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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces  {\em  (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.) {\em  (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. }}{8}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces  {\em  (a) Left Panel:} Confidence region on the $w^\prime $ vs $w_0$ plane for a simulation matched to the current literature supernovae sample but with underlying cosmology ($w_0 = -1$; $w^\prime =0$). The parameters are quite poorly constrained because uncertainties in color measurement are magnified by $R_B \approx 4$. {\em  (b) Middle Panel:} To remedy this problem, one might try using a prior on the extinction distribution to be less sensitive to the color measurement and hence its large uncertainty as shown by the solid red contour. However this introduces systematic biases in the extinction correction, shown by the shift from the underlying cosmology (dashed contour), if the uncertainties are higher at high redshift than at low redshift as is the case with the actual data. The filled gray contour is the result reported in Riess et al 2004 using this extinction-prior approach. The short-dashed contour shows that this approach is also sensitive to shifts in the value of $R_B$ with redshift; the example shifts from 4.1 to 3.5. {\em  (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). }}{9}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces  {\em  (a) Left Panel:} Elliptical host supernovae at $z \mathrel {\raise 0.27ex\hbox {$>$}\kern -0.70em \lower 0.71ex\hbox {{$\scriptstyle \sim $}}}1$ will be found much more frequently in our cluster sample than in the field. The ratio $L_B/<L_B>$ of rest frame blue luminosity for early type galaxies with $z > 1$ within an ACS FOV, relative to the average field value of this quantity, is plotted for clusters in our sample from the optically selected Red-sequence Cluster Survey (RCS - Gladders \& Yee 2004), the X-ray selected ROSAT Deep Cluster Survey (RDCS - Rosati et al.\ 1998), and the 4.5 micron selected Infrared Array Camera Shallow Survey (IRAC - Eisenhardt et al.\ 2004). \newline  {\em  (b): Right Panel:} The lower panel shows the redshift distribution of our cluster sample vs.\ the GTO clusters. Above that is the redshift distribution of the $\sim 10$ SNe that we expect to find in the elliptical galaxies of the clusters, and the distribution of the $\sim 10$ SNe that we will find in the field. Our observing strategy will yield lightcurves for {\it  both} samples of supernovae. }}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces  {\em  (a) Left Panel:} The dust-free nature of ellipticals (filled circles) and S0 galaxies (filled squares) in RX1252-29 at $z=1.23$ is supported by the small scatter of the color-magnitude relation. The relation for the Coma cluster, transformed to the observed bands with no evolution correction, is shown as a dot-dash line. The solid line is this relation at the redshift of RX1252 assuming WMAP cosmology and $-1.4$ mag of luminosity evolution. \newline  {\em  (b) Right Panel:} Scatter in rest frame $U-B$ CM relation for early-type galaxies in clusters as a function of redshift. In order of increasing redshift the points are from Bower et al.\ (1992), van Dokkum et al. (1998), Ellis et al.\ (1998), van Dokkum et al.\ (2000), Blakeslee et al.\ (2003), and van Dokkum et al.\ (2001). The dashed line is the average value, indicating no change with redshift in the scatter. }}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces  The simulated data set for this proposal, with signal-to-noise at a given redshift and SN epoch based on actual data from our previous SN photometry with HST ACS and NICMOS. The simulated data was fit with the lightcurve-fitting program of our actual analysis to test the feasibility of the chosen cadences. Even after propagating the uncertainty in the lightcurve timescale stretch used for correction, we obtain typical errors of 0.07 to 0.13 mag for a redshift range between 0.9 and 1.5. The bars at the top of the figure show the observing time period covered for each cluster, and the symbols show when observations are scheduled (with slightly different cadences depending on the redshift of the cluster). The same symbols are used for the observations on the lightcurves, to show where a supernova 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 during the year, in addition to the host galaxies that can be observed any time after the supernova is observed. }}{12}}