A Definitive Measurement of Time Dilation in the Spectral Evolution of the Moderate-Redshift Type Ia Supernova 1997ex

We have obtained high-quality Keck optical spectra at three epochs of the Type Ia supernova 1997ex, whose redshift z is 0.361. The elapsed calendar time between the first two spectra was 24.88 d, and that between the first and third spectra was 30.95 d. In an expanding universe where 1 + z represents the factor by which space has expanded between the emission and detection of light, the amount of aging in the supernova rest frame should be a factor of 1/(1 + z) smaller than the observed-frame aging; thus, we expect SN 1997ex to have aged 18.28 d and 22.74 d between the first epoch and the second and third epochs, respectively. The quantitative method for determining the spectral-feature age of a SN Ia, developed by Riess et al. (1997), reveals that the corresponding elapsed times in the supernova rest frame were 16.97 ±2.75 d and 18.01 ±3.14 d, respectively. This result is inconsistent with no time dilation with a significance level of 99.0%, providing evidence against “tired light ” and other hypotheses in which no time dilation is expected. Moreover, the observed timescale of spectral evolution is inconsistent with that expected in the “variable mass theory. ” The result is within ∼1σ of the aging expected from a universe in which redshift is produced by cosmic expansion. Subject headings: stars: supernovae: individual (SN 1997ex) — cosmology: observations – 3 – 1.