for our needs.

The pulsation frequencies in this series are then rotationally shifted using the traditional approximation, as described by Eq.\[eq:4\] and assuming the star is rigidly rotating. The values of the pulsation periods in the inertial reference frame are then obtained by $$P_{\rm inert} = \frac{1}{f_{co}
  + mf_{\rm rot}}.\label{eq:6}$$ This introduces a slope into the model spacing series, as shown in Fig.\[fig:method\]. The resulting pattern is subsequently fitted to the observed period spacing series using $\chi^2$-minimisation, optimising for the variables $\Delta\Pi_l$ and $f_{rot}$. Finally, we select the best solution for all studied $l$ and $m$ values, taking into account the theoretical expectations for the asymptotic spacing $\Delta\Pi_l$, as shown in Fig.\[fig:Spacing\_dist\] and derived from our model grid in Sec.\[sec:grid\]. From this fit, we then obtain estimates for the rotation rate $f_{rot}$ and the asymptotic spacing $\Delta\Pi_l$, as well as a mode identification.

![\[fig:method\] Illustration of our methodology to derive the rotation rate $f_{\rm rot}$ and asymptotic spacing $\Delta\Pi_l$ from an observed period spacing pattern (black dots). An equidistant spacing series (grey squares) is defined, rotationally shifted (white squares) and fitted to the observed pattern using $\chi^2$-minimisation, optimising for the variables $l$, $m$, $\Delta\Pi_l$ and $f_{rot}$.](method_fig.pdf){width="88mm"}

Applications {#sec:appl}
============

Synthetic 