New Model of Density Distribution for Fermionic Dark Matter Halos

  • A. V. Rudakovskyi Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine; Taras Shevchenko National University of Kyiv; Main Astronomical Observatory, Nat. Acad. of Sci. of Ukraine
  • D. O. Savchenko Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine; Main Astronomical Observatory, Nat. Acad. of Sci. of Ukraine

Abstract

We formulate a new model of density distribution for halos made of warm dark matter (WDM) particles. The model is described by a single microphysical parameter – the mass (or, equivalently, the maximal value of the initial phase-space density distribution) of dark matter particles. Given the WDM particle mass and the parameters of a dark matter density profile at the halo periphery, this model predicts the inner density profile. In the case of initial Fermi–Dirac distribution, we successfully reproduce cored dark matter profiles from N-body simulations. We calculate also the core radii of warm dark matter halos of dwarf spheroidal galaxies for particle masses mFD = 100, 200, 300, and 400 eV.

Keywords dark matter: warm, cold, dark matter halo profile, cores, Navarro–Frenk–White profile

References


  1. S.D.M. White, C.S. Frenk, M. Davis. Clustering in a neutrino-dominated universe. Astrophys. J. 274, L1 (1983).
    https://doi.org/10.1086/184139">https://doi.org/10.1086/184139">https://doi.org/10.1086/184139

  2. S. Tremaine, J. E. Gunn. Dynamical role of light neutral leptons in cosmology. Phys. Rev. Lett. 42, 407 (1979).
    https://doi.org/10.1103/PhysRevLett.42.407

  3. L. Bergstr?om. Non-baryonic dark matter: observational evidence and detection methods. Rep. Progr. Phys. 63, 793 (2000).
    https://doi.org/10.1088/0034-4885/63/5/2r3

  4. G. Bertone, D. Hooper, J. Silk. Particle dark matter: Evidence, candidates and constraints. Phys. Rep. 405, 279 (2005).
    https://doi.org/10.1016/j.physrep.2004.08.031

  5. J.L. Feng. Dark matter candidates from particle physics and methods of detection. Ann. Rev. Astron. Astrophys 48, 495 (2010).
    https://doi.org/10.1146/annurev-astro-082708-101659

  6. S. Gardner, G.M. Fuller. Dark matter studies entrain nuclear physics. Progr. Part. Nucl. Phys. 71, 167 (2013).
    https://doi.org/10.1016/j.ppnp.2013.03.001

  7. A. Palazzo, D. Cumberbatch, A. Slosar, J. Silk. Sterile neutrinos as subdominant warm dark matter. Phys. Rev. D 76, 10, 103511 (2007).

  8. A. Boyarsky, O. Ruchayskiy, M. Shaposhnikov. The role of sterile neutrinos in cosmology and astrophysics. Ann. Rev. Nucl. Part. Sci. 59, 191 (2009).
    https://doi.org/10.1146/annurev.nucl.010909.083654

  9. J.R. Primack. Dark matter and structure formation in the universe. arXiv:astro-ph/9707285.

  10. S.D. M. White, M.J. Rees. Core condensation in heavy halos – A two-stage theory for galaxy formation and clustering. Mon. Not. R. Astron. Soc. 183, 341 (1978).
    https://doi.org/10.1093/mnras/183.3.341

  11. G.R. Blumenthal, S.M. Faber, J.R. Primack, M.J. Rees. Formation of galaxies and large-scale structure with cold dark matter. Nature 311, 517 (1984).
    https://doi.org/10.1038/311517a0

  12. G.S. Bisnovatyi-Kogan, I.D. Novikov. Cosmology with a nonzero neutrino rest mass. Soviet Ast. 24, 516 (1980).

  13. J.R. Bond, G. Efstathiou, J. Silk. Massive neutrinos and the large-scale structure of the universe. Phys. Rev. Lett. 45, 1980 (1980).
    https://doi.org/10.1103/PhysRevLett.45.1980

  14. J.F. Navarro, C.S. Frenk, S.D.M. White. The structure of cold dark matter halos. Astrophys. J. 462, 563 (1996).
    https://doi.org/10.1086/177173

  15. J.F. Navarro, C.S. Frenk, S.D.M. White. A universal density profile from hierarchical clustering. Astrophys. J. 490, 493 (1997).
    https://doi.org/10.1086/304888

  16. J.E. Taylor, J.F. Navarro. The phase-space density profiles of cold dark matter halos. Astrophys. J. 563, 483 (2001).
    https://doi.org/10.1086/324031

  17. A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi. A lower bound on the mass of dark matter particles. J. Cosmol. Astropart. Phys. 3, 005 (2009).

