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    {\small\rm\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
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    {\small\rm  suppl.\hfill H. Wang \& X. Wu: Geometric Analysis of the Profiles
for Pulsar PSR B1857-26  %%�����ߣ���Ŀ���ƣ�
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\zihao{5}\songti

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    Vol.44~ Suppl.
    \hfill\hspace{8mm} %%% if ``October/January'' then \hspace{8/10 mm} July
    \small ACTA ASTRONOMICA SINICA
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      Feb.,~2003 \\[-1.5 true mm] %%January
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\vs\vs\vs \bc {\Large\bf Geometric Analysis of The Average Profiles
for\\[2mm] Pulsar PSR B1857-26    %%�����⣩
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize Huaxiang Wang\hs\&\hs  Xinji Wu }  %%���������ߣ�

\vs
 (\footnotesize  \pka)\\
 ({\footnotesize {\it CAS-PKU Joint Beijing Astrophysics Center, Beijing}~100871})\\
 ({\footnotesize {\it Urumqi Astronomical Observatory, NAO, CAS, Urumqi}~ 830011})
\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
Applying the method of Gaussian fit separation of the average
profile (GFSAP), we studied the pulsar PSR B1857-26. It has been
observed at 410, 610, 925, 1408 and 1642MHz, providing an
excellent sample for a multi-frequency analysis. This method
allows us to study the pulsar emitting geometry carefully.

 \vn
 \no{\bf Key words}~~  pulsar, average profiles, geometry
\end{quotation}

%%%% ����
 \para{\large\bf{1}~~ Introduction}

\vs\vs In some way, the geometry of pulsar emission beams has
provided important insight into pulsar radiation physics. Rankin's
work (1983, 1986, 1990, 1993) established an empirical theory of
pulsar emission and brought forward a comprehensive pulsar
classification scheme. Wu et al (1992a,b; 1998) proposed the GFSAP
method and analyzed the pulsar PSR B1451-68. The
``core-double-cone'' model requires a large population of
five-component pulsars to support it. However the amount of such
pulsars is small till now. The frequency range used in some
analyses was not wide enough; and some results are still
argumentative. Searching for more five-component pulsars still is
a meaningful topic.

There is debate on the mechanisms of core and cone. Rankin pointed
out that the spectrum of the core is steeper than that of cone,
and she deems that they have different emission mechanisms. It is
important to study the spectrum of each component in wider
frequency range.

\para{\large\bf{2}~~ The Gaussian Fit Separation of Average Profile Method}

\vs\vs  The main idea of GFSAP is that the average profile is
superposed by many independent emission components, each of which
follows a Gaussian shape. Fitting the observed curve with
multi-component model we get the position, intensity and width of
each individual component.

The full profile is represented by $f(\phi)$, as a sum of
individual Gaussian components:
\begin{equation} f(\phi)=\sum_{j=1}^M g_j=\sum_{j=1}^M
h_je^{-4ln2(\phi-p_j)^2/w_j^2}\,,
\end{equation}
where $w_i$ is the half-power width of component $i$, $p_i$ is the
peak position, and $h_i$ the amplitude.

The method of GFSAP follows the usual fitting procedure, i.e. the
sum of the squared residuals between the observed profile and
equation (1) is minimized by searching parameter space for that
set of parameters which best represents the observational curve.

\vspace*{1mm}\para{\large\bf{3}~~ Analysis of Fitting Results}

\vs\vn{\bf{3.1~~The Emission Region Geometry}}

 Assuming a dipolar
magnetic field configuration and taking the emission region to be
roughly circularly symmetric about the magnetic axis, the problem
of determining the conal radius  $\rho$ reduces to a relation of
spherical geometry (Gil 1981):
\begin{equation}
\rho=cos^{-1}[cos\beta-2sin{\alpha}sin{\zeta}sin^2(\Delta\phi/4)]\,
\end{equation}
where $\alpha$ is the angle between the magnetic axis and the spin
axis, $\beta$ is the impact angle, and $\zeta$ is the impact angle
of the line of sight with respect to the rotation axis and
$\Delta\phi$ is the half power width of the conal component pairs.

