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Pramana

, 92:43 | Cite as

A parametric model to study the mass–radius relationship of stars

  • Safiqul IslamEmail author
  • Satadal Datta
  • Tapas K Das
Article
  • 5 Downloads

Abstract

In static space–time, we solve the Einstein–Maxwell equations. The effective gravitational potential and the electric field for charged anisotropic fluid are defined in terms of two free parameters. For such configurations, the mass of the star as a function of stellar radius is found in terms of two aforementioned parameters subjected to certain stability criteria. For various values of these two parameters, one finds that such a mass–radius relationship can model stellar objects located at various regions of the Hertzsprung–Russel diagram.

Keywords

General relativity relativistic star electric field gravitational potential ab parameter space stars Hertzprung–Russel diagram 

PACS Nos

95.30.Sf 98.80.Jk 98.52.-b 

Notes

Acknowledgements

SI is thankful to P Tarafdar of S.N. Bose National Centre for Basic Sciences for providing some useful insights in the paper. SD is thankful to his sister Nibedita Datta for useful discussions about the cubic polynomial appearing in the paper and he is also thankful to his colleague Md. A Shaikh for helping him with the plots. TKD acknowledges the support from the Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India, in the form of a long-term visiting scientist (one-year sabbatical visitor).

References

  1. 1.
    Ksh Newton Singh et al, Eur. Phys. J. C 77, 100 (2017)ADSCrossRefGoogle Scholar
  2. 2.
    P Mafa Takisa et al, Eur. Phys. J. C 77, 713 (2017)ADSCrossRefGoogle Scholar
  3. 3.
    D Kileba Matondo, S D Maharaj and S Ray, Eur. Phys. J. C 78, 437 (2018)ADSCrossRefGoogle Scholar
  4. 4.
    K N Singh, N Pradhan and N Pant, Pramana – J. Phys. 89: 23 (2017)ADSCrossRefGoogle Scholar
  5. 5.
    P Mafa Takisa and S D Maharaj, Astrophys. Space Sci. 361, 262 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    D Kileba Matondo et al, Astrophys. Space Sci. 362, 186 (2017)ADSCrossRefGoogle Scholar
  7. 7.
    R L Bowers and E P T Liang, Astrophys. J. 188, 657 (1917)ADSCrossRefGoogle Scholar
  8. 8.
    S K Maurya and M Govender Eur. Phys. J. C 77, 347 (2017)ADSCrossRefGoogle Scholar
  9. 9.
    R I Adam and A Sulaksono, AIP Conf. Proc. 1729, 020010 (2016)CrossRefGoogle Scholar
  10. 10.
    S Ray et al, Phys. Rev. D 68, 084004 (2003)ADSCrossRefGoogle Scholar
  11. 11.
    C L Rosen, Astrophys. Space Sci. 1, 372 (1968)ADSCrossRefGoogle Scholar
  12. 12.
    M Gleiser and K Dev, Int. J. Mod. Phys. D 13, 7 (2004)Google Scholar
  13. 13.
    C W Misner and H S Zapolsky, Phys. Rev. Lett. 12, 22 (1964)CrossRefGoogle Scholar
  14. 14.
    R Garattini and G Mandanici, Eur. Phys. J. C 77, 57 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    D Shee et al, arXiv:1612.05109 (2017)
  16. 16.
    F Rahaman et al, Eur. Phys. J. C 75, 564 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    R Tikekar et al, Grav. Cosmol. 4, 294 (1998)ADSMathSciNetGoogle Scholar
  18. 18.
    K Komathiraj and S D Maharaj, arXiv:gr-qc/0702102v1 (2007)
  19. 19.
    S Islam et al, Astrophys. Space Sci. 355, 2205 (2014)Google Scholar
  20. 20.
    S Thirukkanesh and F C Ragel, Astrophys. Space Sci. 352, 743 (2014)ADSCrossRefGoogle Scholar
  21. 21.
    R C Tolman, Phys. Rev. 55, 364 (1939)ADSCrossRefGoogle Scholar
  22. 22.
    M Malaver, Int. J. Mod. Phys. Appl. 2, 1 (2015)Google Scholar
  23. 23.
    A Einstein, Sitz. Deut. Akad. Wiss. Math. Phys. Berlin 8, 142 (1917)Google Scholar
  24. 24.
    W de Sitter, Proc. R. Acad. Amst. 19, 1217 (1917)Google Scholar
  25. 25.
