We present results from a deep Suzaku observation of the black hole in LMC X–1 , supplemented by coincident monitoring with RXTE .
We identify broad relativistic reflection features in a soft disc-dominated spectrum .
A strong and variable power-law component of emission is present which we use to demonstrate that enhanced Comptonisation strengthens disc reflection .
We constrain the spin parameter of the black hole by modelling LMC X–1 ’ s broad reflection features .
For our primary and most comprehensive spectral model , we obtain a high value for the spin : a _ { * } = 0.97 ^ { +0.01 } _ { -0.13 } ( 68 per cent confidence ) .
However , by additionally considering two alternate models as a measure of our systematic uncertainty , we obtain a broader constraint : a _ { * } = 0.97 ^ { +0.02 } _ { -0.25 } .
Both of these spin values are entirely consistent with a previous estimate of spin obtained using the continuum-fitting method .
At 99 % confidence , the reflection features require a _ { * } > 0.2 .
In addition to modelling the relativistically broadened reflection , we also model a sharp and prominent reflection component that provides strong evidence for substantial reprocessing in the wind of the massive companion .
We infer that this wind sustains the ionisation cone surrounding the binary system ; this hypothesis naturally produces appropriate and consistent mass , time , and length scales for the cone structure .