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(a): 3D rendering of the simulated star. We represent the radial velocity divided by its rms value at each radius. (b): Equatorial slice. Like in the 3D view, IGWs pattern are visible in the inner radiative zone as quasi-circular spirals. (c): rms profiles of the total (solid line) and radial (dotted line) velocities as a function of the normalized radius, averaged over longitude, latitude, and time (about 10 convective overturning times). (d): Energy spectrum of gravity waves computed at r 0 = 0.5 R as a function of degree and frequency ω. Ridges are formed by g modes of same radial order n, and we see that they tend to the maximum Brunt-Väisälä frequency at high order (dotted white line). The black solid line denotes the separation between g modes (above) and progressive waves (below).
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The revolution of helio- and asteroseismology provides access to the detailed
properties of stellar interiors by studying the star's oscillation modes. Among
them, gravity (g) modes are formed by constructive interferences between
progressive internal gravity waves (IGWs), propagating in stellar radiative
zones. Our new 3D nonlinear simulations of...
Similar publications
Asteroseismology allows us to probe the physical conditions inside the core
of red giant stars. This relies on the properties of the global oscillations
with a mixed character that are highly sensitive to the physical properties of
the core. However, overlapping rotational splittings and mixed-mode spacings
result in complex structures in the mixed...
Citations
... Analytical approaches are also possible (Kumar et al. 1999;Montalbán & Schatzman 2000;Lecoanet & Quataert 2013), but they inevitably rely on a number of assumptions (e.g., the wave excitation mechanism, the shape of the power spectrum). Multi-dimensional hydrodynamics simulations of IGWs excitation and propagation have been performed for main-sequence stars (Rogers & Glatzmaier 2005;Dintrans et al. 2005;Rogers et al. 2013;Brun et al. 2011;Alvan et al. 2014Alvan et al. , 2015Edelmann et al. 2019;Horst et al. 2020;Ratnasingam et al. 2020;Le Saux et al. 2022;Herwig et al. 2023b; Thompson et al. 2023), but to our knowledge no results currently exist for RGB stars. In this work, we present the first hydrodynamics simulations of IGW excitation and propagation in RGB stars. ...
... The most striking aspect of this wave spectrum is it blurriness. In contrast, hydrodynamics simulations of IGWs in stellar radiative interiors usually yield spectra where the power is predominantly contained in a set of discrete, welldefined ridges in the ℓ − space (Alvan et al. 2014(Alvan et al. , 2015Rogers et al. 2013;Horst et al. 2020;Thompson et al. 2023), with each ridge corresponding to a specific radial order of standing IGW modes (or modes). The absence of such ridges in Figure 13 suggests that standing modes are not formed in our simulations or, in other words, that the mode lifetime is very short. ...
... The absence of standing modes in Figure 13 therefore suggests that only inward moving progressive waves exist in our simulations. This situation is analogous to that described in Alvan et al. (2015) for a solar-like star, where low-frequency IGWs are damped before reaching their reflection point near the centre. In the solar case, the reflection point is located where the Brunt-Väisälä frequency becomes equal to the IGW frequency. ...
We present the first 3D hydrodynamics simulations of the excitation and propagation of internal gravity waves (IGWs) in the radiative interiors of low-mass stars on the red giant branch (RGB). We use the PPMstar explicit gas dynamics code to simulate a portion of the convective envelope and all the radiative zone down to the hydrogen-burning shell of a 1.2$M_{\odot}$ upper RGB star. We perform simulations for different grid resolutions (768$^3$, 1536$^3$ and 2880$^3$), a range of driving luminosities, and two different stratifications (corresponding to the bump luminosity and the tip of the RGB). Our RGB tip simulations can be directly performed at the nominal luminosity, circumventing the need for extrapolations to lower luminosities. A rich, continuous spectrum of IGWs is observed, with a significant amount of total power contained at high wavenumbers. By following the time evolution of a passive dye in the stable layers, we find that IGW mixing in our simulations is weaker than predicted by a simple analytical prescription based on shear mixing and not efficient enough to explain the missing RGB extra mixing. However, we may be underestimating the efficiency of IGW mixing given that our simulations include a limited portion of the convective envelope. Quadrupling its radial extent compared to our fiducial setup increases convective velocities by up to a factor 2 and IGW velocities by up to a factor 4. We also report the formation of a $\sim 0.2\,H_P$ penetration zone and evidence that IGWs are excited by plumes that overshoot into the stable layers.
