Towards the Super-Massive Black Hole Seeds

  • Eduardo S. Pereira
  • Pedro A. Santos
  • Haroldo F. de Campos VelhoEmail author


Massive and super-massive black-holes (BH) can be found in the center of all galaxies, according to the opinion from the scientific community. However, an open question is to know the origin of such BHs. One explanation is to consider such objects coming from the stars with large redshifts—very old stars collapsed during the ancient eras (population-III stars: the first-born stars created in the universe). A framework to investigate this scenario is to derive a mathematical model describing the evolution of the black hole distribution. From nowadays, observations show super-massive black holes with mass about 109M are ubiquitous in galaxy centers. The regularized inverse solution can be computed using an optimizer to identify the best solution for the functional to be minimized. Preliminary results are shown using synthetic observational data.



The authors would like to thank the FAPESP and CNPq, Brazilian agencies for research support.


  1. [BaEtal00]
    Baeck, T., Fogel, D.B., Michalewicz, Z.: Evolutionary Computation 1: Basic Algorithms and Operators, Taylor & Francis (2000).Google Scholar
  2. [CaEtAl97]
    Campos Velho, H. F., Ramos, F. M.: Numerical Inversion of Two-Dimensional Geoelectric Conductivity Distributions from Electromagnetic Ground Data, Braz. J. Geophys., 15, 133–143 (1997).Google Scholar
  3. [ChEtAl03]
    Chiwiacowsky, L.D., Campos Velho, H. F.: Different Approaches for the Solution of a Backward Heat Conduction Problem, Inverse Problems in Engineering, 11, 471–494 (2003).CrossRefGoogle Scholar
  4. [CoBo80]
    Conte, S. D., de Boor, C.: Elementary Numerical Analysis: An Algorithmic Approach, McGraw Hill, 3rd Edition (1980).Google Scholar
  5. [FoEtal12]
    Fortin, F.-A., De Rainville, F.-M., Gardner, M.-A., Parizeau, M., Gagné, C.: DEAP: Evolutionary Algorithms Made Easy. Journal of Machine Learning Research, 13, 2171–2175 (1992).MathSciNetzbMATHGoogle Scholar
  6. [Ha52]
    Hadarmard, J.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover (1952).Google Scholar
  7. [Li12]
    Li Y., Wang J., Ho L. C.: Cosmological Evolution of Supermassive Black Holes II. Evidence for Downsizing of Spin Evolution, The Astrophysical Journal, 749, 187–198 (2012).CrossRefGoogle Scholar
  8. [Ma96]
    Madsen, M. S.: The Dynamic Cosmos – Exploring the Physical Evolution of the Universe, Chapman & Hall, New York (NY), USA (1996).zbMATHGoogle Scholar
  9. [Mo84]
    Morosov, V. A.: Methods for Solving Incorrectly Posed Problems, Springer Verlag (1984).Google Scholar
  10. [NoWr06]
    Nocedal, J., Wright, S. J.: Numerical Optimization, Springer (2006).Google Scholar
  11. [PeMi14]
    Pereira, E. S., Miranda, O. D., Accretion history of active black holes from type 1 AGN. Astrophys Space Sci, 352, 801–807 (2014).CrossRefGoogle Scholar
  12. [PeMi10]
    Pereira, E. S., Miranda, O. D., Stochastic background of gravitational waves generated by pre-galactic black holes Monthly Notices Of Royal Astronomic Society, 401, 1924–1932 (2010).CrossRefGoogle Scholar
  13. [RaFa09]
    Raimundo, S. I., Fabian, A. C. Eddington ratio and accretion efficiency in active galactic nuclei evolution, Monthly Notes of Royal Astronomic Society, 396, 12–17, (2009).Google Scholar
  14. [RaEtAl99]
    Ramos, F. M., Campos Velho, H. F.,Carvalho, J. C., Ferreira, N. J.: Novel Approaches on Entropic Regularization, Inverse Problems, bf 15, 1139–1148 (1999).MathSciNetCrossRefGoogle Scholar
  15. [ShEtAl04]
    Shiguemori, E. H., Campos Velho, H. F., Silva, J. D. S.: Generalized Morosov’s Principle. In: Inverse Problems, Design and Optimization Symposium (IPDO), Angra dos Reis (RJ), Brazil, 290–298 (2004).Google Scholar
  16. [SmBl92]
    Small, T. A., Blandford R. D.: Quasar evolution and the growth of black holes. Monthly Notices of the Royal Astronomical Society, 259, 4, 725–737 (1992).CrossRefGoogle Scholar
  17. [ShEtAl10]
    Shankar F., et al.: On the Radiative Efficiencies, Eddington Ratios, and Duty Cycles of Luminous High-Redshift Quasars, The Astrophysical Journal, 718, 213–250 (2010).CrossRefGoogle Scholar
  18. [ShEtAl9]
    Shankar F., Weinberg D.H., Miralda-Escude J.: Self-Consistent Models of the AGN and Black Hole Populations: Duty Cycles, Accretion Rates, and the Mean Radiative Efficiency The Astrophysical Journal, 690, 20–41 (2009).CrossRefGoogle Scholar
  19. [Ti77]
    Tikhonov, A. N., Arsenin, V. Y.: Solution of Ill-posed Problems, John Wiley & Sons (1977).Google Scholar
  20. [YuTr02]
    Yu, Q., Tremaine, S.: Observational constraints on growth of massive black holes, Monthly Notices of the Royal Astronomical Society, 335, 965–976 (2002).CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Eduardo S. Pereira
    • 1
  • Pedro A. Santos
    • 1
  • Haroldo F. de Campos Velho
    • 1
    Email author
  1. 1.Instituto Nacional de Pesquisas Espaciais (INPE)São José dos CamposBrazil

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