IMPLEMENTING FEW-BODY ALGORITHMIC REGULARIZATION WITH POST-NEWTONIAN TERMS

By S. Mikkola, D. Merritt. 2007

152 citations recorded by the source corpus.

We discuss the implementation of a new regular algorithm for simulation of the gravitational few-body problem. The algorithm uses components from earlier methods, including the chain structure, the logarithmic Hamiltonian, and the time-transformed leapfrog. This algorithmic regularization code, AR-CHAIN, can be used for the normal N-body problem, as well as for problems with softened potentials and/or with velocity-dependent external perturbations, including post-Newtonian terms, which we include up to order PN2.5. Arbitrarily extreme mass ratios are allowed. Only linear coordinate transformations are used and thus the algorithm is somewhat simpler than many earlier regularized schemes. We present the results of performance tests which suggest that the new code is either comparable in performance or superior to the existing regularization schemes based on the Kustaanheimo–Stiefel (KS) transformation. This is true even for the two-body problem, independent of eccentricity. An important advantage of the new method is that, contrary to the older KS-CHAIN code, zero masses are allowed. We use our algorithm to integrate the orbits of the S stars around the Milky Way supermassive black hole for one million years, including PN2.5 terms and an intermediate-mass black hole. The three S stars with shortest periods are observed to escape from the system after a few hundred thousand years.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/4a40c7f4d9a0ad88251f6ad9b442e5fde1a2666d

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Citations in the corpus

• SECULAR EVOLUTION OF COMPACT BINARIES NEAR MASSIVE BLACK HOLES: GRAVITATIONAL WAVE SOURCES AND OTHER EXOTICA (2012, methodology): “These simulations were carried out using the AR-CHAIN integrator (Mikkola & Merritt 2008), which includes PN corrections to all pairwise forces up to order PN2.”
• BLACK HOLE TRIPLE DYNAMICS: A BREAKDOWN OF THE ORBIT AVERAGE APPROXIMATION AND IMPLICATIONS FOR GRAVITATIONAL WAVE DETECTIONS (2013, methodology): “We did this by using the direct numerical integrator ARCHAIN which includes PN corrections to the equations of motion up to order 2.5 and the algorithmically regularized chain structure to avoid singularities (Mikkola & Merritt 2008).”
• Black hole and neutron star mergers in galactic nuclei (2018, methodology): “The integrations are performed using the archain code (Mikkola & Merritt 2006, 2008), a fully regularized code able to model the evolution of systems of arbitrary mass ratios and large eccentricities with extreme accuracy. archain includes PN corrections up to order PN2.”
• Stellar-mass black holes in young massive and open stellar clusters and their role in gravitational-wave generation (2016, methodology): “The relativistic treatment, following the Post-Newtonian (PN) approach, is included in the ARC procedure (Mikkola & Merritt 2008).”
• MONITORING STELLAR ORBITS AROUND THE MASSIVE BLACK HOLE IN THE GALACTIC CENTER (2008, background): “Mikkola & Merritt (2008) have shown that an IMBH with a mass of 10−3 MMBH in a distance of 1 mpc would make the Sstars cluster unstable.”
• Binary Black Hole Mergers from Field Triples: Properties, Rates, and the Impact of Stellar Evolution (2017, methodology): “We study this problem using a combination of high-precision direct integrations (Mikkola & Merritt 2008) and a code that combines secular three-body dynamics with stellar evolution and their mutual influences (Toonen et al. 2016).”
• BLACK HOLE MERGERS AND BLUE STRAGGLERS FROM HIERARCHICAL TRIPLES FORMED IN GLOBULAR CLUSTERS (2015, methodology): “We refer the reader to Mikkola & Merritt (2008) for a more detailed description of ARCHAIN.”
• High‐inclination orbits in the secular quadrupolar three‐body problem (2009, background): “Another field of application of the outer restricted problem is the study of the motion of stars orbiting around binary black holes (Mikkola & Merritt 2008; Gillessen et al. 2009; Merritt et al. 2009).”
• Rapid Eccentricity Oscillations and the Mergers of Compact Objects in Hierarchical Triples (2013, background): “These difficulties are compounded by the roundoff error introduced by integrating close encounters far from the origin (see, e.g., Mikkola & Merritt 2008, for further discussion).”