= Solution
Using the stipulated $570\,\mathrm{nm}$ as a wavelength-density peak, <Wien's displacement law> gives
$$
\boxed{T_{\rm inferred}=\frac{0.002897}{570\times10^{-9}}\simeq5.08\times10^3\,\mathrm K.}
$$
This is a rough estimate from the supplied characteristic <wavelength>, not an accurate measurement of the Sun's <effective temperature>. The Sun emits a broad, approximately thermal visible <spectrum> and appears white outside the atmosphere; its familiar yellow appearance does not identify a monochromatic thermal peak. A photospheric <effective temperature> near $5770\,\mathrm K$ instead corresponds to a wavelength-density maximum near $502\,\mathrm{nm}$.<Sun colouring page by NASA Space Place>[Statement that the Sun emits all visible colours and appears white]{ref}<Solar physics facts by NASA Marshall>[Surface temperature approximately 5770 K]{ref}
The core must be much hotter to provide the <pressure> required for <hydrostatic equilibrium> and to sustain <nuclear fusion>. Outward <energy transport> through an opaque interior proceeds down a <temperature gradient>, by <radiative diffusion> and then <convection> through much of the outer envelope. The observable <photosphere> radiates to space at the temperature needed to carry the solar <luminosity>, $L_\odot=4\pi R_\odot^2\sigma T_{\rm eff}^4$; it is not an unobstructed view of the hot core. The printed core estimate above $20$ million degrees is also too high for the present Sun: the standard central <temperature> is about $1.56\times10^7\,\mathrm K$. This correction leaves the large core-to-surface contrast and its explanation intact.<Solar physics facts by NASA Marshall>[Central temperature approximately 15,600,000 K]{ref}
Back to article page
