A novel algebraic criterion for the Bisognano-Wichmann property of one-particle nets was recently found by V. Morinelli. In this talk I will explain how to apply this criterion to the case of massless, integer spin particles using the Mackey subgroup theorem. In the next step the result will be lifted from the one-particle nets to Haag-Kastler nets using the assumption of asymptotic completeness. The argument relies on scattering theory of massless particles due to Buchholz and its recent simplifications. Also ideas from the massive case, which had been solved by Mund, enter into the discussion. This is a joint project with Vincenzo Morinelli.