Post-Asymptotic-Giant-Branch Age and Shell Budget of Hen 2-104, the Southern Crab

This paper computes a self-contained budget for Hen 2-104 from published observational values, with every derived number produced by the deposited computation script. Hen 2-104, the Southern Crab Nebula, is a bipolar nebula with an outer hourglass and an inner set of crab-like legs, associated with a symbiotic Mira system. Its expansion speeds are high for a planetary-nebula-like object, reflecting the influence of the interacting binary. The outer lobes provide a radius and a speed, hence a dynamical age, while the density in the lobes gives a shell mass that can be set against the mass a Mira wind can deliver. The object tests how far single-star budget methods can be pushed when a companion is clearly involved. The headline results are: R_pc = 0.35; v_exp_km_s = 90; dynamical_age_yr = 3803; electron_density_cm3 = 800; thermal_pressure_Pa = 2.1e-10; ionised_mass_Msun = 0.208; kinetic_energy_J = 1.67e+39; emitting_volume_fraction = 0.05; sound_speed_km_s = 11.4; mach_number = 7.87. The lobe age is short despite the large physical size, because the expansion is fast. The shell pressure remains high, consistent with continuing shaping by fast outflows rather than a freely coasting shell. The mass budget is within the supply a long-lived Mira wind can provide, so the budgets alone do not demand an exotic ejection event, even though the geometry plainly records binary interaction. Distinguishing supply from shaping is the central lesson of this object. The calculation is presented with its inputs, relations and sensitivities stated openly, so that any revised distance, density or stellar parameter can be substituted and the verdict recomputed directly.