* Balmer lines are caused by electron transitions in hydrogen. Specifically, they arise from electrons transitioning from higher energy levels down to the n=2 energy level.
* Temperature dictates the electron energy levels in atoms. At extremely high temperatures, atoms are highly ionized and lose their electrons completely. At very low temperatures, electrons are mostly in the ground state (n=1).
* Stars around 3200 K are considered "cool" stars. Their temperatures are too low to excite many hydrogen atoms to the higher energy levels necessary for Balmer transitions.
So, why might we see hydrogen Balmer lines in cooler stars?
* There might be other elements present. While hydrogen Balmer lines are prominent in hotter stars, cooler stars might exhibit other spectral lines from elements like sodium or calcium.
* The presence of a companion. If the cooler star is part of a binary system with a hotter companion, the hotter star's light could excite the cooler star's hydrogen atoms and produce Balmer lines.
* Other spectral features. Cooler stars often have strong molecular bands, especially from titanium oxide (TiO), which can mask the Balmer lines.
In summary: While hydrogen Balmer lines are characteristic of hotter stars, they are generally not prominent in stars around 3200 K. The spectral features of cooler stars are dominated by other elements and molecules.
