The Physics of the Nebular Phase in Black Hole X-ray Binaries: Modelling V404 Cygni
Some of the most extreme galactic black hole transients exhibit a nebular phase at the end of their outbursts. This stage was first identified in the 2015 outburst of V404 Cygni, when it dominated the optical spectrum for ~4 days. It is characterised by exceptionally strong optical emission lines, together with a significant increase in the Balmer decrement. The emission features show broad wings reaching velocities consistent with outflow speeds derived from prominent P-Cygni profiles that preceded the nebular phase. They are thus interpreted as arising from previously launched ejecta that expand and recombine as X-ray irradiation declines. In this work, we modelled this phase using the photoionisation code Cloudy. Adopting simple assumptions for the irradiating continuum and emitting gas, we quantitatively reproduced key observables, such as the Balmer decrement and the H$\alpha$ equivalent width, and qualitatively reproduced the observed spectra. Our simulations show that the Balmer decrement remains roughly stable within the observed range across orders-of-magnitude changes in the density and ionisation parameter, spanning $n_\mathrm{H} \sim 10^{10.5}-10^{12.5}\,\text{cm}^{-3}$ and $-1.5 \lesssim \log\xi \lesssim 1$. This supports the scenario in which the nebular phase can persist through moderate ejecta expansion and cooling, consistent with observations. Finally, we used different approaches to constrain the general properties of the nebular phase, which we propose is produced by clumpy, partially ionised ejecta whose total mass likely exceeds the mass accreted during the outburst.