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    {\small\rm\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
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    {\small\rm  suppl.\hfill Z. Li \& X. Wang: Supernovae and Radio Supernovae  %%（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
Supernovae and Radio Supernovae  %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize Zongwei Li \up{1}\hs\&\hs
Xiaofeng Wang\up{1,2}}  %%（本文作者）

\vs
(\footnotesize 1~\bnua) \\%%（本文作者单位）
 (\footnotesize 2~ \nao)
\vs\vs \ec

\normalsize
\begin{quotation}

 \no{\bf A{\scriptsize\bf BSTRACT }}~~~\small
One of the most energetic explosive events known is a supernova.
This occurs at the end of a star's lifetime, when its nuclear fuel
is exhausted and it is no longer supported by the release of
nuclear energy. As calibrated standard candles, type Ia supernovae
now provide the main route to determine the main cosmological
parameters, such as the Hubble constant, the cosmological density
parameters. The study of radio supernovae has been briefly
reviewed. Radio supernovae may also be promising objects to
determine the distances, with an empirical relation between the
turn-on time and peak flux density at $6$ cm. Current study in
radio supernovae is rather limited by the sensitivity of radio
telescopes.

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

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

\vs\vs The study of supernovae (SNe) is in vogue today. They are
at the confluence of many different streams of astronomical
researches. As the final episode of the life of many kinds of
stars, SNe allow crucial tests of stellar evolution theories.
During and immediately after the explosions, there are a variety
of fundamental physical mechanisms which can be probed, such as
neutrino and gravitational wave emissions, flame propagation and
explosive nucleosynthesis, radioactive decays and shocks with
circumstellar medium (CSM). SNe play a vital role in galactic
evolution through chemical enrichment, through energy input into
the interstellar medium, through production of stellar remnants
such as neutron stars, pulsars, and black holes. SNe are also
being utilized as a powerful distance probes to determine various
cosmological parameters, such as the Hubble constant and the
density parameters.

SNe have three basic types: Ia, Ib/c and II. Both SNe Ia and SNe
Ib/c lack hydrogen lines in their optical spectra, while SNe II
all show hydrogen in their optical spectra with varying strengths
and profiles (Filippenko 1997). SNe Ib and SNe Ic do not show the
deep Si II absorptions trough near 6150 $\AA$ (blueshifted) that
characterizes SNe Ia, and SNe Ib show moderately strong He I
lines, especially at 5876 $\AA$, while SNe Ic do not.
Additionally, SNe II can also be further subdivided into SNe II-P
(plateau) and II-L (linear) according to the shape of their light
curves.

The spectral differences may indicate the differences in
progenitors. SNe Ia generally believed to originate from the
thermonuclear explosions of accreting white dwarfs in close binary
systems. The central carbon ignition would take place when the
mass of the primary white dwarf approaches to the Chandrasekar
limit M$_{ch}$ (e.g. 1.39 M$_{\odot})$. However, the propagation
of the burning in the star and the progenitor systems are still
debated. In contrast, SNe II are likely the core-collapse induced
explosions of massive stars ($>8M_{\odot})$. SNe Ib and Ic are
also believed to be core-collapse supernovae because they share
most properties with SNe II except for the deficit of H lines. The
hydrogen envelope of their massive progenitors may be stripped
through stellar winds or binary interactions. Possible progenitors
for SNe Ib/c are exploding Wolf-Rayet stars that evolve from stars
with $M > 40M_{\odot}$. An alternative candidate is exploding,
relatively less-massive helium stars in interacting binary system.

Possible variants of normal SNe II are the ``Type IIn'' and the
``Type IIb'', which both show unusual optical characteristics. SNe
IIn are characterized by very narrow emission lines superposed on
top of broad Balmer emission lines. The narrow component
presumably arises from interaction with a dense ($n>10^{7}$cm$^{ -
3})$ CSM surrounding the SN. SNe IIb look optically like normal
SNe II at early time, but evolve to more closely resemble SNe Ib
at late time. It may represent a transitional subclass between SNe
II and Ib (e.g. SNe 1993J and 1996cb).

