  Temperature anisotropy and field-aligned skewness are commonly observed
non-thermal features in electron velocity distributions in the solar wind.
These characteristics can act as a source of free energy to destabilize
different electromagnetic wave modes, which may alter the plasma state through
wave-particle interactions. Previous theoretical studies have mainly focused on
analyzing these non-thermal features and self-generated instabilities
individually. However, to obtain a more accurate and realistic understanding of
kinetic processes in the solar wind, it is necessary to examine the interplay
between these two energy sources. By means of linear kinetic theory, in this
paper we investigate the excitation of the parallel-propagating whistler mode,
when it is destabilized by electron populations exhibiting both temperature
anisotropy and field-aligned strahl or skewness. To describe the solar wind
electrons, we adopt the Core-Strahlo model as an alternative approach. This
model offers the advantage of representing the suprathermal features of halo
and strahl electrons, using a single skew-Kappa distribution already known as
the strahlo population. Our findings show that when the electron strahlo
exhibits an intrinsic temperature anisotropy, this suprathermal population
becomes a stronger and more efficient source of free energy for destabilizing
the whistler mode. This suggests a greater involvement of the anisotropic
strahlo in processes conditioned by wave-particle interactions. Present results
also suggest that the contribution of core anisotropy can be safely disregarded
when assessing the importance of instabilities driven by the suprathermal
population. This allows for a focused study, particularly regarding the
regulation of electron heat flux in the solar wind.
