Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Condensed matter physics wikipedia , lookup
Nuclear physics wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Electromagnet wikipedia , lookup
Superconductivity wikipedia , lookup
Density of states wikipedia , lookup
History of subatomic physics wikipedia , lookup
Elementary particle wikipedia , lookup
Woodward effect wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Snowbird - March 2015 Kinetic Simulations of Particle Acceleration at Astrophysical Shocks Damiano Caprioli Princeton University in collaboration with A. Spitkovsky 1 Collisionless shocks Mediated by collective electromagnetic interactions Sources of non-thermal particles and emission Reproducible in laboratory 2 A universal acceleration mechanism Fermi mechanism (Fermi, 1954): random scattering leads to energy gain In shocks, particles gain energy at any reflection (Blandford & Ostriker; Bell; Axford et al.; 1978): Diffusive Shock Acceleration (DSA) ! ! ! ! Downstream (post-shock) Upstream (pre-shock) ∝ 2 Test-particle squeezed between converging flows -𝛼 DSA produces power-laws N(p) 4𝜋p p in momentum, depending on the compression ratio R=ρd/ρu only. For strong shocks: 𝛼=4 4Ms2 R= 2 Ms + 3 3R ↵= R 1 3 Acceleration from first principles Full Particle-In-Cell approach (…, Spitkovsky 2008, Niemiec+2008, Stroman+2009, Riquelme & Spitkovsky 2010, Sironi & Spitkovsky 2011, Park+2012,2015, Niemiec+2012, Guo+2014, DC+15…) Define electromagnetic field on a grid Move particles via Lorentz force Evolve fields via Maxwell equations Computationally very challenging! Hybrid approach: Fluid electrons - Kinetic protons (Winske & Omidi; Lipatov 2002; Giacalone et al.; Gargaté & Spitkovsky 2012, DC & Spitkovsky 2013-2015,…) massless electrons for more macroscopical time/length scales 4 Hybrid simulations of collisionless shocks Reflecting wall DENSITY + PARTICLES Upstream Flow Shock propagation dHybrid code (Gargaté et al, 2007) Out of plane B FIELD Initial B field 5 Spectrum evolution Diffusive Shock Acceleration: f(p) p-4 ∝ 4𝜋p2f(p)dp=f(E)dE ! Downstream Spectrum Maxwellian 85% Energy ∝ f(E)∝E f(E) E-2 (relativ.) -1.5 (non rel.) Non-thermal Tail 15% Energy DC & Spitkovsky, 2014a 6 CR-driven instability DC & Spitkovsky, 2013 7 3D simulations of a parallel shock DC & Spitkovsky, 2014a 8 −1.5 0 Parallel vs Oblique shocks 1000 2000 3000 4000 5000 x [c/ p] 6000 7000 8000 9000 MA=10 1 10 Thermal M=10 0 10 ϑ=0 ϑ = 20 ϑ = 30 ϑ = 45 ϑ = 50 ϑ = 60 ϑ = 80 Non-Thermal −1 E f(E) 10 . c c A rift −2 10 B0 D k c ho −3 10 S −4 10 −3 −2 10 15 10000 −1 10 0 10 10 E/Esh e i 1v s ffu10 Di . c c A 2 3 10 10 Each point is a simulation with about 9 10 particles DC & Spitkovsky, 2014 Efficiency (%) M= 5 M=10 10 𝜗 Vsh M=30 M=50 5 DC & Spitkovsky, 2014 0 0 10 20 30 40 θ (deg) 50 60 70 80 9 n/n0 (t = 200ωc−1) 6 2000 y[c/ωp ] 1500 4 1000 2 500 0 2000 4000 6000 8000 10000 12000 14000 0 16000 x[c/ωp ] Btot /B0 (t = 200ωc−1 ) 30 2000 25 y[c/ωp ] 1500 20 1000 15 10 500 5 0 2000 4000 6000 8000 10000 12000 14000 16000 1 x[c/ωp ] y[c/ωp ] Bx (t = 200ωc−1) 2000 10 1500 5 1000 0 500 −5 0 2000 4000 6000 8000 10000 12000 14000 16000 x[c/ωp ] y[c/ωp ] By (t = 200ωc−1) 2000 10 1500 5 1000 0 500 −5 0 2000 4000 6000 8000 10000 12000 14000 16000 −10 x[c/ωp ] y[c/ωp ] Bz (t = 200ωc−1) 2000 10 1500 5 1000 0 500 −5 0 2000 4000 6000 8000 10000 x[c/ωp ] 12000 14000 16000 Hybrid simulations of a very strong shock: M=100 −10 ! Total 𝜹B/B larger than 10 in the precursor! ! Very expensive to study in the hybrid limit 10 8 Caprioli & Spitkovsky Dependence on