A Linear Relation between the Color Stretch s <SUB> BV </SUB> and the Rising Color Slope {s}_{0}({*) }(B-V) of Type Ia Supernovae

Using data from the Complete Nearby (redshift z <SUB>host</SUB> < 0.02) sample of Type Ia Supernovae (CNIa0.02), we find a linear relation between two parameters derived from the B - V color curves of Type Ia supernovae: the color stretch s <SUB> BV </SUB> and the rising color slope ${s}_{0}^{* }(B-V)$ after the peak, and this relation applies to the full range of s <SUB> BV </SUB>. The s <SUB> BV </SUB> parameter is known to be tightly correlated with the peak luminosity, especially for fast decliners (dim Type Ia supernovae), and the luminosity correlation with s <SUB> BV </SUB> is markedly better than with the classic light-curve width parameters such as Δm <SUB>15</SUB>(B). Thus, our new linear relation can be used to infer peak luminosity from ${s}_{0}^{* }$ . Unlike s <SUB> BV </SUB> (or Δm <SUB>15</SUB>(B)), the measurement of ${s}_{0}^{* }(B-V)$ 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.