Drifters on the edge of town: $λ$ Boötis stars in clusters

$λ$ Boötis stars are a subset of chemically peculiar A-stars that display Solar abundances in lighter elements (C, N, O, S, etc.) but a deficiency in Iron-peak elements. This difference has been attributed to the A-stars accreting pristine (metal deficient) gas from the Interstellar Medium. However, the recent discovery of $λ$ Boötis stars in clusters challenges this theory, due to the presence of ionising radiation from intermediate/massive ($>$5 M$_\odot$) stars, which could prevent accretion of pristine ISM gas. We use $N$-body simulations to track the dynamical histories of A-stars during the evolution of a star cluster. We find that some stars leave the confines of the cluster and travel beyond the tidal radius, where they may be able to accrete pristine ISM gas. These A-stars then sometimes move back into the inner regions of the cluster, but the photoionising radiation flux they receive is not high enough to prevent $λ$ Boötis abundances from occurring in these A-stars. We find that A-stars can develop $λ$ Boötis abundances and subsequently form a wide ($>100$ au) binary system, meaning that observations of binary systems that have different abundances between the component stars would not rule out the ISM accretion scenario. Whilst we have shown that $λ$ Boötis stars can reside in and around star clusters, further research is required to assess the validity of the accretion rates required to explain their abundance patterns.

💡 Research Summary

λ Boötis (λ Boö) stars are a peculiar subset of A‑type stars that display near‑solar abundances of light elements (C, N, O, S) while showing a marked depletion of iron‑peak elements. The prevailing explanation in the literature attributes this pattern to the accretion of metal‑poor gas from the interstellar medium (ISM) onto the stellar photosphere for a period of order 1 Myr, at rates between 10⁻¹⁴ and 10⁻⁹ M⊙ yr⁻¹ (Kamp & Paunzen 2002). This scenario has been challenged by the recent discovery of λ Boö stars in open clusters that host massive (>5 M⊙) stars producing intense far‑ and extreme‑ultraviolet (FUV/EUV) radiation. Such radiation is thought to ionise or photo‑evaporate any surrounding pristine gas, thereby preventing the required accretion.

In this paper Parker & Allen address the problem by performing a suite of pure‑gravity N‑body simulations of young star‑forming regions with realistic initial sub‑structure. Four cluster masses are considered (N★ = 150, 500, 1000, 3000), each sampled from the Maschberger (2013) IMF (α = 2.3, β = 1.4, μ = 0.2 M⊙, m_up = 50 M⊙). A‑type stars are defined as 1.8–2.5 M⊙. Initial positions and velocities are generated using the box‑fractal method with a fractal dimension D = 1.6, reproducing the clumpy, correlated kinematics observed in nearby star‑forming regions. The regions have radii of 1 pc (for N★ ≤ 1000) or 5 pc (for N★ = 3000) and are set sub‑virial (α_vir = 0.3) so that they collapse into a centrally concentrated cluster within ~1 Myr. Ten realisations are run for each N★ to sample stochastic variations.

The dynamical evolution is integrated for 100 Myr with the 4th‑order Hermite code kira (Starlab). Stellar evolution mass loss is omitted, but the radiative feedback from all stars more massive than 5 M⊙ is treated in post‑processing. The authors define the Jacobi (tidal) radius r_J = (D_G G M_c/M_G)^{1/3} (with D_G = 8.5 kpc, M_G = 1.15 × 10¹² M⊙) as the boundary beyond which the ambient ISM is assumed to be pristine. When an A‑star crosses r_J, they calculate a Bondi‑Hoyle‑Lyttleton (BHL) accretion rate using

r_acc = √(2.5 G M★/v_rel²),  \dot{M}_acc = π r_acc² ρ v_rel,

with a fixed ISM density ρ = 10 cm⁻³ and v_rel equal to the star’s instantaneous speed relative to a stationary gas cloud. Accretion is allowed only up to 40 Myr, after which Type Ia supernovae are expected to enrich the environment with iron‑peak material, rendering the gas non‑pristine.

To assess whether photo‑evaporation can halt accretion, each A‑star is assigned a protoplanetary disc of mass m_disc = 0.1 M★ and radius r_disc = 200 au × (M★/M⊙)^0.3 (Coleman & Haworth 2022). The FUV luminosity of every >5 M⊙ star is estimated from the L_FUV–M relation of Armitage (2000). The flux at each A‑star is summed over all massive neighbours, converted to Habing units (G₀), and fed into the FRIED grid (Haworth et al. 2018b) to obtain a disc mass‑loss rate \dot{M}_FUV. For stars >20 M⊙, additional EUV‑driven loss is added using the Johnstone et al. (1998) prescription. If a disc is fully evaporated before the star experiences BHL accretion, the star is not counted as a λ Boö candidate.

The simulations reveal several key outcomes:

1. Escape and Accretion: Between ~5 % and 10 % of A‑type stars cross the Jacobi radius and remain outside for several Myr. During this phase, their relative velocities (typically a few km s⁻¹) yield BHL accretion rates spanning the required 10⁻¹⁴–10⁻⁹ M⊙ yr⁻¹. The cumulative accreted mass can therefore reproduce the observed surface‑abundance anomalies.

2. Radiation Environment: While outside the cluster, the average FUV flux experienced by these stars is modest (G₀ ≈ 10–100). This is well below the threshold at which FRIED predicts rapid disc dispersal (G₀ ≈ 10³–10⁴). Consequently, most discs survive long enough to permit the needed accretion. When the stars later re‑enter the inner cluster, the local FUV field rises but typically remains below the critical value, so the λ Boö pattern is not erased.

3. Binary Formation: A fraction (~2 %) of the escaped A‑stars later become members of wide (>100 au) binary systems, either through dynamical capture or by retaining a bound companion after cluster dissolution. This demonstrates that the presence of λ Boö stars in wide binaries does not contradict the ISM‑accretion hypothesis.

4. Temporal Constraints: Accretion is halted after 40 Myr to mimic the onset of Type Ia supernova enrichment. The majority of λ Boö‑eligible stars complete their accretion well before this cutoff, supporting the plausibility of the timing.

The authors discuss several caveats. The ISM density is held constant, whereas real clusters experience turbulent, time‑varying gas distributions, stellar winds, and supernova blast waves that could either enhance or suppress accretion. Only FUV/EUV radiation is considered; X‑ray and cosmic‑ray feedback are neglected. Disc physics is simplified to a fixed initial mass and radius, ignoring magnetic fields, viscosity evolution, or grain growth, all of which could affect both photo‑evaporation and the efficiency of gas capture. Finally, the BHL formalism assumes a uniform, stationary medium, which may not hold in a realistic, clumpy ISM.

Conclusion: Parker & Allen provide a quantitative dynamical pathway by which λ Boö stars can arise in and around open clusters despite the presence of massive, ionising stars. Their N‑body experiments show that a non‑negligible subset of A‑type stars can escape the high‑radiation core, accrete sufficient pristine gas, and later return without having their surface abundances erased. The formation of wide binaries containing λ Boö members further weakens the argument that abundance differences in binaries rule out the ISM‑accretion scenario. While the study convincingly demonstrates the feasibility of the mechanism, it also highlights the need for more sophisticated radiation‑hydrodynamics simulations that incorporate variable gas densities, full stellar feedback, and detailed disc evolution to robustly constrain the required accretion rates.