  18. R. Ruffini, L. Stella. On semi-degenerate equilibrium configurations of a collisionless self-gravitating Fermi gas. Astron. Astrophys. 119, 35 (1983).

  19. N. Bili’c, R.D. Viollier. Gravitational phase transition of fermionic matter. Phys. Lett. B 408, 75 (1997).
    https://doi.org/10.1016/S0370-2693(97)00825-3

  20. G.W. Angus. A lower limit on the dark particle mass from dSphs. J. Cosmol. Astropart. Phys. 3, 026 (2010).

  21. H. J. de Vega, P. Salucci, N.G. Sanchez. Observational rotation curves and density profiles versus the Thomas–Fermi galaxy structure theory. Mon. Not. R. Astron. Soc. 442, 2717 (2014).
    https://doi.org/10.1093/mnras/stu972

  22. H.J. de Vega, N.G. Sanchez. The dark matter distribution function and halo thermalization from the Eddington equation in galaxies. Int. J. Mod. Phys. A 31, 1650073 (2016).
    https://doi.org/10.1142/S0217751X16500731

  23. M. Merafina, G. Alberti. Self-gravitating Newtonian models of fermions with anisotropy and cutoff energy in their distribution function. Phys. Rev. D 89 (12), 123010 (2014).
    https://doi.org/10.1103/PhysRevD.89.123010

  24. V. Domcke, A. Urbano. Dwarf spheroidal galaxies as degenerate gas of free fermions. J. Cosmol. Astropart. Phys. 1, 002 (2015).

  25. R. Ruffini, C.R. Arg?uelles, J.A. Rueda. On the core-halo distribution of dark matter in galaxies. Mon. Not. R. Astron. Soc. 451, 622 (2015).
    https://doi.org/10.1093/mnras/stv1016

  26. P.-H. Chavanis, M. Lemou, F. M?ehats. Models of dark matter halos based on statistical mechanics: The fermionic King model. Phys. Rev. D 92, 12, 123527 (2015).

  27. C.R. Arg?uelles, A. Krut, J.A. Rueda, R. Ruffini. Novel constraints on fermionic dark matter from galactic observables. arXiv:1606.07040 [astro-ph.GA].

  28. S. Shao, L. Gao, T. Theuns, C.S. Frenk. The phasespace density of fermionic dark matter haloes. Mon. Not. R. Astron. Soc. 430, 2346 (2013).
    https://doi.org/10.1093/mnras/stt053

  29. A.V. Macci`o, S. Paduroiu, D. Anderhalden, A. Schneider, B. Moore. Cores in warm dark matter haloes: a Catch 22 problem. Mon. Not. R. Astron. Soc. 424, 1105 (2012).
    https://doi.org/10.1111/j.1365-2966.2012.21284.x

  30. A.V. Macci`o, S. Paduroiu, D. Anderhalden, A. Schneider, B. Moore. Erratum: Cores in warm dark matter haloes: a Catch 22 problem. Mon. Not. R. Astron. Soc. 428, 3715 (2013).
    https://doi.org/10.1093/mnras/sts251

  31. A. V. Macci`o, O. Ruchayskiy, A. Boyarsky, J.C. Mu?noz-Cuartas. The inner structure of haloes in cold + warm dark matter models. Mon. Not. R. Astron. Soc. 428, 882 (2013).
    https://doi.org/10.1093/mnras/sts078

  32. D. Anderhalden, A. Schneider, A.V. Macci`o, J. Diemand, G. Bertone. Hints on the nature of dark matter from the properties of Milky Way satellites. J. Cosmol. Astropart. Phys. 3, 014 (2013).

