Rathish Previn-Ratnasingam

Internal gravity waves (IGWs) are thought to cause mixing in stellar interiors, a process that has been widely studied both theoretically and numerically. Our aim is to determine the physical mechanism responsible for the wave-induced mixing in stellar interiors. We compare the mixing profiles obtained from two-dimensional (2D) equatorial hydrodynamical and tracer particle simulations with theoretical predictions from R. J. Garcia Lopez & H. C. Spruit and J. P. Zahn (1992) on wave mixing due to wave-induced shear turbulence. Our results show that, despite not satisfying the vertical shear instability threshold, the mixing profiles from the simulations agree remarkably well with the theoretical predictions of both prescriptions, strongly suggesting that shear from IGWs plays an important role in mixing even at low shear rates. This agreement remains robust across different stellar masses, ages, rotation and simulation parameters. This provides an important step in providing realistic parameterisations for wave mixing in stellar structure and evolution models.

We present 2D numerical simulations of convection and waves in a 7M _⊙ star across stellar ages ranging from zero age to terminal age main sequence. We show that waves efficiently transport angular momentum across the stellar radiative envelope at young ages. However, as the core recedes, leaving behind a “spike” in the Brunt–Väisälä frequency at the convective–radiative interface, the waves are severely attenuated. This, coupled with the changing stratification throughout the radiation zone, leads to significantly reduced angular momentum transport at later stages on the main sequence. Indeed the angular momentum transport at mid–main sequence is typically 3–4 orders of magnitude lower than at zero age, though we expect this to be somewhat mitigated by the chemical mixing also induced by such waves. We provide measures of the angular momentum transport, both in terms of the divergence of the Reynolds stress and a typical “wave luminosity.” However, we caution that the angular momentum transport drives shear flows, resulting in both slowing and speeding up of radiative interiors. While the values of Reynolds stress and angular momentum transport are only within the context of these limited simulations, they are not significantly different to those found previously using simpler prescriptions, providing some confidence in their applicability.

Context. Internal gravity waves (IGWs) have been shown to contribute to the transport of chemical elements in stars with a convective core and radiative envelope. Recent two-dimensional hydrodynamical simulations of convection in intermediate-mass stars have provided estimates of the chemical mixing efficiency of such waves. The chemical diffusion coefficient from IGW mixing is described by a constant A, times the squared wave velocity. However, the value of A remains unconstrained by such simulations. Aims. This work aims to investigate what values A can take in order to reproduce the observed nitrogen surface abundances of the most nitrogen-enriched massive stars. Furthermore, we discuss the prevalence of IGW mixing compared to rotational mixing. Methods. We provide an implementation of these (time-dependent) mixing profiles predicted from hydrodynamical simulations in the one-dimensional stellar evolution code MESA. We computed evolution tracks for stars between 3 and 30 M_⊙ with this new implementation for IGW mixing and studied the evolution for the surface abundances of isotopes involved in the CNO cycle, particularly the nitrogen-14 isotope. Results. We show that this one-dimensional framework that predicts the chemical diffusion coefficient from IGW mixing yields consistent morphologies of the mixing profile in comparison with hydrodynamical simulations. We find that the value of A must increase with mass in order to reproduce the most nitrogen-enriched stars. If we assume these calibrated values for A, mixing by IGWs is a potential mechanism to reproduce well-mixed stars without needing rapid rotation. Conclusions. We have provided observational limits on the efficiency of IGW mixing for future theoretical studies. Furthermore, future asteroseismic modelling efforts that take IGW mixing into account will be able to place additional constraints on the convective core mass, as our models predict that the convective core would be significantly more massive if IGW mixing is indeed efficient.

It is well-known that the cores of massive stars sustain a stellar dynamo with a complex magnetic field configuration. However, the same cannot be said for the field's strength and geometry at the convective–radiative boundary, which are crucial when performing asteroseismic inference. In this Letter, we present 3D magnetohydrodynamic (MHD) simulations of a 7 M _⊙ mid-main-sequence star, with particular attention given to the convective–radiative boundary in the near-core region. Our simulations reveal that the toroidal magnetic field is significantly stronger than the poloidal field in this region, contrary to recent assumptions. Moreover, the rotational shear layer, also important for asteroseismic inference, is specifically confined within the extent of the Brunt–Väisälä frequency peak. These results, which are based on the inferred properties of HD 43317, have widespread implications for asteroseismic studies of rotation, mixing, and magnetism in stars. While we expect our results to be broadly applicable across stars with similar Brunt–Väisälä frequency profiles and stellar masses, we also expect the MHD parameters (e.g., Re_m) and the initial stellar rotation rate to impact the geometry of the field and differential rotation at the convective–radiative interface.

Internal gravity waves are likely to cause mixing in stellar interiors. Studies show that the mixing by these waves changes drastically across age and mass. Here, we study the effect of rotation on this wave mixing by considering a 7 M _⊙ model at zero-age main sequence and mid-main sequence. We compare the mixing profiles at a range of rotation rates (1 × 10⁻⁵, 2 × 10⁻⁵, 3 × 10⁻⁵, 4 × 10⁻⁵, and 1 × 10⁻⁴ rad s⁻¹) and observe that the mixing decreases with decreasing Rossby number. This can be attributed to the effect of rotation on convection, which influences the amplitude with which the waves are excited near the convective–radiative interface.

