9 772161471005 03 International Journal of Astronomy and Astrophysics, 2019, 9, 173-353 http://www.scirp.org/journal/ijaa ISSN Online: 2161-4725 ISSN Print: 2161-4717 Table of Contents Volume 9 Number 3 September 2019 N-Body Simulations of Gas-Free Disc Galaxies with SMBH Seed in Binary Systems R. Chan…………………………………………………………………………………………………………………173 The Analysis of Interplanetary Shocks Associated with Six Major Geo-Effective Coronal Mass Ejections during Solar Cycle 24 S. L. Soni, P. R. Singh, B. Nigam, R. S. Gupta, P. K. Shrivastava………….…………………………………………191 Re-Entry of Space Objects from Low Eccentricity Orbits C. S. Lawrence, R. K. Sharma……………………………………………….....………………………………………200 Analytical Solution for Formation Flying Problem near Equatorial-Circular Reference Orbit S. A. Altalhi, M. I. El Saftawy…………………………………………….……………………………………………217 The Distance Modulus in Dark Energy and Cardassian Cosmologies via the Hypergeometric Function L. Zaninetti………………………………………………………..……………………………………………………231 Gamma-Ray Bursts Generated by Hyper-Accreting Kerr Black Hole F. Sado…………………………………………….....…………………………………………………………………247 Gravity Constraints on the Measurements of the Speed of Light F. Ramdani…………………………………………….……………………….………………………………………265 Halo Orbits in the Photo-Gravitational Restricted Three-Body Problem S. Ghotekar, R. K. Sharma…………………..…………………………………………………………………………274 Convective Models of Jupiter’s Zonal Jets with Realistic and Hyper-Energetic Excitation Source H. G. Mayr, K. L. Chan………………………………………….…………………..…………………………………292 Models for Velocity Decrease in HH34 L. Zaninetti…………………………………………………………………………..…………………………………302 Optical Spectroscopic Monitoring Observations of a T Tauri Star V409 Tau H. Akimoto, Y. Itoh…………………………………..……………………………..…………………………………321 Parameter Inversions of Multi-Layer Media of Mars Polar Region with Validation of SHARAD Data C. Liu, Y.-Q. Jin………………....…………………………………………………..…………………………………335 The figure on the front cover is from the article published in International Journal of Astronomy and Astrophysics, 2019, Vol. 9, No. 3, pp. 231-246 by Lorenzo Zaninetti. International Journal of Astronomy and Astrophysics (IJAA) Journal Information SUBSCRIPTIONS The International Journal of Astronomy and Astrophysics (Online at Scientific Research Publishing, https://www.scirp.org/) is published quarterly by Scientific Research Publishing, Inc., USA. Subscription rates: Print: $79 per issue. To subscribe, please contact Journals Subscriptions Department, E-mail: [email protected] SERVICES Advertisements Advertisement Sales Department, E-mail: [email protected] Reprints (minimum quantity 100 copies) Reprints Co-ordinator, Scientific Research Publishing, Inc., USA. E-mail: [email protected] COPYRIGHT Copyright and reuse rights for the front matter of the journal: Copyright © 2019 by Scientific Research Publishing Inc. 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PRODUCTION INFORMATION For manuscripts that have been accepted for publication, please contact: E-mail: [email protected] International Journal of Astronomy and Astrophysics, 2019, 9, 173-190 http://www.scirp.org/journal/ijaa ISSN Online: 2161-4725 ISSN Print: 2161-4717 N-Body Simulations of Gas-Free Disc Galaxies with SMBH Seed in Binary Systems R. Chan Coordenação de Astronomia e Astrofsica, Observatório Nacional, Rio de Janeiro, RJ, Brazil How to cite this paper: Chan, R. (2019) Abstract N-Body Simulations of Gas-Free Disc Ga- laxies with SMBH Seed in Binary Systems. We have shown the outcome of N-body simulations of the interactions of two International Journal of Astronomy and disc galaxies without gas with the same mass. Both disc galaxies have halos of Astrophysics, 9, 173-190. dark matter, central bulges and initial supermassive black hole (SMBH) seeds https://doi.org/10.4236/ijaa.2019.93013 at their centers. The purpose of this work is to study the mass and dynamical Received: May 1, 2019 evolution of the initial SMBH seed during a Hubble cosmological time. It is a Accepted: July 6, 2019 complementation of our previous paper with different initial orbit conditions Published: July, 2019 and by introducing the SMBH seed in the initial galaxy. The disc of the sec- ondary galaxy has a coplanar or polar orientation in relation to the disc of the Copyright © 2019 by author(s) and Scientific Research Publishing Inc. primary galaxy and their initial orbit are eccentric and prograde. The primary This work is licensed under the Creative and secondary galaxies have mass and size of Milky Way with an initial Commons Attribution