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    {\small\rm\zihao{6}\songti\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
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    {\small\rm \zihao{6}\songti suppl.\hfill T. Yang et al.: A
    Program for Pulsar Time Study in China  %%（作者：题目名称）
    \vspace{1.5mm}
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    \zihao{6}\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
A Program for Pulsar Time Study in China    %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize Tinggao Yang,\hs\hs  Guangren Ni\hs\&\hs
Xizheng Ke}  %%（本文作者）

\vs ({\footnotesize 1~{\it National Time Service Center, Chinese
Academy of Sciences, Lintong, Shaanxi}~ 710600}) \\%%（本文作者单位）
\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
We review research progress on pulsar time scales resulting from
millisecond pulsar timing observations.  An algorithm for ensemble
pulsar time scale is introduced.  The results from wavelet
decomposition algorithm for ensemble pulsar time scale are shown.
We introduce in some details a newly designed pulsar timing
program in China. One of the scientific goals of the program is to
study pulsar time by timing millisecond pulsar using Chinese 50 m
radio telescope.

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

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

\vs\vs Millisecond pulsars exhibit a very stable spinning period.
The time derivative of the rotational period $\dot{P}$ for
millisecond pusars is usually less than 10$^{-19}$s/s.  Timing
observations of pulsars measure the time of arrival (TOA) of the
radio pulses relative to an atomic time scale. The technique
allows mesurement of TOA with a precision better than 1$\mu$s.
Long term timing data analysis to some millisecond pulsars, for
example PSR1937+21 and PSR1855+09, showed that the stability of
rotation of such millisecond pulsars rivals that of atomic clocks:
the relative frequency instability for averaging time over one
year is of order 10$^{-14}$\rf{1,2}.  It is difficult to interpret
the instability of the timing data by instability of the
millisecond pulsar rotation itself because some phenomena are
known to possibly disturb the timing data. These may
 include
errors in atomic time standard used as reference, effect of solar system
ephemeris used as
reference frame to transform the observed TOAs to an inertial frame.
Unmodeled effect of
interstellar propagation could also contribute to the timing error.  A passing
gravitational wave could cause a
change in the observed rotational frequency of pulsar by an amount proportional
 to the amplitude
of the wave.  Among these, the errors in atomic time scale would
produce similar effects for all observed millisecond pulsars.
Comparison between pulsar time scale PT and atomic time scale AT
can reveal some errors of AT.  In doing this, G. Petit and P.
Tavella proposed a scheme to establish an ensemble pulsar time
$PT_{\rm ens}$. $PT_{\rm ens}$ can be more stable and accurate
than any individual PT, because effects of some sources of noise
which are independent for different pulsars may be removed from
$PT_{\rm ens}$.


As many new millisecond pulsars are discovered, it is possible that we monitor
almost
simultaneously several millisecond pulsars using one radio telescope.  Applying
 timing array, we
could study $PT_{\rm ens}$ for long time scales and detect
background of gravitational radiation (GWB)\rf{3}. Chinese 50\,m
radio telescope which is specially designed for timing millisecond
 pulsars will take
part in studying $PT_{\rm ens}$ and detecting GWB.



\para{\large\bf{2}~~Long Term Stability of PT and Algorithm for $PT_{\rm ens}$}

\vs\vs Timing measurement precision depends mainly on observing
system. A large effort has been made to improve the precision of
timing observations.  The pioneering work
 in this area  is
research work at Princeton University.  High quality timing data
spanning almost a decade from the Arecibo radio telescope has
demonstrated that the timing stability of millisecond pulsars over
long time scales is comparable to terrestrial atomic clocks\rf{4}.
The results from Ref.[4] indicated that the stability for
PSR1855+09 becomes competitive with the atomic clocks in about 3
yr scale. The timing stability of PSR1937+21 seems to be limited
by a power law component. If a cubic term of time is added to the
timing model for PSR1937+21, consequently the phenomena stability
becomes similar to PSR1855\rf{1}.  The absence of timing noise in
long time scales for PSR1855+09 is probably related to its
characteristic age 5\,Gyr which is about a factor of 20 larger
than PSR1937+21\rf{5}. In order to evaluate the long term
stability of millisecond pulsars timing data set spanning a large
time scale is needed.

