#
Supermassive Black Holes and Dark Halo from the Bose-Condensed Dark Matter^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- (universality in the Universe) Why most of the galaxies harbor SMBH of huge size ${10}^{6-10}{M}_{\odot}$?
- (location in the galaxy) Why all the SMBH is located at the center of the galaxy?
- (causal relation with galaxy) Why SMBH form so early at least as $z\approx 6-7.5$?
- (correlation with galaxy) Why SMBH is firmly correlated with the galaxy bulge ${M}_{BH\xb7}\propto {\sigma}^{4}$?
- (correlation with dark halo (DH)) Why SMBH mass is correlated with the galaxy dark halo mass ${M}_{DH}$ as ${M}_{BH\xb7}\approx {10}^{-4}{M}_{DH}$?

## 2. How Do SMBHs Form?

## 3. SMBH from BEC

#### 3.1. Isotropic Collapse

#### 3.2. Anisotropic Collapse

#### 3.3. Collapse with Angular Momentum

## 4. Collapse of Axion Field -Attractive Interaction-

## 5. Conclusions and Discussions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kormendy, J.; Ho, L. Coevolution (or not) of supermassive black holes and host galaxies. Ann. Rev. Astron. Astrophys.
**2013**, 51, 511–653. [Google Scholar] [CrossRef] - Bañados, E.; Venemans, B.P.; Mazzucchelli, C.; Farina, E.P.; Walter, F.; Wang, F.; Decarli, R.; Stern, D.; Fan, X.; Davies, F.B.; et al. An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5. Nature
**2018**, 553, 473. [Google Scholar] [CrossRef] - Morikawa, M. Galaxies nurtured by mature black holes. arXiv
**2015**, arXiv:1508.05436. [Google Scholar] - Rees, M.J. Black hole models for active galactic nuclei. Annu. Rev. Astron. Astrophys.
**1984**, 22, 471–506. [Google Scholar] [CrossRef] - Volonteri, M.; Haardt, F.; Madau, P. The assembly and merging history of supermassive black holes in hierarchical models of galaxy formation. Astrophys. J.
**2003**, 582, 559. [Google Scholar] [CrossRef] - Oh, S.P.; Haiman, Z. Second-generation objects in the Universe: Radiative cooling and collapse of halos with virial temperatures above 104 K. Astrophys. J.
**2002**, 569, 558. [Google Scholar] [CrossRef] - Nishiyama, M.; Morita, M.; Morikawa, M. Bose Einstein condensation as dark energy and dark matter. arXiv
**2004**, arXiv:astro-ph/0403571. [Google Scholar] - Liebling, S.L.; Palenzuela, C. Dynamical boson stars. Living Rev. Relativ.
**2017**, 20, 5. [Google Scholar] [CrossRef] - Heckman, M.T.; Philip, N. The Coevolution of Galaxies and Supermassive Black Holes: Insights from Surveys of the Contemporary Universe. Annu. Rev. Astron. Astrophys.
**2014**, 52, 589–660. [Google Scholar] [CrossRef] - Fukuyama, T.; Morikawa, M. The relativistic gross–pitaevskii equation and cosmological Bose–Einstein condensation: Quantum structure in the universe. Prog. Theor. Phys.
**2006**, 115, 1047–1068. [Google Scholar] [CrossRef] - Fukuyama, T.; Tatekawa, T.; Morikawa, M. Cosmic structures via Bose–Einstein condensation and its collapse. J. Cosmol. Astropart. Phys.
**2008**, 2008, 033. [Google Scholar] [CrossRef] - Fukuyama, T.; Morikawa, M. Stagflation: Bose–Einstein condensation in the early universe. Phys. Rev. D
**2009**, 80, 063520. [Google Scholar] [CrossRef] - Schive, H.Y.; Chiueh, T.; Broadhurst, T. Cosmic structure as the quantum interference of a coherent dark wave. Nat. Phys.
**2014**, 10, 496. [Google Scholar] [CrossRef] - Gross, E.P. Structure of a quantized vortex in boson systems. Nuovo Cimento
**1961**, 20, 454–477. [Google Scholar] [CrossRef] - Pitaevskii, L.P. Vortex lines in an imperfect Bose gas. Sov. Phys. JETP
**1961**, 13, 451–454. [Google Scholar] - Wimberger, S.; Mannella, R.; Morsch, O.; Arimondo, E. Resonant nonlinear quantum transport for a periodically kicked Bose condensate. Phys. Rev. Lett.
**2005**, 94, 130404. [Google Scholar] [CrossRef] - Wimberger, S.; Mannella, R.; Morsch, O.; Arimondo, E.; Kolovsky, A.R.; Buchleitner, A. Nonlinearity-induced destruction of resonant tunneling in the Wannier-Stark problem. Phys. Rev. A
**2005**, 72, 063610. [Google Scholar] [CrossRef] - Gupta, P.; Thareja, E. Supermassive black holes from collapsing dark matter Bose–Einstein condensates. Class. Quant. Gravity
**2017**, 34, 035006. [Google Scholar] [CrossRef] - Ebrov’a, I. Shell Galaxies: Kinematical Signature of Shells, Satellite Galaxy Disruption and Dynamical Friction. Ph.D. Thesis, Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czechia, 2013. [Google Scholar]
- Nakamichi, A.; Morikawa, M. Acquired scaling relations in dark matter turbulence. J. Cosmol. Astropart. Phys.
**2010**, 2010, 11. [Google Scholar] [CrossRef] - Sugerman, B.; Summers, F.J.; Kamionkowski, M. Testing linear-theory predictions of galaxy formation. Mon. Not. R. Astron. Soc.
**2000**, 311, 762–780. [Google Scholar] [CrossRef] - Sikivie, P. Dark matter axions. arXiv
**2009**, arXiv:0909.0949. [Google Scholar] - Dynamical Friction, I. General Considerations: The Coefficient of Dynamical Friction. Astrophys. J.
**1943**, 97, 255–262. [Google Scholar]