International SMBH seed. We have found that the merger of the primary and secondary License (CC BY 4.0). discs can result in a final normal disc or a final warped disc. After the fusion http://creativecommons.org/licenses/by/4.0/ of discs, the final one is thicker and larger than the initial disc. The tidal ef- Open Access fects are very important, modifying the evolution of the SMBH in the primary and secondary galaxy differently. The mass of the SMBH of the primary ga- laxy has increased by a factor ranging from 52 to 64 times the initial seed mass, depending on the experiment. However, the mass of the SMBH of the secondary galaxy has increased by a factor ranging from 6 to 33 times the ini- tial SMBH seed mass, depending also on the experiment. Most of the accreted particles have come from the bulge and from the halo, depleting their par- ticles. This could explain why the observations show that the SMBH with 6 masses of approximately 10 M is found in many bulgeless galaxies. Only a small number of the accreted particles has come from the disc. In some cases of final merging stage of the two galaxies, the final SMBH of the secondary galaxy was ejected out of the galaxy. Keywords Simulation, Disc Galaxy, Supermassive Black Hole, Binary Galaxies, Merger, Warped Disc Galaxies DOI: 10.4236/ijaa.2019.93013 Jul. 9, 2019 173 International Journal of Astronomy and Astrophysics R. Chan 1. Introduction It is well known in the literature that supermassive black holes (SMBH) exist in the majority of the galaxies, within elliptical, disc to even in dwarf galaxies [1] [2]. Several recent works in numerical simulations with SMBH with gas [3] [4] [5] show us how complex is the dynamical evolution and mass growing with gas ac- cretion can be. Moreover, many papers have been published about simulations of binary mergers with BH seeds including complex dissipative processes but not included in the present simulations [6]-[14]. Simulations of binary mergers with BH seeds and no dissipative effects, simi- lar to the ones presented in this work are published by several authors [15]-[22]. On the other hand, there are only few works in the literature based on simula- tions of interaction of gas-free disc galaxies [23]-[29], but none has treated the problem of the existence of a SMBH at the center of the galaxies. In a recent paper of Li et al. (2017), it is presented the results of the gas-free interaction of SMBHs in very eccentric galaxy orbits. Besides, there are rare works studying the evolution of such a binary galaxy in a long interval of time [28] [29] [30] in small eccentricity orbits. This work is a complementation of our previous work [29] where, there, the focus was the evolution of the discs, but here we use different initial orbit conditions and with a SMBH seed in the initial galaxy. Thus, differently, we will focus in the SMBH seed evolution in a cosmo- logical time and covering a wider range of orbits of the galaxy binary than in the work of Li et al. (2017). Thus, the main goal of the present work is to perform numerical N-body si- mulations to study the time evolution of the mass and dynamics of the initial SMBH seed in the two disc galaxies. We also want to know if the tidal forces af- fect the evolution of the SMBH. This paper explores the scenario as follows: first, we assume a disc galaxy with the characteristics of the Milky Way (disc, bulge, halo and SMBH). Second, we let a secondary galaxy with the same characteristics orbit on pro- grade coplanar or polar disc (orientation in relation to the primary disc ga- laxy). The paper is organized as follows: in Section 2, we describe the numerical method used in the simulations. In Section 3 we present the initial conditions. In Section 4, we describe the results of the simulations. Finally, in Section 5, we summarize the results. 2. Numerical Method The N-body simulation code used was GADGET [31]. A modified version of this basic code was made in order to introduce the SMBH gravitational interaction with the other particle. Here we have used only the N-body integration but without gas. DOI: 10.4236/ijaa.2019.93013 174 International Journal of Astronomy and Astrophysics R. Chan The units used in all the simulations are G = 1 , [length] = 4.500 kpc, [mass] = 10 7 5.100× 10 M , [time] = 1.993× 10 years ( H0 = 100 km/s/Mpc) and [velocity] = 220.730 km/s. Hereinafter, all the physical quantities will be referred to these units. The Hubble time tH corresponds to 490 time units. We assumed in all the simulations the tolerance parameter θ = 0.577 .