Calibrating the effective magnitudes of type Ia supernovae with a model-independent method

This research explores the correlation between the absolute magnitude and the redshift of type Ia supernovae (SNe Ia) with a model-independent approach. The Pantheon sample of SNe Ia and strong gravitational lensing systems (SGLS) are used. With the cosmic distance-duality relation (CDDR), the evolution parameter of the magnitude, the light curve parameters of SNe Ia, and the parameters of the SGLS geometric model are constrained simultaneously. Considering the consistency of the redshifts, we selected a subsample of SNe Ia in which the redshift of each SNe Ia is close to the corresponding redshift of the SGLS sample. Two parametric models are used to describe this evolution, which can be written as ${\delta }_M=ϵz$ and ${\delta }_M=ϵ\log (1+z)$, respectively. Our analysis reveals that $ϵ=-0.036_{-0.339}^{+0.357}$ in the first parametric model and $ϵ=-0.014_{-0.630}^{+0.588}$ in the second model, indicating that no significant evolution ($ϵ=0$) is supported at the $1\sigma$ confidence level in this study. These results represent a significant advancement in our understanding of the intrinsic properties of SNe Ia and provide important constraints for future SNe Ia study.

Figure 1

The green solid line represents the relation between the $\mathrm{\Delta }z$ and $z$ in $\mathrm{\Lambda }\mathrm{CDM}$ with $\mathrm{\Delta }d/d=5\%$. The orange solid line represents $\mathrm{\Delta }z=0.005$. The red squares indicate the absolute difference between the lens redshift of a SGLS and the redshift of a pair of SNe Ia. The blue triangles indicate the absolute difference between the redshift of the source of a SGLS and that of a paired SNe Ia.

Figure 2

The 2-D regions and 1-D marginalized distributions with $1\sigma$ and $2\sigma$ contours for the parameters $\alpha$, $\beta$, $f_e$, $ϵ$, $\gamma$, $m_{\mathrm{step}}$, and $\tau$ for parametric model of ${\delta }_M=ϵz$ (the red regions and the red curve) and ${\delta }_M=ϵ\log (1+z)$ (the green regions and the green curve).