  33. J.S. Bullock, M. Boylan-Kolchin. Small-Scale Challenges to the ?CDM Paradigm, Ann. Rev. Astron. Astrophys 55, 343 (2017).
    https://doi.org/10.1146/annurev-astro-091916-055313

  34. J.H. Jeans. On the theory of star-streaming and the structure of the universe. Mon. Not. R. Astron. Soc. 76, 70 (1915).
    https://doi.org/10.1093/mnras/76.2.70

  35. D. Lynden-Bell. Stellar dynamics. Only isolating integrals should be used in Jeans theorem. Mon. Not. R. Astron. Soc. 124, 1 (1962).
    https://doi.org/10.1093/mnras/124.1.1

  36. C. Efthymiopoulos, N. Voglis, C. Kalapotharakos. Special features of galactic dynamics, in Lecture Notes in Physics edited by D. Benest, C. Froeschle, and E. Lega (Springer, 2007).

  37. G. Contopoulos. A classification of the integrals of motion. Astrophys. J. 138, 1297 (1963).
    https://doi.org/10.1086/147724

  38. R.A. Ibata, G. Gilmore, M.J. Irwin. A dwarf satellite galaxy in Sagittarius. Nature 370, 194 (1994).
    https://doi.org/10.1038/370194a0

  39. S.R. Majewski, M.F. Skrutskie, M.D. Weinberg, J.C. Ostheimer. A two micron all sky survey view of the sagittarius dwarf galaxy. I. Morphology of the sagittarius core and tidal arms. Astrophys. J. 599, 1082 (2003).
    https://doi.org/10.1086/379504

  40. J.D. Simon, M. Geha. The kinematics of the ultrafaint Milky Way satellites: Solving the missing satellite problem. Astrophys. J. 670, 313 (2007).
    https://doi.org/10.1086/521816

  41. R. Smith, M. Fellhauer, G.N. Candlish, R.Wojtak, J.P. Farias, M. Bla?na. Ursa Major II – reproducing the observed properties through tidal disruption. Mon. Not. R. Astron. Soc. 433, 2529 (2013).
    https://doi.org/10.1093/mnras/stt925

  42. J.L. Carlin, C.J. Grillmair, R.R. Mu?noz, D.L. Nidever, S.R. Majewski. Kinematics and metallicities in the Bo?otes III stellar overdensity: A disrupted dwarf galaxy? Astrophys. J. 702, L9 (2009).
    https://doi.org/10.1088/0004-637X/702/1/L9

  43. S. Kazantzidis, J. Magorrian, B. Moore. Generating equilibrium dark matter halos: Inadequacies of the local Maxwellian approximation. Astrophys. J. 601, 37 (2004).
    https://doi.org/10.1086/380192

  44. S.H. Hansen, J. Stadel. The velocity anisotropy – density slope relation. J. Cosmol. Astropart. Phys. 5, 014 (2006).

  45. A. Zait, Y. Hoffman, I. Shlosman. Dark matter halos: Velocity anisotropy-density slope relation. Astrophys. J. 682, 835 (2008).
    https://doi.org/10.1086/589431

  46. M. Sparre, S.H. Hansen. The behavior of shape and velocity anisotropy in dark matter haloes. J. Cosmol. Astropart. Phys. 10, 049 (2012).

  47. G.A. Mamon, A. Biviano, G. Bou’e. MAMPOSSt: Modelling anisotropy and mass profiles of observed spherical systems – I. Gaussian 3D velocities. Mon. Not. R. Astron. Soc. 429, 3079 (2013).
    https://doi.org/10.1093/mnras/sts565

  48. L. Beraldo e Silva, G.A. Mamon, M. Duarte, R. Wojtak, S. Peirani, G. Bou’e. Anisotropic q-Gaussian 3D velocity distributions in ?CDM haloes. Mon. Not. R. Astron. Soc. 452, 944 (2015).
    https://doi.org/10.1093/mnras/stv1321

  49. C.A. Vera-Ciro, L.V. Sales, A. Helmi, J.F. Navarro. The shape of dark matter subhaloes in the Aquarius simulations. Mon. Not. R. Astron. Soc. 439, 2863 (2014).
    https://doi.org/10.1093/mnras/stu153

  50. K. El-Badry, A.R. Wetzel, M. Geha, E. Quataert, P.F. Hopkins, D. Kere?s, T.K. Chan, C.-A. Faucher-Gigu`ere. When the jeans do not fit: How stellar feedback drives stellar kinematics and complicates dynamical modeling in low-mass galaxies. Astrophys. J. 835, 193 (2017).
    https://doi.org/10.3847/1538-4357/835/2/193

  51. A. Eilersen, S. H. Hansen, X. Zhang. Analytical derivation of the radial distribution function in spherical dark matter haloes. Mon. Not. R. Astron. Soc. 467, 2061 (2017).

