Understanding the pulsar magnetosphere through first-principle simulations

Understanding the pulsar magnetosphere through first-principle simulations Alexander Y. Chen In collaboration with: Andrei Beloborodov Rui Hu The Many Faces of Neutron Stars August 25, 2015

Pulsars: Rotating Magnetized Neutron Stars Pulsars are accepted to be rotating magnetized neutron stars. Rotation produces pulses, and we receive radiation when the emission beam sweeps across us Pulse period increases due to the loss of rotational energy into dipole radiation Surrounded by huge magnetic field ( 10 12 G) A. Y. Chen Pulsar Simulations August 25 2 / 34

Goldreich-Julian Model Simplest pulsar model: spherical rotating magnet in vacuum A. Y. Chen Pulsar Simulations August 25 3 / 34

Goldreich-Julian Model Simplest pulsar model: spherical rotating magnet in vacuum Huge electric field develops in the vacuum, ripping charged particles from the surface A. Y. Chen Pulsar Simulations August 25 3 / 34

Goldreich-Julian Model Simplest pulsar model: spherical rotating magnet in vacuum Huge electric field develops in the vacuum, ripping charged particles from the surface The particles fill the surroundings of the star, forming a charged magnetosphere, with charge density ρ GJ = Ω B/2πc, screening E B A. Y. Chen Pulsar Simulations August 25 3 / 34

Goldreich-Julian Model Simplest pulsar model: spherical rotating magnet in vacuum Huge electric field develops in the vacuum, ripping charged particles from the surface The particles fill the surroundings of the star, forming a charged magnetosphere, with charge density ρ GJ = Ω B/2πc, screening E B The magnetosphere co-rotates with the star, up to a radius beyond which co-rotation speed is larger than c. This is called the light cylinder A. Y. Chen Pulsar Simulations August 25 3 / 34

Goldreich-Julian Model Simplest pulsar model: spherical rotating magnet in vacuum Huge electric field develops in the vacuum, ripping charged particles from the surface The particles fill the surroundings of the star, forming a charged magnetosphere, with charge density ρ GJ = Ω B/2πc, screening E B The magnetosphere co-rotates with the star, up to a radius beyond which co-rotation speed is larger than c. This is called the light cylinder Magnetic field lines opens up beyond the light cylinder. It is no longer a dipole field globally A. Y. Chen Pulsar Simulations August 25 3 / 34

Goldreich-Julian Model Goldreich & Julian 1969 A. Y. Chen Pulsar Simulations August 25 4 / 34

Goldreich-Julian Model Goldreich & Julian 1969 Is plasma extracted from the surface sufficient to fill the magnetosphere? A. Y. Chen Pulsar Simulations August 25 4 / 34

Electrosphere In the case of aligned rotator, the plasma simply form a dome plus torus configuration A. Y. Chen Pulsar Simulations August 25 5 / 34

Electrosphere In the case of aligned rotator, the plasma simply form a dome plus torus configuration Jackson 1975 A. Y. Chen Pulsar Simulations August 25 5 / 34

Electrosphere In the case of aligned rotator, the plasma simply form a dome plus torus configuration Jackson 1975 Spitkovsky 2002 A. Y. Chen Pulsar Simulations August 25 5 / 34

Pair Creation Curvature radiation from highly energetic particles can interact with the magnetic field to produce electron-positron pairs Ruderman & Sutherland 1974 Polar Gap A. Y. Chen Pulsar Simulations August 25 6 / 34

Pair Creation Curvature radiation from highly energetic particles can interact with the magnetic field to produce electron-positron pairs A single seed particle can start an avalanche, creating a large number of pairs Ruderman & Sutherland 1974 Polar Gap A. Y. Chen Pulsar Simulations August 25 6 / 34

Pair Creation Curvature radiation from highly energetic particles can interact with the magnetic field to produce electron-positron pairs A single seed particle can start an avalanche, creating a large number of pairs Naturally creating both signs of charges, possibly leading to charge bunching and coherent radio emission Ruderman & Sutherland 1974 Polar Gap A. Y. Chen Pulsar Simulations August 25 6 / 34

Pair Creation Various local acceleration regions (gaps): A. Y. Chen Pulsar Simulations August 25 7 / 34

Pair Creation Various local acceleration regions (gaps): Outer gap (Cheng et. al. 1986) A. Y. Chen Pulsar Simulations August 25 7 / 34

Pair Creation Various local acceleration regions (gaps): Outer gap (Cheng et. al. 1986) Slot gap (Arons 1981) A. Y. Chen Pulsar Simulations August 25 7 / 34

