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Register a new userAn N-body approach to modeling debris and ejecta off small bodies: Implementation and application
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We introduce here our new approach to modeling particle cloud evolution off surface of small bodies (asteroids and comets), following the evolution of ejected particles requires dealing with various time and spatial scales, in an efficient, accurate and modular way. In order to improve computational efficiency and accuracy of such calculations, we created an N-body modeling package as an extension to the increasingly popular orbital dynamics N-body integrator Rebound. Our code is currently a stand-alone variant of the Rebound code and is aimed at advancing a comprehensive understanding of individual particle trajectories, external forcing, and interactions, at the scale which is otherwise overlooked by other modeling approaches. The package we developed -- Rebound Ejecta Dynamics (RED) -- is a Python-based implementation with no additional dependencies. It incorporates several major mechanisms that affect the evolution of particles in low-gravity environments and enables a more straightforward simulation of combined effects. We include variable size and velocity distributions, solar radiation pressure, ellipsoidal gravitational potential, binary or triple asteroid systems, and particle-particle interactions. In this paper, we present a sample of the RED package capabilities. These are applied to a small asteroid binary system (characterized following the Didymos/Dimorphos system, which is the target for NASAs Double Asteroid Redirection Test mission)
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When fitting N-body models to astronomical data - including transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model optimization and posterior sampling. Here we describe a general-purpose symplectic integrator for arbitrary orbital architectures, including those with close encounters, which we have recast to maintain numerical stability and precision for small step sizes. We compute the derivatives of the N-body coordinates and velocities as a function of time with respect to the initial conditions and masses by propagating the Jacobian along with the N-body integration. For the first time we obtain the derivatives of the transit times with respect to the initial conditions and masses using the chain rule, which is quicker and more accurate than using finite differences or automatic differentiation. We implement this algorithm in an open source package, NbodyGradient.jl, written in the Julia language, which has been used in the optimization and error analysis of transit-timing variations in the TRAPPIST-1 system. We present tests of the accuracy and precision of the code, and show that it compares favorably in speed to other integrators which are written in C.
In this article, theory-based analytical methodologies of astrophysics employed in the modern era are suitably operated alongside a test research-grade telescope to image and determine the orbit of a near-earth asteroid from original observations, measurements, and calculations. Subsequently, its intrinsic orbital path has been calculated including the chance it would likely impact Earth in the time ahead. More so specifically, this case-study incorporates the most effective, feasible, and novel Gausss Method in order to maneuver the orbital plane components of a planetesimal, further elaborating and extending our probes on a selected near-earth asteroid (namely the 12538-1998 OH) through the observational data acquired over a six week period. Utilizing the CCD (Charge Coupled Device) snapshots captured, we simulate and calculate the orbit of our asteroid as outlined in quite detailed explanations. The uncertainties and deviations from the expected values are derived to reach a judgement whether our empirical findings are truly reliable and representative measurements by partaking a statistical analysis based systematic approach. Concluding the study by narrating what could have caused such discrepancy of findings in the first place, if any, measures are put forward that could be undertaken to improve the test-case for future investigations. Following the calculation of orbital elements and their uncertainties using Monte Carlo analysis, simulations were executed with various sample celestial bodies to derive a plausible prediction regarding the fate of Asteroid 1998 OH. Finally, the astrometric and photometric data, after their precise verification, were officially submitted to the Minor Planet Center: an organization hosted by the Center for Astrophysics, Harvard and Smithsonian and funded by NASA, for keeping track of the asteroids potential trajectories.
We present a novel, iterative method using an empirical Bayesian approach for modeling the limb darkened WASP-121b transit from the TESS light curve. Our method is motivated by the need to improve $R_{p}/R_{ast}$ estimates for exoplanet atmosphere modeling, and is particularly effective with the limb darkening (LD) quadratic law requiring no prior central value from stellar atmospheric models. With the non-linear LD law, the method has all the advantages of not needing atmospheric models but does not converge. The iterative method gives a different $R_{p}/R_{ast}$ for WASP-121b at a significance level of 1$sigma$ when compared with existing non-iterative methods. To assess the origins and implications of this difference, we generate and analyze light curves with known values of the limb darkening coefficients (LDCs). We find that non-iterative modeling with LDC priors from stellar atmospheric models results in an inconsistent $R_{p}/R_{ast}$ at 1.5$sigma$ level when the known LDC values are as those previously found when modeling real data by the iterative method. In contrast, the LDC values from the iterative modeling yields the correct value of $R_{p}/R_{ast}$ to within 0.25$sigma$. For more general cases with different known inputs, Monte Carlo simulations show that the iterative method obtains unbiased LDCs and correct $R_{p}/R_{ast}$ to within a significance level of 0.3$sigma$. Biased LDC priors can cause biased LDC posteriors and lead to bias in the $R_{p}/R_{ast}$ of up to 0.82$%$, 2.5$sigma$ for the quadratic law and 0.32$%$, 1.0$sigma$ for the non-linear law. Our improvement in $R_{p}/R_{ast}$ estimation is important when analyzing exoplanet atmospheres.
We present FlowPM, a Particle-Mesh (PM) cosmological N-body code implemented in Mesh-TensorFlow for GPU-accelerated, distributed, and differentiable simulations. We implement and validate the accuracy of a novel multi-grid scheme based on multiresolution pyramids to compute large scale forces efficiently on distributed platforms. We explore the scaling of the simulation on large-scale supercomputers and compare it with corresponding python based PM code, finding on an average 10x speed-up in terms of wallclock time. We also demonstrate how this novel tool can be used for efficiently solving large scale cosmological inference problems, in particular reconstruction of cosmological fields in a forward model Bayesian framework with hybrid PM and neural network forward model. We provide skeleton code for these examples and the entire code is publicly available at https://github.com/modichirag/flowpm.
Aims. We present here a new theoretical approach to population synthesis. The aim is to predict colour magnitude diagrams (CMDs) for huge numbers of stars. With this method we generate synthetic CMDs for N-body simulations of galaxies. Sophisticated hydrodynamic N-body models of galaxies require equal quality simulations of the photometric properties of their stellar content. The only prerequisite for the method to work is very little information on the star formation and chemical enrichment histories, i.e. the age and metallicity of all star-particles as a function of time. The method takes into account the gap between the mass of real stars and that of the star-particles in N-body simulations, which best correspond to the mass of star clusters with different age and metallicity, i.e. a manifold of single stellar sopulations (SSP). Methods. The theory extends the concept of SSP to include the phase-space (position and velocity) of each star. Furthermore, it accelerates the building up of simulated CMD by using a database of theoretical SSPs that extends to all ages and metallicities of interest. Finally, it uses the concept of distribution functions to build up the CMD. The technique is independent of the mass resolution and the way the N-body simulation has been calculated. This allows us to generate CMDs for simulated stellar systems of any kind: from open clusters to globular clusters, dwarf galaxies, or spiral and elliptical galaxies. Results. The new theory is applied to an N-body simulation of a disc galaxy to test its performance and highlight its flexibility.
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