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Supernov æ as Cosmic-ray sources. Isolated Supernov æ. A. Marcowith (L.P.T.A.). Outlines. The Galactic cosmic-ray (GCR) spectrum & the supernova hypothesis. The standard model of Galactic cosmic ray Multi-wavelength observations Diffusive shock acceleration
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Supernovæ as Cosmic-ray sources Isolated Supernovæ A. Marcowith (L.P.T.A.)
Outlines • The Galactic cosmic-ray (GCR) spectrum & the supernova hypothesis. • The standard model of Galactic cosmic ray • Multi-wavelength observations • Diffusive shock acceleration • Turbulence in supernova (SN) shocks • Conclusions
The galactic cosmic rays • The Cosmic-ray spectrum • The supernova hypothesis Standard books: Berezinsky ’90, Gaisser ’94, Schlickeiser ’03.
Galactic Cosmic rays eV The Cosmic-ray spectrum
The Supernova hypothesis Hypothesis: Same CR energy density in the galactic disc. • Local energy density of GCRs: E ~ 1 eV/cm3(@ 1 GeV) • Power necessary to supply CRs: Pcr = V E / tr ~ 1041 erg/s • Typical power (of type II) SN (majority of SN in Spiral galaxies): PSN ~ 3 x 1042 erg/s Pcr ~ few % PSN Supernovae are the main sources of GCR
Type I Type II WITHOUT H Absorption lines WITH H Absorption lines Massive star collapse Type Ib & Ic Type Ia Ib He lines Ic no He & no Si lines No He lines Si lines White dwarf/giant system explosion Type of Supernova • SN frequency (Nb/century/Galaxy) SNII ~ 0.88 SNIa ~ 0.24 SNIbc ~ 0.16
Tycho SN remnant Crab remnant & nebula Type Ia Type II Both processes inject ~ 1051ergs into ~ 1 solar mass…
Historical galactic Supernovæ www.seds.org/Messier/more/mw_sn.html Clark & Stephenson ‘77
Outlines • The Galactic cosmic-ray (GCR) spectrum & the Supernova hypothesis • The standard model of Galactic cosmic ray • Multi-wavelength observations • Shock acceleration • Conclusions
The standard model of GCRs • SN evolution phases • Effects of the environment • Diffusive shock acceleration - Test particle solutions. • GCRs propagation [see R.Terrier & M. Lemoine] • GCRs composition
Supernova evolution phases • 3 main phases: • Free expansion • Self-similar expansion or Sedov-Taylor • Radiative phase • Fiducial case: SN explosion with uniform ejecta and E0= 1051 erg, Mej= 1 solar mass, standard ISM with uniform ext = 10-24 g/cm-3
Free expansion phase [100-103 yrs] • SN explosion supersonic expansion shock. • The free expansion stage starts once the shock reaches the edge of the atmosphere of the star. • Mechanical energy kinetic energy. MSNR = Mej: ejecta dominated phase VSNR ~ (2 E0/ Mej)1/2= cst RSNR = VSNR t • Fiducial SN: VSNR ~ 5000 km/s
ejecta Ambient ISM Reverse shock • The shocked ISM is heated and compressed by the blast wave pushes on the ejecta back the ejecta are compressed and heated Reverse shock.
Self-similar phase [103-104 yrs] • MSNR = Mswept-up = 4/3 ISM RSNR3: swept-up material dominated phase • The remnant interior has been heated by the reverse shock and the remnant expands bounded by the blast wave. • Evolution laws: RSNR t 2/5 VSNR t -3/5
Self similar expansion laws • Energy in the remnant (1) • RH: Pressure eq. interior/shell (2) • RH: Velocity expansion (3) • (2) & (3) (1) and MSNR RSNR3 RSNR = (E0 t2/0)1/5 • Sedov (1959) solved the stationary spherical HD Eq ~ 1.1516 for = 5/3
Adiabatic phase: numerical 1D results • Truelove & McKee ‘99 Rt2/5 Rt
Radiative phase [104-105 yrs] • 2 sub-phases: cool exp (see Cioffi et al ’88) • Pressure conserved phase • Momentum conserved phase Pressure conserved phase (snowplough phase) • The swept-up collapse into a dense and thin shell • The interior expands adiabatically and pushes the shell like a snowplough • Energy not conserved (radiated away), Pressure conserved. Momentum conserved phase • Pressure Equilibrium: PSNR=PISM • No force is acting on the remnant, its momentum is conserved.
