Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites Raees Noorbhai University of the Witwatersrand Centre for Astrophysics rnoorbhai@gmail.com Supervised by Dr Geoffrey Beck University of the Witwatersrand Centre for Astrophysics geoffrey.beck@wits.ac.za September 2023 Dissertation submitted to the School of Physics of the University of the Witwatersrand, in fulfillment of the academic requirements of the Master of Science postgraduate degree 1 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Abstract First suggested 90 years ago, the Dark Matter (DM) mystery has been deepened by a range of astronomical observations, from the galactic to the cosmological scale, demonstrating anomalous gravitational phenomena which necessitate the existence of some unknown DM. In the 1970s, particle DM models, including the WIMP hypothesis considered in this work, were proposed and have subsequently been subjected to empirical scrutiny. Over the past 2 decades, all DM direct detection experiments, collider searches and indirect detection searches have failed to detect a DM signal, placing stringent constraints upon WIMP parameters and ruling out WIMP-Hadron interactions. Following the detection of an excess e−/e+ flux at approximately 1.4 TeV by DAMPE in 2017, a number of Massive Leptophilc Majorana Particle (MLMP) WIMP hypotheses were proposed to explain the flux. To conduct a model-independent test of these hypotheses, Leptophilic WIMPs in the 1-2 TeV mass-energy range are considered, accounting for self-Annihilation along all leptonic channels, as well as the 3l democratic case. The dwarf spheroidal galaxies orbiting the Milky Way (MW), particularly the Ultrafaints, are DM-dominated and are thus strong candidates for indirect DM searches using next-generation telescopes - such as CTA in gamma, KM3NeT in neutrinos and MeerKAT in radio, with sensitivities that dwarf those of prior telescopes like LHAASO. Accounting for the respective fields-of-view of these telescopes, 6 dwarf spheroidals, 4 Ultrafaints and 2 Classicals, are chosen as potential target environments for the multi-messenger analysis. Equations are also derived for the Mean Free Path (MFP) and Mean Annihilation Period (MAP) of the WIMPs in the respective DM Halos, for the case of both an arbitrary Halo boundary and at the virial radius boundary. Utilising conservative estimates of telescope sensitivities, non- detection upper bounds are placed upon the Annihilation cross-section ⟨σv⟩ψ and Decay rate Γψ . These bounds are taken in comparison to the bounds imposed by the Super-Kamiokande neutrino search in the MW Halo and centre, the ATCA radio search in Reticulum II and the ASKAP/EMU radio search in the LMC. In all cases, the non-detection bounds imposed by observations of the Ultrafaints are more stringent, but with greater error margins than is the case with the Classicals. For CTA, non-detection bounds in the case of all Ultrafaints are competitive with those imposed by the ASKAP/EMU search and stronger than those imposed by both the ATCA and the Super- Kamiokande searches. For KM3NeT, no novel non-detection bounds are imposed for observations of all 6 dwarf spheroidals. For MeerKAT, in the case of the µ−/µ+ channel, observations of Reticulum II are competitive with the ASKAP/EMU bounds. From the multi-messenger analysis, it is concluded that the strongest non-detection bounds are imposed by CTA observations of Segue 1 and MeerKAT observations of Reticulum II. In the Decay case, the bounds are compared to those imposed by the Fermi indirect search in the IGRB. In the case of all next-generation telescopes, no novel non-detection constraints can be imposed upon Γψ . In the case of the MFP and MAP results, the non-detection lower limits are often many orders of magnitude greater the Hubble time. At the relic density limit, the Halo-independent MAP at the virial limit is 14 orders of magnitude greater than the age of the Universe. This illustrates the severe extent to which the Annihilation channel for WIMPs has been suppressed, since successive instances of non-detection have placed tight bounds on ⟨σv⟩ψ . In light of this, proposed astrophysical explanations for the DAMPE flux are favourable, as they do not require the presupposition of WIMP Dark Matter. 2 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Dedication and Acknowledgments For Raees at six years old, dreaming out loud about being a scientist one day. This one’s for you. With boundless gratitude to Dr. Geoffrey Beck. For his insight, feedback and guidance. For his understanding, sympathy and patience. And for a kindness all too rare, in a world where cruelty is too often normalised. To have conducted this research under his supervision has been nothing short of a blessing. With many thanks too to my father, Mubeen Noorbhai, for his repeated assistance in dealing with the unique way in which my work is obstructed by the deafening nag of a cigarette craving. And lastly, with much gratitude to my mother, Yasmeen Omar, for her needed material support and, more importantly, for always taking my calls at odd hours of the morning when I have to share with someone the overwhelming joy of finding out something new. 3 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Contents I Introduction 6 II Literature Review 11 1 A Historical Overview of the Dark Matter Mystery . . . . . . . . . . . . . . . . . . . 11 2 Collider Experiments and Dark Matter Direct Detection . . . . . . . . . . . . . . . . 16 3 Dark Matter Indirect Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 i Indirect Searches Conducted Thus Far . . . . . . . . . . . . . . . . . . . . . . 19 4 The Wukong WIMPs: Massive Leptophilic Majorana Particles . . . . . . . . . . . . . 20 5 Established Constraints on the Annihilation Cross-Section . . . . . . . . . . . . . . . 22 i The Relic Density Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 ii The Planck CMB constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 iii The LEP Collider Constraints on Z’, the Mediator Particle . . . . . . . . . . . 24 iv The Dark Matter Direct Detection Constraints . . . . . . . . . . . . . . . . . . 25 6 Existing Multi-messenger Dark Matter Indirect Detection Constraints . . . . . . . . 27 i ATCA Indirect Radio Search in Reticulum II . . . . . . . . . . . . . . . . . . . 27 ii Super-Kamiokande Indirect Neutrino Search in MW Halo and Centre . . . . 28 iii ASKAP/EMU Indirect Radio Search in the Large Magellanic Cloud . . . . . 29 iv The DAMPE Excess Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 7 Established Constraints upon the Decay Rate . . . . . . . . . . . . . . . . . . . . . . . 31 i Isotropic Gamma Ray Background Indirect Search . . . . . . . . . . . . . . . 31 8 Dwarf Spheroidal Galaxies as Target Objects for DM Indirect Detection . . . . . . . 32 9 Unprecedented Detection Capabilities of Next-Generation Telescopes . . . . . . . . 33 i CTA and LHAASO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ii KM3NeT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 iii MeerKAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 III Theoretical Basis for Research 36 1 Dwarf Spheroidal Galaxy Density Profiles . . . . . . . . . . . . . . . . . . . . . . . . . 36 2 The Astrophysical J- and D-factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3 WIMP Velocity-Averaged Annihilation Cross-Section . . . . . . . . . . . . . . . . . . 38 i Derivation of 3l Democratic Annihilation Constraints . . . . . . . . . . . . . . 39 4 WIMP Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 i Derivation of 3l Democratic Decay Rate Constraints . . . . . . . . . . . . . . 40 5 Accounting for Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6 Radio Wave Production from Synchrotron Emission . . . . . . . . . . . . . . . . . . . 42 7 WIMP Mean Free Path and Mean Annihilation Period . . . . . . . . . . . . . . . . . 44 IV Implementation of Theory 47 1 Choice of Target Dwarf Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 i Sculptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 ii Sextans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 iii Segue I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 iv Tucana II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 v Reticulum II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 vi Triangulum II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 vii Overview of Selected Target Objects . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 2 Annihilation and Decay Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3 Importing Established Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Imposing Constraints in the Gamma Ray Domain: CTA and LHAASO . . . . . . . . 55 5 Imposing Constraints in the Neutrino Domain: KM3NeT . . . . . . . . . . . . . . . . 56 6 Imposing Constraints in the Radio Domain: MeerKAT . . . . . . . . . . . . . . . . . 56 i Halo Density Profile Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 57 ii Electron Gas Density Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 iii Magnetic Field Spatial Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 iv Diffusion Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 7 Interpreting the Mean Free Path and Mean Annihilation Period Limits . . . . . . . . 59 8 The Potential of Multi-Messenger Astronomy . . . . . . . . . . . . . . . . . . . . . . 60 V Results and Discussion 61 1 LHAASO and CTA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 i Annihilation Cross-Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 ii Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 iii Mean Free Path and Mean Annihilation Period . . . . . . . . . . . . . . . . . 68 2 KM3NeT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 i Annihilation Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 ii Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 iii Mean Free Path and Mean Annihilation Period . . . . . . . . . . . . . . . . . 77 3 MeerKAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 i Annihilation Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 ii Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 iii Mean Free Path and Mean Annihilation Period . . . . . . . . . . . . . . . . . 83 4 Analysis of MFP and MAP Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5 Multi-messenger Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 i Segue 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 ii Reticulum II and Sculptor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 VI Summary and Conclusions 91 VII Appendices 93 1 Appendix A: Alternate Explanations for the DAMPE Excess Flux . . . . . . . . . . . 93 2 Appendix B: Empirical Scaling Relations for J- and D-Factors . . . . . . . . . . . . . 93 3 Appendix C: D-factor Relation at the Virial Radius Boundary . . . . . . . . . . . . . 94 4 Appendix D: Literature Review on Alternative Dark Matter models to WIMPs . . . 95 i Sterile Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 ii Modified Newtonian Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 95 iii Axions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5 Appendix E: Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 i WIMP Annihilation Cross-Section . . . . . . . . . . . . . . . . . . . . . . . . . 97 ii WIMP Decay Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 iii WIMP Mean Free Path and Mean Annihilation Period . . . . . . . . . . . . . 97 6 Appendix F: Table Cross-Referencing Dark Matter History Timeline . . . . . . . . . 