Abstract.
We determine the mass-radius relation of self-gravitating Bose-Einstein condensates with an attractive -1/r external potential created by a central mass. Following our previous work (P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)), we use an analytical approach based on a Gaussian ansatz. We consider the case of noninteracting bosons as well as the case of self-interacting bosons with a repulsive or an attractive self-interaction. These results may find application in the context of dark matter halos made of self-gravitating Bose-Einstein condensates. In that case, the central mass may mimic a supermassive black hole. We apply our results to ultralight axions with an attractive self-interaction. We determine how the central black hole affects the mass-radius relation and the maximum mass of axionic halos found in our previous papers. Our approximate analytical results based on the Gaussian ansatz are compared with exact analytical results obtained in particular limits.
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References
M.R. Baldeschi, G.B. Gelmini, R. Ruffini, Phys. Lett. B 122, 221 (1983)
M.Yu. Khlopov, B.A. Malomed, Ya.B. Zeldovich, Mon. Not. R. Astron. Soc. 215, 575 (1985)
M. Membrado, A.F. Pacheco, J. Sanudo, Phys. Rev. A 39, 4207 (1989)
S.J. Sin, Phys. Rev. D 50, 3650 (1994)
S.U. Ji, S.J. Sin, Phys. Rev. D 50, 3655 (1994)
J.W. Lee, I. Koh, Phys. Rev. D 53, 2236 (1996)
F.E. Schunck, astro-ph/9802258
T. Matos, F.S. Guzmán, F. Astron. Nachr. 320, 97 (1999)
V. Sahni, L. Wang, Phys. Rev. D 62, 103517 (2000)
F.S. Guzmán, T. Matos, Class. Quantum Grav. 17, L9 (2000)
W. Hu, R. Barkana, A. Gruzinov, Phys. Rev. Lett. 85, 1158 (2000)
P.J.E. Peebles, Astrophys. J. 534, L127 (2000)
J. Goodman, New Astron. 5, 103 (2000)
T. Matos, L.A. Ureña-López, Phys. Rev. D 63, 063506 (2001)
A. Arbey, J. Lesgourgues, P. Salati, Phys. Rev. D 64, 123528 (2001)
M.P. Silverman, R.L. Mallett, Class. Quantum Grav. 18, L103 (2001)
M. Alcubierre, F.S. Guzmán, T. Matos, D. Núñez, L.A. Ureña-López, P. Wiederhold, Class. Quantum. Grav. 19, 5017 (2002)
M.P. Silverman, R.L. Mallett, Gen. Relativ. Gravit. 34, 633 (2002)
J. Lesgourgues, A. Arbey, P. Salati, New Astron. Rev. 46, 791 (2002)
A. Arbey, J. Lesgourgues, P. Salati, Phys. Rev. D 68, 023511 (2003)
T. Fukuyama, M. Morikawa, Prog. Theor. Phys. 115, 1047 (2006)
C.G. Böhmer, T. Harko, J. Cosmol. Astropart. Phys. 06, 025 (2007)
T. Fukuyama, M. Morikawa, T. Tatekawa, J. Cosmol. Astropart. Phys. 06, 033 (2008)
A. Bernal, T. Matos, D. Núñez, Rev. Mex. Astron. Astrofis. 44, 149 (2008)
T. Fukuyama, M. Morikawa, Phys. Rev. D 80, 063520 (2009)
P. Sikivie, Q. Yang, Phys. Rev. Lett. 103, 111301 (2009)
T. Matos, A. Vázquez-González, J. Magaña, Mon. Not. R. Astron. Soc. 393, 1359 (2009)