Sedov-Snowplough transitions • Free expansion Sedov: • Sedov Snowplough: tST 273 yr, RST 3.7 pc, tSP 4.4x104 yr, RSP 25 pc
Radius Shock Velocity Environment/Ejecta effects • Environment is not uniform[see Lecture II] - Molecular clouds, cavities in the ISM, galactic density gradients - Wind ( r-2), radiation of a massive star in type II SN (see SN1987A). • Strong influence of the circumstellar shell [Dwarkadas ’05, Chevalier ‘82] • = Shell mass/ Ejecta mass = 3.5
Ejecta are not uniform: - Ejecta profiles structure of the pre-SN star. - Parametric representation: w-n t-3, w=v/vej, vej= initial velocity of the gas at the outermost surface of the ejecta - SNII: steep n ( 10) - SNIa: exponential profiles. • Detailed discussions in Dwarkadas ’05, Truelove & McKee ’99, Matzner & McKee ’99 • Influence on the blast wave dynamics in the stellar envelope on the shock velocity.
Diffusive shock acceleration & source spectra • Diffusive shock acceleration • Test-particle solutions • SN phases & CR acceleration See J. Kirk lectures
// shock Udown=Uup/r Uup=Ush Downstream escapes at const. probability Dup Ddown Efficient pitch-angle diffusion V ~ c >> ush, f is nearly isotropic Diffusive shock acceleration: in short
Test-particle solutions • Microscopic treatement: - Constant energy gain at each cycle + constantprobability to escape downstream scale invariant spectrum Stationary solutions: N(p) p-1-Pesc/[p/p] s = 3r/(r-1) = 4 for r = 4. • Acceleration timescale:
SN phases and CR maximal energy • Free-expansion phase: Rapid expansion + steep ejecta profiles adiabatic losses • The acceleration timescale vsh-2 vsh Snowplough phase • Sedov phase: SN dynamics controlled by the swept-up ISM. CR are injected from ISM gas. - Maximum CR energy fixed by the SN age: Emax (Vsh2 t) t-1/5 The highest CRs are accelerated in the transition Free expansion-Sedov [Lagage & Cesarsky ’83, Kirk’94]
CR spectrum • Onion-shell model: Acceleration at the shock + adiabatic losses downstream [Bogdan & Voelk ’83] Ftot(p)= iFi(p,rsh(ti), si) (Fi particle distribution produced at radius r=rsh(ti) in Sedov expansion, sol. of a diffusion-convection Eq.) Ftot(p) p-4.1
CRs composition (at earth) • At zeroth order: GCR and solar abundances are similar. • LiBeB/CNO are 106 more abundant in GCR • (also for subFe elements) • GCR = accelerated solar coronal material + propagation in the ISM (spallation, energy losses) ? 70-280 MeV/A 1-2 GeV/A (p+Fe) Sc-Ti-V-Cr-Mn (p+C/O) Li-Be-B
CRs propagation • See lectures by R. Terrier, M. Lemoine
GCR source composition SS: Anders & Grevesse GCR: CRIS/ACE • Source spectrum has similar abundances / solar system • GCR are accelerated from ordinary ISM • Not as clear; see Lecture II ….
