arXiv subjects

Seppo Mikkola

Publications and source records attributed to Seppo Mikkola.

17 recordsLinked to original sources

arXiv2016

Quasi-satellite dynamics in formation flight

The quasi-satellite (QS) phenomenon makes two celestial bodies to fly near each other (Mikkola et al. 2006) and that effect can be used also to make artificial satellites move in tandem. We consider formation flight of two or three satellites in low eccentricity near Earth orbits. With the help of weak ion thrusters it is possible to accomplish tandem flight. With ion thrusters it is also possible to mimic many kinds of mutual force laws between the satellites. We found that both a constant repulsive force or an attractive force that decreases with the distance are able to preserve the formation in which the eccentricities cause the actual relative motion and the weak thrusters keep the mean longitude difference small. Initial values are important for the formation flight but very exact adjustment of orbital elements is not important. Simplicity is one of our goals in this study and this result is achieved at least in the way that, when constant force thrusters are used, the satellites only need to detect the directions of the other ones to fly in tandem. A repulsive acceleration of the order of 10^-6 times the Earth attraction, is enough to effectively eliminate the disruptive effects of all the perturbations at least for a timescale of years.

astro-ph.EP↗

arXiv2015

Brown Dwarf Binaries from Disintegrating Triple Systems

We have carried out 200,000 N-body simulations of three identical stellar embryos with masses from a Chabrier IMF and embedded in a molecular core. The bodies are initially non-hierarchical and undergo chaotic motions, while accreting using Bondi-Hoyle accretion. The coupling of dynamics and accretion often leads to one or two dominant bodies controlling the center of the cloud core, while banishing the other(s) to the lower-density outskirts, leading to stunted growth. Eventually each system transforms either to a bound hierarchical configuration or breaks apart into separate single and binary components. The orbital motion is followed for 100 Myr. To illustrate the simulations we introduce the 'triple diagnostic diagram', which plots two dimensionless numbers against each other, representing the binary mass ratio and the mass ratio of the third body to the total system mass. Numerous freefloating BD binaries are formed in these simulations. The separation distribution function is in good correspondence with observations, showing a steep rise at close separations, peaking around 13 AU and then declining more gently. Unresolved BD triple systems may appear as wider BD binaries. Mass ratios are strongly peaked towards unity, as observed, but this is partially due to the initial assumptions. Eccentricities gradually increase towards higher values, due to the lack of viscous interactions in the simulations, which would both shrink the orbits and decrease their eccentricities. The main threat to newly born triple systems is internal instabilities, not external perturbations. Dynamical interactions in newborn triple systems of stellar embryos embedded in and accreting from a cloud core naturally form a population of freefloating BD binaries, and this mechanism may constitute a significant pathway for the formation of BD binaries. (Abstract abbreviated).

astro-ph.SR↗

arXiv2013

Black hole triple dynamics: breakdown of the orbit average approximation and implications for gravitational wave detections

Coalescing black hole (BH) binaries forming in the dense core of globular clusters (GCs) are expected to be one the brightest sources of gravitational wave (GW) radiation for the next generation of ground-based laser interferometers. Favorable conditions for merger are initiated by the Kozai resonance in which the gravitational interaction with a third distant object, typically another BH, induces quasi-periodic variations of the inner BH binary eccentricity. In this paper we perform high precision N-body simulations of the long term evolution of hierarchical BH triples and investigate the conditions that lead to the merging of the BH binary and the way it might become an observable source of GW radiation. We find that the secular orbit average treatment, adopted in previous works, does not reliably describe the dynamics of these systems if the binary is orbited by the outer BH on a highly inclined orbit at a moderate distance. During the high eccentricity phase of a Kozai cycle the torque due to the outer BH can drive the binary to extremely large eccentricities in a fraction of the binary's orbital period. This occurs before relativistic terms become important to the evolution and allows the binary GW signal to reach large GW frequencies (>~10 Hz) at high eccentricities. We show that ~50 % of coalescing BH binaries driven by the Kozai mechanism in GCs will have eccentricities larger than 0.1, with 10 % of them being extremely eccentric, (1-e)<~10^-5, when they first chirp in the frequency band of ground based laser interferometers. This implies that a large fraction of such GW sources could be missed if conventional quasi-circular templates are used for analysis of GW detectors data. The efficient detection of all coalescing BH binaries in GCs will therefore require template banks of eccentric inspiral waveforms for matched-filtering and dedicated search strategies.

