Ball Lightning as a Profound Manifestation of Dark Matter Physics

Abstract

Ball lightning (BL) has been observed for centuries. There are a large number of books, review articles, and original scientific papers devoted to different aspects of the BL phenomenon. Yet, the basic features of this phenomenon have never been explained by known physics. The main problem is the source which could power the dynamics of BL. We advocate the idea that dark matter (DM) in the form of axion quark nuggets (AQNs) made of standard model quarks and gluons (similar to the old idea of Witten’s strangelets) could internally generate the required power. The AQN model was invented long ago without any relation to BL physics. It was invented with a single motivation to explain the observed similarity, ${\Omega }_{\mathrm{DM}}\sim {\Omega }_{\mathrm{visible}}$, between visible and DM components. This relation represents a very generic feature of this framework, not sensitive to any parameters of the construction. However, with the same set of parameters being fixed long ago, this model is capable of addressing the key elements of the BL phenomenology, including the source of the energy powering the BL events. In particular, we argue that the visible size of BL, its typical life time, the frequency of its appearance, etc., are all consistent with the suggested proposal that BL represents a profound manifestation of DM physics represented by AQN objects. In this work, we limit ourselves to the analysis of the thunderstorm-related BL phenomena, though weather-unrelated BL events are also known to occur. We also formulate a number of specific possible tests which can refute or unambiguously substantiate this unorthodox proposal on the nature of BL.

1. Introduction

The title of this work seemingly includes two contradictory terms: The first one is “ball lightning”, which is a very bright luminous object, though of unknown nature. The second term of the title is “dark matter” (DM), which must, by definition, be decoupled from radiation, as it cannot emit light. Indeed, the BL phenomenon has been known for centuries; see the recent book [1] and review papers [2,3,4] with a large number of references therein. See also the recent review article [5] with several historical comments on BL observations by scientists and trained professionals. The main goal of this work is to argue that the numerous puzzling observations of ball lightning (BL) could be explained from a unified viewpoint within a specific dark matter model, the so-called axion quark nugget (AQN) dark matter model [6]; see also the brief review [7] for a short overview of the AQN framework.

We overview the basic ideas of the AQN construction in next section. The main outcome of this construction is that the AQN behaves as a chameleon: it serves as a proper DM object in a dilute environment, but becomes a very strongly interacting object when it hits stars or planets. Therefore, the contradiction in the title is only apparent as DM in the form of AQNs become strongly interacting objects in a dense environment and can indeed produce profound and very powerful events such as BL, which is the topic of the present work.

Before we proceed with our explanations of the BL phenomenology within the AQN framework, we should, first of all, highlight the mysterious properties of the observations [1,2,3,4] which are impossible to understand if interpreted in terms of conventional physics. In fact, a complete failure to understand even the very basic features of the BL phenomenology (such as the required power, or passing through a solid glass) forced researchers to look for possible answers within subatomic physics, well outside the conventional mechanisms considered in the past. In particular, in ref. [8], it was suggested that the magnetic monopole might be powering the BL, while in ref. [9], this idea was modified by adding an electrical charge into the system by making a dyon (a magnetic monopole with a non-vanishing electric charge). Our proposal is also deeply rooted in subatomic physics, but in a dramatically different way, as we discuss below.

1.1. Brief Overview of Weather-Related Ball Lightning Phenomenology

The first term of the title is “ball lightning”. Therefore, we have to explain and list the basic features of BL. As we mentioned in the abstract in this work, we limit ourselves to thunderstorm-related BL events. It is known that weather-uncorrelated BL events may also occur; see the recent book [1] with a large number of references to original older books and scientific papers. It is possible that weather-unrelated BL events may also be associated with the AQN-induced events. However, the corresponding studies are well outside the scope of the present studies and shall not be addressed in the present work.

We literally follow (quote) the review article [4], which states that a successful model should explain the following observed features:

(i)

Ball lightning’s association with thunderstorms or with cloud-to-ground lightning;

(ii)

Its reported shape, diameter, and duration, and the fact that its size, luminosity, and appearance generally do not change much throughout its life time;

(iii)

Its occurrence in both open air and in enclosed spaces, such as buildings or aircraft;

(iv)

The fact that ball lightning motion is inconsistent with the convective behaviour of a hot gas;

(v)

The fact that it may decay either silently or explosively;

(vi)

The fact that ball lightning does not often cause damage;

(vii)

The fact that it appears to pass through small holes, through metal screens, and through glass windows;

(viii)

The fact that it is occasionally reported to produce acrid odours and/or to leave burn marks, is occasionally described as producing hissing, buzzing, or fluttering sounds, and is sometimes observed to rotate, roll, or bounce off the ground.

In addition to these well-established features of BL, we want to add a few very important recent quantitative measurements suggesting that there is a new scale of the problem on the 240 μm [10] level. Studies were performed with optical and scanning microscopes and laser beam probing of the glass that experienced the action of a 20 cm BL. Furthermore, the spectrum from BL has been observed with two slitless spectrographs at a distance of 0.9 km, and it includes the soil components (Si I, Fe I, and Ca I) as well as the air components (N I and O I) [11,12]. Furthermore, it has been recently claimed that BL radiation must be accompanied by UV or even X-ray emission [13]. Therefore, we add a few more items to the list:

(ix)

A new scale emerges in the BL problem: 240 μm, which is dramatically different from the visible size of the BL [10];

(x)

The spectrum from BL includes lines from soil components (Si I, Fe I, and Ca I) as well as air components (N I and O I) [11,12];

(xi)

The spectrum from BL must include UV or/and X-ray emission [13].

