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 \begin{document}
 \title{Search for spectral evolution with {\bf redshift in} Type Ia supernovae.}

 \author{G.~Garavini, G.~Folatelli, A.~Goobar, C.~Lidman, S.~Nobili,
 and the Supernova Cosmology Project Collaboration}


 \offprints{G.~Garavini , garavini@in2p3.fr}

 \institute{Department of Physics, Stockholm University, \\
          SCFAB, S--106 91 Stockholm, Sweden }

 \date{Received ...; accepted ...}
 \authorrunning{G.~Garavini}


\titlerunning{Search for Spectral Evolution}

\date{} \abstract{A quantitative comparison of low and high-redshift
  Type Ia supernovae spectra is presented. Measurements of the Ca~{\sc
  ii}~H\&K expansion velocity and pseudo-equivalent widths of 12
  high-redshift supernovae (0.212 < $z$ < 0.912) are found to be
  statistically consistent with those of a sample nearby supernovae.
  We find no evidence for evolution in the spectral properties of SNe
  Ia with redshift.  One supernova, SN~2002fd, ($z$=0.279) {\bf is
  found} shows spectral characteristics similar to peculiar
  SN~1991T/SN~1999aa-like SNe.}

\maketitle

\section{Introduction}
Precision measurements of cosmological parameters using high-redshift
SNe~Ia as distance indicators assumes that the shape-brightness
corrections that are derived from low-redshift samples are applicable
to high-redshift SNe~Ia, this implies testing that
type Ia SNe do not evolve with redshift. 

The spectral energy distribution provides an avenue for
testing this assumption. The average metallicity of the Universe
increases with cosmic time, so it is not unreasonable to expect that
high-redshift SNe~Ia are in environments that have lower
metallicity. The effect on the spectral energy distribution of a
lower metallicty progenitor has been modeled by
\citet{1998ApJ...495..617H} and \citet{2000ApJ...530..966L}. These
studies find that such SNe~Ia are expected to show enhanced flux in
the UV, weaker absorption features in the optical and a shift in the
minima of optical features to redder wavelengths.

With the large number of well-observed low-redshift supernovae now
available, a wide range of spectral diversities is being found (see
e.g \citet{2003astro.ph.10685B}). The physical origin of these
differences and their possible drift as a function of redshift are
still not completely understood. Statistical studies are useful to
probe for differences between high and low-redshift SN data sets.  As
of now few attempts have been made to quantitatively compare supernovae
properties at different redshifts and only based on light curve
parameters
\citep{1999AJ....118.2675R,2000AJ....119.2110A,2001ApJ...558..359G}.
Systematic differences in the brightness of SNe~Ia have been found in
the low-redshift sample depending on host galaxy type: slow-decliner
supernovae have been claimed to be more common in young progenitor
systems and under luminous SNe more common in old progenitors systems
\citep{1995AJ....109....1H,1996AJ....112.2391H,2000AJ....120.1479H,2001ApJ...554L.193H}.
This trend could not be confirmed by \citet{2003MNRAS.340.1057S} in a
study of 39 distant SNe in a redshift range of $0.3<z<0.8$, possibly
due to the limited span of light curve widths in their SN sample.

Low-redshift SNe Ia are usually classified in three sub-types
according to their spectral appearance around $B$-band maximum
light. Normal supernovae, which are represented by objects such as
SN~1981B \citep{1983ApJ...270..123B}, SN~1989B
\citep{1990A&A...237...79B}, SN~1992A \citep{1993ApJ...415..589K}, and
SN~1972E \citep{1973ApJ...185..303K}, are the most common SNe~Ia
sub-type and show strong absorption features due to intermediate mass
elements (IME), such as Si, S, Ca and Mg. Peculiar SN~1991bg-like
supernovae
\citep{1992AJ....104.1543F,1993AJ....105..301L,1996MNRAS.283....1T,1997MNRAS.284..151M},
are characterized by enhanced Si~{\sc ii} lines and strong Ti~{\sc ii}
absorption features. Peculiar SN~1991T-like supernovae
\citep{1992ApJ...384L..15F,1992AJ....103.1632P,
1992ApJ...387L..33R,1992ApJ...397..304J,1995A&A...297..509M}, have
very weak IMEs -- virtually absent in pre-maximum spectra -- yet
strong doubly ionized iron absorption features. Recently, supernovae
with spectral characteristics in between those of normal and
SN~1991T-like have been identified. These show weak Si~{\sc ii} lines,
yet an evident Ca~{\sc ii}~H\&K absorption, and they are sometimes
called SN~1999aa-like supernovae
\citep{2001ApJ...546..734L,garavini99aa}. In general, objects
resembling these two prototypes are, however, classified as
SN~1991T/SN~1999aa-like supernovae. Few type Ia SNe which do not fall
into this classification scheme have been recently discovered
(e.g. SN~2002cx {\bf \citep{2003PASP..115..453L},
SN~2002bo\citep{2004MNRAS.348..261B})}.

