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

\setcounter{page}{245}

%\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\zihao{6}\songti\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
%%%单页
    \def\@oddhead{\underline{\parbox{\textwidth}
    {\small\rm \zihao{6}\songti suppl.\hfill R. X. Xu: Strange Quark Stars  %%（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
Strange Quark Stars   %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize R. X. Xu}  %%（本文作者）

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

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
A nonmathematical review of strange (quark) stars is presented.
After a historical notation of the research, we discuss the
physics of strange stars, including the possible ways to identify
them in astrophysics.

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

\para{\large\bf{1}~~ Historical Notes}

\vs\vs Soon after the Fermi-Dirac form (in 1926) of statistical
mechanics was proposed for particles which obey Pauli's exclusion
principle (in 1925), Fowler (1926) realized that the electron
degeneracy pressure can balance for those stars, called as white
dwarfs, discovered by astronomers in 1914.
%
Chandrasekhar's numerical calculation (1931) for a polytropic gas
of extremely relativistic electrons found a unique mass, which was
interpreted as a mass limit of white dwarfs.
%
Landau (1932) presented an elementary explanation of the
Chandrasekhar limit by considering the lowest total energy of
stars, and recognized that increasing density favors energetically
the formation of neutrons, discovered only several months before
by Chadwick, through the action
%
$p+e^-\leftrightarrow n+\nu_{\rm e}$\,.
%
A very massive compact object with much high density may have
almost neutrons in the chemical equilibrium, which was then called
as {\em neutron stars} (NSs).

Detailed calculations of NS structures showed (e.g., Oppenheimer
\& Volkoff 1939) that an NS can have a mass of $\sim 1 M_\odot$,
but is only $\sim 10$\,km in radius, which makes it hard to be
observed by astronomers.
%
However, on one hand, a few authors indeed investigated possible
astrophysical implications of NSs. For example, Baade \& Zwicky
(1934) combined the researches of supernovae, cosmic rays, and
NSs, and suggested that NSs may form after supernovae; Pacini
(1967) even proposed that the stored energy in rotational form of
an NS could be pumped into the supernova remnant by emitting
electromagnetic waves.
%
On the other hand, NS models were developed with improved
treatments of equation of states, involving not only
\{$n,p,e^-$\}, but also mesons and hyperons. The cooling behavior
of NSs was also initiated in 1960s due to the discovery of X-ray
sources which were at first thought mistakenly to be the thermal
emission from NSs.

The discovery of {\em radio pulsars} by Hewish \& Bell (and their
coauthors 1968) is a breakthrough in the study, and this kind of
stars were soon identified as spinning NSs by Gold (1968).
%
Since then more and more discoveries in other wave bands have
broadened greatly our knowledge about these pulsar-like compact
stars, including X-ray pulsars, X-ray bursts, anomalous X-ray
pulsars, soft $\gamma$-ray repeaters, and ROSAT-discovered
``isolated neutron stars''.
%
It is still a current concept among astrophysicists that such
stars are really NSs.
%
NS studies are going on in two major directions: 1, the emission
mechanisms for the stars, both rotation-powered and
accretion-powered; 2, the NS interior physics.

However, neutrons and protons are in fact {\em not} structureless
points although they were thought to be elementary particles in
1930s; they (and other hadrons) are composed of {\em quarks}
proposed by Gell-Mann and Zweig, respectively, in 1964.
%
The quark model for hadrons developed effectively in 1960s, and
Ivanenko \& Kurdgelaidze (1969) began to suggest a quark core in
massive compact stars. Itoh (1970) speculated about the exist of
3-flavor {\em full} quark stars (since only $u$, $d$ and $s$
quarks were recognized at that time), and even calculated the
hydrostatic equilibrium of such quark stars which are now called
as {\em strange stars} (SSs).
%
Is it possible that strange stars really exist in nature?
%
The possibility increases greatly if the Bodmer-Witten's
conjecture, i.e., strange quark matter (next section) is absolutely stable,
is correct (Bodmer 1971, Witten 1984).
%
Farhi \& Jaffe's (1984) calculation in the MIT bag model showed
that the energy per baryon of strange matter is lower than that of
nucleus for QCD parameters within rather wide range although we
can hardly prove whether the Bodmer-Witten's conjecture is correct
or not from first principles.
%
Haensel, Zdunik \& Schaeffer (1986) and Alcock, Farhi \& Olinto
(1986) then modelled SSs, and found that SSs can also have typical
mass (of $\sim 1-2M_\odot$) and radius (of $\sim 10$ km), which
means that {\em the pulsar-like stars believed previously to be
NSs might actually be SSs}.

