**BINARY BLACK HOLES SYSTEMS IN CENTERS OF GALAXIES. ****DYNAMICAL MODELS & OBSERVED STRUCTURES OF PECULIAR and INTERACTING GALAXIES ARP 1, 5, 22, 29 and 77**

**Dr.** **Joanna
Anosova***

** **

**ABSTRACT**

** We construct and study numerically the dynamics of models of galaxies assuming that the centers of models contain very massive
double black holes, surrounded by relatively low mass particles such as star clusters, gas, and dust complexes. Our work shows that the dynamical evolution of that models produce many structures similar to those observed in the nuclei of galaxies, including
dumb-bell bars, rings and various types of flows, jets and spirals. The basic dynamical processes of formation of different elements of structures are formulated. It is shown that significant changes of structures often occur after the gravitational slingshot
effect in the centers of systems. We found combinations of initial conditions and model parameters that produce in some time structures similar to the structures of the peculiar and interacting galaxies. In this paper, we show our results for the peculiar
galaxies Arp 1, 5, 22, 29, 77 from the Atlas of Peculiar Galaxies by Halton Arp, 1966. ****Our figures show comparison of the model and observed structures of these galaxies as well as the past and future dynamical evolution of the
models.**

** Keywords: the three body problem, computer simulations, massive central**

** binary ****black holes, dynamical evolution, galaxy structure**

*** - tjmurs@yahoo.com**

** **** **

**1.INTRODUCTION**

** On 14 Sept, 2015 (see Abbott et al., 2016) The LIGO reported the ****first direct detection**** of gravitational waves and the ****first direct observation**** of
a binary black hole. These observations demonstrate the ****real existence**** of binary black hole systems predicted by Einstein in his General theory of relativity a century earlier. Therefore, the study of the
dynamics of galaxy systems with the central massive binary black holes is especially interesting and actual now.**

** It has long been believed that most of celestial objects are dominated by single centers of attraction
in them. It was more or less natural because the solar system had been the unique model of celestial objects for a long time and even in modern times the sun and stars were the typical celestial objects.**

** Recently
however a lot of violent and/or complicated phenomena are discovered to take place in every part of the Universe in every scale. Many of these phenomena are caused by multiple centers of attraction: planetary rings and shepherding satellites, unusually large
eccentricities of millisecond pulsars, accretion discs of various scales, peculiar structures of single galaxies, irregular and interacting galaxies, etc.**

** The gravitational N body problem was applied to celestial mechanics
soon after the discovery of Newton's universal law. However, in the course of three centuries the analytical studies have not provided an effective solution to the main problem. Today, numerical methods may be used for obtaining detailed solutions.**

** Most dynamical studies of such complicated galaxy systems by computer simulations have utilized hydrodynamics, gravitational potential theory, stellar orbit theory, as well as the gravitational N body problem with large N (see
Combes,1993; Sellwood,1987and 1993; Binney and Tremaine,1987; Yoshiaki and Keiichi,1996; Baba, 2015; Athanassoulla, 2018 as well as reviews by Kormendy, Combes, Athanassoula,Brooks, Graham, 2016, in book “Galactic Bulges”,ed.
Laurikainen et al. and references therein). All these dynamical studies have assumed collision-less systems. But we are still far from a complete understanding of the dynamical structure and the kinematics of galaxies and their features.**

** Computer simulations of the gravitational N body problem were first performed by von Hoerner,1960 who studied the evolution of small system (N = 4 - 25). Further advances of the direct method as well as increased computer power have yielded
significant results for systems with N = 500 components (Aarseth,1974; Wielen, 1974).**

** It should be noted that the study of large N body systems required considerable amount of computer time (roughly proportional to N in
3), hence, the number of different initial conditions which can be examined is relatively limited. On the other hand, small N systems offer good prospects of systematical investigations, particularly in the case of N = 3. The shortening of computer process-time
permits statistical methods to be used for studying the behavior of triple systems. This is achieved by selection a representative sample of initial conditions which then reveal general features of the evolution (Agekian and Anosova,1967; Anosova,1986).**

** A wide range of triple systems occur among stars and galaxies, and their kinematics and dynamics have a considerable cosmogonic interest. Moreover, studies of dynamical evolution of N body systems with N = 10 - 500 have shown that three
body interactions play a crucial role in the central regions of open and globular clusters, as well as galaxy clusters. Consequently, the study of the three body problem is relevant to the subjects of celestial mechanics, stellar dynamics and astrophysics
alike. **

**Many authors** **have studied numerically the dynamical evolution of different galaxy systems, using computer simulations in the restrict three body problem where one body is a mass-less
particle: **

