Astrophysics and Space Science

, Volume 121, Issue 1, pp 161–191 | Cite as

cD galaxies of apparent supergiant sizes due to the curvature of space

  • Jaroslav Souček
Article

Abstract

By combining two two-dimensional subspaces, closed into themselves due to curvature, it is possible to create a model of three-dimensional space of the same properties. If the Universe is a space of this type, its effect is that of a monstrous lens. Close objects are observed to diminish according to the normal law of perspective; however, the remote galaxies are seen to be very highly magnified.

The apparent angular size2θ of a galaxy is more than the size1θ in flat space according to relation:2θ =1θχ cosec χ, where χ is the angular distance from the observer to the galaxy. The diameter2d of a galaxy in curved space must be in the same relation to a diameter1d with no curvature of space:2d=1dχ cosec χ. The apparent angular size2θ and diameter2d are distorted shapes in consequence of an optical illusion caused by the spatial curvature.

It is necessary to distribute the multitude of galaxies into two parts in accordance with their location on the close or reverse hemihypersphere of the Universe. The minimum of apparent angular size2θ of a galaxy of diameter1d is at the equatorial zone.

The most likely candidates for location in the reverse hemi-hypersphere are cD's of apparent supergiant sizes due, probably, to the curvature of space. The existence of supergiant sizes of galaxies is the second indirect proof, besides superluminal velocities, that the Universe is closed into itself through curvature. The third indirect evidence, i.e., inductive confirmation of the same fact, is the superposition of galaxies which need not inevitably be a new alternative to the present theories of collisions, cannibalism, merger, etc.

The fourth indirect proof of the positive curvature of the Universe is the occurrence of background radiation, because that must vanish in hyperbolic space irrespective of its origin. The gravitational lens effect acquires another theoretical form, as usual, in the case of remote galaxies, because it is impossible to distinguish between gravitator and lensing image.