We also want to list some BL characteristics which have been collected for decades and which play a very important role in our discussions. We start with the energetic characteristics of BL. The energies of BL events dramatically vary from case to case and can be estimated as follows [2]:

$$\begin{array}{c}\hfill E_{\min }={10}^{-0.8\pm 0.2}\mathrm{kJ},E_{\max }={10}^{3.2\pm 0.2}\mathrm{kJ},\overline{E}={10}^{1.3\pm 0.2}\mathrm{kJ}.\end{array}$$

(1)

The energy density $ϵ$ also varies for different observations and has been estimated as [2]:

$$\begin{array}{c}\hfill {ϵ}_{\min }={10}^{-0.6\pm 0.5}{\displaystyle \frac{J}{{\mathrm{cm}}^3}},{ϵ}_{\max }={10}^{3\pm 0.5}{\displaystyle \frac{J}{{\mathrm{cm}}^3}},\overline{ϵ}={10}^{1.2\pm 0.5}{\displaystyle \frac{J}{{\mathrm{cm}}^3}}.\end{array}$$

(2)

The typical diameter of BL has been estimated as [2]:

$$\begin{array}{c}\hfill d=28\pm 4\mathrm{cm},\end{array}$$

(3)

while the life time $\tau$ and velocity $v_{\mathrm{BL}}$ have been estimated from a variety of observations as [2]:

$$\begin{array}{c}\hfill \tau =9_{-4}^{+6}\mathrm{s},v_{\mathrm{BL}}\in (0.1-10){\displaystyle \frac{\mathrm{m}}{\mathrm{s}}},{\overline{v}}_{\mathrm{BL}}=4{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}.\end{array}$$

(4)

Another important parameter we need for our discussions is radiated power (extracted from studies of visible frequency bands), which also strongly varies, and on average can be estimated as [2]:

$$\begin{array}{c}\hfill P={10}^{2.0\pm 0.2}W.\end{array}$$

(5)

The main obstacle preventing the development of a successful BL phenomenology is the failure to explain the source of the required energy. Any conventional theory (including any known sources of energy) cannot explain one particular well-established property of ball lightning: its ability to pass through closed glass windows [14]. The authors of ref. [10] arrived to a similar conclusion by analyzing the glass damaged by passing BL using the scanning electron microscope as listed in item (ix) above. The only physical entities which can easily pass through a few mm of solid glass are subatomic particles, which recently motivated the authors of refs. [8,9] to consider the magnetic monopole as a possible source of BL’s energy, powering its dynamics.

1.2. Brief Overview of Dark Matter

The second term of the title is “dark matter”. Therefore, we have to briefly explain the term “dark matter”. From the cosmological viewpoint, there is a fundamental difference between dark matter and ordinary matter (aside from the trivial difference, dark vs. visible). Indeed, DM played a crucial role in the formation of the present structure of the Universe. Without dark matter, the Universe would have remained too uniform to form galaxies. Ordinary matter could not produce fluctuations to create any significant structures because it remains tightly coupled to radiation, preventing it from clustering, until recent epochs. The key parameter which enters all the cosmological observations is the corresponding cross section $\sigma$ (describing the coupling of DM with standard model particles) to mass $M_{\mathrm{DM}}$ ratio, which must be sufficiently small to play the role of DM as briefly mentioned above (see e.g., recent review [15]):

$$\begin{array}{c}\hfill {\displaystyle \frac{\sigma }{M_{\mathrm{DM}}}}\ll 1{\displaystyle \frac{{\mathrm{cm}}^2}{\mathrm{g}}}.\end{array}$$

(6)

The Weakly Interacting Massive Particles (WIMPs) obviously satisfy criteria (6) to serve as DM particles due to their very tiny cross section $\sigma$ for a typical mass $M_{\mathrm{WIMP}}\in ({10}^2-{10}^3)\mathrm{GeV}$. However, the WIMP miracle has failed as dozens of dedicated instruments could not find any traces of WIMPs though the sensitivity of the instruments had dramatically improved by many orders of magnitude during the last decades.

In the present work, we consider a fundamentally different type of DM which is in the form of macroscopically large composite objects of nuclear density, similar to Witten’s quark nuggets [16,17,18]. The corresponding objects are called axion quark nuggets (AQNs) and behave as chameleons: they are (almost) not interacting entities in dilute environment, such that AQNs may serve as proper DM candidates as the corresponding condition (6) is perfectly satisfied for AQNs during the structure formation when the ratio $\sigma /M_{\mathrm{AQN}}\lesssim {10}^{-10}$${\mathrm{cm}}^2{\mathrm{g}}^{-1}$. However, the same objects interact very strongly with materials when they hit the Earth, or other planets and stars.

The main distinct feature of the AQN model (which plays an absolutely crucial role in the present work) in comparison with the old Witten’s construction is that AQNs can be made of matter as well as antimatter during the QCD transition as a result of the charge segregation process; see brief overview [7]. This charge segregation mechanism separates quarks from anti-quarks during the QCD transition in the early Universe as a result of the dynamics of the $\mathcal{CP}$ odd axion field; see more detailed explanations and references in the next section, Section 2. This separation of baryon charges leads to the formation of the quark nuggets and anti-quark nuggets at a similar rate.

The presence of the antimatter nuggets in the system implies that there will be annihilation events leading to very profound strong effects when antimatter AQNs hit the Earth. Our claim here is that the basic features of the BL phenomenology, as listed by items (i)–(xi), along with the basic BL characteristics, expressed by (1)–(5), may naturally emerge as a result of these powerful and energetic annihilation events.

We reiterate the main claim of this work slightly differently: our proposal is that the source of energy which is powering BL events is related to the annihilation events of the antimatter hidden in the form of AQNs with the surrounding atoms and molecules1. The fuel which is powering the BL physics is the antimatter nuggets which had been formed during the QCD transition in the early Universe. It has also been shown that the dominant fraction of these antimatter nuggets mostly survive until the present epoch; see brief review on formation mechanism and survival pattern in the next section, Section 2.1.

