Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Sekatchev, Michael
Master of Science - MSc
University of British Columbia
Observations of background radiation in the Milky Way have revealed a puzzling excess of far-ultraviolet (FUV) emission (1350–1750 Å), confirmed by the GALEX space telescope and the New Horizons mission. The origin of this excess remains unexplained by conventional astrophysical sources. This thesis investigates the potential role of the Axion Quark Nugget (AQN) dark matter model in accounting for this mysterious emission. The model proposes that dark matter is dominated by macroscopic composite objects of nuclear density, in the form of matter and antimatter nuggets. Matter (antimatter) AQNs contain quarks (antiquarks) surrounded by an electrosphere (positron-sphere). When antimatter AQNs collide with baryonic matter in the Milky Way, the baryons annihilate leading the AQN to emit a broadband electromagnetic radiation, which includes FUV photons. By simulating these annihilation events within a high-resolution cosmological hydrodynamic model of a Milky Way-like galaxy (the FIRE-2 Latte suite), we estimate the AQN-induced FUV signal. Our analysis reveals that the predicted AQN signal is consistent with the observed FUV excess within the same order of magnitude. More specifically, AQN annihilations can produce an FUV signal of 100–200 photon cm⁻² s⁻¹ sr⁻¹ Å⁻¹ for nugget masses m_AQN ~ 0.1–1 kg, consistent with the excess from GALEX. These findings suggest that AQN-baryon annihilations could provide a viable explanation for the diffuse FUV background and shed light on the nature of dark matter and its interaction with visible matter. We motivate future studies of the broadband AQN emission to probe other Galactic excesses (e.g., X-ray, radio) and cosmological tensions (e.g. reionization).
Axion Quark Nuggets: A Recipe for a Glowing MilkyWay?byMichael SekatchevB.Sc. Honours Physics, Minor in French, University of British Columbia,2019A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)April 2025© Michael Sekatchev, 2025The following individuals certify that they have read, and recommend tothe Faculty of Graduate and Postdoctoral Studies for acceptance, the thesisentitled:Axion Quark Nuggets: A Recipe for a Glowing Milky Way?submitted by Michael Sekatchev in partial fulfillment of the requirementsfor the degree of Master of Science in Physics.Examining Committee:Ariel Zhitnitsky, Professor, Physics and Astronomy, UBCCo-supervisorLudovic Van Waerbeke, Professor, Physics and Astronomy, UBCCo-supervisoriiAbstractObservations of background radiation in the Milky Way have revealed apuzzling excess of far-ultraviolet (FUV) emission (1350–1750 A˚), confirmedby the GALEX space telescope and the New Horizons mission. The originof this excess remains unexplained by conventional astrophysical sources.This thesis investigates the potential role of the Axion Quark Nugget(AQN) dark matter model in accounting for this mysterious emission. Themodel proposes that dark matter is dominated by macroscopic compositeobjects of nuclear density, in the form of matter and antimatter nuggets.Matter (antimatter) AQNs contain quarks (antiquarks) surrounded by anelectrosphere (positron-sphere). When antimatter AQNs collide with bary-onic matter in the Milky Way, the baryons annihilate leading the AQN toemit a broadband electromagnetic radiation, which includes FUV photons.By simulating these annihilation events within a high-resolution cos-mological hydrodynamic model of a Milky Way-like galaxy (the FIRE-2Latte suite), we estimate the AQN-induced FUV signal. Our analysis re-veals that the predicted AQN signal is consistent with the observed FUVexcess within the same order of magnitude. More specifically, AQN annihi-lations can produce an FUV signal of 100–200 photoncm−2 s−1 sr−1 A˚−1fornugget masses mAQN ∼ 0.1–1 kg, consistent with the excess from GALEX.These findings suggest that AQN-baryon annihilations could provide aviable explanation for the diffuse FUV background and shed light on thenature of dark matter and its interaction with visible matter. We motivatefuture studies of the broadband AQN emission to probe other Galactic ex-cesses (e.g., X-ray, radio) and cosmological tensions (e.g. reionization).iiiLay SummaryAll matter known to us (visible matter) only makes up a small fraction ofthe total matter content in our Universe. A remaining 80% is ”dark matter”,which has so far eluded detection. Many dark matter models have beenproposed, but none of them have been experimentally confirmed, leav-ing its true nature one of the most significant open questions in modernphysics.Another puzzle is a mysterious glow pervading from our Galaxy, iden-tified by several telescopes. No explanation for this excess light has beendetermined. In this thesis, I investigated a potential link between this mys-terious excess and a particular dark matter candidate, the Axion QuarkNugget. This candidate has an interaction with visible matter which al-lows it to emit light. Through simulation, I found that this interaction couldproduce a light signal comparable to the mysterious glow observed in ourGalaxy.11My 2024 3-Minute Thesis presentation, accessible here, summarizes my work at a levelaccessible to a general audience.ivPrefaceThis thesis contains original research produced under the supervision ofProf. Ariel Zhitnitsky and Prof. Ludovic Van Waerbeke. Part of the researchdescribed here has become the subject of a paper [1], which at the time ofwriting is in preparation. Certain figures and derivations in the TheoryChapter 2 were created during my undergraduate Honours thesis project[2], and are referenced appropriately. Generative Artificial Intelligence (AI)tools (namely ChatGPT’s GPT-4 model) were used in a limited capacity, forchecking spelling and grammar only.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 A Mysterious Galactic Background Radiation . . . . . . . . . 11.2 Emission from Axion Quark Nugget (AQN) Dark Matter . . 42 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1 Dark Matter and Axion Quark Nuggets . . . . . . . . . . . . 62.2 Axion Quark Nugget Emission Mechanism . . . . . . . . . . 102.3 Estimating Axion Quark Nugget FUV Flux . . . . . . . . . . 123 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1 Milky Way-like Galaxy Simulations . . . . . . . . . . . . . . . 163.2 Simulation Pre-Processing – Voronoi Tessellation . . . . . . . 17vi3.3 Velocity distribution . . . . . . . . . . . . . . . . . . . . . . . 223.4 Filtering solar neighbourhood locations . . . . . . . . . . . . 244 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Comparing Simulated Emission with GALEX . . . . . . . . . 294.2 Emission Sensitivity to Local Parameters . . . . . . . . . . . 315 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37viiList of TablesTable 3.1 Solar region parameters . . . . . . . . . . . . . . . . . . . . 25viiiList of FiguresFigure 2.1 Diagram of antinugget model . . . . . . . . . . . . . . . . 8Figure 2.2 Diagram of proton annihilation within antinugget . . . . 10Figure 3.1 2D Voronoi tessellation example . . . . . . . . . . . . . . 19Figure 3.2 Dark matter and gas distributions from m12i simulation 20Figure 3.3 Probability density, electron fraction vs. gas temperature 21Figure 3.4 Relative velocity, analytical versus m12i simulation . . . 24Figure 3.5 Pre- and post-convolution ionized gas density . . . . . . 26Figure 3.6 Probability density, parameters of selected solar region . 28Figure 4.1 Exceedance probability, AQN signal vs. GALEX excess . 