  52. K. Hayashi, M. Chiba. Probing non-spherical dark halos in the galactic dwarf galaxies. Astrophys. J. 755, 145 (2012).
    https://doi.org/10.1088/0004-637X/755/2/145

  53. K. Hayashi, M. Chiba. Structural properties of nonspherical dark halos in Milky Way and Andromeda dwarf spheroidal galaxies. Astrophys. J. 810, 22 (2015).
    https://doi.org/10.1088/0004-637X/810/1/22

  54. C.F.P. Laporte, M.G. Walker, J. Pe?narrubia. Measuring the slopes of mass profiles for dwarf spheroidals in triaxial cold dark matter potentials. Mon. Not. R. Astron. Soc. 433, L54 (2013).
    https://doi.org/10.1093/mnrasl/slt057

  55. M.G. Walker, J. Pe?narrubia. A method for measuring (slopes of) the mass profiles of dwarf spheroidal galaxies. Astrophys. J. 742, 20 (2011).
    https://doi.org/10.1088/0004-637X/742/1/20

  56. A. Genina, A. Ben’?tez-Llambay, C.S. Frenk, S. Cole, A. Fattahi, J.F. Navarro, K.A. Oman, T. Sawala, T. Theuns. The core-cusp problem: A matter of perspective. Mon. Not. R. Astron. Soc. 474, 1398 (2018).
    https://doi.org/10.1093/mnras/stx2855

  57. D.J.R. Campbell, C.S. Frenk, A. Jenkins, V.R. Eke, J.F. Navarro, T. Sawala, M. Schaller, A. Fattahi, K.A. Oman, T. Theuns. Knowing the unknowns: Uncertainties in simple estimators of galactic dynamical masses. Mon. Not. R. Astron. Soc. 469, 2335 (2017).
    https://doi.org/10.1093/mnras/stx975

  58. N.C. Amorisco, N. W. Evans. A troublesome past: Chemo-dynamics of the fornax dwarf spheroidal. Astrophys. J. 756, L2 (2012).
    https://doi.org/10.1088/2041-8205/756/1/L2

  59. N. Ho, M. Geha, R.R. Mu?noz, P. Guhathakurta, J. Kalirai, K.M. Gilbert, E. Tollerud, J. Bullock, R.L. Beaton, S.R. Majewski. Stellar kinematics of the Andromeda II dwarf spheroidal galaxy. Astrophys. J. 758, 124 (2012).
    https://doi.org/10.1088/0004-637X/758/2/124

  60. A. del Pino, E.L. Lokas, S.L. Hidalgo, S. Fouquet. The structure of Andromeda II dwarf spheroidal galaxy. Mon. Not. R. Astron. Soc. 469, 4999 (2017).
    https://doi.org/10.1093/mnras/stx1195

  61. M.G. Walker, M. Mateo, E.W. Olszewski, R. Bernstein, X.Wang, M.Woodroofe. Internal kinematics of the Fornax dwarf spheroidal galaxy. AJ 131, 2114 (2006).

  62. A. Koch, M.I. Wilkinson, J.T. Kleyna, G.F. Gilmore, E.K. Grebel, A.D. Mackey, N.W. Evans, R.F.G. Wyse. Stellar kinematics and metallicities in the Leo I dwarf spheroidal galaxy-wide-field implications for galactic evolution. Astrophys. J. 657, 241 (2007).
    https://doi.org/10.1086/510879

  63. P.M. Frinchaboy, S.R. Majewski, R.R. Mu?noz, D.R. Law, E.L. Lokas, W.E. Kunkel, R.J. Patterson, K.V. Johnston. A 2MASS All-sky view of the Sagittarius Dwarf Galaxy. VII. Kinematics of the main body of the Sagittarius dSph. Astrophys. J. 756, 74 (2012).
    https://doi.org/10.1088/0004-637X/756/1/74

  64. A.W. McConnachie. The Observed Properties of Dwarf Galaxies in and around the Local Group. Astron. J. 144, 4 (2012).
    https://doi.org/10.1088/0004-6256/144/1/4