So far, very few distant SN~Ia spectra have been compared with
low-redshift data sets in a systematic manner {\bf
\citep{1998Natur.391...51P,2000ApJ...544L.111C,2003astro.ph.10843B,2003astro.ph..8185R,2003ApJ...589..693B,2004astro.ph.11357M}}.
Moreover, very few of the spectroscopically confirmed high-redshift
SNe has been reported as peculiar.  \citet{2001ApJ...546..734L}
estimated that, in a magnitude-limited supernova search and assuming
that fraction of peculiar SNe is constant with redshift, less than
2\% of the discovered SNe should be {SN~1991bg-like) and hence
under-luminous, and between 18.6\% and 6\% (the fraction depends on the
chosen age bias) should be SN~1991T/SN~1999aa-like and hence
over-luminous (but see \citet{2001PASP..113..169B}).  The observed
rate mismatch of the "over-luminous" type, between low and
high-redshift data sets could be due to the limited statistical
significance of the distant supernova sample, but could also be
interpreted as a sign of evolution
\citep{2001ApJ...546..734L,2001ApJ...546..719L}.  The identification
of SN~1991T/SN~1999aa-like supernovae at high-redshift is an important
step in demonstrating that the range of SNe~Ia that are observed at
low-redshifts is also observed at high-redshifts.

During 2000, 2001 and 2002, the Supernova Cosmology Project (SCP)
obtained the spectra of 20 high-redshift SNe~Ia with FORS2 on the ESO Very
Large Telescope \citep{Lidman}. In this paper, we analyze the 14
spectra with the best signal-to-noise ratios and we perform a
quantitative comparison between these spectra and the spectra of
low-redshift SNe. We also develop approach to identify SN~Ia sub-types
at $z$ $\sim$ 0.5. The paper is organized as follows. The dataset and
identification scheme are presented in section \ref{data}.  The
comparison of high and low-redshift SNe are presented in section
\ref{measurements} together with a statistical analysis of the
results."


\section{Data set and Supernova Identification} %
\label{data}
\begin{table*}[th!]
\small
\caption[table data]{A summary of the high-redshift data. For each SN,
the redshift, the Modified Julian Date (MJD), the epoch since B-band
maximum light, the telescope, the instrument, the instrument
setting, the exposure time, the signal-to-noise ratio (per 20 \AA\
bin), the percentage of galaxy contamination and SN~Ia sub-type are
given. See text for details.}
\begin{center}
\small
\begin{tabular}{lcccccccccl}
\hline
 SN-name & Red-shift$\tablenotemark{a}$& Date  & Days from$\tablenotemark{b}$& Instrument  & setup & telescope & Exposure& S$/$N$\tablenotemark{c}$&Galaxy$\tablenotemark{d}$&ID\\
  & &(MJD) & B-band  & &  & & time (s) && \%& \\
  &  &     & Maximum & &  & & \\
\hline
SN~2001gy &0.511& 52021.3 & -7,5(1) & FORS1 & 300V grism + GG435  & VLT-UT1 &  2400 &11&20&Ia\\
SN~2002fd &0.279& 52376.1 & -7(2) & FORS2 & 300V grism + GG435  & VLT-UT4 &  600&46&28&{\bf Ia-pec}\\
SN~2000fr &0.543& 51676.2 & -5.5(2) & FORS1 & 300V grism + GG435  & VLT-UT1 &  7200 &21&16&Ia\\
SN~2001gw &0.363& 52021.4 & -1(2) & FORS1 & 300V grism + GG435  & VLT-UT1 &  1200&8&19 &Ia\\
SN~2001ha &0.58& 52022.0 & 0(2) & FORS1 & 300V grism + GG435  & VLT-UT1 &  3600 &4&6&Ia\\
SN~2002gl &0.510& 52413.1 & 0(2) & FORS2 & 300V grism + GG435  & VLT-UT4 &  3000& 9&23&Ia\\
SN~2001hc &0.35& 52022.1 & 0(2) & FORS1 & 300V grism + GG435  & VLT-UT1 &  1800 &14&14&Ia\\
SN~2001gr &0.540& 52021.0 & 2(2) & FORS1 & 300V grism + GG435  & VLT-UT1 &  3600& 5&57&Ia\\
SN~2002gi &0.912& 52407.2 & 2(2) & FORS1 & 300I grism + GG435  & VLT-UT3 &  7200&3&37&Ia \\
SN~2001gm &0.478&52021.3 & 5(2)  & FORS1 & 300V grism + GG435  & VLT-UT1 & 2400&3&28&Ia\\
SN~2001go &0.552& 52021.3  & 5.6(1) & FORS1 & 300V grism + GG435  & VLT-UT1 &  2400&5&13&Ia\\
SN~2002gk &0.212& 52413.3 & 6(2) & FORS2 & 300I grism + GG435  & VLT-UT4 &  900&34&66&Ia \\
SN~2001go &0.552& 52027.1 & 9.5(1) & FORS1 & 300V grism + GG435  & VLT-UT1 &  7200 &10&19&Ia\\
SN~2001go &0.552& 52058.1 & 29.5(1) & FORS1 & 300V grism + GG435  & VLT-UT1 &  9000& 4&53&Ia\\
\hline
\end{tabular}
\label{tabledata}
\tablenotetext{a}{The redshift is quoted to three significant figures if it is determined from host galaxy lines, otherwise two.}
\tablenotetext{b}{Uncertainties are quoted in parenthesis}
\tablenotetext{c}{For  a 20 \AA\ bin element}
\tablenotetext{d}{Estimated contribution of the host to the total flux.} 
\end{center}
\end{table*}
\normalsize

\subsection{The high-redshift spectroscopic data set}

The supernova spectra that are analyzed in this work were obtained as
part of a study by the SCP to discover and follow a large number of
SNe~Ia over a wide range of redshifts. Out of the 20 spectrally
confirmed SNe~Ia in \citet{Lidman}, we select the 12 SNe~Ia
($z$=0.212-0.912) with the highest signal-to-noise ratios (S/N per 20
\AA\ resolution element greater than 3) to pursue the quantitative
analysis that is presented below.  Since SN~2001go was observed at
three epochs, there are 14 spectra in total.

