The discovery of a system of Herbig-Haro objects ejected by young, low mass stars in the &sigma Orionis region (Reipurth et al. 1998) has given rise to models of the photoionization of a neutral jet by an external source. We present long-slit spectra of high spectral resolution of HH 444 and numerical simulations for this Herbig-Haro object using ``yguazú'', a 3D gasdynamic +radiative transfer code (Raga et al. 1999). We find that a velocity profile in the jet beam is necessary to explain the observed accelaration in the position-velocity diagram of the HH jet. We also need also assume a non-zero opening angle at the base of the jet to explain the decreasing H α intensity at increasing distances from the source and a variable ejection velocity to reproduce the well separated knots observed along the jet.