\para{\large\bf{2}~~Type Ia Supernovae as Distance Indicators}

\vs\vn{\bf{2.1~~ SNe Ia as Standard Candles }}

 SNe Ia has long
been proposed as good distance indicators for cosmology, first
through their standard candle character, i.e., identical peak
luminosity, and later normalized by corrections from light curve
shapes. Their Hubble diagram (i.e. magnitude-redshift relation)
can be used to trace the expansion history of the universe. The
linear part of the Hubble diagram with absolute magnitude
calibration determines the Hubble constant (see Branch 1998 for a
review); curvature in the diagram probes evolution in the
expansion rate, e.g. acceleration or deceleration, and different
combinations of cosmological parameters (Riess et al 1998;
Perlmutter et al 1999; Leibundgut 2001 for a recent review). It is
generally accepted that brighter SNe Ia have broader light curves
around optical maxima. The peak luminosity-decline rate relation
(Phillips 1993; Hamuy et al. 1996) or width luminosity relation
(Riess et al. 1996; Perlmutter et al. 1997) has been proposed to
further reduce the scatters of maximum brightness. We briefly call
this kind of relation WLR in this report. This relation now
becomes the basic law for the use of SNe Ia as cosmological
yard-stick.

\begin{figure}[h]
\center {\includegraphics [bb=0 0 281 222,scale=1]{fig1.eps}}

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

      Fig.\,1~~ The plot of the amount of $^{56}$Ni produced
in SN Ia explosion vs. decline rate $\Delta $m$_{15}$. The open
squares correspond to calculations made by varying the $^{56}$Ni
mass in DD4. The filled circles show measurements from nearby SNe
Ia with independent distance calibrations.}

    \end{figure}

The WLR has been very well substantiated observationally, yet it
is an empirical relation that needs to be understood from the
physical point of view. A priori, the light curve may depend on
many parameters, such as the total mass M of the exploding star,
the explosion energy E, the $^{56}$Ni mass synthesized in the
explosion and the opacity k etc. Since the light curves of SNe Ia
are believed to be powered by the radioactive decay chain
$^{56}$Ni $ \to ^{56}$Co$ \to ^{56}$Fe (Kuchner 1994; Bowers et
al. 1997), it is reasonable to attribute the variation in peak
luminosity to different amounts of $^{56}$Ni produced in the
explosions (see Figure 1). The WLR may be a natural consequence of
the radiation transport in SNe Ia explosion (H\"{o}flich P et al.
1996; Pinto {\&} Eastman 2001). The $^{56}$Ni yield sets the scale
of the peak luminosity and the heating rate of the gas. The
resulting temperature determines the ionization and hence the
cooling rate of the gas. More $^{56}$Ni leads to more heating,
higher temperature, less efficient cooling, and hence broader and
brighter light curves. Note that an additional physical parameter
that regulates the WLR may be the r-ray escape fraction, which
sets the evolution rate of the energy deposition and therefore
influences the light curve declines. Greater r-ray escape
fractions would result in a narrower light curve even for bright
SNe Ia. This may explain why some luminous SNe Ia have relatively
faster decline rates while their colors remain bluer, e.g.SN
1992bp. On the other hand, the observed correlation between the
peak luminosity and maximum B-V color of SNe Ia is also expected,
since the color at maximum light is a measure of the opacities in
the ejecta, which is an indicator of the temperature (Khokholov,
Muller{\&}Wheeler 1993). More $^{56}$Ni would cause higher
temperature and opacities that are contributed primarily by
particular species (such as cobalt, iron and sulfur) (Bowers et
al. 1997), and consequently, bluer color at maxima. Note that,
under the delayed detonation models, H\"{o}flich P et al.(1996)
reproduced well the observed $M_{max}-(B-V)$ correlation.

The dispersion of the Hubble diagram could be reduced to
$\sim0.08$ mag when applying the combined $M_{max}(\Delta m_{15},
(B-V))$ relation to the peak luminosity of an extinction-free SN
sample.% (Wang et al. 2002).
Such a small luminosity dispersion is
now the same order as the observational error, which leaves little
room for other possible correlations such as the type (or color)
of the host galaxies (Hamuy et al. 1996b; 2000) as well as the
galactocentric distances (Wang, H\"{o}flich \& Wheeler 1997;
Ivanov et al. 2001).

\vn{\bf{2.2~~The Absolute Magnitudes of SNe Ia and the Hubble
Constant}}

As the best distance indicators beyond the Virgo cluster, SNe Ia
now provide the main route to determine the Hubble constant
(H$_{0})$. The distance dispersion inferred from standardized
luminosity of SNe Ia is only 5\%. Although other distance
indicators are still discussed, in most cases they enter the
analysis with lower weight.

Knowing their absolute magnitudes at maxima is the premise to
determine the H$_{0}$ value by SNe Ia. Sandage/Saha Type Ia SNe
HST calibration Program has provided us accurate Cepheid-based
distances to some nearby galaxies that hosted SNe Ia. In a series
of papers, Saha and Sandage have published the Cepheid distances
to IC 4182 (SN 1937C), NGC 5253 (SNe 1895B, 1972E), NGC 4536
(1981B), NGC 4496A (SN 1960F), NGC 4639 (SN 1990N), NGC 3627 (SN
1989B), NGC 3982 (SN 1998aq), and NGC 4527(SN 1991T) (see Saha et
al. 2001 and references therein). Tanvir et al(1995) and Turner
(1998) gave the Cepheid distances to NGC 3368 (SN 1998bu) and NGC
4414 (SN 1974G). Using all or some of these distances, the
absolute magnitudes of normal SNe Ia are estimated to be
$-19.55\pm0.08$(statistical) mag in $V$ band, which is in
agreement with the result predicted by theoretical models with
equal decline rate and color (H\"{o}flich P et al. 1996).

