1. Pulsar Radio Emission Height: PSR 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

2. Pulsar Radio Emission Height: PSR 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

3. Pulsar radiation Pulsar radiation

4. Emission beams Emission beams Rankin, 1983, ApJ,274,333

5. Rankin (1983, 1993) Gil & Krawczyk 1996; Mitra & Deshpande 1999; Gangadhara & Gupta 2001,  Lyne & Manchester 1988 Han & Manchester 2001  Core and Cones Core and Cones

6. Wu et al 92y r 1,r 2,r 3 …  same frequency PSR B1451-68

7. Pulsar Radio Emission Height: PSR 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

8. RS model RS model Ruderman & Sutherland, 1975, ApJ

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

10. Pulsar Radio Emission Height: PSR 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

11.  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

12. 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.

13. Wu et al(1992). developed the Gaussian fit separation of the average profile method and analysed PSR B1451-68.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 B1451-68

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

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

17. ICS Model: emission beams----Core +cones Qiao ， 1992,

18. ICS model fitting result

19. 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.

20. Thanks!