... By doing so they generate internal gravity waves and pump magnetic field. Because we are in this study mostly interested in the magnetic state of our simulation, we refer the reader to the following multidimensional studies of internal gravity wave generation in solar-like stars (Rogers & Glatzmaier 2006;Brun et al. 2011;Alvan et al. 2014Alvan et al. , 2015. Turning to the radial flux balance, we note that the enthalpy flux (dashed-triple-dotted line) dominates energy transport in most of the convective envelope. ...
We use the anelastic spherical harmonic code to model the convective dynamo of solar-type stars. Based on a series of 15 3D MHD simulations spanning four bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ( Δ Ω ∝ ( ∣ Ω ∣ / Ω ⊙ ) 0.46 ) in the MHD solutions than in their HD counterpart ∣ Ω ∣ / Ω ⊙ 0.66 ), yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between 0.15 ≲ Ro f ≲ 0.65, the solutions possess long magnetic cycle, if Ro f ≲ 0.42 a short cycle and if Ro f ≳ 1 (antisolar-like differential rotation), a statistically steady state. We show that short-cycle dynamos follow the classical Parker–Yoshimura rule whereas the long-cycle period ones do not. We also find efficient energy transfer between reservoirs, leading to the conversion of several percent of the star's luminosity into magnetic energy that could provide enough free energy to sustain intense eruptive behavior at the star’s surface. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ( B L , surf ∼ Ro f − 1.26 ) agrees better with observations ( B V ∼ Ro s − 1.4 ± 0.1 ) and differs from dynamo scaling based on the global magnetic energy ( B bulk ∼ Ro f − 0.5 ).
... The influence of small-scale eddies has been semi-analytically been modelled for IGWs by Press (1981) and Zahn et al. (1997) for example, whereas the impact of larger-scale flows modelled analytically as collections of plumes on IGWs has been considered by Schatzman (1993) and Pinçon et al. (2016) for example. These excitation mechanisms have also been observed in 2D and 3D local and global numerical simulations (e.g., Hurlburt et al. 1986;Browning et al. 2004;Dintrans et al. 2005;Kiraga et al. 2005;Rogers & Glatzmaier 2005;Rogers et al. 2006Rogers et al. , 2013Alvan et al. 2014Alvan et al. , 2015Augustson et al. 2016;Edelmann et al. 2019). In addition, turbulent Reynolds stresses in the bulk of convective regions also contribute to the generation of IGWs both in late-type stars (e.g., Belkacem et al. 2009b) and in early-type stars (e.g., Samadi et al. 2010;Shiode et al. 2013) through their coupling to the evanescent tail of the IGWs in the convective zone (e.g., Lecoanet & Quataert 2013). ...
... Finally, the model examined here for the wave energy flux and excitation of GIWs has assumed a particular form of the convective Reynolds stresses that is valid only in local domains. However, this neglects globalscale shearing flows seen in 3D convection simulations in spherical geometry (e.g., Brun et al. 2011;Augustson et al. 2012;Alvan et al. 2015;Emeriau-Viard & Brun 2017) and theoretically predicted (Busse 2002;Julien et al. 2006;Grooms et al. 2010), as well as neglecting the more extremal convective events that can still occur frequently enough to influence the wave energy flux (e.g., Pratt et al. 2017b,a). These events have typically been modeled as collections of plumes for gravity waves (e.g., Schmitt et al. 1984;Schatzman 1993Schatzman , 1996Pinçon et al. 2016Pinçon et al. , 2017, and they are tied closely to the interfacial excitation model as such events are more likely to deform the average interface depth at least in the local region near the plume. ...
Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter dependence of the amplitude of those waves, a monomodal model for stellar and planetary convection as described in Paper I is employed, which provides the magnitude of the rms convective velocity as a function of rotation rate. With this convection model, two channels for wave driving are considered: excitation at a boundary between convectively stable and unstable regions and excitation due to Reynolds-stresses. Parameter regimes are found where the sub-inertial waves may carry a significant energy flux, depending upon the convective Rossby number, the interface stiffness, and the wave frequency. The super-inertial waves can also be enhanced, but only for convective Rossby numbers near unity. Interfacially excited waves have a peak energy flux near the lower cutoff frequency when the convective Rossby number of the flows that excite them are below a critical Rossby number that depends upon the stiffness of the interface, whereas that flux decreases when the convective Rossby number is larger than this critical Rossby number.
