
Physics Letters B 785 (2018) 9–13
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Relativistic collapse of axion stars
Florent Michel
a,∗
, Ian G. Moss
b
a
Centre for Particle Theory, Durham University, South Road, Durham, DH1 3LE, UK
b
School of Mathematics, Statistics and Physics, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK
a r t i c l e i n f o a b s t r a c t
Article history:
Received
2 March 2018
Received
in revised form 6 July 2018
Accepted
7 July 2018
Available
online 20 August 2018
Editor:
M. Trodden
We study the gravitational collapse of axion dark matter in null coordinates, assuming spherical
symmetry. Compared with previous studies, we use a simpler numerical scheme which can run, for
relevant parameters, in a few minutes or less on a desktop computer. We use it to accurately determine
the domains of parameter space in which the axion field forms a black hole, an axion star or a relativistic
Bosenova.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Amongst the possible dark matter candidates, a coherent scalar
field with very low mass is an enticing possibility. The idea orig-
inated
with the QCD axion [1], but the concept has since been
extended to a class of axion-like particles (ALP’s) with ultra-light
masses [2]. In ALP scenarios, the dark matter forms gravitation-
ally
bound objects which may form into galaxy cores [3], or for
larger masses into axion mini-clusters [4–6]. These objects are of-
ten
stable only for a particular mass range, leaving the possibility
of detectable cosmological signatures from the axion bound struc-
tures
or from the remnants of their collapse [3,7].
ALP’s
are characterised by their mass m and decay constant (or
symmetry breaking scale) f . Coherent ALP dark matter scenarios
envision the dark matter energy density in the form of large-scale
coherent axion oscillations of frequency ∼ m, with density param-
eter
[1,7]
ALP
∼ 0.1
f
10
17
GeV
2
m
10
−22
eV
1/2
, (1)
although this is rather dependent on initial conditions. Spatial gra-
dients
in the oscillating axion field induce “quantum” pressure
forces which are capable of supporting structures on the Kpc scale
for axion masses around m ∼ 10
−22
eV, or galaxy Halo scales for
m ∼ 10
−24
eV [2].
We
follow the recent trend of referring to stable axion struc-
tures
as axion stars (though the term Bose star is also frequently
*
Corresponding author.
E-mail
addresses: florent.c.michel@durham.ac.uk (F. Michel),
ian.moss@newcastle.ac.uk (I.G. Moss).
used in this context). So far three distinct scenarios of gravitational
collapse for APL’s have been identified [8,9]: they can settle down
quietly to an axion star; they can radiate away energy in bursts of
relativistic axions or they can collapse to a black hole. The second
outcome is a relativistic analogue of the Bosenova phenomena in
cold-atom physics [10]. Like the cold atoms in a Bosenova, the ax-
ions
have an attractive self-interaction force which can overcome
the quantum pressure. We will use the term Bosenova in this pa-
per
to refer to the axion collapse and radiation phenomenon.
The
fate of an axion clump can be represented on phase dia-
grams
labelled by parameters describing the axion properties and
the initial conditions. Recently, Helfer et al. [9]have produced a
phase diagram for spherically symmetric collapse with axion decay
constant f and the initial mass of the axion clump, and they have
speculated that there is a tricritical point joining phase boundaries
between the three outcomes. The aim of this paper is to provide
convincing numerical evidence for the tricritical point using a par-
ticularly
amenable form of the field equations, and to determine
the parameter values accurately at the phase boundaries.
We
use the null-coordinate integration schemes introduced into
spherically symmetric gravitational collapse by Goldwirth and Pi-
ran
[11]. The null techniques are particularly efficient because the
coordinate grid flows inwards with the collapsing matter. For ex-
ample,
the null methods can reproduce the universal scaling phe-
nomena
in massless scalar collapse [12], which otherwise is only
possible with less efficient mesh refinement techniques [13].
Throughout
this work, we use units in which the reduced
Planck constant
¯
h and velocity of light c are equal to unity. The
reduced Planck mass M
p
= (8π G)
−1/2
, where G is Newton’s con-
stant.
https://doi.org/10.1016/j.physletb.2018.07.063
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.