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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?)