MCMC determination of the cosmic UV background at $z\simeq 0$ from
  H$\alpha$ fluorescence
  In a recent paper (Fumagalli et al. 2017) we reported on the detection of a
diffuse H$\alpha$ glow in the outskirts of the nearby, edge-on disc galaxy UGC
7321 observed with the Multi Unit Spectroscopic Explorer (MUSE) at the ESO Very
Large Telescope. By interpreting the H$\alpha$ emission as fluorescence arising
from hydrogen ionised by an external (i.e., extragalactic) radiation field, we
estimated the UV background (UVB) intensity in terms of HI ionisation rate (per
ion) at $z\simeq 0$ to be in the range $\Gamma_{\rm HI}\sim 6-8\times 10^{-14}$
s$^{-1}$. In the present work, by performing radiative transfer calculations
over a large set of models of the gaseous disc of UGC 7321, we refine our
estimate and through an MCMC analysis derive a value for the photoionisaton
rate of $\Gamma_{\rm HI}=7.27^{+2.93}_{-2.90}\times 10^{-14}$ s$^{-1}$. In
particular, our analysis demonstrates that this value is robust against large
variations in the galaxy model and that the uncertainties are mainly driven by
the errors associated with the observed H$\alpha$ surface brightness. Our
measurement is consistent with several recent determinations of the same
quantity by a completely independent technique (i.e., flux decrement analysis
of the Ly$\alpha$-forest), and support the notion that the low redshift UVB is
largely dominated by active galactic nuclei (AGNs), possibly with no need of
further contribution from star forming galaxies.