\begin{figure}[h]
\center {\includegraphics [bb=0 0 351 249,scale=0.8]{ytg1.eps}}

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   \footnotesize

      Fig.\,1~~ Phase-difference Between Two Pulsars and TAI.}

    \end{figure}

In addition to the intrinsic noise of the rotation of millisecond
pulsars and errors of AT used as a reference, several other
sources of noise could affect timing data, mainly interstellar
propagation effects, uncertainties in the ephemeris of the solar
system, and gravitational waves.  In order to find a stable pulsar
time scale, an ensamble pulsar time scale $PT_{\rm ens}$  can be
constructed using individual PTs.  In convenience, one assumes
that all sources of timing noise except AT are independent for
different pulsars and then average them by defining $PT_{\rm ens}$
as a weighted average of the individual PT from all the available
pulsars.  G.Petit et al.~(1992) have designed a stability
algorithm which is similar to that used for atomic clocks\rf{1,2}.
$PT_{\rm ens}$ is weighted average of the available PTs. Hereafter
AT-PT refers to timing residuals which are obtained after
correctly applying a timing model to the observed pullsar timing
data. $AT-PT_{\rm ens}$ can be defined by

\be
AT-PT_{\rm ens}=\sum{W(AT-PT)}\,,
 \ee
 where W is the relative weight
assigned to each pulsar.  Weights are designed as inversely
proportional to the instability of each pulsar.  This can be
realized by simply
 taking the inverse
of the Allan variance and normalized to unity.  Each pulsar enters the ensemble
 with a fixed
weight according to its level of instability.  When the number of pulsars
changes a suitable
correction should be added to avoid a time jump.  So the removal or entry of a
new pulsar is
accompanied by a time correction $\alpha$  which is defined as

 \be
  AT-PT_{ens}=AT-(PT'_{ens}+\alpha)\,,
  \ee
where  $PT'_{\rm ens}$ is the new ensemble pulsar time computed
from the data after the change. Following this algorithm G. Petit
et al.~(1992) calculated an ensemble pulsar time scale using data
from PSR1937+21 and PSR1855+09\rf{1}.

\begin{figure}[h]
\center {\includegraphics [bb=0 0 331 251,scale=0.9]{ytg2.eps}}

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   \footnotesize

      Fig.\,2~~ High frequency content}

    \end{figure}

We have applied wavelet decomposition algorithm (WDA) to define
ensemble pulsar time scale using the same data of these two
pulsars.  The method of using wavelet analysis to calculate time
scales is different from that of uniform weighting in the time
domain.  WDA can decompose signal's subsection components in the
range of various frequencies and then pick up them again to weight
in subdomains. WDA considers, analyzes and solves the stability of
subsection frequency in the range of various frequencies. So the
time scale calculated by the wavelet analysis may be more stable.
The results from the wavelet decomposition algorithm is shown in
Fig.\,1.- Fig.\,4.

\para{\large\bf{3}~~50\,m Radio Telescope and Designed Pulsar Timing Program}

\vs\vs Construction of 50\,m radio telescope is underway and will
be available in 2004.
  The
details for the parameters of the telescope can be found in ``An
introduction to the new Miyun 50\,m radio telescope" by Chengjin
Jin in this proceeding.  Observational frequency 1420\,MHz is used
and second frequency will be lower than 1420\,MHz, $T_{\rm sys}$
is 30\,K, bandwidth 300\,MHz. More than 10 millisecond pulsars
will be monitored regularly .  Integration time is 60\,min or more
in each day observation for each pulsar.  Assuming signal to noise
ratio S/N=1, then sensitivity S can be given by

