The Theory of Supernova Remnants

The Theory of Supernova Remnants • Some comments on Supernova Remnants and the production of Cosmic Rays • Don Ellison, North Carolina State University 104 Galactic Cosmic Rays Tycho’s Supernova Remnant Flux Solar modulation blocks low energy CRs 1020 eV 1015 eV 10-28 http://chandra.harvard.edu/photo/2005/tycho/ Energy [eV] 109 eV 1021 eV Hillas_Rev_CRs_JPhysG2005.pdf

Consider efficient production of Cosmic Rays by Diffusive Shock Acceleration (DSA) in SNRs DSA is also called the first-order Fermi mechanism  Particle acceleration in Collisionless Shocks  Many 100’s of references. Some review papers: Axford 1981; Drury 1983; Blandford & Eichler 1987; Jones & Ellison 1991; Berezhko & Ellison 1999; Malkov & Drury 2001; Bykov 2004; Bykov et al 2011, 2012, 2013 Discovery papers for first-order Fermi mechanism in shocks: Krymskii (1976), Axford, Leer & Skadron (1977), Bell (1978), Blandford & Ostriker (1978) So called “Universal” test-particle power law for particles (in a strong shock) If particles are fully relativistic: Don Ellison, NCSU

1-D: Model Type Ia or core-collapse SN with Pre-SN wind Forward Shock Reverse Shock Contact Discontinuity Spherically symmetric: No clumpy structure for now (Note Yamazaki’s talk)

1-D: Model Type Ia or core-collapse SN with Pre-SN wind Shocked ISM material : Weak X-ray lines; Strong DSA and CR prod. Forward Shock Reverse Shock Contact Discontinuity Spherically symmetric: No clumpy structure for now (Note Yamazaki’s talk)

1-D: Model Type Ia or core-collapse SN with Pre-SN wind Shocked ISM material : Weak X-ray lines; Strong DSA and CR prod. Forward Shock Reverse Shock Shocked Ejecta material :Strong X-ray emission lines ! DSA not obvious for RS unless B-field strongly amplified Contact Discontinuity Spherically symmetric: No clumpy structure for now (Note Yamazaki’s talk)

1-D: Model Type Ia or core-collapse SN with Pre-SN wind Shocked ISM material : Weak X-ray lines; Strong DSA and CR prod. Forward Shock • Cosmic Ray electrons and ions accelerated at FS • Protons  pion-decay -rays • Electrons  synchrotron, IC, & non-thermal brems. • High-energy CRs escape from shock precursor & interact with external mass • Evolution of shock-heated plasma between FS and contact discontinuity (CD) • Electron temperature, density, charge states of heavy elements, and X-ray line emission varies with ionization age Reverse Shock Escaping CRs Shocked Ejecta material :Strong X-ray emission lines ! DSA not obvious for RS unless B-field strongly amplified Contact Discontinuity Spherically symmetric: No clumpy structure for now (Note Yamazaki’s talk)

Main effects from DSA that influence SNR hydrodynamics : Nonthermal particles (i.e., swept-up ISM or ejecta) are turned into relativistic CRs by DSA. This lowers specific heat ratio (5/3  4/3) Some of the highest energy CRs will escape upstream from the forward shock.This also lowers specific heat ratio (4/3  1)  Effects (1) and (2) cause the shock compression ratio to increase above r = 4(find typical values with efficient DSA : r ~ 5 - 10 ) 3) If DSA is efficient, to conserve energy, temperature of shocked gas MUST decrease below value expected without CR production SNR shocks that efficiently produce CRs willhave large compression ratios and low shocked temperatures  Production of CRs influences SNR hydrodynamics & thermal X-ray emission Don Ellison, NCSU

Test-particle power law hardens with increasing comp. ratio, r • For strong shocks, “universal power law” diverges unless acceleration stopped by finite size or finite age. “Universal” power law diverges for r = 4 Diverges for strong shocks with compression ratio r  4  In strong shocks, CRs must modify the shock, and some of the highest energy CRs must escape if acceleration is efficient  strong nonlinear effects

What happens to the test-particle prediction when nonlinear effects are taken into account? First: Collisionless plasmas :

Collisionless plasmas :  We see “thin” structures in solar wind and ISM : e.g., planetary bow shocks and SNR shocks  The length scale of these structures must be many orders of magnitude smaller than the collisional mean-free-path NGC 2736: The Pencil Nebula Thin structures are possible because wave-particle interactions produce short mfp for particle isotropization Hydrogen emission SN 1006