The Hubble constant is estimated to be 64$\pm
$2\,km\,s$^{-1}$\,Mpc$^{-1} $(1$\sigma)$ by matching the local
calibration value to the distant Hubble-flow SNe Ia. The errors
only account for statistical errors. The possible systematic
errors include the specific photometry (i.e. ALLFRAME vs. DoPHOT)
and associated method of detecting variable stars; the metal
dependence of the P-L relation; the shape of Cepheids' P-L
relation; the zero point of the P-L relation. Considering the
those systematic effects discussed above, the final result for the
Hubble constant could be 64$\pm $2$\pm
$6\,km\,s$^{-1}$\,Mpc$^{-1}$(1$\sigma)$ (see Wang et al. 2001).
Further improvement of the accuracy would rely on the full
understanding of various systematic effects that possibly
influence the calibration value of the absolute magnitudes for
Type Ia supernovae.

\vn{\bf{2.3~~The Accelerating Expansion Implied from SNe Ia}}

Using SNe Ia as distance indicators to trace the history of the
cosmic expansion, a deviation from the linear Hubble flow can be
measured at higher redshift which is related to the
(de)acceleration of the local Universe. For a precision of $\Delta
$m in distance modulus at redshift z, the deceleration can be
measured to an accuracy of $\Delta q_{0}\approx 0.9 \Delta$m/z.
Statistical accuracies of 0.1 mag in an ensemble of supernovae at
z$\approx$0.5 can lead to a error in $q_{0}$ of less than 0.2
units, which is adequate to determine the sign of the
acceleration.

Spectacular and surprising claims have been made about the
detection of an acceleration away from the linear local Hubble
flow, which is interpreted as a positive cosmological constant
$\Omega _{\Lambda }$(Riess et al 1998; Perlmutter et al 1999).
After the initial excitement, the reliability of above results
needs to be further tested. For example, the peak $B-V$ colors of
high-redshift SNe Ia seem to be bluer than the local counterparts
(e.g. $-0.15\pm0.03$ vs. $-0.04\pm0.01$), which may imply
evolution of peak luminosity or systematic errors in extinction
correction. The most direct method of testing systematic effect is
to further extend the m-z relation of SNe to z$\ge$1, since there
exists a transition from decelerated expansion (where the energy
density was dominated by matter) to accelerated expansion if
current universe is $\Lambda $-dominated. In a flat Universe model
$\Omega _{\Lambda}$=0.2, $\Omega _{M}$=0.8, this transition
occurred at z$\sim $1, where the SNe become less faint relative to
an empty universe. If the current SN data were explained by
evolution or extinction, for instance a systematic uncertainty
which grows linearly with redshift, we would expect that SN Ia
results at higher redshift to diverge significantly from the
cosmological prediction. Thus, observations of SN Ia at z$\sim $1
will provide an excellent test to confirm or refute the current
cosmological paradigm.

\para{\large\bf{3}~~Radio Supernovae}

\vs\vs The radio emitting supernovae (RSNe) have been extensively
searched for since at least 1970 and several weak detections of SN
1970G have been obtained. The radio emission is an indicator of
the presence of CSM. Therefore, analysis of the radio emission
provides vital insight into the interaction of the SN shock with
preexisting CSM lost by the progenitor star or progenitor system,
and, therefore, into the nature of pre-supernova evolution.
Moreover, because of their high radio luminosities and slow decay
time, RSNe may be significant contributors to the total radio flux
of starburst galaxies, and hence it is of interest in studying the
FIR-radio correlation. Finally, if some RSNe are optically dim or
invisible (as SN1986J appears to have been), and if these are also
the most massive stars (with a corresponding large yield of
processed stellar material), there will be important consequences
for our understanding of the chemical enrichment history of
galaxies.