This model was invented long ago to resolve fundamental problems in cosmology, not related in any way to BL phenomena (in contrast with numerous proposals which were specifically designed to explain different aspects of the BL phenomenology). Nevertheless, this AQN framework may also shed a light on another long-standing problem, which is the nature of BL. We stress that all parameters for this model were fixed long ago in our previous applications to explain some mysterious and puzzling observations at the galactic and solar scales, to be reviewed in the Conclusion in Section 6.2. We keep all these parameters of the AQN model identically the same and we do not attempt to modify them to better fit the observations related to BL phenomenology.

The presentation of this work is organized as follows. The next section, Section 2, represents a brief overview of the AQN construction. In our main section, Section 3, we argue that the various observations, as formulated above and collected for decades, can be naturally explained within the AQN framework. In Section 4 we estimate the BL event rate and find it is consistent with our observations. In Section 5 we briefly mention the possible relation between BL and the so-called pseudo-meteorite events. In our concluding section, Section 6, we suggest a number of specific tests which can substantiate or refute our proposal on the close relation between BL and dark matter physics within the AQN framework.

2. The AQN Dark Matter Model

We give an overview of the fundamental ideas of the AQN model in Section 2.1, while in Section 2.2 and Section 2.3, we list some specific features of the AQNs relevant to the present work.

2.1. The Basics

The original motivation for the AQN model can be explained as follows. It is commonly assumed that the Universe began in a symmetric state with zero global baryonic charge and later (through some baryon-number-violating process, non-equilibrium dynamics, and $\mathcal{CP}$-violation effects, realizing the three famous Sakharov criteria) evolved into a state with a net positive baryon number.

As an alternative to this scenario, we advocate a model in which “baryogenesis” is actually a charge-separation (rather than charge-generation) process in which the global baryon number of the Universe remains zero at all times. This represents the key element of the AQN construction.

In the AQN scenario, the DM density, ${\Omega }_{\mathrm{DM}}$, representing the matter and antimatter nuggets, and the visible density, ${\Omega }_{\mathrm{visible}}$, will automatically (irrespective of the axion mass $m_a$ or miss-alignment angle ${\theta }_0$) assume the same order of magnitude densities ${\Omega }_{\mathrm{DM}}\sim {\Omega }_{\mathrm{visible}}$ as they are both proportional to the one and the same fundamental dimensional parameter of the theory, the ${\Lambda }_{\mathrm{QCD}}$. Therefore, the AQN model, by construction, actually resolves two fundamental problems in cosmology (it explains the baryon asymmetry of the Universe, and the presence of DM with proper density ${\Omega }_{\mathrm{DM}}\sim {\Omega }_{\mathrm{visible}}$) without the necessity to fit any parameters of the model.

The strongest direct detection limit2 on the baryon charge B of a nugget is set by the IceCube Observatory (see Appendix A in [22]):

$$\begin{array}{c}\hfill \langle B\rangle >3·{10}^{24}[\mathrm{direct}\left(\mathrm{non}\right)\mathrm{detection}\mathrm{constraint}].\end{array}$$

(7)

The basic idea of constraint (7) is that IceCube, with its surface area $\sim {\mathrm{km}}^2$, has not detected any events during its 10 years of observations. In estimate (7), it was assumed that the efficiency of detection of a macroscopically large nugget is 100%, which excludes AQNs with small baryon charges $\langle B\rangle <3·{10}^{24}$ with ∼$3.5\sigma$ confidence level.

In other words, the unobserved antibaryons in the visible sector in this model comprise dark matter being in the form of dense nuggets of anti-quarks and gluons in the colour superconducting (CS) phase. The result of this “charge-separation process” is the formation of two populations of AQNs carrying positive (nuggets) and negative baryon numbers (anti-nuggets). We refer to the recent paper [23] with a detailed overview of the relevant AQN physics and typical characteristics of the nuggets, such as size, mass distribution, survival pattern, basic constraints, etc. The only comment we would like to make here is as follows. The AQNs are very rare events because they are very heavy in comparison to conventional WIMPs. The AQN flux can be estimated as follows [22]:

$$\begin{array}{c}\hfill {\displaystyle \frac{d\Phi }{dA}}={\displaystyle \frac{\Phi }{4\pi R_{\oplus }^2}}=4·{10}^{-2}\left({\displaystyle \frac{{10}^{25}}{\langle B\rangle }}\right){\displaystyle \frac{\mathrm{events}}{\mathrm{year}·{\mathrm{km}}^2}},\end{array}$$

(8)

where $R_{\oplus }=6371$ km is the radius of the Earth, while $\langle B\rangle \approx {10}^{25}$ is the typical baryon charge of AQNs, and $\Phi$ is the total hit rate of AQNs on Earth [22]:

$$\begin{array}{c}\hfill \Phi \approx {\displaystyle \frac{2·{10}^7}{\mathrm{year}}}\left({\displaystyle \frac{{\rho }_{\mathrm{DM}}}{0.3\mathrm{GeV}{\mathrm{cm}}^{-3}}}\right)\left({\displaystyle \frac{v_{\mathrm{AQN}}}{220\mathrm{km}{\mathrm{s}}^{-1}}}\right)\left({\displaystyle \frac{{10}^{25}}{\langle B\rangle }}\right),\end{array}$$

(9)

where ${\rho }_{\mathrm{DM}}$ is the local density of DM within the Standard Halo Model (SHM).

