Plasma physics of pulsars

Yuri Lyubarsky

Ben-Gurion University

Pulsars – what do we see?

Spin period, P: ms – seconds

Period slowndown, 𝑃 : 10-15 – 10-19

Age, 𝜏 = 𝑃/𝑃 : kyr – 10 Gyr

Radio signal

Gamma signal

cRL

RL

50,000 kmLR P

V 1010 191521 BRVc

Rotationally induced

voltage drop

implies cascade e+e- creation

wind region

Pulsars are rapidly-rotating,

highly-magnetized neutron stars

Energy budget

Radio emission <1%

Gamma-emission 1-10%

Transferred away

by the pulsar wind 90-100%

E I

384 10 erg/sE

3810 erg/sL Luminosity of the Crab nebula,

For the Crab pulsar,

Synchrotron cooling time (O, X, g)

< nebula age = 1000 years

How is the plasma generated?

Where is the emission coming from ?

What are emission mechanisms?

What is the structure of the pulsar magnetosphere?

How is the rotational energy transferred away by

the pulsar wind and how is it eventually transferred

to radiating particles in the nebula?

Some of the big questions

synchrotron

curvature

γ-B absorption

Plasma production

The basic model (Sturrock ‘71 and

then many others…):

E B 0

E B 0

In the gap, particles are accelerated

(primary beam) and emit photons with

e~100 MeV, which are converted to

e+e-; then cascade due to synchrotron

radiation.

But…

Primary particles (extracted from the surface) themselves provide the

charge density sufficient for . No gap! E B 02

GJc

B

Plasma production (cont)

General relativity comes to rescue (Beskin ‘90, Muslimov&Tsygan ‘92 …) Due to GR frame dragging, the rotationally induced electric field is

determined not by but by

where . . The correction is small but depends on R

therefore could not be maintained in the charge separated

flow. Efficient acceleration of the primary beam.

3'

gaR

R

2

*0.4a R

E B 0

Gamma radiation of the primary beam:

1. Curvature emission at g~106.

2. Cyclotron and Compton scattering of thermal X-rays from the

surface of the star at g~104. Plasma production is not very efficient

but sufficient for shielding of E.

The pair multiplicity (# of pairs per primary particle) calculated

with account of all these effects (Hibschamnn&Arons ‘02).

Marginally sufficient for radio emission.

Plasma production (cont)

Electric current adjustment. In the accelerating gap, the current density

j=GJc; not matched with the magnetospheric currents. Non-steady

pair production (Timokhin 10; Timokhin&Arons13;

Chen&Beloborodov14 ; Philippov+ 15)?

Radio emission - still mysterious

Narrow pulses, complicated, variable

internal structure. Variability at ms, ms

and sometimes ns scales.

Brightness temperature >> 1020 K

coherent emission

High polarization

From Lorimer&Kramer ‘05

Lyne+ 71

Standard picture: radio emission is generated the open

field line tube deep inside the magnetosphere (R<<RL)

narrow beam

1/2P

polarization sweep

beam width

Excitation of collective plasma motions

1D motions, “beads on a wire” B B

Two-stream (beam) instability – main candidate

But…

g gb~104 gp~102

primary

beam

secondary

plasma F(g)

3 vv

d dm m

dt dtg gIn 1D,

Because of large “longitudinal mass”, mg3 , growth rate of the

instability is too small for beam energies.

Radio emission from long-wavelength oscillations in the

plasma outflow

The unsteady polar cap cascade

produces long-wavelength oscillations

in the plasma outflow.

Excitation of collective plasma motions (cont)

Philippov+ 16

The observed radio emission could be

generated by induced scattering of long-

wavelength oscillations in the

relativistic outflow.

1/2

0 'p p g g

In the comoving plasma frame: ' 'p

In the observer frame:

Long-wavelength oscillations in the open filed line tube give rise

to plasma turbulence around 0 (L 96).

