Pulsar wind nebulae

Carlo Ferrigno Department of astronomy - University of Geneva https://cms.unige.ch/isdc/ferrigno/ 2017 March 22

• Based on High energy astrophysics - an introduction - T. J.-L. Courvoisier • The Evolution and Structure of Pulsar Wind Nebulae – Gaensler1 and Slane – Annu. Rev. Astron. Astrophys. 2006. 44:17?47 Introduction Pulsar wind nebulae

• Spin-down radiation • Characteristic age • Dipole model • Aligned rotator • Pair wind • High-energy radiation • Pulsar wind nebulae • Supernova renmants Different evolutionary phases

Introduction 1 P – P˙ diagram • Census of rotationally-powered pulsars • Lines of equal spin-down age found from dipole model (braking index n = 3) " # 3 × 105  P  P˙ t = yr n − 1 0.1 s 10−14 • Lines of equal magnetic field found similarly as s 2 ˙ 3MNSPNSPNS BNS = ' 2 4 2 5π RNS sin α " #1/2  P 1/2 P˙ 1012 G 0.1 s 10−14 • Order of magnitude estimate Spin-down 1 The pulsar energy spectrum • Spectra of pulsars are non thermal with two bumps at X-ray and GeV energies. (Radio is another bump) • Accelerated particles must be present • Rotation of B-field produces intense E-field, potential is:

2 17 −1 |Φ| ∼ RNSΩB ' 2 × 10 B12P1 V • X-ray bump is due to curvature emis- 12 sion (Emax,cur ∼ 10 eV) 3 8 Epeak,cur = γ /R ' 10 eV • γ-ray bump is due to IC on the NS 9 th. emission (Emax,IC ∼ 10 eV) 2 9 From Kuiper et al. (2010). Epeak,IC = γ Ei ' 10 eV

Spin-down 2 Crab Pulsar spectrum

From Massaro et al. (2006). • The spectrum can be described by phenomenological models, accounting for both pulsed emission and spectral evolution. • Not a direct link to physically motivated models.

Spin-down 3 Pulsar Magnetosphere

• Pairs are produced by interaction of photons. • Charges are separated and migrate • At poles, gaps might form due to open filed lines

Spin-down 4 Pulsar magnetosphere • Photons of high-enough energy in- • this deluge of charges should neu- teract with lower energy photons and tralize the electric field as accelerator produce electron-positron pairs (discharge) 2 • For the Crab, FX ∼ 1 keV/s/cm , • by assuming a plasma that is coro- 44 which is LX ∼ 10 erg/s tating as in the interior and the force- with a density of X-ray photons free condition, one can find the 2 21 −3 nX ' LX /(4πRNSc) ' 10 cm . density of electrons in the magneto- • The flux of photons with multi-GeV sphere of a pulsar energy is suppressed by a factor e−τ ρGJ ∼ ∇ · E ∼ BΩ ' with the optical depth ' 1011B P−1 cm−3  −1 12 0.1 s R 2 R τ = = σγγnX R ' 10 λγγ RNS −25 2 with σγγ = 10 cm • The space around a NS is then populated by electrons and positrons

Spin-down 5 Pulsar magnetosphere 2 • between the extremes, there must be regions with gaps in the magneto- sphere and regions full of pairs. • the light cyclinder forms a limit: parti- cles along the closed field lines • Particles along the open filed lines are free to escape from the magne- tosphere and form a wind. therefore outer gaps are depleted by pairs • Inner gaps are depleted because filed lines are open • pattern of emission is highly anisotropic due to the motion of charged particles and form beam with different orientation

Spin-down 6 Pulsed emission

• Pulsar emission is highly unstable, but clearly modulated and NOT isotropic • but folding the light curve, it becomes a regular pattern

Spin-down 7 Mode changes

From Hermsen et al. (2013). • Mysterious mode switches require further understanding of physics in pulsar

Spin-down 8 Average pulsed profiles

• shape of pulsed profiles change as function of energy, due to different location of radiating particles and photon beam pattern • The precise modelling of pulsar emission is still an open problem: new models propose current sheets along the open field lines • mysterious switched of pulsation modes between radio and X-rays remain to be understood • the surrounding of pulsars is highly dynamical and changes configuration on time scales of minutes / hours

Spin-down 9 Pulsar wind nebulae

The Crab supernova renmant- The in- teraction of supernova ejecta with the A close-up of the central part of the pul- medium and synchrotron emission from sar wind nebula: powered directly from charged particles produce this pattern the wind of pairs.