30ixAcknowledgementsI would firstly like to thank my supervisors, Prof. Ariel Zhitnitsky andProf. Ludovic Van Waerbeke, for their support and guidance throughoutmy Masters. I am very grateful for their mentorship, and the many uniqueopportunities they provided.I would like to thank our group members: Xunyu Liang, Fereshteh Ma-jidi, and Shiming Gu. Their presence was instrumental in my research andmade for a positive and genuinely enjoyable research environment.Outside of our physics department, I would like to thank Alfredo Fer-reira for his unwavering support and the many open education opportu-nities he offered. It was a pleasure to serve as his TA, and to collaborateon several impactful projects. I always looked forward to sharing personalnews and accomplishments with him. Alfredo’s constant encouragementand belief in my abilities made a lasting impact on my journey at UBC.I would like to acknowledge the students I interacted with through-out the many courses I TAed. Every interaction with them was incred-ibly rewarding—from sharing the satisfaction of figuring out a problemtogether to learning about their journeys. I am very grateful for the oppor-tunity to teach and learn from so many students throughout my degree.On a more personal note, I’m grateful to my friends for their supportand company throughout this process. It’s been a real pleasure to growtogether, both professionally and personally, and consult on all of our chal-lenges and milestones along the way.Finally, I want to thank my family and my parents for their love, sup-port and motivation throughout my degree.xChapter 1IntroductionWe are all in the gutter, but some of us are looking at the stars.— Oscar Wilde1.1 A Mysterious Galactic Background RadiationThe Galaxy Evolution Explorer (GALEX), detailed in [3], observed the dif-fuse Galactic far-ultraviolet (FUV) background using its FUV imager (1350-1750 A˚). The majority of the detected FUV background could be attributedto dust-scattered starlight. However, an isotropic offset of approximately200 photoncm−2 s−1 sr−1 A˚−1(or “photon units”) was identified [4]. Subse-quent studies ([5–7]) were unable to attribute this excess to scattered FUVlight but determined that it must have a Galactic and astrophysical origin,giving rise to the “mystery” of the cosmic diffuse UV background excess.The brightness of the GALEX FUV background was in close agreementwith previous observations made by spacecraft located much farther fromEarth (namely the Dynamics Explorer, [8]). This ruled out the possibility ofa solar-system or terrestrial origin. The origin of this FUV signal remains anopen question and is still under extensive discussion. Possible explanationsfor its source(s) may include one or more of the following: (1) quasars, (2)X-ray binaries, (3) hot interstellar gas, (4) circumgalactic gas, and (5) virial-ized gas [9]. However, the observational properties of the signal reported1in [5–7] remain difficult to interpret within conventional frameworks. Thecounterarguments are primarily based on the following four puzzling char-acteristics of the observations:1. The ”uniformity puzzle”: The diffuse radiation appears to be remark-ably uniform across both hemispheres, as illustrated in Figures 7-10of [5]. This stands in stark contrast to the pronounced non-uniformityin the distribution of UV-emitting stars.;2. The ”Galactic longitude puzzle”: The diffuse radiation exhibits al-most no dependence on Galactic longitude. This is in stark contrast tothe distribution of the brightest UV-emitting stars, which are predom-inantly confined to the longitude range 180◦-360◦. This strong dis-crepancy suggests that the diffuse background radiation is unlikelyto originate from dust-scattered starlight.;3. The ”Galactic latitude puzzle”: The diffuse radiation is brighter to-ward lower Galactic latitudes at all Galactic longitudes. This behav-ior contrasts with conventional modeling [5], which predicts very lowbrightness at low Galactic latitudes. This observation also suggeststhat the recorded diffuse emission has a Galactic, rather than extra-galactic, origin. Indeed, extragalactic light cannot exhibit a strongvariation toward lower Galactic latitudes. For the same reasons, theobservations also conclusively indicate that this emission is celestialrather than terrestrial in nature.;4. The ”non-correlation puzzle”: The conventional model of UV diffuseradiation suggests that it should be correlated with the 100 µm ther-mal emission, as both are assumed to be linked to dust and its dis-tribution in the galaxy. However, this assumption fails dramatically,as the 100 µm thermal emission is highly asymmetric and explicitlycorrelates with the localization of UV-emitting stars, whereas the UVdiffuse emission is highly uniform and shows no correlation with thedust distribution. See Fig. 14 in [5].2A recent analysis [10] of observations from the Alice UV spectrographon the New Horizons spacecraft (912-1000 A˚ and 1400-1800 A˚), located 57AU from the Sun—well beyond the range of most foreground contamina-tion and zodiacal light—confirmed the excess first identified by GALEX.While approximately half of the observed intensity can be attributed toknown sources, the remaining signal could not be explained by known UVsources.The puzzling uniformity of the FUV excess [5] has also led to the consid-eration of dark matter annihilation as a potential source. Various possibili-ties have been proposed, including the decay of a 27 eV τ neutrino and theannihilation of leading dark matter candidates such as Weakly InteractingMassive Particles (WIMPs) and QCD axions. In the case of the τ neutrino,the expected background signal would consist of a single emission linefrom the decay photon, which is inconsistent with the broad, flat-shapeddistribution observed in the GALEX data. For WIMPs, a mass of approxi-mately 100 GeV would be required to produce the necessary spectral signa-ture, but this mass range has been conclusively ruled out by experimentalsearches [11]. Furthermore, if the current favored WIMP mass values areused in the calculations, the predicted UV signal is found to be 12 orders ofmagnitude lower than the FUV radiation detected by GALEX. In contrast,for axions, the reverse problem arises: the predicted flux is 12 orders ofmagnitude too bright and peaks in the X-ray band at 2 A˚ [5]. As a result,conventional WIMPs and QCD axions are ruled out as viable sources of theexcess. Interestingly, [5] speculates that a composite dark matter particlecould potentially produce the observed signal. Specifically, they wrote ”ifthe dark-matter particles should turn out to be composite particles, overallelectrically neutral but involving electrically charged components (as in aneutron), then perhaps our second component could originate in collisionsof those dark-matter particles with the nuclei of the interstellar medium”.31.2 Emission from Axion Quark Nugget (AQN) DarkMatterThis description quoted above precisely matches the Axion Quark Nugget(AQN) dark matter model [12], the dark matter candidate studied in thisthesis. This model proposes that dark matter consists of composite ob-jects with masses typically greater than 1 gram, MDM ≳ 1 g, with nucleardensity, and sub-micrometer size. It is a generalization of Witten’s quarknugget hypothesis [13–15], first developed in the mid-1980s. Unlike con-ventional dark matter candidates such as WIMPs and axions [16], AQNsinteract strongly with baryonic matter. They form during the quark-hadrontransition, at a time when matter and antimatter have not yet completelyannihilated. As a result, some AQNs exist in antimatter form, which allowsthem to collide with normal matter, leading to a broadband electromagneticradiation spanning from the radio to the X-ray.The work in this thesis was performed in parallel with several otherstudies, where the unique emission characteristics of AQNs were appliedto large-scale structure [17] and galaxy cluster analyses [18]. In both cases,it was determined that the energy injection due to AQN annihilation withsurrounding material not only remains consistent with existing constraintsbut also leads to specific predictions that could be tested by Euclid andJWST. This current study differs from these in the following way: here,we explore the possibility that the AQN model could be the source of theobserved FUV excess, aligning with the measured excess emission and po-tentially explaining the puzzling observations reported in [5–7], as initiallyproposed in [19]. In this work, we take a significant step toward supportingthis hypothesis by developing a comprehensive model of the FUV radia-tion generated by AQNs within the Milky Way and using hydrodynamicalsimulation to describe realistically the gas and dark matter distribution ina galactic environment similar to the one surrounding the solar system.4This thesis is organized as follows: It begins with a theory Chapter 2, whichintroduces the Axion Quark Nugget dark matter model (Section 2.1) andexplains the relevant annihilation interaction (Section 2.2). The MethodsChapter 3 discusses all technical implementation details of the AQN an-nihilation interaction theory from the previous chapter, to model the ex-pected AQN FUV signal in the Milky Way. Chapter 4 presents and dis-cusses the results of this work, which culminate in a figure showing the ex-ceedance probability of the AQN FUV signal for three AQN masses, as wellas figures demonstrating the high sensitivity of the AQN signal to severalMilky Way parameters. Finally, the thesis concludes with a discussion offuture extensions and avenues for investigation in the context of the AQNannihilation signal in Chapter 5, and a summary with the implication ofthese results in Chapter 6.5Chapter 2TheoryWe begin by introducing the AQN dark matter model, and concentrate onexplaining the AQN annihilation interaction, the mechanism at the base ofthe investigation in this thesis. We end this chapter with a discussion ofways to obtain Milky Way parameters—due to the limitations of availableobservational data, we present analytical models and simulations of MilkyWay-like Galaxies. A combination of these is used in the modeling of theAQN signal, discussed in the following Chapter 3.2.1 Dark Matter and Axion Quark NuggetsDark matter is a hypothesized form of matter that interacts weakly with theelectromagnetic force, making its direct detection challenging through tra-ditional astronomical methods [20]. Recent measurements of cosmologicalparameters by the Planck Collaboration suggest that dark matter makes up84%1 of the matter in our universe [21].There are several proposed models for dark matter, with Weakly Inter-acting Massive Particles (WIMPs) being one of the most popular. WIMPsare hypothetical particles that are thought to interact with normal matterthrough the weak nuclear force, making them difficult to detect directly.However, they are predicted to produce detectable signals in certain exper-1Calculated using the radio of density parameters from [21]: Ωch2/(Ωch2 + Ωbh2) =0.120/(0.120+ 0.0224) ≈ 0.84.6iments, such as direct detection experiments that search for the scattering ofWIMPs off atomic nuclei [22], or indirect detection experiments that searchfor the products of WIMP annihilation or decay.A popular alternative describes axions, hypothetical particles originallyproposed to solve the Strong CP Problem [23] — the strong force does notappear to violate the combined symmetry of charge conjugation C and par-ity P , despite theoretical expectations that it should. Axions are thoughtto interact very weakly with normal matter, making them difficult to de-tect directly [20]. However, there are still considerable experimental effortsattempting to detect the conversion of axions into photons under a strongmagnetic field [24].Another proposed form of dark matter is in the form of axion quarknuggets (AQNs), which form the basis of this project. AQNs are part ofthe macroscopic dark matter category, which consists of models for darkmatter as large, compact objects with masses ranging from a few gramsto the mass of small planets. AQNs were first introduced in [12] as a po-tential explanation for the observed similarity between dark matter (DM)and visible matter (VM) densities, ΩDM ∼ ΩVM. The model shares simi-larities with Witten’s quark nuggets [13]. AQNs are characterized as large,composite objects with nuclear density, possessing a mass mAQN ≳ 1g andexhibiting a ”cosmologically dark” cross-section to mass ratio, σ/mAQN ≲10−10 cm2g−1, consistent with the observational requirement for cold darkmatter. From this mass range, assuming the nugget is of nuclear densitythen provides an estimate of its radius, which is on the order of µm, viamAQN = ρ0 VAQN where VAQN = 43πR3AQN, where ρ0 is the nuclear densityand mAQN, VAQN, and RAQN are the nugget mass, geometric volume andgeometric radius, respectively.The main distinguishing feature of the model is that AQNs can be com-posed of both matter and antimatter during the quarks-hadrons transitionas a result of the charge segregation process [25]. This charge segregationmechanism separates quarks from antiquarks due to the dynamics of theCP-odd axion field. The resulting separation of baryon charges leads tothe formation of quark nuggets and anti-quark nuggets at a similar (but7not identical) rate, and the baryon net charge of the Universe remains zero.Figure 2.1 shows a diagram of a typical axion quark antinugget. A typ-ical nugget, or antinugget, consists of a quark or antiquark core, immersedin a sphere of electrons (”electrosphere”) or positrons (”positron-sphere”)which ensures the nugget’s neutrality.0.1 - 1 µm1 g - 1 kgantiquark corepositron-sphereFigure 2.1: Antinugget model. Shown is an antiquark core (yellow) ina color superconducting phase, inside a positron-sphere (green).Modified diagram from undergraduate thesis [2].The AQN model relies on the existence of an axion field, with the AQNsforming during the quantum chromodynamic (QCD) phase transition inthe early Universe from axion domain wall bubbles, further discussed indetail in [26–29]. By accumulating quarks during the QCD transition, somebubbles in the axion field may persist, by forming an internal Fermi pres-sure to balance external pressure on the wall. As matter-antimatter anni-hilation continues in the plasma, so does the formation of matter and anti-matter nuggets in axion domain wall bubbles, in the same proportions asthe newly formed protons and neutrons outside. As cooling continues, allanti-baryons outside of the bubbles are depleted, but the AQNs persist inboth matter and anti-matter form—the significant implication here is that,given that the Universe’s total baryon charge is zero, the densities of DMand baryonic matter naturally align to the same order of magnitude. The8quarks in the interior of the AQNs exist in a color superconducting phase,which at high enough pressures has a lower energy per baryon charge thanin hadrons, showing that nuggets are more stable than protons and neu-trons.As mentioned, in the AQN scenario, ΩDM (representing here the matterand antimatter nuggets) and ΩVM naturally assume comparable densities,ΩDM ∼ Ωvisible. This arises because both components are proportional tothe same fundamental dimensional parameter of the theory, ΛQCD. Con-sequently, the AQN model, by construction, simultaneously addresses twofundamental problems in cosmology: it provides an explanation for thebaryon asymmetry of the Universe and accounts for the presence of darkmatter with the appropriate density, ΩDM ∼ ΩVM, without requiring anyparameter fine-tuning.Since this work focuses on the electromagnetic emission of antimatterAQNs, we