low shocked temp. r sub < 4 In efficient acceleration, entire particle spectrum must be described consistently, including escaping particles è much harder mathematically BUT, connects thermal emission to radio & GeV-TeV emission Particle spectra calculated with semi-analytic code of Blasi, Amato, Gabici and co-workers

59 Electron and Proton distributions from efficient (nonlinear) diffusive shock acceleration Thermal X-rays (kev) Radio Synch Pion-decay (GeV-TeV) only emission coming from protons protons X-ray Synch (kev X-rays) compete at TeV energies e s Inverse Compton (GeV-TeV γ-rays) from electrons For this illustration, use spectra from semi-analytic model of Blasi, Gabici & Vannoni 2005 Several free parameters required to characterize particle spectra, including B-field, e/p ratio, diffusion coefficient

60 Particle distributions continuum emission e s p s synch pion For electrons need two extra parameters: K ep & T e /T p Electron/proton ratio, K ep K ep critical for p-p / IC ratio at GeV-TeV K ep and T e /T p not yet determined by theory or plasma simulations! brems Thermal X-ray emission lines è depend on T e /T p and electron equilibration è Coupling with NL DSA helps to constrain parameters IC

61 Must also consider escaping CRs. For efficient DSA, a large fraction of CR energy can be in Qesc Protons trapped in shock

62 Must also consider escaping CRs. For efficient DSA, a large fraction of CR energy can be in Qesc Protons trapped in shock Escaping CRs Escaping CRs produce gamma-rays if impact dense material The shape of the escaping distributions is very different from CRs trapped near the shock Escaping CRs are highly anisotropic making analysis difficult. This is an active area of work by a number of groups! Monte Carlo work in progress by Bykov et al.

63 Forward shock of SNR produces 3 primary particle distributions that will contribute to the photon emission (secondaries may also be important) 1) Ions accelerated and trapped within SNR and precursor 2) Electrons accelerated and trapped within SNR and precursor 3) CRs escaping upstream (mainly ions) Ellison & Bykov 2011 Escaping CRs Some fraction of the highest energy CRs will always escape upstream in DSA trapped V sk Q esc Shock wave CRs need self-generated turbulence to diffuse back toward shock. This ΔB/B will be lacking far upstream

64 Thermal & Non- thermal Emission in SNR RX J1713 Important question for SNR RX J1713 and other SNRs Are highest energy photons produced by Ions (p-p collisions and pion decay) or Suzaku image HESS contours Tanaka et al Electrons (inversecompton off background photons)? (or some combination)? 64

65 Thermal & Non- thermal Emission in SNR RX J1713 SNR RX J1713 Fukui et al 2012 Abdo et al 2011 SNR RX J1713 HESS Fermi LAT NANTEN, HESS Co-workers for cr-hydro-nei code: Pat Slane, Herman Lee, Dan Patnaude, Andrei Bykov, Daniel Castro, John Raymond, Hiro Nagataki

66 SNR RX J1713: Homogeneous Model of Thermal & Non- thermal Emission Look at X-ray energies Suzaku X-rays: smooth continuum well fit by synchrotron from TeV electrons No discernable line emission from shockheated heavy elements Strong constraint on Non-thermal emission at GeV-TeV energies Broad-band emission, including thermal X-rays è In nonlinear DSA the production of gamma rays is coupled to thermal X-ray emission Look at CR-hydro-NEI fit è

67 Generalized cr-hydro-nei code (Lee, Ellison & Nagataki 2012, also Ellison, Slane, Patnaude, Bykov 2012 & previous work) SNR RX J1713 Core-collapse SN explodes in a 1/r 2 pre-sn wind. synch IC Excellent fit to broad-band (integrated) emission p-p brems Constraint from line emission è IC dominates GeV-TeV emission è Most CR energy is sall in ions even with IC dominaang the radiaaon Note: p-p from escaping CRs small unless external mass > 10 4 M sun Pre-SN wind B-field much lower than ISM è Strong Magnetic field amplification occurs but still have B-field low enough to have high electron energy to match HESS points For J1713, we predict average shocked B ~ 10 µg! (Amplification factor ~40)

68 FS radius SNR RX J1713 evolution FS compression ç 4 B-field compression at subshock Frac. of E SN in CRs B [G] Total CRs escaping CRs Magnetic field amplification (MFA) in precursor x40 ~17% of SN explosion energy put into CR ions at 1630 yr proton p max SNR Age [yr]