Assuming that the pulsar has a dipolar magnetic field and the core
component comes from the surface of the pulsar, the emission
altitude of cone component is:
\begin{equation}
r(km)=6.66{\rho}^2P\,.
\end{equation}

The results are listed in Table.1.
\bc{\small\bf

 Table 1~~   The Parameters of Emission Geometry
}\\[2mm]

\fns \tabcolsep 3mm
\begin{tabular}{ccccccc}
\hline\\[-3.6mm]\hline
 Parameter &408\,MHz  &610\,MHz   &925\,MHz   &1408\,MHz  &1642\,MHz\\
  \hline
  $\rho_{core}(deg)$  &2.6    &2.6     &2.8    &3.1    &3.0\\
  $\rho_{inner}(deg)$  &5.8    &5.6    &5.3    &5.6    &5.1\\
  $\rho_{core}(deg)$  &8.6    &8.3     &7.9    &7.7    &7.6\\
  $r_{inner}(km)$  &205.9     &190.7    &169.3    &189.2    &159.3\\
  $r_{outer}(km)$  &451.4     &424.7    &385.4    &366.9    &358.6\\
 \hline\\[-3.6mm]\hline%\\[-4.5mm]\hline
 \end{tabular}
 \ec

\vs\vn{\bf{3.2~~Spectrum Property}}

 Another important thing is the
spectra behavior of difference parts of emission region. We can
study the spectrum difference by taking reference to the results
of flux density measurement. Here reference is given to Lorimer et
al 1995, and the results are listed in Table.2. We can see clearly
that the core spectrum is steeper than the inner and outer cone.
The results are consistent with the results of Wu et al. (1998)
and the conclusion of Rankin, and reveal different emission
mechanism of the emission region.
\bc{\small\bf

 Table 2~~   The flux density of different parts
}\\[2mm]

\fns \tabcolsep 2mm
\begin{tabular}{cccccccc}
\hline\\[-3.6mm]\hline
 Parameter &408\,MHz  &610\,MHz   &925\,MHz   &1408\,MHz  &1642\,MHz\\
  \hline
  Flux &408\,MHz  &610\,MHz   &925\,MHz   &1408\,MHz  &1642\,MHz &Spectra Index\\
  \hline
  Mean(mJy)   &130 &73  &29.3 &2.5    &9.3      &$-1.94\pm0.07$\\
  $F_{core}(mJy)$  &51.5 &17.8 &7.3 &3.5 &2.3   &$-2.31\pm0.14$\\
  $F_{inner}(mJy)$ &34.3 &32.0 &10.5 &4.6 &4.9  &$-1.69\pm0.23$\\
  $F_{outer}(mJy)$ &44.1 &23.1 &11.3 &4.3 &1.9  &$-1.90\pm0,08$\\
 \hline\\[-3.6mm]\hline%\\[-4.5mm]\hline
 \end{tabular}
 \ec

  \newpage\vspace*{1mm}\bc
{\bf References} \ec

\vspace{-4mm} \no \fns

 \nref Gil J.A.,  A\&A, 1981, 104, 69
  \nref Lorimer D.R., Yates J.A., Lyne A.G.,et al., MNRAS, 1995, 411,
  421
  \nref Rankin J.M., ApJ, 1983, 274, 333
  \nref Rankin J.M.,  ApJ, 1986, 301, 901
  \nref Rankin J.M.,  ApJ, 1990,352, 247
  \nref Rankin J.M., ApJ, 1993, 405, 285
  \nref Wu X., Xu W., Rankin J.M., 1992a, in Proc. of IAU
Collq.128, The Magnetospheric Structure and Emission Mechanism of
Radio Pulsars, eds. T.H. Hankins, J.M.Rankin and J.A.Gil
(Pedagogical Univ.Press:Zielona G\'{o}ra, Poland)172
  \nref Wu X., Manchester R.N. 1992b,in Proc. of IAU
Colloq.128, The Magnetospheric Structure and Emission Mechanisms
of Radio Pulsars, eds. T.H.Hankins, J.M.Rankin and
J.A.Gil(Pedagogical Univ.Press: Zielona G\'{o}ra, Poland)362
  \nref Wu Xinji, Gao Xueyan, Rankin J.M., et al., ApJ, 1998, 116, 1984

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