Core-envelope coupling of gravito-inertial waves in pre-main-sequence solar-type stars

Abstract

After the recent detection of solar equatorial Rossby waves, a renewed interest has been brought to the study of gravito-inertial waves propagating in the convective envelope of solar-type stars. In particular, the ability that some of these envelope gravito-inertial modes have to couple with the ones trapped in the radiative interior might open new windows to probe the deep-layer dynamics of solar-type stars. The possibility for such a coupling to occur is particularly favoured in pre-main sequence (PMS) solar-type stars. Indeed, due to the contraction of the protostellar object, they are able to reach large rotation frequencies before nuclear reactions are ignited and magnetic braking becomes the driving mechanism for their rotational evolution. In this work, we therefore study the coupling between the envelope inertial waves and the radiative interior g modes in PMS stars, focusing on the case of prograde dipolar modes. We consider the case of 0.5 Msun and 1 Msun PMS models, each with three different scenarios of rotational evolution. We show that, for stars that have formed with a sufficient amount of angular momentum, this coupling can occur in frequency ranges that are accessible to space-borne photometry, creating inertial dips in the period spacing pattern. With an asymptotic analysis we characterise the shape of these inertial dips to show that they depend on rotation and on the stiffness of the convective-radiative interface.

Figures (7)

• Figure 1: Modulus of the squared Brunt-Väisälä frequency, $|N^2|$ for the 0.5 $\rm M_\odot$ model (top) and the 1 $\rm M_\odot$ model (bottom), with regions where $N^2 \geq 0$ in gray and regions where $N^2<0$ in red. The squared Coriolis frequency, $4\Omega^2$, is indicated by the horizontal dashed line for the slow (orange), the intermediate (yellow), and the fast (blue) case, while the horizontal dotted lines corresponds to $2\Omega^2$. The propagation region of gravito-inertial waves as a function of frequency is highlighted by the hatched areas (orange dots and blue hatches for the slow and fast cases, respectively).
• Figure 2: Top:$\Delta P$ vs $P$ diagram for the ${\tilde{\ell}} = m = 1$ modes in the 0.5 $\rm M_\odot$ model, in the co-rotating frame. The dots correspond to the modes computed considering the full extent of the stellar structure, with the slow case in orange, the intermediate case in yellow, and the fast case in blue. The vertical dashed lines mark the period of the modes computed considering only the convective envelope. The position of the Coriolis frequency, $2 \Omega$, is highlighted for the slow, the intermediate and the fast cases (vertical thick lines in orange, yellow, and blue, respectively) while the $\sqrt{2}\Omega$ frequency is indicated with the vertical dotted lines. Bottom: Same as top panel for the $1~\mathrm{M}_\odot$ model. In the top panel, the location of the modes with the eigenfunctions represented in Fig. \ref{['fig:eigenfunction_coupling_example']} are highlighted with the stellar symbol in light blue.
• Figure 3: Comparison between the eigenfunctions of the $n = - 46$ (orange) and the $n = -40$ (dotted grey) modes. The eigenfunction of the $n = -4$ envelope mode is shown in dashed blue.
• Figure 4: Evolutionary tracks for the stellar models (0.5 $\rm M_\odot$ in blue and 1 $\rm M_\odot$ in orange) considered in this work, from the end of the accreting phase to the ZAMS. The black thick lines shows the location of the ZAMS. The location on the track of the stellar models we consider in this work is highlighted by the star symbol. The other tracks of the Steindl2021 PMS grid ranging between $M_\star = 0.2 \; \mathrm{M}_\odot$ and $M_\star = 1.5 \; \mathrm{M}_\odot$ are shown in grey for comparison, with the structure model saved during the MESA run indicated by grey dots, yellow crosses, and teal plus signs. The crosses signal models which have a convective core while the plus signs correspond to stellar structure that are completely convective.
• Figure 5: Rotational evolution computed for the 0.5 (blue) and 1 $\rm M_\odot$ (orange) models. The rotational track with slow initial condition is represented with a dashed line, the track with intermediate initial condition with a dotted line, and the track with fast initial condition with a thick line. The location of the stellar models we consider in this work is highlighted by the star symbol.