2.2. When the AQN Hits the Earth

The computations of the AQN–visible matter interaction have been originally carried out in [24] in application to the galactic environment with a typical density of surrounding baryons of order $n_{\mathrm{galaxy}}\sim {\mathrm{cm}}^{-3}$ in the galaxy, while the internal temperature is in the $T\sim \mathrm{eV}$ range. We want to avoid the repetition of some formulae, and refer to the recent paper [23] which properly reviews the basic ideas of the construction when AQN propagates in the galaxy, in the Earth’s atmosphere, and in solid rocks.

The only estimates we need in the present work are the AQN’s features when the nuggets propagate in the Earth’s atmosphere. In this case the AQN’s internal temperature starts to rise up to ∼20 keV or so. As a result, the typical internal nugget’s temperature in the Earth atmosphere is estimated as follows:

$$\begin{array}{c}\hfill T\sim 20\mathrm{keV}·{\left({\displaystyle \frac{n_{\mathrm{air}}}{{10}^{21}{\mathrm{cm}}^{-3}}}\right)}^{{\displaystyle \frac{4}{17}}}{\left({\displaystyle \frac{\kappa }{0.1}}\right)}^{{\displaystyle \frac{4}{17}}},\end{array}$$

(10)

where the typical density of the surrounding baryons is $n_{\mathrm{air}}\simeq 30·N_m\simeq {10}^{21}{\mathrm{cm}}^{-3}$, where $N_m\simeq 2.7·{10}^{19}{\mathrm{cm}}^{-3}$ is the molecular density in the atmosphere when each molecule contains approximately 30 baryons. The factor $\kappa$ in (10) is introduced to account for complicated physics, as we discuss below. In a neutral environment when no long-range interactions exist, the value of $\kappa$ cannot exceed $\kappa \sim 1$ which would correspond to the total annihilation of all impacting matter into to thermal photons. The high probability of reflection at the sharp quark matter surface lowers the value of $\kappa$.

Thus, in the atmosphere, the internal nugget’s temperature $T\approx$ 20 KeV. A similar temperature $T\approx 20$ keV had been previously used in [25] to explain the unusual cosmic ray-like events observed by the Telescope Array Collaboration (so-called “TA bursts”), and in [26] to explain “Exotic Events” recorded by the AUGER collaboration.

Another feature which is relevant to our present study is the ionization properties of the AQN. Ionization, as usual, occurs in a system as a result of the high internal temperature T. In our case of the AQN characterized by temperature (10), a large number of weakly bound positrons $\sim Q$ from the electrosphere get excited and can easily leave the system. The corresponding parameter Q can be estimated as:

$$\begin{array}{c}\hfill Q\approx {\displaystyle \frac{4\pi R^2}{\sqrt{2\pi \alpha }}}\left(mT\right){\left({\displaystyle \frac{T}{m}}\right)}^{{\displaystyle \frac{1}{4}}}.\end{array}$$

(11)

Numerically, the number of weakly bound positrons can be estimated from (11) as follows:

$$\begin{array}{c}\hfill Q\approx 3·{10}^{11}{\left({\displaystyle \frac{T}{20\mathrm{keV}}}\right)}^{{\displaystyle \frac{5}{4}}}{\left({\displaystyle \frac{R}{2.25·{10}^{-5}\mathrm{cm}}}\right)}^2.\end{array}$$

(12)

2.3. AQN Spallation

One more feature of the AQN propagating in the Earth’s atmosphere (which plays an important role in the present work) is as follows. As reviewed in [23], the AQN is an absolutely stable object because the energy per unit baryon charge in the CS phase (AQN’s core) is smaller than for nucleons. However, some external strong impact and large energy injection (due to sudden annihilation events within the AQN’s quark core) may disintegrate the AQN when a small chunk from the original AQN material (in the form of anti-quark-matter) is separated from the original parent AQN. In a sense, it is very similar to the well-known and well-studied spallation effect, which is a very common phenomenon in nuclear physics. We coin the corresponding secondary particles as AQN_s, where subscript “s” stands for secondary particle or spallation.

The secondary AQN_s are obviously not absolutely stable objects as the key element for the stability, the axion domain wall with its QCD substructure, cannot remain in the system after spallation. This should be contrasted with the conventional spallation effect in nuclear physics, when both the original nucleus and the secondary particles are absolutely stable objects (with respect to strong interactions) as they both propagate in the same hadronic (low chemical potential, low temperature) phase3, while AQN’s core is assumed to be in the CS phase characterized by a sufficiently large chemical potential (large pressure); see general discussions on CS phases in [27].

Another key difference with the conventional spallation effect in nuclear physics is that the energy deposition in CS is expected to be distributed between a large number of baryons in the CS phase. It is very different from a single energetic event in nuclear physics; see additional comments on this matter at the end of this subsection.

The secondary AQN_s could be much smaller in size than the AQN. The corresponding fragment really represents very small chunk of the original (antimatter) material. As we discuss in next section, Section 3, the secondary AQN_s will be identified with BL events as conjecture (13) states. Precisely, these chunks of antimatter material will play the role of engines powering the BL dynamics in this proposal. These objects should have typical sizes $B_{AQ{N}_s}\approx {10}^{15}$ (to be discussed below), which is 10 orders of magnitude smaller than original AQN with a typical baryon charge $B\approx {10}^{25}$.

