Hot Jupiters in Old Wide-Binary Systems

Abstract

Hot Jupiters (HJs) are giant planets with orbital periods shorter than $10$ days, found around $\sim 0.5$-$1\%$ of Sun-like stars. Their origins remain debated despite decades of study. The high prevalence of stellar companions, the eccentricity distribution of 'Cold' Jupiters on longer orbits, and the wide range of stellar spin-orbit misalignments support high-eccentricity migration: planets are excited to eccentric orbits and subsequently circularised via tidal dissipation. Existing high-eccentricity migration models, however, are inefficient in converting the initial population of Cold Jupiters to HJs. Current models reproduce at most $\lesssim 30\%$ of observed HJs, while the resulting Cold/Hot Jupiter ratios ($\gtrsim 30$) overproduce the observed values of $10$-$15$. These models also fail to form HJs around old stars ($\gtrsim 3$ Gyr) on short tidal decay timescales (e.g., $<40$ Myr). Here we show that wide binaries ($a > 10^3$ au) perturbed by the Galactic tidal field produce $1.8\pm 0.14$ more HJs compared to isolated binary systems, accounting for $26$-$40\%$ of the observed population under conservative assumptions. Wide-binaries predominantly produce Gyr-old systems, consistent with the host-age distribution for $t \ge 2.5\ \rm Gyr$. In $\sim 20\%$ of cases, wide-binary perturbations eject giant planets entirely, resolving the Cold/Hot Jupiter ratio discrepancy while naturally seeding the population of free-floating giant planets. In our dynamical framework, wide binaries emerge as active agents that reshape planetary demographics across billions of years. These results will be decisively tested by forthcoming exoplanet and microlensing surveys.

Figures (8)

• Figure 1: Hierarchical wide three-body system of the two stars in a wide orbit (green ellipse) of semi-major $a_2$, typically above $10^3\ \rm au$. The outer wide binary star orbit is inclined with the galactic plane by an angle $\iota_{\rm out}$ An inner binary giant planet (black ellipse) with semi-major axis $a_1 \gtrsim 5\ \rm au$. The mutual inclination between the orbits is $\iota_\mathrm{mut}$.
• Figure 2: Time evolution for regular and chaotic HJ formation pathways. Top: time evolution of the mutual inclination of a regular orbit (a) and a chaotic orbit (b). Middle: Evolution of the proto-HJ's semi-major axis and pericentre for a regular orbit (c) and a chaotic orbit (d). Bottom: Evolution of the inner (black) and outer (green) eccentricity of a regular orbit (e) and a chaotic orbit (f). The initial conditions for the regular orbit are $a_1 = 5.82\,\mathrm{au}$, $a_2 = 1522.07\,\mathrm{au}$, $e_1 = 0.15$, $e_2 = 0.72$, $i_1 \approx 45.9^\circ$, $i_2 \approx 103.2^\circ$, $\iota_{\rm mut} \approx 87.3^\circ$, $\omega_1 \approx 59.7^\circ$, $\omega_2 \approx 118.6^\circ$, $\Omega_1 \approx 45.7^\circ$, $\Omega_2 \approx 118.5^\circ$, $m_1 = 1.15\,M_\odot$, and $m_3 = 0.50\,M_\odot$. The initial conditions for the chaotic orbit are $a_1 = 27.40\,\mathrm{au}$, $a_2 = 14540.34\,\mathrm{au}$, $e_1 = 0.42$, $e_2 = 0.89$; inclinations $i_1 \approx 138.3^\circ$, $i_2 \approx 30.2^\circ$, $\iota_{\rm mut} \approx 167.9^\circ$, $\omega_1 \approx 261.7^\circ$, $\omega_2 \approx 192.4^\circ$, $\Omega_1 \approx 18.7^\circ$, $\Omega_2 \approx 337.7^\circ$, $m_1 = 0.66\,M_\odot$, $m_3 = 0.65\,M_\odot$ .
• Figure 3: Top panel: Initial $\cos \iota_{\rm mut}$ versus $\mathcal{R}_0$ for the run with GT (a). Migrated (circles) and disrupted (squares) systems are color-coded by the total evolution time. Individual simulations in Figure \ref{['fig:1']} are also shown (stars). Bottom panels: $a_1$-$a_2$ parameter space for the simulations with GT turned on (b) and off (c), coloured by the initial mutual inclination between the orbits ($|\cos \iota_{\rm mut}|$).
• Figure 4: Cumulative delay-time distributions of the simulations overlaid with stellar ages and fits. The occurrence rate fit in green is given by hj_gyr, while the HJ sample with known stellar ages from the NASA exoplanet archive database is in black, with measurement uncertainties represented by the gray shaded area. Disruptions are in red and HJ formation is in blue. Simulations with and without GT are represented by solid and dashed lines, respectively.
• Figure 5: Example of time evolution of a representative system which represents octupole-level ZLK dynamics. The initial conditions are: semi-major axes $a_1 = 5.25\,\mathrm{AU}$, $a_2 = 1236.74\,\mathrm{AU}$; eccentricities $e_1 = 0.29$, $e_2 = 0.80$; inclinations $i_1 \approx 48.1^\circ$, $i_2 \approx 107.3^\circ$, and mutual inclination $\iota_{\rm mut} \approx 76.75^\circ$. The arguments of pericentre are $\omega_1 \approx 12.8^\circ$, $\omega_2 \approx 210.7^\circ$; and the longitudes of ascending node are $\Omega_1 \approx 117.5^\circ$, $\Omega_2 \approx 170.5^\circ$. The masses are $m_1 = 0.77\,M_\odot$, $m_2 = M_J$, and $m_3 = 0.55\,M_\odot$