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Volumn 76, Issue 2, 2007, Pages

White dwarf stars in D dimensions

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EID: 34447626855     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.76.023004     Document Type: Article
Times cited : (46)

References (57)
  • 3
    • 0001733408 scopus 로고
    • PRLAAZ 0080-4630 10.1098/rspa.1926.0133
    • P. Dirac, Proc. R. Soc. A PRLAAZ 0080-4630 112, 661 (1926). 10.1098/rspa.1926.0133
    • (1926) Proc. R. Soc. a , vol.112 , pp. 661
    • Dirac, P.1
  • 5
    • 34447638289 scopus 로고    scopus 로고
    • In Fowler's work, it is assumed that the system is completely degenerate (T=0). The case of a partially degenerate self-gravitating Fermi gas at arbitrary temperature has been discussed more recently by Hertel and Thirring (1971) and Chavanis (2002) in the context of statistical mechanics. They describe the phase transition, below a critical temperature Tc, from a gaseous configuration to a condensed state (with a degenerate core surrounded by a halo). This provides a simple physical mechanism showing how the system can reach highly degenerate configurations as a result of gravitational collapse; see Chavanis (2006) for a review on phase transitions in self-gravitating systems.
    • In Fowler's work, it is assumed that the system is completely degenerate (T=0). The case of a partially degenerate self-gravitating Fermi gas at arbitrary temperature has been discussed more recently by Hertel and Thirring (1971) and Chavanis (2002) in the context of statistical mechanics. They describe the phase transition, below a critical temperature Tc, from a gaseous configuration to a condensed state (with a degenerate core surrounded by a halo). This provides a simple physical mechanism showing how the system can reach highly degenerate configurations as a result of gravitational collapse; see Chavanis (2006) for a review on phase transitions in self-gravitating systems.
  • 8
    • 0002569095 scopus 로고
    • ASJOAB 0004-637X 10.1086/143324
    • S. Chandrasekhar, Astrophys. J. 74, 81 (1931). ASJOAB 0004-637X 10.1086/143324
    • (1931) Astrophys. J. , vol.74 , pp. 81
    • Chandrasekhar, S.1
  • 9
    • 0003737969 scopus 로고
    • Teubner Verlag, Leipzig
    • R. Emden, Gaskugeln (Teubner Verlag, Leipzig, 1907).
    • (1907) Gaskugeln
    • Emden, R.1
  • 10
    • 34447636011 scopus 로고    scopus 로고
    • Landau (1932) made, independently, an equivalent calculation and argued that for M>Mc quantum mechanics cannot prevent the system from collapsing to a point. However, he did not take this collapse very seriously and noted that, in reality, there exists stars with mass M>Mc that do not show this "ridiculous tendency," so that they must possess regions in which the laws of quantum mechanics are violated.
    • Landau (1932) made, independently, an equivalent calculation and argued that for M>Mc quantum mechanics cannot prevent the system from collapsing to a point. However, he did not take this collapse very seriously and noted that, in reality, there exists stars with mass M>Mc that do not show this "ridiculous tendency," so that they must possess regions in which the laws of quantum mechanics are violated.
  • 12
  • 14
    • 36149005547 scopus 로고
    • PHRVAO 0031-899X 10.1103/PhysRev.55.374
    • J.R. Oppenheimer and G.M. Volkoff, Phys. Rev. 55, 374 (1939). PHRVAO 0031-899X 10.1103/PhysRev.55.374
    • (1939) Phys. Rev. , vol.55 , pp. 374
    • Oppenheimer, J.R.1    Volkoff, G.M.2
  • 15
    • 0036926423 scopus 로고    scopus 로고
    • ASNAAN 0004-6337 10.1002/1521-3994(200212)323:6<538::AID- ASNA538>3.0.CO;2-F
    • A.F. Zakharov, Astron. Nachr. 323, 538 (2002). ASNAAN 0004-6337 10.1002/1521-3994(200212)323:6<538::AID-ASNA538>3.0.CO;2-F
    • (2002) Astron. Nachr. , vol.323 , pp. 538
    • Zakharov, A.F.1
  • 16
    • 0011275570 scopus 로고
    • ZEPYAA 0044-3328 10.1007/BF01340146
    • W. Anderson, Z. Phys. ZEPYAA 0044-3328 56, 851 (1929). 10.1007/BF01340146
    • (1929) Z. Phys. , vol.56 , pp. 851
    • Anderson, W.1
  • 17
    • 0001120322 scopus 로고
    • PHMAA4 0031-8086
    • E.C. Stoner, Philos. Mag. PHMAA4 0031-8086 9, 944 (1930).
