arXiv subjects

Zsolt Sándor

Publications and source records attributed to Zsolt Sándor.

8 recordsLinked to original sources

arXiv2026

Jackknife Instrumental Variable Inference

This paper introduces a class of jackknife-based test statistics for linear regression models with endogeneity and heteroskedasticity in the presence of many potentially weak instrumental variables. The tests may be used when considering hypotheses on the full parameter vector or hypotheses defined as linear restrictions. We show that in the limit and under the null the proposed statistics are distributed as a combination of chi squares but by modifying the objective function we derive more familiar chi square limits. An extensive simulation study shows the competitive finite sample properties of the proposed tests in particular against Anderson-Rubin-type of statistics. Finally, we provide an empirical illustration that applies the proposed tests to study the effect of alcohol consumption on body mass index using genetic variants as instrumental variables using the UK Biobank.

econ.EM↗

arXiv2023

A dynamical survey of the trans-Neptunian region II.: On the nature of chaotic diffusion

On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide dynamical pathways even for the distant trans-Neptunian objects to reach the inner solar system. In this Letter, we carry out a thorough investigation of the nature of chaotic diffusion. We analyze the temporal evolution of the mean squared displacement of ten thousand ensembles of test particles and quantify in each case the diffusion exponent (enabling the classification between normal, sub-, and super-diffusion), the generalized diffusion coefficient, and a characteristic diffusion timescale, too. This latter quantity is compared with an entropy-based timescale, and the two approaches are studied in light of direct computations as well. Our results are given in the context of two-dimensional maps, thereby facilitating the understanding of the relationship between the typical phase space structures and the properties of chaotic diffusion.

astro-ph.EP↗

arXiv2022

Stability analysis of planetary systems via second-order Rényi entropy

The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data is continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized Rényi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem is used as the basis of a phase space reconstruction procedure. Then, Poincaré's recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the Rényi entropy. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods, and it requires only a few tens of thousands of orbital period integration time.

astro-ph.EP↗

arXiv2021

Application of the Shannon entropy in the planar (non-restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system

In this paper, we present an application of the Shannon entropy in the case of the planar (non-restricted) four-body problem. Specifically, the Kepler-60 extrasolar system is being investigated with a primary interest in the resonant configuration of the planets that exhibit a chain of mean-motion commensurabilities with the ratios 5:4:3. In the dynamical maps provided, the Shannon entropy is utilized to explore the general structure of the phase space, while, based on the time evolution of the entropy, we determine also the extent and rate of the chaotic diffusion as well as the characteristic times of stability for the planets. Two cases are considered: (i) the pure Laplace resonance when the critical angles of the 2-body resonances circulate and that of the 3-body resonance librates; and (ii) the chain of two 2-body resonances when all the critical angles librate. Our results suggest that case (ii) is the more favourable configuration but we state too that, in either case, the relevant resonance plays an important role to stabilize the system. The derived stability times are no shorter than $10^8$ yrs in the central parts of the resonances.

astro-ph.EP↗

arXiv2021

Increased isolation mass for pebble accreting planetary cores in pressure maxima of protoplanetary discs

The growth of a pebble accreting planetary core is stopped when reaching its \textit{isolation mass} that is due to a pressure maximum emerging at the outer edge of the gap opened in gas. This pressure maximum traps the inward drifting pebbles stopping the accretion of solids onto the core. On the other hand, a large amount of pebbles ($\sim 100M_\oplus$) should flow through the orbit of the core until reaching its isolation mass. The efficiency of pebble accretion increases if the core grows in a dust trap of the protoplanetary disc. Dust traps are observed as ring-like structures by ALMA suggesting the existence of global pressure maxima in discs that can also act as planet migration traps. This work aims to reveal how large a planetary core can grow in such a pressure maximum by pebble accretion. In our hydrodynamic simulations, pebbles are treated as a pressureless fluid mutually coupled to the gas via drag force. Our results show that in a global pressure maximum the pebble isolation mass for a planetary core is significantly larger than in discs with power-law surface density profile. An increased isolation mass shortens the formation time of giant planets.

astro-ph.EP↗

arXiv2015

The Relative Lyapunov Indicators: Theory and Application to Dynamical Astronomy

A recently introduced chaos detection method, the Relative Lyapunov Indicator (RLI) is investigated in the cases of symplectic mappings and continuous Hamiltonian systems. It is shown that the RLI is an efficient numerical tool in determining the true nature of individual orbits, and in separating ordered and chaotic regions of the phase space of dynamical systems. A comparison between the RLI and some other variational indicators are presented, as well as the recent applications of the RLI to various problems of dynamical astronomy.

nlin.CD↗

arXiv2015

Water delivery in the Early Solar System

As part of the national scientific network 'Pathways to Habitable Worlds' the delivery of water onto terrestrial planets is a key question since water is essential for the development of life as we know it. After summarizing the state of the art we show some first results of the transport of water in the early Solar System for scattered main belt objects. Hereby we investigate the questions whether planetesimals and planetesimal fragments which have gained considerable inclination due to the strong dynamical interactions in the main belt region around 2 AU can be efficient water transporting vessels. The Hungaria asteroid group is the best example that such scenarios are realistic. Assuming that the gas giants and the terrestrial planets are already formed, we monitor the collisions of scattered small bodies containing water (in the order of a few percent) with the terrestrial planets. Thus we are able to give a first estimate concerning the respective contribution of such bodies to the actual water content in the crust of the Earth.

astro-ph.EP↗

arXiv2012

Orbital migration of interacting low-mass planets in evolutionary radiative turbulent models

The torques exerted by a locally isothermal disk on an embedded planet lead to rapid inward migration. Recent work has shown that modeling the thermodynamics without the assumption of local isothermality reveals regions where the net torque on an embedded planet is positive, leading to outward migration of the planet. When a region with negative torque lies directly exterior to this, planets in the inner region migrate outwards and planets in the outer region migrate inwards, converging where the torque is zero. We incorporate the torques from an evolving non-isothermal disk into an N-body simulation to examine the behavior of planets or planetary embryos interacting in the convergence zone. We find that mutual interactions do not eject objects from the convergence zone. Small numbers of objects in a laminar disk settle into near resonant orbits that remain stable over the 10 Myr periods that we examine. However, either or both increasing the number of planets or including a correlated, stochastic force to represent turbulence drives orbit crossings and mergers in the convergence zone. These processes can build gas giant cores with masses of order ten Earth masses from sub-Earth mass embryos in 2-3 Myr.

astro-ph.EP↗