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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 J. R. Shi \& G. Zhao: Magnetic Field on Late-Type Stars  %%（作者：题目名称）
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\zihao{5}\songti

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    \zihao{6}\songti
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    Vol.44~ Suppl.
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    \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 Magnetic Field on Late-Type Stars   %%（文题）
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\vs\vs{\normalsize\zihao{4}\fangsong J.R. Shi\hs\&\hs
G. Zhao}  %%（本文作者）

\vs
({\footnotesize \nao}) \\%%（本文作者单位）
 E-mail: sjr@yac.bao.ac.cn

\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small We reviewed the magnetic
 field measurements on late-type stars,
and discussed the correlation between the X-ray emission and the
magnetic fields. We found that the $F_X$ or $L_X / L_{bol}$
correlate fairly well with magnetic flux. We also found a clear
correlation between the high-temperature components and the
magnetic field strength.

\end{quotation}

%%%% 正文


\vs\vs

The magnetic field is very often a crucial parameter in
astrophysical problems. It plays a key role basically everywhere
in the Universe, at all time and spatial scale. In the case of
stars, the magnetic fields affect their formation, evolution,
stellar activity and the late stage of their lives.

Ever since Robinson's (1980), measurements of magnetic field
strength $B$, and surface filling factor of magnetic region, $f$,
on late-type stars have been made by several investigations. Our
knowledge of both the intensity and structure of the magnetic
field of late-type stars has been considerably improved.

\para{\large\bf{1}~~ Measurements of stellar Magnetic Fields}

\vs\vs

Virtually all measurements of stellar magnetic fields make use of
the Zeeman effect. Typically, one of two general aspects of the
Zeeman effect is utilized: (1) Zeeman broadening of magnetically
sensitive lines, or (2) circular polarization of magnetically
sensitive lines (Zeeman Doppler Imaging).

\vn{\bf{1.1~~ Zeeman Broadening}}

In normal Zeeman effect, a spectral line splits into three
components: two $\sigma$ components on either side of the nominal
line center and one unshifted $\pi$ component. The wavelength
shift of a given $\sigma$ component is $\Delta\lambda = k
\lambda^{2} g B$, where $k$ is a constant, $g$ is Land\'{e}
$g$-factor of the specific transition, $B$ is the strength of the
magnetic field, and $\lambda$ is the wavelength of the transition.
Note this shift is $\lambda^2$-dependent, which means that the
infrared observations are generally more sensitive to the magnetic
fields than optical observations.

Robinson et al. (1980) pioneered a very successful
technique to measure the Zeeman broadening of optical and
near-infrared lines by comparing the two or more line profiles
that cover a range in magnetic sensitivity. However, no ``ideal"
pairs (i.e. clean lines identical in all respects except their
Land\'{e} factors) are available, and large magnetic flux ($fB$)
were recorded for stars with widely different rotation rates and
activity levels. Clearly, a refined analysis including treatment
of radiative effects in the Zeeman components themselves is
needed.

Saar and co-workers (Saar \& Linsky 1986 and Saar
1988) developed the method further and used it to measure
the magnetic field strengths and filling factor in the active
regions of many stars, by assuming either a two-component
atmosphere $F_{\rm obs} = fF_{\rm mag}(B) + (1-f) F_{\rm quiet}(B=0)$ or a
three-component atmosphere (including star spots), where $F$
refers to the radiative flux observed from the magnetic or quiet
components of the atmosphere.

Fig.\,1 shows the spectra of EV Lac and the inactive comparison
star GJ 725B. The presence of Zeeman split $\sigma$ components is
clear on either side of the magnetic sensitive Fe I ($g = 2.5$)
line at 8468.4\,\AA. Johns-Krull \& Valenti (1996) determined $B =
3.8 \pm 0.5$\,kG with $f = 0.50 \pm 0.15$ from the data.

\begin{figure}[h]
\center {\includegraphics [bb=0 0 325 168,scale=1]{b1.eps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize

      Fig.\,1~~ Spectra of the flare star EV Lac and inactive star GJ
725B in the vicinity of the magnetically sensitive Fe I line at
8468.4\,\AA. Note that the spectrum of the inactive star matches
the spectrum of EV LAC for all the nearby magnetically insensitive
TiO lines, but fails to match the $\sigma$ components on either
side of the Fe I line, demonstrating the presence of magnetic
field on the flare star. (From  Johns-Krull \& Valenti
2000)}

    \end{figure}

The pre-main-sequence T Tauri stars are bright X-ray sources with
the ratio of X-ray to bolometric ($L_X/L_{\rm bol}$) well above the
level of saturated X-ray emission, $L_X/L_{\rm bol} > 10^{-3}$. It is
believed that there are strong magnetic fields on these stars (Shu
et al. 1997). Using high resolution infrared spectrum
Johns-Krull \& Valenti (2000) also derived the magnetic
flux $fB = 2.4$ kG for naked T Tauri star Hubble 4.

