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Fig. 1

image

Total cross-section (cyan) due to bound-bound and bound-free transitions in the isolated hydrogen atom around the Balmer limitλth, considering natural broadening (top), or including both natural broadening and Gaussian broadening for a thermal velocity of 15 m s −1 (bottom). The cross-section is normalized to its analytic value at the Balmer limit λth. At longer wavelengths, the actual continuum (blue curve), defined as the lower envelope of the bound-bound cross-section, deviates from the nominal quasi-continuum (almost-horizontal green curve that was computed by assuming the approximation of Eq. (10) to be valid at all wavelengths λ > λth). The orange vertical solid lines show the location of the Balmer limit λth. The blue vertical lines show the location at which the FWHM of spectral lines and the separation between consecutive spectral lines are equal (λt). In the bottom plot, this line is displaced to longer wavelength due to the additional broadening caused by the thermal velocity.

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