Realising efficient computation of individual frequencies for red-giant models

In order to improve the asteroseismic modelling efforts for red-giant stars, the numerical computation of theoretical individual oscillation modes for evolved red-giant models has to be made feasible. We aim to derive a method for circumventing the computational cost of computing oscillation spectra for models of red-giant stars with an average large frequency separation $\Delta\nu<15$ $\mu$Hz, thereby allowing for asteroseismic investigations of giants utilising individual frequencies. The proposed Truncated Scanning Method serves as a novel method detailing how the observable individual $l=0,1,2$ frequencies of red giants may be computed on realistic timescales through so-called model truncation. By carefully removing the innermost region of the stellar models, the g-mode influence on the oscillation spectra may be avoided, allowing estimation of the observable regions from the resulting pure p-mode oscillations. The appropriate observable frequency regions are subsequently scanned for the complete and un-truncated stellar model. The observable regions are determined by considering the limitations on observability from the internal mode coupling and damping, yielding consistent frequency spectra obtained at a much reduced computational cost. The Truncated Scanning Method proves the feasibility of obtaining the individual frequencies of red-giant models for a wide range of applications and research, demonstrating an improved computational efficiency by a factor of 10 or better. This means that the inclusion of $l=1,2$ individual frequencies is now a possibility in future asteroseismic modelling efforts of red-giant stars. Further potential avenues for improvements to this method are outlined for future pursuits.