J.W. Lee, Phys. Lett. B 681, 118 (2009)
T.P. Woo, T. Chiueh, Astrophys. J. 697, 850 (2009)
J.W. Lee, S. Lim, J. Cosmol. Astropart. Phys. 01, 007 (2010)
P.H. Chavanis, Phys. Rev. D 84, 043531 (2011)
P.H. Chavanis, L. Delfini, Phys. Rev. D 84, 043532 (2011)
P.H. Chavanis, Phys. Rev. D 84, 063518 (2011)
F. Briscese, Phys. Lett. B 696, 315 (2011)
T. Harko, Mon. Not. R. Astron. Soc. 413, 3095 (2011)
T. Harko, J. Cosmol, Astropart. Phys. 05, 022 (2011)
A. Suárez, T. Matos, Mon. Not. R. Astron. Soc. 416, 87 (2011)
P.H. Chavanis, Astron. Astrophys. 537, A127 (2012)
H. Velten, E. Wamba, Phys. Lett. B 709, 1 (2012)
M.O.C. Pires, J.C.C. de Souza, J. Cosmol. Astropart. Phys. 11, 024 (2012)
C.-G. Park, J.-C. Hwang, H. Noh, Phys. Rev. D 86, 083535 (2012)
V.H. Robles, T. Matos, Mon. Not. R. Astron. Soc. 422, 282 (2012)
T. Rindler-Daller, P.R. Shapiro, Mon. Not. R. Astron. Soc. 422, 135 (2012)
P.H. Chavanis, T. Harko, Phys. Rev. D 86, 064011 (2012)
V. Lora, J. Magaña, A. Bernal, F.J. Sánchez-Salcedo, E.K. Grebel, J. Cosmol. Astropart. Phys. 02, 011 (2012)
J. Magaña, T. Matos, A. Suárez, F.J. Sánchez-Salcedo, JCAP 10, 003 (2012)
G. Manfredi, P.A. Hervieux, F. Haas, Class. Quantum Grav. 30, 075006 (2013)
A.X. González-Morales, A. Diez-Tejedor, L.A. Ureña-López, O. Valenzuela, Phys. Rev. D 87, 021301(R) (2013)
F.S. Guzmán, F.D. Lora-Clavijo, J.J. González-Aviles, F.J. Rivera-Paleo, J. Cosmol. Astropart. Phys. 09, 034 (2013)
H.Y. Schive, T. Chiueh, T. Broadhurst, Nat. Phys. 10, 496 (2014)
H.Y. Schive et al., Phys. Rev. Lett. 113, 261302 (2014)
B. Li, T. Rindler-Daller, P.R. Shapiro, Phys. Rev. D 89, 083536 (2014)
D. Bettoni, M. Colombo, S. Liberati, JCAP 02, 004 (2014)
V. Lora, J. Magaña, JCAP 09, 011 (2014)
P.H. Chavanis, Eur. Phys. J. Plus 130, 181 (2015)
E.J.M. Madarassy, V.T. Toth, Phys. Rev. D 91, 044041 (2015)
A. Suárez, P.H. Chavanis, Phys. Rev. D 92, 023510 (2015)
A. Suárez, P.H. Chavanis, J. Phys.: Conf. Ser. 654, 012088 (2015)
P.H. Chavanis, Phys. Rev. D 92, 103004 (2015)
A.H. Guth, M.P. Hertzberg, C. Prescod-Weinstein, Phys. Rev. D 92, 103513 (2015)
J.C.C. de Souza, M. Ujevic, Gen. Relativ. Gravit. 47, 100 (2015)
R.C. de Freitas, H. Velten, Eur. Phys. J. C 75, 597 (2015)
J. Alexandre, Phys. Rev. D 92, 123524 (2015)
K. Schroven, M. List, C. Lämmerzahl, Phys. Rev. D 92, 124008 (2015)
D. Marsh, A.R. Pop, Mon. Not. R. Astron. 451, 2479 (2015)
J. Eby, C. Kouvaris, N.G. Nielsen, L.C.R. Wijewardhana, JHEP 02, 028 (2016)
J.A.R. Cembranos, A.L. Maroto, S.J. Núñez Jareño, JHEP 03, 013 (2016)
E. Braaten, A. Mohapatra, H. Zhang, Phy. Rev. Lett. 117, 121801 (2016)
S. Davidson, T. Schwetz, Phys. Rev. D 93, 123509 (2016)
B. Schwabe, J. Niemeyer, J. Engels, Phys. Rev. D 94, 043513 (2016)
