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We present spectra of high-redshift supernovae (SNe) that were taken with the Subaru low-resolution optical spectrograph, FOCAS. These SNe were found in SN surveys with Suprime-Cam on Subaru, the CFH12k camera on the Canada-France-Hawaii Telescope, and the Advanced Camera for Surveys on the Hubble Space Telescope. These SN surveys specifically targeted $z >$1 Type Ia supernovae (SNe Ia). From the spectra of 39 candidates, we obtained redshifts for 32 candidates and spectroscopically identified 7 active candidates as probable SNe Ia, including one at $z =$1.35, which is the most distant SN Ia to be spectroscopically confirmed with a ground-based telescope. An additional 4 candidates were identified as likely SNe Ia from the spectrophotometric properties of their host galaxies. Seven candidates are not SNe Ia, either being SNe of another type or active galactic nuclei. When SNe Ia were observed within one week of the maximum light, we found that we could spectroscopically identify most of them up to $z =$1.1. Beyond this redshift, very few candidates were spectroscopically identified as SNe Ia. The current generation of super red-sensitive, fringe-free CCDs will push this redshift limit higher.

We present the first high-redshift Hubble diagram for Type II-P supernovae (SNe II-P) based on five events at redshift up to z ~ 0.3. This diagram was constructed using photometry from the Canada-France-Hawaii Telescope Supernova Legacy Survey and absorption-line spectroscopy from the Keck Observatory. The method used to measure distances to these supernovae is based on recent work by Hamuy & Pinto and exploits a correlation between the absolute brightness of SNe II-P and the expansion velocities derived from the minimum of the Fe II l5169 P Cygni feature observed during the plateau phases. We present three refinements to this method that significantly improve the practicality of measuring the distances of SNe II-P at cosmologically interesting redshifts. These are an extinction correction measurement based on the V-I colors at day 50, a cross-correlation measurement for the expansion velocity, and the ability to extrapolate such velocities accurately over almost the entire plateau phase. We apply this revised method to our data set of high-redshift SNe II-P and find that the resulting Hubble diagram has a scatter of only 0.26 mag, thus demonstrating the feasibility of measuring the expansion history, with present facilities, using a method independent of that based on supernovae of Type Ia.

A sample of 109 Type Ia supernovae (SNe Ia) with recession velocity [?]30,000 km s-1 is compiled from published SN Ia light curves to explore the expansion rate of the local universe. Based on the color parameter DC12 and the decline rate Dm15, we found that the average absorption-to-reddening ratios for SN Ia host galaxies are RUBVI = 4.37 +- 0.25, 3.33 +- 0.11, 2.30 +- 0.11, and 1.18 +- 0.11, which are systematically lower than the standard values in the Galaxy. We investigated the correlations of the intrinsic luminosity with light-curve decline rate, color index, and SN environmental parameters. In particular, we found that SNe Ia in E/S0 galaxies close to the central region are brighter than those in the outer region, which may suggest a possible metallicity effect on SN luminosity. The dependence of SN luminosity on galactic environment disappears after corrections for the extinction and DC12. The Hubble diagrams constructed using 73 Hubble flow SNe Ia yield a 1 s scatter of [?]0.12 mag in BVI bands and ~0.16 mag in U band. The luminosity difference between normal SNe Ia and peculiar objects (including SN 1991bg-like and SN 1991T-like events) has now been reduced to within 0.15 mag via DC12 correction. We use the same precepts to correct the nearby SNe Ia with Cepheid distances and found that the fully corrected absolute magnitudes of SNe Ia are MB = -19.33 +- 0.06 and MV = -19.27 +- 0.05. We deduced a value for the Hubble constant of H0 = 72 +- 6 (total) km s-1 Mpc-1.

We present measurements of the rates of high-redshift Type Ia supernovae derived from the Subaru/XMM-Newton Deep Survey (SXDS). We carried out repeated deep imaging observations with Suprime-Cam on the Subaru Telescope, and detected 1040 variable objects over 0.918 deg2in the Subaru/XMM-Newton Deep Field. From the imaging observations, light curves in the observed i′band are constructed for all objects, and we fit the observed light curves with template light curves. Out of the 1040 variable objects detected by the SXDS, 39 objects over the redshift range 0.2 < z< 1.4 are classified as Type Ia supernovae using the light curves. These are among the most distant SN Ia rate measurements to date. We find that the Type Ia supernova rates increase up to z∼ 0.8 and may then flatten at higher redshift. The rates can be fitted by a simple power law, rV(z) = r0(1 + z)αwith $r_0=0.20^{+0.52}_{-0.16}$(stat.)$^{+0.26}_{-0.07}$(syst.) × 10−4yr−1Mpc−3, and $\alpha =2.04^{+1.84}_{-1.96}$(stat.)$^{+2.11}_{-0.86}$(syst.).