Dimitri Veras

Context. The time evolution of the observed periodicities of transiting rocky debris around white dwarfs (WDs) potentially signposts ongoing dynamical interactions between the debris and co-orbital asteroids or planets with similar orbital periods (1/1 mean-motion resonance). In Paper I, we analysed these WD-secondary-dust particle systems within the framework of the circular restricted three-body problem (CRTBP). Aims. We aim to extend Paper I to the eccentric secondary orbit case and now analyse the elliptic restricted three-body problem (ERTBP). Our secondary masses include Ceres, Mercury, Earth, and Neptune so that we can help infer the presence of both large asteroids and planets through our analysis. We study dust particles on both planar (2D-ERTBP) and non-coplanar (3D-ERTBP) orbits. Methods. We computed families of 1/1 resonant symmetric and asymmetric periodic orbits in the 2D-ERTBP and 3D-ERTBP. Doing so produces novel results in their own right and diagnostic tools for precise guidance for our next steps. Based on them, we generated detailed phase portraits. Finally, we run suitably seeded N -body simulations to compare with the periodic orbits, and to provide observational links with debris close to WDs. Results. New families of asymmetric periodic orbits, called E ₄₁ ^A , E ₄₂ ^A , and E ₄₃ ^A in the high-eccentricity 2D-ERTBP regime were discovered. They are generated by the new bifurcation point, B _T ⁴ , along the new A ₂ family, showcased in Paper I. Moreover, new isolated families of asymmetric periodic orbits, namely E ₄₄ ^A , E ₄₅ ^A , and E ₄₆ ^A were discovered. Families of short- and long- period asymmetric orbits starting from L ₄ , called E _S ^A and E _L ^A , were also computed. Conclusions. In both the 2D- and 3D-ERTBP regimes, highly eccentric motion is exhibited for the dust particles in the majority of the families of either symmetric or asymmetric periodic orbits. The portraits reveal stability domains as a function of the dust’s eccentricity, argument of pericentre, mean anomaly and longitude of ascending node with slight semi-major axis deviations from the 1/1 MMR. The N -body simulations reveal that over ten years, the orbital period deviations of the dust are higher than in the CRTBP; in some architectures, Mercury-mass planets can regularly generate deviations exceeding ∼100 s, which potentially aids observational inferences of hidden asteroids or planets orbiting WDs.

Context . Mounting observations of transiting dusty debris orbiting white dwarfs (WDs) display complex signatures that often feature orbital period drifts. The asteroid or planet progenitor of this debris might still be partly intact on a near-circular orbit that is inclined or coplanar, with a period that is similar to that of the dust. Alternatively, the debris could persist concurrently with other intact asteroids or planets that had tidally circularised around the WD at a later time, but still remain directly unobservable. Aims . We sought to first improve the identification of this detectability threshold by expanding our previous investigation of the WD-secondary-dust co-orbital circular restricted three-body problem (CRTBP) to higher secondary masses corresponding to Ceres, Mercury, Earth, and Neptune. Next, we continued to explore the link between the analytic and numerical characterisations of the CRTBP. Methods . First, we computed families of periodic orbits in the 1/1 mean-motion-resonance (MMR) in both the planar and spatial CRTBP cases, where the dust is on an arbitrarily eccentric orbit. Second, we generated global phase space portraits with dynamical stability (DS) maps. Third, we determined observational links with debris located in very close proximity to WDs via N -body simulations. Results . For each method we applied, we report a novel set of results. These include three newly discovered bifurcation points, B _T ⁴ , B _cs ⁴ , and B _cs ⁵ , two branches of asymmetric periodic orbits, called A ₂ and A ₃ , at high dust eccentricity regime in the 2D-CRTBP, and two families of symmetric orbits in the 3D-CRTBP. The maps reveal stability domains as a function of the dust’s eccentricity, argument of pericentre, and slight semi-major axis deviations from the 1/1 MMR. The N -body simulations reveal that over 10 yr, mass analogues of Mercury, Earth, and Neptune generate orbital period deviations in the dust of, respectively, ∼1–10 s, ∼10–100 s, and over 100 s. Conclusions . We identified strong links between analytic periodic orbits, numerical DS maps, and numerical N -body simulations. The observed period deviations are easily detectable, aiding in efforts to obtain indirect detections of exoplanets orbiting WDs.

White dwarfs are unique laboratories for understanding the formation, evolution and survivability of planetary systems. Post-main sequence mass-loss will change planetary orbital properties and stir up debris discs, leading to the observed pollution of white dwarf atmospheres. However, to date, very few studies have investigated the impact of the stellar birth environment on white dwarf planetary systems. In this paper we simulate the evolution of giant planets around white dwarf progenitors from their formation in a star-forming region until 1 Gyr, when the most massive stars (>2 M⊙) have left the main sequence. Our simulations self-consistently model N-body interactions between stars and planets while stars evolve into white dwarfs within the cluster lifetime. We find that although scattering interactions in dense star-forming regions create free-floating planets, and alter the orbital properties of up to 20 percnt of the surviving planets, the effects of mass-loss from the star dominate the dynamics. This behaviour is independent of the stellar density of the birth star-forming region, and largely independent of the initial planet orbital properties. Our simulations produce both captured planets around white dwarfs (potentially similar to WD 0806-661 b), and triple systems with white dwarfs and planets (potentially similar to PSR B1620-26 (AB) b), and our results yield a population synthesis of giant planets from 1 – 100 au that may be relevant to Roman, Gaia and JWST observations.