Force-free Magnetosphere If one assumes that the gaps can supply enough plasma to screen E B everywhere in the magnetosphere, one approaches the force-free limit Contopoulos et. al. 1999 A. Y. Chen Pulsar Simulations August 25 8 / 34

Problem with Force-free To have a stable supply of plasma, an operating gap is needed in the magnetosphere. But the assumption of force-free cannot allow this. A. Y. Chen Pulsar Simulations August 25 9 / 34

Problem with Force-free To have a stable supply of plasma, an operating gap is needed in the magnetosphere. But the assumption of force-free cannot allow this. Does the pulsar magnetosphere self-consistently evolve to a state similar to the electrosphere, or force-free solution, or somewhere in-between? A. Y. Chen Pulsar Simulations August 25 9 / 34

Other Questions Which gaps, if any, are present in a pulsar magnetosphere? A. Y. Chen Pulsar Simulations August 25 10 / 34

Other Questions Which gaps, if any, are present in a pulsar magnetosphere? Are the gaps static? Do they move around? Do they turn on and shut off with time? A. Y. Chen Pulsar Simulations August 25 10 / 34

Other Questions Which gaps, if any, are present in a pulsar magnetosphere? Are the gaps static? Do they move around? Do they turn on and shut off with time? How to explain the high pair multiplicity as observed in some of the young pulsars? A. Y. Chen Pulsar Simulations August 25 10 / 34

Other Questions Which gaps, if any, are present in a pulsar magnetosphere? Are the gaps static? Do they move around? Do they turn on and shut off with time? How to explain the high pair multiplicity as observed in some of the young pulsars? Where is the high-energy radiation produced? Can we explain the broadband emission from pulsars? A. Y. Chen Pulsar Simulations August 25 10 / 34

Other Questions Which gaps, if any, are present in a pulsar magnetosphere? Are the gaps static? Do they move around? Do they turn on and shut off with time? How to explain the high pair multiplicity as observed in some of the young pulsars? Where is the high-energy radiation produced? Can we explain the broadband emission from pulsars? What is the mechanism that produces radio emission? A. Y. Chen Pulsar Simulations August 25 10 / 34

First Principle Simulations We want to answer these questions in a self-consistent way, through first principle simulations. We need: Self-consistent interaction between plasma and electromagnetic field, even at ultra-relativistic energies A. Y. Chen Pulsar Simulations August 25 11 / 34

First Principle Simulations We want to answer these questions in a self-consistent way, through first principle simulations. We need: Self-consistent interaction between plasma and electromagnetic field, even at ultra-relativistic energies A somewhat realistic model of radiative transfer, in particular high energy radiation and its conversion into pairs A. Y. Chen Pulsar Simulations August 25 11 / 34

First Principle Simulations We want to answer these questions in a self-consistent way, through first principle simulations. We need: Self-consistent interaction between plasma and electromagnetic field, even at ultra-relativistic energies A somewhat realistic model of radiative transfer, in particular high energy radiation and its conversion into pairs Ability to resolve the largest scale (the light cylinder) and smallest (plasma skin depth), and everything in between A. Y. Chen Pulsar Simulations August 25 11 / 34

Particle-in-Cell (PIC) Simulation Solving the Maxwell-Vlasov system f s t + u f s x + qs m E = 4πρ B = 0 E = 1 c tb s (E + u B) f B = 1 c te + 4π c j s (γu) = 0 A. Y. Chen Pulsar Simulations August 25 12 / 34

Particle-in-Cell (PIC) Simulation Use meta-particles to approximate a distribution function Fields are discretized on a mesh grid Meta-particles move inside the grid cells Interpolating particle motion to the grid gives the discretized current + + + Use the current to evolve the fields with Maxwell equations A. Y. Chen Pulsar Simulations August 25 13 / 34

Particle-in-Cell (PIC) Simulation Resolves particle motion down to plasma scale Fully kinetic, able to reproduce all kinds of plasma instabilities Able to handle ultra relativistic plasma Inherently scalable, and relatively simple to parallelize Other works using PIC to study the pulsar: A. Philippov 2014 & 2015, B. Cerutti 2015, A. Belyaev 2015 A. Y. Chen Pulsar Simulations August 25 14 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors Esirkepov current deposition A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors Esirkepov current deposition Boris-Vay particle pusher A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors Esirkepov current deposition Boris-Vay particle pusher Fully implicit field update A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors Esirkepov current deposition Boris-Vay particle pusher Fully implicit field update Support orthogonal curvilinear coordinate systems with given g 11, g 22, and g 33 A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors Esirkepov current deposition Boris-Vay particle pusher Fully implicit field update Support orthogonal curvilinear coordinate systems with given g 11, g 22, and g 33 Tracks the production of high energy photons and their conversion to pairs A. Y. Chen Pulsar Simulations August 25 15 / 34