... Due to the large rate of energy generation by nuclear reactions, convective motions near the star's core become very energetic during advanced burning phases such as carbon, neon, oxygen, and silicon burning (e.g., Woosley et al. 2002). The convective motion generates gravity waves that carry a power L wave that scales with the convective luminosity L con as L wave ∼M con L con (Goldreich & Kumar 1990;Alvan et al. 2015), where M con is the mean Mach number of the convective motion. The gravity waves propagate outward and are partially reflected by overlying convective shells, though some wave energy is still transferred outward into acoustic waves after tunneling through these evanescent regions (see, e.g., Fuller et al. 2015;Takata 2016 for applications in low-mass red giant stars). ...
The activity of a massive star approaching core-collapse can strongly affect the appearance of the star and its subsequent supernova. Late-phase convective nuclear burning generates waves that propagate toward the stellar surface, heating the envelope and potentially triggering mass loss. In this work, we improve on previous one-dimensional models by performing two-dimensional simulations of the pre-supernova mass ejection phase due to deposition of wave energy. Beginning with stellar evolutionary models of a 15 M_⊙ red supergiant star during core O-burning, we treat the rate and duration of energy deposition as model parameters and examine the mass-loss dependence and the pre-explosion morphology accordingly. Unlike one-dimensional models, density inversions due to wave heating are smoothed by Rayleigh–Taylor instabilities, and the primary effect of wave heating is to radially expand the star's hydrogen envelope. For low heating rates with long durations, the expansion is nearly homologous, whereas high but short-lived heating can generate a shock that drives envelope expansion and results in a qualitatively different density profile at the time of core-collapse. Asymmetries are fairly small, and large amounts of mass loss are unlikely unless the wave heating exceeds expectations. We discuss implications for pre-supernova stellar variability and supernovae light curves.
... The extant studies of Quataert & Shiode (2012);Fuller et al. (2015); Fuller (2017) strongly rely on the analytic theory of wave excitation by turbulent convection that has been developed over decades (Lighthill 1952;Townsend 1966;Goldreich & Kumar 1990;Quataert & Lecoanet 2013). Numerical simulations of IGW excitation at convective boundaries have been conducted for earlier evolutionary stages in 2D (Rogers et al. 2013) and 3D (Alvan et al. 2014(Alvan et al. , 2015Edelmann et al. 2019), but cannot be easily extrapolated to the late, neutrino-cooled burning stages where the Péclet number is lower and compressibility effects play a bigger role. During the early evolutionary stages, asteroseismology can be used to directly test the underlying theories for IGW excitation by convection (Aerts & Rogers 2015;Aerts et al. 2017). ...
It has been suggested based on analytic theory that even in non-rotating supernova progenitors stochastic spin-up by internal gravity waves (IGWs) during the late burning stages can impart enough angular momentum to the core to result in neutron star birth spin periods below 100ms, and a relatively firm upper limit of 500ms for the spin period. We here investigate this process using a 3D simulation of oxygen shell burning in a $3M_\odot$ He star. Our model indicates that stochastic spin-up by IGWs is less efficient than previously thought. We find that the stochastic angular momentum flux carried by waves excited at the shell boundary is significantly smaller for a given convective luminosity and turnover time than would be expected from simple dimensional analysis. This can be explained by noting that the waves launched by overshooting convective plumes contain modes of opposite angular wave number with similar amplitudes, so that the net angular momentum of excited wave packets almost cancels. We find that the wave-mediated angular momentum flux from the oxygen shell follows a random walk, but again dimensional analysis overestimates the random walk amplitudes since the correlation time is only a fraction of the convective turnover time. Extrapolating our findings over the entire life time of the last burning stages prior to collapse, we predict that the core angular momentum from stochastic spin-up would translate into long birth spin periods of several seconds for low-mass progenitors and no less than 100ms even for high-mass progenitors.
