CONSTRAINTS ON m s and θ s

1. Accounting for the unresolved X-ray background with radiatively-decaying sterile neutrino dark matter D.T. Cumberbatch (dtc@astro.ox.ac.uk) and J. Silk (silk@astro.ox.ac.uk)Astrophysics Department, University of Oxford, Keble Road, Oxford, OX1 3RH. ABSTRACT We consider a scenario where keV sterile neutrinos constitute all of the currently inferred dark matter abundance. Here we consider a scenario where contributions to the X-ray background (XRB) flux from unresolved sources in the observations of the Lockman Hole by XMM-Newton (XMM-LH) and the north/southChandra deep field survey's (CDF-N/S) can be accounted for by the radiative flux emitted by decaying sterile neutrino dark matter. We consequently place stringent constraints on the sterile neutrino mixing angle as a function of mass and perform statistical fits of the predicted spectra to these two data sets. MOTIVATIONS FOR STERILE NEUTRINO DARK MATTER Recent observations of neutrino oscillations indicate that it is possible to incorporate sterile neutrinos which can undergo radiative decays into standard model active neutrinos and photons νS → νaγ , where the energy of the photon is approximately ms/2 for sterile neutrinos of mass ms which decay at rest. Such warm dark matter models have several independent motivations including reconciling the apparent overestimation of the frequency of low mass galactic satellites, reconciling the prediction by ΛCDM simulations of a diverging density at the galactic centre, providing an explanation for the non-spherical nature of the Milky Way, as well as providing an explanation for the unusual rotational dynamics of pulsars. CONSTRAINTS ON ms and θs Imposing the condition that the extragalactic radiative intensity resulting from the decay of sterile neutrino dark matter, given by is less than the unresolved XRB intensity, where ρcis the present-day critical density and ν is the observed photon energy, for a canonical ΛCDM Universe (ΩΛ=0.7, ΩDM=0.26, ΩTotal=1), and accounting for energy resolution effects (see fig.2), we have constrained the mass and mixing angle of sterile neutrinos (displayed in fig.3), assuming that they constitute all of the currently inferred dark matter abundance. Fig.2 The theoretical spectrum, given by eq.(2) (black),and experimental spectra (magenta), resulting from extragalactic sterile neutrino decay, after accounting for the finite energy resolution of instrumentation (acknowledged here by adopting a Gaussian energy broadening ΔE=0.1E), for sterile neutrinos of masses 5, 10, 20 and 30keV. The normalisation of each spectrum has been appropriately determined so that the maximum intensity equals the unresolved XRB intensity at the same energy (displayed here for the XMM-LH data). STERILE NEUTRINO DECAY We adopt a model where sterile neutrinos possess a mass, ms, of order 1keV, which is intimately related to the mixing angle, sin2(2θs),with standard model SU(2) doublets, and its radiative decay rate, Γs, through the equation THE X-RAY BACKGROUND The origin of the XRB has been a subject of much debate since its discovery over 40 years ago. For energies above approximately 1keV, much of the XRB can be attributed to emissions from point sources, predominantly active galactic nuclei (AGN). It is crucial to the understanding of AGN and galaxy populations that we resolve these point sources. Furthermore, such observations allow us to impose stringent constraints on the residual diffuse X-ray emissions that are purely extragalactic in origin. Utilising the increased spatial resolution and improved sensitivity of Chandra and XMM-Newton, compared to earlier observatories such as ROSAT, a significantly larger proportion of the XRB was resolved into point sources. However, a significant proportion of the XRB remains unresolved (see fig.1). Fig.3 Upper limits on the sterile neutrino mixing angle θsas a function of its mass ms , when utilising the CDF-N/S (red/green) and XMM-LH (blue) data. For comparison, we also display the corresponding results obtained by Boyarsky et al.(astro-ph/0512509), (magenta), which for some masses provide significantly less stringent limits on the sterile neutrino parameters. The results displayed in fig.3 for the upper limits on the sterile neutrino mixing angle can be conveniently summarised by the following approximate empirical relation: for the mass range 0.4<ms/keV<24, which corresponds to the range of photon energies spanned by the available data on the unresolved XRB. Fig.1 The total extragalactic XRB intensity (black) compared with the XRB component which remains unresolved after summing the fluxes of sources resolved in the CDF-N/S (red/green) and XMM-LH (blue) survey’s. (Data acquired from Worsley et al. astro-ph/0412266). CONCLUSION: ARE STERILE NEUTRINOS THE ANSWER? In order to determine if the extragalactic spectrum resulting from sterile neutrino decay compares well with the unresolved XRB, we performed a χ2 fit of the two spectra for a wide range of masses (see fig.4). We obtain an increasingly better fit for heavier neutrinos up to a mass of approximately 15-25keV, after which the fit lessens in quality. LOCAL FLUX CONTRIBUTIONS We also investigated the relative significance of local contributions to the XRB, originating from sterile neutrino dark matter decay from within the Milky Way. Utilising several typical density profiles for the galactic dark matter distribution we deduced that such contributions are generally less than 10% of the extragalactic flux when orientated towards the galactic centre (excluding centrally diverging profiles, e.g. the NFW profile, which yield infinite fluxes). Hence, from fig.3, we see that since the constraints on the mixing angle scales approximately as ms, a 10% increase in the flux will only alter the permitted mass range by a factor 0.10.2≈0.6 at an observed photon energy Eγ≈ms/2, which has a negligible effect on our conclusions. Fig.4 A χ2 fit of the extragalactic radiative spectrum resulting from sterile neutrino dark matter decay to the unresolved XRB, using the CDF-N/S (red/green) and XMM-LH (blue) data sets.