Keywords

Hyperbolic Space Positive Curvature Angular Distance Distort Shape Flat Space 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aaronson, M.: 1980, in C. G. Wynn-Williams and D. P. Cruikshank (eds.), ‘Infrared Astronomy’,IAU Symp. 96, 360 (Russian).Google Scholar
  2. Aaronson, M. and Olszewski, E. W.: 1984,Nature 309, 414.Google Scholar
  3. Abell, G. O.: 1958,Astrophys. J., Suppl. 3, 211.Google Scholar
  4. Albert, C. E., White, R. A., and Morgan, W. W.: 1977,Astrophys. J. 211, 309.Google Scholar
  5. Anderson, B., Donaldson, W., Palmer, H. P., and Rowson, B.: 1965,Nature 205, 375.Google Scholar
  6. Arp, H. and Bertola, F.: 1969,Astrophys. Letters 4, 23.Google Scholar
  7. Arp, H. and Bertola, F.: 1971,Astrophys. J. 163, 195.Google Scholar
  8. Arsac, J.: 1959,Optica Acta 6, 7.Google Scholar
  9. Artjukh, V. S., Vitkevitch, V. A., Dagkesamansky, R. D., and Kozukhov, V. N.: 1968,Astron. J. U.S.S.R. 45, 712.Google Scholar
  10. Baade, W. and Minkowski, R.: 1954,Astrophys. J. 119, 206.Google Scholar
  11. Bahcall, N. A.: 1977a,Ann. Rev. Astron. Astrophys. 15, 505.Google Scholar
  12. Bahcall, N. A.: 1977b,Astrophys. J. 217, L77.Google Scholar
  13. Barnothy, J. M. and Barnothy, M. F.: 1968,Science 162, 348.Google Scholar
  14. Barnothy, J. M. and Barnothy, M. F.: 1972, in D. S. Evans (ed.), ‘External Galaxies and Quasi-Stellar Objects’,IAU Symp. 44, 478.Google Scholar
  15. Barnothy, J. M. and Barnothy, M. F.: 1984,Bull. Am. Astron. Soc. 16, 486.Google Scholar
  16. Bautz, L. P. and Morgan, W. W.: 1970,Astrophys. J. 162, L149.Google Scholar
  17. Beers, T. C. and Geller, M. J.: 1983,Astrophys. J. 274, 491.Google Scholar
  18. Biermann, P. and Silk, J.: 1976,Astron. Astrophys. 48, 287.Google Scholar
  19. Bolton, J. G., Stanley, G. J., Slee, O. B.: 1949,Nature 164, 101.Google Scholar
  20. Bracewell, R. N. and Riddle, A.: 1967,Astrophys. J. 150, 427.Google Scholar
  21. Burbidge, G.: 1983, in G. O. Abell and G. Chincarini (eds.), ‘Early Evolution of the Universe and Its Present Structure’,IAU Symp. 104, 65.Google Scholar
  22. Burns, J. O. and Owen, F. N.: 1977,Astrophys. J. 217, 34.Google Scholar
  23. Burns, J. O., White, R. A., and Hough, D. H.: 1981,Astron. J. 86, 1.Google Scholar
  24. Butcher, H. and Oemler, A.: 1978,Astrophys. J. 219, 18.Google Scholar
  25. Canizares, C. R.: 1981,Nature 291, 620.Google Scholar
  26. Canizares, C. R., Clark, G. W., Markert, T. H., Berg, C., Smedira, M., Bardas, D., Schnopper, H., and Kalata, K.: 1979,Astrophys. J. 234, L33.Google Scholar
  27. Carter, D.: 1977,Monthly Notices Roy. Astron. Soc. 178, 137.Google Scholar
  28. Chalupa, M.: 1982, private communication.Google Scholar
  29. Chincarini, G., Rood, H. J., Sastry, G. N., and Welch, G. A.: 1971,Astrophys. J. 168, 11.Google Scholar
  30. Dall'Oglio, G., de Bernardis, P., Masi, S., and Melchiorri, F.: 1983, in G. O. Abell and G. Chincarini (eds.), ‘Early Evolution of the Universe and Its Present Structure’,IAU Symp. 104, 135.Google Scholar
  31. De Bernardis, P., Masi, S., Melchiori, B., Melchiori, F., and Moreno, G.: 1984,Astrophys. J. 278, 150.Google Scholar
  32. Dressler, A.: 1978a,Astrophys. J. 223, 765.Google Scholar
  33. Dressler, A.: 1978b,Astrophys. J. 226, 55.Google Scholar
  34. Dressler, A.: 1978c,Astrophys. J. 231, 659.Google Scholar
  35. Dressler, A.: 1980,Astrophys. J. Suppl. 42, 565.Google Scholar