  65. M.E. Spencer, M. Mateo, M.G. Walker, E.W. Olszewski. A multi-epoch kinematic study of the remote dwarf spheroidal galaxy Leo II. Astrophys. J. 836, 202 (2017).
    https://doi.org/10.3847/1538-4357/836/2/202

  66. A.S. Eddington. The distribution of stars in globular clusters. Mon. Not. R. Astron. Soc. 76, 572 (1916)
    https://doi.org/10.1093/mnras/76.7.572

  67. J. Binney, S. Tremaine. Galactic Dynamics (Princeton Univ. Press, 2008).

  68. L.M.Widrow. Distribution functions for cuspy dark matter density profiles. Astrophys. J. Suppl. 131, 39 (2000).
    https://doi.org/10.1086/317367

  69. P. Bode, J.P. Ostriker, N. Turok. Halo formation in warm dark matter models. Astrophys. J. 556, 93 (2001).
    https://doi.org/10.1086/321541

  70. L. Randall, J. Scholtz, J. Unwin. Cores in dwarf Galaxies from Fermi repulsion. Mon. Not. R. Astron. Soc. 467, 1515 (2017).
    https://doi.org/10.1093/mnras/stx161

  71. A. Burkert. The structure of dark matter halos in dwarf galaxies. Astrophys. J. 447, L25 (1995).
    https://doi.org/10.1086/309560

  72. C. Di Paolo, F. Nesti, F.L. Villante. Phase-space mass bound for fermionic dark matter from dwarf spheroidal galaxies. Mon. Not. R. Astron. Soc. 475, 5385 (2018).
    https://doi.org/10.1093/mnras/sty091

  73. N.C. Amorisco, A. Agnello, N.W. Evans. The core size of the Fornax dwarf spheroidal. Mon. Not. R. Astron. Soc. 429, L89 (2013).
    https://doi.org/10.1093/mnrasl/sls031

  74. J.I. Read, G. Iorio, O. Agertz, F. Fraternali. The stellar mass-halo mass relation of isolated field dwarfs: a critical test of ?CDM at the edge of galaxy formation. Mon. Not. R. Astron. Soc. 467, 2019 (2017).
    https://doi.org/10.1093/mnras/stx147

  75. P.S. Corasaniti, S. Agarwal, D.J.E. Marsh, S. Das. Constraints on dark matter scenarios from measurements of the galaxy luminosity function at high redshifts. Phys. Rev. D 95 (8), 083512 (2017).
    https://doi.org/10.1103/PhysRevD.95.083512

  76. A. Schneider, S. Trujillo-Gomez, E. Papastergis, D.S. Reed, G. Lake. Hints against the cold and collisionless nature of dark matter from the galaxy velocity function. Mon. Not. R. Astron. Soc. 470, 1542 (2017).
    https://doi.org/10.1093/mnras/stx1294

  77. N. Menci, A. Merle, M. Totzauer, A. Schneider, A. Grazian, M. Castellano, N.G. Sanchez. Fundamental physics with the hubble frontier fields: Constraining dark matter models with the abundance of extremely faint and distant galaxies. Astrophys. J. 836, 61 (2017).
    https://doi.org/10.3847/1538-4357/836/1/61

  78. J.F. Cherry, S. Horiuchi. Closing in on resonantly produced sterile neutrino dark matter. Phys. Rev. D 95 (8), 083015 (2017).
    https://doi.org/10.1103/PhysRevD.95.083015

  79. S. Birrer, A. Amara, A. Refregier. Lensing substructure quantification in RXJ1131-1231: A 2 keV lower bound on dark matter thermal relic mass. J. Cosmol. Astropart. Phys. 5, 037 (2017).

  80. V. Ir?si?c, M. Viel, M.G. Haehnelt, J.S. Bolton, S. Cristiani, G.D. Becker, V. D'Odorico, G. Cupani, T.-S. Kim, T.A.M. Berg, S. L’opez, S. Ellison, L. Christensen, K.D. Denney, G. Worseck. New constraints on the free-streaming of warm dark matter from intermediate and small scale Lyman-a forest data. Phys. Rev. D 96 (2), 023522 (2017).

  81. C. Y`eche, N. Palanque-Delabrouille, J. Baur, H. du Mas des Bourboux. Constraints on neutrino masses from Lyman-alpha forest power spectrum with BOSS and XQ-100. J. Cosmol. Astropart. Phys. 6, 047 (2017).

