\documentstyle[twoside,epsfig,CJK]{carticle}
%\documentclass[twoside]{carticle}
%\usepackage{epsfig}
\pagestyle{empty}
\headsep=0.6cm %%%%%%%

\setcounter{page}{235}

%\input cchead.sty
%\input Vatola.sty

\def\thefootnoot{}

\textwidth=140mm \textheight=210mm \topmargin=0pt
\oddsidemargin=0pt \evensidemargin=0pt \footskip 0.2 truecm

%%...................
%\vspace*{1\baselineskip}
\doublerulesep=0pt
%%..................
% \renewcommand{\baselinestretch}{1.4} %%cc
\parindent=7.5mm

\setlength{\parskip}{0 true pt}
    \def\hang{\hangindent\parindent}
    \def\RE{\par\hang\textindent}
    \catcode`@=11
%%%双页
    \def\@evenhead{\underline{\parbox{\textwidth}
    {\small\rm\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
%%%单页
    \def\@oddhead{\underline{\parbox{\textwidth}
    {\small\rm  suppl.\hfill H. G. Wang et al.: Interpretation for the Spectral Behavior of Pulsar
Average Profiles %%（作者：题目名称）
    \vspace{1.5mm}
    \hfill\thepage}}} %%%%%%%
    \normalsize\rm
\zihao{5}\songti

  %  \begin{CJK}{GB}{song}
    \begin{document}


%%篇首
    \thispagestyle{empty}
    \vspace*{-1.5 true cm}
    \small\rm
    \zihao{6}\songti
    \noindent
    \\%%%[-0.5 true mm]
    Vol.44~ Suppl.
    \hfill\hspace{8mm} %%% if ``October/January'' then \hspace{8/10 mm} July
    \small ACTA ASTRONOMICA SINICA
    \hfill
      Feb.,~2003 \\[-1.5 true mm] %%January
    \rule {\textwidth}{0.12 true mm}\\[-3.2 true mm]
    \rule {\textwidth}{0.12 true mm}
%%%%%%%

\input{../newcom.ctx}

\renewcommand{\baselinestretch}{1}

\setcounter{footnote}{1}

\vs\vs\vs \bc {\Large\bf A Possible Interpretation for the
Spectral Behavior\\[2mm] of Pulsar
Average Profiles    %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize H. G. Wang,\hs\hs G. J. Qiao\hs\&\hs R. X. Xu}  %%（本文作者）

\vs
({\footnotesize ~{\it School of Physics, Peking University,}~ 100871}) \\%%（本文作者单位）
\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
We present a novel interpretation for the spectral behavior of the
average-pulse width on the assumption that the emission is broad
band, which is essentially different from the widely accepted
narrow-band scenario of ``radius-to-frequency mapping''. The
implication towards the physical processes in the conal emission
region is discussed.

 \vn
 \no{\bf Key words}~~  pulsar-mode  change-spectrum
\end{quotation}

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

\vs\vs The spectral behavior of the mean pulse width (or component
separation) has been studied extensively for radio pulsars. Early
observations found that the frequency dependence was a power law
function or two power laws with a break at a certain frequency
(see references in Thorsett 1991). However, after using more
complete data, Thorsett modified the relationship to be a smooth
form $\Delta\theta=A\nu^{-\alpha}+\Delta\theta_{\min}$, which was
further confirmed by the late observations at very high frequency
(Xiouris et al. 1996). Most recently, Mitra \& Rankin (2002,
hereafter MR) reinvestigate this phenomenon. Apart from confirming
the relationship introduced by Thorsett for seven widely studied
pulsars, they investigate another three pulsars with 'conal'
emission and found that the average pulse widths almost do not
show narrowing with frequency. So there are two (and at least two)
kinds of spectral behavior for the conal emission (Fig.1).

\begin{figure}[h]

\includegraphics [bb=75 39 582 744,angle=270,scale=0.28]{fig1a.eps}
\includegraphics [bb=81 44 536 739,angle=270,scale=0.28]{fig1b.eps}

%\parbox[b]{7cm}
%{\hspace{10mm}\includegraphics [bb=75 39 582 744,angle=270
%,scale=0.28]{fig1a.eps}}

%\vspace{-70mm}
% \ \hfill \
%\parbox[b]{6cm}
%{\includegraphics [bb=81 44 536
%739,angle=270,scale=0.28]{fig1b.eps}}

   \parbox[tb]{14cm}
   %{\hspace{3.5cm}
   {%\center
   \vspace{2mm}\footnotesize

      Fig.\,1~~ Observational results for two types of spectral behavior
of pulse width (from Mitra \& Rankin 2002)}

