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

Abstract Using data from the Complete Nearby (redshift z host &lt; 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 BV and the rising color slope <?CDATA ${s}_{0}^{* }(B-V)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>B</mml:mi> <mml:mo>−</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> after the peak, and this relation applies to the full range of s BV . The s BV 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 BV is markedly better than with the classic light-curve width parameters such as Δ m 15 ( B ). Thus, our new linear relation can be used to infer peak luminosity from <?CDATA ${s}_{0}^{* }$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> . Unlike s BV (or Δ m 15 ( B )), the measurement of <?CDATA ${s}_{0}^{* }(B-V)$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>B</mml:mi> <mml:mo>−</mml:mo> <mml:mi>V</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> 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.