The population of pulsars with interpulses and the implications for beam evolution (astro-ph/ ) 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 evolution The 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   90 o, 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%) J J J 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 (  = 0 0 ) and 0.62 (  = 90 0 ) 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  sin 2  Why timescale so slow?

Conclusions IP population suggests that  align = 7x10 7 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.