99 References 100 5 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 I. Introduction Dark Matter (DM) dominates the matter content of the Cosmos, from the galactic scale to that of the particle horizon, yet questions around its nature and properties remain open and pressing. First suggested over 80 years ago by Fritz Zwicky [1], DM constitutes approximately 25 percent of all mass-energy in the Universe [2]. Since Zwicky’s observation of the Coma Cluster’s missing mass in the early 1930s [1], anomalies from different sources - multiple observations of unexpected galaxy rotation curves as in [3], along with the studies of the stability of disk galaxies as in [4], began to necessitate the existence of an unobserved DM halo, as suggested by Zwicky [1]. More- over, in order to account for observations of the Cosmic Microwave Background (CMB) radiation (see [5] [6] [7]) and to account for structure formation in the early Universe, the existence of an unobserved ’Cosmological Dark Matter’, which constitutes the majority of the Universe’s mass content, became necessary [8]. The interactions of this substance with ordinary (Baryonic) matter are overwhelmingly and primarily through gravitation, and so the gravitational implications of its existence alone can theoretically account for the aforementioned gravitational anomalies observed through the 20th Century [9]. However, beyond its bulk mass properties, we have no firm understanding of this mysterious, invisible substance. A number of hypothetical extensions to the Standard Model that conceptualise DM as a particle have been proposed, notably with the introduction in 1977 of heavy neutral particles which would have observable interactions on the scale of the Weak force [10] [11]. This Weakly Interacting Massive Particle (WIMP) hypothesis is the most extensively studied contender for particle DM and is the DM model under consideration in this work [2]. Yet with each passing experiment, the empirical ground is shrinking beneath its feet. Collider searches [12] [13] [14] and Direct detection experiments [15] [16] [17] have thus far failed to detect any WIMPs, ruling out the hypothetical particle over significant mass ranges and imposing stringent constraints, particularly with respect to WIMPs that couple to Standard Model (SM) Hadrons. This led to the postulation of DM particles with no hadronic interactions, interacting exclusively with Standard Model (SM) leptons at tree-level, as laid out in [2]. DM indirect detection is capable of constraining the annihilation cross-section and decay rate of these Leptophilic WIMPs by searching for the products of DM Annihilation and Decay. A set of such Leptophilic WIMP models [18] [19] [20] were put forward to account for the detection of the excess electron/positron flux at approximately 1.4 TeV by Wukong, the Dark Matter Particle Explorer, in 2017 [21]. These models must now be tested in the context of new observational targets. The dwarf spheroidal galaxies which orbit the Milky Way are chosen as observational targets for the multi-messenger indirect search. These ancient dwarf spheroidal galaxies are DM dominated, with high mass-to-luminosity ratios, and are thus prime targets of observation for multi-messenger indirect DM searches [22]. Through simulating the expected indirect emissions from DM annihilation or decay in the gamma ray, radio and neutrino domains, we can utilize the predicted sensitivities of upcoming multi-messenger experiments, including the expected performance of MeerKAT, to calculate non-detection constraints by these next-generation telescopes. The projected non-detection upper limits upon⟨σv⟩ψ are compared to those imposed by previous searches using ATCA in radio [23] and Super-Kamiokande in neutrinos [24]. Projected non-detection constraints by LHAASO are also calculated as a point of comparison. The constraints imposed are a metric of both the suitability of 6 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Ultrafaint dwarf spheroidal galaxies as suitable observational targets for DM indirect detection, along with the large extent to which detector sensitivities, in multiple observational domains, have improved, allowing them to probe deeper into the nature of DM through indirect detection experiments. Through calculating the consequences of non-detection for multi-messenger observations in the case of each target dwarf galaxy, we can suggest the optimal combinations of telescope and target galaxy to impose the most stringent constraints upon the WIMP parameter space, primarily with respect to the Annihilation channel, since the Decay channel is highly suppressed in the WIMP model under consideration. We nonetheless calculate the decay rate upper limits and utilise the Γψ non-detection constraint from the Fermi indirect search in the Isotropic Gamma Ray Background as a point of comparison [25]. The large extent to which the Decay channel has been suppressed can be contextualised through comparison of the Decay lifetime (the inverse of the Decay rate) to the Hubble time. In order to afford us a similar point of comparison for the Annihilation channel, we derive equations for the Mean Free Path (⟨λ⟩ψ) and Mean Annihilation Period ( ⟨T⟩ψ ) for a DM par- ticle in a particular Halo, as a function of both the particle’s velocity-averaged Annihilation cross-section and the global properties of the Halo environment. Through linking the particle physics to the physics governing the macroscopic properties of the Halo, we can describe the kinematic behaviour of the WIMPs, calculating the Mean Annihilation Period and affording us a physical interpretation of the Annihilation cross-section constraints. Like the Decay lifetime, the Mean Annihilation Period can be contextualised through comparison to the age of the universe. This work begins with a a review of the relevant body of literature in Chapter 2, beginning with a sub-chapter synthesising the salient points in the history of the Dark Matter mystery into a coherent historical overview of the Dark Matter paradigm and the means through which we’ve attempted to solve the Mystery of the Missing Mass, along with the testable consequences of these hypotheses and the extent to which they have been empirically constrained. The literature review thereafter expands and elaborates upon aspects of the historical overview in the first sub-chapter, beginning with a sub-chapter on Collider searches and Direct detection experiments, followed by a sub-chapter on indirect detection, juxtaposed by the preceding sub-chapter to motivate indirect detection as a means through which we can probe the remaining regions of the WIMP parameter space which cannot be probed by Collider and Direct detection experiments. In the next sub-chapter, our analysis on DM indirect detection is extended through considera- tion of the unexplained e−/e+ flux detected by Wukong in 2017 [21], along with the Leptophilic WIMP models proposed to explain the flux [18] [19] [20]. This is followed by a sub-chapter explor- ing existing empirical constraints upon the annihilation channel, imposed by Collider searches, Direct detection and indirect detection. Similarly, the subsequent sub-chapter considers existing constraints upon the Decay channel. In the final two sub-chapters of the literature review, we investigate the suitability of dwarf spheroidal galaxies as observational targets for DM indirect detection and subsequently investigate the discovery potential of next-generation telescopes with unprecedented sensitivities in the gamma ray, radio and neutrino domains. Chapter three focuses on the theoretical basis of the research, investigating different halo density profiles, conceptualising and defining the astrophysical J- and D-factors, reproducing the derivation for ⟨σv⟩ψ and Γψ and presenting the derivation of ⟨λ⟩ψ and ⟨T⟩ψ . In the neutrino 7 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 domain, we also derive equations which account for neutrino oscillations and in the radio domain, it also becomes necessary to extend the theory to account for the fact that we are working with diffuse synchrotron emission, which results when electrons produced via DM Annihilation interact with the magnetic field of the Halo. Chapter four then goes on to detail the manner in which the theoretical analysis is imple- mented. In the first sub-chapter, a set of six suitable dwarf spheroidals are motivated as promising observational targets for the purposes of this work. Thereafter, the WIMP Annihilation and Decay spectra, produced using event generators, are discussed, since we utilise them for imposing constraints in the gamma ray and neutrino domains. The next sub-chapter focuses upon imposing constraints with CTA and LHAASO, detailing how the Annihilation and Decay spectra, along with the sensitivity data for the respective telescope, are combined to calculate the projected non-detection constraints for both instruments in the gamma ray domain. The following sub-chapter focuses upon KM3NeT, with the implementation process differing for telescopes operating within different observational domains. Therefore, the implementation in the neutrino domain differs from the implementation process for CTA and LHAASO, both of which operate within the gamma ray domain. In the case of KM3NeT, the phenomenon of neutrino oscillations must be taken into account when calculating the non-detection constraints. This is achieved through the amendment of the equations for ⟨σv⟩ψ and Γψ to reflect the influence of oscillations. These amended equations are then solved, utilising the KM3NeT sensitivity data, to produce the constraints imposed upon the WIMP parameters in the case of non-detection by the KM3NeT. The implementation process for MeerKAT differs substantially from those in the gamma ray and neutrino domains, since we are searching for synchrotron emission in the radio domain, resulting from the hypothetical production of relativistic electrons through the Annihilation of Leptophilic WIMPs and the subsequent interaction between the electron and the magnetic field of the DM Halo under consideration. Therefore, imposing non-detection constraints in the radio domain requires for us to provide additional information concerning the properties of the Halo environment, including its magnetic field profile, electron gas profile and diffusion environment. In order to compute the constraints imposed by the non-detection of synchrotron emission by MeerKAT, we must again solve amended equations for the WIMP Annihilation cross-section and Decay rate, which must now take into account the necessary theoretical extension required in order to impose constraints in the radio domain. Having established the methodology for computing constraints in the gamma ray, neutrino and radio domains respectively, a strategy is then formulated for conducting a multi-messenger analysis, comparing the constraints imposed by non-detection for observations with CTA, KM3NeT and MeerKAT, for cases where the chosen target dwarf spheroidal is within the fields of view of our multi-messenger telescopes. The final sub-chapter of Chapter four proposes a strategy for interpreting the bounds on the Mean Free Path and Mean Annihilation Period, both of which are calculated using the equations derived in this work. Chapter five presents the results and discussions of the projected multi-messenger non- detection constraints, beginning with the non-detection constraints imposed by CTA and LHAASO in the gamma ray domain. This is followed by the projected non-detection constraints using KM3NeT in the neutrino domain and MeerKAT in the radio domain. A multi-messenger analysis 8 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 is thereafter conducted, comparing the bounds imposed by non-detection utilising the telescopes under consideration in this work, each of which operates within a specific observational domain. The final set of results are obtained by setting ⟨σv⟩ψ to a constant value (which we have chosen as the canonical Annihilation cross-section) and thereafter computing both the Mean Free Path and the Mean Annihilation Period for a subset of dwarf spheroidals, at both the scale and virial radii, utilising the equations derived in this work. These MFP and MAP results are then interpreted through comparison to the Hubble distance and the Hubble time, along with the lower limits imposed upon the WIMP lifetime, τψ. Chapter six goes on to summarise the body of work, highlighting and contextualising its most crucial tenets. The salient conclusions of this work (which are considered in