inclination and MA 20 M = 100 M = 80 15 5 10 15 20 25 30 Btot /B0 (t = 200ωc−1 ) M = 30 Btot /B0 1 10 y[c/ωp ] ⃗0 B 5 100 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 0 x[c/ωp ] M = 20 Angle dependence due to ion injection (DC, Pop, Spitkovsky 2015) M = 10 500 300 100 200 300 400 500 x − xsh [c/ωp ] y[c/ωp ] 500 300 1500 2000 2500 3000 3500 4000 4500 50 5000 300 100 1500 2000 2500 3000 3500 4000 4500 5000 y[c/ωp ] 500 ⌧ 30 20 10 300 0 10 100 1500 2000 2500 3000 3500 4000 4500 x[c/ωp ] y[c/ωp ] 500 300 100 1500 2000 2500 3000 3500 4000 4500 3500 4000 4500 3500 4000 4500 x[c/ωp ] y[c/ωp ] 500 300 100 1000 1500 2000 2500 3000 x[c/ωp ] y[c/ωp ] 500 300 100 1000 900 1000 Simulations x[c/ωp ] 1000 800 40 ⟨Btot /B0 ⟩2 y[c/ωp ] 500 1000 700 ⟨Btot /B0 ⟩2 ∝ MA x[c/ωp ] 1000 600 60 100 1000 M = 50 1500 2000 2500 3000 x[c/ωp ] 20 30 40 50 60 Btot B0 70 2 up ⇡ 3⇠cr MA 80 90 100 MA 5000 Figure 6. Top panel : Magnetic field profile immediately upstream of the shock, for different Mach numbers as in the legend, at t = 100ω The profile is calculated by averaging over 200c/ωp in the transverse size and over 20ωc−1 in time, in order to smoothen the time and sp fluctuations due to the Bottom panel : Total magnetic field amplification factor in the precursor, averaged over a distance ∆x = 10M c ahead of the shock, as a function of the Alfvénic Mach number (red symbols). The dashed line ⟨Btot /B0 ⟩2 ∝ MA is consistent with prediction of resonant streaming instability (see text for details). A color figure is available in the online journal. More B amplification for stronger (higher MA) shocks! where Pw and Pcr are the pressure (along x) in magnetic field and in CRs, and M̃A = (1 + 1/r)MA is the Alfvénic 5000 Mach number in the shock reference frame (r ≈ 4 for a strong shock, thereby typically M̃A ≃ 1.25MA); We have also introduced the transverse (self-generated) com! 2 ponent of the field, B⊥ (x) = By (x) + Bz2 (x). Assuming isotropy in the self-generated magnetic field, 2 Btot 2 2 one has B⊥ = 23 Btot , and in turn Pw ≈ 12π . Dividing 5000 2 both members of eq. 1 by ρũ , where ũ is the fluid velocity int the shock frame, and introducing the normalized (xsh ) CR pressure at the shock position ξcr = Pcrρũ , one 2 finally gets " #2 Btot ≈ 3ξcr M̃A . (2) B0 sh 5000 The actual value of ξcr can be derived by measuring the Mach numbers considered here, it varies between 10 a 15% at t = 200ωc−1 (also see figure 3 in Paper I). Qu remarkably, if we pose ξcr = 0.15, eq. 2 provides a v good fitting to the amplification factors inferred from simulations (dashed line in figure 6). The extrapolation of the presented results to hig Mach numbers according to eq. 2 is consistent with hypothesis that CR-induced instabilities can account the effective magnetic field amplification inferred at blast waves of young SNRs, even with moderate CR celeration efficiencies of about 10–20%. It would be tempting to conclude that resonant strea ing instability is the almost effective channel throu which the CR current amplify the pre-existing magn field, but there are some caveats. The non-reson streaming instability (Bell 2004, 2005) is predicted to the fastest to grow, and it might saturate on time-sca 11 re shorter than the advection time in the precursor: nant (and also long-wavelength modes, see Bykov et In agreement with the prediction of CR-driven streaming instability 3D simulations Simulations of ion acceleration at shocks: DSA efficiency 16 Caprioli & Spitkovsky 17 Self-generated B Bz /B0 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 0 0.5 