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A planetary nebula combines a hot post-asymptotic-giant-branch stellar core, its ionized expelled envelope, neutral/molecular material and interstellar dust. Its ultraviolet-to-infrared spectral energy distribution is therefore not a single-temperature blackbody. The principal components are:

The observed mixture also contains attenuation by internal and foreground interstellar extinction. A spectrum containing all these components need not spatially coincide: stellar light, ionized gas, dusty clumps and the molecular envelope sample different regions.

At $T=100\mathrm{K}$ with $\mu =2.3$, $c_s=\sqrt{k_{B}T/(\mu m_p)}\simeq 599\mathrm{m}{\mathrm{s}}^{-1}$. A solar-mass Keplerian disk has $v_K\simeq 29.8\mathrm{km}{\mathrm{s}}^{-1}$ at $1\mathrm{AU}$, so $\boxed{h/r\simeq 0.020}$: the thin-disk approximation is consistent.

For fixed central mass, $h/r\propto T^{1/2}{r}^{1/2}$. If $T\propto r^{-q}$, thenA flared outer disk intercepts more stellar radiation than a flat or self-shadowed disk, affecting its temperature, chemistry, vertical structure and observed spectral energy distribution. Heating changes the sound speed and therefore transport and dispersal; it can also enhance irradiation-driven mass loss. The actual coupled evolution depends on optical properties and transport, so flaring alone does not fix a unique lifetime. “Mid-planet” in the source is read as mid-plane.

A continuum peak gives a color temperature through Wien's law, provided the continuum is approximately Planckian and extinction is corrected. Broad-band colors or a fitted spectral energy distribution compare flux ratios with model atmospheres; they require a reddening estimate, abundance and gravity assumptions, and calibrated passbands. Spectroscopic line ratios or excitation/ionization balances provide another thermometer, requiring atomic data and a suitable atmosphere model, often local thermodynamic equilibrium.

For this cool giant, line blanketing and molecular absorption substantially distort a simple continuum peak, so Wien's law is the least reliable of these approximations. A detailed spectroscopic analysis, checked against a multi-band atmosphere fit, would generally be the strongest of the three if good data and model parameters are available. There is no unconditional accuracy ranking without measurement errors and model systematics; an accurately measured angular diameter plus bolometric flux would offer a more direct effective-temperature determination, if obtainable.

The spectral energy distribution of a planetary nebula combines hot central-star radiation, nebular free-free/free-bound/two-photon continua, recombination and collisionally excited lines, infrared dust emission and sometimes molecular emission. Ionizing-photon supply, gas thermal/ionization balance, density, composition, geometry and extinction determine their relative strengths. A line-dominated broad-band flux is not by itself a continuum temperature measurement.

A radiation spectrum whose spectral flux density follows a power law over a stated frequency range. For $F_{\nu }\propto {\nu }^{-\alpha }$, the spectral energy distribution satisfies $\nu F_{\nu }\propto {\nu }^{1-\alpha }$. Thus $\alpha =1$ gives equal energy flux in equal logarithmic frequency intervals. A spectral break invalidates extrapolation with a single index.