A Linear Relation between the Color Stretch sBV and the Rising Color Slope s0*(B−V) of Type Ia Supernovae

Abstract

<p>Using data from the Complete Nearby (redshift <em>z</em>_host < 0.02) sample of Type Ia Supernovae (CNIa0.02), we find a linear relation between two parameters derived from the <em>B</em> − <em>V</em> color curves of Type Ia supernovae: the <em>color stretch</em> <em>s</em><em>BV</em> and the rising color slope <img alt="${s}_{0}^{* }(B-V)$"> after the peak, and this relation applies to the full range of <em>s</em><em>BV</em>. The <em>s</em><em>BV</em> parameter is known to be tightly correlated with the peak luminosity, especially for <em>fast decliners</em> (dim Type Ia supernovae), and the luminosity correlation with <em>s</em><em>BV</em> is markedly better than with the classic light-curve width parameters such as Δ<em>m</em>₁₅(<em>B</em>). Thus, our new linear relation can be used to infer peak luminosity from <img alt="${s}_{0}^{* }$">. Unlike <em>s</em><em>BV</em> (or Δ<em>m</em>₁₅(<em>B</em>)), the measurement of <img alt="${s}_{0}^{* }(B-V)$"> does not rely on a well-determined time of light-curve peak or color maximum, making it less demanding on the light-curve coverage than past approaches.</p>