Modeling the Dynamical and Radiative Evolution of a Pulsar Wind Nebula inside a Supernova Remnant
Joseph Gelfand (NYUAD / NSF)
Patrick Slane (CfA), Weiqun Zhang (NYU) arxiv:0904.4053
1 What is a Pulsar Wind Nebula?
Electromagnetic forces accelerate charges off neutron star surface (“pulsar wind”) Escape magnetosphere along open field lines Confinement by surrounding terminates, shocks wind Shocked pulsar wind (Handbook of Pulsar Astronomy, Lorimer & Kramer) inflates “Pulsar Wind Nebula” (Credit: NASA/CXC/ASU/J.Hester et al.)
(Credit: NASA/CXC/ASU/J.Hester et al.; NASA/ESA/ASU/J.Hester & A.Loll; NASA/JPL-Caltech/Univ. Minn./R.Gehrz ) 2 Why study a Pulsar Wind Nebula inside a Supernova Remnant?
Neutron Star Initial Spin Period and Spin- down Luminosity Spin-down Timescale Braking Index Pulsar Wind Fraction of energy in magnetic field, electrons, and ions Acceleration mechanism: minimum and maximum particle energy, energy spectrum Progenitor Supernova Ejecta Mass Initial Kinetic Energy
(Credit: NASA/CXC/Eureka Scientific/M.Roberts et al.; NRAO/AUI/NSF ) 3 Schematic of a Pulsar Wind Nebula inside a Supernova Remnant
+ − p 1 t p − 1 Neutron Star E = E 1 + 0 τ s d Termination Shock Emission: η Magnetic Field: BĖ SupernovaSynchrotron Electrons: η Ė InverseRemnant Compton off CMB e Synchrotron Self-Compton Ions: η Ė Pressure: P (R ) i Inverse Compton offsnr Starlightpwn Injection Spectrum Velocity: v (R ) snr pwn Pulsar Wind ρ Density: snr(Rpwn) Pulsar Wind Nebula Swept-up Material Ejecta mass: M Mass: Msw,pwn ej Pressure: Ppwn Kinetic energy: E Velocity: v sn Magnetic Field: B pwn pwn (Gelfand et al. 2009, ApJ in press) Density ISM: nism
4 Model Output
Soft X-ray Optical / Near-IR TeV γ-ray Mid-IR ISM Shocked Ejecta & ISM GeV γ-ray Unshocked Ejecta Radio Hard X-ray Pulsar + Termination Shock
5 Example: Crab Nebula
Dynamical Properties Pulsar Properties fully PWN Radius Terminationdetermined by Shock age, radio Expansion Velocity timing observations Termination Shock Pulsar WindR Radius Magnetizationpwn at termination shock Radiative Properties Minimum and Maximum Radio Luminosity and Energy, Spectrum of Spectral Index Injected Electrons X-ray Luminosity and SupernovaRpwn Explosion Spectral Index Mass and initial kinetic energy of ejecta ISM Density (Figure 1; Volpi et al. 2008)
6 Best Fit: Single Power-law Injection Spectrum Best-fit parameters from MCMC fit Pulsar Wind Properties η +0.1 Magnetization B=0.05-0.03 Electron Injection Energy 60 GeV – 600 TeV Injection Power Law index 2.5 ± 0.2 Supernova Explosion
Ejecta Mass = 8 ± 1 M☼ +2.0 51 Initial KE = 0.6-0.2 ×10 ergs Low density (n < 1 cm-3) environment
7 Best Fit: Single Power-law Injection Spectrum Quantity Observed Predicted
Rpwn 1.5-2.0 pc 1.3 pc 1125 –1500 km/s 1570 km/s vpwn Termination Shock 0.14 pc 0.12 pc Radius Radio Luminosity 1.8×1035 ergs/s 1.76×1035 ergs/s Radio Spectral Index -0.26 +0.1 X-ray Luminosity 1.3×1037 ergs/s 1.0×1037 erg X-ray Photon Index 2.1 (1.8 – 3) 2.26
8 Crab Nebula: Maxwellian + Power- Law Injection Spectrum
Quantity Observed Predicted
Rpwn 1.5-2.0 pc 1.3 pc 1125 –1500 km/s 1600 km/s vpwn Termination Shock 0.14 pc 0.12 pc Radius Radio Luminosity 1.8×1035 ergs/s 1.83×1035 ergs/s Radio Spectral Index -0.26 -0.30 X-ray Luminosity 1.3×1037 ergs/s 1.4×1037 erg X-ray Photon Index 2.1 (1.8 – 3) 2.2
9 Crab Nebula: Maxwellian + Power- Law Injection Spectrum
Pulsar Wind Properties Problems: Magnetization η =0.015 B Not most realistic Power Law: 96% Ė injection spectrum Injection Energy 50 GeV – 1500 TeV Injection Index 2.4 MCMC fit in progress Maxwellian: 4% Ė kT = 1.8 keV ( γ = 3500) Supernova Explosion Will also try broken Ejecta Mass = 8 M ☼ power-law and PL+PL Initial KE = 1051 ergs injection spectrum ISMPRELIMINARY! n = 0.01 cm-3
10 Future Directions Distinguish between injection scenarios Better incorporate results form multi-D simulations Magnetic field structure Growth and effect of instabilities Apply model to other systems Thank you Chandra!
11 Back up slides
12 Model Limitations and Advantages
Model Limitations: Model Advantages: Can not reproduce Simultaneously predict morphological features both dynamical and radiative properties of inside the PWN (e.g. PWN jets and torus) Computationally Can not reproduce inexpensive spectral variations Easily adjustable inside PWN Well suited for parameter Can only estimate exploration, error analysis effect of instabilities Applicable to many (e.g. Raleigh-Taylor) systems on PWN. (Figure 3; Mori et al. 2004)
13 Dynamical and Radiative Evolution for a Trial Set of Parameters
Neutron Star Supernova properties: properties: 51 Esn = 10 ergs Ė = 1040 ergs/s 0 M = 8 M τ ej ☼ sd = 500 years Initial ejecta density p = 3 profile: constant density v = 120 km/s γ psr core + ρ∝r-9 envelope- e Pulsar Wind properties: ISM properties: η η Constant density e = 0.999, B = 0.001, η n = 0.1 cm-3 i = 0 Emax Emin = 511 keV, Energy per Number Unit Emin Emax = 500 TeV, γ = 1.6 e Energy
14 Evolutionary Model for a Pulsar Wind Nebula Inside a Supernova Remnant
Homogeneous ISM, PWN 1D problem Dynamical evolution of 2 PWN determined4π Rbypwn Ppwn dynamics of swept-up material 2 Force result of pressure 4πRpwn Psnr(Rpwn) difference between PWN Pulsar Wind Nebula and SNR Momentum conserved PWN’s radiative losses dominated by synchrotron, IC scattering off CMB
(Gelfand et al. 2009, ApJ submitted) Supernova Remnant(Figure 6; Gelfand et al. 2007)
15 Importance of Injection Spectrum
Single Power Law unlikely to be correct Two component SNR Radius models: Broken Power-law Maxwellian + Power-law Two power-laws? PWN Radius Very different spectral and dynamical evolution (Gelfand et al., in prep.)
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