Boson stars from self-interacting dark matter

Published for SISSA by Springer Received: December 8, 2015 Accepted: January 13, 2016 Published: February 3, 2016 Joshua Eby,a Chris Kouvaris,b Niklas Grønlund Nielsenb and L.C.R. Wijewardhanaa a University of Cincinnati, Dept. of Physics, Cincinnati, OH 45221, U.S.A. b CP3 -Origins University of Southern Denmark, Campusvej 55, DK-5230, Odense M, Denmark E-mail: , , , Abstract: We study the possibility that self-interacting bosonic dark matter forms starlike objects. We study both the case of attractive and repulsive self-interactions, and we focus particularly in the parameter phase space where self-interactions can solve well standing problems of the collisionless dark matter paradigm. We find the mass radius relations for these dark matter bosonic stars, their density profile as well as the maximum mass they can support. Keywords: Cosmology of Theories beyond the SM, Classical Theories of Gravity ArXiv ePrint: 1511.04474 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP02(2016)028 JHEP02(2016)028 Boson stars from self-interacting dark matter Contents 1 2 SIDM parameter space 2.1 DM scattering with boson stars 3 4 3 Bosonic dark matter 3.1 Non-interacting case 3.2 Repulsive interactions 3.3 Attractive interactions 5 5 5 7 4 Conclusions 12 1 Introduction Bosonic degrees of freedom arise generically and naturally in theories of fundamental physics, both in the Standard Model and beyond. The Higgs boson is of paramount importance, being the only fundamental scalar in the Standard Model [1–4], but many other scalar degrees of freedom have been proposed to extend particle physics to high energy scales. These include (among many others) the axion of QCD [5–9] or the scalar which drives the expansion of the universe in quintessence models [10]. These bosonic particles often make good Dark Matter (DM) candidates as well. One reason for this is that unlike the Higgs, many of these new scalars would be stable or longlived enough that they could coalesce into DM halos which constitute the seeds of galaxy formation. Unlike the usual collisionless cold DM picture, however, we are interested in the scenario where large collections of these bosons form bound states of macroscopic size due to their self-gravitation (and self-interaction generically). For this picture to be consistent, the scalars are taken to be sufficiently cold so that they may coalesce into a Bose-Einstein Condensate (BEC) state, and can thus be described by a single condensate wavefunction. These wavefunctions can indeed encompass an astrophysically large volume of space and have thus been termed “boson stars” [11]. It was shown many years ago that objects of this type are allowed by the equations of motion, first by Kaup [12] and subsequently by Ruffini and Bonazzola [13] in non-interacting systems. They found a maximum mass for boson stars of the form Mmax ≈ 0.633MP2 /m, where MP = 1.22 × 1019 GeV is the Planck mass and m is the mass of the individual bosons. (This is very different from the analogous limit for fermionic stars, termed the Chandrasekhar limit, which scales as MP3 /m2 ). Later, it was shown by Colpi et al. [11] that self interactions in these systems can cause significant phenomenological changes. In particular, they examined systems with repulsive self-interactions, and show that the upper –1– JHEP02(2016)028 1 Introduction 1 Note that the Colpi et al. result does not reduce to the Kaup bound as λ → 0 because the former is derived by rescaling the equations of motion and dropping higher-order terms in the strong coupling limit, as we see in section 3. –2– JHEP02(2016)028 √ limit on the mass is Mmax ≈ 0.02 λMP3 /m2 , where λ is a dimensionless φ4 coupling.1 This extra factor of MP /m as compared to the noninteracting case makes it more plausible that boson stars can have masses even larger than a solar mass. A different method of constraining the boson star parameter space, which fits the coupling strength using data from galaxy and galaxy cluster sizes, has been considered in [14, 15]. The situation for attractive self-interactions is slightly more complex. The simplest case involves a self-interaction of the form λφ4 , where λ < 0 for attractive interactions. If this were the highest-order term in the potential, then it would not be bounded below, and so one typically stabilizes it by the addition of a positive φ6 term. We will assume that the contribution of such higher-order terms is negligible phenomenologically (we address the validity of that assumption in section 3.3). Furthermore, in this scenario the typical sizes of gravitationally bound BEC states is significantly smaller than the repulsive or noninteracting cases. This is because the only force supporting the condensate against collapse comes from the uncertainty principle. Gravity and attractive self-interactions tend to shrink the condensate. We will see in section 3 that the maximum mass for an attractive condenp sate scales as Mmax ∼ MP / |λ|. This result was originally derived using an approximate analytical method [16], and was later confirmed by a precise numerical calculation [17]. DM self-interactions have already been proposed and studied in different contexts [18– 37]. One of the main reasons why DM self-interactions can play an important role is due to the increasing tension between numerical simulations of collisionless cold DM and astrophysical observations, the resolution of which (for the moment) is unknown. The first discrepancy, known as the “cusp-core problem”, is related to the fact that dwarf galaxies are observed to have flat density profiles in their central regions [38, 39], while N-body simulations predict cuspy profiles for collisionless DM [40]. Second, the number of satellite galaxies in the Milkly Way is far fewer than the number predicted in simulations [41–46]. Last is the so-called “too big to fail” problem: simulations predict dwarf galaxies in a mass range that we have not observed, but which are too large to have not yet produced stars [47]. The solution of these problems is currently unknown, but a particularly well-motivated idea involves self-interacting DM (SIDM). Simulations including such interactions suggest that they have the effect of smoothing out cuspy density profiles, and could solve the other problems of collisionless DM as well [25, 48, 49]. These simulations prefer a self-interaction cross section of 0.1 cm2 /g . σ/m . 10 cm2 /g. There are, however, upper bounds on σ/m from a number of sources, including the preservation of ellipticity of spiral galaxies [50, 51]. The allowed parameter space from these constraints nonetheless intersects the range of cross sections which can resolve the small-scale issues of collisionless DM, in the range 0.1 cm2 /g . σ/m . 1 cm2 /g. Self-gravitation and additionally extra self-interactions among DM particles can lead in some cases to the collapse of part of the DM population into formation of dark (...truncated)