adopt the same convention as in [17, 18] and define the numberdensity of AQNs as:nAQN ≡ 23 ×35× ρDMmAQNc2, (2.1)where the factor of 23 accounts for the electromagnetic fraction of theAQN emission, the factor of 35 represents the antimatter sector of the AQNs,ρDM is the dark matter energy density, and c is the speed of light in vacuum.For simplicity, we assume that AQNs constitute the dominant componentof dark matter and that all AQNs have the same mass, mAQN.It is specifically the antimatter nuggets that play a crucial role in thediscussions that follow. These antimatter nuggets can collide with visiblematter, leading to annihilation processes and subsequent radiation, as ex-plained in Section 2.2. The analysis of the resulting electromagnetic emis-sion in the UV frequency bands is the central focus of this thesis work.92.2 Axion Quark Nugget Emission MechanismAs discussed previously, in addition to the quarks contained within AQNsby the axion field, matter-based nuggets are surrounded by a cloud of elec-trons to maintain overall charge neutrality. Similarly, antimatter nuggetsare enveloped by a cloud of positrons. It is this antimatter variant thatis of particular interest to this project: while the collision of matter AQNswith regular baryonic matter does not result in substantial energy exchangeand thus produces negligible radiation, the interaction of antimatter AQNswith regular matter leads to annihilation events that release significant en-ergy (2 GeV per event). Despite the strong interactions involved, the ab-sence of an astrophysical prominent electromagnetic signature within theAQN framework can be attributed to the low number density of AQNs,which is a consequence of their large individual mass. As a result, theglobal rate of annihilation interactions remains relatively low.p+p-0.1 - 1 µm1 g - 1 kgantiquark corepositron-sphereFigure 2.2: Diagram showing proton annihilation within an antin-ugget. The proton annihilates with antiquarks in the antiquarkcore, represented together as p−. A portion of the 2 GeV of avail-able energy is thermalized, heating the positron-sphere, causingit to radiate this energy in a broadband radiation spectrum.10A simple diagram of this annihilation interaction is shown in Figure 2.2.This annihilation of antimatter AQNs with surrounding matter generates aBremsstrahlung emission signature spanning from radio to γ-rays. The ra-diation is produced by positrons in the electrosphere that have been heatedby a fraction of the annihilation energy. The UV emission spectrum consti-tutes a component of this signal. The spectral emissivity Fν from the surfaceof an AQN, expressed in units of [erg,cm−2s−1Hz−1], is determined by theAQN temperature TAQN [30]:Fν =8α5/245h¯2c2(kBTAQN)3(kBTAQNmec2) 14H(2πh¯νkBTAQN);H(x) ≈{(1+ x)e−x (17− 12ln(x/2)) , if x < 1;(1+ x)e−x(17+ 12ln2) , if x ≥ 1,(2.2)where ν is the frequency of the photon emission, α is the fine structureconstant, kB is the Boltzmann constant, h¯ is the reduced Planck constant,and me is the electron mass.As shown in [17, 18], the AQN emission is dominated by the ionizedgas rather than the neutral gas. The reason is that the Coulomb force willenhance the interaction cross-section between AQNs and ionized gas, com-pared to the AQN-neutral gas cross-section. In the ionized gas scenario,the AQN temperature can be expressed as follows (derived recently in [17],and in more detail in my undergraduate thesis [2]):TAQN =mec2kB[2GeV (1− g)h¯8α3/2k2B3πnion∆vR2T2gas,eff] 47, (2.3)where nion is number density of the ionized gas, g ≈ 0.1 is the fraction ofthe non-thermal emission, ∆v is the relative bulk speed between the AQNand the ionized gas, R is the geometrical radius of the AQN, and Tgas,effis the effective gas temperature that accounts for the thermal temperatureTgas of the ionized gas and its relative bulk kinetic energy with respect to11the AQN:kBTgas,eff ≡ kBTgas + 12mp∆v2 . (2.4)Here, we assume the ionized gas is composed of ionized hydrogen of pro-ton mass mp. The first term (kBTgas) specifies the random thermal motion ofthe gas, while the last term ( 12 mp∆v2) accounts for the relative bulk motionbetween baryon gas and AQNs. The effective gas motion (kBTgas,eff) deter-mines whether the gas particle will be captured by the Coulomb attractionof the charged AQN. The kinetic term ( 12 mp∆v2) is insignificant comparedto the thermal term (kBTgas) outside galaxies because both matter and darkmatter undergo a free fall so that ∆v is small. This implies Tgas,eff ≈ Tgasis a good approximation outside the galaxy [17, 18]. This is no longer truein this work, as we focus on the scenario inside the Milky Way. Here, thebaryon gas is circulating on the stellar disk, while the dark matter movesrandomly within the dark halo. The kinetic term can become larger thanthe thermal term, especially when the gas is relatively cold. We introducethe precise definition (2.4) of Tgas,eff to account for this effect.2.3 Estimating Axion Quark Nugget FUV FluxWe expect that the AQN dark matter and ionized gas in a large region sur-rounding the solar system will interact to form a sky glow, the intensity ofwhich, Iν in [ergs−1 cm−2 Hz−1 sr−1], is defined as:∫∆ΩIν(nˆ)dΩ =∫ϵν(r, nˆ)4πr2e−τν(r,nˆ)dr r2dΩ, (2.5)where r is the distance from the observer to the source in directionnˆ, ϵν(r, nˆ) is the spectral emission per volume in [ergs−1cm−3Hz−1] andτν(r, nˆ) is the optical depth. The spectral emission is given by:ϵν = 4πR2nAQNFν (2.6)where Fν is given by Eq. (2.2). By taking the derivative with respect to Ω12on both sides, we obtainIν(nˆ) =14π∫ ∞0dr ϵν(r, nˆ)e−τν(r) , (2.7)A full treatment of optical depth is beyond the scope of this work. In-stead, we will assume a uniform cutoff at distance L. For a wavelengthin the range of the GALEX FUV λ ∈ [1350,1750]A˚, we adopt the choice ofL = 0.6kpc, consistent with the estimations done in [31]. This assumptionis equivalent to modeling optical depth as a step function—allowing fulltransmission up to r = L, with no transmission beyond r > L.In the GALEX analysis [31], the observable is characterized by the pho-ton number flux density Φλ [photoncm−2 s−1 sr−1 A˚−1 sr−1]. The conver-sion from Iν to Φλ is given by:Φλ(nˆ) =Iν(nˆ)2πh¯νdνdλ∣∣∣∣ν=c/λ=18π2h¯λ∫ L0dr ϵν(r, nˆ)∣∣∣∣ν=c/λ. (2.8)The observed averaged flux over a given solid angle on the sky ∆Ω isgiven by:⟨Φλ⟩ = 1∆Ω∫ L0r2dr∫∆ΩdΩΦλ(nˆ)r2(2.9)=18π2h¯λ∆Ω∫ L0r2dr∫∆ΩdΩϵν(r, nˆ)r2∣∣∣∣ν=c/λ, (2.10)In the next section, we will introduce the simulations used in this work;for this reason, it is useful to introduce the discretized version of Eq. (2.10),⟨Φλ⟩ = ∆r38π2h¯λ∆Ω ∑i,j,kϵν(i, j,k)r2∣∣∣∣∣ν=c/λ, (2.11)where (i, j,k) is the Cartesian coordinate of the voxels in the simulationcube, ∆r is the voxel width, and r specifies the distance between the (i, j,k)-th voxel and the observer (at the Sun location). The sum ∑i,j,k is taken overall voxels with 0< r < L and within solid angle ∆Ω.13One final step remains: Eq. (2.11) defines the flux ⟨Φλ⟩ for a specificwavelength λ. To compare our signal forecast with the measured GALEXFUV excess, we must average over the GALEX FUV bandwidth (1350-1750A˚). As a first approximation, we assume a flat filter response function forGALEX, so that the AQN signal forecast is given by:⟨Φλ⟩GALEX = 1∆λ∫ λmaxλmindλ ⟨Φλ⟩, (2.12)with λmin = 1350 A˚, λmax = 1750 A˚, and ∆λ = λmax − λmin.We see that final quantity of interest in Eq. (2.12) has a dependenceon local quantities: it depends on the AQN number density nAQN throughϵν in (2.6), and on the ionized gas temperature Tgas, ionized gas numberdensity nion, and relative bulk speed between AQN and ionized gas ∆v,through Eqs. (2.3) and (2.2). In the Chapters that follow, we will discusshow local estimates of these quantities are