Probing the shape of the mixing profile and of the thermal structure at
  the convective core boundary through asteroseismology
  Aims: We investigate from a theoretical perspective if space asteroseismology
can be used to distinguish between different thermal structures and shapes of
the near-core mixing profiles for different types of coherent oscillation modes
in massive stars with convective cores, and if this capacity depends on the
evolutionary stage of the models along the main sequence. Methods: We compute
1D stellar structure and evolution models for four different prescriptions of
the mixing and temperature gradient in the near-core region. Their effect on
the frequencies of dipole prograde gravity modes in both Slowly Pulsating B and
$\beta$ Cep stars is investigated, as well as for pressure modes in $\beta$ Cep
stars. Results: A comparison between the mode frequencies of the different
models at various stages during the main sequence evolution reveals that they
are more sensitive to a change in temperature gradient than to the exact shape
of the mixing profile in the near-core region. Depending on the duration of the
observed light curve, one can distinguish between either just the temperature
gradient, or also between the shapes of the mixing coefficient. The relative
frequency differences are in general larger for more evolved models, and are
largest for the higher-frequency pressure modes in $\beta$ Cep stars.
Conclusions:In order to unravel the core boundary mixing and thermal structure
of the near-core region, one must have asteroseismic masses and radii with
$\sim 1\%$ relative precision for hundreds of stars.