astro-ph.HE↗

arXiv2012

Formation of the Widest Binaries from Dynamical Unfolding of Triple Systems

The formation of very wide binaries, such as the alpha Cen system with Proxima (also known as alpha Centauri C) separated from alpha Centauri (which itself is a close binary A/B) by 15000 AU, challenges current theories of star formation, because their separation can exceed the typical size of a collapsing cloud core. Various hypotheses have been proposed to overcome this problem, including the suggestion that ultra-wide binaries result from the dissolution of a star cluster - when a cluster star gravitationally captures another, distant, cluster star. Recent observations have shown that very wide binaries are frequently members of triple systems and that close binaries often have a distant third companion. Here we report Nbody simulations of the dynamical evolution of newborn triple systems still embedded in their nascent cloud cores that match observations of very wide systems. We find that although the triple systems are born very compact - and therefore initially are more protected against disruption by passing stars - they can develop extreme hierarchical architectures on timescales of millions of years as one component is dynamically scattered into a very distant orbit. The energy of ejection comes from shrinking the orbits of the other two stars, often making them look from a distance like a single star. Such loosely bound triple systems will therefore appear to be very wide binaries.

astro-ph.GA↗

arXiv2011

Stellar Dynamics of Extreme-Mass-Ratio Inspirals

Inspiral of compact stellar remnants into massive black holes (MBHs) is accompanied by the emission of gravitational waves at frequencies that are potentially detectable by space-based interferometers. Event rates computed from statistical (Fokker-Planck, Monte-Carlo) approaches span a wide range due to uncertaintities about the rate coefficients. Here we present results from direct integration of the post-Newtonian N-body equations of motion descrbing dense clusters of compact stars around Schwarzschild MBHs. These simulations embody an essentially exact (at the post-Newtonian level) treatment of the interplay between stellar dynamical relaxation, relativistic precession, and gravitational-wave energy loss. The rate of capture of stars by the MBH is found to be greatly reduced by relativistic precession, which limits the ability of torques from the stellar potential to change orbital angular momenta. Penetration of this "Schwarzschild barrier" does occasionally occur, resulting in capture of stars onto orbits that gradually inspiral due to gravitational wave emission; we discuss two mechanisms for barrier penetration and find evidence for both in the simulations. We derive an approximate formula for the capture rate, which predicts that captures would be strongly disfavored from orbits with semi-major axes below a certain value; this prediction, as well as the predicted rate, are verified in the N-body integrations. We discuss the implications of our results for the detection of extreme-mass-ratio inspirals from galactic nuclei with a range of physical properties.

astro-ph.CO↗

arXiv2010

Orphaned Protostars

We explore the origin of a population of distant companions (~1000 - 5000 AU) to Class I protostellar sources recently found by Connelley and co-workers, who noted that the companion fraction diminished as the sources evolved. Here we present N-body simulations of unstable triple systems embedded in dense cloud cores. Many companions are ejected into unbound orbits and quickly escape, but others are ejected with insufficient momentum to climb out of the potential well of the cloud core and associated binary. These loosely bound companions reach distances of many thousands of AU before falling back and eventually being ejected into escapes as the cloud cores gradually disappear. We use the term orphans to denote protostellar objects that are dynamically ejected from their placental cloud cores, either escaping or for a time being tenuously bound at large separations. Half of all triple systems are found to disintegrate during the protostellar stage, so if multiple systems are a frequent outcome of the collapse of a cloud core, then orphans should be common. Bound orphans are associated with embedded close protostellar binaries, but escaping orphans can travel as far as ~0.2 pc during the protostellar phase. The steep climb out of a potential well ensures that orphans are not kinematically distinct from young stars born with a less violent pre-history. The identification of orphans outside their heavily extincted cloud cores will allow the detailed study of protostars high up on their Hayashi tracks at near-infrared and in some cases even at optical wavelengths.

