Highenergy Emission from Pulsar Magnetospheres

1
High-energy Emission from Pulsar Magnetospheres
Kouichi HIROTANI TIARA, Taiwan Osaka November
10, 2006
2
The seven highest-confidence g-ray pulsars
by CGRO
3
1 Introduction CGRO observations
Six of them exhibit light curve modulation above
100 MeV
Kanbach (2002) MPE report 278, 91
4
Broad-band spectra (pulsed)
103 yrs

• Power peaked in g-rays
• No pulsed emission above 20 GeV
• High-energy turnover
• Increase in hardness with age. For example, the
  Crab pulsar shows very soft g-ray spectrum.
• B195132 shows the hardest spectrum.

pulsar age
105 yrs
Kanbach 2002
GeV
5
2 Pulsar as a unipolar inductor (contd)
In a rotating NS magnetosphere, the
Goldreich-Julian charge density is induced for a
static observer.
rGJ changes sign at the null surface.
Fig. Goldreich-Julian charge distribution (side
view)
6
2 Pulsar as a unipolar inductor (contd)
In a rotating NS magnetosphere, the
Goldreich-Julian charge density is induced for a
static observer.
If r deviates from rGJ in some region, E
arises. Erot partly dissipated as pulsed
radiation Next question Where is the
particle accelerator, in which E arises?
7
3 Accelerator models (contd)
The modulation of the GeV light curves
Kanbach (2002) MPE report 278, 91
8
3 Accelerator models (contd)

• The modulation of the GeV light curves testifies
  to the ?-ray production in
• inner gap
• (Daugherty Harding
• 1996 ApJ 458, 278)
• slot gap
• (Arons
• 1983, ApJ 302, 301
• Muslimov Harding
• 2004, ApJ 606, 1143)
• outer gap
• (Cheng, Ho, Ruderman
• 1986, ApJ 300, 500)

9
3 Inner-slot-gap Models

• In traditional IG models, energetics and pair
  cascade spectrum have had success in reproducing
  observations.
• However, the predicted beam size is too small to
  produce the wide pulse profiles that are
  observed.
• High-altitude acceleration region along the
  last-open field lines was first considered by
  Arons (1983).
• Muslimov Harding (2003 2004) extended this
  idea by adding GR effects and E screening due
  to gap narrowness.
• Dyks, Harding, Rudak (2004) explained the
  phase-aligned pulse profiles for the Crab pulsar
  and the formation of double peaks with lt180o, and
  off-pulse emission.

10
3 Polar-slot gap model problem
However, their inner-slot-gap model (outward
extension of the IG model) predicts a negative
E when . Elt0 induces an
opposite gap current from the global current flow
patterns.
11
3 Polar-slot gap model problems

• On the other hand, a non-vacuum, active OG should
  extend from the NS surface to the outer
  magnetosphere with positive E (Hirotani,
  Harding Shibata 2003).
• Inward extension of the OG model (Egt0) is
• an alternative way to consider particle
  acceleration
• from the NS surface to the outer magnetosphere.
• So far, various properties of high-energy
  emissions such as double-peak light curves with
  strong bridges, phase-resolved spectra have been
  explained with OG models. Cheng et al. 2000,
  ApJ 537, 964
• Romani 1996, ApJ 470, 469
• Chiang Romani 1994, ApJ 436, 754
• Zhang Cheng 1997, ApJ 487, 370

12
4 New accelerator model

• To this aim, I solve the set of Maxwell
  Boltzmann equations in pulsar magnetospheres on
  2-D poloidal plane.
• Beskin, Istomin Parev 1992,
• Sov. Astron. 36(6), 642
• Hirotani, Harding Shibata 2003 ApJ 591,
  334
• Hirotani 2006, ApJ in press

13
4 New accelerator model
Let us first describe the physical processes that
take part in a stationary pair-production in a
gap.
14
4 New gap model Maxwell equation
The Poisson equation for the electrostatic
potential ? is given by
N/N- distrib. func. of e/e- G Lorentz factor
of e/e-
15
4 New gap model g-ray Boltzmann eqs.
We solve the these Boltzmann eqs.
assuming
16
4 New gap model Boundary conditions
To solve the set of Maxwell Boltzmann
equations, we must impose appropriate BCs.
Assume that inner boundary stellar surface
lower boundary last-open field line
17
4 New gap model Boundary conditions
To solve the Poisson eq. for electrostatic
potential Y, we impose
18
4 New accelerator model

• Three free parameters
• magnetic inclination (e.g., 45o, 75o),
• magnetic dipole moment of NS (e.g., 41030G cm3)
• trans-field gap thickness, hm (0 lt hmlt 1)
• Solve Poisson eq. Boltzmann eqs. in 22 dim.
• Other quantities such gap
• gap geometry,
• acceleration electric field distribution,
• particle density and energy spectrum,
• g-ray flux and energy spectrum,
• pair creation rate outside of the gap,
• are all solved by these three parameters.

19
5 Application to the Crab Pulsar
I applied the theory to two pulsars, Crab, Vela,
and B195132.
20
5 Crab Pulsar sub-GJ current solution
If the gap is transversely thin, it is nearly
vacuum. (i.e., created current ltlt
Goldreich-Julian value) Traditional
outer-gap solution is obtained. (e.g., E is
nearly constant.)
50
33, 67
hm 0.047 mag. incl. a 70o
83
17
21
5 sub-GJ solution insufficient g-ray flux
However, sub-GJ solution ( nearly vacuum
solution traditional outer-gap solution)
predicts too small g-ray flux.
Predicted phase-averaged spectrum
22
5 Crab Pulsar super-GJ current solution
As the gap becomes thicker, it becomes
non-vacuum. (i.e., created current gt
Goldreich-Julian value) Inner part is
substantially screened.
hm 0.048, a 70o
hm 0.060, a 70o
50
33, 67
83
17
23
5 real and GJ charge densities
Examine the real charge density distribution.

