Relativistic Dynamical Stability Criterion of Multiplanet Systems with a Distant Companion

Multiplanetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai–Lidov mechanism. However, the star–planet and the planet–planet interactions can help stabilize the system. In this work, we extend the previous stability criterion that only considered the companion–planet and planet–planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with N inner planets and a relatively distant inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with two and three inner planets, the analytical criterion is consistent with numerical simulations using a combination of Gauss’s averaging method and direct N-body integration. Finally, the criterion is applied to observed systems, constraining the orbital parameter space of a possible undiscovered companion. This new stability criterion extends the parameter space in which an inclined companion of multiplanet systems can inhabit.

Analysis of Tidal Accelerations in the Solar System and in Extrasolar Planetary Systems

Volcanism powered by tidal forces inside celestial bodies can provide enough energy to keep important solvents for living systems in the liquid phase. A prerequisite to calculate such tidal interactions and consequences is depending on simulations for tidal accelerations in a multi-body system. Unfortunately, from measurements in many extrasolar planetary systems, only few physical and orbital parameters are well-known enough for investigated celestial bodies. For calculating tidal acceleration vectors under missing most orbital parameter exactly, a simulation method is developed that is only based on a few basic parameters, easily measurable even in extrasolar planetary systems. Such a method as the one presented here allows finding a relation between the tidal acceleration vectors and potential heating inside celestial objects. Using the values and results of our model approach to our solar system as a “gold standard” for feasibility allowed us to classify this heating in relation to different forms of volcanism. This “gold standard” approach gave us a classification measure for the relevance of tidal heating in other extrasolar systems with a reduced availability of exact physical parameters. We help to estimate conditions for the identification of potential candidates for further sophisticated investigations by more complex established methods such as viscoelastic multi-body theories. As a first example, we applied the procedures developed here to the extrasolar planetary system TRAPPIST-1 as an example to check our working hypothesis.

TiCoCrFeMn (BCC + C14) High-Entropy Alloy Multiphase Structure Analysis Based on the Theory of Molecular Orbitals

High-entropy alloys (HEA) are a group of modern, perspective materials that have been intensively developed in recent years due to their superior properties and potential applications in many fields. The complexity of their chemical composition and the further interactions of main elements significantly inhibit the prediction of phases that may form during material processing. Thus, at the design stage of HEA fabrication, the molecular orbitals theory was proposed. In this method, the connection of the average strength of covalent bonding between the alloying elements (Bo parameter) and the average energy level of the d-orbital (parameter Md) enables for a preliminary assessment of the phase structure and the type of lattice for individual components in the formed alloy. The designed TiCoCrFeMn alloy was produced by the powder metallurgy method, preceded by mechanical alloying of the initial elementary powders and at the temperature of 1050 °C for 60 s. An ultra-fine-grained structured alloy was homogenized at 1000 °C for 1000 h. The X-ray diffraction and scanning electron microscopy analysis confirmed the correctness of the methodology proposed as the assumed phase structure consisted of the body-centered cubic (BCC) solid solution and the C14 Laves phase was obtained.

Exploring the dust ring in the circum-binary disc around GG Tau A

<p>Binaries and multiple systems are common among young stars (Reipurth et al. 2014). These stars are often surrounded by discs of gas and dust, formed due to the conservation of angular momentum of the collapsing cloud, thought to be the site of planet formation.<br />In the case of binary systems, three discs can form: an outer disc surrounding all the stars (called circumbinary disc), and two inner discs around the stars. As circumbinary planets have recently been discovered by Kepler (see e.g., Martin 2018, Bonavita & Desidera 2020), it is crucial to understand the dynamics and evolution of circumbinary discs to better understand the initial conditions of planet formation in multiple systems.<br />The GG Tau A system is an example of a young multiple T Tauri star. The binary is surrounded by a bright disc, observed in the continuum emission at different wavelengths (see e.g., Guilloteau et al. 1999; Dutrey et al. 2014; Phuong et al. 2020b) and in scattered light (e.g., Duchene et al. 2014, Keppler et al. 2020). The disc extends in the dust from 180 to 280 au from the center of mass, and in the gas up to 850 au. The inner (<180 au) part is depleted in gas and dust. Scattered light images show a complex structure in the inner part of the disc, with arcs and filamentary structures connecting the outer ring with the arcs and three shadows.<br />Two different configurations are possible fitting the proper motion data for the system: a co-planar case with a low eccentricity binary with a semi-major axis of 34 au, explored by Cazzoletti et al. 2017 and Keppler et al. 2020, and a misaligned case (i=30) with an eccentric binary (e=0.45) and a wider semimajor axis of 60 au (Aly et al.2018). At the state of the art, all these analyses focused on the gas dynamics only.<br />We will show the results of new 3D SPH simulations of dust and gas performed with the code PHANTOM, devised to test the two possible scenarios. We will describe the dynamics of the system in the two cases, comparing our models with observational results in order to better constraint the orbital parameter of the GG Tau A system. Our predictions will guide future observing campaigns and shed light on the complex evolution of discs in triple stellar systems.</p> <p> </p>