The major drawback of the techniques is that they provide no
information on the three-dimension (3-D) structure of the magnetic
field across the stellar surface.

\vn{\bf{1.2~~ Zeeman Doppler Imaging (ZDI) of Rapid Rotators}}

Semel (1989) proposed to measure, in particular case of
rapidly rotating late-type stars, the full profiles of magnetic
Zeeman signatures in circular and (whenever possible) linear
polarization. This technique can map the radial, meridional and
azimuthal components of the magnetic field for rapidly rotating
stars using profiles of some 2000 spectral lines in circularly
polarized light ( Donati \& Brown 1997; Donati et al.
1997). This technique allows one to access the detailed
topology of the stellar surface magnetic structure as well as its
variation throughout a complete activity cycle. Donati \& Cameron
(1997) and Donati et al. (1999) have found that
magnetic images of rapidly rotating cool stars are indeed
extremely complex.

\para{\large\bf{2}~~Magnetic Fields and X-ray Emission of Late-type Stars}

The spread in the observed X-ray luminosity mainly reflects the
efficiencies of stellar coronal heating, and the heating mechanism
is mainly due to the interaction between stellar magnetic fields
and coronal plasma. Linsky (1999a) concluded that the active
phenomena for late-type stars result from the stressing of
magnetic field by convective motions. So the obvious parameter
related to stellar X-ray emission of late-type stars is the
magnetic field.

\vspace*{1mm}
\vn{\bf{2.1~~X-ray Emission and the Magnetic Fields}}

Falconer et al. (2000) have found that the brighter the
X-ray corona, the stronger the magnetic field in which it resides.
They suggested that if the Sun had no magnetic field, it would
have little or no X-ray corona. Saar (1996, 2000)
found that X-ray emission correlate fairly well with $fB$, and the
data showed a linear relationship. Here, we presented the
relationship between the X-ray flux ($F_X$) or heating efficiency
($L_X/L_{\rm bol}$) and the magnetic flux in Fig. 2. For the single
and wide binary stars, an excellent correlation between $F_X$ or
$L_X/L_{\rm bol}$ and magnetic flux can be seen. It seems that the
coronal activity of late-type stars depends on the magnetic flux,
namely both the magnetic field strength and the area of active
region. For the binaries, the case is complex, maybe all the
companion stars contribute a considerable emission to the total
observed flux as independent components (Maggio et al.
1990), or the active phenomena in close binary stars are
qualitatively different from phenomena on single stars (Linsky
1999b).

\begin{figure}[h]
\center {\includegraphics [bb=0 0 330 119,scale=1]{b2.eps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize

      Fig.\,2~~ The X-ray flux ($F_X$) and ratio of X-ray to
bolometric ($L_{X}/L_{bol}$) versus the magnetic flux. {\bf a} the
X-ray flux to magnetic flux; {\bf b} the $L_{X}/L_{bol}$ to
magnetic flux. The '{\bf opened circle}','{\bf filled circle}',
'{\bf asterisk}' and '{\bf cross}' represent the single, binary,
wide binary and RS CVn stars, respectively.}

    \end{figure}
    \begin{figure}[h]
\center {\includegraphics [bb=0 0 336 119,scale=1]{b3.eps}}

   \parbox[tb]{12cm}
   %{\hspace{3.5cm}
   {%\center
   \footnotesize

      Fig.\,3~~ The X-ray temperatures versus the magnetic
fields. (a) the high-temperature component to magnetic field
strength; (b) the high-temperature component to magnetic flux.
For symbols see Fig. 2.}

    \end{figure}

\vn{\bf{2.2~~ Coronal Temperature and Magnetic Fields}}

Mullan \& Fleming (1996) suggested that the active corona
is heated magnetically while the quiet corona may be heated
acoustically. Shi et al. (1998) have used two-temperature
models to fit the stellar X-ray spectrum (ROSAT) and found that
the magnetic field strength of our program stars is correlated
with the high-temperature component of the corona. Using the new
magnetic field strength, Shi et al. (2002) confirmed this
result, which is shown in Fig.3. For single stars, the
correlation between the high-temperature component and the
magnetic field strength is very clear, while no correlation for
magnetic flux. This result suggests that the high-temperature
component is related to the magnetic field strength at least for
single stars.



\vs\vn{\bf ACKNOWLEDGEMENTS}~~This research was supported by the National
    Natural Science Foundation of China under the grant No.10173014 and
    NKBRSF 1999075406.

   \vs \bc
{\bf References}
\ec

\vspace{-4mm}
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