Differences between ADIPLS and GYRE above acoustic cutoff

[warrick]

Rich,

I'm busy toiling with some model fits and I've ended up fitting models where some of the reported frequencies are above the acoustic cutoff. That almost certainly means that there's something wrong with the fit but it led me to do some cross-checking between ADIPLS and GYRE.

The plot below shows mode inertia versus frequency for ADIPLS (blue) and GYRE (green). As you can see, the mode inertiae are very different. In fact, the frequencies above the acoustic cutoff are also shifted by about 30 uHz (with GYRE frequencies lower than ADIPLS) but that's not obvious here. FYI, the match below the cutoff is pretty good: the largest difference is about 0.27 uHz. The number of points is relatively small in this model (1500ish) and I didn't do any remeshing in either code.

GYRE_ADIPLS_above_cutoff.png (38.4 KiB) Viewed 3147 times

I've attached the various input tools, including the model. Like I said, I realise that the problem is with the model (the acoustic cutoff should be higher!) but I'm interested to know why there's such a difference above the cutoff. I'm not that familiar with what happens in this frequency range but the GYRE frequencies are closer to the model results, so they help steer the fit in the right direction better.

Cheers,
Warrick

[rhtownsend]

Hi Warrick --

As I'm sure you're aware, above the acoustic cutoff frequency there is incomplete reflection of upwardly propagating waves at the outer boundary; thus, these waves should partially leak through the boundary and escape the star.

Mathematically, this leakage introduces imaginary terms in the outer mechanical boundary condition, which in turn means that the stellar eigenfrequencies become complex. Physically, the complex eigenfrequencies arise because, as wave energy leaks through the outer boundary, the pulsation amplitude decays with time to conserve energy.

Both ADIPLS and GYRE (when doing adiabatic calcs) neglect the imaginary terms in the boundary condition when above the cutoff frequency, and force the eigenfrequencies to be real. Exactly how this is done is different in the two codes -- meaning that they give different results. Neither result is correct!

Would you like me to modify GYRE to properly handle cases above the cutoff? Most of the machinery is already there, it will just require a bit of special casing.

cheers,

Rich

[warrick]

Rich,

Sorry for taking so long to check back here. As a feature, don't worry about trying to make sense of stuff above the cutoff. I realise that the adiabatic calculations stop making complete sense out there, and I was more curious about how the codes were treating this situation differently. Like I said, the main reason I asked is because I was trying to fit a particular star that has some very high reported frequencies, near the cutoff. When MESA compared the observed and modelled frequencies, I think the GYRE super-cutoff results were better at steering MESA in the right direction.

The problem, it turned out, was that I wasn't including the atmosphere in the pulsation calculation. Including it increased the acoustic cutoff by enough that the fit to start behaving better again. That is, the seismically-derived model parameters are consistent with the spectroscopic parameters.

Anyway, thanks as ever for the work and support!

W