Log10[Ef(E)](t = 200ωc−1) 2 Log10(E/Esh ) 1.5 1 0.5 0 −0.5 −1 400 𝜗=0o 500 600 700 x[c/ωp ] 800 900 1000 500 600 700 x[c/ωp ] 800 900 1000 500 600 700 x[c/ωp ] 800 900 1000 ϑ = 0 deg 2 Log10(E/Esh ) 1.5 Bz /B0 1 0.5 0 −0.5 −1 400 ϑ = 45 deg 𝜗=45o Log10(E/Esh ) 1 0.5 0 −0.5 −1 Bz /B0 400 1 10 ϑ = 80 deg ϑ = 45 deg ϑ = 0 deg 0 10 −1 Ef(E) 10 −2 10 −3 10 𝜗=80o Post-shock ion spectrum −4 10 ϑ = 80 deg −2 10 −1 10 0 10 E/Esh 1 10 12 2 10 – 27 – SN 1006: a parallel accelerator – 24 – X-ray emission (red=thermal white=synchrotron) Magnetic field amplification and particle acceleration where the shock is parallel Inclination of B wrt to the shock normal Reynoso et al. 2013 (a) Magnetic vectors Polarization (low=turbulent high=ordered) 13 y[ High-beta plasmas 4 2 The Alfvènic Mach # controls magnetic field amplification The (magneto-)sonic Mach # −3 −2.5 −2 −1.5 −1 0 1000 controls −0.5 1500 dynamics 2000 and 2500 3000 shock CR spectrum x[c/ωp ] 0 8 M s = 5; M A = 5 M s = 5; M A = 30 M s = 30; MA = 30 Log10[Ef(E)](t = 130ωc−1) Magnetic fields 1 are amplified also 0 in high-β plasmas! −1 6 1000 2000 3000 x[c/ωp ] Btot /B0 Log10(E/Esh ) 2 4 2 4000 5000 0 6000 1000 1 10 1500 2000 2500 x[c/ωp ] 3000 3500 β=2 β = 60 0 10 CR spectra agree with DSA prediction −1 10 Ef(E) 1 −2 10 −3 10 (steeper than p-4 for r<4) −4 10 −2 10 −1 10 0 1 10 10 E/Esh 2 10 3 10 14 Electron/ion acceleration Full PIC simulations: Tristan-MP code (Park, DC, Spitkovsky 2015, PRL) M=20, vsh=0.1c, quasi-parallel shock Electrons are accelerated: electron/proton ratio is a few % Density Ions Electrons Momentum spectrum Energy spectrum Self-generated B field 15 Electron acceleration o PIC simulations of oblique shocks (𝜗=60 ): DC, Park, Spitkovsky, in prep. Only electrons are accelerated! Density Density Ions Self-generated B field DSA spectra Electrons Btot/B0 ~2-10% in energy ~1% in number Stay tuned for scalings with M, β, Vsh,… 16 Electron acceleration Planetary bow shocks (Earth, Venus, Saturn,…) In situ measurements: Geotail, Venus Orbiter, Polar, SoHO, WIND, Cluster, … Radio relics in galaxy clusters (sausage, toothbrush,…) CIZA J2242.8+5301 Extended polarized structures Fermi-LAT limits on 𝛾-ray emission: constrain e/p ratio! 17 CRAFT: a Cosmic-Ray Fast Analytic Tool (Caprioli et al. 2009-2015, to be publicly released soon) Iterative solution of the CR transport equation: ! Injection ! ! u PB + Pcr ! ! CR distribution function ! Mass+momentum conservation eqs. Pcr Magnetic turbulence transport eq. Very fast: a few seconds on a laptop (vs days on clusters) Embeds microphysics from kinetic simulations into (M)HD 13.0 Tycho: a clear-cutSuzaku hadronic accelerator Log!Ν FΝ " #Jy Hz$ 12.5 G. Morlino and D. Caprioli: Strong evidences of hadron acceleration in Tycho’s Supernova Remnant G. Morlino and D. Caprioli: Strong evidences of hadron acceleration in Tycho’s Supernova Remnant 12.0 13.5 FermiLAT d D. Caprioli: Strong evidences of hadron acceleration in Tycho’s Supernova Remnant lerated electrons is calculated n only the cosmic microwave t also the Galactic background hotons produced by the local 11.5 13.0 1 12.511.0 Suzaku Radio 12.010.5 some observational features, e strongly affected by the past ny reliable calculation has to volution. In this paper we use heory, but we couple this theution of the remnant provided We divide the SNR evolution me that for each time step the like has been done in Caprioli, r, as showed by Caprioli et al. e-dependent approaches return elativistic shocks. r kinetic model with the multiof Tycho from the radio to the dial profile