We study neutrino oscillations and the level-crossing probability $P_{\mathrm{LSZ}}$ in power-law potential profiles $A\left(r\right)\mathrm{}\propto r^n.$ We give local and global adiabaticity conditions valid for all mixing angles $\vartheta$ and discuss different representations for $P_{\mathrm{LSZ}}.$ For the ${1/r}^3$ profile typical of supernova envelopes we compare our analytical to numerical results and to earlier approximations used in the literature. We then perform a combined likelihood analysis of the observed SN 1987A neutrino signal and of the latest solar neutrino data, including the recent SNO CC measurement. We find that, unless all relevant supernova parameters (released binding energy, ${\overline{\nu }}_e$ and ${\overline{\nu }}_{\mu ,\tau }$ temperatures) are near their lowest values found in simulations, the status of large mixing type solutions deteriorates considerably compared to fits using only solar data. This is sufficient to rule out the vacuum-type solutions for most reasonable choices of astrophysics parameters. The LOW solution may still be acceptable, but becomes worse than the SMA-MSW solution which may, in some cases, be the best combined solution. On the other hand the LMA-MSW solution can easily survive as the best overall solution, although its size is generally reduced when compared to fits to the solar data only.

• Received 22 August 2001

DOI:https://doi.org/10.1103/PhysRevD.65.073016