** - Toomre and Toomre,1972 simulated the formation of bridges and tails due to the parabolic passage of a disturber by a galaxy surrounded by zero-mass particles;**

**
- Lin and Saslaw,1977 considered the flyby of a single star and a binary with associated disks of mass-less particles to explain the formation of double radio sources; **

** - Murai and Fujimoto,1980
and Lin and Lynden-Bell,1982 considered the dynamical models of the Magellanic Stream in the triple galaxy system consisting of our Galaxy and the two Magellanic Clouds;**

** - Valtonen,1984a,b;1985 and Valtonen and Byrd,1979;
1986 used a similar method (compilation of many initial conditions for the restrict three body problem) in order to study the process of dynamical formation of structures of galaxy clusters with massive central binary galaxies; **

**
- Valtonen,1988 studied triple black hole systems formed in mergers of galaxies; **

** - Basu et al.,1993 modeled extragalactic jets by mergers of binary black holes surrounded by accretion disks.**

**
In all restricted three or four body investigations above, the motions of main bodies are either parabolic, hyperbolic, or highly elliptic ones.**

** 2.COMPUTER SIMULATIONS**

** We study numerically the dynamical evolution of a galaxy model consisting of the central super-massive binary
black hole with circular orbit and extended shells with numerous low mass particles inside and around the binary orbit. We carry out computer simulations in the framework of the general three body problem, considering about a million initial conditions. **

** This model can be compared with previous ones described above (Toomre and Toomre, 1972, and others; see also books by Valtonen & Karttunen, 2006 and Valtonen, Anosova et al., 2016 and references therein). In those models
authors, considering the restrict three body problem, studied a single approach of the two initially independent massive bodies with parabolic, hyperbolic or highly elliptic relative motions and the mass-less particles around; in this case the mass-less
particles can have only one approach with each massive body. **

** In contrast, in our model (Anosova et al., 1994, 1995, 2000, 2006, 2017 and present) we consider a long-living central massive circular binary
system; the low mass particles may interact with this binary nucleus many times during the dynamical evolution of the entire system. In such model the gravitational slingshot effect may occur many times, especially under total collapse of the system.
**

** We study the dynamical evolution of our models integrating numerically the regularized equations of motions of bodies in the three body problem (see Anosova,1986), accumulating results for numerous initial
conditions and compiling them. For these calculations we use the code ’TRIPLE’ due to Aarseth and Zare,1974. For our models we carry out calculations during the 40 periods P rotations of the binary. **

**
Each model with a massive binary black hole in the center consists of 19 shells inside and outside of the binary orbit. All shells are centered at the center of inertia of the system. Every shell has N = 1000 small mass particles
(such as star clusters, gas, and dust complexes) distributed there uniformly randomly. Initially, these particles have only radial velocities with respect to the center of the binary for realization there of strong interactions of the bodies. **

** This model contains the large number N of particles with the low masses M_{p}, which do not interact to each other. For approximation of self-consistent model, we need to consider a sufficiently
small value of M_{p}. We carried out the trial calculations with the values M_{p}: 0.000001, 0.0001, 0.001, 0.01, assuming that the mass of the heaviest component of the binary is M_{1}=1. For
the four values of M_{p} we obtained almost the same results, but the CPU time increases crucially with decreasing M_{p}. For basic calculations we use the value M_{p} = 0.01. **

** We study the dynamical evolution of such models with numerous initial conditions and different parameters, considering the dynamics of all spherical shells together and separately. Our method permits us to study the individual
trajectories of particles, their close double and triple approaches, and inspect the time-depending structures in the models. Multiple runs of these models allow us to classify the numerous strong triple interactions of bodies resulting in various structures.
**

** It is shown that first at some point in time collapse of the system takes place, when many low-mass particles have close approaches with heavy binary components and strong interactions with them. Frequently,
the gravitational slingshot effect occurs. Further along in time, some part of the particles, which initially were outside the binary orbit, escapes from the system. Other particles or are captured by binary components and compile the central dumb-bell bars,
or form the different types of jets, flows, open and close spirals and rings. The obtained structures are often similar to the observed structures of galaxies - spiral, elliptical, irregular, and different kinds of interacting galaxies. Symmetrical structures
appear in models with the equal masses of bodies of the central binary. Globally, the systems are expanding significantly; they can expand by 300 times after P=40 period of binary rotation.**

**
3.DYNAMICAL EXPLANATION**

** The detail investigation of low mass particles motions shows that we often observe many near simultaneous approaches of them to the center of mass of the binary system. The resulting formation of
different kinds of the structure in the model depends on the initial positions of low mass particles and their motions during close approaches with the binary:**