The spectra, rebinned to 20 \AA\ per pixel, are shown in
Fig. \ref{spectra}, and the properties are summarized in Table
\ref{tabledata}. A full description of the observations and the data
reduction are given in \citet{Lidman}.  Special care was taken in
estimating the statistical error spectrum. It was estimated from
regions free of SN and host galaxy light on the sky-subtracted two
dimensional spectrum and scaled to the width in the trace of the
supernova.

\begin{figure*}[p!]
\centering \includegraphics[width=17cm]{tot3.0.ps}
\caption{ The spectra of the high-redshift SNe~Ia. Each spectrum is
the original observed spectrum re-binned to 20 \AA\ per pixel. See
also Table~\ref{tabledata}}.
\label{spectra}
\end{figure*}

High-redshift supernova spectra  usually suffer from host galaxy
contamination. On the 2d spectra, the host galaxy  and the
SN~Ia are usually spatially unresolved, making  it difficult to
estimate the contribution of the host to the observed
flux.  We estimated this contribution using a template matching
technique based on a large set of nearby supernovae spectra and
galaxy models similar to that used in \citet{Lidman}.  The estimated
galaxy contamination, relative to the observed spectrum, are tabulated
in column 10 of Table~\ref{tabledata}.

The epochs with respect to the $B-$band maximum light -- reported in
table \ref{tabledata} -- were estimated using the light curve, if
available, and/or spectroscopic dating by template matching with
low-$z$ SNe.  The two methods usually agree within two days, therefore
we take this to be the uncertainty on the quoted epoch whenever an
accurate light curve estimate of the maximum was not available. The
redshift of the supernova, when quoted with 3  significant
figures, was estimated from host galaxy lines visible in the SN
spectrum. When this was not possible, the redshift was estimated from
the supernova spectral features, and is then quoted with 2 significant
figures.

\subsection{SN identification}
\label{id}

The identification of low-redshift SN~Ia relies primarily on the
detection of the absorption feature at approximately 6150 \AA\ due to
Si~{\sc ii}~$\lambda$6355.  At redshifts above 0.5, this
characteristic feature is redshifted beyond the wavelength range of
most optical spectrographs and the classification of the supernova has
to rely on spectral features that lie at bluer wavelengths. Because
of the low signal to noise ratio usually available in high-redshift
supernova spectra, this approach is not always conclusive. In
\citet{isobel}, it is shown that four different wavelength regions can
be used to distinguish between SN~Ia and core-collapse supernovae in
this redshift range. The same regions can also be used to identify
spectral peculiarities among SNe~Ia as those found in
SN~1991T/SN~1999aa-like or SN~1986G/SN~1991bg-like supernova. In Table
\ref{table_class}, the characteristics of these four wavelength
regions for different types and sub-types of supernovae are
schematically reported. Each spectral feature is qualitatively
described as {\it strong}, {\it weak} or {\it absent} based on the
absorption strength and {\it broad} or {\it narrow} based on the
wavelength span.  In the absence of a procedure that is based on
quantitative measurements, this scheme helps in identifying the 
SN type and, in the case of SNe~Ia, the sub-type.


\begin{table*}[htb]
\begin{center}
\small
\caption[tableIaID]{ A description of the spectroscopic features used
to type SN at z $\ge$ 0.5. Four wavelength regions are selected for
performing the SN typing. Each spectral feature, in these regions, is
qualitatively described as {\it strong}, {\it evident}, {\it weak} or
{\it absent} based on the absorption strength and {\it broad} or {\it
narrow} based on the wavelength span.} 
\small
\begin{tabular}{lccccccc}
\hline Region Id&$\lambda$-Region&Normal Type Ia& Type Ib/c& Type II & 91T/99aa-like& 91bg/86G-like&comments\\ &Rest Frame[\AA]&&&&&&\\
\hline 
`Ca {\sc ii} H\&K'&3550-3950&strong/broad&evident/broad$\tablenotemark{c}$&absent&weak or absent/broad$\tablenotemark{a,b}$&strong/broad&$\tablenotemark{g}$\\
`Si {\sc ii}' &3950-4100&evident/narrow$\tablenotemark{b}$&absent&absent&weak$\tablenotemark{a,b}$&absent& $\tablenotemark{d}$\\ 

