\documentclass{aa}
%\documentstyle[subfig]{style}
%\usepackage{epsfig,latexsym,graphicx,epsf,subfigure,verbatim,amsmath}
\usepackage{threeparttable,hhline,longtable}
\usepackage{deluxetable} 
\usepackage{epsfig,latexsym,graphicx,epsf,subfigure,verbatim,amsmath}
\usepackage[T1]{fontenc}
\usepackage{txfonts}

%\linespread{1.6}
\usepackage{natbib}
\bibliographystyle{apj}
\citestyle{aa}

 \begin{document}
 \title{Search for spectral evolution in high-redshift 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
  {\bf Type Ia} supernovae {\bf SNe Ia} spectra is
  presented. Measurements of {\bf the} Ca~{\sc ii}~H\&K expansion
  velocity and equivalent width-like measurements of 12 high-redshift
  supernovae (0.212 < $z$ < 0.912) are found {\bf to be} statistically
  consistent with those of a sample nearby supernovae.  We find no
  evidence {\bf for} evolution {\bf in} the spectral properties of SNe
  Ia with redshift.  One supernova, SN~2002fd, ($z$=0.279) shows
  spectral characteristics similar to peculiar SN~1991T/SN~1999aa-like
  {\bf SNe}, making it the first {\bf object of this type identified
  at high reshift.}}

\maketitle

\section{Introduction}

Precision measurements of cosmological parameters using high-redshift
SNe~Ia as distance indicators require a good understanding of
their brightness homogeneity and of the reliability of the
shape-brightness corrections {\bf that are} derived from local
samples.

The spectral energy distribution is the most direct way to investigate
the physics of supernova explosions and{\bf,} thus, {\bf to} search
for possible intrinsic differences between local and distant SNe.
Possible signs of evolution in spectra of high-redshift SNe, such as
those due to a drift toward low metallicity progenitors, have been
modeled, e.g. by \citet{1998ApJ...495..617H} and
\citet{2000ApJ...530..966L}. These studies found that, because of the
plausible lower progenitor metallicity, high-redshift supernovae are
expected to show enhanced UV flux. In addition, lower metallicity in
optical spectral features would : (a) tend to shift the minima of the
spectral line to longer wavelengths and (b) make absorption features
shallower.

With the {\bf large} number of {\bf well-observed} local supernovae
{\bf 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 {\bf a} function of
redshift have to be investigated. Statistical studies are useful to
probe {\bf for} differences between high and low redshift SN data
sets. For example, attempts have been made to compare light curve
parameters but as of now, without conclusive results
\citep{1999AJ....118.2675R,2000AJ....119.2110A}. Possible systematic
differences in the brightness of SNe~Ia have been found in the local
sample depending on host galaxy type: slow-decliner supernovae have
been claimed to be more common in young progenitor systems and
fast-decliner 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.

Local SNe Ia are usually classified in three sub-groups according to
their spectral appearance around $B$-band maximum light. {\bf Normal
supernovae, which are} represented by objects such {\bf 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}, {\bf are the most common SNe~Ia sub-type
and} show strong absorption features due to intermediate mass elements
{\bf (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,garaviniaa}. In general, objects resembling
these two prototypes are, however, classified as
SN~1991T/SN~1999aa-like supernovae.

So far, very few distant SN~Ia spectra have been compared with local
data sets {\bf in a systemmatic manner}
\citep{1998Natur.391...51P,2000ApJ...544L.111C,2003astro.ph.10843B,2003astro.ph..8185R,2003ApJ...589..693B}.
Moreover, none 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 {\bf assuming that
fraction of perculiar SNe is constant with redshift}, less than 2\% of
the discovered SNe should be {SN~1991bg-like) and hence underluminous,
and between 18.6\% and 6\% ({\bf the fraction depends} on the chosen
age bias) should be SN~1991T/SN~1999aa-like {\bf 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 therefore an
important step in securing the use of SNe~Ia for cosmology.

