Eur. Phys. J. C (2014) 74:3062 DOI 10.1140/epjc/s10052-014-3062-5 Regular Article - Theoretical Physics Cluster X-ray line at 3.5 keV from axion-like dark matter Hyun Min Lee1, Seong Chan Park2, Wan-Il Park3,a 1 Department of Physics, Chung-Ang University, Seoul 156-756, Korea 2 Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea 3 School of Physics, KIAS, Seoul 130-722, Korea Received: 10 July 2014 / Accepted: 31 August 2014 / Published online: 20 September 2014 © The Author(s) 2014. This article is published with open access at Springerlink.com Abstract The recently reported X-ray line signal at Eγ interesting to investigate the possible DM candidates with 3.5 keV from a stacked spectrum of various galaxy clusters existing data. One obvious candidate is the sterile neutrino and the Andromeda galaxy may be originating from a decay- in models for the neutrino masses [1,2,4] but there could be ing dark matter particle of the mass 2Eγ . A light axion-like alternative DM explanations [5,6]. scalar is suggested as a natural candidate for dark matter and In this paper, we propose an axion-like particle as the its production mechanisms are closely examined. We show source of the X-ray line at 3.5 keV.1 Axion-like particles (or that the right amount of axion relic density with the pre- simply axions) are ubiquitous in various extensions of the 14 ferred parameters, ma 7 keV and fa 4 × 10 GeV, SM including stringy models with various compactification can be naturally obtainable from the decay of inflaton. If the schemes where pseudo-Goldstone bosons appear in the low axions were produced from the saxion decay, it could not energy after the breakdown of accidental global symmetries have constituted the total relic density due to the bound from [7]. The mass spectra of the axion-like particles can span a structure formation. Nonetheless, the saxion decay is an inter- wide range, covering the keV scale. We may identify one of esting possibility, because the 3.5 keV line and dark radiation them as the axion-like particle explaining the X-ray line.2 The can be addressed simultaneously, being consistent with the axion-like particle could be produced in the early universe Planck data. Small misalignment angles of the axion, rang- by various mechanisms and account for the observed DM −4 −1 ing between θa ∼ 10 –10 depending on the reheating amount: e.g. the axion misalignment, the decay of the radial temperature, can also be the source of axion production. The partner of the axion-like DM, dubbed the saxion, and also model with axion misalignment can satisfy the constraints the decay of the inflaton. We show that an axion-like DM, for structure formation and iso-curvature perturbation. produced preferably in the decay of the inflaton, can provide a good fit to the observed X-ray line by its decay into a pair of photons through anomaly interactions with the decay 1 Introduction 14 constant, fa 4 × 10 GeV. The rest of the paper is organized as follows. In Sect. 2, It has been recently reported by two groups that there exists a we describe our model for an axion-like DM and discuss line signal at 3.5 keV in a stacked X-ray spectrum of galaxy the cosmological bounds from structure formation and iso- clusters and the Andromeda galaxy [1,2]. Since no source curvature perturbation in Sect. 3. In Sect. 4, three scenarios of of X-ray lines, such as atomic transitions, is known at this axion production and relevant observational bounds on them energy, the observed line may suggest the existence of a new are discussed. Finally, conclusions are drawn in Sect. 5. source. It would be tantalizing to notice that the line is con- sistent with the monochromatic photon signal due to a decay- 2 The model with a 7 keV axion for the X-ray line ing dark matter (DM) with the mass, mDM 7 keV, and the τ 28 lifetime, DM 10 s[1,2]. Even though a further confir- We introduce an axion-like particle as a pseudo-Goldstone mation of the line by independent and refined observations, boson associated with a broken anomalous U(1) symmetry. e.g. Astro-H mission [3], is required, it would be timely and 1 We note that there have appeared related papers on the keV axion H. M. Lee, S. C. Park and W.