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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces {\relax \fontsize  {7}{8}\normalfont  {\bf  (a) Left Panel:} The SCP SN Ia Hubble diagram broken into host galaxy types from Sullivan et al.\ (2003). The SNe in elliptical hosts (filled red circles) show significantly less dispersion, $\sigma = 0.16$ mag, including measurement error. (This ground-based measurement error for this $z \sim 0.5$ sample is quite close to the HST measurement error at $z>1$ in this proposal.) {\bf  (b) Right Panel:} The comparison of the Hubble diagram, before and after extinction correction, for a mixture of SNe Ia in all host types shows the dramatic increase in error bars due to the uncertainty in $B - V$ color being multiplied by $R_B \approx 4$ and by the uncertainty in $R_B$. The data shown is from the SCP (Knop et al.\ 2003) and the Riess et al.\ 2004 GOODS search samples. For the SNe at redshifts $z > 1$ this yields an uncertainty of $\sim $0.5 mag, which is consistent with the measured dispersion of 0.5 mag. The ratio of this dispersion to the elliptical-hosted dispersion of panel (a) makes the elliptical-hosted SNe each worth 9 of the extinction-corrected others.}}}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces {\relax \fontsize  {7}{8}\normalfont  {\bf  (a) Left Panel:} Simulated 68\% confidence region on $w^\prime $ vs $w_0$ for the current literature SN sample but with underlying cosmology ($w_0 = -1$; $w^\prime =0$). The parameters are poorly constrained because color errors are magnified by $R_B \approx 4$. {\bf  (b) Middle Panel:} The solid red contour shows reduced uncertainties (excluding systematic bias) using a Baysian prior on the extinction distribution prior to suppress color errors. If the errors are larger at high $z$ than at low $z$ (as with the actual data), this introduces systematic biases. The filled gray contour is from Riess {\it  et al.}\ 2004 using this prior. The short-dashed contour shows that this approach is also sensitive to shifts in $R_B$ with redshift; the example shifts from 4.1 to 2.6. {\bf  (c) Right Panel:} The goal of this proposal is shown as a confidence region for a simulated new sample of $\sim 10$ $z \mathrel {\raise 0.27ex\hbox {$>$}\kern -0.70em \lower 0.71ex\hbox {{$\scriptstyle \sim $}}}1$ SNe Ia found in cluster ellipticals, together with 5 in ellipticals from the past and ongoing GOODS searches, as well as 120 SNe Ia in ellipticals at the lower redshifts now being produced by the ground-based CFHT SN Legacy Survey, the CTIO Essence survey, and (at $z< 0.1$) the Nearby SN Factory. A SN Hubble diagram in ellipticals avoids the large statistical error problem of panel (a) and the large systematics problem of panel (b).}}}{3}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  {\relax \fontsize  {7}{8}\normalfont  FOCAS SPECTRUM HERE.} }}{4}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  {\relax \fontsize  {7}{8}\normalfont  The simulated data set for this proposal, with signal-to-noise at a given redshift and SN epoch based on our previous SN from ACS and NICMOS. The simulated data was fit with our lightcurve analysis program to test the cadence feasibility. We obtain typical errors of 0.07 to 0.13 mag for $0.9 < z < 1.5$, including the in the lightcurve timescale stretch correction uncertainty. The bars and symbols at top show the observing time period and scheduled observations for each cluster (with different cadences depending on the cluster $z$). The same symbols are used for the observations on the lightcurves, to show where a SN might be discovered and followed in its cluster's time window. Note that the observations are well spread throughout the year (allowing easy HST scheduling, with flexibility since there are other clusters to study if one is difficult to schedule). There are therefore SNe to be observed in our ground-based observing program at almost any time, in addition to the host galaxies that can be observed any time. } }}{5}}