During 2000, 2001 and 2002, the Supernova Cosmology Project (SCP) {\bf
obtained spectra of 20 high redshift SNe~Ia {\bf with FORS2 on the}
Very Large Telescope {\bf (VLT)} \citep{Lidman}. In this work we
analyze the 14 spectra with the best signal-to-noise ratios with the
aim of performing a quantitative {\bf comparison between the spectra
of low- and high-redshift SNe}.  A schematic approach used to identify
SN~Ia sub-types at $z$ $\sim$ 0.5 is presented and the spectral
classification of a redshift $z$=0.279 SN as peculiar
SN~1991T/SN~1999aa-like object is reported.  We measure {\bf the}
expansion velocity from the blue-shift of Ca~{\sc ii}~H\&K and
``equivalent width-like'' ({\sc ew}) measurements in the regions:
``Fe~{\sc ii} 4800'', ``Mg~{\sc ii} 4300'' and ``Ca~{\sc
ii}~H\&K''. These quantities have been shown to provide useful
indicators to investigate the homogeneity of supernova spectra
\citet{folatelliew}.  In this paper we compare the {\sc ew}s and the
measured expansion velocities with those of a large sample of
published local supernova spectra.

The paper is organized as follows. The dataset and identification
scheme are presented in section \ref{data}.  Spectral indicator
measurements 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]{\bf A} summary of {\bf the high-redshift} data. For
each SN, {\bf the} redshift, {\bf the Modified} Julian Date {\bf
(MJD)}, {\bf the} epoch since B-band maximum light, the telescope, {\bf
the} instrument, {\bf the instrument} setting, {\bf the} exposure
time, {\bf the signal-to-noise ratio (per 20 \AA\ bin), {\bf the}
percentage of galaxy contamination and {\bf 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}{{\bf The redshift is quoted to three significant figures if it is determined from
host galaxy lines, otherwise two.}
\tablenotetext{b}{Uncertainties {\bf are} quoted in parenthesis}
\tablenotetext{c}{For {\bf a} 20 \AA\ bin element}
\tablenotetext{d}{Estimated {\bf contribution of the host to the total flux}.} 
\end{center}
\end{table*}
\normalsize

\subsection{The high-z spectroscopic data set}

The supernova spectra {\bf 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 Lidman et al., 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. {\bf Since SN~2001go
was observed at three epochs, there are 14 spectra in total.}

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

\begin{figure*}[p!]
\centering \includegraphics[width=17cm]{tot3.0.ps}
\caption{{\bf 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 {\bf usually} suffer from host galaxy
contamination. {\bf On the 2d spectra, t}he host galaxy {\bf and the
SN~Ia are} usually spatially unresolved, making {\bf it} difficult to
estimate {\bf the} contribution {\bf of the host} to the observed
flux.  We estimated this contribution using a template matching
technique based on a large set of nearby supernovae {\bf 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 {\bf light} --
reported in table \ref{tabledata} -- were estimated using {\bf the
light curve, {\bf if available}, and/or spectroscopic dating by template
matching with low-$z$ SNe.  The two methods usually agree within two
days, therefore {\bf 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 {\bf
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 {\bf significant figures}.

\subsection{SN identification}
\label{id}

The identification of low-redshift SN~Ia relies primarily on the {\bf
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 {\bf redshifted} beyond the wavelength range
{\bf of most optical spectrographs} and the classification of the
supernova has to rely on spectral features {\bf 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
photospheric SN~Ia and core-collapse supernovae in this redshift
range. The same regions can {\bf also} be used to identify possible
spectral peculiarities among {\bf 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-groups 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 {\bf that is} based on
quantitative measurements, this scheme helps in identifying the {\bf
SN type and, in the case of SNe~Ia, the sub-type.}


\begin{table*}[htb]
\begin{center}
\small
\caption[tableIaID]{{\bf A description of the} spectroscopic {\bf features used to type} SN  at z $\ge$ 0.5. Four wavelength regions are
selected for performing the SN {\bf 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$\tablenotemark{d}$&absent&weak or absent/broad$\tablenotemark{a,b}$&strong/broad&$\tablenotemark{h}$\\
`Si {\sc ii}' &3950-4100&evident/narrow$\tablenotemark{b}$&absent&absent&weak$\tablenotemark{a,b}$&absent& $\tablenotemark{e}$\\ 

