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\title[Geometrical and kinematical properties of halo CMEs] %% give here short title %%
{Determination of geometrical and kinematical properties of
frontside halo coronal mass ejections (CMEs)}

\author[X. P. Zhao]   %% give here short author list %%
{XuePu Zhao}

\affiliation{W. W. Hansen Experimental Physics Laboratory, Stanford University,
Stanford, CA 94305-4085, USA \break email: xpzhao@solar.stanford.edu}

\pubyear{2004}
\volume{226}  %% insert here IAU Symposium No.
\pagerange{1--5}
\date{Oct. 16, 2004 and in revised form ??}
\setcounter{page}{1}
\jname{Solar and Stellar Mass Ejections, IAU Symposium 226}
\editors{K. Dere \& J. Wang, eds.}
\begin{document}

\maketitle

\begin{abstract}
Recent studies show that the cone model with a circular cross section 
can be used to determine the geometrical and kinematical properties
only for a class of halo CMEs with the semi-minor axis
of the elliptic halo threading the solar disk center. This work shows
how to use an improved cone model with an elliptic cross section to
determine the geometrical and kinematical properties for another class
of halo CMEs with the semi-major axis threading the solar disk center.
\keywords{coronal mass ejections (CMEs), data analysis}
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\end{abstract}

\firstsection % if your document starts with a section,
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\section{Introduction}

Determination of the geometrical and kinematical properties of 
halo CMEs is necessary for understanding the
cause of halo CMEs. It is also necessary for predicting the geoeffectiveness
of frontside halo CMEs.
For broadside CMEs, i.e., the CMEs with the latitudinal span of their
bright feature in the plane of the sky being less than $120^\circ$,
the latitudinal span and its bisector are the measure of the angular width
and central position angle of the broadside CMEs, respectively.
Such geometrical properties for halo CMEs,
i.e., the CMEs with the latitudinal span greater than $120^\circ$,
can not be measured directly from white-light images. The
central position of halo CMEs is often assumed to be located near the 
associated surface activities such 
as solar flares, though it has been reported that CME-associated flares
or active regionsare often located near one leg of CMEs.

The speed profiles of CMEs are often derived by choosing a specific feature 
in a time-lapse movie and tracking its position outward with time.
For broadside CMEs the measured velocity and acceleration are nearly
radial directed; they are, however, projected against the plane of the sky
for halo CMEs.

We have developed a cone model with a circular cross section (\cite{Zhao02}) 
for determining the geometrical and kinematical properties of halo CMEs
from coronal images. The present work shows how to use an improved
cone model with an elliptic cross section to determine 
the geometrical and kinematical properties for another class of halo CMEs that
can not be modeled using the original cone model.

\section{Halo CMEs with minor axis threading solar disk center}

Halo CMEs are interpreted as the result of the Thompson scattering of
Sun's white light by a broad shell or bubble of dense plasma of CMEs
along the line-of-sight (\cite{Howard82}). Specifically, the broad shell
of dense plasma may be a conical shell with a circular cross section, as
shown by Figure 4 of \cite{Howard82}. It has been shown recently 
that the projection
of the circular cross section against the plane of the sky has elliptic shape
with the semi-minor axis threading
the solar disk center (\cite{Xie04} and \cite{Zhao04}). 
Figure~\ref{fig:img1} shows
the images for the 6 January 1997 halo CME observed at various time, $t$, 
and the ellipse
calculated at corresponding heliocentric distance $r(t)$. The determined angular width and central
position of the 6 January 1997 halo CME are shown at the top of the 
first panel.

\begin{figure}
 \includegraphics{fig1.eps}
  \caption{Comparison of the plane-of-sky projection of circular cross sections 
calculated using the cone model at various heliocentric distances $r(t)$ with 
the halos observed in difference images
at various times, $t$.}\label{fig:img1} 
\end{figure}

\section{Halo CMEs with major axis threading solar disk center}

There are halo CMEs with their semi-major, instead of semi-minor, axis
threading the solar disk center, suggesting that the corresponding
cross section must be elliptic if the halo CMEs are formed by Thompson
scattering of a conical shell of dense plasma. 
Figure~\ref{fig:img2} shows
the images for the 7 April 1997 halo CME observed at various time, $t$, 
and the ellipse
calculated at corresponding $r(t)$. The determined angular width and central
position of the 7 April 1997 halo CME are shown at the top of the 
first panel.