astro-ph.GA↗

arXiv2009

Testing Properties of the Galactic Center Black Hole Using Stellar Orbits

The spin and quadrupole moment of the supermassive black hole at the Galactic center can in principle be measured via astrometric monitoring of stars orbiting at milliparsec (mpc) distances, allowing tests of general relativistic "no-hair" theorems (Will 2008). One complicating factor is the presence of perturbations from other stars, which may induce orbital precession of the same order of magnitude as that due to general relativistic effects. The expected number of stars in this region is small enough that full N-body simulations can be carried out. We present the results of a comprehensive set of such simulations, which include a post-Newtonian treatment of spin-orbit effects. A number of possible models for the distribution of stars and stellar remnants are considered. We find that stellar perturbations are likely to obscure the signal due to frame-dragging for stars beyond ~0.5 mpc from the black hole, while measurement of the quadrupole moment is likely to require observation of stars inside ~0.2 mpc. A high fraction of stellar remnants, e.g. 10-Solar-mass black holes, in this region would make tests of GR problematic at all radii. We discuss the possibility of separating the effects of stellar perturbations from those due to GR.

astro-ph.GA↗

arXiv2009

Implementing Few-Body Algorithmic Regularization with Post-Newtonian Terms

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.

astro-ph↗

arXiv2008

Explaining the Orbits of the Galactic Center S-Stars

The young stars near the supermassive black hole at the galactic center follow orbits that are nearly random in orientation and that have an approximately thermal distribution of eccentricities, N(e) ~ e. We show that both of these properties are a natural consequence of a few million years' interaction with an intermediate-mass black hole (IBH), if the latter's orbit is mildly eccentric and if its mass exceeds approximately 1500 solar masses. Producing the most tightly-bound S-stars requires an IBH orbit with periastron distance less than about 10 mpc. Our results provide support for a model in which the young stars are carried to the galactic center while bound to an IBH, and are consistent with the hypothesis that an IBH may still be orbiting within the nuclear star cluster.

astro-ph↗

arXiv2008

A trial symbolic dynamics of the planar three-body problem

Symbolic dynamics is applied to the planar three-body problem. Symbols are defined on the planar orbit when it experiences a syzygy crossing. If the body i is in the middle at the syzygy crossing and the vectorial area of the triangle made with three bodies changes sign from + to -, number i is given to this event, whereas if the vectorial area changes sign from - to +, number i+3 is given. We examine the case of free-fall three-body problem for the first few digits of symbol sequences, and we examine the case with angular momentum only for the first digit of the symbol sequences. This trial experiments show some new aspects of the planar three-body problem.

nlin.CD↗

arXiv2007

Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei

[Abridged] In galactic nuclei with sufficiently short relaxation times, binary supermassive black holes can evolve beyond their stalling radii via continued interaction with stars. We study this "collisional" evolutionary regime using both fully self-consistent N-body integrations and approximate Fokker-Planck models. The N-body integrations employ particle numbers up to 0.26M and a direct-summation potential solver; close interactions involving the binary are treated using a new implementation of the Mikkola-Aarseth chain regularization algorithm. Even at these large values of N, two-body scattering occurs at high enough rates in the simulations that they can not be simply scaled to the large-N regime of real galaxies. The Fokker-Planck model is used to bridge this gap; it includes, for the first time, binary-induced changes in the stellar density and potential. The Fokker-Planck model is shown to accurately reproduce the results of the N-body integrations, and is then extended to the much larger N regime of real galaxies. Analytic expressions are derived that accurately reproduce the time dependence of the binary semi-major axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80 km/s. Formation of a core results from a competition between ejection of stars by the binary and re-supply of depleted orbits via two-body scattering. Mass deficits as large as ~4 times the binary mass are produced before coalescence. After the two black holes coalesce, a Bahcall-Wolf cusp appears around the single hole in one relaxation time, resulting in a nuclear density profile consisting of a flat core with an inner, compact cluster, similar to what is observed at the centers of low-luminosity spheroids.

astro-ph↗

arXiv2007

Correlation of macroscopic instability and Lyapunov times in the general three-body problem

