Red-Giant Asteroseismology of Low-Mass Population III Stars

Abstract

Low-mass stars from the first epoch of star formation may still persist in the Milky Way and its satellite dwarf galaxies today; however, their detection is confounded by surface pollution from interstellar accretion and internal mixing, which obscure their primordial composition and blur their distinction from second-generation stars. Asteroseismology offers a probe of the internal structure and evolutionary state of stars, and hence may aid in the search for primordial stars. In this second paper of the series, we present the first non-radial adiabatic pulsation analysis of low-mass, metal-free stellar models. We use a $0.85\,M_\odot$ red giant as a case study and compare its seismic signatures with those of higher-metallicity models. At the same central hydrogen fractions, Pop III main-sequence models display systematically higher $r_{02}\equivδν_{02}/Δν$ ratio and lower $Δν$ than metal-enriched analogues, a direct consequence of their larger internal sound speeds and steeper core-envelope stratification. To interpret the structural dependence during giant evolution, we introduce a composite asteroseismic diagnostic, $ψ\equivΔν/ΔΠ_1$, which traces how metallicity influences the balance between acoustic and buoyancy cavities through its imprint on opacity, core contraction, and mean molecular-weight gradients. Pop III models occupy a distinct locus in the $ψ-ΔΠ_1$ plane due to their radiative interiors with lower mean densities and delayed development of core mean molecular weight gradients. We find that asteroseismology is a powerful diagnostic for identifying relic Pop III stars despite potentially polluted surfaces, providing a clear pathway for future searches of the Galaxy's oldest surviving stars with upcoming surveys.

Figures (9)

• Figure 1: The ratio $r_{02} \equiv \delta\nu_{02}/\Delta\nu$ as a function of the large frequency separation $\Delta\nu$ on the main sequence. The left panel shows results for Pop III stars of varying mass, and the right panel presents models of fixed mass ($0.85~M_\odot$) at different metallicities. Models with metallicities up to $10^{-5}$, including $Z = 0$, are overlaid in the right panel. Grey dash-dotted lines connect evolutionary stages with the same central hydrogen fraction $X_c$, illustrating how asteroseismic properties evolve as the star ages and depletes hydrogen in its core; its mean density decreases due to expansion, resulting in lower values of both $\Delta\nu$ and $r_{02}$. This reflects the slower sound speed and increased sound travel time across the star (see Equations \ref{['eq:deltanu']}$-$\ref{['eq:r02']}).
• Figure 2: Kiel diagram (top) and Hertzsprung–Russell diagram (bottom) for $0.85~M_\odot$ stellar models at distinct metallicities. As metallicity decreases, the evolutionary sequences systematically shift towards higher $T_{\mathrm{eff}}$ at fixed $\log g$, reflecting the reduced envelope opacity and diminished line blanketing in metal-poor atmospheres. Evolution progresses from higher $\log g$ on the main-sequence and subgiant branch towards lower $\log g$ and cooler $T_{\mathrm{eff}}$ along the red giant branch. Black crosses in the top panels represent Kepler RGB stars from 2016AA...588A..87V for comparison. The same stars are presented in the bottom panel, however, with luminosities retrieved from the Gaia DR3 catalogue 2023AA...674A...1G. Background colours indicate spectral-type domains for both panels. The coloured squares correspond to the evolutionary stages of the $Z = 0$ and $Z = 10^{-3}$ models shown in Table \ref{['tab:Pop_IIvsIII']}. Blue and red squares indicate models matched by effective temperature; green squares indicate those matched by surface gravity; yellow and purple squares correspond to models matched by large frequency separation (see Table \ref{['tab:Pop_IIvsIII']} and Figure \ref{['fig:propagation']}).
• Figure 3: Propagation diagrams for representative Pop II and Pop III stellar models at three evolutionary stages: subgiant (panel (A); when two models share roughly the same effective temperature), SG-RGB transitions (panels (B), (C), and (D); with both models at roughly the same surface gravity and large frequency separations), and advanced RGB (panel (E); both models at roughly the same effective temperature as well). We refer to Table \ref{['tab:Pop_IIvsIII']} for a detailed description of the evolutionary phases. Each panel shows the Brunt-Väisälä frequency $N$ (solid/dashed for Pop II/Pop III), and the Lamb frequency $S_\ell$ for $\ell = 1$ (solid/dashed) as functions of fractional mass, with $\Delta\nu$, $\nu_{\rm max}$ and $\Delta\Pi_1$ indicated for each case. Dashed/dotted horizontal blue lines indicate $\nu_{\rm max}$ for Pop II/Pop III models, respectively. See also Table \ref{['tab:Pop_IIvsIII']} summarises the comparisons.
• Figure 4: Period spacing $\Delta\Pi_1$ along the subgiant and red giant branch as a function of the frequency spacing $\Delta\nu$ for stellar models of varying metallicity. KIC stars 10152909, 5696938, 9326896, 9474201, 9945389, 7509923, and 6273090 are highlighted in green as discussed in Section \ref{['sec:binarity']}. We note that in the $\psi-\Delta\Pi_1$ plane (Figure \ref{['fig:psi']}), the slope of the evolutionary track along the subgiant and red giant branch correspond to approximately the inverse of $\psi$, i.e., $\dd{\Delta\Pi_1}/\dd{\Delta\nu} \sim 1/\psi$ for quasi-linear sections, which provides a visual interpretation of $\psi$ as the gradient of the track, linking steeper slopes to weaker p-g coupling and flatter slopes to stronger coupling.
• Figure 5: Seismic spacing ratio $\psi \equiv \Delta\nu / \Delta\Pi_1$ as a function of central entropy $s$ ($k_B$ per baryon) for $0.85~M_\odot$ models across different metallicities. Metal-free models show broader, lower-amplitude peaks due to slower entropy evolution and less efficient CNO burning, whilst metal-enriched models (e.g., $Z = 10^{-2}$) exhibit sharper, higher peaks from steeper temperature gradients and enhanced opacity.