relation to the aims and objectives outlined in the sub-section following this introduction) are also highlighted and situated within the evolving, mysterious Dark Matter paradigm. In the Appendices, Appendix A investigates alternative, non-Dark Matter explanations for the excess flux detected by Wukong in [21]. Appendix B explores the empirical scaling relations for the J- and D-factors presented in [26], while Appendix C considers the calculated D-factors at the Halo virial radius, solving the equation which emerges from those derived in this work for the WIMP MFP and MAP. Appendix D conducts a brief review of alternative DM hypotheses to WIMPs, while Appendix E presents the error analysis for this work. 9 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Aims and Objectives • Explore the historical search for Dark Matter, the evidence for its existence and the trajectory of the Dark Matter mystery to the present day. • Investigate the potential of DM indirect detection, in contrast to DM Direct detection and Collider experiments, in honing in on the properties of DM. • Investigate dwarf spheroidal galaxies, particularly the Ultrafaints, as target environments for DM indirect detection and based upon this investigation, accounting in particular for the astrophysical J- and D- factors, to select a sample DM-dominant dwarf spheroidals as suitable observational targets for multi-messenger astronomy. • Explore the potential of next-generation telescopes - CTA, KM3NeT and MeerKAT - for multi-messenger DM indirect detection, in the gamma ray, neutrino and radio domains, utilising published sensitivity data sets. This will be contrasted with the sensitivity of the earlier LHAASO telescope in the gamma ray domain. • Explore the various Leptophilic WIMP hypotheses put forward to excess DAMPE flux detected in 2017 and formulate a generalized model to be tested in the context of the target dwarf spheroidals. • Compute upper limits on the Velocity-Averaged Annihilation Cross Section ⟨σv⟩ψ and the Decay Rate Γψ of the Leptophilic WIMPs (ψ) imposed by non-detection in the case of the various telescopes under consideration. • Compare: The projected performance of CTA in constraining the parameter space to that of LHAASO; the projected bounds imposed by MeerKAT non-detection to prior bounds set by the indirect radio search by ATCA; the bounds imposed by projected KM3NeT non-detection to those impose by the indirect neutrino search by Super Kamiokande. • Interpret the non-detection upper bounds and their consequences for the generalised Lep- tophilic WIMP hypothesis put forward to explain the DAMPE flux, along with the WIMP hypothesis more generally. • Derive equations for the Mean Free Path ⟨λ⟩ψ and Mean Annihilation Period ⟨T⟩ψ of WIMPs in the Halo, at both the scale and virial radius, and compute lower limits imposed by non-detection in each case. Thereafter analyze and interpret these lower limits and explore their physical consequences. • Motivate strategies for observations using multi-messenger astronomy that would be optimal in further constraining the parameter space for the hypothetical DM particle. • Explore the terrain of alternate hypotheses that have been put forward as candidates for DM. 10 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 II. Literature Review 1. A Historical Overview of the Dark Matter Mystery In 1933, the Swiss Astronomer Fritz Zwicky published a paper in which he highlighted that in order to gravitationally bind the Coma Galaxy Cluster, the actual mass had to be around 2 orders of magnitude larger than the observed mass in stars [1]. Zwicky’s anomalous Coma cluster observations were simply the first of many anomalous gravitational phenomena, observed over decades, deepening the mystery of the "missing mass", which remains unsolved to this day, almost 9 decades after Zwicky’s Coma cluster observations [1] The next direct clue for DM came more than 25 years after Zwicky’s observations, utilising observations in the optical domain of the Milky Way’s neighbouring galaxy: Andromeda [3]. In 1970, Vera Rubin and Kent Ford, Jr published a spectroscopic survey of emission regions in Andromeda, producing rotation curves for Andromeda that ran contrary to expectations for a bound mass distribution [3]. Beyond a certain threshold, as the distance from the galactic centre grew, the rotational velocity remained constant [3]. Also in the early 1970s, radio astronomers at NRAO in Virginia were observing the distribution and motion of neutral hydrogen in the outer regions of galaxies [9]. In 1973, a collaboration between Morton Roberts at NRAO and Arnold Rots at the Dutch Westerbork Synthesis Radio Telescope (WSRT) discovered three galaxies with rotational curves that suggested the presence of a DM Halo with undetected mass at large distances from the galactic centre [27]. They found that the rotational velocity of the gas remains constant with distance from the galactic centre, beyond the visible edge of the galaxy, contrary to what one would expect for a bound mass distribution [9]. These galactic-scale gravitational anomalies observed in the radio domain mirror the gravitational anomalies that were detected three years prior through observations in the optical domain [3]. In the same year that the NRAO/WSRT collaboration discovered the triplet of galaxies with anomalous rotation curves [27], Ostriker and Peebles published a paper in which they claimed, supported by their N-body simulations of disk galaxies, that such galaxies cannot be rotationally- supported, and as such another, massive spheroidal component of the galaxies – an unobserved Dark Matter Halo, stretching beyond the visible region of the galaxy - must exist [4]. Taking this massive Dark Halo into consideration allows for an explanation of the anomalous galaxy rotation curves observed in both the optical [3] and radio [27] domains. Following the observational and theoretical work on the gravitational anomalies in the early 1970s, two non-Baryonic particle DM models were put forward in 1977, both of which remain contenders for the constituents of the universe’s missing mass. The first emerges from the work independently done by Lee and Weinberg on the one hand [10] and Piet Hut on the other [11]. In both [10] and [11], a new, heavy, neutral particle, which interacts on the scale of the Weak nuclear force, is introduced. This class of DM Candidates came to be known has WIMPs (Weakly Interacting Massive Particles), which is the primary DM hypothesis considered in this work. The second model introduced in 1977 follows from the work of Peccei and Quinn, who theoret- ically account for Charge Parity Conservation in the case of Strong force interactions [28] and then Weak and EM interactions [29], through introduction of a new scalar field. Although the term isn’t used explicitly in the initial papers by Peccei and Quinn, the ultra-light, bosonic quanta of 11 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 this scalar field came to be known as Axions (after a cleaning detergent) which quickly established itself as a strong candidate for particle DM [30]. Departing from the Particle DM paradigm, Mordehai Milgrom published three papers in the Astrophysical Journal in 1983, the first of which lays out a proposed modification of Newtonian dynamics (termed MOND) which would hypothetically eliminate the need for particle DM, or indeed any "missing mass" at all [31]. The second explores the consequences of MOND hypothesis for galaxies [32] and the third explores the consequences for galaxy systems [32]. In 1994, Dodelson and Widrow established another non-Baryonic particle DM candidate, Sterile, Heavy Neutrinos, by extending their model into the Cold Dark Matter (CDM) paradigm and accounting for structure formation [33]. While the Cosmic Microwave Background (CMB) was first detected in 1965 [5] and accounted for within the framework of Big Bang cosmology in the same volume of the Astrophysical Journal [6], it was decades before the anisotropies were first noticed, requiring a DM component to account for structure formation and thereby allowing for constraints to be imposed upon models for particle Dark Matter. When small fluctuations in the CMB spectrum were first observed, non-Baryonic particle DM candidates like WIMPs and Axions, which interact with photons and matter primarily through gravitation, became necessary to explain Cosmological evolution [8]. Since these hypothetical particles would be decoupled from radiation in the early Universe, this would allow for the formation of structure within the confines of a Hot Big Bang [8]. At the beginning of the 21st century, a multitude of gravitational anomalies, such as galaxy rotation curves observed in both the optical and radio domains which ran contrary to expectations, along with the necessary mass required to bind galaxy clusters and stabilise disk galaxies, had established the need DM for DM super-structures like Zwicky’s postulated Dark Halos. The CMB anisotropies further bolstered the case for Cosmological particle DM in order to account for structure formation in the universe. It is generally assumed that the Cosmological DM and the DM comprising the Halos are one and the same. Thus, with the existence of DM firmly established, experiments began to constrain the parameters characterising different DM models. Powerful particle colliders like the Large Electron-Positron (LEP) collider and CERN’s Large Hadron Collider (LHC) began to probe for physics beyond the Standard Model, attempting to detect a signal on account of the hypothetical Z’ gauge boson [12] [13] [14], which in our case mediates the interaction between the Leptophilic WIMPs and the SM Lepton. However, neither collider has detected a DM signal. In 2006, the LEP Collider announced that it found no evidence for physics beyond the SM, thereby imposing non-detection constraints upon the mass of Z’ [12]. In 2012, the CMS experiment at the LHC announced no evidence for physics beyond the SM, failing to detect (at centre-of-mass energy √ s = 7 TeV) any signal consistent with the existence of Z’, thereby strengthening bounds on the parameter space of the mediator boson [13]. In 2014, the LHC’s ATLAS experiment confirmed the CMS experiment’s non-detection of a signal indicating physics beyond the SM [14]. The ATLAS results include those at √ s = 8 TeV and so the bounds on the Z’ parameter space are further strengthened [14]. In light of the failure of Collider experiments to detect a DM signal, Direct detection ex- periments like PANDAX-II, LUX and XENON1T offer another avenue to probe the parameter space. They rely upon the detection of local WIMP-Nucleon scattering events in the detector, 12 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 presupposing a WIMP with Hadronic interactions [2]. However, in all three cases, no DM signal has been detected. In 2016, the PANDAX-II collaboration announced that in its first 98.7 days of data, no sig- nal consistent with the existence of WIMPs was detected [17]. The following year, the Large Underground Xenon (LUX) collaboration announced that it too had found no evidence for WIMP- nucleon scattering events [15]. In 2018, the XENON1T experiment announced its failure to detect WIMP-nucleon scattering events as well, producing the most stringent Direct detection constraints upon the WIMP parameter space [16] [34]. Given the consecutive failures by the aforementioned Collider and Direct detection experiments to identify a DM signal, the development of a third avenue - DM indirect detection, employing observational astronomy to detect the products of DM Annihilation or Decay - was a needed one. Indirect searches can potentially probe the WIMP parameter space more deeply than is possible with terrestrial methods like Collider and Direct detection experiments. Some part of the discovery potential for Indirect detection is reliant upon the choice of a DM- dominated observational target, with the sensitivity of the respective telescope apparatus serving as a limiting