Cooling Timescale and Thermal Balance of the Eskimo Nebula NGC 2392

This paper computes a self-contained budget for NGC 2392 from published observational values, with every derived number produced by the deposited computation script. The Eskimo Nebula has a double-shell structure with a fast inner region and a measured expansion speed well above the typical ten to twenty kilometres per second of mature nebulae. Its thermal state is set by the competition between photoionisation heating and radiative cooling, dominated at ten thousand kelvin by collisionally excited forbidden lines. The cooling timescale computed from the electron density and a standard cooling coefficient states how quickly a parcel of gas would lose its thermal energy if heating ceased, and it is the natural clock against which the expansion time should b The headline results are: electron_density_cm3 = 3e+03; electron_temperature_K = 1.1e+04; cooling_coefficient_erg_cm3_s = 1e-22; cooling_time_yr = 0.481; expansion_age_yr = 3259; ratio_age_to_tcool = 6.77e+03; thermal_pressure_Pa = 9.11e-10. The cooling time is far shorter than the expansion time, so the gas temperature is regulated locally and promptly rather than carried along adiabatically. The sound-crossing and cooling clocks both run fast compared with the dynamical clock, which justifies treating the nebula as a photoionised structure in thermal balance at each radius. The high expansion speed therefore does not imply a thermally disturbed nebula; it implies a mechanically young shell that is nevertheless thermally settled. 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.