Instability domain predictions in the sHR diagram for dipole modes (ℓ = 1, see Sect. 4.1). P-mode instabilities are represented by the blue area and the g-mode domain is shown in red. The ATON non-rotating evolutionary tracks are over plotted. The horizontal dashed line indicates the limit above which strange mode oscillations are most likely expected. Black asterisks stand for nine selected models la A to I which will be more deeply investigated in Sect. 4.2. The global properties of these models are given in Table 1.