obtained, and note the impor-tance of having a precise, high-resolution understanding of all four, due tothe high sensitivity of the AQN signal to these parameters.14Chapter 3MethodsIn this chapter, we discuss the implementation details for modelling theFUV flux from AQN annihilations in the Milky Way. This involves ob-taining estimates of physical quantities using Milky Way-like galaxy sim-ulations, which are introduced in Section 3.1, and require processing, de-scribed in Section 3.2. For the relative velocity, an analytical model is usedinstead, described in Section 3.3. The Milky Way-like simulation is filteredto select regions similar to our solar system—this is done in Section 3.4.This chapter sets the stage for computation of the FUV AQN flux, the re-sults of which are shown in Chapter 4 that follows.The AQN emission mechanism was presented in Section 2.2, and Section2.3 outlines the calculation of the GALEX FUV flux. This calculation re-quires knowledge of following physical quantities: (i) the DM and baryonicmatter densities nDM,ngas, (ii) the relative velocity between DM and bary-onic matter, ∆v, (iii) the gas temperature Tgas, and (iv) the gas ionizationfraction Xe. The standard approach, which employs a variety of simpli-fied models such as the Navarro-Frenk-White [32] or Burkert [33] profilesfor dark matter and the Disk-Bulge-Halo (DBH) model for visible matter[34, 35], lacks the necessary resolution to estimate the AQN signal accu-15rately.Since the mean free path of an FUV photon is on the order of 1-2 kpc[5] in the disk, we must rely on high-resolution simulations of these physi-cal quantities within a small sub-kpc region centered around the Sun. Theadvantage of using hydrodynamical simulations is that they allow us toselect locations that best represent our Solar System environment and pro-vide a more accurate treatment of the fact that the AQN signal does notscale linearly with these parameters, as demonstrated in Chapter 2. Forthese reasons, we have chosen to use the FIRE-2 Latte suite [36]. The fol-lowing sections detail the process of modeling the FUV signal using thesesimulations by implementing Eq. (2.12) and the AQN annihilation emis-sion mechanism discussed in Section 2.2.3.1 Milky Way-like Galaxy SimulationsIn this work, we utilize the m12i Milky Way-like galaxy simulation, whichemploys the Feedback in Realistic Environments 2 (FIRE-2) engine. Them12i simulation is part of the FIRE-2 Latte simulation suite1, first intro-duced in [36]. The Latte project models the formation of Milky Way-mass(MW-mass) galaxies down to redshift 0 within the ΛCDM cosmologicalframework, using the FIRE-2 physical model. This model includes detailedtreatments of star formation, stellar feedback (such as supernovae, stellarwinds, and radiation), and the effects of gas cooling and heating across abroad range of densities and temperatures [37].MW-mass candidate galaxies were selected from a periodic simulationbox of 85.5 Mpc in length, based solely on halo mass, to match M200m =1-2 · 1012M⊙. Each chosen MW-mass halo has a particle mass resolution of7070; M⊙ for gas and 35000; M⊙ for dark matter, with a spatial resolutionof 40 pc for dark matter and a minimum of 1 pc for gas (with a medianresolution of 25-60 pc at z = 0). An adaptive softening kernel is employedto achieve higher resolution when necessary. The data for three MW-mass1fire.northwestern.edu/latte/16halos from the Latte suite are publicly available2, and the m12i simulationwas selected for this project.3.2 Simulation Pre-Processing – Voronoi TessellationIn this section, we describe the processing applied to the m12i MW-likegalaxy data in preparation for the FUV AQN signal calculation. Since them12i simulation provides data in the form of particle information, it is nec-essary to construct a continuous density field. This is achieved by perform-ing a Voronoi tessellation, which converts the discrete particle data intothree-dimensional density fields.As mentioned in the beginning of this Chapter 3, five physical quanti-ties must be determined locally: nDM, ngas, ∆v, Tgas, and Xe. Along withthe AQN mass, these serve as the inputs for estimating the AQN signal, asoutlined in Section 2.2. Before applying the Voronoi tessellation, we alignthe galactic disk with the xy-plane of our coordinate system to simplify cal-culations. This alignment is achieved using a weighted linear least squaresregression fit to a plane equation applied to the gas particles located at dis-tances of 8± 1.2 kpc from the galactic center (approximately the position ofthe Sun). From this, the correct rotation vector is determined.A discretized Voronoi tessellation was applied to the rotated m12i par-ticles to convert the particle data into discretized continuous fields. A20x20x20 kpc cube, centered on the Galactic center, was selected for thisprocess. The cube was discretized to a resolution of 512 voxels per side, re-sulting in each voxel being a cube with a side length of Lvox = 20kpc/512≈0.039kpc. Particles were assigned to voxels based on their spatial positions.The choice of this voxel size was motivated by a trade-off: At higher reso-lutions than 512 voxels per side (i.e. cubes with lengths smaller than 0.039kpc), the number of empty voxels (containing no particles) begins to in-crease significantly in the solar neighbourhood region (precisely definedand discussed in Section 3.4). The added benefit of a finer resolution be-comes negligible compared to the substantial increase in computing time.2ananke.hub.yt/17For voxels containing no particles, a nearest-neighbour search was per-formed using a 3D tree search algorithm. This assigned each empty voxelto the nearest non-empty neighbouring voxel, with the particle data fromthe non-empty voxel applied to all of its empty neighbours, creating a uni-form region. The particle data in each region was then transformed into adensity field as follows: for mass density, the total mass of all particles in aregion was divided by the total region volume. This technique preservedthe total mass in the simulated Galaxy. For gas temperature and neutralhydrogen fraction, the weighted average value of all particles in the regionwas assigned to all voxels within that region.A simple 2D visual demonstration of this Voronoi tessellation processis shown and explained in Figure 3.1 below.181050510 Original1050510 Pre-Voronoi10 5 0 5 10x [kpc]1050510y [kpc]Post-voronoi10 14×10 26×10 2MassFigure 3.1: Demonstration of the 2D discrete Voronoi tessellation pro-cess on a simple set of five particles (top). Particles are binnedinto a square grid, weighed by their mass (middle). A nearest-neighbour search then fills empty grid cells with the mass oftheir nearest non-empty neighbour cell. Finally, the value in eachgroup of cells is divided by the number of cells in that group, ob-taining a mass density in each cell (bottom).An example of the resulting m12i gas density fields is shown in Figure3.2. The mass densities of DM and gas were then converted into numberdensities using a fixed AQN mass mAQN and the assumption that all neu-19tral gas is HI and all ionized gas is HII. This assumption implies that allgas consists of hydrogen, allowing the proton mass to be used in the con-version. With this approach, the number densities niDM, nigas were obtainedfor each i-th voxel. The total mass of DM and gas components was con-served here, since only the mass of the constituent particles is assumed andmodified in this process.1050510 Pre-Voronoi Post-Voronoi10 5 0 5 10105051010 5 0 5 1010 2110 2010 1910 18Density [kgm3 ]x [kpc]y [kpc]Figure 3.2: Dark matter (top) and gas (bottom) distributions in a20x20x4 kpc3 cube around the centre of the m12i galaxy simu-lation. xy-plane projections summed over z ∈ [−1,1] kpc. Left:mass densities, obtained by binning particles over an overlaidgrid. Right: mass density fields, generated by applying theVoronoi Tessellation and nearest-voxel search process discussedin Section 3.2 to the data in the left plots.As discussed in Section 2.2, since neutral gas does not contribute sig-nificantly to the AQN FUV signal, we only need to estimate the ionized20gas number density at each voxel, niion. Since an average gas temperatureis assigned to each gas particle, one possible approach is to use a simpletemperature threshold to distinguish between the neutral and ionized gasphases. This method was applied in [17], where an average ionization tem-perature of 2.6 eV ≃ 3× 104 K was assumed. However, in our case, thisapproximation is not valid because multiple physical processes can influ-ence the ionization fraction within a galactic disk. Moreover, given thatthe AQN signal follows the relation Φ ∝ T−26/7gas , it makes the sensitivity toan artibrary ionization temperature even stronger. Consequently, we optedto use the ionization fraction Xe provided by the m12i simulation. Figure3.3 presents a 2-D histogram of ionization fraction and temperature for gasparticles in the m12i galaxy, illustrating that ionized gas (Xe > 0.5) remainspresent even at temperatures as low as ∼ 104 K. Thus, the number densityof ionized hydrogen gas in each voxel, nigas, was determined based on theionization fraction Xie.101 102 103 104 105 106 107 108Gas Temperature, Tgas [K]0.00.20.40.60.81.01.2Electron Fraction, Xe10 1110 910 710 510 3Probability DensityFigure 3.3: 2D probability density of electron fraction and gas temper-ature for a 20x20x20 kpc cube centered on the Galactic centre ofthe m12i simulation.21Figure 3.3 shows that Xe exceeds 1, which is expected since the simu-lation is accounting for ions heavier than hydrogen. For the remainder ofthis work, we will maintain the simplification that all gas consists solely ofhydrogen, allowing niion to be calculated as niion = Xienigas. Although thisapproach artificially increases the total ions number density by ∼ 20%, wewill show in Section 2.2 that the ionized gas number density from the sim-ulation requires slight scaling to match the conditions of a solar-like region.As a result, at this stage, the uniform 20% overestimate of niion is irrelevant.Each voxel i now contains the following physical quantities: niDM, niion,Tigas. The final required quantity is the relative velocity, ∆v inside eachvoxel. Although velocity data is available in m12i, we found that its reso-lution is insufficient, particularly for low-velocity values. The relative ve-locity between dark matter and baryons is a crucial physical parameter, asevident from Eqs. 2.3 and 2.4. Specifically, a lower ∆v results in more effi-cient baryon capture and annihilation by the AQN, therefore it is importantto model it carefully. Our approach to incorporating velocity informationinto our calculations is detailed in Section 3.3.3.3 Velocity distributionThe spectral emission ϵν(r, nˆ) in Eq. (2.6) depends on the values of thephysical quantities nAQN, ∆v, nion, and Tgas at the location r, nˆ. In practice,this location corresponds to a voxel with a finite resolution, determined bythe numerical simulation. Inside a voxel, it is not possible to resolve indi-vidual AQN-baryon collisions, where the physical quantities can vary sig-nificantly from one collision to the next. Therefore, it is useful to introducethe normalized distribution functions fl(xl) of the physical quantities xl ,where xl = [nAQN,∆v,nion, Tgas], and define the average spectral emissionat the location (r, nˆ) as:ϵν(r, nˆ) =∏l∫dxl fl(xl)ϵν∣∣∣∣(r,nˆ), (3.1)22where the average is taken over all physical quantities given their expecteddistribution fl(xl) at location (r, nˆ).In general, ϵν from Eq. (3.1) is mostly sensitive to the local mean valueof the xl at each voxel rather than the specific form of f (xl). In the simu-lation, f (xl) can be approximated as a discrete distribution such that xl isthe local average in each voxel. This treatment is valid as long as the inte-gral (3.1) converges. One exception is Tgas,eff (namely, Tgas and ∆v), becausewe approximately have ϵν ∝ T13/4AQN ∝ T−26/7gas,eff from Eqs. (2.2) and (2.3). Theintegration diverges at Tgas,eff = 0. In this case, the integral is no longer sen-sitive to the mean value of Tgas,eff, but the lower cutoff of the distribution ofTgas,eff. In this section, we will fix the lower cutoff of Tgas,eff by introducingan analytical distribution of ∆v while keeping Tgas fixed to its local meanvalue.The AQN signal is highly sensitive to ∆v: assuming H(x) from Equa-tion 2.2 is constant, the relationship is about ⟨Φ⟩ ∼ ∆v−5.6. The resolutionof the per-particle velocity information from m12i is insufficient to describethe tail ends of the velocity difference distribution which are critical to themagnitude of the FUV AQN signal. Our solution is to adopt an analyticalmodel of ∆v in the Milky Way instead, using a shifted Maxwell-Boltzmann(MB) distribution: recent comparisons with both satellite observations (see[38]) and cosmological simulations (see [39], a follow-up to [40]) that ashifted MB with a truncated tail models ∆v well. Thus, we choose to modelthe distribution in relative velocity between DM and VM byf (∆v) =√2π∆v2σ3vexp(−(∆v2 + v20)2σ2v)sinh(v0∆v/σ2v)(v0∆v/σ2v ), (3.2)which is a simplified version of the MB distribution from the Standard HaloModel summarized in [38]. Here v0 = 220 km/s is the circular rotationspeed and σv = v0/√2, also taken from [38]. The calculation of the FUVAQN signal involves an integral over Equation 3.2, as will be discussed inChapter 4. Thus, we are able to capture the full sensitivity of the FUV AQNsignal to variations in ∆v. A comparison between the analytical shifted MB∆v distribution and the ∆v distribution obtained from binning FIRE voxels23(filtered to solar neighbourhood locations using the process described inSection 3.4) is shown in Figure 3.4. We note that the binned distributionfrom the FIRE simulation is skewed to lower velocities. Since the AQNsignal scales non-linearly to ∆v, we will see in Chapter 4 that the effect ofthis on the modelled FUV AQN signal is substantial.0 200 400 600 800 1000v [km/s]0.00000.00050.00100.00150.00200.00250.0030P(v)FIRE filtered voxelsMB, v0=220, v=156Figure 3.4: Relative velocity ∆v between dark and visible matter—binned values from FIRE’s m12i simulation (filtered to the so-lar neighbourhood) compared with a shifted Maxwell Boltzmann∆v model described by Equation 3.2.3.4 Filtering solar neighbourhood locationsHaving obtained the necessary parameters at each voxel in the discretizedsimulation, sun-like regions in m12i could be identified. For this, local aver-ages of these parameters from observation are used. The parameters usedfor filtering are shown in Table 3.1 and discussed in detail below.24Parameter Value Range Unit ReferenceDark Matter Density (ρDM) 0.42 0.06 GeV/cm3 [41]Ionized Gas Density (nion) 0.05∗ 0.02 cm−3 [42]Neutral Gas Density (nneut) 0.195 0.033 cm−3 [43]Radial distance of Sun (s⊙) 8.20 0.09 kpc [44]Table 3.1: Solar region parameters and filter criteria with associatedvalues, filter ranges, units, and references. ∗The ionized gas den-sity quoted here is the density within clumps in the solar region—the ionized gas density is averaged over these clumps in the dis-cussion below this table.From Table 3.1, the local dark matter density was obtained from the av-erage of twelve of the most recent studies, computed and tabulated in [41](see Table 1 in this reference). The ionized gas density requires a more in-depth discussion: the quoted value is taken from a result in [42], where,derived from observations, the electron density is