Radio emission has been observed for some supernovae in SNe Ib/c
(e.g. 1983N), IIb (i.e.1993J, 1996cb), IIn (1986J, 1988Z), II-L
and now II-P. However, due to low resolution, background
confusion, and sensitivity limitations of the radio telescopes,
less than 30 RSNe have been detected and even small number of them
have been extensively studied in detail at multiple radio
frequencies. The SN IIpec 1987A was observed in the radio, but it
probably would not have been observed at the distance of a few
megaparsecs (Mpc). The sole II-P observed near the time of its
explosion in the radio is SN 1999em (Lacey et al. 1999);
additionally the SN II-P 1923A has recently been detected in the
radio (Eck et al. 1998). The SN IIn are usually not only in the
optical, but also in the radio, being exceptionally powerful radio
sources ($\ge$10$^{28}$ erg s$^{-1}$ Hz$^{-1})$. Note that radio
emission has not been observed from SNe Ia, but certain models of
SNe Ia (i.e. Hachisu et al. 1999a, b) propose radio emission at
some level before maxima. To determine whether this absence of
radio emission in SNe Ia is real or if it merely represents the
limitations of existing observations has to rely on the future
observations (e.g., an improvement by two orders of magnitude will
give a definite answer).

\vs\vn{\bf{3.1~~The Light Curves and the Model}}

 All RSNe appear
to share the common properties of 1) non-thermal synchrotron
emission with high brightness temperature; 2) a decrease in
absorption with time, resulting in a smooth, rapid turn-on first
at shorter wavelengths and later at longer wavelengths; 3) a
power-law decline of the flux density with time at each wavelength
after maximum flux density is reached at that wavelength; and 4) a
final, asymptotic approach of spectra index $\alpha$ to an
optically thin, non-thermal, and constant negative value.

A ``mini-shell" model is usually used to describe the observed
RSNe, which involves the acceleration of relativistic electrons
and enhanced magnetic field necessary for synchrotron emission,
arising from the SN shock interacting with a relatively
high-density CSM that has been ionized and heated by the initial
SN UV or X-ray flash. The rapid rise in radio flux density results
from the shock overtaking progressively more of the ionized wind
matter, leaving less of it along the line-of-sight to absorb the
emission from the shock region. While the slow decline in flux
density at each wavelength after the peak is then due to the SN
shock expanding into generally lower density regions of the
optically thin CSM. The observed variation in density flux of RSNe
can be represented by a relatively complex function of the time
after the explosion, which consists of the unabsorbed flux
density, the power law term, and two terms describing uniform
external absorption and clumpy absorption respectively. The
readers can refer to Weiler et al. (1986; 1990) for the detailed
parameters of this model.

\vs\vn{\bf{3.2~~RSN Distance Determination}}

 Evidence has recently
been presented that the radio emission from SNe may have
quantifiable properties which allow for distance determinations.
Using a small sample of 12 Type II RSNe, Weiler et al. (1998)
showed that these objects appear to obey a relation
L$_{6\rm\,cm\,peak} \approx $5.5$\times
$10$^{23}$(t$_{6\rm\,cm\,peak}$-
t$_{0})^{1.4}$\,erg\,s$^{-1}$\,Hz$^{-1}$, with time in days. If
these relations are supported by further observations, they
provide a means for determining distances to supernovae, and thus
to their parent galaxies, from purely radio continuum
observations. The $H_{0}$ determination could be made independent
of optical observations. Furthermore, if some bright SNe could be
radio detected to z$\sim$1, the estimation of other cosmological
parameters, such as $q_{0 }$ and $\Omega $, might be possible.

However, due to the sensitivity limitations, the studies of most
RSN can only be restricted to distances smaller than the Virgo
cluster, a cosmologically insignificant distance. In order to be
able to detect the brightest of RSNe, such as Type IIn SN 1988Z
and SN 1986J at the cosmologically interesting distance of z =1,
the sensitivity of radio telescope should be improved to the level
of 1$\mu$\,Jy. While for normal Type II RSNe, such as SNe 1979C
and 1980K, this sensitivity should reach to the level of
0.1$\mu$\,Jy.

\para{\large\bf{4}~~Conclusions}

\vs\vs Empirical WLR makes the thermonuclear SNe one of the most
powerful tool to measure the distances to distant galaxies.
However, the determination of the Hubble constant is still greatly
affected by the accuracy of Cepheid calibrations for nearby SNe
Ia. While the cosmological results from high-z SNe Ia should
experience more strict test against some systematic effects.
Observation of SNe Ia at $z>1$ would help to give judgements. On
the other hand, the RSNe study is severely sensitivity limited by
the radio telescopes, even by VLA. For RSNe study, one would like
to see that the sensitivity should be at the level of 1$\mu$\,Jy
rms or better in 30 minutes. The Square Kilometer Array (SKA), a
VLA Expansion, holds possibility to reach such an accuracy. The
SKA would improve SN environment/progenitor studies, would lead to
improvement in our understanding of galactic chemical and
dynamical evolution, and would provide independent distance and
cosmological parameter estimates.

\vs The report is funded by the National Science Foundation of
China (NSFC grant 10173003).

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

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