In our discussions which follow, we assume that the spallation is likely to occur in thunderclouds as the most important ingredient required for spallation, a high fraction of ionized particles in the surrounding area, is present during the thunderstorms. As we discuss below, the highly ionized environment dramatically increases the effective strength of the interaction of the AQN with the surrounding material, expressed by parameter $\kappa$ in (10), which drastically increases the internal temperature leading to spallation; see Section 3.2 with more comments on this matter. The spallation dynamics, the size distribution of the secondary AQN_s, and other related questions have not been worked out yet (detailed discussions on the formation mechanism for the original AQN can be found in ref. [28]). A proper treatment of spallation in the AQN system requires a deep understanding of many-body physics as well as the phase diagram in a strongly coupled regime, similar to studies of the intermediate states in superconductors [29] when normal and superconducting phases may co-exist in a sample and form the macroscopically large domains, similar to ferromagnetic domains. The size of such macroscopically large domains scale as $\propto \sqrt{R}$ [29].

We assume that a similar intermediate state may occur in CS phases when the chemical potential depends on the distance from the surface of the core, and may not be sufficiently large to maintain the uniform CS phase in the entire volume of the system. This is because the axion domain wall pressure (which is the critical element for AQN stability) strongly depends on the distance. If this is indeed the case, one should expect that a typical size of the corresponding domain is determined by the size R of the parent AQN and the binding energy, which is assumed to be in the MeV range, representing a typical nuclear physics energy scale. In other words, the domain size for the AQN_s can be estimated as $\propto \sqrt{R/\left(\mathrm{MeV}\right)}\sim {10}^{-8}\mathrm{cm}$. We assume that the entire domain of such size can fall apart from the parent AQN as a result of (almost instantaneous) a large number of annihilation events when the AQN enters the strongly ionized atmosphere during the thunderstorms, at which moment the rate of annihilation events dramatically increases.

The corresponding questions on typical time scales (such as the rate of annihilation and rate of cooling), sizes, and structures of these domains are well beyond the scope of the present work as the relevant physics is very complicated, as briefly mentioned in the previous paragraph. We take an agnostic view at this stage on spallation dynamics. We just assume that the spallation occurs and we use a typical size (or what is the same, the baryon charge) of the secondary AQN_s to fit the BL observations (we do not compute this number in the present work). This is the only input parameter to be used in all our estimates below, while all other observables relevant to BL physics will be derived from this single input parameter.

To conclude this overview section on the AQN framework, one should mention here that this model with the same set of parameters to be used in the present work may explain a number of puzzling and mysterious observations which cannot be understood as conventional astrophysical phenomena. In particular, there are many mysterious observations which occur at dramatically different scales in very different cosmological eras, which also might be related to AQN-induced phenomena. It includes the BBN epoch, dark ages, as well as galactic and solar environments. It also includes a number of puzzling and mysterious CR-like events which could also be related to AQN-induced phenomena; see concluding sections, Section 6.1 and Section 6.2, for details and references.

3. Proposal (13) Confronts the Observations

Our proposal can be formulated as follows. The secondary particles (after spallation) in the form of the antimatter AQN_s are identified with ball lightning events, i.e.,

$$\begin{array}{c}\hfill \mathrm{secondary}{\mathrm{AQN}}_{\mathrm{s}}\mathrm{events}\equiv \mathrm{Ball}\mathrm{Lightning}\mathrm{events}.\end{array}$$

(13)

The main goal of this section is to argue that the various observations, as formulated in the Introduction, Section 1, collected for decades can be naturally explained (though very often on a qualitative level)4 if one accepts proposal (13).

3.1. Source of the Energy Powering BL

The source of the energy in the AQN framework is obviously the antimatter annihilation with the surrounding material. Every annihilation event of a single baryon produces approximately 2 GeV of energy. We fix the basic parameter of proposal (13) by fixing the total amount of antimatter in the form of the secondary $AQ{N}_s$. According to (1), the typical energy for BL events varies from 1 kJ to ${10}^3$ kJ. The mean energy for BL is estimated in [2] as $2·{10}^2$ $\mathrm{kJ}$. To simplify our estimates below, we use ${10}^2 kJ$ as a typical average energy for BL events. Therefore, we fix the amount of antimatter hidden in the form of $AQ{N}_s$ accordingly:

$$\begin{array}{c}\hfill {10}^2\mathrm{kJ}\approx {10}^{15}\mathrm{GeV}\to {\mathrm{B}}_{{\mathrm{AQN}}_{\mathrm{s}}}\approx {10}^{15},{\mathrm{R}}_{{\mathrm{AQN}}_{\mathrm{s}}}\approx {\left({\displaystyle \frac{{\mathrm{B}}_{{\mathrm{AQN}}_{\mathrm{s}}}}{\mathrm{B}}}\right)}^{{\displaystyle \frac{1}{3}}}\mathrm{R}\approx {10}^{-8}\mathrm{cm}\end{array}$$

(14)

where we use the conversion factor $J=0.6·{10}^{10}\mathrm{GeV}$. One should emphasize that the chunks of $AQ{N}_s$ could have very different sizes. Therefore, a wide window for the BL energy distribution (as extracted from observations, see Figure 5 in [2]) could be easily accommodated in our proposal (13) to fit the data. However, we stick with the average value (14) in what follows, for the simplicity of our qualitative analysis. One should also add that the large variation in the energies of the BL events (1) strongly suggests that the source of the energy is unlikely to be related to any fundamental subatomic particles, where one should expect similarities for different events. In contrast, proposal (13) is based on a complex classical macroscopical system with a variety of sizes, which is perfectly consistent with the broad distribution of the energy scales (1).

