Left panel: Color map of the ratio γ_esc/γ_MPD (base-10 logarithm) for the Lighthouse Nebula, as a function of the pulsar velocity, V_psr, and ambient number density, n_ISM. The solid black curve shows the relation we used to estimate n_ISM (pressure equilibrium at the bow shock standoff distance, d₀). The black point indicates the position of the system based on the best estimate (Pavan et al. 2014) of n_ISM: n_ISM = 0.1 cm⁻³, V_psr = 1300 km s⁻¹. The vertical lines mark the maximum value of V_psr that makes our model viable for n_ISM = 0.1 cm⁻³ (V_psr, max = 1300 km s⁻¹, dashed line) and n_ISM determined from V_psr and d₀ (V_psr, max = 1600 km s⁻¹, dash-dotted line). Right panel: Color map of ΔB as a function of V_psr and w_f (uncertainties on the source distance reflect on both quantities). The best values for the Guitar and the Lighthouse Nebula are represented as magenta and yellow circles, respectively. The upper and lower limits obtained for J2030+4415 are shown as blue downward and upward arrows, respectively. The horizontal blue line shows the current filament thickness.