KITP: crowd sourcing science

ok, I am mightily puzzled by a technical issue and if anyone knows the answer authoritatively, then cough it up:

question is, does the radial non-adiabatic pulsation of δ Scu/SX Phæ stars really not depend on Y?

there are some theoretical papers in the literature, notably Templeton's thesis papers, which find that the period and period ratio in the δ Scu strip is not sensitive to the helium abundance

the pulsational analysis uses Guenther's solar code, combined with the Yale Rotating Evolution Code

now high Y, helium rich stars, are hotter and more luminous at fixed mass and age, but their mean molecular weight is also higher

naively, I'd have thought the higher μ would push the density up and give higher pulsation frequencies, at fixed mass, but then the same mass star is hotter, so less dense?
Does this really compensate at the better than 1% level or am I missing something?

the observations are all over the place - frequencies and frequency ratios sometimes don't match any theory, and are ascribed to non-radial modes, or even B-fields.
And the observations I've come across for multiple overtones note that the degeneracies are too high to resolve fundamental stellar parameters uniquely

Except in 47 Tuc where CMD and Π agree, where the data is good enough, but in 47 Tuc there is no EHB so presumably no Y variation

argh

I've tracked the papers all the way back to Cox, but don't see μ explicit in the formalism, are people parametrising it through the density?

Anyway, if someone knows the answer, please tell me before I tear my hair out.

Oh, and while I have your attention, what is the status of the EHE stars - are people happy now that they are just naked cores with heavy H envelope loss, or are exotic mechanisms still sought