Off-center observers versus supernovae in inhomogeneous pressure universes

Exact luminosity distance and apparent magnitude formulas are applied to Union2 557 supernovae sample in order to constrain possible position of an observer outside of the center of symmetry in spherically symmetric inhomogeneous pressure Stephani universes which are complementary to inhomogeneous density Lema\^itre-Tolman-Bondi (LTB) void models. Two specific models are investigated. The first which allows a barotropic equation of state at the center of symmetry with no scale factor function being specified (model IIA), and the second which has no barotropic equation of state at the center, but has an explicit dust-like scale factor evolution (model IIB). It is shown that even at $3\sigma$ CL, an off-center observer cannot be further than about 4.4 Gpc away from the center of symmetry which is comparable to the reported size of a void in LTB models with the most likely value of the distance from the center about 341 Mpc for model IIA and 68 Mpc for model IIB. The off-center observer cannot be farther away from the center than about 577 Mpc for model IIB at $3\sigma$ CL. It is evaluated that the best-fit parameters which characterize inhomogeneity are: $\Omega_{inh} = 0.77$ (dimensionless - model IIA) and $\alpha = 7.31 \cdot 10^{-9}$ $(s/km)^{2/3} Mpc^{-4/3}$ (model IIB).