reported to be “clumpedinto regions having an average electron density ne = 0.03-0.08cm−3, andfilling a fraction, f ≈ 0.4-0.2, of the volume within a 2000–3000 pc thicklayer about the Galactic midplane”. From this information, the local ion-ized gas distribution can be obtained by averaging the electron densityfrom these clumps over the local volume being considered. The ionizedgas density voxels will in turn need to be averaged over this larger localvolume, which can be done with a convolution kernel.The given filling fraction f implies many small regions, not a few mas-sive ones, since the warm ionized medium is known to be diffuse ratherthan dominated by large clouds. The average density applies to these ion-ized regions only, while the surrounding regions likely contain neutral gasor are largely empty.Let V be the entire volume being considered here. If the average elec-tron density ne is quoted for a fraction f of this volume, then the averageelectron density in the entire volume is ne,V = f ne = [0.006,0.032] cm−3.The vertical extent is given as z = [2,3] kpc, but the radial extent needs tobe estimated—assuming a horizontal extent of s = [1,2] kpc, we can esti-25mate the volume over which this was averaged as V = πs2z = [6,38] kpc3.This is the volume we can average over to obtain a comparable ionized gasdensity. To implement the averaging on the density field voxels niion com-puted in the previous Section 3.2, a convolution can be performed with asimple averaging kernel,f (r) =1V1r≤R, (3.3)where R = (3V/(4π))1/3. So the range of R given the estimate for therange of V is R = [1.1,2.1] kpc. Using the mean of this range of R andthe mean of the range of ne,V , the filtering was set up to look for ne,V =0.019± 0.013 cm−3 with an averaging radius of 1.6 kpc.The gas density pre- and post-averaging convolution is shown in Figure3.5.10 5 0 5 101050510y [kpc]Pre-convolution10 5 0 5 10Post-convolution0.010.020.030.040.05Ionized GasNumber Density, nion [cm3 ]x [kpc]Figure 3.5: Pre-convolution and post-convolution ionized gas densitydistributions, using the averaging kernel in equation 3.3 with R=1.6 kpc. xy-plane projections summed over z ∈ [−1,1] kpc.Thus, the filtering was applied as follows: Candidate voxels from the20x20x20 kpc cube were filtered by their location, within a shell with z-coordinates |zi| < 1kpc, and radial distances from the centre |si − s⊙| <1.2kpc. This is similar to the solar-like region selection for FIRE-2 simula-tions used in [41], where ring-like regions centered around R⊙ were usedinstead. The voxels were then filtered by density, using the values in Ta-26ble 3.1 for dark matter and neutral gas densities, and using |nie,V − 0.019|<0.013 cm−3 for the ionized gas density averaged over spheres with radius1.6 kpc as described above.It was determined that the averaged ionized gas density from m12iwithin the solar neighbourhood (as defined by the radially and verticallyfiltered shell region described above) was too low to be comparable withobservations documented in Table 3.1. Thus, the averaged ionized gas den-sity was artificially scaled by C = 2.27 chosen such that the mean of thedistribution matches the 0.019 cm−3 estimated average density from obser-vations.The filtering process returned 9884 candidate solar neighbourhood vox-els, of which 10 were selected at random for our analysis. Voxels withina 1.2x1.2x1.2 kpc cube around each selected voxel were considered in theFUV AQN flux calculation, since this is the region covered by the 0.6 kpcmean free path as discussed in Section 2.2. Histograms of the parameters(dark matter, neutral gas and ionized gas densities, and ionized gas tem-perature) from these selected voxel regions are shown in Figure 3.6.2710 4 10 3 10 2 10 1 100Ionized Gas [1 / cm3]0.00.10.20.30.4 OriginalScaled10 3 10 1 101Neutral Gas [1 / cm3]0.00.10.20.30.5 1.0 1.5 2.0Dark Matter [1e-21 kg / m3]0.000.050.100.150.2010 3 10 1 101 103Gas Temperature [eV]0.00.10.20.30.40.5Figure 3.6: Probability density histograms of parameters from neigh-bouring voxels around the selected solar system candidates.Means shown with dashed blue lines. The ionized gas densityplot shows both the scaled (by C = 2.27, shown in blue) and orig-inal (shown in gray) distributions.The clumped nature of the ionized gas as described above is clearlyvisible here—the distribution shows that over 40% of the selected voxelscontain no ionized gas.Armed with these four parameters from the m12i simulation, combinedwith the analytical ∆v model from Section 3.3, we now have all of the vari-ables required to compute the AQN signal in the following Chapter 4. Allcomputations were done using the Canadian Advanced Network for As-tronomical Research (CANFAR) Science Portal3 computing system.3canfar.net/en/.28Chapter 4Results and DiscussionIn this chapter, we present the results of modelling the AQN signal usinglocal physics from a combination of FIRE’s m12i Milky Way-like simulationand analytical estimates (for ∆v). We show that the AQN-baryon annihi-lations are able to produce a signal within the same order of magnitude asthe mysterious FUV excess. Along with this we also demonstrate and dis-cuss the sensitivity of the AQN FUV signal to local physics—the ionizedgas density nion and relative velocity ∆v.4.1 Comparing Simulated Emission with GALEXThe main findings of our investigation are summarized in Figure 4.1. TheAQN FUV signal was computed at each voxel in the filtered set (obtainedby following the procedure described in Section 3.4) by applying Equation2.12, with an integral over both the velocity distribution (Equation 3.2) andGALEX FUV bandwidth, 1350-1750 A˚. A uniform hard extinction cutoff ofL= 0.6 kpc was used, consistent with [5]. The results are shown as distribu-tions of exceedance probability over all candidate regions for three differentAQN masses.290.00.10.20.30.40.5Final estimate0.00.10.20.30.40.5Exceedance Probab., P(>)Unscaled nion100 101 102 103AQN Annihilation FUV Signal, [ph / (Angstrom s sr cm2)]0.00.10.20.30.40.5v from m12iAQN Mass0.5 kg0.1 kg0.01 kgFigure 4.1: Exceedance probability of AQN FUV signal from the vox-els surrounding the candidate solar neighbourhood regions forthree AQN masses (i.e probability that the signal exceeds a given⟨Φλ⟩), in three scenarios: (top) our final estimate, using the scaledHII gas density distribution (Section 3.4), and Maxwell Boltz-mann distribution for ∆v (Section 3.3), (middle) an estimate us-ing the unscaled HII gas density distribution instead, and (bot-tom) an estimate using the ∆v data from voxels from FIRE’s m12isimulation. The magnitude of the GALEX FUV excess (100-200photon units) is shown as a light blue band.From the top panel, we note that within a reasonable AQN mass range,30the estimated FUV AQN signal is well within the magnitude identified byGALEX—at a mass of 0.1 kg, ∼20% of the signal is above the 150 photonunit mean of the GALEX excess. From this we draw the conclusion thatthe AQN emission mechanism has the potential to explain the FUV excessidentified by GALEX and confirmed by other spacecraft. The middle andbottom panels are merely included to support the discussion of sensitivityof the AQN signal in the short section that follows.4.2 Emission Sensitivity to Local ParametersThe purpose of the middle and bottom panels in Figure 4.1 are to demon-strate the sensitivity of the AQN model to local physics parameters. Themiddle panel shows the effect of using the original ionized gas nion distri-bution from m12i: the signal scales with ionized gas via ⟨Φλ⟩ ∼ n1.9ion, whichlowers the signal in the middle panel by C13/7 ≈ 4.6. The most significantsensitivity is shown in the bottom panel: The modification for producingthe estimate shown here is equivalent to replacing the velocity