69 Before Fermi data, possible to get good fit to J1713 continuum with pion-decay dominating GeV-TeV. For example: Zirakashvili & Aharonian 2010 p-p Apologies to many other papers modeling young SNRs including J1713 that I don t mention Even with Fermi data, shape of spectrum at GeV-TeV may not be enough to discriminate between IC and pion-decay (Fukui & Sano et al. 2012; Zirakashvili & Aharonian 2010) è Essential to consider self-consistent X-ray line emission

70 NEI calculaaon of Thermal X- ray emission p-p Don Ellison, NCSU

71 Hadron Coulomb Eq. Compare Hadronic & Leptonic fits for J1713 Suzaku Use range of electron temperature equilibration models Hadron Instant equilibration The high ambient densities needed for pion-decay to dominate at TeV energies result in strong X-ray lines Lepton model Coulomb Eq. To be consistent with Suzaku observations with lines weaker than synchrotron continuum, Must have low density and high accelerated e/p ratio (K ep ~ 0.01) This impacts GeV-TeV emission Best fit models have low shocked B-field B 2 ~ 10 µg Ellison, Patnaude, Slane & Raymond ApJ (2007, 2010) Thermal X-ray constraint è dominates GeV-TeV emission in SNR XJ1713 IC

72 SNR J1713: Tanaka et al 2008 Hadronic model XIS spectrum Leptonic model Simulated Suzaku XIS spectra (n H = cm -2 ) Lines produced by Hadronic model would have been seen! To be consistent with Suzaku observations. That is, to have lines weaker than synchrotron continuum, must have low ISM density and accelerated e/p ratio, K ep ~ 10-2 This determines GeV-TeV emission mechanism

73 Note: Inoue et al 2012; Fukui et al 2012, conclude pion-decay from protons dominates in SNR RX J1713 based on spatial correlation of gas and γ-rays Average density of ISM protons: ~130 cm -3 Total mass ~ M sun over SNR radius ~0.1% of supernova explosion energy in CR protons!! This may be a problem for CR origin Inoue et al (2012) High densities needed for pion-decay may be in cold clumps that don t radiate thermal X- ray emission NANTEN, HESS

74 Vela Jr. Similar to J1713. Parameters that give p-p fit to GeV-TeV over-produce X-ray lines. Inverse-Compton works fine (Lee et al. 2013, POSTER) p-p IC p-p IC Vela Jr. Images from Iyudin et al Without line model, cannot strongly distinguish p-p from IC Get very different parameters for SN, environment & DSA for two cases. Don Ellison, NCSU

75 Tycho s SNR : Example where pion-decay may dominate GeV-TeV emission (Morlino & Caprioli 2012) Morlino & Caprioli 2012 Tycho SNR p-p pion-decay emission SNR environment will largely determine what emission mechanism dominates GeV-TeV emission

76 SNR CTB 109 (Daniel Castro et al 2012) Fermi LAT Fermi LAT 1 TeV MeV XMM-Newton XMM-Newton kev 76

77 Detailed analysis of X-ray emission with CR-hydro-NEI model è Mixed Hadronic-Leptonic model fits best Hadronic Leptonic Mixed Coupling between NL DSA and X-ray line emission critical for interpreting GeV observations. Cannot determine nature of emission without nonlinear model coupling thermal and non-thermal emission

78 Warning: many parameters and uncertainties in model, but : For spherically symmetric model of SNR RX J1713 & Vela Jr.: Inverse-Compton is best explanation for GeV-TeV Other remnants can certainly be Hadronic, e.g. Tycho s SNR or Mixed (CTB 109) Important: For DSA most CR energy (~17% of E SN for J1713) is in ions even with IC dominating the radiation è All nonlinear models show that SNRs produce CR ions!!! Besides question of CR origin: Careful modeling of SNRs can provide constraints on critical parameters for shock acceleration: a) Shape and normalization of CR ions from particular SNRs b) electron/proton injection ratio c) Acceleration efficiency d) Magnetic Field Amplification e) Properties of escaping CRs f) Geometry effects in SNRs such as SN1006