of X-ray and radio existing data of Tycho’s SNR efficient acceleration of CR nuat a fraction around 12 per cent en converted in CRs. Such an ed magnetic field of ∼ 300µG, asured X-ray rim thickness. In field enhances the velocity of cing the effective compression s, whose spectrum turns out to important consequence of this s to fit the observed gamma-ray V band, as due to neutral pion ork it is not possible to explain without violating many other FermiLAT 11.5 Fig. 1. Radio image of the Tycho’s remnant at 1.5 GHz in linear color scale. Image credit: NRAO/VLA Archive Survey, (c) 2005-2007 AUI/NRAO. 10.0 11.0 VERITAS 3 Vsh !"10 km!s# 20 10.5 9.5 10 B2 !"100 ΜG# Radio 5 Ξcr #100 10 15 2 10.0 Rsh !pc 1 10 20 9.5 50 100 200 VERITAS E2 F#E$ !eV%cm2 %s" Log!Ν FΝ " #Jy Hz$ al reaction of the field reduces a and affects the prediction for Caprioli et al., 2009). A cruhe scattering centers, which is to the shock speed, but could the magnetic field is ampliov, 2006; Caprioli et al., 2009; hen this occurs, the total comd particles may be appreciably of accelerated particles may be Log!Ν" #Hz$ 20 Total FermiLAT VERITAS Π0 " ΓΓ 0.1 ICIR 0.01 25 ICCMB brem ICGal Age $yr% Fig. 2. Time evolution of shock radius R , shock velocity V , magnetic Fig. 6. Spatiallyfield integrated distribution curves show synchrotron and pion immediately behind thespectral shock B and CR acceleration efficiency 10 energy 15 of Tycho. The20 25 emission, thermal electron bremsstrahlung 108 109 1010 1011 1012 1013 ξ = P /ρ V . decay as calculated within our model (see text for details). The experimental data are, respectively: radio from Reynolds & Ellison (1992); X-rays lows: in §2 we summarize the from Suzaku (courtesy of Toru Tamagawa), GeV gamma-rays from Fermi-LAT (Giordano et al. 2012) and TeV gamma-rays from VERITAS ar particle acceleration and our a set of parameters has been showed to be suitable for describLog!Ν" #Hz$ E !eV" In §3 we outline the macro- ing the evolution of the FS position and velocity for a type Ia etparamal. 2011). Both given Fermi-LAT VERITAS data include only statistical error at 1σ. ,(Acciari in order to fix the free SNR: the parametrization in table 7 of Trueloveand & Mc Kee widely discuss the comparison (1999) in fact differs from the exact numerical solution of about Gamma-ray emission observed by Fermi-LAT by VERITAS in compared withsupernova spectral energy distribution produced by pion decay (dotFig. Spatiallyspecintegrated of Tycho. The curves show synchrotron emission, thermal electron bremsstrahlung and pion or the 6. multi-wavelength G. Morlino andFig. D.11. Caprioli: Strong evidence for hadron and acceleration Tycho’s remnant 3 per cent spectral typically, and energy of 7 per centdistribution at most. Such a solution, fferent energy band separately. sh sh 2 cr cr 0 2 sh av Brightness #Jy%arcmin2 $ of the shock evolution during the ejecta-dominated stage. The circumstellar medium is taken as homogeneous with proton number density n0 = 0.3 cm−3 and temperature T 0 = 104 K. Following the conclusion of Tian & Leahy (2011), we assume that the remnant expands into the uniform interstellar medium (ISM) without interacting with any MC. With these parameters, the reference value for the beginning of the Sedov- Radio profile " 1.5 GHz 13.0 spherical symmetry, which is somehow expected just because he northeastern region is brighter than the rest of the remnant. 