Charged particle, helix, no “B/B scattering” Particle-particle collisions are rare Uniform B

Charged particle, helix, no “B/B scattering” Particle-particle collisions are rare Uniform B If particle flux large enough, particles will distort the field : Turbulent B

Charged particle, helix, no “B/B scattering” Particle-particle collisions are rare Uniform B If particle flux large enough, particles will distort the field : Turbulent B Particles pitch-angle scatter and turn around  can define a collisionless mean free path. This “collision” is nearly elastic in frame of B-field

In collision-dominated plasmas, particle-particle collisions drive the plasma to thermal equilibrium. If an individual particle gets more energy than average, it will immediately transfer energy via collisions to slower particles  scatterings are Inelastic In a collisionless plasma, particles interact with the background B-field  one proton “scatters” off of ~ Avogadro’s number of particles tied together by nearly “frozen-in” turbulent B-field  scatterings are nearly elastic An individual particle can gain, and keep for long times, much more energy than an average thermal particle B-fields are frozen-in because of high conductivity of diffuse plasmas. If the plasma moves, currents are generated to produce B-fields so magnetic flux remains unchanged. B-field moves with bulk plasma

Hillas_Rev_CRs_JPhysG2005.pdf Extremely non-equilibrium plasma maintained for many millions of years in ISM. Do not see this in laboratory plasmas !! Galactic Cosmic Rays  LHC Flux Solar modulation blocks low energy CRs 1020 eV Need vast machines to produce high energy beam for a brief instant 1015 eV  Do not have diffusive shock acceleration in collision dominated (i.e., lab) shocks  Energy [eV] 109 eV 1021 eV

Diffusive Shock Acceleration: Shocks set up converging flows of ionized plasma Shock wave Interstellar medium (ISM), cool with speed VISM ~ 0 SN explosion VDS Vsk = u0 Post-shock gas  Hot, compressed, dragged along with speed VDS < Vsk

Diffusive Shock Acceleration: Shocks set up converging flows of ionized plasma Shock wave Interstellar medium (ISM), cool with speed VISM ~ 0 SN explosion VDS Vsk = u0 shock frame shock flow speed, u0 charged particle moving through turbulent B-field u2 X Upstream DS Post-shock gas  Hot, compressed, dragged along with speed VDS < Vsk u2 = Vsk - VDS Particles make nearly elastic collisions with background plasma gain energy when cross shock  bulk kinetic energy of converging flows put into individual particle energy  some small fraction of thermal particles turned into (approximate) power law

Test Particle Power Law Plot p4 f(p) Krymsky 77, Axford at al 77, Bell 78, Blandford & Ostriker 78 f(p) ~ p-3r/(r-1) where r is compression ratio, f(p) d3p is phase space density Quasi-Universal power law p4 f(p) If r = 4, &  = 5/3, f(p) ~ p-4 shock flow speed X Normalization of power law not defined in test-particle approximation

Test Particle Power Law Plot p4 f(p) Krymsky 77, Axford at al 77, Bell 78, Blandford & Ostriker 78 f(p) ~ p-3r/(r-1) where r is compression ratio, f(p) d3p is phase space density Quasi-Universal power law p4 f(p) If r = 4, &  = 5/3, f(p) ~ p-4 shock flow speed X Test particle results: ONLY for superthermal particles, no information on thermal particles Normalization of power law not defined in test-particle approximation

Temperature If acceleration is efficient, shock becomes smooth from backpressure of CRs p4 f(p) test particle shock Flow speed subshock p4 f(p) [f(p) is phase space distr.] X NL ►Concave spectrum ► Compression ratio, rtot > 4 ► Low shocked temp. rsub < 4 TP: f(p)  p-4 B-field effects may reduce curvature In efficient acceleration, entire particle spectrum must be described consistently, including escaping particles much harder mathematicallyBUT, connects thermal emissionto radio & GeV-TeV emission

Efficient acceleration  shock becomes smooth from CR backpressure test particle shock Flow speed Weak subshock, r < 4  lower shocked temperature Overall compression ratio > 4  higher shocked density subshock Temperature and density determine non-equilibrium ionization state of shocked plasma  SNR evolution &X-ray emission modified by efficient shock acceleration X • Caution: while basic predictions are extremely robust – They only depend on particle diffusion length being increasing function of energy, • Size of nonlinear effects depend on acceleration efficiency.