Analysis of Tidal Accelerations in the Solar System and in Extrasolar Planetary Systems

Volcanism powered by tidal forces inside celestial bodies can provide enough energy to keep important solvents for living systems in the liquid phase. Moreover, tidal forces and their environmental consequences may strongly influence habitability of planets and other celestial bodies and may result in special forms of live and living conditions. A prerequisite to calculate such tidal interactions and consequences is depending on simulations for tidal accelerations in a multi-body system. Unfortunately, from measurements in many extrasolar planetary systems only few physical and orbital parameters are well enough known for investigated celestial bodies. For calculating tidal acceleration vectors under missing most orbital parameter exactly, a simulation method is developed that is only based on a few basic parameters, easily measurable even in extrasolar planetary systems. Such a method as being presented here, allows finding a relation between the tidal acceleration vectors and potential heating inside celestial objects. Using values and results of our model approach to our solar system as a “gold standard” for feasibility allowed us to classify this heating in relation to different forms of volcanism. This “gold standard” approach gave us a classification measure for the relevance of tidal heating in other extrasolar systems with a reduced availability of exact physical parameters. We would help to estimate conditions for the identification of potential candidates for further sophisticated investigations by more complex established methods like viscoelastic multi-body theories. As a first example, we applied the procedures developed here to the extrasolar planetary system TRAPPIST-1 as an example to check our working hypothesis.

Memories of past close encounters in extreme trans-Neptunian space: Finding unseen planets using pure random searches

Context. The paths followed by the known extreme trans-Neptunian objects (ETNOs) effectively avoid direct gravitational perturbations from the four giant planets, yet their orbital eccentricities are in the range between 0.69−0.97. Solar system dynamics studies show that such high values of the eccentricity can be produced via close encounters or secular perturbations. In both cases, the presence of yet-to-be-discovered trans-Plutonian planets is required. Recent observational evidence cannot exclude the existence, at 600 AU from the Sun, of a planet of five Earth masses. Aims. If the high eccentricities of the known ETNOs are the result of relatively recent close encounters with putative planets, the mutual nodal distances of sizeable groups of ETNOs with their assumed perturber may still be small enough to be identifiable geometrically. In order to confirm or reject this possibility, we used Monte Carlo random search techniques. Methods. Two arbitrary orbits may lead to close encounters when their mutual nodal distance is sufficiently small. We generated billions of random planetary orbits with parameters within the relevant ranges and computed the mutual nodal distances with a set of randomly generated orbits with parameters consistent with those of the known ETNOs and their uncertainties. We monitored which planetary orbits had the maximum number of potential close encounters with synthetic ETNOs and we studied the resulting distributions. Results. We provide narrow ranges for the orbital parameters of putative planets that may have experienced orbit-changing encounters with known ETNOs. Some sections of the available orbital parameter space are strongly disfavored by our analysis. Conclusions. Our calculations suggest that more than one perturber is required if scattering is the main source of orbital modification for the known ETNOs. Perturbers might not be located farther than 600 AU and they have to follow moderately eccentric and inclined orbits to be capable of experiencing close encounters with multiple known ETNOs.