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

\subsection{SN~2002fd: A 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, {\bf the spectrum of} SN~2002fd {\bf 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}
{\bf where it is} compared to other well known peculiar and normal
SN~Ia.  {\bf The `Ca~{\sc ii}~H\&K' feature in SN~2002fd is weaker
than the same feature in normal \bf SNe~Ia, but stronger than the same
feature in SN~1991T-like SNe~Ia}. The `Fe~{\sc ii}' and {\bf `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. {\bf This feature in SN~2002fd is intermediate in
strength to the stregth 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 {\bf the} extreme SN~1991T-like SNe and
normal SNe (e.g.  SN~1994D). {\bf 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 {\bf regions of strong telluric absorption}.}
\label{02fd}
\end{figure}

The increasing sample of supernova discovered in the local universe
tend to show that normal and peculiar slow-decliner SNe may not be two
different classes of objects but could form a `continuum'. 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 $z$ {\bf 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, {\bf 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) {\bf of all
high redshift SNe should be} SN~1991T/SN~1999aa-like SNe. The expected
number could be biased by different SNe search techniques and by the
strengthening evidence that spectroscopically SN~1991T/SN~1999aa-like
SNe do not always come with broad light curves and vice-versa, see for
example SN~1999ee, SN~2002cx or SN~1999aw. SN~2002fd {\bf is} the
first example of a SN~1991T/SN~1999aa-like supernova in the Hubble
flow, and {\bf its discovery demonstrates} that these objects are also
found at high-redshifts.  {\bf Of coarse}, larger data samples are
required to check whether the {\bf fraction of } peculiar
high-redshift SNe is consistent with that found in {\bf the local
Universe} or {\bf if there is evolution in the relative fractions
with redshift.}

\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 local
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{{\bf 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 {\bf spectra} with {\bf
spectra} from a broad sample of local 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}).

\subsection{Velocities}
\label{vel}

{\bf For normal SNe~Ia}, the velocity of Ca~{\sc ii}~H\&K {\bf drops
rapidly}, from values around 22000 km/s {\bf before maximum light} to
14000 km/s {\bf at maximum light}. After maximum light, the {\bf rate
of decrease slows} and the velocity decreases by about 4000 km/s in 50
days.  In Fig.~\ref{ca_vel} the solid line indicates the average trend
for Ca~{\sc ii}~H\&K time evolution computed using a large data set of
local normal type Ia supernovae. The gray band shows the {\it rms} of
the data set around the empirical model.

{\bf The inferred expansion velocity of the ejecta in under-luminous
SNe is lower {\bf 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$6355 absorption feature {\bf where} differences of more
than 2000 km s$^{-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, {\bf 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-z SNe are similar to 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 {\bf velocities are measured by} performing an error-weighted
non-linear {\bf least-sqaures} fit to the whole line profile. {\bf The
line profile is modelled with a Gaussian and the contiuum over the
width of the line is modelled as a straight line.} All the SNe in our
data set where measured, with the exception of SN~2001gk, for which
the line profile {\bf is} incomplete, and SN2001go at +29 days, for
which the signal to noise {\bf 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. {\bf For} SN~2001ha and
SN~2001hc, we could not identify {\bf host galaxy lines}, so their
redshifts were estimated by comparing {\bf their spectra} with {\bf
the spectra of nearby SNe~Ia}. In these cases the uncertainty is {\bf
increased} to 3000 km/s. {\bf These uncertainties dominate
the uncertainties from the fit. The two are added in quadrature to
compute the total uncertainty.}

{\bf 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 represets 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 -- {\bf there is a bias
against discovering} SN~1991bg-like SNe.  Thus, the lack of any such
SNe in our high-redshift SNe sample is {\bf not unexpected}.