`Fe {\sc ii}' &4600-5200&strong/broad&strong/broad&absent$\tablenotemark{h}$&strong/narrow$\tablenotemark{a}$&strong/broad&$\tablenotemark{e,f}$\\
`S {\sc ii} W'&5200-5600&strong/narrow$\tablenotemark{a,b}$&absent&absent&weak or absent$\tablenotemark{a}$&strong/narrow$\tablenotemark{a,b}$&\\ 
\hline
\end{tabular}
\tablenotetext{a}{Before maximum light}
\tablenotetext{b}{Around maximum light}
\tablenotetext{c}{ A few peculiar exceptions.}
\tablenotetext{d}{Marks the beginning of the distinctive strong Ti {\sc ii} absorption feature in 91bg/86G-like SNe~Ia.}
\tablenotetext{e}{In Normal Ia characteristic line profile time evolution.}
\tablenotetext{f}{Dominated by Fe {\sc iii} in pre-maximum spectra of 91T/99aa-like SNe~Ia.}
\tablenotetext{g}{Splitted minimum in some Ia.}
\tablenotetext{h}{In Type II SNe, the H$_\beta$ line lies on the blue side of the ``FeII'' region.}
\label{table_class}
\end{center}
\end{table*}
\normalsize


\subsection{SN~2002fd: A {\bf SN~1991T/}SN~1999aa-like Supernova}
\label{sec:02fd}

SN~2002fd is the only supernova in our data set that clearly deviates
from a ``normal Ia" (see table \ref{table_class}). Within the scheme
described above,  the spectrum of SN~2002fd is to similar
the spectra of SN~1991T/SN~1999aa-like supernovae. The spectrum of
SN~2002fd (re-binned to 20 \AA\ per pixel) is shown in Fig. \ref{02fd}
 where it is compared to other well known peculiar and normal
SN~Ia.   The `Ca~{\sc ii}~H\&K' feature in SN~2002fd is weaker
than the same feature in normal  SNe~Ia, but stronger than the same
feature in SN~1991T-like SNe~Ia. The `Fe~{\sc ii}' and  `S~{\sc
ii} W' regions are similar to those in SN~1999ac
\citep{garaviniac}. Given the low-redshift, Si~{\sc ii}~$\lambda$~6355
is also visible.  This feature in SN~2002fd is intermediate in
strength to the strength of this feature SN~1999aa and SN~1999ac/normal
SNe. From this qualitative analysis of the spectrum, we classify
SN~2002fd as a peculiar SN~1991T/SN~1999aa-like object with
characteristics in between  the extreme SN~1991T-like SNe and
normal SNe (e.g.  SN~1994D). It is similar to SN~1999aa.  In
section \ref{02fdhk}, we show that the {\sc ew}s of the absorption
features in SN~2002fd are also consistent with those found at low
redshift for the SN~1991T/SN~1999aa-like objects.

\begin{figure}[thb]
%\centering \includegraphics[width=8cm]{02fd-mag.eps}
%\centering \includegraphics[width=8cm]{02fd-p.eps}
\centering \includegraphics[width=8cm]{02fd-7_p.eps}
\caption{SN~2002fd at day -7, re-binned to 20 \AA\ per pixel (thick
solid line), compared to normal and peculiar SNe. The $\oplus$ symbols
mark  regions of strong telluric absorption.}
\label{02fd}
\end{figure}
Finding SNe with spectral characteristics similar to those of
SN~1999aa at the redshift of SN~2002fd gives us confidence that
supernova populations at low and intermediate $z$ are the same.
SN~1991T/SN~1999aa-like supernovae appear to make up 20\% of all
supernovae observed at low-$z$ \citep{2001ApJ...546..734L} although
this high peculiarity rate could be the result of the difficulty to
classify spectroscopically peculiar SN~1999aa-like SNe
\citep{2001PASP..113..169B}. Nevertheless, we should find some of
these SNe at high-redshift. \citet{2001ApJ...546..734L} used a
Monte-Carlo simulation to estimate that, in a magnitude-limited
high-redshift supernova search, where SN~1991T/SN~1999aa-like SNe
suffer an additional extinction of 0.4 magnitudes, between 18.6\% and
6\% (for an age bias of +7 and $-$1 days respectively) of all
high-redshift SNe should be SN~1991T/SN~1999aa-like SNe.

The precise number depends on the details of the methods that are used
in the search. Many SN~1991T/SN~1999aa-like SNe may have already been
observed at high-redshift but not clearly identified because the
signal-to-noise ratio in the spectrum was too low or the light-curve
was not exceptionally broad. It is becoming clearer that
SN~1991T/SN~1999aa-like SNe do not always have broad light curves and
vice-versa, see for example {\bf SN~1999ee
\citep{2002AJ....124..417H}, SN~2002cx\citep {2003PASP..115..453L} or
SN~1999aw \citep{2002AJ....124.2905S}} SN~2002fd is on of the first
examples of a SN~1991T/SN~1999aa-like supernova in the Hubble flow,
and its discovery demonstrates that these objects are also found at
higher redshifts.  Of course, larger data samples are required to
check whether the fraction of peculiar high-redshift SNe is consistent
with that found in the low-redshift Universe or if there is an
evolution in the relative fractions with redshift {\bf that could
affect the results derived in cosmology.}  


{\bf DO WE REMOVE THIS?
\subsection{Multi-epoch spectroscopy of a Type Ia SN at z=0.552}