Modifications brought on by efficient CR production depend on Mach number (here show extreme example) Increase in compression ratio and Decrease in shocked temperature with efficient CR acceleration These are large effects when BISM is low. Not so large if B-field amplifed Comp. ratio 20  Efficient DSA NL 10 TP 4  Test-particle accel. Shocked proton temp. TP  Test-particle accel. Compression ratios >> 4 should show in SNR morphology NL  Efficient DSA SNR Age [yr]

Chandra observations of Tycho’s SNR(Warren et al. 2005) Green line is contact discontinuity (CD) CD lies close to outer blast wave determined from 4-6 keV (non-thermal) X-rays No acceleration FS Morphology can be explained by large compression ratio from efficient DSA Efficient DSA acceleration 2-D Hydro simulationBlondin & Ellison 2001

Efficient acceleration  shock becomes smooth from CR backpressure test particle shock Flow speed subshock High momentum CRs feel larger effective compression than low p CRs  Smooth shock produces concave spectrum X Note: plot p4 f(p) Particle spectrum that determines highest energy emission is fundamentally connected to lowest energy thermal plasma High efficiency example

Particle distributions continuum emission p’s e’s synch Kep pion IC Several parameters needed for modeling !! e.g., Electron/proton ratio, Kep brems In addition, emission lines in thermal X-rays. Depends on Te/Tp and electron equilibration model In nonlinear DSA, Thermal & Non-thermal emission coupled  big help in constraining parameters

Have developed a Composite SNR Model (CR-hydro-NEI code) • SNR hydrodynamics, Nonlinear Shock Acceleration, Broadband continuum radiation, and X-ray emission line • Collaborators: Andrei Bykov, Daniel Castro, Herman Lee, Hiro Nagataki, Dan Patnaude, & Pat Slane(early work with: Anne Decourchelle & Jean Ballet 2000,2004) • VH-1 code for 1-D hydrodynamics of evolving SNR (e.g., J. Blondin) • Semi-analytic, nonlinear DSA model (from P. Blasi and co-workers) • Non-equilibrium ionization for X-ray line emission (D. Patnaude, J. Raymond) • NL shock acceleration coupled to SNR hydrodynamics (Herman Lee) • Magnetic field amplification (Blasi’s group & Andrei Bykov) • Electron and Ion distributions from thermal to relativistic energies (T. Kamae) • Continuum photon emission from radio to TeV • Simple model of escaping CRs propagating beyond SNR Apply model to individual SNRs: RX J1713, CTB 109, Vela Jr., Tycho

One example: Thermal & Non-thermal Emission in SNR RX J1713 (Ellison, Lee, Slane, Patnaude, Nagataki et al 2007--2012) Core-collapse SN model SN explodes in a 1/r2pre-SN wind  Shell of swept-up wind material  Inverse-Compton dominates GeV-TeV emission Note good fit to highest energy HESS observations synch IC p-p Note: Large majority of CR energy is still in ions even with IC dominating the radiation  SNRs produce CR ions! brems Inverse-Compton fit to HESS obs: Pre-SN wind B-field lower than ISM  Can have MFA and still have B-field low enough to have high electron energy. For J1713, we predict average shocked B ~ 10 µG !

Multi-component model for SNR RX J1713 (Inoue, Yamazaki et al 2012; Fukui et al 2012): Average density of ISM protons: ~130 cm-3 Total mass ~2 104 Msun 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

Warning: many parameters and uncertainties in CR-hydro-NEI 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 or mixed, e.g. Tycho’s SNR • and CTB 109. • Important: For DSA most CR energy (~17% of ESN for J1713) is in ions even with inverse-Compton dominating the radiation •  All nonlinear models show that SNRs produce CR ions !!!  There is no fundamental difference between IC and pp dominated SNRs • Besides question of CR origin:Careful modeling of SNRs can provide constraints on critical parameters for shock acceleration: • Shape and normalization of CR ions from particular SNRs • electron/proton injection ratio • Acceleration efficiency • Magnetic Field Amplification • Properties of escaping CRs • Geometry effects in SNRs such as SN1006 What about CRs observed at Earth? CREAM Balloon flights

CREAM Balloon flights in Antarctica 40 million cubic foot balloon Float between ~38 and ~40 km Average atmospheric overburden of ~3.9 g/cm2 Total exposure for 5 flights ~156 days

