Abstract
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also self-organizing. The apparent disorder is not random noise, but can be described by a fractal, with a deterministic fractal dimension. We present a new theory of the self-gravity thermodynamics, that could explain the existence of these fractal structures, and predict their fractal dimension. The media obeying scaling laws can be considered critical, as in second order phase transitions for instance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abell G.O.: 1958, ApJS 3, 211
Balian R., Schaeffer R.: 1988, ApJ 335, L43
Balian R., Schaeffer R.: 1989, A&A 226, 373
Bazell D., Desert F.X.: 1988, ApJ 333, 353
Binney J.J., Dowrick N.J., Fisher A.J., Newman M.E.J.: 1992 ‘The Theory of Critical Phenomena’, Oxford Science Publication.
Bond J.R., Cole S., Efstathiou G., Kaiser N.: 1991, ApJ 379, 440
Bouchet F.R., Schaeffer R., Davis M.: 1991, ApJ 383, 19
Brand P., Wouterloot J.G.: 1995, A&A ???
Casoli F., Combes F., Gerin M.: 1984, A&A 133, 99
Castagnoli C., Provenzale A.: 1991, A&A 246, 634
Cole S., 1989, PhD Thesis, Univ. of Cambridge
Coleman P.H., Pietronero L., Sanders R.H.: 1988, A&A 200, L32
Colcman P.H., Pietronero L.: 1992, Phys. Rep. 231, 311
Colombi S., Bouchet F.R., Hernquist L.: 1996, ApJ 465, 14
Combes F., Pfenniger D.: 1997, A&A 327 453
Dame T.M., Elmegreen B.G., Cohen R.S., Thaddeus P.: 1986, ApJ 305, 982
Davis M.A., Meiksin M.A., Strauss L.N., da Costa and Yahil A.: 1988, ApJ 333, L9
Davis M.A.: 1997 in ‘Critical Dialogs in Cosmology’, ed. N. Turok, astro-ph/9610149
Davis M.A., Peebles P.J.E.: 1977, ApJS 34, 425
Davis M.A., Peebles P.J.E.: 1983, ApJ 267, 465
Davis R.J., Diamond P.J., Goss W.M.: 1996, MNRAS 283, 1105
de Vaucouleurs G.: 1960, ApJ 131, 585
de Vaucouleurs G.: 1970, Science 167, 1203
de Vega H., Sánchez N., Combes F.: 1996a, Nature 383, 53
de Vega H., Sánchez N., Combes F.: 1996b, Phys. Rev. D54, 6008
de Vega H., Sánchez N., Combes F.: 1998, ApJ in press
Diamond P.J., Goss W.M., Romney J.D. et al: 1989, ApJ 347, 302
Di Nella H., Montuori M., Paturel G., Pietronero L., Sylos Labini F.: 1996, A&A 308, L33
Domb C., Green M.S.: 1976, ‘Phase transitions and Critical Phenomena’, vol. 6, Academic Press
Dubrulle B., Lachièze-Rey M.: 1994, A&A 289, 667
Falconer K.J.: 1990, Fractal geometry, Wiley, Chichester
Falgarone, E., Phillips, T.G., Walker, C.K.: 1991, ApJ 378, 186
Falgarone, E., Lis D.C., Phillips, T.G. et al: 1994, ApJ 436, 728
Fleck R.C.: 1981, ApJ 246, L151
Fiedler R.L., Dennison B., Johnston K., Hewish A.: 1987, Nature 326, 675
Fiedler R.L., Pauls T., Johnston K., Dennison B.: 1994, ApJ 430, 595
Gell-Mann M., Low F.E.: 1954, Phys. Rev. 95, 1300
Hamilton A.J.S.: 1993, ApJ 417, 19
Hasenfratz A., Hasenfratz P., 1986, Nucl. Phys. B270, 687
Heithausen A.: 1996, A&A 314, 251
Heithausen A., Bensch F., Stutzki J., Fakgarone E., Panis J.F.: 1998, A&A 331, L65
Horwitz G., Katz J., 1978a, ApJ 222, 941
Horwitz G., Katz J., 1978b, ApJ 223, 311
Houlahan P., Scalo J.: 1992, ApJ 393, 172
Hoyle F.: 1953, ApJ 118 513
Hubbard J., 1959, Phys. Rev. Lett, 3, 77
Inutsuka S-I., Miyama S.M.: 1997, ApJ 480 681
Itoh M., Inagaki S., Saslaw W.C.: 1993, ApJ 403, 459
Kadanoff L.P.: 1966 Physics 2, 263
Kolmogorov A.: 1941, in ”Compt. Rend. Acad. Sci. URSS” 30, 301
Lacey C.G., Cole S.: 1993, MNRAS 262, 627
Lacey C.G., Cole S.: 1994, MNRAS 271, 676
Lachièze-Rey M.: 1993, ApJ 407, 1 & ApJ 408, 403
Larson R.B., 1981, MNRAS 194, 809
Larson R.B., 1985, MNRAS 214, 379
Lewis G.F., Miralda-Escude J., Richardson D.C., Wambsganss J.: 1993, MNRAS 261, 647
Lesne A.: 1996, in ”Méthodes de renormalisation”, Eyrolles Sciences