factor in constraining the WIMP parameter space. Over the past decade, several Indirect searches, observing a range of target environments, utilising a number of telescopes in different observational domains, have been conducted. However, as was the case for the Collider and Direct detection experiments, no DM signal has been detected to date. In 2017, an indirect radio search was carried out using the Australia Telescope Compact Array (ATCA), detecting no diffuse synchotron emission from the Ultrafaint dwarf spheroidal galaxy Reticulum II [23], which is also an observational target in this work. In 2020, the Super- Kamiokande collaboration conducted an Indirect neutrino search in 20 years of observational data of the Milky Way halo and centre, finding no DM signal and imposing new upper bounds on ⟨σv⟩ψ for a multitude of Annihilation channels, across a broad mass range [24]. In 2019, a deep indirect gamma search using Fermi, this time with the observational target as Isotropic Gamma Ray Background (GRB), failed to detect a WIMP signal, consequently driving the Decay Rate upper limits downwards and equivalently driving the WIMP mean lifetime lower limits upwards, further illustrating the extreme extent to which the Decay channel has been suppressed [25]. In 2021, Regis et. al. performed an indirect radio search in the Large Magellanic Cloud (LMC) [35]. In line with the Evolutionary Map of the Universe (EMU) survey, they process a deep image taken by ATCA and find no signal that would indicate the occurrence of WIMP Annihilation inside the LMC, thus imposing significant constraints upon the parameter space - eliminating all WIMPs with a mass below 480 GeV, along with all WIMPS which interact with quarks [35]. Thus, it is empirically established in [35] that WIMP-nucleon scattering events cannot occur, since that would require quark interactions and so this result poses challenges to Direct detection experiments which rely upon these interactions. Therefore, the result in [35] is also a vindication of the successive WIMP non-detection results from PANDAX-II [17], LUX [15] and Xenon1T [16]. A key component of the method for DM Indirect detection relies upon the detection of unexplained astrophysical fluxes, with DM models fit to the data so as to account for the unknown signal, which is presupposed to be a consequence of WIMP Annihilation or Decay [2]. As seen in Figure 13 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 1, one such excess e−/e+ flux at ∼ 1.4 TeV was detected by Wukong, China’s DArk Matter Partlice Explorer (DAMPE) in 2017 [21]. Following the DAMPE announcement of the excess flux, a number of TeV WIMP models (such as those in [18] [19] and [20]) were fit to the data, accounting for the previously-established constraints upon the WIMP parameter space. The TeV WIMP models put forward in [18] [19] and [20] to explain the excess DAMPE flux all share a significant characteristic - these WIMPs are Leptophilic. The Leptophilic WIMPS interact (via a TeV Z’ mediator boson) exclusively with electrons, muons and tauons, together with their associated neutrino flavours and all respective anti-particle counterparts [2]. Given that the decade prior featured the successive failures of both collider and direct detection experiments to detect a WIMP signal, the parameter space was quickly shrinking for WIMPs with Hadronic interactions [2]. Therefore, it is unsurprising that the models feature Leptophilic WIMPs, since both PANDAX-II [17] and LUX [15] had already announced the non-detection of a WIMP signal by their respective Direct detection experiments at the time when the DAMPE excess flux was detected in 2017 [21]. The 2021 Indirect radio search in the LMC extended this analysis to empirically rule out all WIMPs hypotheses with quark interactions [35]. Therefore, if WIMPs are truly the constituent particles of Dark Matter, then they can have no interactions with quarks. The Leptophilic WIMP models proposed in the wake of the DAMPE excess flux were initially introduced to relax the stringent constraints upon the parameter space of WIMPs with Hadronic interactions - constraints that were imposed by consecutive failures to detect a DM signal by Collider and Direct detection experiments. Given the result in [35], WIMPs are now necessarily Leptophilic, as presumed by the authors of the TeV WIMP models that were proposed to explain the detection of the anomalous e−/e+ excess flux detected by DAMPE in 2017. Among the many instances of WIMP non-detection since the turn of the century is a single, controversial positive result from the DAMA/LIBRA experiment in 2008, claiming to have detected a seasonal variation consistent with the movement of the solar system through the distribution of (non-relativistic, CDM) WIMPs in the Milky Way Halo [36]. More than a decade later, the ANAIS direct detection experiment performed a model-independent test of the DAMA/LIBRA positive result, utilising the same NaI target medium and Photo-Multiplier Tube detection mechanism [37]. Having taken measurements in the same energy range as the DAMA/LIBRA experiment, the ANAIS experiment announced in 2021 a failure to detect the seasonal modulation reported by DAMA/LIBRA [36], with the results found to be inconsistent at a statistical significance of at least 2.6σ [37]. Therefore, the single positive DAMA/LIBRA result in [36] has been proven by the ANAIS experiment [37], with a high probability, to be a false positive. This is consistent with the failure of every other direct detection experiment, indirect detection experiment and collider search to detect DM and corroborate the anomalous DAMA/LIBRA result. The key events and experimental tests in Figure 1 will feature throughout this work to further elaborate upon the contemporary state of the WIMP hypothesis and to motivate the discovery potential of upcoming telescopes like CTA, KM3NeT and MeerKAT to probe the nature of DM and empirically interrogate the WIMP hypothesis through Multi-messenger indirect DM searches. 1 1Appendix F contains a table cross-referencing the references in the timeline with citations in this work’s bibliography. 14 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Figure 1: A timeline detailing the history of the Dark Matter mystery, beginning with Zwicky’s studies of the Coma Cluster in 1933 [1] and following the trajectory of the WIMP hypothesis from its inception ([10] [11]) through to consecutive failures to detect a signal indicating the existence of WIMPs by Collider experiments ([12], [13], [14]), Direct detection experiments ([15], [37], [16] and Indirect Dark Matter searches ([23], [25], [24]) being conducted in the 21st century 15 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 2. Collider Experiments and Dark Matter Direct Detection In 2006, four collaborations at the Large Electron-Positron (LEP) collider published preliminary Electroweak Measurements , in additional to preliminary Standard Model constraints, following the summer conferences at which the results of the LEP experiments were presented [12]. They find no significant experimental evidence for the existence of the Z’ boson in the data and thus derive lower limits on the mass of the hypothetical Z’ boson, mZ′ [12]. The LEP collider search will be discussed in further detail in the context of the constraints explicitly considered in the context of this work. In 2012, the CMS experiment at CERN’s Large Hadron Collider (LHC) announced the first non-observation of the Standard Model Z boson decaying to four leptons [13]. In 2014, CERN’s ATLAS experiment published their own measurements of the four-lepton production cross section, in proton-proton collisions at the Z resonance in the LHC, operating at√ s = 7 TeV and 8 TeV [14]. Figure 2: Feynman diagram of production of a Z’ boson, radiated from a Lepton in the Drell-Yann process inside a Hadron collider, with the Z’ subsequently decaying to Leptons or WIMPs, ψ (adapted from [2]) Given the failure of Collider experiments at LEP [12] and the LHC [13] [14] to provide any empirical evidence for the existence of WIMPs, Dark Matter Direct detection experiments offer an alternative, seeking to measure the recoil energy of SM nuclei, which would hypothetically arise through local scattering of the nuclei inside the detector by DM particles [2]. DM Direct detection therefore hinges upon DM-Nucleon interactions occurring within the detector medium and non-detection strongly constrains WIMP models with DM couplings to Hadrons. In 2016, the PandaX-II Direct detection experiment, housed at the China JinPing underground Laboratory (CJPL), announced the results from its first 98.7 days of collecting data[17]. Utilising a dual-phase liquid Xenon Time Projection Chamber (TPC), it allows for the reconstruction of both the energy and position of an event [17]. With a total exposure of 33 tonnes × day, the PandaX-II experiment imposes competitive, stringent upper bounds on the scattering cross section for WIMP masses in the range of 5 GeV - 1 TeV, at a Confidence Level of 90% [17]. In March of 2017, in the proceedings of the 52nd Rencontres de Moriond conference in March 2017 on Very High Energy Phenomena in the Universe, the Large Underground Xenon (LUX) 16 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 collaboration reported the results of a WIMP DM Direct detection search in data gathered by the LUX experiment [38]. The LUX Direct detection experiment is housed at the Davis Campus of the Sanford Underground Research Facility [38]. In the publication of the LUX results, the collaboration reports no WIMP signal above background, leading to stringent constraints being placed upon the spin-independent scattering cross-section [15]. Prior to the conference, the LUX collaboration published these results in the Physical Review Letters journal, elaborating upon the methodology employed in the Direct DM search [15]. As one of the Direct detection constraints explicitly considered in this work, the LUX upper bounds on Hadronic DM and its implications for the WIMP hypothesis will be discussed in further detail in a later chapter. In 2018, the XENON collaboration published the results of a WIMP Direct detection experiment using the XENON1T detector, which utilises liquid Xenon with a fiducial mass of (1300 ± 10) kg to search for DM-Nucleon scattering events between the WIMPs and the Xenon nuclei [16]. Since Xenon is a scintillator, the scattering events will result in fluorescence in the visible spec- trum, which would then be detected by Photo-Multiplier Tubes (PMTs) inside the detector[34]. DM-nuclei scattering will also result in ionization. Hence, this inert element is also used as the detector medium in both the PandaX-II and LUX experiments. Observations were performed for a total exposure time of 278.78 days, with the background rate being minimised more than any prior DM search experiment [16]. Despite the reduced background rate and the low error margins, no significant excess was detected and thus non- detection constraints are placed upon the spin-independent cross-section for (elastic) DM-Nucleon scattering σSI [16], as shown in Figure 3. Figure 3: Upper limits on the spin-independent WIMP-nucleon scattering cross section imposed by the failure of the XENON1T experiment to detect WIMPS [16], compared to the non-detection upper-limits imposed by the LUX experiment [15] and the PandaX-II experiment [17]. Among the many instances of non-detection is the anomalous positive result announced by the DAMA/LIBRA direct detection experiment in 2008, reporting the observation of an annual variation in the detection rate, which is consistent with the predictions for DM particles in a typical galactic DM Halo [36]. Located in Italy, the subterranean DAMA/LIBRA detector comprised NaI(Tl) crystal scintillators (which are highly radiopure) connected to Photo-Multiplier Tubes (PMTs), with a total detector mass of approximately 250 kg [36]. DAMA/LIBRA’s reported 17 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 detection of the