Modeling the Dynamical and Radiative Evolution of a Wind inside a 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 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 ?

 Initial Spin Period and Spin- down Luminosity  Spin-down Timescale  Braking Index  Pulsar Wind  Fraction of energy in , 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:

 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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