Figure \ref{01go} shows the spectral time sequence of SN~2001go (thick
solid line) compare to SN~1992a (thin solid line) at the same
epochs. SN~1992a resulted as the best match supernova among the low-redshift 
objects used as models in the statistical comparison procedure during
identification. The epochs of the spectra shown are +5.6, +9.5 and
+29.5. For the latter a color difference is visible at the
red end of the spectrum, which could be due to an incorrect host galaxy
subtraction caused by the low signal to noise in this late
spectrum.

\begin{figure}[thb]
\centering \includegraphics[width=8cm]{go.eps}
\caption{ Spectra of SN~2001go at three epochs (day +5.6, +9.5
and +29.5 with respect to B-band maximum light), re-binned to 20 \AA\
per pixel (thick solid line), are compared to the best statistical
match, the normal type Ia SN~1992a (thin solid line) at the same
epochs.}
\label{01go}
\end{figure}

}
\section{Comparing High and Low-redshift spectra}
%\section{Spectral Indicators}
\label{measurements}

In this section, we compare our high-redshift spectra with spectra
from a broad sample of low-redshift supernovae in order to probe for
possible differences between the low and high-redshift populations. We
first perform a qualitative analysis (sections \ref{vel} and \ref{ew})
and then turn to a more quantitative approach (section \ref{stat}).
The measured values are reported in Table \ref{ewdata}.

\subsection{Velocities}
\label{vel}

%\begin{comment}
\begin{table*}[htb]
\begin{center}
\small
\caption{Measurements of the velocities of Ca~{\sc ii}~H\&K and of the {\sc ew}s of Ca~{\sc ii}H\&K, Mg~{\sc ii} and Fe~{\sc ii}. Measurements errors are reported in parenthesis }
\begin{tabular}{cccccc}
\hline
SN &day&Ca HK vel & Ca~{\sc ii}H\&K {\sc ew}&Mg~{\sc ii} {\sc ew} &Fe~{\sc ii} {\sc ew}\\
\hline
sn2001gy& -7.5(1) &21520(300) &  176.2(8.0)& 110.6(12.4)&    -\\
sn2000fr& -5.5(2) &17405(300) & 122.3(12.5)& 103.1(5.6) &   85.6(14.7)\\
sn2002fd& -7(2)& 14940(300)&  73.6(2.9) &101.0(7.6)  &    91.1(13.1)\\
sn2001gr& 2(2)& 15170(300) & 94.6(9.8)& 140.3(15.8) &   141.2(30.8)\\
sn2001ha& 0(2) &16313(300) & 188.1 (19.0) & 131.6(9.1) &   216.4(33.1)\\
sn2001gw& -1(2) &15445(300) & 130.3(9.0) & 125.3(16.9) &        -\\
sn2002gi& 2(2) &713950(300) &              &&                     -\\
sn2001hc& 0(2) &13115(300) & 111.8(14.9)& 115.8(10.7)     &   140.3(14.6)\\ 
sn2002gl& 0(2)& 13680(300)& 124.3(13.7)&  120.9(11.6)&      167.9 (20.3)\\
sn2001gm& 5(2)& 17577(300) & 128.4(22.4) &123.1(17.4)&        169.4(34.0\\
sn2001go& 5.6(1)& 14467(300)&   93.1(11.0)&      -   &     190.6(27.8)\\
sn2002gk& 6(2) &-&90.9(5.8)& 120.2(10.9) &161.4(13.5)     \\
sn2001go& 9.5(1) &13316(300)&   9111.9(6.3) & 181.3(14.0) &  173.6(20.0)\\
sn2001go& 29.5(1) &- &     & 227.7(22.1)  &      314.9(40.5)\\
\hline 
\end{tabular}
\label{ewdata}
\end{center}
\end{table*}
%\end{comment}

For normal SNe~Ia, the velocity of Ca~{\sc ii}~H\&K drops
rapidly, from values around 22000 km/s  before maximum light to
14000 km/s  at maximum light. After maximum light, the  rate
of decrease slows and the velocity decreases by about 4000 km/s in 50
days. The mean trend for normal SNe~Ia, from 10 days before maximum light  
to 40 days after maximum light, is shown in Fig.~\ref{ca_vel}. The
shaded area represents the dispersion (one standard deviation about
the mean). The trend and the dispersion have been computed from a large
sample of nearby supernova \citep{garavini99aa}.

The inferred expansion velocity of the ejecta in under-luminous SNe is
lower than the expansion velocity in normal SNe
(\citet{1993AJ....105..301L,1994AJ....108.2233W,1996MNRAS.278..111P,Garnavich:2001vx,2003PASP..115..453L}).
The differences are more pronounced in the case of the Si~{\sc
ii}~$\lambda$6355 absorption feature where differences of more than
2000 km s$^{-1}$ are seen \citep{1993AJ....105.2231B}. The separation
is less conspicuous for the Ca~{\sc ii}~H\&K absorption -- measurable
in the redshift range of our data set -- but the trend remains, as can
be seen in Fig.~\ref{ca_vel} where SN~1999by \citep{Garnavich:2001vx}
and SN~1991bg \citep{1993AJ....105..301L}) are plotted with the dashed
and dotted lines, respectively.  Assuming that intrinsically
low-luminosity high-redshift SNe show the same spectral
characteristics of those in the local universe, measured expansion
velocities values on the lower edge of the distribution shown in
Fig.~\ref{ca_vel}, would suggest a possible under-luminous SN.