  36. Dressler, A.: 1981,Astrophys. J. 243, 26.Google Scholar
  37. Eddington, A. S.: 1922,The Mathematical Theory of Relativity, (German) 1925, Cournant R., Göttingen.Google Scholar
  38. Edwards, D.: 1971,Observatory 91, 8.Google Scholar
  39. Einstein, A.: 1920,Über die spezielle und allgemeine Relativitätstheorie, F. Vieweg and Sohn, Braunschweig.Google Scholar
  40. Einstein, A.: 1936,Science 84, 506.Google Scholar
  41. Erickson, W. C. and Cronyn, W. M.: 1965,Astrophys. J. 142, 1156.Google Scholar
  42. Fabian, A. C., Ku, W. H.-M., Malin, D. F., Mushotsky, R. F., Nulsen, P. E. J., and Stewart, G. C.: 1981,Monthly Notices Roy. Astron. Soc. 196, 35 p.Google Scholar
  43. Fabricant, D. and Gorenstein, P.: 1983,Astrophys. J. 267, 535.Google Scholar
  44. Fomalont, E. B. and Rogstad, D. H.: 1966,Astrophys. J. 146, 528.Google Scholar
  45. Ford, H. C. and Butcher, H.: 1979,Astrophys. J. Suppl. 41, 147.Google Scholar
  46. Forman, W. and Jones, C.: 1982,Ann. Rev. Astron. Astrophys. 20, 547.Google Scholar
  47. Ftaclas, C. and Struble, M. F.: 1983,Astrophys. J. 274, 521.Google Scholar
  48. Gallagher, J. S. and Ostriker, J. P.: 1972,Astron. J. 77, 288.Google Scholar
  49. Grandi, S. A. and Osterbrock, D. E.: 1978,Astrophys. J. 220, 783.Google Scholar
  50. Greenfield, P. E., Roberts, D. H., and Burke, B. F.: 1980,Science 208, 495.Google Scholar
  51. Gunn, J. E. and Gott, J. R.: 1972,Astrophys. J. 176, 1.Google Scholar
  52. Guthrie, B. N. G.: 1974a,Monthly Notices Roy. Astron. Soc. 168, 15.Google Scholar
  53. Guthrie, B. N. G.: 1974b,Astrophys. Space Sci. 27, 489.Google Scholar
  54. Harwit, M.: 1973,Astrophysical Concepts, J. Wiley and Sons, New York.Google Scholar
  55. Hausman, M. and Ostriker, J.: 1978,Astrophys. J. 224, 320.Google Scholar
  56. Heckman, T. M.: 1981,Astrophys. J. 250, L59.Google Scholar
  57. Hegyi, D. J. and Burrows, A. S.: 1979,Bull. Am. Astron. Soc. 11, 695.Google Scholar
  58. Hickson, P., Richstone, D. O., and Turner, E. L.: 1977,Astrophys. J. 213, 323.Google Scholar
  59. Hollinger, J. P., Mayer, C. H., and Mennella, R. A.: 1964,Astrophys. J. 140, 656.Google Scholar
  60. Hoyle, F.: 1959, in R. N. Bracewell (ed.)Paris Symposium on Radio Astronomy, Standford University Press, Standford, p. 529.Google Scholar
  61. Jenner, D. C.: 1974,Astrophys. J. 191, 55.Google Scholar
  62. Jones, C. and Forman, W.: 1978,Astrophys. J. 224, 1.Google Scholar
  63. Jones, C. and Forman, W.: 1982, in D. S. Heeschen (ed.) ‘Extra-galactic Radio Sources’,IAU Symp. 97, 97.Google Scholar
  64. Joshi, M.: 1962,Ann. Astrophys. 25, 377.Google Scholar
  65. Kowalski, M. P., Ulmer, M. P., Cruddace, R. G., and Wood, K. S.: 1984,Astrophys. J. Suppl. 56, 403.Google Scholar
  66. Kriss, G. A., Cioffi, D. F., and Canizares, C. R.: 1983,Astrophys. J. 272, 439.Google Scholar
  67. Kristian, J.: 1967,Astrophys. J. 147, 864.Google Scholar
  68. Kristian, J. and Sachs, R. K.: 1966,Astrophys. J. 143, 379.Google Scholar
  69. Kristian, J., Sandage, A. and Katem, B.: 1978a,Astrophys. J. 219, 803.Google Scholar
  70. Kristian, J., Sandage, A. and Westphal, J. A.: 1978b,Astrophys. J. 221, 383.Google Scholar
  71. Kronberg, P. P. and Strom, R. G.: 1977,Astrophys. J. 215, 438.Google Scholar
  72. Leir, A. A. and van den Bergh, S.: 1977,Astrophys. J., Suppl. 34, 381.Google Scholar
  73. Lequeux, J.: 1962,Ann. Astrophys. 25, 221.Google Scholar
