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\begin{document}

\begin{frontmatter}

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\title{Low Redshift Type 1a Supernovae Calibration}

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\author{V.Prasad}

\address{E.O.Lawrence Berkeley National Laboratory, 
1 Cyclotron Road, Berkeley, CA~94720, USA}
\ead{vprasad@lbl.gov}

\begin{abstract}
The calibration of 20 supernovae discovered and observed by the
Supernova Cosmology Project and EROS collaboration in 1999 is
described.  Using novel calibration techniques, we calibrate the
supernova images in the Johnson-Cousins U, B, V, R and I bands
at the 1\% level.
\end{abstract}

\begin{keyword}
% keywords here, in the form: keyword \sep keyword
supernovae \sep photometric calibration \sep cosmology  
% PACS codes here, in the form: \PACS code \sep code
\end{keyword}

\end{frontmatter}

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Recent results by ~\cite{bib:riess} and ~\cite{bib:perlmutter} have
shown that type 1a supernovae (SNe1a) can, to some extent, be used as
standardizable candles to make cosmological measurements of the
acceleration of the universe.  While high-redshift SNe1a ($z>0.4$) are
used to determine the cosmological parameters, $\Omega_M$ and
$\Omega_{\Lambda}$, SNe1a at low redshifts are important in evaluating
the systematic uncertainties in the cosmological measurements,
determining the homogeneity of SNe1a and testing the linearity of the
Hubble Law.

The Supernova Cosmology Project and EROS collaboration discovered and
observed 20 supernovae at redshifts below 0.24 in 1999 and followed up
these observations with reference images of the host galaxies in 2000.
The 20 supernovae were initially classified as SNe1a, although
SN1999as has now been re-classified as a Hypernova
1c~\citep{bib:hatano}.  The supernovae were observed in the U, B, V, R
and I bands using 17 different instruments with about 25 images per
supernova per band, totalling $\sim$2600 images.  However, unlike most
other photometric measurements, calibration images were not taken on
all instruments and on all nights on which supernovae were observed.
As a result, an unconventional photometric calibration strategy is
employed to determine the supernovae lightcurves.  The rest of this
paper summarizes the calibration strategy used.


\section{Calibration Procedure}
\label{calibration}

\subsection{Identification of Objects and Flux Determination}
Before calibrating each image, we identify the objects (stars
and galaxies) in each image and determine their fluxes.  Objects are
identified using a neural network-based algorithm 
%and each object is required to be unsaturated, away from other objects and on at least
%80\% of all images of the same field.  
and the flux of each object is
determined by fitting the point-spread function (PSF) to a Moffat
distribution with image coordinates, $x$ and $y$, and fit parameters, $\sigma_x$, $\sigma_y$,
$\rho$ and $\beta$:

  \begin{equation}
     PSF(x,y) \sim (1 + \frac{1}{2}( \frac{x^2}{\sigma_{x}^2} + \frac{y^2}{\sigma_{y}^2} - 2\frac{\rho x y}{\sigma_x \sigma_y}))^{-\beta}.
  \end{equation}
%where $x$ and $y$ are the image coordinates and $\sigma_x$, $\sigma_y$,
%$\rho$ and $\beta$ are fit parameters.  
\vspace*{-0.5cm}
\subsection{Determination of Tertiary Standard Catalog}
\vspace*{-0.5cm}
Since calibration images were not taken on every night, it is necessary
to create a tertiary standard catalog of the absolute magnitudes of
the objects in each supernova field.  We convert the measured object
fluxes to absolute magnitudes using the relation:
\begin{equation}
  m_x  =  \tilde{m}_x + zp + \alpha_x \chi + \beta_x (m_x - m_y) 
\end{equation}
where $\tilde{m}_x$ is the flux measured in band $x$, $m_x$ and $m_y$
are the absolute magnitudes in bands $x$ and $y$, $\chi$ is the
airmass, $zp$ is the zero point term for the night and $\alpha_x$ and
$\beta_x$ are the extinction and filter correction terms for band $x$.
Using only supernova and calibration images from photometric nights on
which calibration images were taken, we perform a simultaneous fit in
2 bands to determine the absolute magnitude of the objects in the
supernova field, $zp$, $\alpha$ and $\beta$.  The absolute magnitudes
for objects in calibration fields are obtained from
\cite{bib:landolt}.  The fit requires $\beta$ to be the same for all
images on the same instrument and band, and $\alpha$ and $zp$ to be
the same for all images in the same instrument, band and night.