The velocities, of both the low-redshift and high-redshift SNe are
measured by performing an error-weighted non-linear least-squares fit
to the whole line profile. The line profile is modeled with a
Gaussian and the continuum over the width of the line is modeled as a
straight line. All the SNe in our data set were measured, with the
exception of SN~2001gk, for which the line profile is incomplete, and
SN2001go at +29 days, for which the signal to noise is too low to
correctly identify the absorption. The uncertainty in the redshifts is
taken to be 300 km/s if the redshift was estimated from galaxy lines.
For SN~2001ha and SN~2001hc, we could not identify host galaxy lines,
so their redshifts were estimated by comparing their spectra with the
spectra of nearby SNe~Ia. In these cases the uncertainty is increased
to 3000 km/s.  These uncertainties dominate the uncertainties from the
fit. The two are added in quadrature to compute the total uncertainty.

 The velocity of the Ca~{\sc ii}~H\&K feature in all our
high-redshift supernovae lie above the dashed line in
Fig..~\ref{ca_vel}, which represents the velocity of this feature in
the peculiar under-luminous SN~1999by.  We note that the velocities of
our high-redshift SNe are consistent with those of spectroscopically
normal SNe.  \citet{2001ApJ...546..734L}, estimated that 16\% of all
supernovae discovered in the local universe are
under-luminous. However, for magnitude-limited high-redshift supernova
searches -- as those carried out by the SCP --  there is a bias
against discovering SN~1991bg-like SNe.  Thus, the lack of any such
SNe in our high-redshift SNe sample is  not unexpected.

\begin{figure}
\centering \includegraphics[width=8cm]{CaII_vel.eps}
  \caption{ The change in the velocity of the Ca~{\sc ii}~H\&K
  feature with epoch for a sample of high-redshift SNe (presented in
  section \ref{data}) and a sample of low-redshift  SNe. The dashed and dotted
  lines indicate the values of  extremely under-luminous SNe
  SN~1999by \citep{Garnavich:2001vx} and SN~1991bg
  \citep{1993AJ....105..301L} respectively. The solid line indicates
  the average trend for Ca~{\sc ii}~H\&K, which has been computed
  using a large data set of low-redshift  normal  SNe~Ia. The gray
  band shows the  dispersion (1 standard deviation) of the data
  about the average  trend.}
  \label{ca_vel}
\end{figure}

\subsection{Equivalent Widths}
\label{ew}

Equivalent widths can be used to characterize the spectral homogeneity
of SNe~Ia and to measure their intrinsic brightness
\citep{folatelliew}.  We have compared the {\sc ew}s of high-redshift
SNe with those of low-redshift supernovae in search of differences.
The spectra of the high-redshift SN~Ia generally cover regions 1 to 5
of \citet{folatelliew}. These regions are also labeled ``Ca~{\sc
ii}~H\&K'', ``Si~{\sc ii}~4000'', ``Mg~{\sc ii}~4300'', ``Fe~{\sc
ii}~4800'', and ``S~{\sc ii}~W'' respectively. However, because of the
moderate signal to noise ratio of our spectra, we focused our analysis
on the three strong absorption features: ``Mg~{\sc ii}~4300'',
``Fe~{\sc ii}~4800'' and ``Ca~{\sc ii}~H\&K''.  In
Figures~\ref{fig:MgII}, \ref{fig:FeII} and \ref{fig:CaHK}, we compare
the strengths of these features in high and low-redshift SNe. {\bf
Both samples were measured accordingly to the recipe presented in
\citet{folatelliew}}. Since the {\sc ew}s of these features are a
strong function of the phase, the {\sc ew}s are plotted with respect
to B-band maximum light.  In Figs. \ref{fig:MgII} and \ref{fig:FeII}
the solid line indicates the mean trend of the {\sc ew} for normal
SNe~Ia, while the gray, filled region represents the dispersion (one
standard deviation about the mean trend) as described in
\citet{folatelliew}).  Note, that the plotted errors in the {\sc ew}s
of the high-redshift SNe~Ia include both statistical uncertainties,
from the measurement, and systematic uncertainties, from residual
host galaxy contamination. We assumed the latter to be about 10\%, and
estimated the corresponding uncertainty in the {\sc ew}s as in
\citet{folatelliew}.

At around one week after maximum light, the {\sc ew} of ``Mg~{\sc
ii}~4300'' (Fig~\ref{fig:MgII}) suddenly increases from $\sim$100\AA\
to $\sim$250\AA\ on time scales of less than a week. Over this
time-scale, the Mg~{\sc ii}~4300'' feature deepens and blends with the
 neighboring ``Si~{\sc ii} 4000'' feature.  The actual phase at
which this sudden increase takes place depends on the 
intrinsic luminosity of the SNe: for under-luminous SNe~Ia it seems
to occur as early as 5 days before maximum light, while, for normal
SNe~Ia  it occurs around one week after maximum light, and, for
SN~1991T/SN~1999aa-like objects, it  occurs later than day
$+10$.  \citep{folatelliew}. Thus, the ``Mg~{\sc
ii}~4300''  feature can be used to discriminate  between
different type Ia sub-types. The {\sc ew}s of the high-redshift
supernovae (all  except SN~2002gi are measured) are consistent
with  the trend defined by low-redshift  supernova values within
2-$\sigma$. Moreover, SN~2001go, for which measurements  at three
epochs are available, shows the sudden increase at around one week after
maximum, as do most low-redshift  normal SNe. Note, that some of the values
prior to maximum appear to be slightly higher than those of low-redshift  SNe,
although the deviation is not statistically significant, as shown in
the next section.