-I. Park are contributed equally. dark matter [8,9] while we were finalizing our work. 2 The axion-like particles, in general, do not play the role of the QCD a e-mail: [email protected] axion. 123 3062 Page 2 of 8 Eur. Phys. J. C (2014) 74:3062 After the symmetry breaking, the model-independent effec- • Structure formation tive Lagrangian for the axion a and the saxion s (the radial The keV axion may be a decay product of the inflaton component of the symmetry-breaking field) can be expressed and/or the saxion. Suppose that a mother particle, denoted as as X, decays to two axions, each of which carries the energy of L = 1(∂ )2 + 1(∂ )2 + s (∂ )2 − 1 2 2 μs μa μa ms s 2 2 2 fa 2 α = / −1 2 2−1 μν+c1 em ( ˜ μν − μν) Ea,i m X 2(5) maa Fμν F aFμν F sFμν F 2 4 8π fa c2 ¯ μ 5 ¯ / μ ¯ + (∂μa) f γ γ f + i f Dμγ f − m f f f when the axion mass is ignored. The axion of our inter- fa est is expected to be out of thermal equilibrium at tem- c3(s+ia)/fa ¯ −(m f e fL f R + h.c.) + LI (1) peratures well below GUT scale [9]. Hence the momen- tum of the axion is simply red-shifted once it is pro- where αem is the fine structure constant of electromagnetic duced from the decay of X. Then, in order not to destruct interaction, fa is the axion coupling constant, and Fμν and ˜ large scale structures, the axion should be non-relativistic Fμν are the field-strength tensor and its dual for electromag- around the epoch when a Hubble patch contains energy netic field, respectively. We note that c1,2,3 are dimension- less parameters of order one and we have included an extra corresponding to the galactic-sized halo (corresponding ∼ ≡ charged fermion f that is responsible for the generation of to T T∗ 300 eV) (see for example [12,13]). α anomalies. For example, in a supersymmetric axion model More precisely, the most recent analysis of Lyman- for- est data shows that the comoving free-streaming length of [10,11], the axion chiral multiplet A with A|θ=0 = s + ia 2 α DM at the matter-radiation equality is constrained to be appears in the superspace interactions as d θ AW Wα and 2 c A/f ¯ at 95 % CL [14] d θ m f e 3 a where Wα is the field strength super- field, and and ¯ are matter chiral multiplets containing λ <λc ≈ . the extra charged fermion. But the results in our work do not fs fs 0 12 Mpc (6) depend on the presence of supersymmetry. We can add the L Lagrangian for inflation, I . λc where we introduced fs representing the observational For a keV-scale axion, the first term of the second line in bound on the free-streaming length. Including the previ- Eq. (1) provides the main decay channel with a rate given by ous various analyses of Lyman-α forest data [15] and the α2 3 emma phase space densities derived from the dwarf galaxies of →γγ = (2) a π 3 2 the Milky way [16–18], leads to the bound on the free- 64 fa streaming length ranging between 0.12 Mpc λc where we set c = 1 for simplicity. This axion decay can be a fs 1 0.60 Mpc. The comoving free-streaming length of the possible origin of the recently reported X-ray line at 3.5keV, axion produced from the decay of a mother particle X if the axion saturates the dark matter relic density and has the is computed as following properties [1,2]: 28 m = 7.1keV,τ= 1.14 × 10 s teq v tnr teq v a a λ ≡ adt = dt + adt = . × −53 fs or a 5 73 10 GeV (3) τ R(t) τ R(t) t R(t) X X nr 1/2 where τ is the lifetime of the axion. This implies that the 2tnr τX 1 teq a = 1 − + ln axion coupling constant should be Rnr tnr 2 tnr m 3/2 1/2 1/4 14 a 1 H m X /2 Teq fa 4 × 10 GeV . (4) ≈ 0 7keV H0 X ma T0 For notational convenience in the later section, we use f , ≡ / a 0 1 m 2 T 3 2 4 × 1014 GeV. × 1 + ln X a 0 (7) 2 H0 m X /2 Teq 3 Cosmological constraints where va is the velocity of the axion, R(t) is the scale fac- tor, tnr is the time when the axion becomes non-relativistic, Our keV-scale axion can be constrained by astrophysics and τX ( X ) is the lifetime (decay rate) of X, related to the τ = (π 2 / )−1/2 / 2 and cosmology, namely, the structure formation or the iso- decay temperature TX by X g∗ 90 MP TX . 1/2 curvature perturbation of dark matter, depending on how the In the second line, we used R(t) = Req(t/teq) for 1/2 axion is produced.