# Black hole formation from axion stars

## Abstract

The classical equations of motion for an axion with potential V (φ)= m {sub a} {sup 2} f {sub a} {sup 2} [1−cos (φ/ f {sub a} )] possess quasi-stable, localized, oscillating solutions, which we refer to as ''axion stars''. We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an ''axion star stability diagram', parameterized by the initial ADM mass, M {sub ADM}, and axion decay constant, f {sub a} . We identify three regions of the parameter space: i) long-lived oscillating axion star solutions, with a base frequency, m {sub a} , modulated by self-interactions, ii) collapse to a BH and iii) complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate ''triple point' ( M {sub TP}, f {sub TP}) ∼ (2.4 M {sub pl}{sup 2}/ m {sub a} ,0.3 M {sub pl}). For f {sub a} below the triple point BH formation proceeds during winding (in the complex U(1) picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion starsmore »

- Authors:

- King's College London, Strand, London, WC2R 2LS (United Kingdom)
- Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Ciudad Universitaria, CP 58040 Morelia, Michoacán (Mexico)

- Publication Date:

- OSTI Identifier:
- 22679944

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASTROPHYSICS; AXIONS; BLACK HOLES; DECAY; EINSTEIN FIELD EQUATIONS; EQUATIONS OF MOTION; GENERAL RELATIVITY THEORY; INTERACTIONS; MASS; NONLINEAR PROBLEMS; QUANTUM CHROMODYNAMICS; SPACE; STABILITY; STARS

### Citation Formats

```
Helfer, Thomas, Marsh, David J.E., Clough, Katy, Fairbairn, Malcolm, Lim, Eugene A., and Becerril, Ricardo, E-mail: thomas.1.helfer@kcl.ac.uk, E-mail: david.marsh@kcl.ac.uk, E-mail: katy.clough@phys.uni-goettingen.de, E-mail: malcolm.fairbairn@kcl.ac.uk, E-mail: eugene.lim@kcl.ac.uk, E-mail: becerril@ifm.umich.mx.
```*Black hole formation from axion stars*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/03/055.

```
Helfer, Thomas, Marsh, David J.E., Clough, Katy, Fairbairn, Malcolm, Lim, Eugene A., & Becerril, Ricardo, E-mail: thomas.1.helfer@kcl.ac.uk, E-mail: david.marsh@kcl.ac.uk, E-mail: katy.clough@phys.uni-goettingen.de, E-mail: malcolm.fairbairn@kcl.ac.uk, E-mail: eugene.lim@kcl.ac.uk, E-mail: becerril@ifm.umich.mx.
```*Black hole formation from axion stars*. United States. doi:10.1088/1475-7516/2017/03/055.

```
Helfer, Thomas, Marsh, David J.E., Clough, Katy, Fairbairn, Malcolm, Lim, Eugene A., and Becerril, Ricardo, E-mail: thomas.1.helfer@kcl.ac.uk, E-mail: david.marsh@kcl.ac.uk, E-mail: katy.clough@phys.uni-goettingen.de, E-mail: malcolm.fairbairn@kcl.ac.uk, E-mail: eugene.lim@kcl.ac.uk, E-mail: becerril@ifm.umich.mx. Wed .
"Black hole formation from axion stars". United States.
doi:10.1088/1475-7516/2017/03/055.
```

```
@article{osti_22679944,
```

title = {Black hole formation from axion stars},

author = {Helfer, Thomas and Marsh, David J.E. and Clough, Katy and Fairbairn, Malcolm and Lim, Eugene A. and Becerril, Ricardo, E-mail: thomas.1.helfer@kcl.ac.uk, E-mail: david.marsh@kcl.ac.uk, E-mail: katy.clough@phys.uni-goettingen.de, E-mail: malcolm.fairbairn@kcl.ac.uk, E-mail: eugene.lim@kcl.ac.uk, E-mail: becerril@ifm.umich.mx},

abstractNote = {The classical equations of motion for an axion with potential V (φ)= m {sub a} {sup 2} f {sub a} {sup 2} [1−cos (φ/ f {sub a} )] possess quasi-stable, localized, oscillating solutions, which we refer to as ''axion stars''. We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an ''axion star stability diagram', parameterized by the initial ADM mass, M {sub ADM}, and axion decay constant, f {sub a} . We identify three regions of the parameter space: i) long-lived oscillating axion star solutions, with a base frequency, m {sub a} , modulated by self-interactions, ii) collapse to a BH and iii) complete dispersal due to gravitational cooling and interactions. We locate the boundaries of these three regions and an approximate ''triple point' ( M {sub TP}, f {sub TP}) ∼ (2.4 M {sub pl}{sup 2}/ m {sub a} ,0.3 M {sub pl}). For f {sub a} below the triple point BH formation proceeds during winding (in the complex U(1) picture) of the axion field near the dispersal phase. This could prevent astrophysical BH formation from axion stars with f {sub a} || M {sub pl}. For larger f {sub a} ∼> f {sub TP}, BH formation occurs through the stable branch and we estimate the mass ratio of the BH to the stable state at the phase boundary to be O(1) within numerical uncertainty. We discuss the observational relevance of our findings for axion stars as BH seeds, which are supermassive in the case of ultralight axions. For the QCD axion, the typical BH mass formed from axion star collapse is M {sub BH} ∼ 3.4 ( f {sub a} /0.6 M {sub pl}){sup 1.2} M {sub ⊙}.},

doi = {10.1088/1475-7516/2017/03/055},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2017,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}