 \be
 S=\frac{1.4KT_{sys}}{\eta_AA\sqrt{\Delta f\cdot{t}}}
 \ee

\begin{figure}[t]
\center {\includegraphics [bb=0 0 331 251,scale=0.75]{ytg3.eps}}

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   \footnotesize

      Fig.\,3~~ Low frequency content}

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 \no where $K$ is Boltzmann constant, $T_{\rm sys}=30$\,K, A is area of the
antenna, effeciency of the antenna $\eta_A$ =0.5, bandwidth
$\Delta f=300$\,MHz.  For the 10 day observations, the total
integration time t can reach to 10 hours.  So we estemated that
the pulsar with flux density $S>0.018$\,mJy may be observable.
When we observe millisecond pulsar with $S>1$\,mJy $S/N=56$ can be
reached.
\begin{figure}[h]
\center {\includegraphics [bb=0 0 331 251,scale=0.75]{ytg4.eps}}
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   %{\hspace{3.5cm}
   {\center
   \footnotesize
 Fig.\,4~~ Stability of two algorithms}

    \end{figure}

Up to now about 56 Galactic disk millisecond pulsars were
descovered\rf{5}. According to estimated parameters of these
millisecond pulsars, Dr. Han JinLin has selected 27 pulsars
available for Chinese 50\,m telescope timing observation. Finally
about 10 suitable objects with higher flux density , sharper
pulse, and shorter rotational period will be monitored by this
telescope.  When more suitable millisecond pulsars are found, they
can be added
 to the program to
insure that the spatial distribution of monitored pulsar population can be
more isotropical and
more uniform.  This is needed for the scientific goals of the pulsar timing
program.

Ensemble pulsar time study is one of scientific drive for the
pulsar timing program with 50\,m telescope.  The regular and
continuous timing observations should be made for the target
pulsars to get timing data spanning many years.  We hope that some
insight about behavior of long term stability of pulsar time
scales could be learned.  Furthermore, an ensemble pulsar time
$PT_{\rm ens}$ can be studied by a suitable algorithm.  Then
$PT_{\rm ens}$ may be used to detect some errors in atomic time
scales. The observations of a number of millisecond pulsars
distributed across the sky lead to the possibility of timing
several pulsars against each other with terrestrial clocks
providing merely the end point times and a means of interpolating
observations\rf{6}.  Now several long term timing projects are
underway to monitor these millisecond pulsars\rf{5}.
  Timing data
from different sites may be linked together by common target
observations to get more ideal spatial distribution of observed
millisecond pulsars.  In this way timing model should be correctly
determined and any systematic trends in different data sets should
be removed.  To have fruitful results for $PT_{\rm ens}$ study a
continuous effort in pulsar survey is also important to find more
stable millisecond pulsars.


Another scientific goal is to detect low frequency gravitational
radiation.  We hope that
some detail information about GWB can be obtained besides determining limit on
the energy
density of GWB from our elaborately designed pulsar timing program.

\vs\vn{\bf ACKNOWLEDGEMENT}~~Thank Doctor G. Petit for providing
pulsar timing data.

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

 \RE{\,1\,~~}Petit G., Tavella P., Astron. Astrophys., 1996,
308(2), 290-298
 \RE{\,2\,~~} Petit G, Thomas C.,  An
Ensemble Pulsar Time, In: Proc. 24$^{th}$ PTTI meeting, 1992,
73-85
 \RE{\,3\,~~}Foster R.S., Backer D.C.,  1990, 361,
300
 \RE{\,4\,~~}Kaspi V.M., Taylor J.H., et al,  ApJ, 1994, 248, 713
 \RE{\,5\,~~} Lorimer D.R., Binary and Millisecond Pulsars
at the New Millenium,
 Living Reviews in Relativity, Published by the Max Planck Institute for
Gravitational Physics, (www.livingreviews.org), 2001, 4.
 \RE{\,6\,~~}Matsakis D.N., Foster R.S., Application of Millisecond Pulsar Timing to
the Long-term Stability of Clock Ensembles

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