712.8 612.6 Account for spectra, SNR hydrodynamics, and morphology while for Fermi-LAT the systematic uncertainties are comparable or even larger than the statistical error especially for the lowest energy bins due to difficulties in evaluating the galactic background (see Fig. 3 in Giordano et al., 2011, and the related discussion). 13.0 X!ray profile " 1 keV Log$Ν FΝ % "Jy Hz# 1.5 by following the analytic preMc Kee (1999). More precisely, rgy ES N = 1051 erg and one structure function is taken as uelove & Mc Kee, 1999). Such 2 Brightness !Hz!sr# Log!Ν "erg!s!cm FΝ " #Jy Hz$ which doesour not include explicitly possible of the CR The experimental data are, respectivley: radio from Reynolds & Ellison (1992); X-raysdashed line), relativistic bremsstrahlung (dot-dot-dashed) and ICS computed for three different photon fields: CMB (dashed), Galactic background decay as calculated within model (seethe text forrole details). pressure in the SNR evolution, is still expect to hold for moderately acceleration efficiencies, (below 10 per rom Suzaku (courtesy ofsmall Toru Tamagawa) GeVabout gamma-rays from Fermi-LAT (Giordano et al., 2011) and TeV gamma-rays from VERITAS(dotted) and IR photons produced by local warm dust (solid). The thick solid line is the sum of all the contributions. Both Fermi-LAT and cent). We checked a posteriori that the efficiency needed to 813.0 VERITAS data points include only statistical errors at13.5 1σ. For VERITAS data the systematic error is found to be ∼ 30% (Acciari et al., 2011), Acciari et al., 2011).fit Both Fermi-LAT and VERITAS data include only statistical error at 1 σ. observations does not require a more complex treatment 12.5 Log!Ν FΝ " #Jy Hz$ background, we are left with ICS on the IR background due to idence of the fact that SNRs do accelerate protons, at least up to 3 12.8 local dust as the only viable candidate. However, as predicted energies of about 500 TeV. The proton acceleration efficiency is 12.0 1.0 5 2 , corresponding to converting in CRs by standard ICS theory and as showed in Fig. 11, the expected found to be ∼ 0.06ρ0 V sh 12.4 12.6 photon spectrum below the cut-off is typically flatter than par- a fraction of about 12 per cent of the kinetic energy density 3 ent electrons’ one, and more precisely is ∝ ν−1.6 11.5 for an electron 12 ρ0 V sh . As estimated for instance in §3 of the review by Hillas 4 Another subtle but interesting difference is that the emis−2.2 12.4 spectrum ∝ E , clearly at odds with Fermi-LAT data in the (2005), such a value is consistent with the hypothesis that SNRs 12.2 sion peaks slightly more inwards than in our model; as a conGeV range. are the sources of Galactic CRs, provided that the residence time < < 11.0 sequence, 0.5 also the emission detected in the region 0.6 ∼ r/R sh ∼ 3 12.2 Another point worth noticing is that the ICS on the CMB in the Milky Way scales with ∼ E −1/3 . 0.8 is found to be a bit larger than the theoretical prediction. 12.0 radiation is sensitive to the steepening of the total10.5 electron specThis difference might have different explanations. The most ob12.0 2 trum above ∼100 GeV (Fig. 4) due to the synchrotron losses vious, and already mentioned, is the possible deviation from the particles undergo while being advected downstream, while for 11.8 spherical symmetry. Another possibility is given by placing the 11.8 the ICS on the IR+optical background the onset10.0 of the Klein1 CD in 0.0 a different position: if one assumed the CD to be located 8 10 12 14 16 18 20 Nishina regime (above Ee ≈ 7 TeV for photons of 1 eV) does 0.0 0.2 0.4 0.6 0.8 1.0 1.2 It is important to remember that the actual CRs produced by 0.94 0.95 0.96 0.97 0.98 0.99 1.00 18.0 18.2 18.4 18.618.2 18.8 18.4 18.0 18.6 18.8 closer to the center (i.e. if one took the CD/FS ratio to be a few not allow us to probe significantly the steep region of the elec- a single SNR is given by the convolution over time of different Log$Ν% "Hz# per cent smaller), the theoretical prediction would Log!