Plasma turbulence in the strong magnetic field is inevitably electro-

magnetic; escaping e-m waves are generated in any case.

m

nepf

g

g 2

2 )3*

R

R

ecPBn

) GHz 4.1330 *1222

R

R

P

Bf

g

*30

2/1

23 1.0

RR

RR PL

2 12 2

2

3 28

0

28 1/2

2 2 32

2 2.5 10 erg/s

=4 10 erg/s

B

e PL nm c S

E

gg

g

Radio emission power,

(Malov+ ‘94)

231 12

46 10 erg/s

BE

P

multiplicity

Observed frequency

Beam width

Simple estimates

Power of the plasma flow:

-spin-down power ( )I

What is really observed?

Deshpande & Rankin ‘01

Observer’s view (due to Joanna Rankin)

Backer ‘70, Rankin ‘83, ‘93

Gangadhara ‘97

Mitra+ ‘07

Whatever the emission mechanism, the radiation propagates in the form

of two orthogonally polarized normal modes. In the strong magnetic

field, the modes are linearly polarized.

Polarization

Orthogonal modes are observed but

circular polarization is significant.

Polarization angle sweep.

Origin of e-mode emission

But both modes are observed and moreover, in some

cases (e.g. Vela,) the primary polarization mode

corresponds to the e-mode (Lai+ ‘01; Helfand+ ‘01;

Radhakrishnan & Deshpande ‘01…..)

In a straight, infinitely strong magnetic field, e-

mode does not interact with plasma therefore only

o-mode could be generated

The Vela nebula

ordinary mode (polarized in the

plane):

k B

k Bextraordinary mode (polarized in the

direction) – does not interact with plasma

Adiabatical walking condition:

Origin of e-mode emission in the curved magnetic field

3

c

cR

g

| | 1o e

ln n

c

o-mode

o-mode

e-mode o-mode

Then radiation emitted at an angle to the magnetic field plane is

converted into e-mode

Adiabatical walking condition is

violated near the emission point if

Simple example - curvature emission in the pulsar plasma (Gil+ ‘02):

the outgoing radiation is polarized perpendicularly to the plane of

the magnetic field line.

More on propagation effects

Whatever the emission mechanism, the radiation propagates in the

form of two orthogonally polarized normal modes.

The observed polarization is fixed at the polarization

limiting radius above the emission zone.

The rotational sweepback of the open field line tube is

crucially important for the observed polarization.

Accurate self-consistent 3D models of the

magnetosphere are necessary for analyzing the

polarization data.

Large PA sweeps favor for a small

polarization-limiting radius. Strongly

inhomogeneous plasma flow?

Origin of circular polarization

1. Elliptically polarized NM at RLP

2. Linearly polarized NM, rays are not in the plane of

the magnetic field line

Possible only if RLP ~ RL, where the magnetic field is not large.

Incompatible with polarization sweep.

Occurs at small RLP due to rotation of the magnetosphere,

field lines sweepback, refraction.

A challenge: sense reversal of CP near the pulse center

Radio emission: general conclusion

1. Basic picture: plasma outflow in the open field line tube emits

at altitudes ~ hundreds km (dozens R*) at the Lorentz shifted

plasma frequency. Still on the table.

2. Radiation parameters (power, morphology, spectrum,

polarization) are very sensitive to parameters of the plasma

flow (geometry of the open field line tube, structure of plasma

outflow, etc). Self-consistent models are necessary.

3. Such models (PIC and MHD) has been emerging. Hope for

progress.

Two peaks lightcurves

Could the polar cap cascade account for the observed high energy emission

from young pulsars?

No: the observed morphology and power of the HE emission are not

compatible with the polar cap model

2nd Fermi-LAT pulsar catalog

High-energy emission from pulsars

Spitkovsky ‘06

current sheet

Synchrotron radiation from the relativistically

hot plasma in the current sheet

Two-peaked lightcurves are

generic: one peak per crossing

of the current sheet

Beyond the closed part of the

magnetosphere, the current sheet

separates oppositely directed

magnetic fields. The natural place

for the energy release.