predicted model-independent annual modulation is reported at an exposure of 530 kg × yr, over four annual cycles [36]. By combining the data with the results of its earlier DAMA/NaI experiment, DAMA reported the detection of DM particles in the MW galactic Halo at a Confidence Level of 8.2 σ [36]. In 2021, the ANAIS (Annual Modulation with NaI Scintillators) Collaboration in Spain pub- lished the results of a three year long DM Direct detection search [37], with the aim of a model- independent test of the DAMA/LIBRA result in [36]. This followed more than a decade of increasingly sensitive experiments failing to corroborate DAMA/LIBRA’s positive result [37]. Like the DAMA/LIBRA experiment, the subterranean ANAIS experiment utilises NaI(Tl) as the target medium, with a total detector mass of 112.5 kg in the case of ANAIS, which performed the experiment in the same energy regions, allowing for more direct comparisons to be made between the results [37]. At an effective exposure of 313.95 kg × yr, the ANAIS experiment measured modulation amplitudes which indicate the absence of any annual modulation in their data and thus their results are shown to be incompatible with the DAMA/LIBRA results at a statistical significance of at least 2.6 σ [37]. The ANAIS collaboration thereafter proceeds to devise and implement consistency checks for the methods employed in their analysis, demonstrating that their result is unbiased [37]. Even after accounting for the systematic effects, the ANAIS result remains consistent with an absence of annual modulation, with the collaboration aiming to increase the statistical significance of the result to 3 σ within its scheduled five years of operation [37]. Thus, the ANAIS result in [37] demonstrates an exceedingly high probability that the single anomalous DAMA/LIBRA positive result in [36] is due to that experiment’s systematics and not due to interactions between DM particles and the target medium in the DAMA/LIBRA detector. Given this, it is evident that, like the Collider experiments, all Dark Matter Direct detection experiments to date have failed to detect a DM signal. 18 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 3. Dark Matter Indirect Detection Dark Matter Indirect detection experiments seek to detect DM particles through detection of the secondary particles produced by their Annihilation or Decay [39]. It must account for the interplay between the "macrophysics" of the DM Halo and the "microphysics" that governs the particle interactions of a DM candidate [22]. This is done through scanning the astrophysical sky for unexplained fluxes that may be accounted for by DM annihilation or decay [2]. Hypotheses are subsequently put forward to explain the flux, fit to the data and a DM candidate particle is posited with properties that can be independently tested in the context of new observational targets. The candidate particle must also be consistent with prior constraints placed upon the parameter space for the particle DM model, which is the WIMP hypothesis in our case. Given the failure of Direct detection and Collider experiments to shed light on the properties of DM, Indirect detection provides us with an exciting and promising alternate avenue to probe the nature of DM. Nascent astrophysical experiments like the CTA, KM3NeT and SKA (including MeerKAT) have unprecedented sensitivities, providing a new generation of telescopes for DM Indirect detection. i Indirect Searches Conducted Thus Far In 2017, Regis, Richter and Colafrancesco presented a deep radio search, conducted by the Australia Telescope Compact Array (ATCA), in the Reticulum II dwarf spheroidal galaxy [23]. The search found no evidence for a diffuse radio emission due to synchrotron emission from DM annihilation or decay [23]. They therefore place novel constraints/bounds upon the WIMP parameter space [23]. In 2019, Blanco et. al. published an indirect gamma ray search utilising Fermi observations of the Isotropic Gamma Ray Background. Stringent non-detection upper limits are placed upon the Decay rate, further establishing the relative stability of WIMPs. [25]. The Isotropic GRB search constraints in [25] are considered explicitly as a point of reference in this work and will be discussed in further detail in a later chapter. In 2020, the Super-Kamiokande collaboration presented a search for excess neutrino interac- tions due to WIMP self-annihilation in the galactic centre or halo [24]. The reported non-detection by the neutrino search further tightens constraints on ⟨σv⟩ψ over a range of channels for WIMPs in the 1 GeV to 10 TeV range [24]. These Annihilation constraints will be considered as a point of comparison for the calculated non-detection constraints in this work and will be discussed in further detail in the following chapter. In 2021, an indirect radio search in the Large Magellanic Cloud (LMC), processing a deep image taken by ATCA as part of the Evolutionary Map of the Universe (EMU) survey, found no signal consistent with WIMP Annihilation [35]. This allows them to completely eliminate WIMPs which Annihilate to quarks and rules out all WIMPs with masses smaller than 480 GeV [35]. Several groups have recently reported an excess flux (over the expected background) in the anti-proton data from the AMS-02 detector aboard the International Space Station [40]. This excess flux is argued to be consistent with some DM annihilation signal, with the excess producing a common picture of DM properties from different DM models [40]. However, the significance of 19 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 the excess is hotly debated [40] and so will not be taken into consideration for the purposes of this work. The indirect search that is the primary focus of this work involves the detection of an excess electron/positron flux by the Dark Matter Particle Explorer (DAMPE) in late 2017 [21]. Several Leptophilic Weakly Interacting Massive Particle (WIMP) hypotheses were formulated to explain the excess, such as those contained in [18],[19], [20] and [41]. 4. The Wukong WIMPs: Massive Leptophilic Majorana Particles In late 2017, Wukong, the DArk Matter Particle Explorer (DAMPE), directly measured Cosmic Ray Electrons (plus Positrons) (CREs) in the energy range of 25 GeV - 4.6 TeV, in a setting with a low background signal and with unprecedented resolution [21]. As announced by the DAMPE collaboration, Wukong had detected an excess e−/e+ flux at approximately 1.4 TeV, as illustrated in Figure 4 [21]. Figure 4: The CRE flux spectrum (multiplied by E3 ) measured by Wukong, with a clear spectral break at approximately 1.4 TeV [21]. In Figure 4, a smoothly broken power-law model is used to fit the DAMPE data in the range of 55 GeV - 2.63 TeV, producing the dashed red line [21]. The excess flux is apparent when the DAMPE fit is compared with the measured data, represented by the red dots, with the error bars of ±1σ account for systematic and statistical uncertainties [21].This measured flux spectrum in Figure 4 is contrasted by direct CRE measurements by AMS-02 and Fermi-LAT, along with indirect measurements made by H.E.S.S [21]. A number of Weakly Interacting Massive Particle (WIMP) models, as detailed in [18], [19], [41] and [20], were posited to explain the unexplained DAMPE flux. These Leptophilic WIMPs, ψ , are theoretically defined in [2]. The models put forward following the detection of the excess Wukong flux are detailed in Table 1. All masses are quoted in TeV. 20 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Authors mψ mZ′ Particle Type Annihilation/Decay Reference Channels Fan, Huang et. al. 1.5 2.6 Vector-like fermion e−/e+ and µ−/µ+ [20] Yuan, Feng et. al. 1.5 > mψ Dirac or e−/e+ or eµτ [18] Majorana fermion Yang and Su 1.4 > mψ Dirac or e−/e+ [19] Majorana fermion Table 1: Leptophilic WIMP models posited to explain the excess Wukong flux, as detailed in [18], [19] and [20]. In Table 1, Z’ is a boson which mediates the interaction of the WIMPs with SM leptons, while eµτ refers to the 3l democratic case, with equal pairing to each lepton channel. In this work, we adopt a model independent approach, considering WIMPs ψ that possesses the following common features of the models above: • They are Leptophilic, that is, they interact, at tree level, exclusively with Standard Model leptons (electrons, muons and tauons, along with their associated neutrinos) - and their associated anti-particles [2]. • They couple to the leptons via a heavy bosonic mediator particle Z’. • Their masses are on the TeV scale, as are the masses of Z’, with mZ′ > mψ. • They are spin-half Fermions. • They are Majorana particles, identical to their anti-particles and thus self-Annihilating We thus term these particular WIMPs Massive Leptophilic Majorana Particles (MLMPs) which interact on the scale of the Weak force. The Feynman diagram for MLMP self-annihilation into SM Leptons is presented in Figure 5. Figure 5: Feynman diagram for MLMP Annihilation (adapted from [2]) This work aims to test and constrain this generalised MLMP model, calculating projected non-detection bounds in the 1 TeV to 2 TeV range utilising multi-messenger observations of prime target objects by a number of next-generation telescopes. 21 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 5. Established Constraints on the Annihilation Cross-Section We consider the constraints accounted for in [20] - the 2015 Planck CMB constraints [7], the DM Relic Density bound [42], the LEP Z’ constraints [12] and the LUX Direct detection constraints [15] fit to the DAMPE flux as in [20]. We also consider the constraints imposed by the Indirect radio search in Reticulum II using the Australia Telescope Compact Array [23], the constraints imposed by the Super-Kamiokande Indirect neutrino search in the MW Halo and Centre [24] and the constraints imposed by the ASKAP/EMU radio search in the LMC [35]. i The Relic Density Constraints In 1977, astrophysicist Piet Hut [10] on one hand and Lee and Weinberg on the other [11] indepen- dently derived cosmological lower bounds between 1 and 5 GeV on the masses of heavy leptons which are neutral and interact weakly - in two senses, describing both the relative strength of the DM particle interactions, which are extremely low, along with the fact that the particle interactions occur on the scale of the Weak Force. Although neither of the authors of [10] nor [11] intended to put forward a hypothetical non-Baryonic particle model to account for the mounting evidence of the existence of DM, their work nonetheless heralded the birth of the Weakly Interacting Massive Particle (WIMP) Dark Matter hypothesis considered in this work, along with dawn of the field of Astro-Particle Physics [8]. The ’canonical’ thermal cross-section (usually quoted as ⟨σv⟩ψ ≈ 3 × 10−26cm3s−1) is the WIMP Annihilation cross-section required to account for the observed relic DM abundance, within the framework of Big Bang Cosmology, assuming s-wave Annihilation [42] [7]. The authors of [42] calculate the precise value of the thermal relic cross section as ⟨σv⟩ψ = 2.2 × 10−26cm3s−1 for WIMP masses above 10 GeV. Since we are working in this mass-energy range, we can thus state the relation between the canonical cross section and the DM relic density mathematically, following the form in [43]: Ωψh2 = 2.2 × 10−26cm3s−1 ⟨σv⟩ψ (1) where Ωψ is the observed cosmological DM density parameter and h is the reduced Hubble constant. ii The Planck CMB constraints In 1965, Penzias and Wilson reported the detection of an excess antenna temperature at 3.5 K, utilizing the 20-foot horn-reflector at the Crawford Hill Laboratory [5]. The radio signal was reported to be isotropic, free from seasonal variations and unpolarized [5]. Concurrently, in the same volume of the Astrophysical Journal, Peebles, Dicke, Roll and Wilkinson published a paper putting forward a possible explanation for the radio signal which situates it within Big Bang Cosmology [6]. In 2015, the Planck collaboration published updated Cosmological Parameters derived from observations