3.2. BL Is Electrically Charged

Now we want to argue that $AQ{N}_s$ will carry the electric charge $Q_{{\mathrm{AQN}}_{\mathrm{s}}}$ after spallation. The corresponding numerical value can be easily estimated by assuming that the internal temperature of the $AQ{N}_s$ immediately after spallation remains the same as for the original AQN (12). Therefore, one can use rescaling to arrive at the estimate:

$$\begin{array}{c}\hfill {\displaystyle \frac{Q_{{\mathrm{AQN}}_{\mathrm{s}}}}{Q}}\approx {\left({\displaystyle \frac{B_{{\mathrm{AQN}}_{\mathrm{s}}}}{B}}\right)}^{{\displaystyle \frac{2}{3}}}\approx {\left({\displaystyle \frac{{10}^{15}}{{10}^{25}}}\right)}^{{\displaystyle \frac{2}{3}}}\approx 2·{10}^{-7}\to Q_{{\mathrm{AQN}}_{\mathrm{s}}}\approx 6·{10}^4,\end{array}$$

(15)

where we used the feature that the Q charge is the surface effect5, while the baryon B charge is the volume effect. The presence of the charge in the system will play a key role in the dynamics to be discussed below. First of all, the presence of the charge Q in the system in the original AQN implies that the AQN can attract the positively charged ions from the air such that the rate of annihilation may dramatically increase. This effect can be described by the drastic increase in the phenomenological coefficient $\kappa$ in (10) such that effective temperature T also increases during the time when AQN propagates in the region of a highly ionized gas. As a consequence, the spallation phenomenon may be much more efficient (and likely to occur) in this case.

The presence of a large density of ionized particles in the air is known to occur during thunderstorms in thunderclouds (even without strikes). Therefore, the association of BL with thunderstorms, see item (i) from Section 1.1, has its direct explanation within our proposal due to the sudden and dramatic increase in $\kappa$ (and corresponding internal temperature T) as mentioned above. This increase in T will consequently increase the charge of the AQN according to (11), which further increases the cross section, and T. This exponential growth can be coined as the “bootstrap” mechanism6. These dramatic changes may lead to the spallation effect which consequently results in the formation of the secondary particles ${\mathrm{AQN}}_{\mathrm{s}}$ which are identified with BL according to (13).

Furthermore, the secondary particles ${\mathrm{AQN}}_{\mathrm{s}}$ are also charged according to (15). One should emphasize that this estimate for $Q_{{\mathrm{AQN}}_{\mathrm{s}}}$ refers to the internal (bound) charge which are localized very close to the quark core with size (14). The induced charge due to other processes, see below, could be much greater. The presence of the electric charge in the system is also consistent with observations which suggest that BL gets attracted (due to the induced charges) to the metallic surfaces, wires, and antennae [2,4].

3.3. Spectral Properties of BL Radiation: Size of BL (In Visible Frequency Bands)

The spectral properties of the AQN emission have been studied previously, as reviewed in Appendix A. The key feature of this radiation is its very broad spectrum (in contrast with black body radiation) up to the cutoff frequency, which occurs around $\omega \approx T$. What happens to these keV photons emitted by the $AQ{N}_s$ (identified with BL) with internal core temperature $T\approx 6$ keV according to (A5)?

The dominant mechanism of absorption for such energetic X-rays is the atomic photoelectric effect, see Figure 33.15 for $Z=6$ (Carbon) in PDG [30]. For Oxygen (Z = 8) and Nitrogen (Z = 7), the effect is slightly higher due to a very strong dependence on Z [31]:

$$\begin{array}{c}\hfill {\sigma }_{\mathrm{photo}-\mathrm{effect}}\approx {\displaystyle \frac{32\sqrt{2}\pi }{3}}{r}_0^2{Z}^5{\alpha }^4{\left({\displaystyle \frac{m}{\omega }}\right)}^{{\displaystyle \frac{7}{2}}},r_0\equiv {\displaystyle \frac{{\alpha }^2}{m^2}}=2.8·{10}^{-13}\mathrm{cm}.\end{array}$$

(16)

Based on this cross section, the mean free path $\lambda$ for 6 keV photons can be estimated as

$$\begin{array}{c}\hfill {\lambda }^{O,N}\left(6\mathrm{keV}\right)\approx 10\mathrm{cm},\left[\mathrm{to}\mathrm{be}\mathrm{identified}\mathrm{with}\mathrm{visible}\mathrm{size}\mathrm{of}\mathrm{BL}\right].\end{array}$$

(17)

where we used experimental data for $Z=6$ (Carbon), see Figure 33.19 in [30], and rescaled them for Oxygen (Z = 8) and Nitrogen (Z = 7). We emphasize that there is no thermal equilibrium between $AQ{N}_s$ and the surrounding air. However, the 6 keV photons are emitted from $AQ{N}_s$ where the internal temperature is properly defined as the thermal equilibrium is perfectly maintained.

The atomic photoelectric effect is accompanied by electron emission. The life time of a free electron in air is very short, around $0.1$ μs; see, e.g., [32] such that the free electron will be quickly absorbed by atoms in the air over very short distances around ${10}^{-4} \mathrm{m}$, much shorter than (17). These excited and ionized atoms and molecules (made of Oxygen and Nitrogen along with many other elements from the soil) will emit visible light, which is observed as radiation coming from BL according to our proposal (13). Therefore, we identify the size of BL (in visible frequency bands) with mean free path $\lambda$ as stated in (17). This scale is perfectly consistent with observations (3).