    \end{figure}

The narrowing of pulse width with frequency is commonly
interpreted as a scenario of ``radius-to-frequency mapping'' (RFM,
Cordes 1978), which assumes that the low frequency wave is
produced at higher altitudes while the high frequency at lower
locations. Many endeavors have been tried to verify the RFM
through various observational approaches, e.g., geometry, timing
delay and polarimetry (Xilouris et al. 1996 and references
therein). Theoretically, a few models predict different forms of
RFM. Ruderman \& Sutherland (1975) assumed that the radiation
frequency is related to the local plasma frequency, thus the
emission altitude decreases as $\nu^{-2/3}$ and the component
separation varies as $\nu^{-1/3}$. Lyubarskii \& Petrova (1998)
made the same assumption, but they suggested that refraction due
to plasma density gradient could make the frequency dependence of
pulse width differ from the $\nu^{-1/3}$ law. In the Inverse
Compton Scattering (ICS) model, the RFM and the narrowing of pulse
width are predicted for the outer conal component (Qiao \& Lin
1998). Generally speaking, regardless of the details of various
models, the underlying meaning of any RFM is that, the radiation
at a given altitude should be narrow-band compared with the total
observed frequency extent, as suggested by Cordes (1978).

The alternative scenario suggests that the radiation is broad
band. Rickett \& Cordes (1981) proposed that all frequencies may
be radiated from the same narrow radial range but the spectrum
varies systematically with distance from the magnetic axis.
Barnard \& Arons (1986) studied models with the broad-band
emission from a single radius, which could predict either
narrowing (due to refraction) or none-narrowing of pulse width
with frequency (due to lack of refraction).

In this paper, we tentatively proposed a new interpretation for
the spectral behavior of pulse width under the broad-band
assumption. In section 2 we present the details of our
interpretation. In section 3 the physical implications are
discussed.

\para{\large\bf{2}~~The Broad-band Interpretation}

\vs\vs In a realistic pulsar magnetosphere, the particles created
by the pair production process probably follow a wide energy
distribution. It was found that particles only undergo significant
energy loss near the stellar surface and then move out with energy
nearly unchanged (Zhang et al. 1997; Lyubarskii \& Petrova 2000).
Therefore, the particle energy distribution (PED) hardly changes.
These particles produce broad band radiation, leading to a
consequence that the observed emission is also broad band at any
pulse phase. Even though, it is still possible that at high
frequency the emission is too weak to be detected at the outermost
phases. This motivates us to take into account such an issue: is
the pulse narrowing connected with the variation of the spectral
indices at different pulse phases? In fact, at high energy the
spectral indices are found to vary with phase (Fierro et al.
1998), but such absolute phase-resolved spectra have not been
derived at radio band. The conventional method is to normalize the
pulse width at each frequency and then calculate the spectral
indices at the relative phase intervals (Lyne \& Manchester 1988;
Kramer et al. 1994), which do not reflect the property of the
emission from the same region. So in the following simulations the
phase-resolved spectra are simply assumed. We will demonstrate
that the spectral behavior of pulse width could be a by-product of
the phase-resolved spectra.

For simplification, let us consider a symmetrical profile composed
of two Gaussian components with the same amplitudes and the half
power widths. Here the pulsar radio emission is regarded as a
simple power law within a frequency extent of
$f_{\max}/f_{\min}=80$, which is similar to the total observing
band in MR. Firstly, by assuming a uniform spectral index at all
the longitudes, we find that the pulse width and peak separation
do not vary with frequency, as shown in Fig.2. This could be
easily understood because a uniform power law only reduces the
amplitudes by the same ratio so that the centers and the half
power widths of the Gaussian components do not change.

\begin{figure}[h]
\center {\includegraphics [bb=57   189   545
589,scale=0.7]{fig2.eps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize Fig.\,2~~ Right: An uniform power-law index and the evolution of
the average profiles shown at three frequencies (without
narrowing). Left: the component separation and pulse widths vs.
frequency. The dashed, dotted and solid line represent 10\% width,
50\% width and component separation, respectively.}

    \end{figure}

Then we turn to another case that the spectral index gradually
increases from the outer longitudes to the center (longitude=0),
as shown in the right panel of Fig.3. Qualitatively, the amplitude
at an outer phase reduces faster than that at an inner phase as
frequency increases, leading both the peak separation and the
pulse width to keep decreasing. The reduction curves of the
separation as well as the widths measured at 50\% and 10\% level
of the peak intensities are shown in the left panel of Fig.3.

\begin{figure}[h]
\center {\includegraphics [bb= 58   189   545
589,scale=0.7]{fig3.eps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize Fig.\,3~~ Right: the variation of power-law index with pulse
longitude and the evolution of pulse profiles (the narrowing is
clear). Left: cf. Fig.2.}

    \end{figure}

Comparing our simulations (the left panels of Figs. 2 and 3) with
the observation results shown in Fig.1a and Fig.1b respectively,
we see that both types of spectral behavior of profile width (or
separation) can be reproduced, as long as different forms of
phase-resolved spectra are assumed. However, one may question if
there is any physical implication of our empirical assumptions. We
discuss it in the following section.


