Planetary Obliquity Excitation Through Pre-Main Sequence Stellar Evolution

TL;DR

This work investigates how a young, rapidly rotating, distended star can excite planetary obliquities through its evolving quadrupole moment, driving nodal regression of small-body orbits and potential capture into secular spin-orbit resonance. Using a coupled PMS stellar-evolution model and a perturbative Hamiltonian for spin dynamics, the authors derive crossing and adiabatic capture criteria ($g/\alpha$ crossing) and show that close-in planets ($a_p\lesssim1$ AU) are most susceptible to excitation, potentially reaching obliquities near $90^{\circ}$. They validate and extend the analysis with N-body simulations that include disk torques, tides, and planet-planet interactions, revealing that stellar oblateness can seed long-lived non-zero obliquities via later resonances dominated by planet-planet dynamics, though tides and disk perturbations can destabilize or modulate the process. The results imply a general mechanism by which high-obliquity exoplanets can arise early in system evolution, influencing climate, tidal histories, and long-term dynamical architecture. Overall, stellar oblateness during the PMS phase emerges as a potent, transient driver of obliquity that can leave lasting dynamical imprints through subsequent secular interactions.

Abstract

A planet's axial tilt ("obliquity") substantially affects its atmosphere and habitability. It is thus essential to comprehend the various mechanisms that can excite planetary obliquities, particularly at the primordial stage. Here, we explore planetary obliquity excitation induced by the early evolution of the host star. A young, distended star spins rapidly, resulting in a large gravitational quadrupole moment that induces nodal recession of the planet's orbit. As the star contracts and spins down, the nodal recession frequency decreases and can cross the planet's spin axis precession frequency. An adiabatic encounter results in the planet's capture into a secular spin-orbit resonance and excites the obliquity to large values. We find planets within $a \lesssim 1 \ \mathrm{AU}$ are most affected, but adiabatic capture depends on the initial stellar radius and spin rate. The overall picture is complicated by other sources of perturbation, including the disk, multiple planets, and tidal dissipation. Tides make it such that stellar oblateness-induced obliquity excitation is transient since tidal perturbations cause the resonance to break once high obliquities are reached. However, this early transient excitation is important because it can prime planets for long-term capture in a secular spin-orbit resonance induced by planet-planet interactions. Thus, although stellar oblateness-induced resonances are short-lived, they facilitate the prevalence of long-lived non-zero obliquities in exoplanets.

Figures (12)

• Figure 1: Top panel: Evolution of the stellar radius of a solar mass star ($n=3/2$ polytrope) with initial radius $4 \ R_{\odot}$ and effective temperature $4270 \ \mathrm{K}$. Bottom panel: Corresponding rotational evolution accounting for stellar contraction and star-disk interactions. We present three initial conditions corresponding to fast, medium, and slow rotators. The magnitude of the magnetic braking dictates the stellar spin distribution in the later stages of the system's evolution, where a weak braking would lead to a spin-up due to gravitational contraction and accretion, while a more effective magnetic braking would lead to stellar spin-down.
• Figure 2: The limits on the planet's semi-major axis and initial stellar radius for which resonance crossing (equation \ref{['eq: a_max_crossing']}) and capture (equation \ref{['eq: a_max_capture']}) would occur. We consider multiple values of the initial stellar rotation period $P_{\star 0}$.
• Figure 3: Obliquities as a function of $g/\alpha$ corresponding to the four different Cassini states assuming $i = 5^{\circ}$. States 1 and 4 do not exist when $g/\alpha > \left(g/\alpha\right)_{\mathrm{crit}}$, and state 2 is the only possible configuration where the planet can experience high obliquities in secular spin-orbit resonance.
• Figure 4: Phase-space representation of the Hamiltonian (equation \ref{['eq: H']}) as the system evolves. The contour lines trace out level curves of the Hamiltonian. As time advances, the star contracts and spins down due to magnetic braking, and the disk loses its mass. This results in $g/\alpha$ decreasing and gives rise to the secular spin-orbit resonance. These plots use an inclination $i = 5^{\circ}$, the angle between the orbital and disk planes. As the system approaches the critical value of $\left(g/\alpha\right)_{\mathrm{crit}} = 0.766$, a separatrix appears, as do the various Cassini states. The radius of the phase plot increases with time, which indicates that the obliquity increases as the polar radius is equal to $\sqrt{-2\Theta}$, where $\Theta = \cos{\epsilon} - 1$.
• Figure 5: Planetary obliquity evolution from the secular model of the Hamiltonian in equation \ref{['eq: H']}. First $\&$ second panels: Evolution of the stellar radius and spin rate of a solar-like PMS star with initial radius equal to $4 \ R_{\odot}$ and initial rotation period equal to 2 days. Third panel: Evolution of $g/{\alpha}$, the ratio between the orbital and spin axis precession frequencies. The different colors correspond to planets with different semi-major axes. Fourth panel: The resulting planetary obliquity evolution from the numerical integration of the Hamiltonian (equation \ref{['eq: H']}). These calculations use the fiducial values defined in Table \ref{['table: Model Parameters']}.