3D hydrodynamic simulations of massive main-sequence stars -- IV. Internal gravity waves matter for SLF variability

TL;DR

This study investigates the origin of stochastic low-frequency variability in massive main-sequence stars by performing high-resolution 3D hydrodynamic simulations of a non-rotating 25 M⊙ ZAMS star, incorporating a modified Fe-opacity bump to establish an outer envelope convection zone. By comparing full-star runs with configurations that suppress core convection or envelope processes, the authors demonstrate that outer envelope convection is the dominant driver of SLF power, exciting a rich IGW spectrum near the inner boundary that imprints observable surface variability. The IGW characteristics depend on the complete stellar stratification, linking internal structure to surface photometric variability and suggesting that SLF signatures can constrain interior properties such as convective zones and stratification. The results provide a pathway for interpreting SLF in observations and inform modeling of massive-star interiors and their asteroseismic diagnostics.

Abstract

The power spectrum of light curves from satellites like CoRoT and TESS of massive main-sequence stars show stochastic low-frequency (SLF) variability. To investigate the origin of this phenomenon, we conducted high-resolution 3D hydrodynamic \texttt{PPMstar} simulations of a non-rotating \unit{25}{\Msun} zero-age main sequence star, modeling 95\% of the stellar structure with both a core and a thin outer envelope convection zone. The outer envelope convection zone was implemented through modification of the opacity model, shifting the Fe opacity bump inward and enhancing its amplitude for computational feasibility. The luminosity power spectrum from our primary simulation (M424) exhibits qualitative and quantitative characteristics similar to observed SLF variability, with a $\approx2$-dex difference between high- and low-frequency power. The spectrum displays distinct features attributable to internal gravity wave (IGW) eigenmodes. To isolate the contributions of different stellar regions, we performed numerical experiments with suppressed core convection, envelope convection and envelope-only configurations. The comparative analysis demonstrates that outer envelope convection alone produces significantly less low-frequency power than the full-star configuration. In our simulations the outer envelope convection zone excites at its inner boundary a rich IGW eigenmode spectrum in the layer just below. In an otherwise identical simulation where the core convection is not driven by heating, the SLF spectrum is remarkably similar and the integrated power is reduced by only 10\%, suggesting that the envelope convection is the dominant contributor to SLF power spectrum. The IGW spectral characteristics depend on the complete stellar stratification, demonstrating that interior structure could influence observable surface variability.

Figures (4)

• Figure 1: (Left): Kippenhahn diagram of the ZAMS 25 $\mathrm{M_\odot}$MESA model. Grey regions represent convective zones, white regions represent radiative zones, and blue contours indicate nuclear burning regions with intensities shown in the colorbar. The red dashed vertical line marks the initial model used for all the PPMstar simulations presented in this work. (Right): Radial profiles of the radiative ($\nabla_{\rm rad}$, solid orange line), adiabatic ($\nabla_{\rm ad}$, grey solid line), and actual temperature gradients ($\nabla_{\rm T}$, blue dashed line) for the ZAMS MESA model. The light orange dashed vertical line marks the outer boundary of the simulations presented in this work.
• Figure 2: Comparison between the MESA opacity profile and the modified opacity model used in the PPMstar simulations. The grey dashed vertical line indicates the radial location of opacity bump maxima in the MESA profile, the orange dot-dashed line shows the radial location of the maxima in the modified opacity model, and the blue dotted line marks the outer boundary of the simulation domain.
• Figure 3: Comparison of CFL timestep Courant1928 (with Courant number 0.9) with radiation diffusion timestep Rider1999 for the MESA model, dump 0 and dump 4800 ($\approx$ 3779 h) of run M424 using spatial resolution $\Delta x$ = $4.58\;\mathrm{\mathrm{M}\mathrm{m}}$. The red dotted line marks the outer boundary at 4100 Mm.
• Figure 4: Comparison of pressure ($\mathrm{P}$), temperature ($\mathrm{T}$), density ($\mathrm{\rho}$), and linear Brunt--Väisälä frequency ($\mathrm{\nu_{Brunt}}$) stratifications between the MESA state, dump 0, dump 400 ($\approx$$78\;\mathrm{\mathrm{h}}$ and dump 4800 ($\approx$$3779\;\mathrm{h}$) of run M424. All panels share the same legend as shown in the top two panels.