Ν" #Hz$ R%Rsh nicely fit the R!R tron sh spectrum. contributions with non trivial spectra, and namely the flux of Log!Ν" #Hz$ data. However, we can not forget that this explanation would be In other words, ICS on the CMB radiation low and particle escaping the remnant upstream during the SedovFig. is 10.tooSynchrotron emission calculated byfrom assuming constant downFig. 8. X-ray emission due to synchrotron (dashed line) and to synatFig. odds7.with the findings of Warren et al.radio (2005), who estimated cannot be boosted by invoking apoints larger electron density, while Taylor stages and the bulk of particles released in the ISM at the Fig. 9. Projected X-ray emission at 1 keV. The Chandra data Surface brightness of the emission at 1.5 GHz as a funcchrotron plus thermal bremsstrahlung (solid line). Data from the Suzaku Fig. 8. X-ray emission due to synchrotron (dashed line) and to synstream magnetic field equal to 100 (dotted line), 200 (dashed line), and he position of the CD to be more towards the forward shock, on IR and/or optical background, which might as well be SNR’s death (Caprioli, Blasi & Amato, 2009; Caprioli, Amato are from (Cassam-Chenaï et al. 2007, ICS see their Fig. 15). The solid line tion of the radius (data as in Fig. 1). The thin solid line represents the telescope (courtesy of Toru Tamagawa). chrotron plus thermal bremsstrahlung (solid line). Data from the Suzaku 300 µG (solid line).&The normalization the electron spectrumspectrum is takenof namely around 0.93R sh. enhanced with respect to the mean Galactic value, cannot Blasi, 2010a). In thisofrespect, the instantaneous the projected radial profile of locally synchrotron emission convolved projected radial profile computed from our model using Eq. (16), while shows −3 provide a spectral slope in agreement with both and to beFermi-LAT Kep = 1.6 × 10accelerated for all particles the curves. telescope (courtesy of Toru Tamagawa). in Tycho, which is inferred to be as steep (assumed to be 0.5 arcsec). the thick solid line corresponds to the same profile convoluted with a with the Chandra point spread functionVERITAS data. as ∝ E −2.2 , provides a hint of the fact that SNRs can indeed We are therefore forced to conclude that the present multi- produce rather steep CR spectra as required to account for the Gaussian with a PSF of 15 arcsec. wavelength analysis of Tycho’s emission represents the best ev- ∝ E −2.7 diffuse spectrum of Galactic CRs (Caprioli, 2011b). A final comment on the radio profile concerns the effects of 4.2. X-ray emission Hadron acc. eff. ~10% Protons up to 0.5 PeV Only two free parameters: injection efficiency and electron/proton ratio he non-linear Landau damping in the determination of the mag- 19 nonthermal et field al. 2005). A detailed the9lineradio data the magnetic field at the shock has to be !200 µG, electrons in a(Warren magnetic as large as ∼300 model µG. InofFig. Conclusions 15% Acceleration at shocks can be efficient: >15% 85% Btot (t = 500ωc−1 ) 1000 y[c/ωp ] CRs amplify the B field via 500 streaming instability Ion DSA efficient at parallel, strong shocks Electron DSA efficient at oblique shocks 15 2000 Efficiency (%) 0 1500 2500 3000 3500 4000 x[c/ωp ] 4500 Ions 10 5000 5500 M= 5 M=10 M=30 M=50 5 0 0 10 20 30 40 θ (deg) 50 60 70 80 𝜗=60o 20