of the CMB with the space-based telescope [7]. The updated results helped to further reconcile the empirically calculated parameters, which characterise the features of our universe as a totality, with respect to the theoretical predictions for these parameters from the standard 22 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 ΛCDM Cosmological model [7]. During the early history of the universe, the injection of energy from Annihilating DM particles would have altered the event of recombination in a substantial manner, leaving a detectable imprint upon the CMB in the form of anistropies in the temperature, power and polarisation spectra of the CMB [7]. During this era of recombination, the particle cascades which result from WIMP Annihilation determine the heating and ionization of the surrounding gaseous medium [7]. Of particular interest are the e−/e+ pairs, along with photons, produced through Annihilation, since they can couple to the ambient gaseous background [7]. To address this, the proportion of the rest mass/energy which is transferred to the gaseous medium is modelled by a dimensionless, redshift-dependent efficiency factor, f (z) , ranging between 0.01 and 1 [7]. They parameterise the effects of DM Annihilation by defining an Annihilation parameter, dependent on the redshift parameter and explicitly dependent on both the the WIMP mass and Annihilation cross-section [7]: pann ( z, mψ, ⟨σv⟩ψ ) = f (z) ⟨σv⟩ψ mψ (2) They set the efficiency factor to a constant feff , where every Annihilation channel has a corresponding efficiency factor [7]. Thus, the Annihilation parameter contains information on every parameter relevant to the Annihilating WIMP, allowing for the projection of the constraints upon pann for a particular WIMP model [7], where one can simply solve Equation 2 for ⟨σv⟩ψ , a specified Annihilation channel and mass range. Since the effect of DM Annihilation peaks at z ≈ 600 , they utilise this value of the cosmological redshift [7]. Given the proportionality of the Cosmological mass density, ρm, to (1 + z)3 , this corresponds to an epoch where the mass density of the universe was more than 8 orders of magnitude greater than its current value. Through constraining the Annihilation parameter, they find that the Planck TT spectra alone imposes the weakest constraints (which are upper limits at a 95% confidence level), due to the fact that WIMP Annihilation would act to increase the width of last scattering, thereby suppressing amplitude peaks in the temperature spectrum[7]. The strongest constraints are imposed in the case of the full Planck temperature and polarization likelihood (TT, TE, EE + lowP) [7] and the projection of these constraints upon particular DM models produces the plot in Figure 6. 23 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Figure 6: Constraints (at a 95 % Confidence Level) imposed upon ⟨σv⟩ψ at recombination (multiplied by the relevant efficiency factor), resulting from non-detection of a WIMP signal in the CMB anisotropies measured by Planck in 2015 [7]. In Figure 6, the constant efficiency factors used for the respective leptonic Annihilation channels are taken from the results of a 2009 paper which calculates the constraints imposed upon WIMP Annihilation by observations of the CMB [44]. The results for the efficiency factor at a particular WIMP mass (also referred to as the "deposited power fraction") as a function of the redshift z is given in figure 4 of [44], where we focus only on the plots in the bottom two panels, since they concern WIMPs that couple to leptons via a bosonic mediator, as do the generalised Leptophilic WIMPs under consideration in this work. The efficiency factors for the leptonic channels are [44]: • e−/e+ channel: fe f f ≈ 0.60 • µ−/µ+ channel: fe f f ≈ 0.20 • τ−/τ+ channel: fe f f ≈ 0.15 Thus, the Thermal Relic cross-section bound appears as a red band and not a single line, with the upper red line being consistent with 10 GeV WIMPs Annihilating into e−/e+ pairs, where f e e f f = 0.67 [7]. The shaded blue area in the upper left of the plot in Figure 6 denotes the parameter space empirically ruled out by non-detection of a WIMP DM signal in the CMB Anisotropies [7]. Therefore, at a Confidence Level of 95 %, the Planck non-detection results eliminate WIMP models with mψ ≤ 44GeV for Annihilation via the e−/e+ channel [7]. This is evident from the intersection between the upper red line, for the e−/e+ channel Thermal Relic limit, and the dark blue line on the border of the shaded area denoting the parameter space excluded by Planck, since ⟨σv⟩ψ for WIMPs at lower masses than 44 GeV produce cross section bounds which cannot account for the relic density of Dark Matter. Similarly, using the efficiency factors quoted above, WIMPs with mψ ≤ 16 GeV are excluded for the µ−/µ+ Annihilation channel and WIMPs with mψ ≤ 11 GeV are excluded for the τ−/τ+ Annihilation channel [7]. Therefore, for the purposes of the Leptohilic WIMP hypothesis under consideration, we know that our hypothetical WIMPs must be on the order 10 GeV or greater. iii The LEP Collider Constraints on Z’, the Mediator Particle The authors of [12] fit the LEP experimental data to models involving a additional neutral, heavy boson Z’, utilising both the Leptonic forward-backward asymmetries and the combined 24 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 cross-sections in the hadronic and leptonic cases, as presented in Figure 7. Figure 7: Lower limits imposed upon mZ′ by the LEP fit, at a confidence level of 95% [12] In deriving the constraints, they set the mixing angle between the ordinary Z boson and Z’ as ΘZZ′ = 0, based on the results of a single experiment, fit to LEP-I data [12]. In the left panel of Figure 7, the ν , χ and ψ variables denote particular Grand Unified Theory models featuring the additional Z’ boson, as further laid out in [12]. The right panel displays the constraints imposed in the case of Left-Right models, with the mass of Z’ plotted as a function of the dimensionless model parameter, αLR [12]. As can be seen in both panels of Figure 7, across the respective domains of all models concerned, mZ′ must exceed 300 GeV at the very least. Thus, the TeV WIMP models considered in this work, with mZ′ > mψ , are consistent with the calculated LEP lower bounds on the mass of the Z’ mediator particle [45]. iv The Dark Matter Direct Detection Constraints In the parameter space derived from the Wukong fit in [20] and presented in Figure 12, the only DM Direct detection constraints considered are those imposed as a consequence of the reported non-detection by LUX in 2017 [15][38], which are more stringent than those imposed by by the prior PandaX-II experiment. Like the PandaX-II detector detailed in [17], LUX utilises a dual-phase Xenon TPC, with the active detector volume containing 250 kg of ulltrapure liquid Xenon [15]. In order to reduce background noise, the LUX detector is located around one kilometer beneath the surface of the earth [15]. With a total of exposure of 33.5 tonnes × day [15], LUX gathered data from 2012, when the Davis Campus was opened, to 2016, when the experiment was decommissioned [38]. At a 90% confidence level, the LUX non-detection results impose strong upper limits, on the order of 10−46cm2 for 50 GeV WIMPs [38]. The upper bounds upon the spin-independent WIMP-Nucleon scattering cross-section, across a mass-energy range which spans more than four orders of magnitude, are presented in Figure 8. 25 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 Figure 8: Non-detection constraints upon the (spin-independent) WIMP-Nucleon scattering cross-section imposed by the LUX experiment across a mass-energy range spanning 5 orders of magnitude, extending up until 100 TeV [15], in comparison to weaker bounds imposed by earlier Direct detection experiments, including the 2016 PandaX-II search [17]. In August of 2017, a study was published in Physics Letters B on Hadronic probes of hypothet- ical WIMPs, which couple exclusively to SM leptons via a heavy Z’ boson mediator particle [46]. Utilising both the LUX data and projections for the LUX-ZEPLIN experiment, set to replace the now-decommissioned LUX experiment, the authors derive novel constraints upon the Annihilation Cross-section of the Leptophilic WIMPS, which are more relaxed than the constraints placed on Hadronic DM by non-detection by direct detection experiments [46]. This Leptophilic species of WIMP is the subject of study in this work. It’s noteworthy that the lower bounds imposed by non-detection in the case of the Xenon1T experiment [16], as presented in Figure 3, are more stringent than those imposed by both PandaX-II [17] and LUX [15] [38]. However, at the time of the detection of the Wukong flux [21] and the subsequent publication of the Leptophilic WIMP model, fit to the DAMPE flux presented in [20], the Xenon1T non-detection result in [16] had yet to be announced. 26 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 6. Existing Multi-messenger Dark Matter Indirect Detection Constraints i ATCA Indirect Radio Search in Reticulum II In 2017, Regis et. al. presented an Indirect radio search using ATCA, searching for synchrotron emission resulting from WIMP Annihilation or Decay in the Reticulum II dwarf spheroidal [23]. The deep search in [23] finds no evidence for diffuse radio emission from Reticulum II and thus imposes constraints upon the WIMP parameters, particularly the Annihilation cross section, as presented in Figure 9. Figure 9: Non-detection upper bounds imposed upon a number of WIMP Annihilation channels by the ATCA Indirect radio search in Reticulum II, across a mass-energy range from 10 GeV to 10 TeV, with the DM Relic Density limit represented by the dashed black line [23]. Given that we are dealing with a Leptophilic WIMP model, we consider only the ⟨σv⟩ψ constraints imposed by the Indirect Search for the µ+/µ− Annihilation Channel [23]. The upper limits on ⟨σv⟩ψ are at a confidence level of 95% [23]. 27 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 ii Super-Kamiokande Indirect Neutrino Search in MW Halo and Centre The aforementioned Super-Kamiokande (SK) Indirect neutrino search produced 20 years (1996- 2016) of data from Super-Kamiokande-I -II -III and -IV [24]. The SK detector is a 50 kiloton detector, 22.5 kilotons of which comprise the fiducial mass housed within the Inner Detector, relying upon the detection by photo-multipliers of Cherenkov radiation, resulting from charged particles (largely leptons arising from neutrino interactions) moving through the (water) medium faster than light [24]. The observations made of the MW Centre and Halo accounted for any background due to neutrino interactions in the atmosphere [24]. Non-detection of an excess flux places novel constraints upon the Annihilation cross-section [24], presented in the bottom panel of Figure 10. Figure 10: Non-detection upper bounds imposed upon a range of DM Annihilation channels by the SK Indirect neutrino search, across a mass-energy range from 1 GeV to 10 TeV [24] In Figure 10, the non-detection constraints imposed by the SK Indirect search are compared to those imposed by the Antares and IceCube neutrino experiments [24]. As in the case of the Reticulum II radio search, we consider only the µ+/µ− Annihilation channel constraints imposed on ⟨σv⟩ψ by the Indirect neutrino search in [24]. 