A few comments are in order:

• The mean free path $\lambda$ introduced above is highly sensitive to the frequency of radiation (or what is the same, the internal temperature). Therefore, even a minor variation in the internal temperature of the $AQ{N}_s$ can dramatically modify the mean free path. To illustrate this feature, we estimate $\lambda$ for 10 keV photons:

  $$\begin{array}{c}\hfill {\lambda }^{O,N}\left(10\mathrm{keV}\right)\approx 70\mathrm{cm},\left[\mathrm{to}\mathrm{be}\mathrm{identified}\mathrm{with}\mathrm{visible}\mathrm{size}\mathrm{of}\mathrm{BL}\right]\end{array}$$

  (18)
  Our main point with this illustration is that the visible size of the BL in this proposal (13), being identified with $\lambda$, is not related to a basic energetic characteristic (1) which could dramatically vary (three orders of magnitude or more) from one event to another. Rather, the variation in size of the BL is related to very small variations in internal temperature T.
• This picture of emission of visible light is consistent with the observation that the average density of BL is the same as the average density of the surrounding air because the quark matter core with $M_{{\mathrm{AQN}}_{\mathrm{s}}}\approx {10}^{-9}\mathrm{g}$ is negligible in comparison with the weight of the air in the volume ${\lambda }^3$. The observed visible light from BL in this proposal is obviously not related to hot plasma, nor to the convective behaviour of a hot gas; see (item iv) from Section 1.1. This proposal also naturally explains the observation that BL normally moves horizontally as the average density of the BL object is the same as the air density at the same temperature7.
• This picture of emission of visible light is consistent with the observation that the spectrum contains soil components (Si I, Fe I, and Ca I) (item x) from Section 1.1. This is because the soil components have a much larger Z (and therefore, the cross section (16) is much greater). As a result, even a tiny amount of these components in air (e.g., in the form of dust particles) could generate very strong intensity lines associated with these elements, which is consistent with observations [11,12].
• From the estimate (17) of BL size in visible frequency bands, one can estimate the average energy density for our specific parameters (14) for BL propagating in air as follows:

  $$\begin{array}{c}\hfill {ϵ}^{O,N}\equiv {\displaystyle \frac{(B_{{\mathrm{AQN}}_{\mathrm{s}}}·m_p)}{{\left({\lambda }^{O,N}\right)}^2\overline{\mathrm{L}}}}\approx {\displaystyle \frac{{10}^2 kJ}{{\left(10\mathrm{cm}\right)}^2·\left(40\mathrm{m}\right)}}\approx 0.25{\displaystyle \frac{J}{{\mathrm{cm}}^3}},\overline{L}\approx {\overline{v}}_{\mathrm{BL}}·\tau \approx 40\mathrm{m},\end{array}$$

  (19)

  where $\overline{L}$ is the average length for the BL’s path with parameters from (4). This estimate is consistent with value (2) extracted from observations in visible frequency bands.
• This picture of emission is consistent with the observation that BL emits UV or X-ray radiation along with visible light, as discussed above. In fact, UV and X-rays originate from the the core of the $AQ{N}_s$, in contrast to visible light which is a secondary process in the AQN framework, as described above. This picture is perfectly consistent with item xi from Section 1.1, when the presence of UV or X-rays from BL had been directly observed [13]. The presence of UV or X-rays from BL is also supported by our estimate for the total power of emission, which suggests that the power in visible light represents only a small fraction of the total power; see next section, Section 3.4.
• Annihilation of the baryons is always accompanied by annihilation of the electrons from atoms with positrons from the AQN’s electrosphere. The corresponding total energy injection per single event (MeV scale) due to $e^{+}{e}^{-}$ annihilation is negligible (∼${10}^{-3}$) in comparison with the GeV scale due to hadron annihilations. However the emission of the 0.511 MeV photons from $e^{+}{e}^{-}$ annihilation may play a crucial role in the understanding of items viii and xi from Section 1.1. This is because the mean free path for such energetic photons in air is very large, $\lambda \left(0.5\mathrm{MeV}\right)\sim 10\mathrm{m}$, such that these photons can ionize the surrounding space and could be responsible for ionizing radiation. A number of observed phenomena which could be related to ionizing radiation from BL were reported in [3].

3.4. BL Life Time, the Power of Radiation, and BL’s Internal Size

The internal size of the quark matter of the $AQ{N}_s$ is determined by the quark matter core $R\approx {10}^{-8}$ $\mathrm{cm}$ from (14). However, the effective size of the quark matter material with the surrounding positrons is dramatically larger than the quark matter core itself (similar to atoms with typical size $a\approx {10}^{-8}\mathrm{cm}$ being much larger than the size of a nucleus ∼${10}^{-13}\mathrm{cm}$).

We define the effective radius $R_{\mathrm{eff}}$ as the scale where positrons from the electrosphere remain to be strongly bound to the quark’s core at the internal temperature $T\approx 6$ keV. The corresponding scale can be estimated from the condition that the binding energy of the positrons is approximately equal to their internal temperature $T\approx 6\mathrm{keV}$. This gives $R_{\mathrm{eff}}\approx {10}^{-6}\mathrm{cm}$; see (A6) in Appendix A for numerical estimates. The corresponding scale should be treated as the internal structure of the system, in contrast to the scales (17) and (24), which should be treated as environment-dependent scales.

The significance of the scale $R_{\mathrm{eff}}$ is related to the fact that this scale determines the rate of the antimatter annihilation (and therefore BL’s life time in the AQN framework) hidden in the form of the $AQ{N}_s$. To be more precise, the rate of annihilation of the baryon charge due to head-on collisions of the air molecules with antimatter $AQ{N}_s$ can be estimated as follows:

$$\begin{array}{c}\hfill {\displaystyle \frac{dB}{dt}}\approx -\left(\pi R_{\mathrm{eff}}^2\right)·n_{\mathrm{air}}·v_{\mathrm{air}},\end{array}$$