    P Bhar et al, Pramana – J. Phys. 90: 5 (2018)ADSCrossRefGoogle Scholar
  26. 26.
    M Govender and S Thirukkanesh, Astrophys. Space Sci. 358, 39 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    S Thirukkanesh, M Govender and D B Lortan, Int. J. Mod. Phys. D 24, 1550002 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    H Herrera, Phys. Lett. A 165 206, (1992)ADSCrossRefGoogle Scholar
  29. 29.
    M K Mak et al, Europhys. Lett. 55, 310 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    W J Kaufmann, Universe (W H Freeman and Company, USA, 1994)Google Scholar
  31. 31.
    J B Holberg et al, Astron. J. 135, 1225 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    L James et al, Astrophys. J. 630, L69 (2005)CrossRefGoogle Scholar
  33. 33.
    J L Provencal, Astrophys. J. 494, 759 (1998)ADSCrossRefGoogle Scholar
  34. 34.
    P Kervella et al, Astron. Astrophys. 488, 2 (2008)CrossRefGoogle Scholar
  35. 35.
    S H Pravdo et al, Astrophys. J. 700, 623 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    ‘The one hundred nearest star systems’, RECONS. Georgia State University, archived from the original on 2012-05-13, retrieved 2010-06-30Google Scholar
  37. 37.
    J L Linsky et al, Astrophys. J. 455, 670 (1995)ADSCrossRefGoogle Scholar
  38. 38.
    J Tomkin and Daniel M Popper, Astron. J. 91, 6 (1986)CrossRefGoogle Scholar
  39. 39.
    M Güde et al, Astron. Astrophys. 403, 155 (2003)ADSCrossRefGoogle Scholar
  40. 40.
    F Crifo et al, Astron. Astrophys. 320, L29 (1997)ADSGoogle Scholar
  41. 41.
    P Kervella et al, arXiv:astro-ph/0309784 (2003)
  42. 42.
    L Casagrande et al, Astron. Astrophys. 530, A138 (2011)CrossRefGoogle Scholar
  43. 43.
    J Fernandes et al, Astron. Astrophys. 338, 455 (1998)ADSGoogle Scholar
  44. 44.
    M Stix, The Sun: An introduction (Springer, Berlin, 1991), corrected second printGoogle Scholar
  45. 45.
    H Bruntt et al, Mon. Not. R. Astron. Soc. 000, 1 (2010)Google Scholar
  46. 46.
    J Liebert et al, Astrophys. J. 630, L69 (2005)ADSCrossRefGoogle Scholar
  47. 47.
    E J Shaya and P Olling Rob, Astrophys. J. 192, 2 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    A P Hatzes et al, Astron. Astrophys. 457, 335 (2006)ADSCrossRefGoogle Scholar
  49. 49.
    M Aurière et al, Astron. Astrophys. 504, 231 (2009)ADSCrossRefGoogle Scholar
  50. 50.
    T Shenar et al, Astrophys. J. 809, 135 (2015)ADSCrossRefGoogle Scholar
  51. 51.
    P Cruzalébes, Mon. Not. R. Astron. Soc. 434, 437 (2013)Google Scholar
  52. 52.
    I Ramírez and A C Prieto, Astrophys. J. 743, 135 (2011)ADSCrossRefGoogle Scholar
  53. 53.
    K Ohnaka Astron. Astrophys. 533, A3 (2013)CrossRefGoogle Scholar
  54. 54.
    J Zorec et al, Astron. Astrophys. 441, 235 (2005)ADSCrossRefGoogle Scholar
  55. 55.
    Th Kallinger et al, Proc. Int. Astron. Union 848, (2004)Google Scholar
  56. 56.
    H R Neilson et al, ASP Conf. Ser. 451, 117 (2011)ADSGoogle Scholar
  57. 57.
    M Dolan Michelle et al, Astrophys. J. 819, 7 (2016)Google Scholar
  58. 58.
    B Arroyo-Torres et al, Astron. Astrophys. 554, A76 (2013)CrossRefGoogle Scholar
  59. 59.
    M Wittkowski et al, Astron. Astrophys. 540, L12 (2012)ADSCrossRefGoogle Scholar
  60. 60.
    D E Beck et al, Astron. Astrophys. 523, A18 (2010)CrossRefGoogle Scholar
  61. 61.
    S M White et al, Astrophys. J. Suppl. 71, 895 (1989)ADSCrossRefGoogle Scholar
  62. 62.
    M Zechmeister et al, Astron. Astrophys. 491, 531 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Physics, Harish-Chandra Research InstituteHBNIJhunsiIndia
  2. 2.Physics and Applied Mathematics UnitIndian Statistical InstituteKolkataIndia

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