Courtezy to B.Ceruti

Cerutti+ ‘16

Particle acceleration via relativistic

reconnection in the current sheet.

High-energy radiation is

synchrotron radiation from the

current sheet >~ RLC

Radiation flux

Particle energy

Synchrotron radiation from the relativistically

hot plasma in the current sheet (cont)

G e e

Synchrotron radiation from the relativistically

hot plasma in the current sheet (cont)

Gamma rays from energetic

particles in the current sheet

are converted to pairs. They

radiate in X-ray and optics.

Challenge for polar cap pair creation models: synchrotron emission

from young pulsar wind nebulae implies pair multiplicity >105. Pair

production in the current sheet could be a solution.

Pulsar wind nebulae

Young, rapidly rotating pulsars are surrounded

by compact synchrotron nebulae. These nebulae

are continuously pumped by electron-positron

plasma and magnetic field emanating from the

pulsar in the form of relativistic, magnetized

wind.

radio

optics

X-rays

Crab Nebula Spectrum of the Crab Nebula

Pulsar

magnetos

phere Pulsar

wind

Pulsar

wind

nebula

e ,e

electro-magnetic fields

PWN reprocesses rotational energy of the neutron star to

nonthermal accelerated particles and radiation

Pulsar wind nebulae (cont)

Wind from obliquely rotating

magnetosphere: variable fields are

propagated as waves.

MHD outflows have a hollow cone

energy distribution (Bf=0 at the axis).

In pulsar winds, most of the energy is

transferred along the equatorial belt by

alternating fields.

Poynting flux

Kinetic energy flux1In the pulsar wind

Pulsar wind

Waves decay coverts magnetic energy to flow kinetic energy and

“heat”. Where and how do the waves decay?

If the alternating fields survive until the flow arrives at the termination

shock, the sharp compression within the shock structure yields

efficient dissipation (L ‘03, 05; Petri&L ‘07; Sironi&Spitkovsky ‘11).

The morphology of PWN is independent of where the alternating

fields annihilated.

Pulsar wind and PWN

Termination of pulsar wind and formation of the torus-jet structure (L ’02,

Komissarov&L ‘03)

Courtesy to S.Komissarov

pulsar wind

magn

10

thermal

logE

E

Overall structure Inner part of the nebula

3D MHD simulations (Porth+ 14)

PWN, morphology

10loggas

magn

p

p

This implies an extremely hard injection

electron spectrum,

, 0< 0.3.F

( ) , 1< 1.6N E E

All PWNe exhibit flat radio spectra,

such that most of particles remain at the low

energy part of the spectrum whereas most of

energy is at the high energy part.

For the Crab: 1% of particles takes 99% of

the total energy!

PWN, particle acceleration

Dissipation of alternating fields at the termination shock (L ’05,

Petri&L ’07, Sironi&Spitkovsky ’11)? Requires extraordinary

high mass loading of the wind.

Flat radio spectra

PWN, particle acceleration

Rapid gamma flares

Abdo+ ‘11

A few days long GeV flares from the

Crab Nebula. Unless Doppler boosted,

implies E>B at the acceleration site.

Explosive reconnection in the pulsar wind

(Zrake ’16)?

Fast reconnection in the nebula with

acceleration along X-line (Nalewajko,

Uzdensky, Cerutti, Begelman…)?

Instead of conclusion. Pulsars as laboratories for relativistic plasma physics

1. Plasma production in polar gap: cascades, self-regulation via

electro-magnetic coupling to the global magnetospheric

structure.

2. Radio emission from the open field line tube: turbulence in 1D

plasma (but waves are 3D)

3. Global structure of the magnetosphere: current closure problem,

formation of current sheets

4. Reconnection in the current sheet with account of radiation

cooling, plasma production etc.

5. Magnetic energy dissipation in the far wind (dissipation-

acceleration interplay)

6. Particle acceleration at the pulsar wind termination shock (not

DSA?)

7. Reconnection in the nebula (production of PeV electrons?)