\begin{figure}
 \includegraphics{fig2.eps}
  \caption{Comparison of the plane-of-sky projection of elliptic cross sections 
calculated using the cone model at various heliocentric distances $r(t)$ with the halos observed in difference images
at various times, $t$.}\label{fig:img2} 
\end{figure}

Figure~\ref{fig:ht4} shows the hight-time scatter-point
plot based on the fitting result in Figure~\ref{fig:img2}
and the velocity and acceleration inferred for the
7 April 1997 halo CMEs.

\begin{figure}
 \includegraphics{fig4.eps}
  \caption{The hight-time scatter-point plot and fitting curve for the 7 April 1997 halo CMEs (the top panel) and the inferred variation of the velocity with hight
(the bottom panel).}\label{fig:ht4}
\end{figure}

\section{Summary and Disscussion}

Halo CMEs exhibit various shapes. Some show ellipse (including circle), 
and
others show ellipse-like but with ragged structure.
Many elliptic halo CMEs may be interpreted as the Thompson scattering of 
Sun's white light by a conical shell of dense plasma 
along the line-of-sight (\cite{Howard82}).
The halo CMEs with ragged structure is interpreted as the deflection of 
preexisting coronal
features by super-Alfvenic CMEs (\cite{St.98}).
The ragged structure may be used to distinguish the
deflection-formed halo CME from the scattering-formed halo CME
(\cite{Sheeley00}).

Recent studies have shown that the cone model with a circular cross
section can be used to determine geometrical and kinematical properties 
only for a specific class of scattering-formed elliptic halo CMEs 
of which the minor axis threading the solar disk center. We show that
the scattering-formed elliptic halo CMEs with their major axis
threading the solar disk center may be modeled using the cone model
with an elliptic cross section, and their geometrical and kinematical
properties may also be determined. 

There are evidence that the plasma structure for some halo CMEs may be
approximated using the spherical shell model (\cite{Howard82}) or the ice-cream
cone model (\cite{Fisher84}). 
It is interesting to develop a model for determining the geometrical and
kinematical properties for those halo CMEs.

\begin{acknowledgments}
\end{acknowledgments}

\begin{thebibliography}{}

\bibitem[Fisher \& Munro (1984)]{Fisher84}
     {Fisher, R.R. \& Munro, R.H.} 1984,
     \textit{Astrophys. J.} 280, 428

\bibitem[Howard, \etal\ (1982)]{Howard82}
     {Howard, R.A., Michels, D.J., Sheeley Jr., N.R., \& Koomen, M.J.} 1982,
     \textit{Astrophys. J.} 263, L101

\bibitem[Sheeley \etal\ (2000)]{Sheeley00}
     {Sheeley, Jr., N.R., Hakala, W.N. \& Wang, Y.-M.} 2000,
     \textit{J.~Geophys. Res.} 105, A3, 5081

\bibitem[St. Cyr \& Hundhausen (1998)]{St.98}
     {St. Cyr, O.C. \& Hundhausen, A.J.} 1998,
     in: V.P. Pizzo, T. Holzer, \& D.G. Sime (ed.),
     \textit{Proceedings of the 6th International Solar Wind Conference} (Boulder), p.\ 235 

\bibitem[Xie, \etal\ (2004)]{Xie04}
     {Xie, H., Ofman, L. \& Lawrence, G.} 2004,
     \textit{J.~Geophys. Res} 109, A8

\bibitem[Zhao, \etal\ (2002)]{Zhao02}
     {Zhao, X.P., Plunkett, S.P., \& Liu, W.} 2002,
     \textit{J.~Geophys. Res.} 107, A8 

\bibitem[Zhao (2004)]{Zhao04}
     {Zhao, X.P.} 2004,
     in: A.V. Stepanov, E.E. Benevolenskaya \& A.G. Kosovichev (eds.), 
     \textit{Multi-Wavelength Investigations of Solar Activity},
     Proceedings of IAU 223, in press  

\end{thebibliography}

\end{document}
\begin{figure}
 \includegraphics{fig3.eps}
  \caption{Comparison of the plane-of-sky projection of circular cross sections
calculated at various heliocentric distances $r(t)$ with the difference images
observed at various times, $t$.}\label{fig:ht32} 
\end{figure}

