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In a recent paper (Fumagalli et al. 2017) we reported on the detection of adiffuse H$\alpha$ glow in the outskirts of the nearby, edge-on disc galaxy UGC7321 observed with the Multi Unit Spectroscopic Explorer (MUSE) at the ESO VeryLarge Telescope. By interpreting the H$\alpha$ emission as fluorescence arisingfrom hydrogen ionised by an external (i.e., extragalactic) radiation field, weestimated the UV background (UVB) intensity in terms of HI ionisation rate (perion) 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 calculationsover a large set of models of the gaseous disc of UGC 7321, we refine ourestimate and through an MCMC analysis derive a value for the photoionisatonrate of $\Gamma_{\rm HI}=7.27^{+2.93}_{-2.90}\times 10^{-14}$ s$^{-1}$. Inparticular, our analysis demonstrates that this value is robust against largevariations in the galaxy model and that the uncertainties are mainly driven bythe errors associated with the observed H$\alpha$ surface brightness. Ourmeasurement is consistent with several recent determinations of the samequantity by a completely independent technique (i.e., flux decrement analysisof the Ly$\alpha$-forest), and support the notion that the low redshift UVB islargely dominated by active galactic nuclei (AGNs), possibly with no need offurther contribution from star forming galaxies.

MCMC determination of the cosmic UV background at $z\simeq 0$ from H$\alpha$ fluorescence