**1) mostly particles, which initially were inside of the binary orbit,
are captured by the binary components and generate a stable central dumb-bell bar;**

**2) for the particles, which initially were outside of the binary orbit, the results of close approaches with the binary system depend on their
motions relative to the line of apses of the binary orbit at this time:**

**- in the case of almost orthogonal motions (the gravitational slingshot effect), these particles escape from the system and before an escape, form open expanding
spirals;**

**- in the alternative case these particles are captured by the binary black hole and compile a dumb-bell bar;**

**- in the intermediate case particles create different kinds of jets, flows, open
and close spirals and rings;**

**- these effects are more pronounced in the plane of the binary orbit;**

**- the symmetrical structure is formed only in the case of the equal masses of the binary components.**

** Figure 1 demonstrates schematically the basic dynamical mechanisms of formation of different elements of the structure. This scheme shows the trajectories of low mass
particles on the plane [ X, Y ] of the binary orbit during strong interactions with this binary.**

** We use the following denotes:**

**- two small triangles on the horizontal
coordinate X axis show locations of the binary components with the equal masses. In this case, these positions are symmetrical about the vertical coordinate Y axis;**

**- filled circles indicate the
trajectories of escaping particles; they are moving almost along the Y axis and we observe the gravitational slingshot effect;**

**- open squares present the motions of particles that return to the center of
inertia of a system after a failed ejection;**

**- ticks, crosses and stars show trajectories of particles that form different types of the open and close spirals as well as the large and small rings inside the system;**

**- snowflakes show the process of formation of dumb-bell bars;**

**- part of the big circle in the negative quadrant ( x < 0, y < 0) shows schematically the initial positions of
the small particles relative to the center of mass of the binary at the time when strong interactions of bodies begin;**

**- filled squares on this circle indicate roughly the regions of the positions of small particles
at this time with different final motions.**

** 4.RESULTS**

** We compared obtained model structures with observed structures of many galaxies and found combinations
of the initial conditions and model parameters that produce in some time similar structures in the peculiar and interacting galaxies. In this paper we demonstrate our results for peculiar galaxies Arp 1, 5, 22, 29, 77. It is interesting that different kind
observations (ALMA and others - see ****Onishi, Iguchi, et al., 2015 and references thererein) of the galaxy Arp 77 (NGC 1097) confirm that this spiral interacting galaxy indeed has massive central binary black hole and gas and dust spirals
around.**

** ****Figures 2 - 6 show a comparison of model and observed structures of galaxies found and the past and future evolution of models. These figures consist of three parts: a) the picture of the
observed galaxy; b) the best model structure; c) the 10 snapshots of the dynamical evolution of this model over the time span. The third part of each figure presents the dynamical evolution of models during the time P_{f} , where the unit
of the time t is the period P = 1 of rotation of the binary; their semi-axis a = 1 is the unit of the distance; t_{0} = 0.0 is the initial time of the evolution, dt is the time span
when the model structure is fixed; the gravitational constant G = 1. For our system of unites [P = 1, a = 1, G = 1] the masses M_{1}&M_{2} of the binary components must meet the
condition M_{1} + M_{2} = 2π^{2}. **

** The basic parameters of models are the following ones:**

**- the value M 2 = M_{2}
from the interval [0.1, 1.0] is the ratio the mass of the binary components; the fixed value M 3 = M_{p} = 0.01 is the ratio of mass of small particles to the mass M_{1} of the heaviest component of the binary;**

**- the initial radius R of shells centered at the center of mass of the binary; we consider R from the interval [0.25, 50.00]; the initial distribution of low mass particles on these shells (inside and outside
of the central massive binary orbit) is uniformly randomly;**

** - the value V is the ratio of initial radial velocities of small particles to their escape velocity V_{esc}; this ratio V is selected from the interval
[0.0, 1.0).**

** 5. SUMMARY**

** Obtained structures of dynamical models in some time are similar to observed structures of the peculiar galaxies
Arp 1, 5, 22, 29 and 77. According to various observations, the bright galaxy Arp 77 in this list indeed has the central super-massive binary black hole with spirals.**

** Figures 2 - 6 present a comparison of model and
observed structures of these galaxies. We defined the parameters and initial conditions for such models and showed their past and future dynamical evolution.**

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** **

**FIGURE 2. THE GALAXY ARP 1**

** ****FIGURE 3. THE GALAXY ARP 5**

**FUGURE 4. THE GALAXY ARP 22 **

**FIGURE 5. THE GALAXY ARP 29 **

** ****FIGURE 6. THE GALAXY ARP 77 **