Collisions of dark matter axion stars with astrophysical sources

Published for SISSA by Springer Received: February 17, 2017 Accepted: March 28, 2017 Published: April 18, 2017 Collisions of dark matter axion stars with astrophysical sources a Department of Physics, University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, U.S.A. b Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510, U.S.A. E-mail: , , , , Abstract: If QCD axions form a large fraction of the total mass of dark matter, then axion stars could be very abundant in galaxies. As a result, collisions with each other, and with other astrophysical bodies, can occur. We calculate the rate and analyze the consequences of three classes of collisions, those occurring between a dilute axion star and: another dilute axion star, an ordinary star, or a neutron star. In all cases we attempt to quantify the most important astrophysical uncertainties; we also pay particular attention to scenarios in which collisions lead to collapse of otherwise stable axion stars, and possible subsequent decay through number changing interactions. Collisions between two axion stars can occur with a high total rate, but the low relative velocity required for collapse to occur leads to a very low total rate of collapses. On the other hand, collisions between an axion star and an ordinary star have a large rate, Γ ∼ 3000 collisions/year/galaxy, and for sufficiently heavy axion stars, it is plausible that most or all such collisions lead to collapse. We identify in this case a parameter space which has a stable region and a region in which collision triggers collapse, which depend on the axion number (N ) in the axion star, and a ratio of mass to radius cubed characterizing the ordinary star (Ms /Rs3 ). Finally, we revisit the calculation of collision rates between axion stars and neutron stars, improving on previous estimates by taking cylindrical symmetry of the neutron star distribution into account. Collapse and subsequent decay through collision processes, if occurring with a significant rate, can affect dark matter phenomenology and the axion star mass distribution. Keywords: Cosmology of Theories beyond the SM, Classical Theories of Gravity ArXiv ePrint: 1701.01476 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP04(2017)099 JHEP04(2017)099 Joshua Eby,a,b Madelyn Leembruggen,a Joseph Leeney,a Peter Suranyia and L.C.R. Wijewardhanaa Contents 1 2 Variational method for axion stars 2 3 Collisions between two ASts 3.1 Modified energy functional 3.2 Collision rates 3.3 Collapse time 5 5 6 9 4 Collision of an ASt with an ordinary star 4.1 Gravitational potential inside star 4.2 Collision rates 4.3 Collapse 11 11 13 15 5 Collisions of an ASt with a neutron star 17 6 Conclusions 18 1 Introduction Axion stars [1–3] are macroscopic bound states of axion particles [4–11], and their existence can have astrophysical or cosmological implications [12–17]. In particular, axions could form all or part of dark matter in the universe, potentially in the form of axion stars [18–23]. Axions could also be connected to leptonic mass hierarchy and mixings as well [24, 25]. The masses of dilute, or weakly bound, axion stars [26–28] are bounded above by considerations of gravitational stability [29, 30]. The endpoint of collapse of a weakly bound axion star whose mass exceeds the critical value Mc has recently received a lot of attention. By analyzing the energy functional, the author of [31] found that boson stars which possess attractive self-interactions collapse to black holes when M exceeds Mc . Using a similar method, some of us [32] concluded that the full axion potential, which contains both attractive and repulsive interactions, is bounded from below, and the full energy functional is minimized at a dense radius RD . We concluded that the endpoint of collapse for an axion star was a dense state, but with a radius still larger than the corresponding Schwarzschild radius RS . The possibility of such dense states were also proposed earlier by [26, 33], and if they exist in nature, they can have interesting phenomenological consequences [34]. Dense states for axion stars have large binding energies, and following our analysis of axion star decay in [35], we also suggested in [32] that during collapse a large number of relativistic axions are emitted in what is often called a Bosenova [36]. The recent work –1– JHEP04(2017)099 1 Introduction 2 Variational method for axion stars Axion self-interactions can be described by the low-energy potential [32, 33]  s ∗  ∗ψ 2ψ ψ ψ , W (ψ) = m2 f 2 1 − − J0 2 mf 2 2mf (2.1) where m and f are the mass and decay constant of the axion, and ψ is the low-energy wavefunction describing an N -particle condensate of axions. For QCD axions, typical values are m = 10−5 eV and f = 6 × 1011 GeV, which implies the ratio δ ≡ f 2 /MP 2 = O(10−14 )  1, which will be used in what follows.1 The total self-energy of the axion star 1 We denote the Planck mass MP = G−1/2 = 1.22×1019 GeV, where G is Newton’s gravitational constant. –2– JHEP04(2017)099 of [37] and [38], using very different methods, seem to similarly indicate that relativistic axions are emitted from collapsing axion stars. The non-relativistic effective field theory of axion stars, as outlined in [39], can also have sensitivity to unique decay signatures, and such rates increase with the density of the axion star as well [40]. The dominant mechanism for the emission of relativistic axions is the subject of current debate, and we will not attempt to resolve it here. However, a recent paper on oscillon decay [41] supports the mechanism suggested in [35] of decay through emission of a single relativistic axion. A consensus seems to have emerged that as binding energy of an axion star increases, its decay rate through number changing interactions increases rapidly. This condition is satisfied by collapsing axion stars. Collisions of axion stars with astrophysical sources could occur with a relatively high rate, especially if axion stars compose a large fraction of dark matter. Because collisions can change the energy functional for a dilute axion star, they can lead to unique collapse scenarios which, in turn, can suggest high rates of relativistic axion emission. With this in mind, it is interesting to analyze collisions of dilute axion stars with two potentially copious astrophysical sources: ordinary stars and other axion stars. Axions couple at loop-level to photons, which allows decay of free or condensed axions through a process a → 2γ, but this rate is believed to be small enough to be ignored on cosmological timescales [42]. However, in collisions with neutron stars, strong magnetic fields can stimulate these interactions, leading to bursts of photons that are potentially observable [43–46]. The idea that such collisions could lead to the observed Fast Radio Bursts [47–50], which appeared originally several years ago, has been investigated as (...truncated)