\begin{figure}
\centering \includegraphics[width=8cm]{CaII_vel.eps}
  \caption{{\bf 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 local SNe. The dashed and dotted
  lines indicate the values of {\bf 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 local normal {\bf SNe~Ia}. The gray
  band shows the {\bf dispersion (1 standard deviation)} of the data
  about the average {\bf trend}.}
  \label{ca_vel}
\end{figure}

\subsection{Equivalent Widths}
\label{ew}

Equivalent width ({\sc ew}) time evolution measurements have been
empirically shown to be excellent means to study the spectral homogeneity 
of SNe~Ia and to provide reliable indicators of SN~Ia intrinsic brightness  
\citep{folatelliew}.
We have compared {\sc ew}s of high-redshift SNe
with those of local supernovae in search for evidence of evolution. 
The spectra of the high-redshift supernovae
generally cover wavelength regions 1 to 5 in the definition of
\citet{folatelliew}. These are the regions 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
only on three strong absorption features: ``Mg~{\sc ii}~4300'',
``Fe~{\sc ii}~4800'' and ``Ca~{\sc ii}~H\&K''. Figures~\ref{fig:MgII},
\ref{fig:FeII} and \ref{fig:CaHK} show the measurements of our
high-redshift SNe compared to the time evolution of local SNe.  In
Figs. \ref{fig:MgII} and \ref{fig:FeII} the solid line indicates the
identified empirical model for the {\sc ew} time evolution of normal
SNe~Ia, while the gray, filled region represent the 1-$\sigma$
confidence regions ($\sigma$ computed as {\it rms} on the average
model -- solid line -- as described in \citet{folatelliew}).  Note,
that the plotted errors in {\sc ew} include both the statistical
measurement uncertainties and the possible residual host galaxy
contamination left after the host galaxy subtraction procedure as
described in section \ref{data}. We assumed the latter to be about
10\%, and estimated the corresponding uncertainty in the {\sc ew} as
in \citet{folatelliew}.

The {\sc ew} time evolution of ``Mg~{\sc ii}~4300''
(Fig~\ref{fig:MgII}) shows a break at around one week after maximum
for most of the SNe. This is related to blending with ``Si~{\sc ii}
4000'' in coincidence with absorption deepening which makes the values
of {\sc ew} suddenly increase from $\sim$100\AA\ to $\sim$250\AA\ on
time scales of less than a week. The actual phase at which this break
takes place depends on the object characteristics: for under-luminous
SNe~Ia it seems to occur as early as 5 days before maximum light,
while normal SNe~Ia show this behavior around one week after maximum
light, and SN~1991T/SN~1999aa-like objects show it later than day
$+10$. Thus, the ``Mg~{\sc ii}~4300'' results to be useful to
discriminate among the different type Ia sub-classes. The {\sc ew}
values for our high-redshift supernovae (all SNe in table
\ref{tabledata} could be measured but SN~2002gi) are consistent with
corresponding local supernova values within 2-$\sigma$. Moreover,
SN~2001go, for which the measurements of three epochs are available,
shows the typical break at around one week after maximum as most of
the local normal SNe. Note, that some of the values prior to maximum
appear to be slightly higher than those of local SNe, although the
deviation is not statistically significant, as shown in the next
section.
\begin{figure}
%\centering \includegraphics[width=\hsize]{modelMg.sys.ps}
\centering \includegraphics[width=\hsize]{ewhz2.eps}
  \caption{`Mg~{\sc ii}~4300' {\sc ew} measurements of high-redshift
  supernovae presented in section \ref{data} compared with local SNe.
  The solid line indicates the empirical model for normal supernovae
  as described in \citet{folatelliew}. The gray filled regions,
  represents the 1-$\sigma$, confidence region ($\sigma$ computed as
  {\it rms} on the average model) Peculiar under-luminous SNe are shown
  separately for comparison.}
  \label{fig:MgII}
\end{figure}