Aperture APERTURE stands for: Aperture is a code for Particles, Electrodynamics, and Radiative Transfer at Ultra-Relativistic Energies High order finite difference schemes and particle form factors Esirkepov current deposition Boris-Vay particle pusher Fully implicit field update Support orthogonal curvilinear coordinate systems with given g 11, g 22, and g 33 Tracks the production of high energy photons and their conversion to pairs Fully parallelized to run on a multi-node large cluster, as well as on a desktop computer using GPUs A. Y. Chen Pulsar Simulations August 25 15 / 34

Tests Two-stream instability 10 9 10 8 δ TSI = 3γ b /2 4/3 10 7 E 2 z/8πmec 2 10 6 10 5 10 4 10 3 80 90 100 110 120 130 140 150 160 tω p A. Y. Chen Pulsar Simulations August 25 16 / 34

Tests Two-stream instability 10 9 10 8 δ TSI = 3γ b /2 4/3 10 7 E 2 z/8πmec 2 10 6 10 5 10 4 10 3 80 90 100 110 120 130 140 150 160 tω p A. Y. Chen Pulsar Simulations August 25 16 / 34

Tests Dispersion relation A. Y. Chen Pulsar Simulations August 25 17 / 34

Tests Dispersion relation A. Y. Chen Pulsar Simulations August 25 17 / 34

Test: Electrosphere Pulsar without pair creation: A. Y. Chen Pulsar Simulations August 25 18 / 34

Model for Pair Production Magnetic conversion e + e + Photon collision e + e + γ B A. Y. Chen Pulsar Simulations August 25 19 / 34

Model for Pair Production Particles in our simulation produce curvature radiation. The threshold for producing pair-creating photons is γ thr = K(R c /R ) 1/3. When the particle Lorentz factor exceeds this threshold, we allow it to produce photons at a given rate N = N 0 (γ/r c ). The photon can then convert to a pair through two channels: A. Y. Chen Pulsar Simulations August 25 20 / 34

Model for Pair Production Particles in our simulation produce curvature radiation. The threshold for producing pair-creating photons is γ thr = K(R c /R ) 1/3. When the particle Lorentz factor exceeds this threshold, we allow it to produce photons at a given rate N = N 0 (γ/r c ). The photon can then convert to a pair through two channels: Magnetic conversion: If a photon is produced near the star, it has a very high probability of converting to a pair immediately A. Y. Chen Pulsar Simulations August 25 20 / 34

Model for Pair Production Particles in our simulation produce curvature radiation. The threshold for producing pair-creating photons is γ thr = K(R c /R ) 1/3. When the particle Lorentz factor exceeds this threshold, we allow it to produce photons at a given rate N = N 0 (γ/r c ). The photon can then convert to a pair through two channels: Magnetic conversion: If a photon is produced near the star, it has a very high probability of converting to a pair immediately Photon collision: If a photon is produced outside the magnetic conversion region, we assign to it a (large) random free path. At the end of the free path we assume it collides with a target photon and let it convert to a pair, regardless of the local field strength. A. Y. Chen Pulsar Simulations August 25 20 / 34

Pulsar with Pair Creation A. Y. Chen Pulsar Simulations August 25 21 / 34

Pulsar with Pair Creation Features: Electron-positron discharge is sufficient to supply the charges required by the field Formation of thin current sheets and the Y-point near the light cylinder Strong particle acceleration along the current sheets Continuous reconnection near and beyond the Y-point A. Y. Chen Pulsar Simulations August 25 22 / 34

Current and Charge Distribution Figure: Left: Radial current; Right: Charge distribution A. Y. Chen Pulsar Simulations August 25 23 / 34

Discharge Mechanism In the current sheet along the last closed field line: Toroidal magnetic field jumps, which requires charge density ρ B to be negative (Lyubarskii 1990) A. Y. Chen Pulsar Simulations August 25 24 / 34

Discharge Mechanism In the current sheet along the last closed field line: Toroidal magnetic field jumps, which requires charge density ρ B to be negative (Lyubarskii 1990) Required current j B = B is positive due to magnetic field configuration A. Y. Chen Pulsar Simulations August 25 24 / 34