... As discussed in Rogers et al. (2013), the dependence of the wave amplitude on the background density as r -1 2 is linked to the conservation of the pseudomomentum r á ñ f v v r , with á ñ representing a temporal and longitudinal average. Concerning the thermal radiative damping, this is explained in Zahn et al. (1997) and illustrated for a solarlike star in Alvan et al. (2015). The concept of thermal damping can be easily demonstrated through the following derivation. ...
Recent numerical simulations of rotating stellar convection have suggested the possible existence of retrograde (slow equator, fast poles) or so-called antisolar differential rotation states in slowly rotating stars possessing a large Rossby number. We aim to understand whether such rotational states exist from the onset of convective instability or are the outcome of complex nonlinear interactions in the turbulent convective envelope. To this end, we have made a systematic linear analysis of the critical state of convection in a series of 15 numerical simulations published in Brun et al. We have assessed their degree of supercriticality and most-unstable mode properties, and computed the second-order mean zonal flow response. We find that none of the linear critical cases show a retrograde state at the onset of convection even when their nonlinear counterparts do. We also find that the presence of a stably stratified layer coupled to the convectively unstable upper layer leads to interesting gravity-wave excitation and angular momentum transport. We conclude that retrograde states of differential rotation are probably the outcome of complex mode–mode interactions in the turbulent convection layer and are, as a consequence, likely to exist in real stars.
... One likely possibility comes from the convective flows above the tachocline. The strongly concentrated downflows penetrate in the upper part of the tachocline, constantly hammering the radiative zone and generating gravity waves see (Sect. 3 and Alvan et al. 2014aAlvan et al. , 2015a. The exact nature of this mechanism, being either overshooting (the downflows slightly over-extend in the stable layer below) or penetration (the penetrating downflows locally change the properties of the background equilibrium Zahn 1991), is currently in debate in the community. ...
We present recent progress made in modelling stars and their turbulent magnetized dynamics in 3-D. This work is inspired by many years of discussion with Jean-Paul Zahn. I (ASB) first met him as a professor of astrophysical fluid dynamics (AFD) at the Paris-Meudon observatory's graduate school of astrophysics in 1994–1995. He made me the honor of accepting to be my PhD's advisor (1995–1998). He then supported me during my postdoc years in Boulder with his long time friend Prof. Juri Toomre between January 1999 and December 2002 and through the difficult process of getting a tenure position, and then since as a tenure researcher in Department of Astrophysics at CEA Paris-Saclay. I have been fortunate and lucky to share so many years discussing and doing scientific projects with Jean-Paul. As I was getting more experienced and started supervising my own students, he was always available, guiding us with his acute scientific vista and encouraging them. Antoine Strugarek, who co-author this paper, was like me fortunate to share Jean-Paul's knowledge. The three of us published several papers together during Antoine's PhD (2009–2012) addressing the dynamics of the solar tachocline and its interplay with convection. We miss him greatly. In this paper, we discuss mainly two topics that benefited from Jean-Paul's deep understanding of AFD: a) the dynamics of the solar tachocline and angular momentum transport in stellar interior and b) turbulent convection and dynamo action in stellar convection zones.
... This is in sharp contrast with the variety of different mechanisms possible in the terrestrial case (e.g., Fritts & Alexander 2003, and references therein), which also includes orographic generation by winds passing over mountain terrain. Convective overshooting at the location of a convective/stable interface (Hurlburt et al. 1986;Goldreich & Kumar 1990;Rogers & Glatzmaier 2005;Ansong & Sutherland 2010;Lecoanet & Quataert 2013;Alvan et al. 2014Alvan et al. , 2015Pinçon et al. 2016Pinçon et al. , 2017) is thought to be how IGWs are generated in the solar atmosphere. This has been confirmed by reported observations of IGWs in the solar atmosphere by several authors (Komm et al. 1991;Rutten & Krijger 2003;Stodilka 2008;Straus et al. 2008Straus et al. , 2009Kneer & Bello González 2011;Nagashima et al. 2014). ...
