  There is an ongoing debate about the nature of the bosonic excitations
responsible for the quasiparticle self energy in high temperature
superconductors -- are they phonons or spin fluctuations? We present a careful
analysis of the bosonic excitations as revealed by the `kink' feature at 70 meV
in angle resolved photoemission data using Eliashberg theory for a d-wave
superconductor. Starting from the assumption that nodal quasiparticles are not
coupled to the $(\pi,\pi)$ magnetic resonance, the sharp structure at $70 $meV
can be assigned to phonons. We find that not only can we account for the shifts
of the kink energy seen on oxygen isotope substitution but also get a
quantitative estimate of the fraction of the area under the electron-boson
spectral density which is due to phonons. We conclude that for optimally doped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ phonons contribute $\sim 10$% and
non-phononic excitations $\sim 90$%.