%should I include the values of the constants
As shown in Figure~\ref{fig:oldvnewcalib}, we reduce the statistical
uncertainties in the tertiary standard catalog and improve the
inter-telescope calibration by performing a simultaneous fit to a
large number of images on several telescopes.

\begin{figure}
\epsfig{file=/home/users/valp/talks/dust_talk/oldvnewcalib.eps,width=12cm}
\caption{Distribution of B Band Magnitude Residuals,
$M_{meas}-M_{fit}$, for supernova field stars using the current
calibration scheme (top) and for a calibration scheme where the
tertiary standard catalog was determined using the ESO telescope
alone.  Only nights on which calibration data was taken are
considered.}
\label{fig:oldvnewcalib}
\end{figure}

\subsection{Calibration of All Images}
Based on the absolute magnitudes in the tertiary standard catalog and
the measured fluxes, we determine the zero point, $zp_I$, for each image
and filter corrections, $\beta_{1,tel}$ and $\beta_{2,tel}$, for each
instrument using the relation:

  \begin{equation}
  \tilde{m_x} = m_x - zp_I - \beta_{1,tel,x} (m_x - m_y) - \beta_{2,tel,x} (m_x - m_y)^2 
  \end{equation}

Each instrument and band is calibrated separately.  To avoid the
effect of outliers, a data robustification scheme is used.  As shown
in Figure~\ref{fig:noncalfig}, the uncertainties in $zp_I$ and
$\beta_{1,tel}$ are $\sim$0.007 and $\sim$0.004, respectively.


\subsection{Determination of Supernova Lightcurves}
By applying the zero points and filter correction terms for each
image to the measured supernova fluxes and performing a simultaneous
fit in 2 bands, we determine the supernova absolute magnitudes as a
function of time.  The fit is iterated till the supernova lightcurve
converges.

%K-correction, no S-correction, fit yields stretch, peak magnitude. 

\begin{figure}
\epsfig{file=/home/users/valp/talks/dust_talk/noncal_fig.eps,width=12cm}
\caption{Top: V Band Magnitude Residuals for stars in the field of SN
1999au.  Bottom Left: Uncertainty in the zero points for all supernova
images.  Bottom Right: Uncertainty in the linear V-filter (B-V)
correction terms for all supernova images.  Quadratic filter
corrections terms are negligible except for the YALO and CFHT R bands.
Both nights with and without calibration data are considered.}
\label{fig:noncalfig}
\end{figure}

\section{Conclusions}
We have been able to calibrate the images of 20 nearby supernovae
discovered in 1999 at the 1\% level in the U, B, V, R and I bands.  We
look forward to lightcurves and results from this sample of
low-redshift SNe1a.


% Bibliographic references with the natbib package:
% Parenthetical: \citep{Alcock:2001} produces (Alcock et al 2001).
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\begin{thebibliography}{}

% \bibitem[]{} [Names(Year)]{label} or \bibitem[]{} [Names(Year)Long names]{label}.
% (\harvarditem{Name}{Year}{label} is also supported.)
% Text of bibliographic item

\bibitem[Riess et al (1998)]{bib:riess} Riess A.G. et al: 1998, AJ 116, 1009
\bibitem[Perlmutter et al (1999)]{bib:perlmutter} Perlmutter S. et al: 1999, ApJ 517, 586
\bibitem[Hatano et al (2001)]{bib:hatano} Hatano K. et al: 2001, AAS 33, 838 
\bibitem[Landolt (1992)]{bib:landolt} Landolt A.U..: 1992, AJ 104, 340

\end{thebibliography}

%%\begin{table}
%%    \centering
%%    \begin{tabular}{lcccc}
%% Telescope &  Filter & \multicolumn{2}{c}{Number of Nights} & Images \\  % Images=SN Images ONLY
%%           &         &   Calibration & SN Fields &    (SN)   \\ \hline
%%  CTIO 1.5m (3 setups) &   UBVRI &   25 &   23 &   537 \\
%%  CTIO 0.9m &   UBVRI &   7 &   7 &   132 \\
%%  ESO 1.5m &   UBVRI &   25 &   29 &   475 \\
%%  JKT &   UBVRI &   9 &   10 &   91 \\
%%  Lick 1m (3 setups) &   UBVRI &   28 &   34 &   655 \\
%%  YALO &   UBVRI &   0 &   44 &   456 \\
%%  ESO 3.6m&   UBVRI &   3 &   3 &   26 \\
%%  KPNO &   UBVRI &   2 &   3 &   121 \\
%%  CFHT &   UBVRI &   3 &   3 &   62 \\
%%  Keck &   R &   0 &   1 &   4 \\
%%  WIYN &   UBVRI &   1 &   6 &   49 \\ 
%%  Marly &   RI &   0 &   20 &   37 \\ 
%%  MLO &   U &   2 &   5 &   19 \\ \hline
%%  TOTAL &   UBVRI &   105 &   188 &   2664 \\ \hline
%%        &        &       &       &        \\
%%    \end{tabular}
%%    \caption{Summary of data in nearby supernovae sample}
%%    \label{tab:snimages}
%%\end{table}


\end{document}