28 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 iii ASKAP/EMU Indirect Radio Search in the Large Magellanic Cloud The 2021 Indirect radio search in [35] utilises a deep image of the LMC obtained from ASKAP observations at 888 MHz (with a bandwidth of 288 MHz) and a total observation time of 12 hours and 40 minutes [35]. Utilising a J-factor of ∼ 1020 GeV2 cm−5 for the LMC, strong non-detection upper bounds are placed on the velocity-averaged Annihilation cross-section, as seen in Figure 11. Figure 11: Non-detection upper bounds imposed upon ⟨σv⟩ψ by the ASKAP/EMU radio search in the LMC for the µ−µ+ and bb Annihilation channels, across a mass-energy range from 10 GeV to 10 TeV, with the DM Relic Density limit shown as the black dashed line [35]. While the ASKAP/EMU non-detection constraints upon the bb Annihilation channel are the most stringent, we are concerned with the constraints imposed upon the µ−µ+ , since we dealing with a Leptophilic WIMP model in this work. 29 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 iv The DAMPE Excess Flux When the aforementioned constraints (excluding the Indirect radio and searches in [23] and [35] and the Indirect neutrino search in [24]) are taken into consideration and fit to the DAMPE excess flux at approximately 1.4 TeV reported in [21], the ⟨σv⟩ψ constraint contours in Figure 12 are produced. Figure 12: ⟨σv⟩ψ parameter space presented in [20], produced by fitting the excess e−/e+ flux detected by Wukong [21] to: i) The DM Relic Density constraints [42]. ii) The 2015 Planck CMB constraints [7]. iii) The 2006 LEP Collider constraints on Z’ [12]. iv) The 2017 LUX Direct detection constraints[15]. In Figure 12, the inner contour represents the constraints in [20] at a Confidence Level of 68%, while the outer contour represents constraints at a Confidence Level of 95%. 30 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 7. Established Constraints upon the Decay Rate i Isotropic Gamma Ray Background Indirect Search We account for the constraints placed upon the Decay Rate through utilising the Isotropic Gamma- Ray Background (GRB) observations by Fermi, presented in a 2019 paper published by Blanco and Hooper [25]. When considered alongside the ATCA Reticulum II radio search in [23] and the Milky Way halo neutrino search by Super-Kamiokande in [24], the Fermi Isotropic GRB constraints in [25] offers a multi-messenger benchmark, in the case of both Annihilation and Decay, for DM Indirect detection using existing telescopes. For a wide range of DM particle masses and annihilation channels, the authors calculate a mean life-time of the decaying DM generally in the range of τψ ∼ (1 − 5)× 1028s, which is approximately 10-11 orders of magnitude greater than the age of the universe [25]. These con- straints are made more stringent by consideration of multi-messenger analyses of the astrophysical contributions to the Isotropic GRB [25]. The immense magnitude of the mean life-time, in relation to the Hubble time, is an illustration of the severe extent to which the Decay channel is constrained. We focus on DM decay into SM Leptons as in Figure 13, accounting for the fact that the DM Decay Rate, Γψ is simply the inverse of the mean life-time calculated in [25]: Γψ− = 1 τψ (3) Hence, the lower limits calculated in [25], as displayed in Figure 13, translate to upper limits upon the Decay Rate, Γψ . Figure 13: Lower limits placed upon the DM lifetime, τψ , by observations of the Isotropic GRB by Fermi, for DM Decay across a broad range of masses into SM leptons [25]. In Figure 13, the solid curves (the upper 3 curves), which treat the systematic errors as entirely independent and uncorrelated, are taken to be the primary results [25]. The constraints are lower limits at a 95% Confidence Level [25]. 31 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 8. Dwarf Spheroidal Galaxies as Target Objects for DM Indirect Detection Dwarf spheroidal galaxies, particularly the Ultrafaints, lie at one extreme of the luminosity distri- bution, at the least luminous and massive end [22]. Alongside galaxy clusters, which lie at the other extreme (most luminous and massive) of the luminosity distribution, dwarf spheroidals are some of the most Dark Matter dominated systems in the Cosmos [22]. These DM-dominated target galaxies have high observed ratios of DM to Baryons, corresponding to high mass-to-luminosity ratios [47]. Dwarf spheroidals also have very old stellar populations (with a typical age of ∼ 10 Gyr) and those used as target environments for Indirect detection have virtually no gas associated with them, are relatively close to the Milky Way and have extremely low background in (high energy) photons, due to the absence of observable, Baryonic astrophysical processes [22]. Consequently, the DM Annihilation signals from dwarf spheroidals will be uncontaminated by Baryonic backgrounds in Gamma, Radio and Neutrinos, which make them ideal candidates for a multi-messenger Indirect search for Particle DM [48]. The dwarf spheroidal galaxies in the Local Group considered in this work (including both the Ultrafaint and ’Classical’ dwarfs) lie within the virial radius of the Milky Way Galaxy (∼ 300 kpc) and therefore orbit our galaxy as Milky Way satellites [22]. In order to ascertain the DM distributions of these MW Satellites, which are crucial for DM Indirect detection experiments, the kinematics of the luminous stars and gas is studied and analyzed [22]. It is assumed that the identified member stars of a dwarf spheroidal are unaffected by the Milky Way’s DM Halo, so that they function as ’tracers’ of the dwarf spheroidal’s local potential [22] While the MW Satellites in this work are referred to throughout as dwarf ’spheroidal’ galaxies, in actuality the Halos are generally ellipsoids that are not perfectly spherical, which may be prob- lematic when studying the stellar and gas kinematics to determine the respective DM distribution utilising a Jeans method, since these methods operate upon the assumption of spherical symmetry [22]. However, spherically symmetric modeling remains standard practice, since these models tend to provide accurate potential estimates, particularly when dealing with the central regions of the system in the limit of isotropic orbits [22] Several other systematic issues arise as well when calculating these DM distributions for dwarf spheroidals, including the possibility that the MW Satellites evolve over time as they orbit the Milky Way, along with the prospect of their member stars being stripped away by tidal forces [22]. Moreover, given that the velocity dispersions for dwarf spheroidals are extremely low and so are generally just above the detection threshhold for instruments that measure the velocities of member stars and their (intrinsic) dispersions, another challenge is faced in effectively identifying member stars and conducting a thorough kinematic analysis [22]. Nonetheless, continuing observations of dwarf galaxies, utilising a range of astrophysical techniques, have afforded us better stellar kinematic data sets, so as to refine our physical description of the dwarf spheroidal Halo environments. We can thus reduce our error margins when conducting Indirect DM searches within the Halo of the dwarf galaxy under consideration. In general, the J- (and D-) factors of the more-recently discovered Ultrafaints are larger, but have broader error margins than those of their Classical counterparts, which have been imaged over many decades and are generally more luminous than the Ultrafaints [22]. 32 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 9. Unprecedented Detection Capabilities of Next-Generation Telescopes Powerful upcoming telescopes like the Cherenkov Telescope Array (CTA), the Cubic Kilometer Neutrino Telescope (KM3NeT) and MeerKAT boast unprecedented sensitivities in their respective domains and thus allow for a strong multi-messenger astrophysical test of the MLMP models. We compare these sensitivites to the sensitivities of prior telescopes like the Large High Altitude Air Shower Observatory (LHAASO) and compare the constraints imposed by the different telescopes. i CTA and LHAASO CTA is an array of ground-based, Imaging Atmospheric Cherenkov Telescope (IACT) which detect Very High Energy (VHE, with E ≥ 200 GeV) gamma rays [49]. It consists of one IACT array in the Canary Islands in the Northern hemisphere and one array in Chile in the Southern hemisphere, with full coverage of the sky [49]. The CTA nodes detect the Cherenkov light from air showers that result from the collision of gamma rays with atmospheric particles [22]. Cherenkov telescopes like CTA are instruments that can integrate for long periods of time on individual observational targets [22]. CTA extends the mass-energy range that can be probed by Indirect searches, encompassing and extending beyond the TeV range considered in this work, with a better angular resolution than the Fermi Large Area Telescope (LAT) [22]. LHAASO is a ground-based cosmic ray and gamma ray telescope located in China [50]. Unlike CTA, which detects the Cherenkov light resulting from the primary atmospheric interaction with the incident gamma rays, LHAASO observes the effects of the secondary cosmic rays that are produced by the primary atmospheric interaction [51]. In estimating the LHAASO sensitivity, the authors of [50] utilise as a point of reference the sensitivity calculated through analysis of Fermi Bubble observations by the High Altitude Water Cherenkov (HAWC) telescope [50], as seen in Figure 14. Figure 14: Left: Sensitivity curves for CTA for a number of opening angles, from the analysis conducted in [49] Right: Sensitivity curve for LHAASO, from the analysis conducted in [50], with one year of exposure time. In in the left panel of Figure 14, the conservative sensitivity data for CTA is taken from the analysis in [49], at a minimum confidence level of 5σ and an observation time of 50 hours. We utilize the sensitivity data at an opening angle of 0.5 degrees, in line with the opening angle used in the calculation of the J- (and -D) factors. In comparison to its predecessors (H.E.S.S, MAGIC and VERITAS), CTA has a flux sensitivity that is one order of magnitude larger, with an angular 33 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 resolution of 1-2 arcminutes [49]. In the right panel of Figure 14, we see that the LHAASO sensitivity is significantly greater than that of the HAWC telescope, across a mass-energy range spanning more than 4 orders of magnitude, with a maximum mass/energy of approximately 105 TeV. It is also seen in Figure 14 that the LHAASO sensitivity notably improves with increasing energy, with the minimum sensitivity at the lower end of the mass/energy range, in the TeV region, which is the energy region of focus in this work. Therefore, the sensitivity improvement over HAWC is minimal in our mass/energy range of 1 TeV - 2 TeV and so we utilise the projected LHAASO non-detection constraints as a bench- mark for the projected non-detection constraints imposed by the next-generation telescopes: the aforementioned CTA, along with KM3NeT and MeerKAT. Existing constraints imposed by the Super-Kamiokande indirect neutrino search in the MW Halo and centre [24] and the Indirect radio search in [23] are also used as points of comparison. ii KM3NeT Located deep beneath the Mediterranean sea, the upcoming KM3NeT infrastructure, like other high energy neutrino telescopes, functions through the detection of Cherenkov radiation (produced by the interaction of the high energy neutrinos with the surrounding medium, which is primarily sea water in the case of KM3NeT) by a large three-dimensional array of photo-multiplier tubes (PMTs) [49]. The KM3NeT PMTs observe the position, time and charge deposits to infer the direction of the incoming neutrinos, along with their energies [49]. Figure 15: Sensitivity curves for Km3NeT, from the analysis conducted in [49]. As was the case with CTA, the conservative sensitivity data for KM3NeT in Figure 15 is taken from the analysis in [49], at a minimum confidence level of 3σ, with an opening angle of 0.5 ◦ and a total exposure time of 10 years [49]. The angular resolution of KM3NeT is higher than it is for CTA, with the former reaching an angular resolution of 0.2 degrees at 10 TeV [49]. iii MeerKAT The MeerKAT radio interferometry telescope infrastructure is the first phase of the Square Kilome- ter Array (SKA), located in the Karoo desert in South Africa’s Northern Cape province [52]. The 34 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 MeerKAT array currently consists of 64 radio dishes, operating within the sensitivity range of 580 - 1670 MHz [53]. The existing MeerKAT antennae will be integrated into the future SKA-1 mid telescope infrastructure, which will also be located in the Karoo and will comprise a total of 197 radio dishes [53]. The MeerKAT sensitivity plot in Figure 16 is derived using the MeerKAT Continuum Calculator 2. By accounting for the beam size, the confusion noise, scaled noise and tapered thermal noise are calculated. Figure 16: Sensitivity curves for MeerKAT (in µJy) at observation time of 20 hours respectively, at an opening angle of 0.5◦ The calculator assumes 58 radio dishes, since this is the minimum requirement for a science array. The calculator requires both the declination of the observational target, which we set to −30◦ , along with the observation time, as input parameters 3. Following [54] for the L-band sensitivity, we assume a beam size of 19.8” × 16.5”, with a total synthesis time of 20 hours. In a 2020 analysis of the SKA phase 1 sensitivity, projected constraints were calculated for the Draco dwarf, with the SKA 1-MID infrastructure demonstrating great capabilities in constraining the Annihilation parameters of WIMPs, up to mass/energy values of 10 TeV [55]. 