X-Ray Lines from Dark Matter Annihilation at the keV Scale

In 2014, several groups reported hints for a yet unidentified line in astrophysical x-ray signals from galaxies and galaxy clusters at an energy of 3.5 keV. While it is not unlikely that this line is simply a reflection of imperfectly modeled atomic transitions, it has renewed the community’s interest in models of keV-scale dark matter, whose decay would lead to such a line. The alternative possibility of dark matter annihilation into monochromatic photons is far less explored, a lapse that we strive to amend in this Letter. More precisely, we introduce a novel model of fermionic dark matter $\chi$ with $\mathcal{O}(\mathrm{keV})$ mass, annihilating to a scalar state $\varphi$ which in turn decays to photons, for instance via loops of heavy vectorlike fermions. The resulting photon spectrum is box shaped, but if $\chi$ and $\varphi$ are nearly degenerate in mass, it can also resemble a narrow line. We discuss dark matter production via two different mechanisms—misalignment and freeze-in—which both turn out to be viable in vast regions of parameter space. We constrain the model using astrophysical x-ray data, and we demonstrate that, thanks to the velocity dependence of the annihilation cross section, it has the potential to reconcile the various observations of the 3.5 keV line. We finally argue that the model can easily avoid structure formation constraints on keV-scale dark matter.

Figure 1

(a) Feynman diagram for DM annihilation to photons via the intermediate scalar $\varphi$. Blobs represent the effective $\varphi \gamma \gamma$ coupling from Eq. (1). Diagram (b) shows a possible UV completion for this vertex; see Eq. (2).

Figure 2

Parameter space of the annihilating keV-scale DM models defined in Eqs. (1) and (2). We show the relevant constraints as a function of the DM mass $m_{\chi }$ and the Yukawa coupling between $\chi$ and the mediator $\varphi$, assuming a degeneracy parameter of $\delta \equiv (m_{\chi }-m_{\varphi })/m_{\chi }={10}^{-4}$. Shaded regions are excluded by x-ray observations of the Andromeda Galaxy (M31) [5], the Galactic Center (NuSTAR Galactic Center) [97], the galactic (Galactic diffuse) [7] and extragalactic (EG. gal and EG. dwarfs) [6] diffuse x-ray background, and by Pauli blocking arguments (Tremaine-Gunn) [98, 99]. The red star [100] corresponds to the excess of monochromatic x rays at 3.5 keV observed in Refs. [8, 15]. Horizontal blue lines indicate the suppression scale $\mathrm{\Lambda }$ of the $\varphi \gamma \gamma$ coupling required to obtain the correct DM relic abundance via UV freeze-in, assuming $T_{\mathrm{RH}}=1\mathrm{TeV}$. To the right of the dashed line, part of the initially produced abundance of $\chi$ gets transferred to $\varphi$ via $\varphi \varphi \leftrightarrow \overline{\chi }\chi$ at $T\sim \mathrm{keV}$. The region to the right of the dashed line can also be reached via freeze-in through misalignment (see text). The vertical green band indicates where low temperature freeze-in via $\varphi \varphi \to \overline{\chi }\chi$ yields the correct relic abundance.

Figure 3

Parameter regions of our annihilating DM scenario favored by observations of the 3.5 keV x-ray line ($1,2,3\sigma$), and 90% CL exclusion limits from null results. We have assumed a degeneracy parameter of $\delta \equiv (m_{\chi }-m_{\varphi })/m_{\chi }={10}^{-4}$. From the compilation in Ref. [102], we adopt observations from stacked galaxy clusters using the MOS and PN instruments on the XMM Newton satellite [8], from the Perseus cluster alone [8], from the Andromeda Galaxy (M31) [15], and from the Chandra Deep Field [101]. Limits are based on nonobservations in M31 [5], dwarf spheroidal galaxies [18], and the Perseus cluster [21, 85], and the regions above the solid lines are excluded.