\begin{figure}
\centering \includegraphics[width=\hsize]{ewhz2v3.eps}
  \caption{ A comparison between the `Mg~{\sc ii}~4300' {\sc ew}s in
  low- and high-redshift SNe~Ia. High-redshift supernova are indicated
  by large symbols. The solid line indicates the mean trend for normal
  low-redshift SNe~Ia, while the gray, filled region represents the
  dispersion (one standard deviation about the mean trend) as
  described in \citet{folatelliew}). Peculiar under-luminous SNe are
  shown separately for comparison.}
  \label{fig:MgII}
\end{figure}

  The trend in the {\sc ew} of ``Fe~{\sc ii}~4800'' {\sc ew}s is
 the same for all SN Ia sub-types (see
Fig.~\ref{fig:FeII}). {\sc ew}s increase from around 100\AA\
before maximum light to 350\AA\ two weeks after. All SNe ( with
the exception of SN~2001gu, SN~2001gw, SN~2001gy and SN~2002gi, for
which the absorption feature was not easily identifiable), were
measured and were found  to be well within the intrinsic spread
of low-redshift  supernovae.


\begin{figure}
\centering \includegraphics[width=\hsize]{ewhz1v3.eps}
  \caption{A comparison between the `Fe~{\sc ii}~4800' {\sc ew}s in
  low- and high-redshift SNe~Ia. As in figure \ref{fig:MgII},
  high-redshift supernova are indicated by large symbols, the solid
  line marks the mean trend for normal low-redshift SNe~Ia, while the
  gray, filled region represents the dispersion (one standard
  deviation about the mean trend) as described in
  \citet{folatelliew}}
  \label{fig:FeII}
\end{figure}

The trend in the {\sc ew} of ``Ca~{\sc ii}~H\&K'' is shown in
Fig.~\ref{fig:CaHK}. The distribution of points is less homogeneous
than that of other features, especially before maximum light, so the
mean trend was not modeled in \citet{folatelliew}. Instead, {\bf the
portion of the plot where most low-redshift normal and under-luminous
SNe are located is indicated}, for clarity, by a gray-filled
region. However, some outliers are found among normal SNe and these
are indicated with the small diamond symbols. The overall intrinsic
spread in this {\sc ew} is the largest of all the features analyzed in
this work. Before maximum light, peculiar SN~1991T-like objects show
systematically low values, as indicated by the small square
symbols. The high-redshift supernovae (all except SN~2002gi are
plotted) do not show significant deviations with respect to the
low-redshift sample shown in the plot.

\begin{figure}
\centering \includegraphics[width=\hsize]{ewhz3v3.eps}
  \caption{A comparison between the `Ca~{\sc ii}~H\&K' {\sc ew}s in
  low- and high-redshift SNe~Ia. High-redshift supernova are indicated
  by large symbols. The location of most normal and under-luminous SNe
  is indicated by the gray filled region. However, some normal SNe,
  are outliers and these are indicated with the diamond symbols. Slow
  decliner SNe are indicated by the square symbols.}
  \label{fig:CaHK}
\end{figure}

\subsection{Statistical comparison}
\label{stat}

In this section, a quantitative -- statistical -- comparison of the
low- and high-redshift SNe is performed using the spectral indicators
described in section \ref{ew}.  \citet{folatelliew} modeled the mean
trends in the {\sc ew}s of the `Fe~{\sc ii} 4800' and `Mg~{\sc ii}
4300' features in normal -- low-redshift -- supernovae with cubic
splines. These models are plotted in Figs.  \ref{fig:MgII} and
\ref{fig:FeII} and they can be used to test if high-redshift
supernovae {\sc ew}'s follow the same trends as low-redshift SNe. The
results of a $\chi^{2}$ test is shown in Table \ref{emdata}. The
intrinsic dispersion around the models for normal low-$z$ supernovae
-- as quoted in \citet{folatelliew} -- was added in quadrature to the
statistic and systematic (i.e.  due to the host galaxy subtraction
residuals) uncertainties to perform the test.  The first two columns
of Table~\ref{emdata} reports the $\chi^{2}$ refer to the comparison
with the `Fe~{\sc ii} 4800' and `Mg~{\sc ii} 4300' {\sc ew} models for
normal supernovae. The last two columns refer instead to the
comparison with under-luminous SNe (e.g. SN~1986G
\citep{1987PASP...99..592P} and SN~1991bg). The hypothesis that our
high-redshift supernovae are same as low-redshift normal supernovae is
statistically more significant that the hypothesis that they are the
same as under-luminous SNe.  However, note that the {\sc ew} of the
`Mg~{\sc ii} 4300' feature for high-redshift SNe~Ia is, on average,
higher than the mean trend (all the points are however included within
2-$\sigma$), especially before maximum light {\bf reflecting in the
relatively large value for the $\chi^{2}$. This could be due to a
residual systematic effect in the host galaxy contamination
subtraction. In order to understand if this 2-$\sigma$ effect could
instead being pointing toward evolution a larger dataset
should be included in the analysis.}