\para{\large\bf{2}~~Strange Matter and Strange Stars}

\vs\vs One of the most greatest achievements in the last century
is the construction of the standard model in particle physics,
which asserts that the material in the universe is made up of
elementary fermions (divided into quarks and leptons) interacting
though gauge bosons: photon (electromagnetic), W$^\pm$ and Z$^0$
(weak), 8 types of gluons (strong), and graviton (gravitational).
%
There are totally 62 types of ``building blocks'' in the model.
Besides the 13 types of gauge bosons, there are three generations
of fermions (1st: \{$\nu_{\rm e}$, e; u, d\}, 2nd: \{$\nu_{\rm
\mu}$, $\mu$; c, s\}, and 3rd: \{$\nu_{\rm \tau}$, $\tau$; t, b\}.
Note that each types of quarks has three colors) and their
antiparticles. The final one, which is still not discovered, is
the Higgs particle that is responsible for the origin of mass.

As is well known that the nucleus of an atom is composed of
nucleons (protons and neutrons), whilst nucleons are of quarks
(proton = \{uud\}, neutron = \{udd\}).
%
It is expected that the confined quarks may become free as long as
the energy density (temperature or baryon number density) is high
enough, and a quark-gluon-plasma (QGP) state then forms.
%
This new state has not been found with certainty yet.
%
Unfortunately, the critical values, at which a phase transition
from hadron gas state to QGP occurs, can not yet obtained exactly
in the standard model of particle physics.

{\em Strange} ({\em quark}) {\em matter} could be such a kind of
QGP, which may composed of equal numbers of $u$, $d$, and $s$
quarks, and possible a small ratio of electrons, which may have
baryons from several hundreds called as {\em strangelets}, to
about that of our sun, called as {\em strange stars} (SS).
%
SSs are not really ``{\em strange}''; they, with strangeness, are
just named after the {\em strange} quark.

Although the SS idea is not new, SS identification becomes a hot
topic only in recent years due to advanced techniques in space
science.
%
Since SSs may have similar masses and radii to those of NSs, which
are conventional quantities observable in astronomy, it is very
difficult to find observational signals of quark matter in the
pulsar-like stars.
%
It was argued that the SS and NS cooling behaviors could be
distinguishable, since SSs may cool much faster than NSs (e.g.
Pizzochero 1991). However, recent more complete analyses on this
issue indicate that this may be impossible except for the first
$\sim$30 years after their births (Schaab et al. 1997).
%
Nevertheless, the author thinks there may still be three effective
ways to do.

1. The minimum rotation periods of SSs are smaller than that of
NSs.
%
Rotating stars composed of ideal fluid are subject to
rotation-mode instability, which leads to the loss of rotation
energy by gravitational radiation and results in substantial
spindown. However the matter of a real star is not ideal but has
viscosity; the calculated bulk viscosity, based on the work of
Wang \& Lu (1984), of strange matter is much higher than that of
neutron matter although their shear viscosities are similar;
therefore SSs could have smaller periods at which their higher
viscosity can prevent them from developing the instability (Madsen
1998).
%
The 2.14 ms optical source in SN 1987A (Middleditch  et al 2000)
should be an SS if being confirmed in further observations.

2. The approximate mass-radius ($M-R$) relations of SSs ($M\propto
R^3$) are in surprising contrast to that of NSs ($M\propto
R^{-3}$), and SSs can have much small radii.
%
Comparisons of observation-determined relations in X-ray binaries
with modelled ones may thus tell if an object is an NS or an SS
(Li et al. 1999). Also, a pulsar-like star with radius
$^<_\sim8$\,km could be an SS (Drake et al. 2002).

