# Phillips relationship

In astrophysics, the Phillips relationship is the relationship between the peak luminosity of a Type Ia supernova and the speed of luminosity evolution after maximum light.[1] During the course of the Calán/Tololo Supernova Survey, Mark M. Phillips discovered that the faster the supernova faded from maximum light, the fainter its peak magnitude was. It has been recast to include the evolution in multiple photometric bandpasses[2][3] and as a stretch in the time axis relative to a standard template.[4] The relation is typically used to bring any Type Ia supernova peak magnitude to a standard candle value.

It was originally defined as the decline in the B-magnitude light curve from maximum light to the magnitude 15 days after B-maximum, a parameter he called $\Delta{m}_{15}$. The relation states that the maximum intrinsic B-band magnitude is given by [5]

$M_\mathrm{max}(B) = -21.726 + 2.698 \Delta m_{15} (B).$

The original $\Delta{m}_{15}$ definition drawn by Phillips around 1995.

## References

1. ^ Phillips, M. M. (1993). "The absolute magnitudes of Type IA supernovae". Astrophysical Journal Letters 413 (2): L105–L108. Bibcode:1993ApJ...413L.105P. doi:10.1086/186970.
2. ^ Hamuy, M., Phillips, M. M., Maza, J., Suntzeff, N. B., Schommer, R. A., & Aviles, R. 1995, Astronomical Journal, 109, 1
3. ^ Riess, A. G., Press, W. H., & Kirshner, R. P. 1996, AstrophysicsJournal, 473, 88
4. ^ Perlmutter, S. A., & et al. 1997, NATO ASIC Proc. 486: Thermonuclear Supernovae, 749
5. ^ Rosswog & Bruggen. High Energy Astrophysics.