distributionfunction f in Equation 2.12 with a delta function f (∆v,∆vi0) = δ(∆v−∆vi0),where ∆vi0 is the difference in velocity for voxel i, obtained from the tes-sellated m12i simulation data. The result is a significant decrease in fluxmagnitude estimate, linked to the strongly non-linear inverse relationshipbetween the signal and ∆v, with ⟨Φλ⟩ ∼ ∆v−5.6 as discussed in Section 3.2.Although the average of the m12i velocity distribution is lower than theshifted MB distribution as seen in Figure 3.4, the m12i ∆v becomes un-physical for small ∆v (the distribution remains constant and nonzero for∆v≲ 80 km/s). The signal computed using the MB distribution still domi-nates as a result.31Chapter 5Future WorkIn addition to the current discussion about the magnitude of the myste-rious diffuse FUV radiation detected by GALEX, the broadband and dif-fuse nature of the flux from AQN annihilations opens the door for furtherworthwhile investigations across different frequencies, which we will dis-cuss here.One such avenue is a discussion of the spectrum of the UV radiationin the Milky Way, and is closely related to optical depth. In the currentpaper, we estimated the expected AQN flux using a hard cutoff of 0.6 kpcdue to dust extinction, and assuming a constant extinction near the FUVGALEX bandwidth range, 1350-1750 A˚. However, as λ approaches the Ly-mann limit of 912 A˚, the extinction of the signal becomes stronger, and thisno longer holds. Below 912 A˚, the extinction is exponentially stronger dueto gas absorption effects, leading to a sharp decrease in the observed flux.Estimating the corresponding optical depth τ in this part of the spectrumis challenging due to the large uncertainties in measurements near the Lyαline. Recent UV observations of the spectrum by the New Horizons space-craft [10] have identified an offset in the range 912-1100 A˚, only half ofwhich can be explained by known sources. These findings suggest a poten-tial underestimation of local dust extinction or an incomplete model of UVbackground sources. Obtaining an estimate of the contribution from theAQN annihilation interaction in this part of the spectrum has the potential32to shed light on both the excess signal in this region, and the UV absorp-tion modelling (namely the optical depth and E(B−V)), in a region whereisolating a signal from observations is difficult.Another avenue is a discussion of a long standing problem related tothe nature of the re-ionization of the Universe. Indeed, by studying the va-riety of spectra the authors of [45] argued that the same DM source which isresponsible for FUV diffuse emission in the Milky Way (which is the topicof the present work) must also emit (direct quote) “a continuum of pho-tons in the range ∼ 850 A˚ to about 2000 A˚”. The AQN-induced mechanismproposed in this work potentially is capable to address this long standingproblem as all required features are present in the system.Furthermore, the same DM source in form of the AQNs may also con-tribute to the resolution of another long standing problem related to theExtragalactic Background Light (EBL). Indeed, it has been known for sometime that the conventional measurements cannot be explained by diffusegalaxy halos or intergalactic stars. The discrepancy could be as large as afactor of ∼ (2− 3) or even more, see e.g. recent review [46]. Our commenthere is that the AQNs may fulfill this shortage as the spectrum is very broadand includes optical and IR light.Another potential investigation is related to a newly identified reioniza-tion tension: recent James Webb Space Telescope (JWST) results revealed atension between different probes of reionization: an excess in ionizing pho-tons was inferred from newly observed early galaxies, implying that reion-ization may have ended earlier than previously inferred from cosmic mi-crowave background (CMB) and Lyman-α forest observations, thus lead-ing to a “photon budget crisis” [47]. A key element in this discussion isthe escape fraction fesc, the fraction of ionizing photons that escape fromgalaxies to contribute to reionization. The JWST observations suggest thatearly galaxies are highly efficient at producers ionizing photons, and theirinferred fesc values, when combined with the observed abundance of galax-ies, lead to an overproduction of ionizing photons and thus an earlier com-pletion of reionization, in conflict with CMB constraints. Our original com-ment here is as follows. The implied UV photon budget crisis may find33its natural resolution by accounting for the AQN-induced photons whichis the topic of the present work. Indeed, we propose a new mechanism ofthe UV emission which is not related in anyway with UV emitting stars,representing the main source in canonical analysis of the UV diffuse flux.This suggested additional mechanism of the UV photon’s production mayalter the canonical view on ionization history of the Universe. To be moreprecise, the AQN-induced photons may provide a way to reconcile thesepuzzling observations by accounting for the observed tension in the ioniz-ing photon budget.34Chapter 6ConclusionThis thesis proposed a new mechanism for the production of diffuse UVphotons in the Milky Way, where a mysterious FUV emission has beenrecorded [5–7]. We argued that the puzzling features of this excess listed inChapter 1 can be naturally explained within the proposed AQN-inducedmechanism. Specifically, we demonstrated that the FUV emission frombaryon annihilations with anti-AQNs has the potential to explain the iden-tified excess. We did this by estimating the expected magnitude of the AQNsignal within the Milky Way, using parameters from a combination of aMilky Way-like galaxy simulation and analytical models. Within a reason-able AQN mass range, the magnitude of the AQN flux matches the GALEXexcess.In the context of this AQN emission mechanism, many potential av-enues for investigation were discussed in Chapter 5. More specific to thisproject, however, two important directions should be taken moving for-ward: First, a spatial distribution of the AQN FUV flux estimate can beobtained. This will require a more precise modelling of the local param-eters and the optical depth in our Milky Way. The AQN model offers aunique coupling between dark matter and visible matter densities that isnot present in other dark matter models. If the mysterious FUV emissionalso follows the same distribution (i.e. the excess is proportional to ρDMρVM),then showing a spatial consistency with the identified FUV excess in ad-35dition to the consistency in magnitude in this present work can make astrong case for the AQN model. Secondly, another consistency check canbe performed with other Galactic excesses: the constraints on the AQNmass which result from the comparison of the AQN signal with the Galac-tic FUV excess can be compared with constraints from comparison withother Galactic excesses, such as in the radio [48] and x-ray [49]. Yet an-other unique feature of the AQN annihilation mechanism is the fact thatthe resulting emission is a broadband spectrum, offering the ability to es-timate the AQN flux across these different bandwidths corresponding toentirely independent observations. Demonstrating a consistency amongstthese comparisons will offer very compelling evidence for dark matter inthe form of axion quark nuggets, indicating that it is possible to explainmultiple entirely independent phenomena within a single model and a sin-gle set of parameters.36Bibliography[1] M. Sekatchev, X. Liang, L. Van Waerbeke, and A. Zhitnitsky. TheGlow of Axion Quark Nugget Dark Matter: III. 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Axion quark nuggets : a recipe for a glowing Milky Way?
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