Cosmic rays measured at Earth Spectral shape of cosmic ray electron spectrum is similar to ions when radiation losses are considered. Figure from P. Boyle & D. Muller via Nakamura et a. 2010 Side note: Stochastic (second-order) acceleration cannot reproduce such similar spectral shapes. Stochastic acceleration is NOT acceleration mechanism for these galactic CRs

Recent balloon and spacecraft observations of cosmic rays show “unexpected” spectral shapes, e.g.: ATIC-2 (Wefel et al. 2008); CREAM (Ahn et al 2010); PAMELA (Adriani et al. 2011) Hint of curvature in CR spectra  this might be concave curvature predicted by nonlinear DSA !? CR helium spectrum is slightly harder that the proton spectrum at energies where both are fully relativistic  This is impossible to explain with “simple” NL DSA. Must be more complicated. p/He Rigidity (GV), R = pc/(eZ) PAMELA (Adriani et al. 2011) Don Ellison, NCSU

Different shape for H and He spectra & Hint of curvature in CR spectra seen at Earth !? He C Protons(open) O Helium (solid) Ne Mg CREAM data from Ahn et al 2010 Si Concave curvature? iron

What does basic model of Nonlinear DSA predict ? Consider spectral curvature when have different ion species.  In test-particle acceleration, DSA predicts spectra ordered by velocity Velocity Scale, v << c Electrons Test-particle Protons High A/Q ions Log f(v) (p.s.d.) Test-particle: All have identical spectral shapes in velocity (if scale to number of particles accelerated) • This results from assumption that scatterings are elastic in local frame • nature of “collisionless” plasma • Once all particles are fully relativistic they are treated the same Test-particle power laws Log Velocity

Test Particle Shock Acceleration Momentum scale Velocity Scale, v << c electrons electrons, proton high A/Q identical protons High A/Q Log f(v) (p.s.d) Log f(p) (phase space) Test-particle power laws Test-particle power laws Log Momentum Log Velocity Heavy particles get more energy purely from the kinematics of energy gain in the converging plasmas on either side of the shock Test-particle power-law: same for all ion species

If shock is efficient, nonlinear effects are important and shock is smoothed: Small A/Q particles feel a smaller effective compression ratio, reff, high A/Q ions feel a larger reff than protons at same velocity High A/Q particles gain more energy in each crossing  have a flatter spectrum than protons until both are relativistic This effect depends on acceleration efficiency and on shock Mach number Test Particle Flow speed Modified shock Modified shock  concave spectrum Note: plot p4 f(p) X

Test Particle When nonlinear effects become important, momentum dependence of mfp gives CONCAVE spectra (Eichler 79, 84) Flow speed Modified shock Momentum scale electrons protons high A/Q ions X e’s p A/Q Log f(p) (phase space) Diffusion length proportional to A/Q means high A/Q species suffer LESS from modified shock Non-linear effects A/Q p Log Momentum e’s enhancement depletion If shock is modified mainly by protons, high A/Q ions will be enhanced, in acceleration process

Bottom line: • Nonlinear DSA predicts : • Enhancement of high A/Q (mass/charge) particles. Heavy elements accelerated more efficiently than protons • Observed at quasi-parallel Earth bow shock • May explain difference in H/He slopes, but detailed modeling necessary • Essential for modeling the composition of Galactic Cosmic Rays High A/Q (mass / charge) ions gain more energy in each crossing and have a flatter spectrum than protons as long as they are non-relativistic. Enhancement then persists to relativistic energies Test Particle Flow speed Modified shock X

Quasi-parallel Earth Bow Shock AMPTE / IRM observations of diffuse ions at Q-parallel Earth bow shock H+, He2+, & CNO6+ Observed during time when solar wind magnetic field was nearly radial. Ellison, Mobius & Paschmann 90 H+ He2+ CNO6+ DS UpS DS Critical range for injection Modeling suggests nonlinear effects important Data shows high A/Q solar wind ions injected and accelerated preferentially. These observations are consistent with A/Q enhancement in nonlinear DSA (Eichler 1979)

A/Q enhancement applied to Galactic Cosmic Ray Composition Observed CR composition NOT so similar to solar system !!! Scale to Silicon Here, scale to Silicon Note composition measurements restricted to low energy CRs < 100 GeV Li, Be, B produced by heavier CRs breaking up as collide in ISM Lodders 2003