Standard CR model • SNR hypothesis • Energetics • Spectrum (DSA, SNr dynamics) • Maximum energy(see next) • Composition(see lectures II)
Outlines • The Galactic cosmic-ray (GCR) spectrum & the Supernova hypothesis • The standard model of Galactic cosmic ray • Spectral energy distribution • Shock acceleration • Conclusions
Spectral energy distribution • Radio • Infra-red • Optical lines • X-rays • Gamma-rays
Radio (theory): synchrotron emission • Emission by relativistic (GeV) electrons accelerated at shocks (f / r) or/and by MHD turbulence. • Frequency MHz = [16.5] x BG x EGeV2 sin() • Non-thermal spectraF -related to particle distribution Ne E-q by = (q-1)/2. • Polarisation = (q+1)/(q+7/3)~70% for q = 2 • MF derived by Faraday rotation [see Lect.II] RM = ne B// ds [cm-3 G pc]
Radio (observation) I • Morphology: Limb-brightened radiation, spectral softening behind the blast wave [Delaney et al’02, Kepler]
Radio (observation) II • Indices: [0.4-0.7] (0.05) q [1.8,2.4] peak at ~ 0.55 Good agreement with DSA linear theory. • < 0.5 requires more observations/alternative explanations • Polarisation: a few % (<<70%) high degree of disorder + effects of integration along the l.o.s. SNr catalogue: 265 objects http://www.mrao.cam.ac.uk/surveys/snrs/[Green ’04]
Radio observation: magnetic field structure • Radial structure Rayleigh-Taylor instability [Milne ‘88]in young SNr • Transverse structure in older remnants Compression at forward shock Képler Delaney et al ‘02
- D relation • = mean surface • brightness = Radio luminosity per unit surface • D diameter. D-2.4 Sample of 37 galactic SNr Case & Bhattacharya ‘98
Infra-red • IR produced by dust heating (Spitzer observations , Hines et al’04) • Weak IR synchrotron: Cassiopae A[Rho et al’03, Jones et al’03, Tuffs et at.’97] - PolarisationP(%, 2.2m) = 4-10% P(%, 6cm) - Radial magnetic field profiles. - IR (2.2 m) and radio (6 cm) images correlate each other. - (20-6 cm) = 0.76 and (6 cm-2.2 m) = 0.7 IR flux higher than expected
Optical lines • Non-radiative lines (H Balmer lines): H, H collisional excitation of neutrals with post shock ions Directly slow neutrals/fast ions: Narrow lines Indirectly fast neutrals produced form charge exchange from fast ions: Broad lines. - Broad Line width Proton post shock thermal To - Broad/narrow line flux ratio feq (fraction of thermal post shock energy for e-), Shock velocity.
Compare observations with radiative transfer calculations [Ghavamian et al’01] Tycho (knot g) feq < 0.2 (Te/Tp < 0.1) vsh = 1.9-2.3 103 km/s.
Kepler SNR in X-rays Si S Ar Ca ISM Fe X-rays • Thermal X-rays of shock heated gas at a few 106 K. - Heavy metals lines (O to Fe) produced by metal rich ejecta. • Non-thermal X-rays: - Under 10 keV: cut-off domain of synchrotron radiation of shock accelerated electrons (see next) - Above 10 keV: Unclear origin either synchrotron or Bremsstrahlung (Vink & Laming ’03) Court. J.Ballet
X-ray imaging Cas A
X-ray filaments • Few arc second sizes (Chandra 4-6 keV continuum) • Observation in young SNr [Ballet ’06, AM’06] • Tycho, CasA, Kepler, SN1006, G347.3-0.5, RCW86,G28.6-0.1 • Synchrotron radiation of TeV electrons [Ballet ’06] Bamba et al’06
Multi-wavelength profiles Cas A • High angular resolution observations (Chandra, VLA) : blast wave radiation [Gotthelf et al ’01] • Cas A: NT X-ray emission peaks at the interface Blast wave
SN1006 Thin black: 0.5-0.8 keV; Thick black: 1.2-2.0 keV; gray: radio Long et al’03
Gamma-rays • EGRET • Tcherenkov & HESS observations
GeV SNRs • Sturner et al ’96: 2nd EGRET catalogue 7 objects (among which IC443, Cygni, Monoceros, W44, W28). Interacting with molecular clouds ? • Torres et al ’03: 3rd EGRET catalogue 26 objects. Diamonds: EGRET Unidentified sources Circles: SNR from the Green catalogue
TeV (confirmed) SNR SN1006 • Before HESS: Cangaroo (SN1006, RXJ1713.7-3946, Tanimori et al’98, Muraishi et al’02) HEGRA (CasA, Aharonian et al’02, TBC) • HESS did not confirm SN1006 [Aharonian et al ’05a] Detection of RXJ1713.7-3946, Vela Junior. • 2 SNR in the galactic survey [Aharonian et al’04, 05b] Total: 4-5 sources RXJ0852
RXJ1713.7-3946 • First spectro-imagery at TeV of a SNR. • Non-significative indices variation across the remnant. • Possible correlation with molecular cloud.
Dense targets • Gamma-ray emission process: • Inverse Compton (e-) e- + CMB/IR e- + E ~ 4/3 (E/mec2)2 ECMB/IR (Thomson regime) • Non-thermal Bremsstrahlung (e-) e- + p+ e- + p+ + E ~ Ep/2 • Neutral pion decay (p+) p+ + p+ p+ + p+ + 0 ; 0 2 E ~ Ep/6 Case of an electron/CR distribution: ne/CR E-se/sp