  82. L. Lopez-Honorez, O. Mena, S. Palomares-Ruiz, P. Villanueva-Domingo. Warm dark matter and the ionization history of the Universe. Phys. Rev. D 96 (10), 103539 (2017).
    https://doi.org/10.1103/PhysRevD.96.103539

  83. P. Dayal, T.R. Choudhury, F. Pacucci, V. Bromm. Warm dark matter constraints from high-z direct collapse black holes using the JWST. Mon. Not. R. Astron. Soc. 472, 4414 (2017).
    https://doi.org/10.1093/mnras/stx2282

  84. J. Baur, N. Palanque-Delabrouille, C. Y`eche, A. Boyarsky, O. Ruchayskiy, ? E. Armengaud, J. Lesgourgues. Constraints from Ly-a forests on non-thermal dark matter including resonantly-produced sterile neutrinos. J. Cosmol. Astropart. Phys. 12, 013 (2017).

  85. N. Menci, E. Giallongo, A. Grazian, D. Paris, A. Fontana, L. Pentericci. Observing the very low surface brightness dwarfs in a deep field in the VIRGO cluster: Constraints on dark matter scenarios. Astron. Astrophys. 604, A59 (2017).
    https://doi.org/10.1051/0004-6361/201731237

  86. A. Dekel, J. Silk. The origin of dwarf galaxies, cold dark matter, and biased galaxy formation. Astrophys. J. 303, 39 (1986).
    https://doi.org/10.1086/164050

  87. A. Ferrara, E. Tolstoy. The role of stellar feedback and dark matter in the evolution of dwarf galaxies. Mon. Not. R. Astron. Soc. 313, 291 (2000).
    https://doi.org/10.1046/j.1365-8711.2000.03209.x

  88. J.I. Read, G. Gilmore. Mass loss from dwarf spheroidal galaxies: The origins of shallow dark matter cores and exponential surface brightness profiles. Mon. Not. R. Astron. Soc. 356, 107 (2005).
    https://doi.org/10.1111/j.1365-2966.2004.08424.x

  89. J.I. Read, A.P. Pontzen, M. Viel. On the formation of dwarf galaxies and stellar haloes. Mon. Not. R. Astron. Soc. 371, 885 (2006).
    https://doi.org/10.1111/j.1365-2966.2006.10720.x

  90. S. Mashchenko, J. Wadsley, H.M.P. Couchman. Stellar feedback in dwarf galaxy formation. Science 319, 174 (2008).
    https://doi.org/10.1126/science.1148666

  91. A. Pontzen, F. Governato. How supernova feedback turns dark matter cusps into cores. Mon. Not. R. Astron. Soc. 421, 3464 (2012).
    https://doi.org/10.1111/j.1365-2966.2012.20571.x

  92. F. Governato, A. Zolotov, A. Pontzen, C. Christensen, S.H. Oh, A.M. Brooks, T. Quinn, S. Shen, J. Wadsley. Cuspy no more: how outflows affect the central dark matter and baryon distribution in cold dark matter galaxies. Mon. Not. R. Astron. Soc. 422, 1231 (2012).
    https://doi.org/10.1111/j.1365-2966.2012.20696.x

  93. R. Teyssier, A. Pontzen, Y. Dubois, J.I. Read. Cuspcore transformations in dwarf galaxies: Observational predictions. Mon. Not. R. Astron. Soc. 429, 3068 (2013).
    https://doi.org/10.1093/mnras/sts563

  94. A. Di Cintio, C.B. Brook, A.V. Macci`o, G.S. Stinson, A. Knebe, A. A. Dutton, J. Wadsley. The dependence of dark matter profiles on the stellar-to-halo mass ratio: A prediction for cusps versus cores Mon. Not. R. Astron. Soc. 437, 415 (2014).
    https://doi.org/10.1093/mnras/stt1891

  95. J.I. Read, O. Agertz, M.L.M. Collins. Dark matter cores all the way down. Mon. Not. R. Astron. Soc. 459, 2573 (2016).
    https://doi.org/10.1093/mnras/stw713

Published
2018-09-24
How to Cite
Rudakovskyi, A., & Savchenko, D. (2018). New Model of Density Distribution for Fermionic Dark Matter Halos. Ukrainian Journal Of Physics, 63(9), 769. doi:10.15407/ujpe63.9.769
Section
Fields and elementary particles