We present 3D full star simulations, reaching up to 90% of the total stellar radius, for three 7 M _⊙ stars of different ages: zero-age main sequence (ZAMS), mid–main sequence (midMS), and terminal-age main sequence (TAMS). A comparison with several theoretical prescriptions shows that the generation spectra for all three ages are dominated by convective plumes. Two distinct overshooting layers are observed, with most plumes stopped within the layer situated directly above the convective boundary; overshooting to the second, deeper layer becomes progressively more infrequent with increasing stellar age. Internal gravity wave (IGW) propagation is significantly impacted in the midMS and TAMS models as a result of some IGWs getting trapped within their Brunt–Väisälä frequency spikes. A fundamental change in the wave structure across radius is also observed, driven by the effect of density stratification on IGW propagation causing waves to become evanescent within the radiative zone, with older stars being affected more strongly. We find that the steepness of the frequency spectrum at the surface increases from ZAMS to the older models, with older stars also showing more modes in their spectra.

Stars that are over 1.6 solar masses are generally known to possess convective cores and radiative envelopes, which allows for the propagation of outwardly travelling internal gravity waves (IGWs). Here, we study the generation and propagation of IGWs in such stars using two-dimensional, fully non-linear hydrodynamical simulations with realistic stellar reference states from the one-dimensional stellar evolution code, Modules for Stellar Astrophysics. Compared to previous similar works, this study utilises radius-dependent thermal diffusivity profiles for five different stellar masses at the middle of the main sequence: 3 M_⊙, 5 M_⊙, 7 M_⊙, 10 M_⊙, and 13 M_⊙. From the simulations, we find that the surface perturbations are larger for higher masses, but no noticeable trends are observed for the frequency slopes with different stellar masses. The slopes are also similar to the results from previous works. We compared our simulation results with stellar photometric data from a recent survey and we found that for frequency intervals above 8 μHz, there is a good agreement between the temperature frequency slopes from the simulations and the surface brightness variations of these observed stars. This indicates that the brightness variations are caused by core-generated IGWs.

Stars with masses above 1.6 solar masses generally possess convective cores and radiative envelopes, which allows the propagation of outward-travelling internal gravity waves. We have studied the generation and propagation of IGWs in such stars using two-dimensional, fully nonlinear hydrodynamical simulations with realistic stellar reference states from the one-dimensional stellar evolution code, Modules for Stellar Astrophysics. Compared to previous similar works, this study utilises radius-dependent thermal diffusivity profiles for 5 different stellar masses at the middle of main sequence: 3 - 13 solar masses. From the simulations, we find that the surface perturbations are larger for higher masses, but no noticeable trends are observed for the frequency slopes with different stellar masses. The slopes are also similar to the results from previous works. We compare our simulation results with stellar photometric data from a recent survey and find that for frequency intervals above 8 microHz, there is a good agreement between the temperature frequency slopes from the simulations and the surface brightness variations of these observed stars, indicating that the brightness variations are caused by core-generated IGWs.

Internal gravity waves can cause mixing in the radiative interiors of stars. We study this mixing by introducing tracer particles into 2D hydrodynamic simulations. Following the work of Rogers & McElwaine, we extend our study to different masses (3, 7, and 20 M _⊙) and ages (ZAMS, midMS, and TAMS). The diffusion profiles of these models are influenced by various parameters such as the Brunt–Väisälä frequency, density, thermal damping, the geometric effect, and the frequencies of waves contributing to these mixing profiles. We find that the mixing profile changes dramatically across age. In younger stars, we noted that the diffusion coefficient increases toward the surface, whereas in older stars the initial increase in the diffusion profile is followed by a decreasing trend. We also find that mixing is stronger in more massive stars. Hence, future stellar evolution models should include this variation. In order to aid the inclusion of this mixing in 1D stellar evolution models, we determine the dominant waves contributing to these mixing profiles and present a prescription that can be included in 1D models.

Context. Recent, nonlinear simulations of wave generation and propagation in full-star models have been carried out in the anelastic approximation using spectral methods. Although it makes long time steps possible, this approach excludes the physics of sound waves completely and requires rather high artificial viscosity and thermal diffusivity for numerical stability. A direct comparison with observations is thus limited. Aims. We explore the capabilities of our compressible multidimensional Seven-League Hydro (SLH) code to simulate stellar oscillations. Methods. We compare some fundamental properties of internal gravity and pressure waves in 2D SLH simulations to linear wave theory using two test cases: (1) an interval gravity wave packet in the Boussinesq limit and (2) a realistic 3 M_⊙ stellar model with a convective core and a radiative envelope. Oscillation properties of the stellar model are also discussed in the context of observations. Results. Our tests show that specialized low-Mach techniques are necessary when simulating oscillations in stellar interiors. Basic properties of internal gravity and pressure waves in our simulations are in good agreement with linear wave theory. As compared to anelastic simulations of the same stellar model, we can follow internal gravity waves of much lower frequencies. The temporal frequency spectra of velocity and temperature are flat and compatible with the observed spectra of massive stars. Conclusion. The low-Mach compressible approach to hydrodynamical simulations of stellar oscillations is promising. Our simulations are less dissipative and require less luminosity boosting than comparable spectral simulations. The fully-compressible approach allows for the coupling of gravity and pressure waves in the outer convective envelopes of evolved stars to be studied in the future.