    • (1930) Philos. Mag. , vol.9 , pp. 944
    • Stoner, E.C.1
  • 18
    • 34447632776 scopus 로고    scopus 로고
    • This historical point has been noted, independently, by Blackman.
    • This historical point has been noted, independently, by Blackman.
  • 19
    • 0000834388 scopus 로고
    • ASJOAB 0004-637X 10.1086/151568
    • M. Nauenberg, Astrophys. J. 175, 417 (1972). ASJOAB 0004-637X 10.1086/151568
    • (1972) Astrophys. J. , vol.175 , pp. 417
    • Nauenberg, M.1
  • 20
    • 35949024439 scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.56.137
    • S. Chandrasekhar, Rev. Mod. Phys. 56, 137 (1984). RMPHAT 0034-6861 10.1103/RevModPhys.56.137
    • (1984) Rev. Mod. Phys. , vol.56 , pp. 137
    • Chandrasekhar, S.1
  • 21
    • 3342973415 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.69.016116
    • P.H. Chavanis and C. Sire, Phys. Rev. E 69, 016116 (2004). PLEEE8 1063-651X 10.1103/PhysRevE.69.016116
    • (2004) Phys. Rev. e , vol.69 , pp. 016116
    • Chavanis, P.H.1    Sire, C.2
  • 22
    • 42749104980 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.69.066126
    • P.H. Chavanis, Phys. Rev. E 69, 066126 (2004). PLEEE8 1063-651X 10.1103/PhysRevE.69.066126
    • (2004) Phys. Rev. e , vol.69 , pp. 066126
    • Chavanis, P.H.1
  • 23
    • 33646524082 scopus 로고    scopus 로고
    • AAEJAF 0004-6361 10.1051/0004-6361:20054008
    • P.H. Chavanis, Astron. Astrophys. 451, 109 (2006). AAEJAF 0004-6361 10.1051/0004-6361:20054008
    • (2006) Astron. Astrophys. , vol.451 , pp. 109
    • Chavanis, P.H.1
  • 24
    • 0012705443 scopus 로고
    • edited by H.P. Dürr (Vieweg, Braunschweig
    • P. Hertel and W. Thirring, in Quanten und Felder, edited by, H.P. Dürr, (Vieweg, Braunschweig, 1971).
    • (1971) Quanten und Felder
    • Hertel, P.1    Thirring, W.2
  • 25
    • 37649027643 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.65.056123
    • P.H. Chavanis, Phys. Rev. E 65, 056123 (2002). PLEEE8 1063-651X 10.1103/PhysRevE.65.056123
    • (2002) Phys. Rev. e , vol.65 , pp. 056123
    • Chavanis, P.H.1
  • 28
    • 34447646252 scopus 로고
    • AJPIAS 0002-9505 10.1119/1.17241
    • J. Bechhoefer and G. Chabrier, Am. J. Phys. 61, 460 (1993). AJPIAS 0002-9505 10.1119/1.17241
    • (1993) Am. J. Phys. , vol.61 , pp. 460
    • Bechhoefer, J.1    Chabrier, G.2
  • 30
    • 0012332991 scopus 로고
    • PHMAA4 0031-8086
    • E.C. Stoner, Philos. Mag. PHMAA4 0031-8086 7, 63 (1929).
    • (1929) Philos. Mag. , vol.7 , pp. 63
    • Stoner, E.C.1
  • 31
    • 34447643184 scopus 로고    scopus 로고
    • Note that Stoner uses the exact expression 3 of the kinetic energy in his treatment. This leads to more complicated expressions with, however, qualitatively similar conclusions. Since the models are based on the (unrealistic) approximation that the stellar density is homogeneous, the results cannot be expected to be more than qualitatively correct. Therefore, the approximation 61 made by Nauenberg for the kinetic energy is sufficient for the purposes of this simplified approach.
    • Note that Stoner uses the exact expression 3 of the kinetic energy in his treatment. This leads to more complicated expressions with, however, qualitatively similar conclusions. Since the models are based on the (unrealistic) approximation that the stellar density is homogeneous, the results cannot be expected to be more than qualitatively correct. Therefore, the approximation 61 made by Nauenberg for the kinetic energy is sufficient for the purposes of this simplified approach.