We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small bodies in the Solar System. Numerical integrations of several sets of differently randomised initial conditions produced the same relationship of the instability time and Lyapunov time. Marginal probability densities of the various times in the three-body experiments are also discussed. Our high accuracy numerical method for three-body orbit computations and Lyapunov time determinations is concisely described.

astro-ph↗

arXiv2006

Algorithmic regularization with velocity-dependent forces

Algorithmic regularization uses a transformation of the equations of motion such that the leapfrog algorithm produces exact trajectories for two-body motion as well as regular results in numerical integration of the motion of strongly interacting few-body systems. That algorithm alone is not sufficiently accurate and one must use the extrapolation method for improved precision. This requires that the basic leapfrog algorithm be time-symmetric, which is not directly possible in the case of velocity-dependent forces, but is usually obtained with the help of the implicit midpoint method. Here we suggest an alternative explicit algorithmic regularization algorithm which can handle velocity-dependent forces. This is done with the help of a generalized midpoint method to obtain the required time symmetry, thus eliminating the need for the implicit midpoint method and allowing the use of extrapolation.

astro-ph↗

arXiv2005

Evolution of Binary Supermassive Black Holes via Chain Regularization

A chain regularization method is combined with special purpose computer hardware to study the evolution of massive black hole binaries at the centers of galaxies. Preliminary results with up to N=260,000 particles are presented. The decay rate of the binary is shown to decrease with increasing N, as expected on the basis of theoretical arguments. The eccentricity of the binary remains small.

astro-ph↗

arXiv2005

The Decay of Accreting Triple Systems as Brown Dwarf Formation Scenario

We investigate the dynamical decay of non-hierarchical accreting triple systems and its implications on the ejection model as Brown Dwarf formation scenario. A modified chain-regularization scheme is used to integrate the equations of motion, that also allows for mass changes over time as well as for momentum transfer from the accreted gas mass onto the bodies. We integrate an ensemble of triple systems within a certain volume with different accretion rates, assuming several prescriptions of how momentum is transferred onto the bodies. We follow their evolution until the systems have decayed. We analyze the end states and decay times of these systems and determine the fraction of Brown Dwarfs formed, their escape speeds as well as the semi-major axis distribution of the formed Brown Dwarf binaries. We find that the formation probability of Brown Dwarfs depends strongly on the assumed momentum transfer which is related to the motion of the gas. Due to ongoing accretion and consequent shrinkage of the systems, the median escape velocity is increased by a factor of 2 and the binary separations are decreased by a factor of 5 compared with non-accreting systems. Furthermore, the obtained semi-major axis distribution drops off sharply to either side of the median, which is also supported by observations. We conclude that accretion and momentum transfer of accreted gas during the dynamical decay of triple systems is able to produce the observed distribution of close binary Brown Dwarfs, making the ejection model a viable option as Brown Dwarf formation scenario.

astro-ph↗

arXiv1999

Earth Trojan asteroids: A study in support of observational searches

Observational searches for asteroids orbiting near Earth's triangular Lagrange points face unique obstacles. A population of such asteroids would occupy a large projected area on the sky (possibly hundreds of square degrees) and is not favorably placed with respect to the Sun. Here we examine the properties of synthetic populations of Earth ``Trojans'' in order to aid in the optimization of observational searches for them. We find that the highest on-sky projected number densities are not located at the positions of the L4 and L5 points themselves, but rather a few degrees closer to the Sun. Also, asteroids on orbits about the L4 and L5 points typically brighten as the difference between their ecliptic longitude and that of the Sun increases owing to phase effects, but their number density on the sky concurrently falls rapidly.

astro-ph↗

arXiv1993

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with $-1/r$ pairwise potential). We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change (with negative total energy). For two mass choices we have calculated 18000 full orbits (with initial states on a $100\times 180$ lattice on the Poincaré section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincaré maps for $10\times 18$ starting points. Our results show that the Poincaré section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: 1) There is a region of fast scattering, with a minimum of pairwise collisions and smooth dependence on initial values. 2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincaré section. For both 1) and 2) the initial and final states consists of a binary + single particle. 3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is the periodic Schubart orbit, whose stability turns out to correlate strongly with the global behavior.

chao-dyn↗