\begin{table}[htb]
\begin{center}
\small
\caption{ The result of the $\chi^{2}$ test comparing the {\sc ew}s
of high-redshift SNe with the models representing normal low-redshift
SNe for `Fe~{\sc ii} 4800' and `Mg~{\sc ii} 4300' (column 2, 3) and
with values of under-luminous SNe (column 4, 5).}
\begin{tabular}{ccccc}
\hline
Feature&$\chi^{2}$/dof&P$_{\rm norm}$&$\chi^{2}$/dof&P$_{\rm faint}$ \\
\hline 
 Fe~{\sc ii}&9.5/11&0.58&26.3/11& 0.006\\ 
 Mg~{\sc ii}&18.1/13&0.15& 386.5/13&0.00\\
\hline
\end{tabular}
\label{emdata}
\end{center}
\end{table}

\citet{2000ApJ...530..966L} claim that the strength of supernova
absorption features should be affected by the drift toward lower
metallicity progenitor expected at high-redshift. However, measuring
the intrinsic spread of {\sc ew}s of the absorption features of their
models relative to those of the one solar metallicity synthetic
spectrum, we found values lower than what is measured on the low-redshift 
supernovae. Thus, the range in which {\sc ew} vary -- studied in
\citet{folatelliew} -- is dominated by other effects than their
prediction from metallicity variations. The possible change of
rest frame U-B color in high-redshift SNe is probably a more sensitive
parameter to investigate the effects of varying metallicity.

\subsection{The "Ca~II~H\&K" EW of SN~2002fd}
\label{02fdhk}

Prior to maximum light, the {\sc ew} of Ca~{\sc ii}~H\&K  can be
used to separate peculiar SN~1991T/SN~1999aa-like SN~Ia from normal
 SNe~Ia,  see Fig. \ref{fig:CaHK}). If the identification of
SN~2002fd as a peculiar object is correct, we expect the {\sc ew} to
be lower than  that of normal SNe. The average {\sc ew} prior to
light curve maximum in normal SNe is $<${\mbox{{\sc ew}}}$>$ = 114.1
 and the scatter around the mean value is
$\sigma_{<{\mbox{\scriptsize {\sc ew}}}>}$= 14.2  For peculiar
SN~1991T/SN~1999aa-like SNe we find $<${\mbox{{\sc ew}}}$>$ = 68.7 and
$\sigma_{<{\mbox{\scriptsize {\sc ew}}}>}$ = 6.1 The value measured for
SN~2002fd, (${\mbox{{\sc ew}}}$ = 73.6 $\pm$ 2.9), is consistent --
within one standard deviation -- with  that found for 
SN~1991T/SN~1999aa-like SN~Ia.

\section{Summary and Conclusions}
\label{conc}
Spectroscopic data of 12 high-redshift supernovae, in the redshift
 interval $z$=0.212 to 0.912, were analyzed and a qualitative
classification scheme was proposed to classify high-redshift SN~Ia.
Based on this classification scheme, all our SNe,  except
SN~2002fd at $z$=0.27, were classified as normal  SNe~Ia. 

A quantitative comparison between low and high-redshift SN~Ia by means
of spectral indicators is presented. The velocities of the ejecta
in high-redshift supernovae, as inferred from the minimum of Ca~{\sc
ii}~H\&K feature, are compared to those of low-redshift  SNe with the aim 
of uncovering differences. No differences could be found. 
The equivalent widths of ``Fe~{\sc ii} 4800'', ``Mg~{\sc ii} 4300'' and
``Ca~{\sc ii}~H\&K'' in high-redshift SNe~Ia are found to follow the
same trends with epoch as those observed in low-redshift SNe.
Furthermore, by means of a $\chi^2$ test, the equivalent widths of
``Fe~{\sc ii} 4800'' and ``Mg~{\sc ii} 4300'' in high-redshift SNe are
found to be statistically consistent with the equivalent widths
observed in low-redshift  normal SNe.


Expansion velocity and equivalent widths  are shown
to be a valuable means for comparing low and high-redshift supernova
spectra thanks to the low signal to noise ratio required to perform 
the measurements. 
A systematic error on the equivalent widths measurements could be
introduced by the subtraction the light from the host galaxy. This
is more likely to affect supernova at high-reshift than at low
redshift and it is difficult to quantify. As a possible solution the
reference host galaxy spectrum should be acquired and used to perform
the subtraction.


The {\sc ew}s of Ca~{\sc ii}~H\&K in the spectrum of SN~2002fd are
consistent with those observed in SN~1991T/SN1999aa-like objects in
the local universe quantitatively confirming the sub-type
identification of this SN and pointing out that this feature can be
successfully to identify peculiar object at high-redshift.

Supernova {\sc ew}'s intrinsic spread of optical absorption lines is
found to be larger than what is predicted modeling metallicity
variation alone. The ultra-violet flux is however, theoretically
expected to be more affected by possible progenitors population
drift. This suggests that to isolate the effect of metallicity on
supernova spectra at high-redshift accurate studies of rest frame
$U-B$ color should be undertaken.

\bibliography{/data/snova/bibtex/bib}
\end{document}