In this second paper of the series on internal gravity waves (IGWs), we present a study of the generation and propagation of IGWs in a model solar atmosphere with diverse magnetic conditions. A magnetic field-free and three magnetic models that start with an initial, vertical, homogeneous field of 10, 50, and 100 G magnetic flux density, are simulated using the CO ⁵ BOLD code. We find that the IGWs are generated in similar manner in all four models in spite of the differences in the magnetic environment. The mechanical energy carried by IGWs is significantly larger than that of the acoustic waves in the lower part of the atmosphere, making them an important component of the total wave energy budget. The mechanical energy flux (10 ⁶ -10 ³ W m ⁻² ) is a few orders of magnitude larger than the Poynting flux (10 ³ -10 ¹ W m ⁻² ). The Poynting fluxes show a downward component in the frequency range corresponding to the IGWs, which confirm that these waves do not propagate upward in the atmosphere when the fields are predominantly vertical and strong. We conclude that, in the upper photosphere, the propagation properties of IGWs depend on the average magnetic field strength and therefore these waves can be potential candidates for magnetic field diagnostics of these layers. However, their subsequent coupling to Alfvénic waves is unlikely in a magnetic environment permeated with predominantly vertical fields, and therefore they may not directly or indirectly contribute to the heating of layers above plasma-β less than 1. © 2019. The American Astronomical Society. All rights reserved..
... To date, no numerical simulations have been able to reproduce any of the theoretically predicted wave spectra (Rogers et al. 2013;Alvan et al. 2014Alvan et al. , 2015 and similarly, neither have any laboratory experiments (Ansong & Sutherland 2010). However, a recent work by Couston et al. (2018) has confirmed one of theoretical generation spectra investigated in this work through numerical simulations involving the Boussinesq approximation. ...
... tween convective and radiative regions and convective overshoot (Hurlburt et al. 1986;Brummell et al. 2002) with a few having focused on IGW generation (Rogers & Glatzmaier 2005;Brun et al. 2011;Rogers et al. 2013;Alvan et al. 2014Alvan et al. , 2015. For instance, Rogers et al. (2013) predicts that for a star with zero rotation, the energy carried 1 by IGW scales as ...
Internal gravity waves (IGW) propagate in the radiation zones of all stars. During propagation, their amplitudes are affected by two main features: radiative diffusion and density stratification. We have studied the implications of these two features on waves traveling within the radiative zones of non-rotating stars with stellar parameters obtained from the one dimensional stellar evolution code, MESA. As a simple measure of induced wave dynamics, we define a criterion to see if waves can become nonlinear and if so, under what conditions. This was done to understand the role IGW may play in angular momentum transport and mixing within stellar interiors. We find that the IGW generation spectrum, convective velocities and the strength of density stratification all play major roles in whether waves become nonlinear. With increasing stellar mass, there is an increasing trend in nonlinear wave energies. The trends with different metallicities and ages depend on the generation spectrum.
... where ωcon,max is the maximum value obtained within a convective zone (for core convection, we find ωcon does not vary much within a convective zone). Our implementation of waves is a drastic simplification (see simulations of, e.g., Rogers et al. 2013;Rogers 2015;Alvan et al. 2014Alvan et al. , 2015, as discussed in Fuller (2017), but represents a first step in implementing wave energy transport into a stellar evolution code. Figure 2 shows a wave propagation diagram for our hydrogen-free model during core oxygen burning. ...
Pre-supernova (SN) outbursts from massive stars may be driven by hydrodynamical wave energy emerging from the core of the progenitor star during late nuclear burning phases. Here, we examine the effects of wave heating in stars containing little or no hydrogen, i.e., progenitors of type IIb/Ib SNe. Because there is no massive hydrogen envelope, wave energy is thermalized near the stellar surface where the overlying atmospheric mass is small but the optical depth is large. Wave energy can thus unbind this material, driving an optically thick, super-Eddington wind. Using 1D hydodynamic MESA simulations of $\sim \! 5 \, M_\odot$ He stars, we find that wave heating can drive pre-SN outbursts composed of a dense wind whose mass loss rate can exceed $\sim \! 0.1 \, M_\odot/{\rm yr}$. The wind terminal velocities are a few $100 \, {\rm km}/{\rm s}$, and outburst luminosities can reach $\sim \! 10^6 \, L_\odot$. Wave-driven outbursts may be linked with observed or inferred pre-SN outbursts of type Ibn/transitional/transformational SNe, and pre-SN wave-driven mass loss is a good candidate to produce these types of SNe. However, we also show that non-linear wave breaking in the core of the star may prevent such outbursts in stars with thick convective helium-burning shells. Hence, only a limited subset of SN progenitors are likely to experience wave-driven pre-SN outbursts.
