Dynamics of the TWA 7 planetary system and possibility of an additional planet

Abstract

The debris disk surrounding the young star TWA 7 exhibits morphological features that tightly constrain its planetary architecture. JWST/MIRI observations have recently revealed a directly imaged outer planet at large separation. The disk also displays a sharply defined inner edge near 23 au and an extended asymmetric structure that may trace a horseshoe-like distribution of material indicative of gravitational interactions between planets and planetesimals. We investigate whether the observed disk morphology and the possible co-orbital material can be explained by the combined gravitational influence of the known outer planet and an undetected inner companion. We aim to identify planetary configurations consistent with both the disk structure and the long-term stability of the system. We combined N-body simulations and secular perturbation theory to explore how an undetected inner planet could shape the inner edge of the disk while maintaining the dynamical coldness required for stable co-orbital structures around the outer planet. The analytical framework quantifies the secular coupling between the two planets and delineates dynamically viable configurations. The inner edge of the disk near 23 au can be reproduced by a sub-Jovian planet orbiting between 13 and 23 au. Secular interactions further restrict this companion to nearly circular orbits, as higher eccentricities would excite the outer planet and destabilize the co-orbital material. Together, these constraints confine the system to a narrow region of parameter space. The TWA 7 system appears dynamically cold, with all components, including the planets and the debris disk, sharing nearly circular and coplanar orbits. Such a quiescent configuration likely reflects the weak dynamical stirring, making it a promising laboratory to study the early interplay between planet formation, co-orbital dynamics, and debris-disk evolution.

Figures (5)

• Figure 1: Dynamical status at the end of an example of a simulation of the dynamics of the TWA 7 planetary system with two planets, TWA 7 b (red), an additional planet TWA 7 c (blue), and the disk of planetesimals. The initial orbital parameters of TWA 7 b are $m_b=0.3$$\textnormal{M}_{\textnormal{Jup}}$, $a_b=52$ au Lagrange+2025, and $e_b=0$, consistent with the constraints derived in Sect. \ref{['twa7b_constraints_coorbital']}. In this example, the initial orbital parameters of TWA 7 c are $m_c=0.4$$\textnormal{M}_{\textnormal{Jup}}$, $a_c=18$ au, and $e_c=0$. Left: View of the system from above. The planetesimals are depicted with small black dots, and the orbits of the planets are indicated with dashed colored lines. Middle: View of the system in terms of semi-major axis and eccentricity. Right: Radial profile of the planetesimal disk (solid black line) superimposed to the observations of Ren+2021 (green dotted line). This configuration reproduces the observed inner edge of the disk while preserving a population of horseshoe co-orbitals along the orbit of TWA 7 b.
• Figure 2: Combinations of the mass and initial semi-major axis of TWA 7 c within the observational limits that successfully reproduce the inner edge of the disk at 23 au. For several values of $m_c$, the corresponding acceptable ranges of $a_c$ are shown in green. These ranges reflect the width of the inner edge of the disk as defined in Sect. \ref{['twa7c_constraints_inner_edge_method']}. A power-law fit is overlaid in blue, accounting for the extent of each semi-major-axis range. Shaded areas correspond to regions that are not dynamically accessible to TWA 7 c.
• Figure 3: Allowed configurations for a possible inner planet in the $(a_c, m_c)$ plane for increasing values of initial eccentricity, $e_c$, under the constraint that the simulated disk reproduces the observed inner edge at 23 au. The plotting conventions are the same as in Fig. \ref{['fig:simus_c_e000']}. The red line marks the upper mass limit set by observations and, when applicable, by the additional requirement that the outer planet TWA 7 b remains dynamically cold enough to support stable horseshoe-like co-orbitals (Sect. \ref{['twa7b_constraints_coorbital']}). The red dot indicates the intersection point where, for a given eccentricity, all solutions above this limit are excluded. As $e_c$ increases, this constraint becomes increasingly restrictive, eventually ruling out all configurations compatible with the observed disk morphology.
• Figure 4: Accessible mass of the additional planet TWA 7 c as a function of its eccentricity $e_{c}$, based on the results of Fig. \ref{['fig:twa7c_e']}, whose plot conventions are similar.
• Figure 5: View from above of the same simulation as in Fig. \ref{['fig:ExSimuValide']}, but with an initial eccentricity of $e_c = 0.2$ for the additional planet TWA 7 c. This configuration reproduces the observed inner edge of the disk but fails to preserve a stable population of horseshoe co-orbitals along the orbit of TWA 7 b, leaving only two separate arcs consisting of particles moving on tadpole orbits.