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Recent studies on the environmental dependence of Type Ia supernova (SN Ia)luminosity focus on the local environment where the SN exploded, consideringthat this is more directly linked to the SN progenitors. However, there is adebate about the local environmental, specifically local star formation rate(SFR), dependence of the SN Ia luminosity. A recent study claims that thedependence is insignificant ($0.051 \pm 0.020$ mag; $2.6\sigma$), based on thelocal SFR measurement by fitting local $ugrizy$ photometry data. However, wefind that this photometric local SFR measurement is inaccurate. We argue thisbased on the theoretical background of SFR measurement and the methodology usedto make that claim with their local $ugrizy$ photometry data, especially due toa limited range of extinction parameters used when fitting the data. Therefore,we re-analyse the same host galaxies with the same fitting code, but with morephysically motivated extinction treatments and global $ugriz$ photometry ofhost galaxies. We estimate global stellar mass and SFR. Then, local starformation environments are inferred by using the method which showed that SNeIa in globally passive galaxies have locally passive environments, while thosein globally star-forming low-mass galaxies have locally star-formingenvironments. We find that there is significant local environmental dependenceof SN Ia luminosities: SNe Ia in locally star-forming environments are$0.072\pm0.021$ mag ($3.4\sigma$) fainter than those in locally passiveenvironments, even though SN Ia luminosities have been further corrected by theBBC method that reduces the size of the dependence.

Reconsidering photometric estimation of local star formation environment and its correlation with Type Ia Supernova luminosity