Panel a) shows the radial distribution of opposite polarity flux as a fraction of the net flux |B_z|  from the SOT/SP observations. Panel b) displays the radial distribution of opposite polarity flux for the MHD simulation. Panel c) corresponds to opposite flux from inversions of synthesized Stokes profiles from the MHD simulation which was degraded with a Gaussian of width. Black, blue, and red curves correspond to log τ = 0.0, log τ = −0.9, and log τ = −2.5, respectively. Solid and dashed curves in panel (d) display the numbers of pixels where (ΔB/ Δlog τ)_0.0,−2.3 < 0 at native and degraded spatial resolution in the MHD simulation, respectively. Dotted vertical lines in all the panels indicate the umbra-penumbra boundary and the outer boundary of the sunspot.