The excitations responsible for producing high-temperature superconductivity in the copper oxides have yet to be identified. Two promising candidates are collective spin excitations and phonons 1 . A recent argument against spin excitations is based on their inability to explain structures observed in electronic spectroscopies such as photoemission 2-5 and optical conductivity 6,7 . Here, we use inelastic neutron scattering to demonstrate that collective spin excitations in optimally doped La 2−x Sr x CuO 4 are more structured than previously thought. The excitations have a two-component structure with a lowfrequency component strongest around 18 meV and a broader component peaking near 40-70 meV. The second component carries most of the spectral weight and its energy matches structures observed in photoemission 2-5 in the range 50-90 meV. Our results demonstrate that collective spin excitations can explain features of electronic spectroscopies and are therefore likely to be strongly coupled to the electron quasiparticles.Since their discovery, considerable progress has been made in understanding the properties of the high-critical-temperature, T c , cuprate superconductors. We know, for example, that the superconductivity involves Cooper pairs, but with d-wave rather than the s-wave pairing of conventional Bardeen-CooperSchrieffer (BCS) superconductors. One outstanding issue is the pairing mechanism itself. For conventional superconductors, identifying the bosonic excitations that strongly couple to the electron quasiparticles played a pivotal role in confirming the phonon-mediated pairing mechanism 8,9 . In the case of the copper oxide superconductors, electronic spectroscopies such as angle-resolved photoemission (ARPES) and infrared optical conductivity measurements 6,7 have revealed structures in the lowenergy electronic excitations, which may reflect coupling to bosonic excitations. ARPES measurements on Bi 2 Sr 2 CaCu 2 O 8 , Bi 2 Sr 2 CuO 6 and La 2−x Sr x CuO 4 have shown rapid changes or 'kinks' in the quasiparticle dispersion, E(k), for energies in the range 50-80 meV (refs 2-5). These features in ARPES have been interpreted in terms of coupling to phonon modes 5 . However, the ARPES measurements do not distinguish between coupling to lattice and spin excitations. Identifying phonons as the strongly coupled bosons is not without its difficulties: we must explain what is special about the phonons in the cuprates; interactions with phonons do not naturally explain other important properties of the cuprates, such as the large linear temperature dependence of the normal-state resistivity at optimal doping and the origin of d-wave symmetry of the superconducting gap itself.The interpretation of the kinks and other features in electronic spectroscopies 2-7 in terms of coupling to collective spin excitations 10 has been hampered by the lack of magnetic spectroscopy data. Most neutron scattering data refer to YBa 2 Cu 3 O 6+x , a compound for which ARPES data are scarce. Although ARPES kinks have also been re...