  74. Liebes, S.: 1964,Phys. Rev. B133, 835.Google Scholar
  75. Lilly, S. J. and Longair, M. S.: 1982,Monthly Notices Roy. Astron. Soc. 199, 1053.Google Scholar
  76. Longair, M. S.: 1965,Monthly Notices Roy. Astron. Soc. 129, 419.Google Scholar
  77. Longair, M. S. and Pooley, G. G.: 1969,Monthly Notices Roy. Astron. Soc. 145, 121.Google Scholar
  78. Malumuth, E. M. and Kirshner, R. P.: 1981,Astrophys. J. 251, 508.Google Scholar
  79. Mathews, W. G.: 1978,Astrophys. J. 219, 413.Google Scholar
  80. Matthews, T. A., Morgan, W. W., and Schmidt, M.: 1964,Astrophys. J. 140, 35.Google Scholar
  81. McGlynn, T. A. and Ostriker, J. P.: 1980,Astrophys. J. 241, 915.Google Scholar
  82. McVittie, G. C.: 1956,General Relativity and Cosmology, Chapman and Hall, London.Google Scholar
  83. McVittie, G. C.: 1965,General Relativity and Cosmology, Chapman and Hall, London.Google Scholar
  84. Merritt, D.: 1983,Bull. Am. Astron. Soc. 15, 945.Google Scholar
  85. Merritt, D.: 1984,Astrophys. J. 276, 26.Google Scholar
  86. Miller, R. H. and Smith, G.: 1980,Astrophys. J. 235, 421.Google Scholar
  87. Minkowski, R.: 1960,Astrophys. J. 132, 908.Google Scholar
  88. Minkowski, R.: 1961,Astrophys. J. 66, 558.Google Scholar
  89. Morgan, W. W., Kayser, S., and White, R. A.: 1975,Astrophys. J. 199, 545.Google Scholar
  90. Morgan, W. W. and Lesh, J. R.: 1965,Astrophys. J. 142, 1364.Google Scholar
  91. Mushotzky, R. F. and Smith, B.: 1980,Highlights Astron. 5, 735.Google Scholar
  92. Oemler, A.: 1973,Astrophys. J. 180, 11.Google Scholar
  93. Oemler, A.: 1974,Astrophys. J. 194, 1.Google Scholar
  94. Oemler, A.: 1976,Astrophys. J. 209, 693.Google Scholar
  95. Oort, J. H.: 1983, in G. O. Abell and G. Chincarini (eds.), ‘Early Evolution of the Universe and Its Present Structure’,IAU Symp. 104, 1.Google Scholar
  96. Ostriker, J. P. and Hausman, M. A.: 1977,Astrophys. J. 217, L125.Google Scholar
  97. Ostriker, J. P. and Tremaine, S. D.: 1975,Astrophys. J. 202, L113.Google Scholar
  98. Owen, F. N.: 1975,Astrophys. J. 195, 593.Google Scholar
  99. Partridge, R. B. and Peebles, P. J. E.: 1967,Astrophys. J. 147, 868.Google Scholar
  100. Peach, J. V.: 1969,Nature 223, 1141.Google Scholar
  101. Peacock, J. A.: 1982,Monthly Notices Roy. Astron. Soc. 199, 987.Google Scholar
  102. Peebles, P. J. E.: 1971,Physical Cosmology, Princeton University Press, Princeton.Google Scholar
  103. Peterson, B. A.: 1981,Astron. J. 75, 695.Google Scholar
  104. Quintana, H. and Lawrie, D. G.: 1982,Astron. J. 87, 1.Google Scholar
  105. Reboul, H. J.: 1981,Astron. Astrophys. Suppl. 45, 129.Google Scholar
  106. Redman, R. O. and Shirley, E. G.: 1938,Monthly Notices Roy. Astron. Soc. 98, 613.Google Scholar
  107. Refsdal, S.: 1964,Monthly Notices Roy. Astron. Soc. 128, 295.Google Scholar
  108. Richstone, D. O.: 1975,Astrophys. J. 200, 535.Google Scholar
  109. Richstone, D. O.: 1976,Astrophys. J. 204, 642.Google Scholar
  110. Richstone, D. O. and Malumuth, E. M.: 1983,Astrophys. J. 268, 30.Google Scholar
  111. Riley, J. M. and Pooley, G. G.: 1978,Monthly Notices Roy. Astron. Soc. 183, 245.Google Scholar
  112. Robertson, H. P.: 1938,Z. Astrophys. 15, 69.Google Scholar
  113. Sadeh, D.: 1967,Science 158, 1176.Google Scholar
  114. Sandage, A.: 1961,Astrophys. J. 133, 355.Google Scholar
  115. Sandage, A.: 1972,Astrophys. J. 173, 485.Google Scholar