79 Ackermann et al. Science 2013 Fermi LAT observations of SNRs interacting with dense material (molecular clouds) è Strong case for pion-decay gamma-rays dominating GeV- TeV emission è Smoking gun for SNRs being a primary source of galactic CR ions, but other compelling reasons to believe SNRs are primary source of the bulk of CRs Energy budget and Ionic composition are most compelling reasons

80 Using the CR-hydro-NEI model to follow the evolution of a SNR to late stages Preliminary work headed by Daniel Castro with Herman Lee and CR-hydro-NEI group

81 R FS [pc] FS radius Follow evolution from early stages (~ 20 yr after explosion) to 20,000 yr FS speed Hydro coupled to DSA over entire evolution E CR /E SN Trapped CRs Escaping CRs Particles accelerated by forward shock are tracked and emission calculated B [G] ISM shocked For this preliminary work, we assume a uniform circumstellar environment Electrons Protons SNR Age [yr]

82 360 yr 36 yr Broad-band continuum emission: 36 yr to 360 yr

83 630 yr Broad-band continuum emission: 6300 yr 630 yr to 6300 yr

84 11,300 yr Broad-band continuum emission: 20,000 yr 11,300 yr to 20,000 yr

85 Broad-band continuum emission: ~60 yr to ~16,000 yr Radical changes in continuum emission in X-ray and GeV-TeV bands over lifetime Pion-decay / IC ratio can vary widely 6300 yr 2000 yr 630 yr 350 yr 200 yr 63 yr 16,000 yr 13,000 yr

86 Can also follow the evolution of individual X-ray lines keeping track of temperature and ionization history

87 Conclusions 1) The most violent and exoac objects in the universe are revealed to us through non- thermal emission First radio, now X- rays and gamma- rays 2) ParAcle acceleraaon the producaon of strongly non- thermal paracle distribuaons must occur if radio, gamma- rays, or non- thermal X- rays are observed 3) To understand energy budgets of most exoac phenomena CRs, SNRs, QSOs, GRBs acceleraaon mechanism must be highly efficient 4) Collisionless shocks are widespread and collisionless shocks are known to accelerate paracles efficiently. 5) Diffusive shock acceleraaon is highly developed and therefore gehng complicated NL shock structure, MFA, escaping CRs, large dynamic range, etc. 6) Other mechanisms stochasac acceleraaon, magneac reconnecaon are certainly important in some objects solar flares, GRBs, pulsar winds

88

89 Radial structure for core-collapse model for J1713 ρ 340 yr 990 yr 1630 yr FS ρ 1/r 2 pre-sn wind density profile Log Pres. Pressure precursor from shock accelerated CRs Flow Speed FS Modified shock speed from CR pressure Low B-field in pre-sn wind: <10-7 G at forward shock at 1600 yr B [G] Can include shell Radius [pc]

90 Conclusions 1)Shocks and shock acceleration important in many areas of astrophysics: Shocks accelerate particles and generate turbulence 2)DSA process can be efficient, i.e., ~50% of shock energy may go into rel. CRs! 3)Good evidence B-field, at shock, amplified well above compressed ambient field (i.e., B amp >> 4 x B 0 ) 4)Resonant and non-resonant wave generation instabilities both at work 5)Complete NL problem currently beyond PIC simulation capabilities, but PIC is only way to study full plasma physics (critical for injection process) 6)Several approximate techniques making progress: Semi-analytic, MC, MHD 7)Important problems where work remains: a) What are maximum energy limits of shock acceleration, i.e., E max? b) Effect of escaping particles at E max? c) Electron to proton (e/p) ratio? (GeV/TeV emission from SNRs) d) Realistic shock geometry, i.e., shock obliquity? (SN1006) e) Heavy element acceleration? (CR knee region) f) How do details of plasma physics influence results? (e.g., injection efficiency; saturation of Bell s instability; spectral shape at maximum energy)

91 east Efficient R FS /R CD ~ 1 SE inefficient R FS /R CD > 1 south Evidence for efficient particle acceleration in SNRs R R FS CD SNR SN1006 Cassam-Chenai et al (2008) In east and south è strong nonthermal emission è R FS /R CD ~ 1 Hα (FS) keV(CD) Efficient DSA: R FS /R CD ~ 1 SNR Morphology: Forward shock close to contact discontinuity è clear prediction of efficient DSA of protons SE