J. Fan, Phys. Dark Univ. 14, 84 (2016)
E. Calabrese, D.N. Spergel, Mon. Not. R. Astron. Soc. 460, 4397 (2016)
D. Marsh, Phys. Rep. 643, 1 (2016)
P.H. Chavanis, Phys. Rev. D 94, 083007 (2016)
E. Cotner, Phys. Rev. D 94, 063503 (2016)
P.H. Chavanis, T. Matos, Eur. Phys. J. Plus 132, 30 (2017)
T. Helfer et al., JCAP 03, 055 (2017)
L. Hui, J. Ostriker, S. Tremaine, E. Witten, Phys. Rev. D 95, 043541 (2017)
D.G. Levkov, A.G. Panin, I.I. Tkachev, Phys. Rev. Lett. 118, 011301 (2017)
A. Suárez, P.H. Chavanis, Phys. Rev. D 95, 063515 (2017)
B. Li, T. Rindler-Daller, P.R. Shapiro, Phys. Rev. D 96, 063505 (2017)
P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)
P. Mocz et al., Mon. Not. R. Astron. Soc. 471, 4559 (2017)
J. Eby, M. Ma, P. Suranyi, L.C.R. Wijewardhana, JHEP 01, 066 (2018)
P.H. Chavanis, Phys. Rev. D 98, 023009 (2018)
A. Suárez, P.H. Chavanis, Phys. Rev. D 98, 083529 (2018)
J. Zhang, Y.L. Sming Tsai, J.L. Kuo, K. Cheung, M.C. Chu, Astrophys. J. 853, 51 (2018)
P. Mocz, L. Lancaster, A. Fialkov, F. Becerra, P.H. Chavanis, Phys. Rev. D 97, 083519 (2018)
V. Desjacques, A. Kehagias, A. Riotto, Phys. Rev. D 97, 023529 (2018)
P.H. Chavanis, Phys. Dark Univ. 22, 80 (2018)
P.H. Chavanis, arXiv:1810.08948
B. Moore, T. Quinn, F. Governato, J. Stadel, G. Lake, Mon. Not. R. Astron. Soc. 310, 1147 (1999)
G. Kauffmann, S.D.M. White, B. Guiderdoni, Mon. Not. R. Astron. Soc. 264, 201 (1993)
A. Klypin, A.V. Kravtsov, O. Valenzuela, Astrophys. J. 522, 82 (1999)
B. Moore, S. Ghigna, F. Governato, G. Lake, T. Quinn, J. Stadel, P. Tozzi, Astrophys. J. Lett. 524, L19 (1999)
M. Kamionkowski, A.R. Liddle, Phys. Rev. Lett. 84, 4525 (2000)
M. Boylan-Kolchin, J.S. Bullock, M. Kaplinghat, Mon. Not. R. Astron. Soc. 415, L40 (2011)
A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, J. March-Russell, Phys. Rev. D 81, 123530 (2010)
F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71, 463 (1999)
E. Madelung, Z. Phys. 40, 322 (1927)
H. Poincare, Acta Math. 7, 259 (1885)
S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover, 1958)
C. Sulem, P.L. Sulem, The Nonlinear Schrödinger Equation (Springer, 1999)
P. Ledoux, C.L. Pekeris, Astrophys. J. 94, 124 (1941)
P.H. Chavanis, C. Sire, Phys. Rev. E 73, 066103 (2006)
P.H. Chavanis, Phys. Rev. D 76, 023004 (2007)
P.H. Chavanis, C. Sire, Phys. Rev. E 69, 016116 (2004)
P.H. Chavanis, in preparation
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Chavanis, PH. Mass-radius relation of self-gravitating Bose-Einstein condensates with a central black hole. Eur. Phys. J. Plus 134, 352 (2019). https://doi.org/10.1140/epjp/i2019-12734-7
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DOI: https://doi.org/10.1140/epjp/i2019-12734-7