Spin-down 10 Pulsar wind nebulae 2

• It is possible to estimate the Poyting fluxthrough the light cylinder as 2 B 2 2 2 E˙em ∼ 4πR ∼ R B 4π LC LC LC 6 4 • The current of charged relativistic ∼ B0RNSΩ particles is • Compatible to the power of magnetic

ΩBLC dipole ! JGJ = cnGJ = 2π • Relativistic flow with bulk Lorentz • The magnetic field produced by this factor ΓW and density n = knGJ, with current is of the same order of the k >> 1, because of the unknown pulsar magnetic field multiplication of the pair cascade

Spin-down 11 The termination shock • We define the wind magnetization as • a Fraction of the spin-down energy the ratio of Poynting flux to particle will heat the surrounding medium via energy flux as shocks • With magnetohydroninamcal ccalcu- E˙em σ = 2 lations, it is seen that for σ >> 1 the kcnGJΓW meRLC 2 2 termination shock is relativistic, for BLC B0R ω ' ' NS ' σ << 1, it is sub-relativistic kΩΓW me kΓW me    −1  −2 • the termination shock is slow: B0 ΓW P 104k −1 12 6 in the Crab nebule, we see 10 G 10 30 ms 3 vshock ∼ 10 km/s → σCrab ' 0.003 • The pulsar wind is freely expanding • The wind changes from radiation- with no losses because the magnetic dominated to matter-dominated; this field is frozen-in and opens radially is unexplained • at relativistic speed, it will impact on the supernova renmant

Spin-down 12 Crab nebula spectrum • The termination shock is at 0.1 pc from the pulsar and we can compute the density of the spin-down power

E˙ spin−down UPW ∼ 2 4πRshockc  −2 E˙ spin−down Rshock ∼ 10−8 5 × 1038 erg/s 0.1 pc • The density of magnetic field is / B 8π ∼ σUPW, which implies that the magnetic field is around 10−4 G. From Yuan et al. (2011). • the magnetic field becomes non- • particles produce synchtoron emis- radial at the shock and particles sion at suffer from synchrotron losses.    2 B Ee • particle energy is Ee ∼ ΓW me ∼ 5 ×  ' 5 eV synchr −4 12 1011 eV 10 G 10 eV

Spin-down 13 Crab spectrum 2

• The Synchrotron cooling time is comparable to the object age  −2  −1 3 B Ee ts = 10 yr 10−4 G 1012 eV • From the slope of the synchrotron spectrum (0.5), we infer the photon index 1.5, which implies an electron slope -2 • the synchrotron spectrum extends to From Yuan et al. (2011). 1 GeV, which implies that electrons • acceleration efficiency is very high ! are accelerated to • acceleration region must be small as  −1/2 16 B we observed variability on hour time Emax,s ∼ 10 10−4 G scale 1/2 h s i • higher bump is Compton scattering eV 1 GeV of synchrotron emission

Spin-down 14 Pulsar and PWN spectra in Crab

• Pulsar emission is less intense than PWN • A significant fraction of the spin-down power of the Crab goes into the rela- tivistic wind and produces emission far from the pulsar

Spin-down 15 Moving pulsars

From Gaensler & Slane (2006). • Pulsars have often kick velocities that push them in the Galactic medium • The pulsar wind is deformed into a Bow-shock pulsar wind nebula

Spin-down 16 Moving pulsars 2

Radio and X-ray images of a PWN from Pavan et al. (2014). Notice the different extensions.

Spin-down 17 Spin-down 18 RX J1713.7−3946

• Ratio of peak intensity is 2 γ UTh I /I = ' 10 IC Sy 2 γ UB √ 3 −5 • UTh ' 1 ev/cm → B = 8πUB ' 10 G • From the magnetic field, it is possible to infer the energy of accelerated electrons

Broad-band spectrum of this SNR with  −1/2 1/2 14 B hsynchri Ee ' 10 eV the Synchrotron plus external Compton 10−5 G 5 keV model. From Yang & Liu (2013). • These electrons can scatter CMB photons, −4 • Best example of particle acceleration which have energy CMB ∼ 3 × 10 eV     in the filaments during transition to Ee  E '  γ2 ' 1013 IC CMB e 14 Sedov phase (exploded in 393 AD) 10 eV CMB

Spin-down 19 Spin-down 0–21a

Bibliography Massaro, E., Campana, R., Cusumano, G., & Mineo, T. 2006, A&A, 459, 859 Pavan, L., Bordas, P., Pühlhofer, G., et al. 2014, Astronomy and Astrophysics, 562, Gaensler, B. M. & Slane, P. O. 2006, Annual Review of Astronomy & Astrophysics, A122 44, 17 Yang, C. & Liu, S. 2013, ApJ, 773, 138 Hermsen, W., Hessels, J. W. T., Kuiper, L., et al. 2013, Science, 339, 436 Yuan, Q., Yin, P.-F., Wu, X.-F., et al. 2011, ApJ, 730, L15 Kuiper, L., Hermsen, W., Urama, J. O., et al. 2010, A&A, 515, A34

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