\para{\large\bf{3}~~Physical Implications}

\vs\vs In general, a power-law distribution of particles
($N(\gamma)\propto\gamma^{\rm -q}$) results in a power-law
emission intensity ($I(\nu)\propto\nu^{\rm -n}$). The relationship
between the two indices follows $n=(q-1)/2$ no matter via
synchrotron radiation, curvature radiation or inverse Compton
scattering in the case of incoherent emission (coherent emission
will steepen the photon spectrum). Therefore, it is reasonable to
think that the phase-resolved spectra actually reflect the PEDs at
specific locations in pulsar magnetosphere.

The narrowing of profile needs the PEDs to be nonuniform.
Generally there are two kinds of possibility, (1) the PEDs are
flatter at lower emission heights, or (2) the PED flattens when
the azimuthal angle of the magnetic field (defined as the acute
angle between two planes: one containing the magnetic axis and the
field line, the other containing the magnetic and rotational axes)
decreases. However, the first possibility could be ruled out
because of the reasons described at the first paragraph in section
2. The second one is possibly related to the sparking process in
the gap from which the secondary particles are produced. It was
suggested the energy spectrum of these particles could be
remarkably affected by the configuration of the local magnetic
fields (e.g., Daugherty \& Harding 1983). The detailed process
needs to be studied further.

As to the other type of pulsars which exhibit constant pulse width
at different frequencies, it requires an uniform PED at different
magnetic fields. MR suggested that the pulses of these pulsars are
inner conal emission. Then it is puzzling why the outer and the
inner conal emission could behave so differently.

To summarize, we present that the frequency dependence behavior of
pulse width may be a probe for the PEDs in the conal emission
region, which is an interesting problem that has not been
extensively studied. Simultaneous observations at multi-frequency
bands are expected to test our empirical interpretation. Finally,
we suggest that the spectral difference between the leading and
trailing conal components observed in some pulsars (Wang et al.
2000 and references therein) may be also related to this issue.

\vs\vn{\bf ACKNOWLEDGEMENTS}~~ This work is partly supported by NSF
of China, the Climbing Project-the National Key Project for
Fundamental Research of China, and the Doctoral Programm
Foundation of Institution of Higher Education in China.

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

 \nref Barnard J.J., Arons J.,  ApJ, 1986, 302,138
\nref Cordes J.M.,  ApJ, 1978, 222, 1006 \nref Daugherty J.K.,
Harding A.K., ApJ, 1983, 273, 761 \nref Fierro J.M., Michelson
P.F., Nolan P.L.et al., ApJ, 1998, 494, 734 \nref Kramer M.,
Wielebinski R., Jessner A.,et al., A\&AS, 1994, 107, 515 \nref
Lyne A.G., Manchester R.N., MNRAS, 1988, 234,477 \nref Lyubarskii
Y.E., Petrova S.A., A\&A, 1998, 333, 181 \nref Lyubarskii Y.E.,
Petrova S.A., A\&A, 2000, 355, 406 \nref Mitra D., Rankin J.M.,
Astro-ph/0205356, 2002 \nref Qiao G.J., Lin W.P., A\&A, 1998, 333,
172 \nref Rickett B.J., Cordes J.M., inSieber W., Wielebinski R.,
eds, Pulsars, 13 years of Research on Neutron Stars. D. Reidel:
Dordrecht, 1981, pp.133-140 \nref Ruderman M.A., Sutherland P.G.,
ApJ, 1975, 196 5 \nref Thorsett S.E., ApJ, 1991, 377, 263 \nref
Wang H.G., Han J.L., Qiao G.J., Chinese Astro. \& Astrophy.
(Pergamon), 2001, 25, 73 \nref Xilouris K.M., Kramer M., Jessner
A., et al., A\&A, 1996, 309, 481 \nref Zhang B., Qiao G.J., Han
J.L., ApJ, 1997, 491, 891

%\end{CJK}
\end{document}
