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Simulation of orbits around the galactic centre black hole with a relativistic Newtonian analogous potential

Abstract

We study the dynamics of a test particle around a central mass taking into account general relativistic effects within the formalism of Lagrangian mechanics, and investigate a real astrophysical object to probe the model. We consider a generalized potential for the Lagrangian of the particle, compute the corresponding equations of motion, and present a numerical scheme to integrate them. Within this approach, we run simulations to fit the orbital parameters of the star S2 around the SMBH Sgr A\(^*\), using a Markov Chain Monte Carlo method. We estimate the radius and speed of the star at periapsis, its apsidal precession and the black hole mass. Our results are consistent with results available in previous literature.

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References

  1. Artemova I. V., Bjoernsson G., Novikov I. D. 1996, Astrophys. J., 461, 565

    ADS  Article  Google Scholar 

  2. Casetti L. 1995, Phys. Scr., 51, 29

    ADS  Article  Google Scholar 

  3. Foreman-Mackey D. 2016, The Journal of Open Source Software, 1, 24

    ADS  Article  Google Scholar 

  4. Foreman-Mackey D., Hogg D. W., Lang D., Goodman J. 2013, Publications of the Astronomical Society of the Pacific, 125, 306

    ADS  Article  Google Scholar 

  5. Gainutdinov R., Baryshev Y. 2020, Universe, 6, 177

    ADS  Article  Google Scholar 

  6. Ghez A. M., Salim S., Weinberg N. N., et al. 2008, Astrophys. J., 689, 1044

    ADS  Article  Google Scholar 

  7. Ghosh S., Sarkar T., Bhadra A. 2016, The Astrophysical Journal, 828, 6

    ADS  Article  Google Scholar 

  8. Gillessen S., Eisenhauer F., Trippe S., et al. 2009, The Astrophysical Journal, 692, 1075

    ADS  Article  Google Scholar 

  9. Goldstein H., Poole C., Safko J. 2002, Classical Mechanics, 3rd ed., Vol. 70 (American Association of Physics Teachers)

  10. Gravity Collaboration, Abuter R., et al. 2020, Astron. Astrophys., 636, L5

  11. Hees A., Do T., Ghez A. M., et al. 2017, Phys. Rev. Lett., 118, 211101

    ADS  Article  Google Scholar 

  12. Hintz G. R. 2015, Orbital Mechanics and Astrodynamics (Cham, Switzerland: Springer International Publishing)

  13. Landau R. H., Páez M. J., Bordeianu C. C. 2015, Computational Physics (Weinheim, Germany: Wiley)

  14. Parsa M., Eckart A., Shahzamanian B., et al. 2017, Astrophys. J., 845, 22

    ADS  Article  Google Scholar 

  15. Pasha I. 2020, MCMC: A (very) Beginnner’s Guide, https://prappleizer.github.io/Tutorials/MCMC/MCMC_Tutorial.html [Online; accessed 28. Jan. 2021]

  16. Peißker F., Eckart A., Zajaček M., Ali B., Parsa M. 2020, Astrophys. J., 899, 50

    ADS  Article  Google Scholar 

  17. Price M. P., Rush W. F. 1979, Am. J. Phys., 47, 531

    ADS  Article  Google Scholar 

  18. Reich S. 2000, J. Comput. Phys., 157, 473

    ADS  MathSciNet  Article  Google Scholar 

  19. Schutz B. 2009, A First Course in General Relativity (Cambridge, UK: Cambridge University Press)

  20. Stewart M. G. 2005, American Journal of Physics, 73, 730

    ADS  MathSciNet  Article  Google Scholar 

  21. Tejeda E., Rosswog S. 2013, Monthly Notices of the Royal Astronomical Society, 433, 1930

    ADS  Article  Google Scholar 

  22. Zakharov A. F. 2018, Eur. Phys. J. C, 78, 689

    ADS  Article  Google Scholar 

  23. Zhang F., Lu Y., Yu Q. 2015, Astrophys. J., 809, 127

    ADS  Article  Google Scholar 

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Acknowledgements

We thank professors L. O. Manuel and C. M. Silva for their feedback, encouragement, and useful discussions. We also thank the anonymous reviewer whose comments greatly helped to improve the quality of the manuscript.

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Correspondence to S. Scozziero.

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Scozziero, S. Simulation of orbits around the galactic centre black hole with a relativistic Newtonian analogous potential. J Astrophys Astron 42, 100 (2021). https://doi.org/10.1007/s12036-021-09777-5

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Keywords

  • Gravitation–Galaxy:
  • centre—apsidal precession—stars:
  • kinematics and dynamics—numerical simulation—black hole physics