Second Generation Planet Formation in Post-AGB Discs: Testing the Role of Gravitational Instability

TL;DR

The study asks whether gravitational instability can drive second-generation planet formation in post-AGB circumbinary discs. It develops an analytic framework based on the Toomre criterion $Q$, cooling times with $t_{cool}<\frac{\beta}{\Omega}$, and physically motivated disc density and temperature profiles, then benchmarks the approach on well-studied YSO discs before applying it to typical post-AGB systems with masses $M_{disc}\sim0.01$–$0.1\,M_\odot$. The results show post-AGB discs are generally gravitationally stable today ($Q>1$) and remain so even when evolved backward in time via viscous evolution, implying that GI is unlikely to dominate second-generation planet formation in these environments; planetary signals in some systems would require unrealistically high disc masses if GI were responsible. The work also demonstrates that while NN Ser could in principle form planets via GI under a high-mass disc, contemporary common-envelope constraints make such massive fallback discs less plausible, suggesting core accretion-like pathways may be more viable for planets around evolved binaries.

Abstract

Post-asymptotic giant branch (post-AGB) binary stars are evolved systems that host circumbinary discs formed through mass loss during late stage binary interactions. Their structural, morphological, kinematic, and chemical similarities to planet-forming discs suggest that these systems may act as sites of "second generation" planet formation. In this study, we assess whether the disc instability mechanism -- a proposed pathway for rapid, giant planet formation in some protoplanetary discs - can operate in post-AGB discs; motivated by their short lifetimes. Using the Toomre criterion under well motivated assumptions for disc structure and size, mass, and thermal properties, we assess the conditions for gravitational instability. We first benchmark our analytical framework using well studied protoplanetary disc systems (including HL Tauri, Elias 2-27, GQ Lupi) before applying the same analysis to observed post-AGB discs. We find that post-AGB discs are generally gravitationally stable at present, due primarily to their low masses. Using viscous disk theory, we find that the discs were stable against collapse even in the past, when their masses were potentially higher. In contrast, several protoplanetary discs analysed in the same way show that they likely experienced gravitationally unstable phases early on. We also find that higher viscosity parameters are better aligned with expected post-AGB disc lifetimes. Finally, we revisit the planet formation scenario proposed for the post-common envelope system NN Ser, first carried out by Schleicher and Dreizler and we show that gravitational instability could be feasible under specific, high disc mass assumptions. Overall, our results provide the first systematic theoretical assessment of gravitational instability in post-AGB discs, demonstrating that this mechanism is unlikely to dominate second generation planet formation in these systems.

Figures (11)

• Figure 1: Power-law surface density functions with $n=1$ as a function of orbital distance for $M_{\rm disc}=0.15~M_\odot$ for different values of $r_{\rm out}$, to demonstrate why the surface density is highly sensitive to $r_{\rm out}$.
• Figure 2: Toomre parameter $Q$ versus disc radius for the YSOs tabulated in Table \ref{['tab:yso']}. Only AB Aurigae with the disc mass reported in 2023Speedie, and L1448 IRS3B fall below $Q=1$.
• Figure 3: The Toomre parameter $Q$ as a function of radius for typical post-AGB discs, assuming $M_1+M_2=1.5$ M$_\odot$, $R_{\rm star} =100$ R$_\odot$, $T_{\rm star} =5,000$ K, $r_{\rm in}=3$ au, and $r_{\rm out}=100$ au as a lower limit of post-AGB disc truncation radii. The index $n$ is the power-law index of the surface density profile for each of the curves. Even in this relatively compact scenario, we see that the discs are generally stable.
• Figure 4: The Toomre parameter $Q$ as a function of radius for the post-AGB system IRAS 08544-4431. The shaded region indicates the uncertainty in the total disc mass, based on estimates from Bujarrabal_2018 and Corporaal_2023.
• Figure 5: Contours showing variation of the Toomre parameter $Q$ as a function of disc radius and mass, evaluated at the outermost radius $r_{\rm out}$ for post-AGB discs with surface density exponent $n=0.5$ and $n=1$ (left and centre panels), and at the innermost radius $r_{\rm in}$ for $n=3$ (right panel). All calculations adopt $R_{\rm star}=100$ R$_\odot$, $T{\rm star}=5000$ K, and $M_{\rm cnt}=1.5$ M$_\odot$.