2https://apps.sarao.ac.za/calculators/continuum 3https://skaafrica.atlassian.net/wiki/spaces/ESDKB/pages/1486750321/Sensitivity+calculators#Quick-look-tables- of-sensitivities 35 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 III. Theoretical Basis for Research 1. Dwarf Spheroidal Galaxy Density Profiles We consider different density profiles because there exists in the literature an uncertainty consider- ing the structure of dwarf spheroidal galaxies [56]. We consider the three density profiles in [57]. Einasto Density Profile In 1965, Jaan Einasto put forward a density profile which would explain the kinematic features of the Milky Way galaxy [58]. Equation 4 is a special case of the one originally put forward by Einasto, with the logarithmic density gradient set to 2 in our case [58]: ρE(r) = ρs exp ( − 2 α (( r rs )α − 1 )) (4) where: • ρs is the scale density, normalising the density profile to the virial mass of the Halo, Mvir . • rs is the scale radius. • α is the free Einasto parameter. The Einasto profile is cored, since the mass density converges as the radius tends to 0: As r → 0, ρE → ρs exp ( 2 α ) (5) It’s noteworthy that for the Einasto profile, with the scale density held constant, the density in the core region increases exponentially as the free Einasto parameter is decreased. The scale radius, where ρE = ρs for the Einasto profile, is related to the virial radius by [56]: rvir = rsCvir (6) where Cvir is the dimensionless virial concentration parameter. This relation between the scale radius and the virial radius applies to all of the density profiles under consideration in this work. Burkert Density Profile In a 1995 paper, Burkert proposes the following Halo mass density profile [59]: ρB(r) = ρs( 1 + r rs )( 1 + ( r rs )2 ) (7) The Burkert density profile, like the Einasto profile, is cored and the Burkert density tends the to scale density as the radius tends to 0. At the scale radius, the Burkert density is simply one quarter of the scale density: ρB(rs) = ρs 4 (8) 36 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 NFW Density Profile A year after the publication of the cored Berkert density profile, Navarro, Frenk and White (NFW) formulated a Halo density model, based on their earlier work with x-ray clusters, which assumed a cuspy density profile [60]. ρNFW(r) = ρs r rs ( 1 + r rs )2 (9) ρNFW(r) does not converge as the radius tends to 0, since as r → 0 , ρNFW → ∞ , illustrating the cuspy nature of the NFW Halo density profile [60]. Like the Burkert density profile given by Equation 7, the NFW density given by Equation 9 is one quarter of the scale density, ρs, when the radius is set to the scale radius, r = rs . Shortly following the publication of the NFW paper, Zhao generalised the density profile analysis as follows [61]: ρNFWz(r) = ρs( r rs )β ( 1 + r rs )3−β (10) where β is a dimensionless parameter, related to the (arbitrary) power law density profile of the core region by ρ(r) ∼ r−β with the outer regions falling off with ρ(r) ∝ r−3 [62]. We retrieve the original NFW profile in Equation 9 when β = 1. DM Halo Mass at the Half-light Radius The approximate mass at the half-light radius of the Halo is given by Equation 11, as presented in the review in [22]. Mh ≈ 4 σ2 losrh G (11) where: • σlos is the line-of-sight velocity dispersion • rh is the half-light radius • G is Newton’s Gravitational constant Equation 11 follows from a Jeans analysis, as is utilised in [26] for the calculation of the Astrophysical J- and D-factors discussed in the following chapter, which assumes a spherically symmetric Halo with a velocity dispersion that is constant with respect to the Halo radius [22]. 2. The Astrophysical J- and D-factors There are two metrics which are considered when determining the suitability of a dwarf spheroidal galaxy as a suitable target object for DM Indirect detection: the astrophysical J- and D- factors, corresponding to DM Annihilation and Decay respectively. Both are dependent on the choice of an appropriate DM mass density profile, along with the availability of kinematic data for the member stars of the dwarf spheroidals, which determine the form and accuracy of the density 37 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 profiles. They are defined as follows: The astrophysical J-factor is defined as the WIMP mass density squared, integrated over a solid angle ∆Ω = 2π[1 − cos θ], where θ is the opening angle, and along the line of sight l [63]: J = J(θ) = ∫∫ [ρψ(l, Ω)]2dl dΩ (12) Assuming a spherical DM halo, the integral of the density squared over the solid angle subtended by the halo and along the line of sight is similar to the integral of the density squared over the volume of the halo, distributed over a sphere with radius DL , where DL is the luminosity distance between the earth and the Halo under consideration. The J-factor is dependent on the density distribution of the dwarf spheroidal galaxy and is hence a feature intrinsic to the Dark Matter Halo under consideration. We can thus write the J-Factor as: J = ∫ VHalo [ρψ(r)]2 4πD2 L d3r (13) The astrophysical D-factor, which is empirically determined by kinematic observation of the motion of stars, as in [64], is similar in form to the J-factor and is given by: D = D(θ) = ∫∫ ρψ(l, Ω)dl dΩ (14) As with the J-factor, the D-factor is intrinsic to the Halo and can be written as the integral of the DM density over the volume of the halo, distributed over a sphere with radius DL : D = ∫ VHalo ρψ(r) 4πD2 L d3r (15) The suitability of a given DM Halo as a target in the search for DM self-annihilation is quantified by the Astrophysical J-factor [47], and similarly with regard to DM decay and the Astrophysical D-factor. Both the J- and D- factors account for observational factors (like DL ), as well as features intrinsic to the Halo like the density distribution. For the purposes of this work, we will take the J- and D-factors at an opening angle of θ = 0.5◦ . 3. WIMP Velocity-Averaged Annihilation Cross-Section We suppose that the Dark Matter Halos for the dwarf spheroidal galaxies are comprised of MLMPs. The source function for the annihilation of MLMPs into final state SM particles i with energy E at position r in the Halo is given by a generalisation of the source function in [65], accounting for anti-particles: Qi(E, r) = 1 2 ⟨σv⟩ψ ( ρψ(r) mψ )2 ∑ l Bl dNi l dE (16) where: • ⟨σv⟩ψ is the velocity-averaged cross-section at 0 K. • Bl is the branching function for the intermediate state, l - which signifies the Annihilation channel. 38 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 • dNi l dE is the differential yield of particle species i from WIMP Annihilation via the l channel. • ρψ(r) mψ is the number density, Nψ(r),̇ of the MLMP, ψ . The temperature is set to 0 K due to limits from quantum field theory. Since we are working with velocity-independent parameters, the Annihilation cross-section is p-wave suppressed. When each channel is studied independently, the summation in 16 is dropped and the branching function is set to unity. The flux of particles i from WIMP Annihilation in the DM halo under consideration is given by: Si(E) = ∫ VHalo Qi(E, r) 4πD2 L d3r = J 2 ⟨σv⟩ψ m2 ψ ∑ l Bl dNi l dE (17) where we have applied the definition of the Astrophysical J-factor in 13. Re-arranging Equation 17 and equating the flux of particles i to the minimum flux detectable by telescopes on earth yields the following equation for the upper limits on the velocity-averaged Annihilation cross-section of the WIMPs: ⟨σv⟩ψ = 2 m2 ψ J Smin i (E) ( ∑ l Bl dNl i dE )−1 (18) When each channel is considered in isolation, Equation 18 can be equivalently stated in terms of the Annihilation parameter pl ann in Equation 2, defined by the Planck collaboration in [7]. pl ann = f l eff mψ J Smin i (E) ( dNl i dE )−1 (19) where the dimensionless efficiency factor f l eff is set to a constant for each leptonic channel l , as further discussed in the prior chapter of this work. i Derivation of 3l Democratic Annihilation Constraints We compute the 3l democratic constraints from the constraints from each individual channel by manipulating Equation 18, setting Bl = 1 3 , as follows: ⟨σv⟩3l ψ = 2 m2 ψ J Smin i (E) ( 1 3 ( dNe i dE + dNµ i dE + dNτ i dE ))−1 (20) We now work with the inverse of the equation for ⟨σv⟩ψ in 20: 1 ⟨σv⟩3l ψ = J 6m2 ψ ( dNe i dE + dNµ i dE + dNτ i dE ) Smin i (E)−1 (21) For any single Leptonic channel f treated independently, with B f = 1 , the inverse of ⟨σv⟩ψ is given by: 1 ⟨σv⟩l ψ = J 2m2 ψ dNl i dE Smin i (E)−1 (22) Thus, the inverse of the 3l democratic velocity-averaged Annihilation cross-section in Equation 21 can be written as: 39 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 1 ⟨σv⟩3l ψ = 1 3 ( 1 ⟨σv⟩e ψ + 1 ⟨σv⟩µ ψ + 1 ⟨σv⟩τ ψ ) (23) The explicit expression for ⟨σv⟩ψ in the 3l democratic case can be found from simple algebraic manipulation of Equation 23. 4. WIMP Decay Rate The source function for DM Decay is given in [56]: Qi(E, r) = Γψ ρψ(r) mψ ∑ f B f dNi f dE (24) where [56]: • Γψ is the WIMP decay rate, our free parameter. • dNi f dE is differential yield of particle species i on account of WIMP Decay via the f channel. As before, the minimum observable flux at energy E is given by: Smun i (E) = ∫ VHalo Qi(r, E) 4πD2 L d3r = D Γψ mψ ∑ f B f dNi f dE (25) where we have employed the definition of the astrophysical D-factor in 15. Rearranging Equation 25, we have the upper limit on the WIMP Decay rate: Γψ = mψ D ( ∑ f B f dN f i dE )−1 Smin i (E) (26) i Derivation of 3l Democratic Decay Rate Constraints Similarly to the case for ⟨σv⟩ψ , we compute the 3l democratic Γψ constraints from those provided in Figure 13 by first manipulating Equation 26, setting B f = 1 3 , as follows: 1 Γ3l ψ = 1 3 D mψ ( dNe i dE + dNµ i dE + dNτ i dE ) Sobs i (E)−1 = 1 3 ( 1 Γe ψ + 1 Γµ ψ + 1 Γτ ψ ) (27) This is equivalent to stating that the 3l democratic mean lifetime ( τ3l ψ = 1 Γ3l ψ ) is simply the average of the mean lifetimes when each Leptonic channel is considered independently. 5. Accounting for Neutrino Oscillations The analysis of the KM3NeT sensitivity in [49] accounts only for muon neutrinos. However, the phenomenon of neutrino oscillations requires us to account for production of both electron neutrinos and tauon neutrinos. When we consider the e−/e+ Annihilation/Decay channel independently (where f = e and Be = 1) and we require the muon neutrino flux (i = νµ), the differential νµ yield is given by: 40 Multi-Messenger Indirect Dark Matter Searches in Milky Way Satellites • September 2023 dNe νµ dE = Bµ dNe νµ dE + Be dNe νe dE + Bτ dNe ντ dE = ∑ l Bl dNe νl dE (28) where l is the respective lepton and Bl is the respective lepton flavour fraction. Since our observational targets are at large distances, on the kpc scale, we are in the limit of fully averaged (vacuum) oscillations, where the oscillation probabilities can b