  • 33
    • 0008601618 scopus 로고
    • PYLAAG 0375-9601 10.1016/0375-9601(71)90148-4
    • L. Gurevich and V. Mostepanenko, Phys. Lett. A 35, 201 (1971). PYLAAG 0375-9601 10.1016/0375-9601(71)90148-4
    • (1971) Phys. Lett. a , vol.35 , pp. 201
    • Gurevich, L.1    Mostepanenko, V.2
  • 34
    • 0000299816 scopus 로고
    • PTRMAD 1364-503X 10.1098/rsta.1983.0095
    • J.D. Barrow, Phil. Trans. R. Soc. A PTRMAD 1364-503X 310, 337 (1983). 10.1098/rsta.1983.0095
    • (1983) Phil. Trans. R. Soc. a , vol.310 , pp. 337
    • Barrow, J.D.1
  • 37
    • 0000034685 scopus 로고
    • PRPLCM 0370-1573 10.1016/0370-1573(90)90051-3
    • T. Padmanabhan, Phys. Rep. 188, 285 (1990). PRPLCM 0370-1573 10.1016/0370-1573(90)90051-3
    • (1990) Phys. Rep. , vol.188 , pp. 285
    • Padmanabhan, T.1
  • 38
    • 0036190825 scopus 로고    scopus 로고
    • AAEJAF 0004-6361 10.1051/0004-6361:20011438
    • P.H. Chavanis, Astron. Astrophys. 381, 340 (2002). AAEJAF 0004-6361 10.1051/0004-6361:20011438
    • (2002) Astron. Astrophys. , vol.381 , pp. 340
    • Chavanis, P.H.1
  • 39
    • 34447646683 scopus 로고    scopus 로고
    • There exists a formal analogy between the Chandrasekhar limiting mass MChandra=5.76M/μ2 for relativistic white dwarf stars in D=3 (corresponding to a polytrope n=n3=3), the critical mass Mc=8π of bacterial populations described by the Keller-Segel model in D=2 (corresponding to n=n3=+), and the critical mass Mc=4kBT/Gm or critical temperature kBTc=GMm/4 of self-gravitating isothermal systems in D=2 (corresponding to n=n3=+). At these critical values M=Mc or T=Tc, the system forms a Dirac peak. This analogy, sketched in Sec. 8 of astro-ph/0604012v1, is addressed specifically in.
    • There exists a formal analogy between the Chandrasekhar limiting mass MChandra=5.76M/μ2 for relativistic white dwarf stars in D=3 (corresponding to a polytrope n=n3=3), the critical mass Mc=8π of bacterial populations described by the Keller-Segel model in D=2 (corresponding to n=n3=+), and the critical mass Mc=4kBT/Gm or critical temperature kBTc=GMm/4 of self-gravitating isothermal systems in D=2 (corresponding to n=n3=+). At these critical values M=Mc or T=Tc, the system forms a Dirac peak. This analogy, sketched in Sec. 8 of astro-ph/0604012v1, is addressed specifically in.
  • 40
    • 0001128919 scopus 로고
    • ASJOAB 0004-637X 10.1086/147938
    • S. Chandrasekhar, Astrophys. J. 140, 417 (1964). ASJOAB 0004-637X 10.1086/147938
    • (1964) Astrophys. J. , vol.140 , pp. 417
    • Chandrasekhar, S.1
  • 41
    • 0003410218 scopus 로고
    • Princeton Series in Astrophysics (Princeton University, Princeton, NJ
    • J. Binney and S. Tremaine, Galactic Dynamics, Princeton Series in Astrophysics (Princeton University, Princeton, NJ, 1987).
