# Phillips relationship

For the Phillips relationship in labour-market economics, see Phillips curve.

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. It was originally discovered by American astronomer Bert W. Rust in 1974 and Soviet astronomer Yury P. Pskovskii in 1977. They found that the faster the supernova faded from maximum light, the fainter its peak magnitude was.[1][2][3]

This correlation was rediscovered in 1993 by M. Phillips during the course of the Calán/Tololo Supernova Survey.[4] It has been recast to include the evolution in multiple photometric bandpasses[5][6] and as a stretch in the time axis relative to a standard template.[7] The relation is typically used to bring any Type Ia supernova peak magnitude to a standard candle value.

It was 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 [8]

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

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

## References

1. ^ Rust, B. W. "The Use of Supernovae Light Curves for Testing the Expansion Hypothesis and Other Cosmological Relations" (PDF). [PhD thesis, University of Illinois].
2. ^ Pskovskii, Yu. P. (1977). "Light curves, color curves, and expansion velocity of type I supernovae as functions of the rate of brightness decline". Soviet Astronomy 21: 675. Bibcode:1977SvA....21..675P.
3. ^ Pskovskii, Yu. P. (1984). "Photometric classification and basic parameters of type I supernovae". Soviet Astronomy 28: 658–664. Bibcode:1984SvA....28..658P.
4. ^ 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.
5. ^ Hamuy, M., Phillips, M. M., Maza, J., Suntzeff, N. B., Schommer, R. A., & Aviles, R. 1995, Astronomical Journal, 109, 1
6. ^ Riess, A. G., Press, W. H., & Kirshner, R. P. 1996, AstrophysicsJournal, 473, 88
7. ^ Perlmutter, S. A., & et al. 1997, NATO ASIC Proc. 486: Thermonuclear Supernovae, 749
8. ^ Rosswog; Bruggen. High Energy Astrophysics.