 ``Fe~{\sc ii}~4800'' {\sc ew}s have a very smooth and homogeneous
time evolution for all kind of type Ia SNe (see Fig.~\ref{fig:FeII}).
{\sc ew} values increase from around 100\AA\ before maximum light to
350\AA\ two weeks after. All the measured SNe (those in table
\ref{tabledata} but SN~2001gu, SN~2001gw, SN~2001gy and SN~2002gi were
measured for which the absorption features was not easily
identifiable) are found well within the intrinsic spread of local
supernovae.
\begin{figure}
%\centering \includegraphics[width=\hsize]{modelFe.sys.ps}
\centering \includegraphics[width=\hsize]{ewhz1.eps}
  \caption{`Fe~{\sc ii}~4800' {\sc ew} measurements of high-redshift
  supernovae presented in section \ref{data} compared with local SNe.
  The solid line indicates the empirical model for normal supernovae
  as described in \citet{folatelliew}.The gray filled region
  represents the 1-$\sigma$ confidence regions ($\sigma$ computed as
  {\it rms} on the average model).}
  \label{fig:FeII}
\end{figure}

Fig.~\ref{fig:CaHK} shows the time evolution of ``Ca~{\sc ii}~H\&K''
{\sc ew}. The behavior is less homogeneous than that for the other two
features analyzed, especially before maximum light, therefore no
empirical model was identified in \citet{folatelliew}. In
Fig.~\ref{fig:CaHK} the trend of the {\sc ew} time evolution found for
most of normal and fast decliner SNe is indicated, for clarity, by a
gray-filled region. However, some out-layers are found among normal SNe
and are indicated by the small diamond symbol. The overall intrinsic
spread of {\sc ew} values is the largest among the features analyzed
in this work. However, before maximum light, peculiar SN~1991T-like
objects show systematically low values, indicated by the small square
symbols. The high-redshift supernovae values (all SNe in Table
\ref{tabledata} were measured but SN~2002gi) do not show significant
deviations with respect to those of the local sample shown in the
plot.

%A statistical comparison between {\sc ew} of high-$z$ and low-$z$
%supernova the analyzed spectral features is carried out in section
%\ref{stat}.
\begin{figure}
\centering \includegraphics[width=\hsize]{ewhz3.1.eps}
  \caption{`Ca~{\sc ii}~H\&K' {\sc ew} measurements of high-redshift
  supernovae presented in section \ref{data}. For comparison the {\sc
  ew} time evolution trend of local normal and under luminous SNe is
  indicated by the gray filled region. Among normal SNe, some show
  out-layer values which are indicated by the diamond symbol. Slow
  decliner SNe are indicated by the square symbol.}
  \label{fig:CaHK}
\end{figure}

%\begin{figure}
%\centering \includegraphics[width=\hsize]{SW.ps}
%  \caption{}
%  \label{fig:SWew}
%\end{figure}

%\section{Evolution: High-$z$ vs Low-$z$ }
\subsection{Statistical comparison}
\label{stat}
In this section, a quantitative -- statistical -- analysis of the
high-redshift SNe is performed using the spectral indicators described
in section \ref{ew}.
%Furthermore, we compare the {\sc ew} measurements with what
%theoretical expected from a population drift of high-redshift
%supernova progenitors.
%\subsection{Empirical Models}
%\label{Empirical}
\citet{folatelliew} identified empirical models to describe the time
evolution of {\sc ew} for `Fe~{\sc ii} 4800' and `Mg~{\sc ii} 4300'
features in normal -- low redshift -- supernovae. These models can be
used to test if high-redshift supernovae {\sc ew}'s follow the same
evolution trends as local SNe. The results of a $\chi^{2}$ test is
shown in Table \ref{emdata}. The empirical models derived from local
supernovae and high-redshift SNe data are plotted in Figs.
\ref{fig:MgII} and \ref{fig:FeII}. 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} 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 well described by the
same model as for local normal supernovae is statistically more
significant that them being consistent with under-luminous SNe. Note
however, that the statistical significance of our SNe being as local
normal SNe is lower for `Mg~{\sc ii} 4300' than for `Fe~{\sc ii} 4800'
because of the slightly higher than average {\sc ew} values measured
prior to maximum light.