    • (1987) Galactic Dynamics
    • Binney, J.1    Tremaine, S.2
  • 42
    • 29144437420 scopus 로고    scopus 로고
    • PHYADX 0378-4371 10.1016/j.physa.2005.03.046
    • P.H. Chavanis and C. Sire, Physica A (Amsterdam) 356, 419 (2005). PHYADX 0378-4371 10.1016/j.physa.2005.03.046
    • (2005) Physica a (Amsterdam) , vol.356 , pp. 419
    • Chavanis, P.H.1    Sire, C.2
  • 43
    • 0036187942 scopus 로고    scopus 로고
    • AAEJAF 0004-6361 10.1051/0004-6361:20011424
    • P.H. Chavanis, Astron. Astrophys. 381, 709 (2002). AAEJAF 0004-6361 10.1051/0004-6361:20011424
    • (2002) Astron. Astrophys. , vol.381 , pp. 709
    • Chavanis, P.H.1
  • 44
    • 0036569344 scopus 로고    scopus 로고
    • AAEJAF 0004-6361 10.1051/0004-6361:20020306
    • P.H. Chavanis, Astron. Astrophys. 386, 732 (2002). AAEJAF 0004-6361 10.1051/0004-6361:20020306
    • (2002) Astron. Astrophys. , vol.386 , pp. 732
    • Chavanis, P.H.1
  • 45
    • 0037382152 scopus 로고    scopus 로고
    • AAEJAF 0004-6361 10.1051/0004-6361:20021779
    • P.H. Chavanis, Astron. Astrophys. 401, 15 (2003). AAEJAF 0004-6361 10.1051/0004-6361:20021779
    • (2003) Astron. Astrophys. , vol.401 , pp. 15
    • Chavanis, P.H.1
  • 46
    • 33744783693 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.73.066104
    • P.H. Chavanis and C. Sire, Phys. Rev. E 73, 066104 (2006). PLEEE8 1063-651X 10.1103/PhysRevE.73.066104
    • (2006) Phys. Rev. e , vol.73 , pp. 066104
    • Chavanis, P.H.1    Sire, C.2
  • 48
    • 25044479199 scopus 로고
    • ASJOAB 0004-637X 10.1086/144317
    • P. Ledoux and C.L. Pekeris, Astrophys. J. 94, 124 (1941). ASJOAB 0004-637X 10.1086/144317
    • (1941) Astrophys. J. , vol.94 , pp. 124
    • Ledoux, P.1    Pekeris, C.L.2
  • 49
    • 33744783693 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.73.066103
    • P.H. Chavanis and C. Sire, Phys. Rev. E 73, 066103 (2006). PLEEE8 1063-651X 10.1103/PhysRevE.73.066103
    • (2006) Phys. Rev. e , vol.73 , pp. 066103
    • Chavanis, P.H.1    Sire, C.2
  • 50
    • 34447644712 scopus 로고    scopus 로고
    • We could simply account for dissipative effects by introducing a friction force -ξu in the Euler Eq. 2. In that case Ẇ=-ξ ρu2dr≤0, so that the system evolves so as to minimize the functional W[ρ,u] at fixed mass.
    • We could simply account for dissipative effects by introducing a friction force -ξu in the Euler Eq. 2. In that case Ẇ=-ξ ρu2dr≤0, so that the system evolves so as to minimize the functional W[ρ,u] at fixed mass.
  • 51
    • 33745667790 scopus 로고    scopus 로고
    • CRPOBN 1631-0705 10.1016/j.crhy.2006.01.005
    • P.H. Chavanis, C.R. Physique 7, 331 (2006). CRPOBN 1631-0705 10.1016/j.crhy.2006.01.005
    • (2006) C.R. Physique , vol.7 , pp. 331
    • Chavanis, P.H.1
  • 52
    • 0001708396 scopus 로고
    • ASJOAB 0004-637X 10.1086/148792
    • D.W. Meltzer and K.S. Thorne, Astrophys. J. 145, 514 (1966). ASJOAB 0004-637X 10.1086/148792
    • (1966) Astrophys. J. , vol.145 , pp. 514
    • Meltzer, D.W.1    Thorne, K.S.2
  • 53
    • 33749256260 scopus 로고    scopus 로고
    • IJPBEV 0217-9792 10.1142/S0217979206035400
    • P.H. Chavanis, Int. J. Mod. Phys. B 20, 3113 (2006). IJPBEV 0217-9792 10.1142/S0217979206035400
    • (2006) Int. J. Mod. Phys. B , vol.20 , pp. 3113
    • Chavanis, P.H.1
  • 55
    • 33644867041 scopus 로고    scopus 로고
    • NATUAS 0028-0836 10.1038/440148d
    • E. Blackman, Nature (London) NATUAS 0028-0836 440, 148 (2006). 10.1038/440148d
    • (2006) Nature (London) , vol.440 , pp. 148
    • Blackman, E.1
  • 56


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