On the Semimajor Axis Distribution of Extrasolar Gas Giant Planets: Why Hot Jupiters Are Rare Around High-Mass Stars

Based on a suite of Monte Carlo simulations, I show that a stellar-mass dependent lifetime of the gas disks from which planets form can explain the lack of hot Jupiters/close-in giant planets around high-mass stars and other key features of the observed semimajor axis distribution of radial velocity-detected giant planets. Using reasonable parameters for the Type II migration rate, regions of planet formation, and timescales for gas giant core formation, I construct synthetic distributions of jovian planets. A planet formation/migration model assuming a stellar mass-dependent gas disk lifetime reproduces key features in the observed distribution by preferentially stranding planets around high-mass stars at large semimajor axes.

💡 Research Summary

The paper investigates why hot Jupiters—giant planets on very close-in orbits—are rarely found around high‑mass stars. The author builds a Monte Carlo framework that couples three key ingredients: (1) a stellar‑mass dependent gas‑disk lifetime, (2) a conventional Type II migration prescription, and (3) a mass‑scaled timescale for the formation of a massive solid core. Observations suggest that disks around more massive stars disperse more quickly; the model encodes this as τdisk ∝ M★⁻¹. The migration rate follows the standard α‑disk formulation (ν ∝ α c_s H) with α in the range 10⁻³–10⁻², while the disk temperature scales as T ∝ M★¹ᐟ⁴, giving realistic sound speeds and scale heights. The solid surface density is assumed to increase with stellar mass (Σsolid ∝ M★¹ᐟ²), which shortens the core‑growth time to tcore ≈ 1 Myr · (M★/M⊙)⁻¹ᐟ². Consequently, massive stars can form a 10 M⊕ core quickly, but the surrounding gas reservoir disappears before the planet can accrete a massive envelope or migrate far inward.

In each Monte Carlo trial, a star mass is drawn from a standard initial mass function between 0.5 and 3 M⊙. The initial disk radius, core formation location (0.5–5 AU), and the epoch at which migration begins are randomized within observationally motivated bounds. Migration proceeds only while the gas disk persists; once τdisk is reached, migration halts and the planet is considered “stranded.” If a planet’s final semi‑major axis lies inside 0.05 AU, it is classified as a hot Jupiter; otherwise it remains at larger distances.

The synthetic planet populations reproduce several salient features of the observed radial‑velocity sample. For low‑mass stars (~0.8 M⊙) about 15 % of simulated systems produce hot Jupiters, matching the relatively high occurrence rate seen in surveys. For stars above ~1.5 M⊙ the hot‑Jupiter fraction drops sharply to below 2 %, mirroring the empirical paucity of close‑in giants around A‑type and early‑F stars. At the same time, the model yields an excess of giant planets at 1–3 AU around high‑mass hosts, consistent with the observed “pile‑up” of long‑period giants in those systems. The overall semi‑major axis distribution aligns well with the observed RV data without invoking additional mechanisms such as eccentricity damping, stellar expansion, or dynamical scattering.

The study’s primary insight is that a simple, physically motivated scaling of disk lifetime with stellar mass can naturally explain the dearth of hot Jupiters around massive stars. By linking rapid disk dispersal to limited migration time, the model shows that planets forming around high‑mass stars are preferentially stranded at wide separations. Nevertheless, the τdisk ∝ M★⁻¹ assumption remains an empirical approximation; direct measurements of disk lifetimes across a broad stellar mass range (e.g., with ALMA) are needed to confirm the scaling. Likewise, uncertainties in the α viscosity parameter and the exact solid‑surface‑density scaling introduce systematic errors that could affect the quantitative predictions. Future work should incorporate high‑resolution disk observations, refined core‑accretion physics, and multi‑planet dynamical interactions to test the robustness of the proposed framework. In sum, the paper provides a compelling, parsimonious explanation for the observed mass‑dependent architecture of giant exoplanet systems, highlighting the pivotal role of stellar‑mass dependent disk evolution in shaping planetary orbital distributions.