\begin{table}[htb]
\begin{center}
\small
\caption{Result of the $\chi^{2}$ test comparing {\sc ew} measurements
of high-redshift SNe with the models described is section
\ref{measurements} 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\tablenotemark{1}\\
\hline
\end{tabular}
\tablenotetext{1}{Formally, this probability
is $<10^{-74}$. However, this assumes ideal conditions.} 
\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 local
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}
By means of {\sc ew} measurements we can make statistical tests of our
qualitative classification of SN~2002fd. Prior to maximum light, {\sc
ew} measurements of Ca~{\sc ii}~H\&K shown in Fig. \ref{fig:CaHK}, are
useful to separate peculiar SN~1991T/SN~1999aa-like SN~Ia from
normals. If the identification of SN~2002fd as a peculiar object is
correct, we expect the {\sc ew} value to be lower than the average for
normal SNe. The average {\sc ew} prior to light curve maximum in
normal SNe is $<${\mbox{{\sc ew}}}$>$ = 114.06. The measured scatter
around the mean value is $\sigma_{<{\mbox{\scriptsize {\sc ew}}}>}$=
14.16.  For peculiar SN~1991T/SN~1999aa-like SNe we find
$<${\mbox{{\sc ew}}}$>$ = 68.69 and $\sigma_{<{\mbox{\scriptsize {\sc
ew}}}>}$ = 6.08. The value measured for SN~2002fd (${\mbox{{\sc ew}}}$ =
73.60 $\pm$ 2.90) is consistent -- within one standard deviation --
with what was found for peculiar objects.

%Furthermore, comparing the measurements obtained for SN~2002fd with
%that a the same epoch of SN~1991T ($ ew $ = 79.16 $\pm$ 1.46)) we
%found that they are consistent within 2$\sigma$.

\section{Summary and Conclusions}
\label{conc}
Spectroscopic data of 12 high-redshift supernovae, in the redshift
range $z$=0.212 to 0.912 were analyzed and a qualitative
classification scheme proposed to classify high-redshift SN~Ia. 

Based on this classification scheme all our SNe, but one, were
classified as normal type Ia. SN~2002fd ($z$=0.279) showed weaker
Ca~{\sc ii}~H\&K, Si~{\sc ii}~$\lambda$4000, S~{\sc ii}~`W' and
Si~{\sc ii}~$\lambda$6355 consistently with what observed in
SN~1991T/SN1999aa-like objects in the local universe. This
classification was confirmed by means of the {\sc ew}
measurements. Prior to maximum light, Ca~{\sc ii}~H\&K {\sc ew}s show
a clear distinction between the values typically found for normal and
SN~1991T/SN1999aa-like SNe. The value measured for SN~2002fd ($
{\mbox{{\sc ew}}} $ = 73.60 $\pm$ 1.89) results consistent with that
of SN~1991T/SN~1999aa-like object ($< {\mbox{{\sc ew}}} >$ = 68.69,
$\sigma_{< {\mbox{\scriptsize {\sc ew}}} >}$ 6.08).

A first quantitative comparison between low and high-redshift SN~Ia
by means of spectral indicators is presented. Measurements of the
expansion velocities as inferred from the minimum of Ca~{\sc ii}~H\&K
for the high-redshift supernovae are compared with those of local SNe
with the aim to point out possible evolution effects. No signs of
evolution with redshift were found in the spectral
characteristics. Equivalent widths values and time evolution for the
regions we labeled ``Fe~{\sc ii} 4800'', ``Mg~{\sc ii} 4300'' and
``Ca~{\sc ii}~H\&K'' are also found within the intrinsic distribution
of nearby supernovae.  Furthermore, by means of a $\chi^2$ test,
high-redshift SNe data are found statistically consistent with the
empirical models describing the time evolution of ``Fe~{\sc ii}
4800'', ``Mg~{\sc ii} 4300'' {\sc ew}'s \citep{folatelliew} for local
normal SNe.

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}