Histogram of the relative error in the single-star parallax (() resulting from the addition of surface brightness asymmetries for supergiant stars at different distances. The distribution for stars in the right panel (d > 5.5 kpc) closely reproduces the expected N(0,1). In the central panel (3.5 < d < 5.5 kpc), the distribution is wider with a best-fit N(0,2.5). Finally, for the left panel (d < 3.5 kpc) the σ of the distribution increases to four. Parameters of the Markov chain used here are σ_P = 0.09 AU and τ = 4 × 10⁶ s. The x-axes in the three panels are at the same scale.