The Clustering Dynamics of Primordial Black Boles in N-Body Simulations

We explore the possibility that Dark Matter (DM) may be explained by a nonuniform background of approximately stellar mass clusters of Primordial Black Holes (PBHs) by simulating the evolution from recombination to the present with over 5000 realisations using a Newtonian N-body code. We compute the cluster rate of evaporation and extract the binary and merged sub-populations along with their parent and merger tree histories, lifetimes and formation rates, the dynamical and orbital parameter profiles, the degree of mass segregation and dynamical friction and power spectrum of close encounters. Overall, we find that PBHs can constitute a viable DM candidate, and that their clustering presents a rich phenomenology throughout the history of the Universe. We show that binary systems constitute about 9.5% of all PBHs at present, with mass ratios of q¯B=0.154, and total masses of m¯T,B=303M⊙. Merged PBHs are rare, about 0.0023% of all PBHs at present, with mass ratios of q¯B=0.965 with total and chirp masses of m¯T,B=1670M⊙ and m¯c,M=642M⊙, respectively. We find that cluster puffing up and evaporation leads to bubbles of these PBHs of order 1 kpc containing at present times about 36% of objects and mass, with one-hundred pc-sized cores. We also find that these PBH sub-haloes are distributed in wider PBH haloes of order hundreds of kpc, containing about 63% of objects and mass, coinciding with the sizes of galactic halos. We find at last high rates of close encounters of massive Black Holes (M∼1000M⊙), with ΓS=(1.2+5.9−0.9)×107yr−1Gpc−3 and mergers with ΓM=1337±41yr−1Gpc−3.

Einstein@Home Discovery of the Gamma-ray Millisecond Pulsar PSR J2039−5617 Confirms Its Predicted Redback Nature

The Fermi Large Area Telescope gamma-ray source 3FGL J2039.6−5618 contains a periodic optical and X-ray source that was predicted to be a “redback” millisecond pulsar (MSP) binary system. However, the conclusive identification required the detection of pulsations from the putative MSP. To better constrain the orbital parameters for a directed search for gamma-ray pulsations, we obtained new optical light curves in 2017 and 2018, which revealed long-term variability from the companion star. The resulting orbital parameter constraints were used to perform a targeted gamma-ray pulsation search using the Einstein@Home distributed volunteer computing system. This search discovered pulsations with a period of 2.65 ms, confirming the source as a binary MSP now known as PSR J2039−5617. Optical light curve modelling is complicated, and likely biased, by asymmetric heating on the companion star and long-term variability, but we find an inclination i ≳ 60 ○, for a low pulsar mass between 1.1 M⊙ < Mpsr < 1.6 M⊙, and a companion mass of 0.15–0.22 M⊙, confirming the redback classification. Timing the gamma-ray pulsations also revealed significant variability in the orbital period, which we find to be consistent with quadrupole moment variations in the companion star, suggestive of convective activity. We also find that the pulsed flux is modulated at the orbital period, potentially due to inverse Compton scattering between high-energy leptons in the pulsar wind and the companion star’s optical photon field.

Going back to basics: accelerating exoplanet transit modelling using Taylor-series expansion of the orbital motion

ABSTRACT A significant fraction of an exoplanet transit model evaluation time is spent calculating projected distances between the planet and its host star. This is a relatively fast operation for a circular orbit, but slower for an eccentric one. However, because the planet’s position and its time derivatives are constant for any specific point in orbital phase, the projected distance can be calculated rapidly and accurately in the vicinity of the transit by expanding the planet’s x and y positions in the sky plane into a Taylor series at mid-transit. Calculating the projected distance for an elliptical orbit using the four first time derivatives of the position vector (velocity, acceleration, jerk, and snap) is ∼100 times faster than calculating it using the Newton’s method, and also significantly faster than calculating z for a circular orbit because the approach does not use numerically expensive trigonometric functions. The speed gain in the projected distance calculation leads to 2–25 times faster transit model evaluation speed, depending on the transit model complexity and orbital eccentricity. Calculation of the four position derivatives using numerical differentiation takes $\sim 1\, \mu$s with a modern laptop and needs to be done only once for a given orbit, and the maximum error the approximation introduces to a transit light curve is below 1 ppm for the major part of the physically plausible orbital parameter space.