= Thermal cutoff of Lyman-alpha line widths
{title2=$b_{\rm th}^2=2k_BT/m_{\rm H}$}
A purely thermal hydrogen <absorption line> has velocity-space optical depth proportional to $\exp[-(v-v_0)^2/b^2]$ with the displayed width. Additional independent Gaussian broadening contributes positive terms to $b^2$. Fitting the lower envelope of width against neutral-hydrogen <column density>, with numerical calibration for density and pressure smoothing, estimates the <temperature-density relation of photoionized intergalactic gas>. A single broad line only bounds the temperature from above when its nonthermal width is unknown.
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