Lin H. et al: 1996, ApJ 471, 617
Magnani L., Blitz L., Mundy L. 1985, ApJ 295, 402
Mandelbrot B.B.: 1975, ‘Les objets fractals’, Paris, Flammarion
Mandelbrot B.B.: 1982, ‘The fractal geometry of nature’, New York: Freeman
Martinez V.J., Paredes S., Saar E.: 1993, MNRAS 260, 365
McLaughlin D.E. & Pudritz R.E.: 1996, ApJ 469, 194
Miesch M., & Scalo J.M.: 1995, ApJ 450, L27
Morris T.R., 1994a: Phys. Lett. B329, 241
Morris T.R., 1994b: Phys. Lett. B334, 355
Myers P.C.: 1983, ApJ 270, 105
Ostriker J.P.: 1993, ARAA 31, 689
Padmanabhan 1990, Phys. Rep. 188, 285
Parisi G.: 1988, ‘Statistical field theory’, Addison Wesley, Redwood City
Peebles P.J.E.: 1980, ‘The Large-scale structure of the Universe’, Princeton Univ. Press
Peebles P.J.E.: 1993, ‘Principles of physical cosmology’ Princeton Univ. Press
Pfenniger D., Combes F., Martinet L.: 1994, A&A 285 79
Pfenniger D., Combes F.: 1994, A&A 285, 94
Pietronero L., Montuori M., Sylos Labini F.: 1997, in ‘Critical Dialogs in Cosmology’, ed. N. Turok, astro-ph/9611197
Pietronero L.: 1987, Physica A, 144, 257
Postman M., Geller M.J., Huchra J.P.: 1986, AJ 91, 1267
Postman M., Huchra J.P., Geller M.J.: 1992, ApJ 384, 404
Press W.H., Schecter P.: 1974, ApJ 187 425
Rees M.J.: 1976, MNRAS 176, 483
Saslaw W.C., Fang F.: 1996, ApJ 460, 16
Saslaw W.C., Hamilton A.J.S.: 1984, ApJ 276, 13
Scalo J.M.: 1985, in Protostars and Planets II, ed. D.C. Black & M.S. Matthews, Univ. of Arizona Press, Tucson, p. 201
Scalo J.M., 1987 in ‘Interstellar Processes’, D.J. Hollenbach and H.A. Thronson Eds., D. Reidel Pub. Co, p. 349
Scalo J.M., Lazarian A.: 1996, ApJ 469, 189
Schechter P.L.: 1976, ApJ 203, 297
Scott E.L., Shane S.D., Swanson M.D.: 1954, ApJ 119, 91
Shandarin S.F., Zel'dovich Ya. B.: 1989, Rev. Mod. Phys. 61, 185
Shapiro P.R., Kang H.: 1987, ApJ 318 32
Shapley H.: 1934, MNRAS 94, 791
Sheth R.K., Saslaw W.C.: 1996, Apj 470, 78
Smoot G., et al: 1992, ApJ 396, L1
Solomon P.M., Rivolo A.R., Barrett J.W., Yahil A.: 1987, ApJ 319, 730
Soneira R.M., Peebles P.J.E.: 1978, AJ 83, 845
Sreenivasan K.R., & Méneveau C.: 1986, J. Fluid Mech. 173, 357
Stratonovich R.L., 1958, Doklady, 2, 146
Sylos Labini F., Amendola L.: 1996, ApJ 438, L1
Sylos Labini F., Gabrielli A., Montuori M., Pietronero L.: 1996, Physica A 226, 195
Sylos Labini F., Pietronero L.: 1996, ApJ 469, 26
Sylos Labini F.: 1994, ApJ 433, 464
Toomre A.: 1964, ApJ 139, 1217
Totsuji H., Kihara T.: 1969; PASJ 21, 221
Vazquez-Semadeni E.: 1994, ApJ 423, 681
Vazquez-Semadeni E., Ballesteros-Paredes J., Rodriguez L.F.: 1997, ApJ 474, 292
Vazquez-Semadeni E., Canto J., Lizano S.: 1998, ApJ 492, 596
Uehara H., Susa H., Nishi R., Yamada M., Nakamura T.: 1996, ApJ 473 L95
Vergassola M., Dubrulle B., Frisch U., Noullez A.: 1994, A&A 289, 325
Vogelaar M.G.R., Wakker B.P.: 1994, A&A 291, 557
White S.D.M., Rees M.J.: 1978, MNRAS 183 341
White S.D.M.: 1979, MNRAS 186, 145
White S.D.M., Kauffmann G.: 1994, in ”The formation and evolution of galaxies”, V Canary Islands Winter School, ed. C. Munoz-Tunon & F. Sanchez, p. 455
Wilson K.G., Kogut, J.: 1974, Phys. Rep. 12, 75
Wilson K.G.: 1975, Rev. Mod. Phys. 47, 773
Wilson K.G.: 1983, Rev. Mod. Phys. 55, 583
Zamalodchikov A.B. 1989, Int. J. Mod. Phys. A4, 4235
Zel'dovich Ya. B.: 1970, Astrofizika 6, 319
Zinn-Justin J.: 1989, ‘QFT and Critical Phenomena’, Clarendon Press, Oxford
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Combes, F. Fractal Structures Driven by Self-gravity: Molecular Clouds and the Universe. Celestial Mechanics and Dynamical Astronomy 72, 91–127 (1998). https://doi.org/10.1023/A:1008370831608
Issue Date:
DOI: https://doi.org/10.1023/A:1008370831608