Zanstra method

The Zanstra method estimates a central star's effective temperature by comparing its observed nonionizing continuum with the absorbed ionizing-photon rate inferred from nebular recombination lines. If ${\Phi }_{E_0}(T)={\int }_{E_0/h}^{\infty }{B}_{\nu }(T)/(h\nu )d\nu$, then $[F_{\ell }/(h{\nu }_{\ell }{F}_{{\nu }_o,\ast })][\beta /{\alpha }_{\ell }^{\mathrm{eff}}]={\Phi }_{E_0}(T_s)/B_{{\nu }_o}(T_s)$ when the line traces the full appropriate ionizing budget. Both the distance and stellar radius cancel. Density inhomogeneity also cancels from the integrated recombination estimate when the coefficient ratio is known; photon leakage, dust and mixed-species transfer can invalidate the simple budget.