Discharge Mechanism In the current sheet along the last closed field line: Toroidal magnetic field jumps, which requires charge density ρ B to be negative (Lyubarskii 1990) Required current j B = B is positive due to magnetic field configuration α = j B /cρ B < 0, current cannot simply be carried by a charge-separated outflow from the star A. Y. Chen Pulsar Simulations August 25 24 / 34

Discharge Mechanism In the current sheet along the last closed field line: Toroidal magnetic field jumps, which requires charge density ρ B to be negative (Lyubarskii 1990) Required current j B = B is positive due to magnetic field configuration α = j B /cρ B < 0, current cannot simply be carried by a charge-separated outflow from the star Due to mismatch between j B and j means that E needs to be induced, which accelerates particles to produce pair discharge A. Y. Chen Pulsar Simulations August 25 24 / 34

Discharge Mechanism In the current sheet along the last closed field line: Toroidal magnetic field jumps, which requires charge density ρ B to be negative (Lyubarskii 1990) Required current j B = B is positive due to magnetic field configuration α = j B /cρ B < 0, current cannot simply be carried by a charge-separated outflow from the star Due to mismatch between j B and j means that E needs to be induced, which accelerates particles to produce pair discharge Gap has to be time-dependent due to the nature of induction A. Y. Chen Pulsar Simulations August 25 24 / 34

Gamma Ray Photons Figure: Photon distribution A. Y. Chen Pulsar Simulations August 25 25 / 34

Energy Flux Figure: Poynting and particle energy flux, L 0 = µ 2 Ω 4 /c 3 A. Y. Chen Pulsar Simulations August 25 26 / 34

Energy Flow Figure: Left panel: average ion energy in units of m e c 2, with m i = 5m e ; Right panel: ratio of matter energy density U m to the magnetic energy density U B = B 2 /8π A. Y. Chen Pulsar Simulations August 25 27 / 34

Type I and Type II Pulsars The formation of Y-point and current sheets depends crucially on whether pairs can be created near to the light cylinder Type I: Young, fast rotating pulsars that can create pairs all the way to the light cylinder through γ-γ interaction Type II: Weak pulsars that can only produce pairs through magnetic interaction, therefore pair creation is limited to where B field is strong A. Y. Chen Pulsar Simulations August 25 28 / 34

Comparison of Type I and Type II Pulsars A. Y. Chen Pulsar Simulations August 25 29 / 34

Comparison of Type I and Type II Pulsars Type II pulsars seem not able to self-consistently form a Y-point. There is not enough pair creation to support the current sheet. Structure looks like electrosphere However, Type II pulsar is not dead. Pair activity periodically switch on to conduct the return current The pairs are created by secondary electrons accelerated backwards by the vacuum electric field between the dome and the torus A. Y. Chen Pulsar Simulations August 25 30 / 34

Polar Cap For both types of pulsars, plasma outflows at mildly relativistic energies near the polar cap Figure: Current flow across the polar cap, normalized to j GJ = cρ GJ. α = j pol /j GJ. Left is from PIC simulation, right is from a force-free model (Parfrey et. al. 2012) A. Y. Chen Pulsar Simulations August 25 31 / 34

Summary PIC simulations prove to be a powerful tool to study the structure of the pulsar magnetosphere We obtain overall results similar to the force-free models, but with a lot of extra information We now know from first principles where the gap is and its mechanism Gamma ray photons are mainly produced in the Y-shaped current sheets Weak pulsars seem to be deviate qualitatively from the standard force-free pulsar picture A. Y. Chen Pulsar Simulations August 25 32 / 34

Next Steps Oblique rotators: Gamma ray light curve from first principles A. Y. Chen Pulsar Simulations August 25 33 / 34

Next Steps Oblique rotators: Gamma ray light curve from first principles Particle acceleration: Reconnection and particle acceleration inside the current sheet A. Y. Chen Pulsar Simulations August 25 33 / 34

Next Steps Oblique rotators: Gamma ray light curve from first principles Particle acceleration: Reconnection and particle acceleration inside the current sheet Higher resolution simulations: Closer to Force-free? A. Y. Chen Pulsar Simulations August 25 33 / 34

Next Steps Oblique rotators: Gamma ray light curve from first principles Particle acceleration: Reconnection and particle acceleration inside the current sheet Higher resolution simulations: Closer to Force-free? Radio emission: Plasma oscillations are well resolved, can we extract radio emission from this kind of simulations? A. Y. Chen Pulsar Simulations August 25 33 / 34

Thank you! A. Y. Chen Pulsar Simulations August 25 34 / 34