3. There are striking differences between the surfaces of bare
strange stars (BSSs) and that of NSs. The very properties of the
quark surface, e.g., strong bounding of particles, abrupt density
change from $\sim 4\times 10^{14}$\,g/cm$^3$ to $\sim 0$ in $\sim
1$ fm, and strong electric fields, may eventually help us to
identify a BSS.
%
There may be three parts of possible evidence for BSSs.
%
a. The RS-type (Ruderman \& Sutherland 1975) sparking model, with
an ``user friendly'' nature, faces at least two difficulties for
NSs: the binding energy problem and the antipulsar issue, which
can be solved completely if radio pulsars are BSSs (Xu et al.
1999).
%
b. The strong binding of quark surface may help to constrain the
fireball of SGR 0526-66 (Zhang et al. 2000, Usov 2001).
%
c. BSSs are expected to have featureless spectra (of both surface
thermal and magnetospheric non-thermal components) since no ion is
above the quark surface nor in the magnetosphere, except for
electron cyclotron lines due to the Landau levels appearing in
strong fields (Xu \& Qiao 1998, Xu 2002).
%
Recent observations known hitherto of several pulsar-like stars
actually show featureless spectra except for two sources 1E1207
and SGR1806, the lines of which may originate from Landau level
transitions in suitable field strength for the space facilities
(Xu et al. 2003).

\para{\large\bf{3}~~Conclusions}

\vs\vs The theoretical bases of SSs are, to some extent, solid in
physics and the formation of strange quark stars is possible in
astrophysics; SSs could thus exist.
%
Although each of the observed phenomena from pulsar-like compact
stars may be interpreted under the NS regime with unusual or
artificial physical properties, it could be a simple and natural
way to understand the observations by updating NSs with SSs.
%
The Nobel physics prizes had awarded pulsar researchers two times
for discovering the first radio pulsar and checking the general
theory of relativity with strong gravity, respectively. Pulsar
researchers could be awarded for the third time if strange stars
are identified.

\vs\vn{\bf ACKNOWLEDGEMENTS}~~ The work is supported by NSF of
China (10273001, 10173002) and the Special funds for Major State
Basic Research Projects of China (G2000077602).

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

 \nref Alcock C., Farhi E., Olinto A., ApJ, 1986, 310, 261
\nref Baade W., Zwicky F., Phys.Rev., 1934, 45, 138 \nref Bodmer
A.R., Phys.Rev., 1971, D4, 1601 \nref Chandrasekhar S., ApJ, 1931,
74, 81 \nref Drake J.J., et al.,  ApJ, 2002, 572, 996 \nref Farhi
E., Jaffe R.L., Phys. Rev., 1984, D30, 2379 \nref Fowler R.H.,
MNRAS, 1926, 87, 114 \nref Gold T., Nature, 1968, 218, 731 \nref
Haensel P., Zdunik J.L., Schaeffer R., A\&A, 1986, 160, 121 \nref
Hewish A., Bell S.J., Pilkington, et al., Nature, 1968, 217, 709
\nref Itoh N., Prog. Theor. Phys., 1970, 44, 291 \nref Ivanenko
D., Kurdgelaidze D.F., Lett. Nuovo Cimento, 1969, 2, 13 \nref
Landau L.D., Phys. Z. Sowjetunion, (an expanded discussion of his
ideal can be found in one of their courses ``{\em Statistical
Physics}''.), 1932, 1, 285 \nref Li X.D., et al.,  Phys.Rev.Lett.,
1999, 83, 3776 \nref Madsen J., Phys.Rev.Lett., 1998, 81, 16 \nref
Middleditch J., et al., New Astronomy, 2000, 5, 243 \nref
Oppenheimer J.R., Volkoff G.M., Phys.Rev., 1939, 55, 374 \nref
Pacini F., 1967, Nature, 1967, 216, 567 \nref Pizzochero P.M.,
Phys.Rev.Lett., 1991, 66, 2425 \nref Ruderman M.A., Sutherland
P.G., ApJ, 1975, 196, 51 \nref Schaab C., Hermann B., Weber F., et
al.,  ApJ, 1997a, 480, L111 \nref Usov V.V., Phys.Rev.Lett., 2001,
87, 021101 \nref Wang Q.D., Lu T., Phys.Lett., 1984, B148, 211
\nref Witten E., Phys.Rev., 1984, D30, 272 \nref Xu R.X., ApJ,
2002, 570, L65 \nref Xu R.X., Qiao G.J.,  Chin.Phys.Lett., 1998,
15, 934 \nref Xu R.X., Qiao G.J., Zhang B., ApJ, 1999, 522, L109
\nref Xu R.X., Wang H.G., Qiao G.J., Chin.Phys.Lett., 2003, 20,
314 \nref Xu R.X., Zhang B., Qiao G.J., Astropart. Phys., 2001,
15, 101 \nref Zhang B., Xu R.X., Qiao G.J., ApJ, 2000, 545, L127

%\end{CJK}
\end{document}
