The population of pulsars
with interpulses and the
implications for beam
evolution
(astro-ph/0804.4318)
Patrick Weltevrede
&
Simon Johnston
ATNF
Low-Frequency Pulsar Science
Leiden 2008
Pulsar timing for
GLAST
• Timing ~ 160 pulsars with
Parkes
• Perfect dataset to study
young & energetic pulsars
Standard model for pulsar beams
Gould 1994, Rankin 1990, Rankin 1993,
Kramer et al. 1994, Gil et al. 1993
Pulse width distribution
• Expect W  P -1/2
• Large scatter
because of
unknown geometry
• Correlation is flatter
(slope is ~ - 0.3)
• Same as in the
Gould & Lyne
(1998) data
Idea: beam evolution
The magnetic axis evolves towards alignment with
the rotation axis (Tauris & Manchester 1998)
Long period pulsar
older
more aligned beams
W  P -1/2 (P large, W small)
W increasing with P
W - P correlation flatter
Idea: consequence for IP
If   90o, we can
see the interpulse
Most pulsars with
interpulses should
be young if there is
beam evolution
Observations: interpulses
• Literature: 27/1487 slow pulsars
have an interpulse (1.8%)
IP pulsars
• Includes 3 new weak interpulses
• Some “interpulses” will be aligned
rotators
observed
fraction
J0905-5127
J1126-6054 slow pulsarsJ1637-4553
is an upper-limit
The model: beam geometry
• Pick a random
pairs from the pulsar
catalogue (slow pulsars)
• Calculate beam size:
• Pick random birth  and a random line of
sight (both  and + distributions are
sinusoidal)
• Allow alignment:
The model: elliptical beams
• If polar cap is bounded by the last open field
lines, the beam could be elliptical
• Axial ratio:
(McKinnon 1993)
• Axial ratio between 1 ( = 00) and 0.62 ( =
900)
• Model most likely oversimplified, but interesting
to investigate consequences
• We can force circular beams by setting
for all 
Model: detection condition
• We can check with the following conditions if
the beams intersect the line of sight:
• We keep picking new ’s and ’s until at least
one beam is detected
No alignment and circular
beams
• IP fraction: 4.4% (observed: < 1.8%)
• There are too many
fast IP pulsars
• W  P -1/2
Model fails
No alignment and elliptical
beams
• IP fraction: 2.3% (observed: < 1.8%)
• There are too many
fast IP pulsars
• W  P -1/2
Model fails
Alignment of the magnetic axis
• IP fraction 1.8% (for align = 70 Myr)
• P distribution fits
• W  P -0.4
• Elliptical beams:
- align = 2 Gyr
- P distribution no
longer fits data
Implications of alignment
• Beaming fraction = fraction of
the celestial sphere
illuminated by the pulsar =
probability to see the pulsar
• Older pulsars are less likely to
be found in a pulsar survey
• Average beaming fraction is
8% instead of 17%
inferred total population of
pulsars is 2x larger
Orthogonal (young)
Aligned (old)
Implications for spin-down
• Braking torque can change 
– Braking torque depends on 
– Characteristic age, B, Edot etc. is a function of 
– Vacuum dipole: Edot  sin2 
• Why timescale so slow?
Conclusions
• IP population suggests that align = 7x107 yr
• Consistent with align found by Tauris &
Manchester
• The model is simple and intuitive. No ad-hoc
assumptions are required.
• Different  - P relations without alignment is
not able to fit the data
• Elliptical beams are inconsistent with the data
• Older pulsars are more difficult to find and
total inferred population is 2x larger
• Standard spin-down formula is questionable
What can LOFAR/SKA do?
• Find many more pulsars.
– Constrain beam shapes
– Constrain functional forms  evolution
– Better understanding braking torques
• Comparison of the high and low frequency IP
populations provides information about
frequency dependence of pulsar beams.