**Figure 1.**Time evolution of the typical collapsing dynamics of BEC. (

**Left**) Isotropic collapse. The time evolution of the dispersion $\sigma \left(t\right)$ and the phase $\alpha \left(t\right)$ of the condensate filed. If the minimum size ${\sigma}_{min}$ is smaller than the corresponding Schwarzschild radius, a BH is formed, otherwise it simply bounces. (

**Right**) Anisotropic collapse. The time evolution of the dispersion ${\sigma}_{i}\left(t\right)$ and the ratio ${\sigma}_{3}\left(t\right)/{\sigma}_{1}\left(t\right)$ of the condensate filed. Anisotropic BEC can easily collapse to form BH as well.

**Figure 2.**Time evolution of a dissipative anisotropic BEC collapse. (

**Left**) A damping collapse of BEC. This is a typical solution derived from the effective Lagrangian Equation (14). (

**Right**) The superposition of the snapshots of BEC field at each maximum expansion. It forms the concentric almost spherical shells around the formed SMBH.

**Figure 3.**The effective potentials for the Axion DM. (

**Left**) There is a barrier formed by the angular momentum and a bottom formed by the gravity on its right. (

**Right**) The barrier top and the bottom merge at a special scale (marked by a red point) and the BEC portion inside this scale generates SMBH.

**Figure 4.**The mass distribution functions of BH within a single galaxy. The broken line shows the case for ${a}_{s}={10}^{-29}$ m, while the solid line and the separate point show for ${a}_{s}={10}^{-30.4}$ m. The latter case represents a more realistic estimate for the SMBH formation considering the coalescence at the central region by the dynamical friction within the time scale ${t}_{d}=6.8\times {10}^{7}\phantom{\rule{3.33333pt}{0ex}}\mathrm{years}$.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Morikawa, M.; Takahashi, S.
Supermassive Black Holes and Dark Halo from the Bose-Condensed Dark Matter. *Proceedings* **2019**, *13*, 11.
https://doi.org/10.3390/proceedings2019013011

**AMA Style**

Morikawa M, Takahashi S.
Supermassive Black Holes and Dark Halo from the Bose-Condensed Dark Matter. *Proceedings*. 2019; 13(1):11.
https://doi.org/10.3390/proceedings2019013011

**Chicago/Turabian Style**

Morikawa, Masahiro, and Sakura Takahashi.
2019. "Supermassive Black Holes and Dark Halo from the Bose-Condensed Dark Matter" *Proceedings* 13, no. 1: 11.
https://doi.org/10.3390/proceedings2019013011