Pulsar Radio Emission Height:Pulsar Radio Emission Height:PSR B1451-68PSR B1451-68

Zhang Hui

National Astronomical Observatories, Chinese Academic of Science

Sino-German Bilateral Workshop on Radio Astronomy, 2005 September 7-14 , Kashi & Urumqi , China

2005 September 12

Pulsar Radio Emission Height:Pulsar Radio Emission Height:PSR B1451-68PSR B1451-68

1. Observatory facts a. core + cone(s) b. r1,r2,r3… same frequency

2. Observatory facts . vs Theory , discrepancy a. RS ≠> Core b. RS : r~-

3. Radio Emission height: 3D calculation ICS model vs Observatory facts , ICS fit

Pulsar radiationPulsar radiation

Emission beamsEmission beams

Rankin, 1983, ApJ,274,333

Rankin (1983, 1993)

Gil & Krawczyk 1996;Mitra & Deshpande 1999;

Gangadhara & Gupta 2001,

Lyne & Manchester 1988

Han & Manchester 2001

Core and ConesCore and Cones

Wu et al 92y

r1,r2,r3… same frequency

PSR B1451-68

Pulsar Radio Emission Height:Pulsar Radio Emission Height:PSR B1451-68PSR B1451-68

1. Observatory facts a. core + cone(s) b. r1,r2,r3… same frequency

2. Observatory facts . vs Theory , discrepancy a. RS ≠> Core b. RS : r~-

3. Emission height: 3D calculation ICS model vs Observatory facts , ICS fit

RS modelRS model

Ruderman & Sutherland , 1975 , ApJ

Emission beams in RS Emission beams in RS modelmodel

1. Hollow Cone Beam2. Power-law Form : r ~-

Pulsar Radio Emission Height:Pulsar Radio Emission Height:PSR B1451-68PSR B1451-68

1. Observatory facts a. core + cone(s) b. r1,r2,r3… same frequency

2. Observatory facts . vs Theory , discrepancy a. RS ≠> Core b. RS : r~-

3. Emission height: 3D calculation ICS model vs Observatory facts , ICS fit

is the inclination angle.

θµ is the inclination of radiation direction to the magnetic axis.

is the inclination of radiation direction to the rotation axis.

is azimuth angle to the rotation axis.

is azimuth angle to the magnetic axis.

Two assumptions:1. The radio emission comes from the last open field line of dipole magnetic field.2. All the emission regions are symmetrical to the --µ plane.

1. Three dimensional calculation of emission height

According to this geometry, the equations can be easily written out :

cos cos cos sin sin cos (1)

cos cos cos sin sin cos (2)

Eq(1) gives the emission height that denoted with angle. Eq (2) ascertains which magnetic field line emits the radiation. There is another relation:

3sin(2 )tan

1 3cos(2 )

(3)

The equation of dipolar magnetic field is :

2Resinr (4)

Where θ is dipolar angle.

Re can be numerically solved. So from equation (1)~(4) we can work out the emission height . r

Wu et al(1992). developed the Gaussian fit separation of the average profile method and analysed PSR B1451-68 .They found the profile ofthis pulsar is quintuble instead of triple. The results are as follows:

p1~p5 are the peak positions of the five gaussian components(Wu et al.1992).

p1 and p5 correspond to the out conal component, p2 and p4 correspondto the inner conal component. p3 belongs to the core component.

215, 224, 23 is the width of two pulses according to the peak positions.

2. Applied to PSR B1451-68

The three dimensional calculation results are showed in the table below.

For this pulsar =23.5°=3.3°p=0.263s .

ω=2γ2ω0(1-βCosθi)

Qiao & Lin, 1998,A&A

ICS model

ICS Model: emission beams----ICS Model: emission beams----Core +conesCore +cones

Qiao ， 1992,

ICS model fitting result

Conclusions and Discussions

(1). We gave a three dimensional method to calculate the emission height. Applied to PSR B1451-68 , we found that the same emission frequency can be produced at the different heights. So it didn’t meet the power-law form.

(2). Accordering to the ICS model we can easily get the core component, which the RS model can not get.

(3). The area enveloped by the dashed line and the solid curve line can constrain the emission region. In this case, it near the center of the gap, but not symmetry to the gap center.

(4). The method can be utilized to other pulsars, this work is in progress.

Thanks!Thanks!