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MNRAS 000,1–15 (2020) Preprint 24 June 2021 Compiled using MNRAS LATEX style file v3.0 Joint constraints on thermal relic dark matter from strong gravitational lensing, the Lyman-U forest, and Milky Way satellites Wolfgang Enzi,1¢ Riccardo Murgia,2 Oliver Newton,3 Simona Vegetti,1 Carlos Frenk,4 Matteo Viel,5,6,7,8 Marius Cautun,4,9 Christopher D. Fassnacht,10 Matt Auger,11 Giulia Despali,1,12 John McKean,13,14 Léon V. E. Koopmans13 and Mark Lovell15 1Max Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, D-85740 Garching, Germany 2Laboratoire Univers & Particules de Montpellier (LUPM), CNRS & Université de Montpellier (UMR-5299) 3University of Lyon, UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, France 4Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK 5SISSA-International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy 6INFN, Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy 7INAF - Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34143 Trieste, Italy 8IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy 9Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands 10Department of Physics and Astronomy, University of California, Davis, USA 11Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK 12Zentrum für Astronomie der Universität Heidelberg, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg 13Kapteyn Astronomical Institute, University of Groningen, P.O.Box 800, 9700AV, Groningen, the Netherlands 14ASTRON, Netherlands Institute for Radio Astronomy, P.O. Box 2, 7990 AA Dwingeloo, the Netherlands 15Center for Astrophysics and Cosmology, Science Institute, University of Iceland, Dunhagi 5, 107 Reykjavik, Iceland Accepted XXX. Received YYY; in original form ZZZ ABSTRACT We derive joint constraints on the warm dark matter (WDM) half-mode scale by combining the analyses of a selection of astrophysical probes: strong gravitational lensing with extended sources, the Lyman-U forest, and the number of luminous −1 satellites in the Milky Way. We derive an upper limit of _hm = 0.089 Mpc h at the 95 per cent confidence level, which we show to be stable for a broad range of prior choices. Assuming a Planck cosmology and that WDM particles are thermal relics, 7 −1 this corresponds to an upper limit on the half-mode mass of "hm < 3 × 10 M h , and a lower limit on the particle mass −1 of <th ¡ 6.048 keV, both at the 95 per cent confidence level. We find that models with _hm ¡ 0.223 Mpc h (corresponding 8 −1 to <th ¡ 2.552 keV and "hm < 4.8 × 10 M h ) are ruled out with respect to the maximum likelihood model by a factor ≤ 1/20. For lepton asymmetries !6 ¡ 10, we rule out the 7.1 keV sterile neutrino dark matter model, which presents a possible explanation to the unidentified 3.55 keV line in the Milky Way and clusters of galaxies. The inferred 95 percentiles suggest that we further rule out the ETHOS-4 model of self-interacting DM. Our results highlight the importance of extending the current constraints to lower half-mode scales. We address important sources of systematic errors and provide prospects for how the constraints of these probes can be improved upon in the future. Key words: cosmology: dark matter – gravitational lensing: strong – Galaxy: structure – galaxies: haloes, structure, intergalactic medium arXiv:2010.13802v3 [astro-ph.CO] 22 Jun 2021 1 INTRODUCTION include warm dark matter models (WDM; e.g. Bode et al. 2001), in which dark matter particles have higher velocities in the early Uni- The nature of dark matter is one of the most important open ques- verse than in the CDM model. This characteristic leads to the sup- tions in cosmology and astrophysics. While the standard cold dark pression of gravitationally bound structures at scales proportional to matter (CDM) paradigm successfully explains observations of struc- the mean free path of the particles at the epoch of matter-radiation tures larger than ∼ 1 Mpc, it remains unclear whether observations equality (e.g. Schneider et al. 2012; Lovell et al. 2014). Until now, on smaller (galactic and subgalactic) scales are consistent with this several complementary approaches have been used to test CDM and model (e.g. Bullock & Boylan-Kolchin 2017). Possible alternatives WDM on these scales. Among these are methods based on observa- tions of strong gravitational lens systems, the Lyman-U forest, and the satellite galaxies of the Milky Way (MW). ¢ E-mail: [email protected] Strong gravitational lensing, being sensitive only to gravity, al- © 2020 The Authors 2 W. Enzi et al. lows one to detect low-mass haloes independently of their baryonic is structured as follows. We introduce the dark matter model under content. Therefore, it provides a direct method to quantify the dark consideration