  116. Sandage, A.: 1973,Astrophys. J. 183, 711.Google Scholar
  117. Sandage, A. and Hardy, E.: 1973,Astrophys. J. 183, 743.Google Scholar
  118. Sastry, K. S. and Alladin, S. M.: 1977,Astrophys. Space Sci. 46, 285.Google Scholar
  119. Schmidt, M. S.: 1965,Astrophys. J. 141, 1.Google Scholar
  120. Segal, I. E.: 1975,Proc. Nat. Acad. Sci. 72, 2473.Google Scholar
  121. Segal, I. E.: 1983,Phys. Rev. D 28, 2393.Google Scholar
  122. Seielstad, G. A., Morris, D., and Radhakrishnan, V.: 1964,Astrophys. J. 140, 53.Google Scholar
  123. Simkin, S. M.: 1977,Astrophys. J. 217, 45.Google Scholar
  124. Souček, J.: 1983,Astrophys. Space Sci. 94, 319 (Paper I).Google Scholar
  125. Spinrad, H. and Stauffer, J. R.: 1982,Monthly Notices Roy. Astron. Soc. 200, 153.Google Scholar
  126. Spitzer, L. and Baade, W.: 1951,Astrophys. J. 113, 413.Google Scholar
  127. Struble, M. F. and Rood, H. J.: 1982,Astron. J. 87, 7.Google Scholar
  128. Struble, M. F. and Rood, H. J.: 1984,Astron. J. 89, 1487.Google Scholar
  129. Thuan, T. X. and Romanishin, W.: 1981,Astrophys. J. 248, 439.Google Scholar
  130. Toomre, A.: 1973, in J. R. Shakeshaft (ed.), ‘The Formation and the Dynamics of Galaxies’,IAU Symp. 58, 347.Google Scholar
  131. Tovmassian, H. M. and Shirbakian, M. S.: 1974a,Astrofizika U.S.S.R. 10, 29.Google Scholar
  132. Tovmassian, H. M. and Shirbakian, M. S.: 1974b,Nature 250, 474.Google Scholar
  133. Tsien, S. C.: 1982,Monthly Notices Roy. Astron. Soc. 200, 377.Google Scholar
  134. Tully, R. B. and Fisher, J. R.: 1977,Astron. Astrophys. 54, 661.Google Scholar
  135. Tyson, J. A.: 1981,Astrophys. J. 248, L89.Google Scholar
  136. van den Bergh, S.: 1961,Astrophys. J. 134, 970.Google Scholar
  137. van den Bergh, S.: 1984,Quart. J. Roy. Astron. Soc. 25, 135.Google Scholar
  138. van den Bergh, S. and de Roux, J.: 1978,Astrophys. J. 219, 352.Google Scholar
  139. Vorontsov-Velyaminov, B. A. and Arkhipova, V. P.: 1962–1968,Morphological Catalogue of Galaxies, Moscow University, Moscow.Google Scholar
  140. Wagoner, R. V.: 1967,Astrophys. J. 149, 465.Google Scholar
  141. Walsh, D., Carswell, R. F., and Weymann, R. J.: 1979,Nature 279, 381.Google Scholar
  142. White, R. A.: 1978,Astrophys. J. 226, 591.Google Scholar
  143. White, R. A., Sarazin, C. L., Quintana, H., and Jaffe, W. J.: 1981,Astrophys. J. 245, L1.Google Scholar
  144. Wolf, R. A. and Bahcall, J. N.: 1972,Astrophys. J. 176, 559.Google Scholar
  145. Wright, G. S., Joseph, R. D., and Meikle, W. P. S.: 1984,Nature 309, 430.Google Scholar
  146. Yee, H. K. C. and Oke, J. B.: 1978,Astrophys. J. 226, 753.Google Scholar
  147. Young, P., Gunn, J. E., Kristian, J., Oke, J. B., and Westphal, J. A.: 1980,Astrophys. J. 241, 507.Google Scholar
  148. Zwicky, F.: 1973a,Phys. Rev. Ser. II 51, 290.Google Scholar
  149. Zwicky, F.: 1973b,Phys. Rev. Ser. II 51, 679.Google Scholar
  150. Zwicky, F.: 1957,Morphological Astronomy, Springer-Verlag, Berlin, p. 215.Google Scholar
  151. Zwicky, F., Herzog, E., Wild, P., Karpowicz, M., and Kowal, C. T.: 1961–1968,Catalogue of Galaxies and Clusters of Galaxies, California Institute of Technology, Pasadena.Google Scholar

Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • Jaroslav Souček
    • 1
  1. 1.Astronomical SocietyCzechoslovak Academy of SciencesPragueCzechoslovakia

Personalised recommendations