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Title: On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center

Abstract

We perform detailed numerical analyses of the orbital motion of a test particle around a spinning primary, with the aim of investigating the possibility of using the post-Keplerian (pK) corrections to the orbiter’s periods (draconitic, anomalistic, and sidereal) as a further opportunity to perform new tests of post-Newtonian gravity. As a specific scenario, the S-stars orbiting the massive black hole (MBH) supposedly lurking in Sgr A* at the center of the Galaxy are adopted. We first study the effects of the pK Schwarzchild, Lense–Thirring, and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. It turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the sizes of the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH’s spin axis orientation are considered as well. The pK accelerations lead to corrections of the orbital periods of the order of 1–100 days (Schwarzschild), 0.1–10 hr (Lense–Thirring), and 1–10{sup 3} s (quadrupole) for a target star with a = 300–800more » au and e ≈ 0.8, which could be measurable with future facilities.« less

Authors:
 [1];  [2]
  1. Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione (Italy)
  2. School of Physics and Astronomy, Sun Yat-Sen University, Guangzhou 510275 (China)
Publication Date:
OSTI Identifier:
22661173
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 839; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; APPROXIMATIONS; BLACK HOLES; COMPUTERIZED SIMULATION; CONFIGURATION; CORRECTIONS; GALAXIES; GRAVITATION; NUMERICAL ANALYSIS; QUADRUPOLE MOMENTS; QUADRUPOLES; RELATIVISTIC RANGE; SPIN; STARS; TWO-BODY PROBLEM

Citation Formats

Iorio, Lorenzo, and Zhang, Fupeng, E-mail: lorenzo.iorio@libero.it, E-mail: zhangfp7@mail.sysu.edu.cn. On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center. United States: N. p., 2017. Web. doi:10.3847/1538-4357/AA671B.
Iorio, Lorenzo, & Zhang, Fupeng, E-mail: lorenzo.iorio@libero.it, E-mail: zhangfp7@mail.sysu.edu.cn. On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center. United States. doi:10.3847/1538-4357/AA671B.
Iorio, Lorenzo, and Zhang, Fupeng, E-mail: lorenzo.iorio@libero.it, E-mail: zhangfp7@mail.sysu.edu.cn. Mon . "On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center". United States. doi:10.3847/1538-4357/AA671B.
@article{osti_22661173,
title = {On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center},
author = {Iorio, Lorenzo and Zhang, Fupeng, E-mail: lorenzo.iorio@libero.it, E-mail: zhangfp7@mail.sysu.edu.cn},
abstractNote = {We perform detailed numerical analyses of the orbital motion of a test particle around a spinning primary, with the aim of investigating the possibility of using the post-Keplerian (pK) corrections to the orbiter’s periods (draconitic, anomalistic, and sidereal) as a further opportunity to perform new tests of post-Newtonian gravity. As a specific scenario, the S-stars orbiting the massive black hole (MBH) supposedly lurking in Sgr A* at the center of the Galaxy are adopted. We first study the effects of the pK Schwarzchild, Lense–Thirring, and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. It turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the sizes of the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH’s spin axis orientation are considered as well. The pK accelerations lead to corrections of the orbital periods of the order of 1–100 days (Schwarzschild), 0.1–10 hr (Lense–Thirring), and 1–10{sup 3} s (quadrupole) for a target star with a = 300–800 au and e ≈ 0.8, which could be measurable with future facilities.},
doi = {10.3847/1538-4357/AA671B},
journal = {Astrophysical Journal},
number = 1,
volume = 839,
place = {United States},
year = {Mon Apr 10 00:00:00 EDT 2017},
month = {Mon Apr 10 00:00:00 EDT 2017}
}
  • The center of our Galaxy hosts almost two hundred very young stars, a subset of which is orbiting the central supermassive black hole (SMBH) in a relatively thin disk-like structure. First analyses indicated a power-law surface density profile of the disk, Σ∝R {sup β} with β = –2. Recently, however, doubts about this profile arose. In particular, it now seems to be better described by a sort of broken power law. By means of both analytical arguments and numerical N-body modeling, we show that such a broken power-law profile is a natural consequence of the two-body relaxation of the disk.more » Due to the small relative velocities of the nearby stars in co-planar Keplerian orbits around the SMBH, two-body relaxation is effective enough to affect the evolution of the disk on timescales comparable to its estimated age. In the inner, densest part of the disk, the profile becomes rather flat (β ≈ –1) while the outer parts keep imprints of the initial state. Our numerical models show that the observed projected surface density profile of the young stellar disk can result from two-body relaxation driven evolution of a disk with initial single power-law profile with –2 ≲ β ≲ –1.5. In addition, we suggest that two-body relaxation may have caused a significant radial migration of the S-stars toward the central SMBH, thus playing an important role in their formation scenario.« less
  • The perturbed orbital equations governing the behavior of a nonrelativistic, elliptical, self-gravitating binary system with the impinging of weak, monochromatic gravitational plane waves are studied with solutions for the radial deviation expressed in terms of the observable, ''coordinate'' angle phi. Explicit expressions for the components of the perturbing force in terms of the Eulerian angles are also presented in the case of oblique incidence. Complete analytical solutions, however, are obtained only for (a) normal incidence and small eccentricity and (b) the z-component of a circular orbit at oblique incidence, and are compared with those of other authors. In particular, themore » nature of the occurrence of secular variations for nonintegral values of the ratio of the frequency of the wave to the orbital frequency of the unperturbed system is discussed. Extensive numerical analysis has been carried out for different states of polarization as well as various values of the eccentricity and wave frequency, and representative results are presented.« less