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    {\small\rm\zihao{6}\songti\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
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    {\small\rm \zihao{6}\songti suppl.\hfill X. H. Li et al.: Single Pulses of Millisecond Pulsar PSR J0437$-$4715  %%（作者：题目名称）
    \vspace{1.5mm}
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    Vol.44~ Suppl.
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      Feb.,~2003 \\[-1.5 true mm] %%January
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\vs\vs\vs \bc {\Large\bf
Single Pulses of Millisecond Pulsar PSR J0437$-$4715    %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize X.H. Li\up{1}\hs\hs  S. Qi\up{2}
\hs\hs J.L. Han\up{1}}  %%（本文作者）

\vs
(\footnotesize 1~\nao) \\%%（本文作者单位）
 (\footnotesize 2~ \nua)\\

\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
Properties of single pulses of millisecond pulsar PSR J0437$-$4715
have been investigated. We examined and found no evidences for
nulling, giant pulses, or giant micropulses. The gated pulse
profiles show a relative variation among the flux densities of main
peak and other components. The investigation of stability of
pulses suggests the pulse profile is easy to be stable.

\end{quotation}


\vs\vn Single pulse studies have long been concerned as a key to
understanding the structure of pulsar emission region. Most of
previous works has been done with regards to normal pulsars, and
few millisecond pulsars (MSPs) are bright enough for such investigations. 
PSR J0437$-$4715
is one of the brightest MSP with a low dispersion measure of 2.6469\,$\rm
cm^{-3}\,pc$, thus it is an ideal source for single pulse
investigations. Our data were obtained at 1517\,MHz using
Parkes 64\,m telescope with a sampling time of 0.08\,ms and total
bandwidth of 256\,MHz.

\para{\large\bf{1}~~Nulling and Giant Pulses}

\vs\vs Pulse nulling takes place when the pulse power drops
dramatically for some periods, while giant pulses are very
luminous pulses occational occuring at some pulse periods. Normalized
flux density distribution is plotted in Fig.1. According to
Ritchings (1976), an increasing fraction of noise probability
distribution centred on zero energy has to be subtracted from the
observed probability distribution until some portion of the
$'$residual$'$ distribution either became negative or no longer
remained smooth. This particular value of the fraction is adopted
as an upper limit of probability for pulse nulling. We got the upper limit of
0.61$\%$. In addition,  there is apparently not many luminous pulses in Fig.1.

\para{\large\bf{2}~~Giant Micropulses}

\vs\vs Giant micropulses are not so luminous as giant pulses, they
are very narrow and high intensity pulses (Johnston et al. 2001). We
investigated giant micropulses by checking the distribution of the
signal-to-noise ratio (SNR). We take the ratio between the highest
flux density in each single pulse and the noise level of off-pulse
window and show the statistical results in Fig.2. One can see that
the distribution is similiar to a $\chi^{2}$ distribution with a
mean about 10. The highest SNR less than 80 suggests there is
no evidence for giant micropulses. The 1-bit sampling may
affect this distribution.

\begin{figure}[h]
\parbox[b]{6.5cm}
{\hspace{5mm}\includegraphics[bb=33 0 396
504,scale=0.3,angle=-90]{fig1.eps}

    {\footnotesize
    Fig.\,1~~Histogram of flux density in
windows of on-pulses(shaded) and off-pulses}
 }
 \end{figure}
 \begin{figure}[h]
 \vspace{-51mm}
 \ \hfill \
\parbox[b]{6.5cm}
{\hspace{5mm}\includegraphics[bb=27 0 399
504,scale=0.3,angle=-90]{fig2.eps}

    {\footnotesize
    Fig.\,2~~The signal-to-noise ratio of the highest flux density
    in each period}
 }
 \end{figure}

\para{\large\bf{3}~~Gated Pulse Profiles}

\vs\vs Single pulses have been grouped into 9 groups according
to SNRs, then 9 gated pulse profiles have been obtained. The normalized
profiles are shown in Fig.3. The SNRs of single pulses are increasing
from bottom to top. One can see that the width of main peaks are
narrowing with increasing of the SNR, and the side components get relatively 
weaker from bottom to top after main peaks are scaled to the unit.

\vs{\begin{minipage}[h]{14cm}
%\begin{figure}[h]
\begin{minipage}[h]{7cm}
  {\mbox{~~}{\includegraphics[bb=41 0 394 504,scale=0.3,angle=-90]{fig3.eps}\\[-3mm]}

\parbox[b]{6cm} {\footnotesize
  \vs  Fig.\,3~~Normalized pulse profiles (gated with the SNR). The SNRs are
    increasing from bottom to top}
 }
 \end{minipage} \  \

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 \ \hfill \
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{\mbox{~~}{\includegraphics[bb=40 0 394
504,scale=0.3,angle=-90]{fig4.eps}

    \parbox[b]{6cm}{\footnotesize
    Fig.\,4~~The variations of log(1-$\rho$) with number of periods
  included in the subaverage}
 }}
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 %\end{figure}
\end{minipage}}

\para{\large\bf{4}~~Stability of Average Profiles}

\vs\vs The stabilization rate of average profile is studied by
coefficients of cross correlations between the global profile and
subaveraged profiles.
 Rathasree \& Rankin (1995)
studied over two dozen normal pulsars, and found the range of slopes for 
normal pulsars $-$0.19$\,\sim\,-$0.98.
From our linear fitting in Fig.4, the slope for PSR J0437$-$4715 is 
$-$0.8 $\pm$0.06, so it is a pulsar easy to have stabilized profile.

\vn{\bf ACKNOWLEDGEMENTS}~~ Many thanks to X.H. Sun, X.J. Wu, A.
Jessner, W. Sieber for their discussions. XHL wish to express
gratitude to D. Mitra for his suggestions. This work is supported
by the National Natural Science Foundation of China (19903003 and
10025313) and the National Key Basic Research Science Foundation
of China (G19990754) as well as the partner group of MPIfR at
NAOC.

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

 \no  Johnston S., van Straten W., Kramer M., et al., ApJ, 2001,
549, L101\\
\no Krishnamohan S., Downs G.S., ApJ, 1983, 265, 372\\
\no Rathnasree N., Rankin J.M., ApJ, 1995, 452, 814\\
\no Ritchings R.T., MNRAS, 1976,  176, 249\\

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