Pulsar Radio Emission Height: PSR B 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: PSR B 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 radiation Pulsar radiation

Emission beams Emission 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 Cones Core and Cones

Wu et al 92y r 1,r 2,r 3 …  same frequency PSR B

Pulsar Radio Emission Height: PSR B 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 model RS model Ruderman & Sutherland, 1975, ApJ

Emission beams in RS model Emission beams in RS model 1.Hollow Cone Beam 2.Power-law Form : r ~ - 

Pulsar Radio Emission Height: PSR B 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. θ µ 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 : (1) (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: (3) The equation of dipolar magnetic field is : (4) Where θ is dipolar angle. R e can be numerically solved. So from equation (1)~(4) we can work out the emission height.

Wu et al(1992). developed the Gaussian fit separation of the average profile method and analysed PSR B They found the profile of this 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 correspond to the inner conal component. p3 belongs to the core component. 2  15, 2  24, 2  3 is the width of two pulses according to the peak positions. 2. Applied to PSR B

The three dimensional calculation results are showed in the table below. For this pulsar  =23.5°  =3.3°p=0.263s.

ω=2γ 2 ω 0 (1-βCosθ i ) Qiao & Lin, 1998,A&A ICS model

ICS Model: emission beams----Core +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 B , 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!