The population of pulsars with interpulses and the

implications for beam evolution

(astro-ph/0804.4318)

Patrick Weltevrede &

Simon Johnston

Low-Frequency Pulsar Science Leiden 2008

ATNF

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 evolutionThe magnetic axis evolves towards alignment with the rotation axis (Tauris & Manchester 1998)

Long period pulsar

older

W P -1/2 (P large, W small)

more aligned beams

W increasing with P

W - P correlation flatter

If 90o, we can see the interpulse

Most pulsars with interpulses should be young if there is beam evolution

Idea: consequence for IP

Observations: interpulses

• Literature: 27/1487 slow pulsars have an interpulse (1.8%)

J0905-5127 J1126-6054 J1637-4553

• Includes 3 new weak interpulses

• Some “interpulses” will be aligned rotators observed fraction is an upper-limit

IP pulsars

slow pulsars

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:

• 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

(McKinnon 1993)

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

• 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

Alignment of the magnetic axis

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.