HAT-P-26,b is a well-characterized Neptunian exoplanet ̊m p R_⊕) orbiting a K1V star. It lies within the Neptunian ridge (P_ ̊m orb days), following a moderately eccentric orbit (e and hosting a water-rich atmosphere. The possible presence of a stellar companion hinted at by near-infrared (NIR) spectral emission, along with candidate planetary companions inferred from transit timing variations, calls for further investigations of the system architecture. Hence, the HAT-P-26 system is a prominent target for investigating the atmospheric and dynamical evolution of exo-Neptunes and, in particular, via the study carried out by the Ancestry, Traits, and Relations of Exoplanets Inhabiting the Desert Edges and Savanna (ATREIDES) collaboration. We combined three transit observations of HAT-P-26,b using ESPRESSO on ESO's VLT to precisely characterize its orbital architecture and to investigate whether it has a misaligned orbit, as reported in cases of other evaporating and eccentric planets in the ridge. We employed the workflow to perform a careful and robust data reduction. We explored the system's orbital architecture using the in-built Rossiter-McLaughlin Revolutions (RMR) technique. ANTARESS HAT-P-26,b exhibits a polar orbit (projected obliquity angle of łambda = -78_ -13 ^ +13 ^ ̧irc and a 3D true obliquity angle of ψ = 85_ -5 ^ +5 ^̧irc). This places it alongside GJ,436,b, HAT-P-11,b, and GJ,3470,b as polar-orbit and eccentric planets lying within the ridge population. It has the lowest density (0.40 ) of these four planets, placing it near the density brink where full atmospheric erosion after early disk-driven migration or tidal disruption after high-eccentricity migration has been proposed to occur. Our dynamical analysis suggests that the observed polar orbit might either be a transient state arising from orbital-plane precession or a relic of high-eccentricity migration via Von Zeipel–Lidov–Kozai cycles driven by an inclined stellar companion. We note that in the latter case, the existence of planet,c would be strongly disfavored. g cm^ -3 HAT-P-26,b stands out as a special target in the Neptunian ridge, owing to its low density and polar orbit. The current dynamical analysis is limited by the uncertainties surrounding companion(s) in this system. As better constraints on the companion(s) become available, it will be particularly interesting to further explore the origin of this fluffy ridge Neptune through a joint analysis of migration, evaporation, tidal disruption, and inflation. Our results also demonstrate the importance of homogeneous data reduction when combining multi-epoch transit observations for accurate spin-orbit characterization.

Compact disks of planetary debris orbiting white dwarfs provide a crucial window into our understanding of evolved planetary systems. The formation of these disks has been widely modeled with tidal fragmentation of minor planets that are rubble piles with no internal strength. However, rubble piles do have nonzero cohesive strength from Van der Waals forces, and here we demonstrate the consequences: breakup of these rubble piles sets a maximum fragment size, and we calculate this size for water ice, iron, and material densities corresponding to the lunar highlands, Vesta, and the Earth. We find that for typical minimum rubble pile strengths of ∼10–1000 Pa, the maximum fragment size is as large as small asteroids (0.1–1 km). This limit—the kilometer-size barrier—also represents the characteristic sizes of tidal fragments. Most of the debris mass is contained in fragments of this size. Consequently, subsequent disk evolution should first feature a prominent dust-forming process, such as collisional grinding, before Poynting–Robertson drag can significantly shape the final disk. Further, we find that nonzero internal strength more narrowly radially confines the fragments than in the strengthless case. This correction to previous assumptions adds to the growing evidence of the importance of collisions in the formation and evolution of white-dwarf debris disks, while also helping to bound the size distribution in these disks for modeling efforts.

The population of short-period exo-Neptunes is thought to be shaped by an interplay between different dynamical mechanisms, such as orbital migration and tidal effects, and photoevaporation. We can gain insight into these processes by studying observables such as the stellar obliquity. Here we study the Rossiter-McLaughlin (RM) effect and measure the projected obliquity, λ, of the Neptunian ridge planet WASP-156 b. We analyse new ESPRESSO and MAROON-X spectroscopic transit observations, and new NGTS photometry simultaneous to the ESPRESSO data. Our analyses show an aligned orbit (λ = −8 ± 16○, based on the ESPRESSO observations), in contrast to a previous report of a highly misaligned orbit. We also find the star’s projected rotational velocity to be vsin i⋆ ≤ 2 km s−1 from spectral line modelling and vsin i⋆ = 0.40 ± 0.11 km s−1 from the RM modelling. This is lower than the previously reported value of ∼4 km s−1, which could partly explain the previously derived polar orbit. We also update the system’s orbital parameters and rule out Jupiter-mass companions within 5 au using long-term radial velocity data. The planet’s aligned and circular orbit (e < 0.16 at 3σ), and lack of nearby massive companions, are consistent with in situ formation or early disc-driven migration. Our findings move WASP-156 b from a tentative cluster of close-in Neptunes in polar orbits to the group of aligned Neptunes.