We present ACS, NICMOS, and Keck AO-assisted photometry of 20 Type Ia supernovae (SNe Ia) from the HST Cluster Supernova Survey. The SNe Ia were discovered over the redshift interval 0.623 < z < 1.415. Fourteen of these SNe Ia pass our strict selection cuts and are used in combination with the world's sample of SNe Ia to derive the best current constraints on dark energy. Ten of our new SNe Ia are beyond redshift z = 1, thereby nearly doubling the statistical weight of HST-discovered SNe Ia beyond this redshift. Our detailed analysis corrects for the recently identified correlation between SN Ia luminosity and host galaxy mass and corrects the NICMOS zeropoint at the count rates appropriate for very distant SNe Ia. Adding these supernovae improves the best combined constraint on dark energy density, ρ DE (z), at redshifts 1.0 < z < 1.6 by 18% (including systematic errors). For a flat ΛCDM universe, we find Ω Λ = 0.729 +0.014 −0.014 (68% CL including systematic errors). For a flat wCDM model, we measure a constant dark energy equation-of-state parameter w = −1.013 +0.068 −0.073 (68% CL). Curvature is constrained to ∼ 0.7% in the owCDM model and to ∼ 2% in a model in which dark energy is allowed to vary with parameters w 0 and w a . Tightening further the constraints on the time evolution of dark energy will require several improvements, including high-quality multi-passband photometry of a sample of several dozen z > 1 SNe Ia. We describe how such a sample could be efficiently obtained by targeting cluster fields with WFC3 on HST.The updated supernova Union2.1 compilation of 580 SNe is available at http://supernova.lbl.gov/Union ⋆ is less than the mass threshold. We begin by noting that.We can then integrate this probability over all true host masses less than the threshold:⋆ )P (m true ⋆ ) up to a normalization constant found by requiring the integral to be unity when integrating over all possible true masses. P (m true ⋆ ) is estimated from the observed distribution for each type of survey. The SNLS (Sullivan et al. 2010) and SDSS (Lampeitl et al. 2010) host masses were assumed to be representative of untargeted surveys, while the mass distribution in Kelly et al. (2010) was assumed typical of nearby targeted surveys. As these distributions are approximately log-normal, we use this model for P (m true ⋆) using the mean and RMS from the log of the host masses from these surveys (with the average measurement errors subtracted in quadrature), giving log 10 P (m true ⋆ ) = N (µ = 9.88, σ 2 = 0.92 2 ) for untargeted surveys and log 10 P (m true ⋆ ) = N (10.75, 0.66 2 ) for targeted surveys. When host mass measurements are available, P (m obs ⋆ |m true ⋆ ) is also modeled as a log-normal; when no measurement is available, a flat distribution is used.For a supernova from an untargeted survey with no host mass measurement (including supernovae presented in this paper which are not in a cluster), P (m trueis the integral of P (m true ⋆ ) up to the threshold mass: 0.55. Similarly, nearby supernovae from targeted surveys w...

The systematic errors in the virial mass-to-light ratio, M v /L, of galaxy clusters as an estimator of the field M/L value are assessed. We overlay 14 clusters in redshift space to create an ensemble cluster which averages over substructure and asymmetries. The combined sample, including background, contains about 1150 galaxies, extending to a projected radius of about twice r 200 . The radius r 200 , defined as where the mean interior density is 200 times the critical density, is expected to contain the bulk of the virialized cluster mass. The dynamically derivedoverestimate is attributed to not taking into account the surface pressure term in the virial equation. Under the assumption that the velocity anisotropy parameter is in the range 0 ≤ β ≤ 2 / 3 , the galaxy distribution accurately traces the mass profile beyond about the central 0.3r 200 . There are no color or luminosity gradients in the galaxy population beyond 2r 200 , but there is 0.11 ± 0.05 mag fading in the r band luminosities between the field and cluster galaxies. We correct the cluster virial mass-to-light ratio, M v /L = 289 ± 50h M ⊙ / L ⊙ (calculated assuming q 0 = 0.1), for the biases in M v and mean luminosity to estimate the field M/L = 213 ± 59h M ⊙ / L ⊙ . With our self-consistently derived field luminosity density, j/ρ c = 1136 ± 138h M ⊙ / L ⊙ (at z ≃ 1 / 3 ), the corrected M/L indicates Ω 0 = 0.19 ± 0.06 ± 0.04 (formal 1σ random error and estimated potential systematic errors) for those components of the mass field in rich clusters.