in Section2. In Section3, we describe the method with matter distribution on subgalactic scales, where most of the structures which the different probes are analysed and combined. In Section4, are expected to be non-luminous. In practice, these low-mass haloes we discuss the results obtained from the individual probes and their are detected via their effect on the flux ratios of multiply imaged joint analysis. We discuss the different sources of systematic errors compact sources (flux-ratio anomalies; Mao & Schneider 1998) or and the future prospects of each individual probe in Sections5 and on the surface brightness distribution of magnified arcs and Einstein 6, respectively. Finally, we summarize the main results of this work rings from lensed galaxies (surface brightness anomalies or gravi- in Section7. tational imaging; Koopmans 2005; Vegetti & Koopmans 2009). In this work, we focus on the latter method, while leaving the inclusion of analyses of flux ratios for future works. So far, both approaches 2 DARK MATTER MODEL have led to the detection of individual low-mass haloes (Vegetti et al. 2010, 2012; Nierenberg et al. 2014; Hezaveh et al. 2016), as well as We assume that dark matter is a thermal relic, that is, it consists statistical constraints on the halo and subhalo mass functions, and on of particles that were produced in thermodynamic equilibrium with 1 the related dark matter particle mass for sterile neutrino and thermal photons and other relativistic particles in the early Universe . As the relic warm dark matter models (Dalal & Kochanek 2002; Vegetti temperature of the Universe drops, dark matter decouples chemically et al. 2014; Birrer et al. 2017; Vegetti et al. 2018; Ritondale et al. and kinetically from the surrounding plasma (at the freeze-out time). 2019; Gilman et al. 2019b; Hsueh et al. 2019). In particular, the most Its density relative to the total entropy density of the Universe is then recent analyses by Hsueh et al.(2019) and Gilman et al.(2019b) frozen in time (see e.g. Bertone et al. 2005) and it starts to free have derived a lower limit on the mass of a thermal relic dark matter stream. As a result, the dark matter power spectrum is suppressed on particle of 5.6 and 5.2 keV at the 95 per cent confidence level (c.l.), scales related to the particles’ free-streaming lengths and the size of respectively. the horizon at the time of decoupling. The warmer the dark matter While methods based on strong gravitational lensing target the particles (i.e., the larger their free-streaming length), the larger the detection of mostly dark low-mass haloes, the number of luminous scale at which the suppression happens. In this context, CDM and satellite galaxies in the MW and other galaxies can also constrain the WDM belong to a continuum spectrum of free-streaming length or properties of dark matter (e.g. Moore et al. 1999; Nierenberg et al. particle mass. From a statistical standpoint, this means that they are 2013). For example, Lovell et al.(2016) compared the luminosity effectively nested models. ¹ º function of the MW satellites to predictions from semi-analytical The cut-off in the WDM power spectrum %WDM : can be ex- ¹ º models and derived lower constraints on the sterile neutrino particle pressed as a modification to the CDM power spectrum, %CDM : , ¹ º mass of 2 keV. More recently, by comparing the luminosity function via the following transfer function )matter : (see e.g. Bode et al. of MW dwarf satellite galaxies to simulations and incorporating 2001), i.e.: ¹ º 2 observational incompleteness in their model, Jethwa et al.(2017) 2 %WDM : 2`C −5/`C )matter ¹:º = = ¹1 ¸ ¹U:º º , (1) derived a lower limit of 2.9 keV on the thermal relic particle mass %CDM ¹:º at the 95 per cent confidence level. Nadler et al.(2019b) derived with the slope parameter ` = 1.12 and the break scale U, which for a more stringent lower limit of 3.26 keV from the analysis of the C a given thermal relic density parameter Ω and Hubble constant ℎ classical MW satellites and those discovered by the Sloan Digital th is determined to be (see Viel 2005): Sky Survey (SDSS). Combining data from the Dark Energy Survey − (DES, Abbott et al. 2018) and the Pan-STARRS1 surveys (Chambers < 1.11 Ω 0.11 h 1.22 − U = 0.049 th th Mpc h 1. (2) et al. 2019), Nadler et al.(2020a) derived a lower limit on the mass 1 keV 0.25 0.7 of thermal relic dark matter of 6.5 keV at the 95 per cent c.l. from 2 The half-mode scale , _hm, at which the transfer function becomes the census of MW satellites. equal to 1/2, is then defined as: The Lyman-U forest is one of the primary observational probes of − 1 the intergalactic medium (IGM; see Meiksin 2009; McQuinn 2016, h −` /5 i 2`C _ = 2cU 0.5 C − 1 .

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