• First, consider a lower-latitude B field line.
• g-rays propagate in the convex side to
  materialize preferentially in higher colatitudes.
• Lower latitudes almost vacuum.

rGJ/B
re /B 0
24
5 real and GJ charge densities
a 70o
rGJ/B
r /B
re /B
This negative reff in the lower colatitudes
attempts to make E be positive.
25
5 real and GJ charge densities
Along further higher field lines, it is enough
for re to have a comparable gradient with rGJ.
rGJ/B
r /B
re /B
26
5 real and GJ charge densities
Along further higher field lines, it is enough
for re to have a comparable gradient with rGJ.
rGJ/B
r /B
re /B
This is because
27
5 real and GJ charge densities
Created current becomes super-GJ.
a 70o
Goldreich-Julian charge density
charge density including ions
At r r, reff r rGJ lt 0 Egt0
Ion emission (as SCLF)
created charge density
28
5 super-GJ solution Crab flat spectrum
This super-GJ solution (a new OG solution)
predicts flat spectrum below a few GeV.
Crab pulsar spectrum
hm 0.100
m 41030 G cm3
viewing angle 60o-106o 78o-84o 84o-90o 90o-96o 96o
-102o 102o-108o 108o-114o
n Fn
GeV
MeV
keV
TeV
eV
29
5 super-GJ solution Crab flat spectrum
A flat spectrum is commonly obtained. Ex.) a 75o
Crab pulsar spectrum
hm 0.100
m 41030 G cm3
viewing angle 75o-111o 93o-99o 99o-105o 105o-111o
111o-117o 117o-123o 123o-129o
n Fn
GeV
MeV
keV
TeV
eV
30
5 Vela pulsar
Applying the same scheme to the Vela pulsar, we
find that optical and MeV-10GeV spectrum is
reproduced.
hm 0.320
m 41030 G cm3
viewing angle 75o-109o 93o-99o 99o-105o 105o-111o
111o-117o 117o-123o 123o-129o
n Fn
GeV
MeV
keV
TeV
eV
31
5 Vela pulsar
Close up 10 GeV region. The cutoff feature
strongly depends on the latitudinal angles in
which the photons that we observe are emitted.
IG/OG discrimination is one of the key science
projects of GLAST, competing two american
models But its not so simple.
32
5 Vela pulsar
Close up 10 GeV region. The cutoff feature
strongly depends on the latitudinal angles in
which the photons that we observe are emitted.
That is, 3-D B field structure near the light
cylinder is crucial to quantify the spectrum.
33
5 PSR B195131
Applying the same scheme to B195132, we find
that the predicted SED has a turnover around 10
GeV.
hm 0.210
m 21029 G cm3
viewing angle 75o-111o 93o-99o 99o-105o 105o-111o
111o-117o 117o-123o 123o-129o
n Fn
GeV
MeV
keV
TeV
eV
34
5 PSR B195131

• Close up 10 GeV region.
• Present result is consistent with MAGIC upper
  limits.
• Strong ICS component appears around TeV.

The ICS fluxes are the upper limits, because all
the synchrotron soft photons (emitted inside of
LC) are assumed to illuminate the equatorial
region in which e are migrating outwards.
35
5 PSR B195131

• Close up 10 GeV region.
• Present result is consistent with MAGIC upper
  limits.
• Strong ICS component appears around TeV.

In any case, GLAST will give a meaningful
constraint.
36
Discussion gap electrodynamics
Without pair creation, electron density per B
will be constant along the field line. However,
it results in a reversal of E due to the sign
change of r -rGJ.
37
Discussion back to electrodynamics
Solving the same basic eqs. for the the same
pulsar under essentially the same BDCs, Muslimov
Harding (2004) obtained a different solution in
their inner-slot gap model. They considered a
space-charge-limited flow, which consists of only
electrons extracted from NS surface at slightly
smaller than the G-J rate.
38
Discussion gap electrodynamics
To avoid the reversal of E sign, they assumed
that r /B changes in the same manner as rGJ/B.
39
Discussion gap electrodynamics
Because of this small (r -rGJ)/B, weak E
appears in the slot gap. This weak E results in
a less efficient pair creation and guarantees the
completely-charge-separated-flow approx.
40
Discussion gap electrodynamics
In short,
If (r -rGJ)/B is a small positive constant
without pair creation by some mechanism for a
sub-GJ current, slot-gap solution becomes MH04
way with negative E, extracting electrons from
NS surface,
On the other hand,
If (r -rGJ)/B is a small negative value with pair
creation by the discharge of created pairs for a
super-GJ current, slot-gap solution becomes
this-work way with positive E., extracting ions
from NS surface.
41
Discussion gap electrodynamics
In another word, IG and OG models (or their
extensions) are physically the same. Assumed
perpendicular thickness is the only
difference. Its not the era to discriminate IG
or OG models.
42
Summary

• A stationary pair-creation cascade in pulsar
  magnetospheres is self-consistently solved from
  the set of Maxwell Boltzmann eqs. on 2-D
  poloidal plane.
• A transversely thin gap gives a traditional
  outer-gap solution (e.g., constant positive E).
  g-ray flux is negligible.
• A thick gap gives a super-GJ current solution,
  which is a mixture of traditional inner- and
  outer-gap models (SCLF Egt0). E is highly
  unscreened in the outer magnetosphere.
• Crab pulsed spectrum is reproduced in 1eV-10
  TeV.
• Velas turnover spectrum cannot be simply
  predicted as in a conventional argument on IG/OG
  discrimination.
• PSR B195132 exhibits spectral turnover below 10
  GeV, which is to be checked with GLAST.