Galactic Cosmic Ray Composition Simpson 83 Scale to Hydrogen Consistent explanation of CR source material: Nonlinear SNR shocks accelerate ISM gas and dust with A/Q enhancement Li B Be Galactic abundances ►Main effect is enhancement of all heavy elements relative to Hydrogen & Helium (factor of ~10) ►Secondary effect is enhancement of refractory elements (Dust) relative to volatile ones (Gas) (factor of ~10) Meyer, Drury & Ellison 1997

Those elements that are most abundant in CRs are locked in dust in ISM ! ISM gas-phase abundances 100% in gas phase Si Silicon Iron Fe >99% in dust Al Ni Aluminum Ti Calcium Ca Dust Meyer, Drury, & Ellison 97 You must accelerate ISM dust to reproduce observed (low energy) CR composition

Ellison, Drury & Meyer 1997 A/Q enhancement of ISM gas and dust accelerated by SNR shock. Dust sputters off refractory ions which are then re-accelerated by shock 100 Elements that are locked in dust in ISM 10 CR source/solar Gaseous elements H Large error bars here, but more recent observations by TIGER and ACE are much better  1 He 1 10 100 Mass, A ~ (A/Q) Scale to Hydrogen

Figure (preliminary) from M. Israel (Denver CR meeting, June 2012) New data from TIGER and ACE. M. Israel et al. compare with 80% mixed ISM and 20% massive star outflow & ejecta. Support for Gas-Dust model. Clear evidence for A/Q enhancement of both Volatiles & Refractories Refractories (Dust) Volatiles (Gas) Note: Mass, A ~ (A/Q) H and He are not on this plot. Until Meyer et al 1997, H and He were treated as “exceptions” and not included with heavy elements. H and He did not fit FIP scenario.

Magnetic Field Amplification (MFA): Particle acceleration requires magnetic turbulence to work. This turbulence must be far stronger than typical ISM B/B to produce CRs to high energy 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 : • currents will be generated by particles reflecting off barrier, • small-scale B-fields result (call this the Weibel instability if you like), • fresh, unshocked particles now gyrate in these fields and become randomized, • a shock quickly forms, • particles start to be accelerated by the shock and the streaming instability generates more magnetic field, etc….

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

How do you start with BISM 3 G and end up with B  300 G 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  apply Q-linear theory when B/B >> 1; Bell 2004  non-resonant streaming instabilities Amato & Blasi 2006; Blasi, Amato & Caprioli 2006; Vladimirov, Ellison & Bykov 2006, 2008 } calculations coupled to nonlinear particle accel.

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): Amato, Blasi, Caprioli, Morlino, Vietri: Semi-analytic Bell: Semi-analytic and PIC simulations Berezhko, Volk, Ksenofontov: Semi-analytic Malkov: Semi-analytic Niemiec & Pohl: PIC Pelletier and co-workers: MHD, relativistic shocks Reville, Kirk & co-workers: MHD, PIC Spitkovsky and co-workers; Hoshino and co-workers; other PIC simulators: Particle-In-Cell simulations, so far, mainly rel. shocks Caprioli & Spitkovsky; Giacalone et al.: hybrid simulations Vladimirov, Ellison, Bykov: Monte Carlo Zirakashvili & Ptuskin: Semi-analytic, MHD Bykov et al Apologies to people I missed …

Magnetic Field Amplification in DSA is a hard problem • Magnetic field generation intrinsic part of particle acceleration  cannot treat DSA and MFA separately • Strong turbulence means Quasi-Linear Theory (QLT) not good approximation  But QLT is our main analytic tool (QLT assumes B/B << 1) • Length and momentum scales are currently well beyond reach of 3D particle-in-cell (PIC) simulations if wish to see full nonlinear effects  Particularly true for non-relativistic shocks • Problem difficult because TeV protons influence injection of keV protons and electrons • To cover full dynamic range, must use approximate methods: e.g., Monte Carlo, Semi-analytic, MHD simulations

Work with Bykov, Osipov & Vladimirov Using approximate plasma physics (quasi-linear theory, Bohm diffusion, etc.) Can iteratively solve nonlinear DSA problem with MFA (Monte Carlo work with Andrei Bykov, Andrey Vladimirov & Sergei Osipov) Thermal leakage Injection Acceleration Efficiency magnetic turbulence,B/B  diffusion coefficientdissipation, & cascading iterate Shock structure 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)

The Theory of Supernova Remnants