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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 Sulliven 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, Gibbons 2004) and the Riess 2004 GOODS search samples. For the SNe at redshifts $z > 1$ this yields an uncertainty of $\sim $0.5 mag, which is consistant with the measured dispersion of 0.5 mag. The ratio of this dispersion to the elliptical-hosted disperson of panel (a) makes the elliptical-hosted SNe each worth 9 (= $32$) 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 known 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 my 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 [[[CHECK]]] {\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 and 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). }}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces a couple of images of 1252-29; perhaps worth sending in a color image because there is the reasonable chance that the proposal will be viewed in color on a laptop by the panel members, as opposed to a greyscale printout. The first one is an HST ACS image of the central region, and the second is a ground-based image covering a larger area along with X-ray contours. }}{10}}
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces {\it  upper panel:} Relative uncertainty in the weak lensing mass estimate as a function of cluster redshift for a cluster with M=$5\times 10^{14}M_\odot $ and $10^{15}M_\odot $. The calculations assume that we can only use the shape measurements at $r>60"$, because of substructure in the cluster core. For some clusters we might be able to use the lensing signal at smaller radii, thus reducing the uncertainties. The average mass of the clusters in our sample is thought to be $\sim 5\times 10^{14} M_\odot $. The most massive clusters ($\sim 10^{15} M_\odot $) in the sample can be detected with high significance out to $z=1.4$. {\it  lower panel:} Relative error in the zero-point of the mass-observable (i.e., $M-T_X$, $M-L_X$, $M-$richness) relation in four independent redshift bins. The relative errors are $<15\%$, allowing us to constrain the evolution in cluster properties, especially once tied to the ongoing work at lower redshifts. The resulting accuracy is sufficient to enable cluster abundance studies out to $z\sim 1.4$!}}{11}}
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces  Figure XX?: 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 that these cadences will provide a final peak magntiude uncertainty for each SN that is below the intrinsic dispersion of 0.15 mag, even after propagating the uncertainty in the lightcurve timescale stretch used for calibration. 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}}