(20)

where we assume that the successful annihilation events represent a finite fraction of order one for all collisions. Another finite fraction of collisions are elastic scattering events when molecules of air scatter without annihilation. In formula (20), we take the typical density of the surrounding baryons as $n_{\mathrm{air}}\simeq 30·N_m\simeq {10}^{21}{\mathrm{cm}}^{-3}$, with $N_m\simeq 2.7·{10}^{19}{\mathrm{cm}}^{-3}$ being the molecular density in the atmosphere when each molecule contains approximately 30 baryons. The $v_{\mathrm{air}}$ (typical velocity of molecules in air) can be estimated from condition

$$\begin{array}{c}\hfill {\displaystyle \frac{m_{\mathrm{air}}{v}_{\mathrm{air}}^2}{2}}\approx {\displaystyle \frac{3}{2}}{T}_{\mathrm{air}}\to v_{\mathrm{air}}\approx 5·{10}^4{\displaystyle \frac{\mathrm{cm}}{\mathrm{s}}},\end{array}$$

(21)

where $T_{\mathrm{air}}\approx 300$ K is the air temperature. Collecting all the numerical factors together, we arrive at the following estimate:

$$\begin{array}{c}\hfill {\displaystyle \frac{1}{B_0}}{\displaystyle \frac{dB\left(t\right)}{dt}}\approx -{\displaystyle \frac{1}{B_0}}{\displaystyle \frac{1.5·{10}^{14}\mathrm{baryons}}{\mathrm{s}}}{\left({\displaystyle \frac{R_{\mathrm{eff}}}{{10}^{-6}\mathrm{cm}}}\right)}^2\approx -{\displaystyle \frac{1}{\tau }},\tau \approx 6.7s\end{array}$$

(22)

where we inserted $B_0^{-1}$ for normalization, with $B_0=B(t=0)$ being defined as the initial (anti)baryon charge of the $AQ{N}_s$ with its effective radius as estimated in (A6). In reality, the time scale (22) for our benchmark value for $B_0$ as given by (14) is slightly longer as we ignored in our numerical estimates the elastically scattered events (which obviously decrease the rate (20) and consequently increase the estimate for $\tau$) as mentioned above. A few comments are in order:

• The time scale which appears in (22) is perfectly consistent with the observations according to (4). This is a highly nontrivial consistency check for the entire proposal (13) because the two observed parameters (the total energy of the BL (14) and its life time (22)) are unambiguously connected in this proposal. It is very hard to imagine any other mechanism when these two very different entities are tightly connected and in agreement with the observed values.
• The power of radiation (total power) can be estimated as

  $$\begin{array}{c}\hfill P_{\mathrm{tot}}\approx {\displaystyle \frac{B_{{\mathrm{AQN}}_{\mathrm{s}}}·m_p}{\tau }}\approx {\displaystyle \frac{{10}^2\mathrm{kJ}}{\tau }}\approx 10\mathrm{kW},\end{array}$$

  (23)

  which is consistent with (5) extracted from studies in visible frequency bands. Our estimate (23) for the total power suggests that the emission in visible light (5) could be only a small fraction of the total power generated by BL.
• Formula (22) holds as long as portion $f\left(t\right)\equiv B\left(t\right)/B_0$ represents a finite fraction of the initial baryon charge. In this case, the annihilation events can be thought of as a steady process. However, for very small $f\left(t\right)\ll 1$, some dramatic changes in the rate of annihilation may occur, which consequently may result in explosion instead of the smooth and slow decay determined by the time scale $\tau$; see next comment. This behaviour is consistent with item (v) from the list in Section 1.1.
• The explosion occurs if the the annihilation rate (22) suddenly increases due to some external impacts or as a result of the successful simultaneous annihilation of a large number of baryons from air when internal temperature must instantaneously increase to equilibrate heating and cooling processes. This temperature increase will lead to a corresponding increase in the charge (15) with a further increase in the interaction cross section. In this case the time scale (22) suddenly and dramatically decreases, resulting in a very intense flash of broad-band radiation and the consequent formation of an acoustic shock wave. We have coined the term “bootstrap” mechanism for this process; see Note 6. This would appear as an explosion of BL when all remaining antimatter in the $AQ{N}_s$ get annihilated at once. The properties of the resulting shock wave are different from conventional chemical or nuclear explosions, but similar to the ones studied in [33].
• The size of the BL in visible bands during a smooth evolution in this framework is determined by the photon’s mean free path, as explained in Section 3.3. This scale is not very sensitive to a slow decrease in the (anti)baryon charge in the quark core during the BL evolution, as it is determined by the (almost) constant internal temperature T, according to formula (A5) from Appendix A. This conclusion is in agreement with observations from item (ii) from the list in Section 1.1.

3.5. BL Passing Through Glass Windows: The New Scale of the BL Problem

The authors of ref. [10], with the help of optical and scanning microscopes and a laser beam probing the glass, have found traces which are left by 20 cm BL passing through the window glass. The authors discovered a cavity of 0.24 mm diameter; see Figure 3 in that paper. The authors correctly interpreted this event as undeniable evidence of the “material” nature of BL. The scale of this cavity is dramatically different from the 20 cm scale of the BL as observed in visible frequency bands.

In the AQN framework, the emergence of this new scale (0.24 mm in comparison with the 20 cm scale as observed in visible light) has a very natural explanation. Indeed, the mean free path for similar energy photons in Si (12 keV in Si instead of 6 keV in air; see relevant comment in Note8) is dramatically shorter in comparison with O and N atoms from air. It can be extracted from Figure 33.19 from PDG [30] which gives the following estimate:

$$\begin{array}{c}\hfill {\lambda }^{Si}\left(12\mathrm{keV}\right)\approx 0.25\mathrm{mm},\left[\mathrm{to}\mathrm{be}\mathrm{identified}\mathrm{with}\mathrm{size}\mathrm{of}\mathrm{a}\mathrm{cavity}\mathrm{in}\mathrm{glass}\right]\end{array}$$

(24)

where we use $\rho \left(Si\right)=2.3$ g/cm³ for the estimate. Estimate (24) is very instructive as it shows a dramatic difference between two scales, (17) and (24). A proper computation of the internal temperature (and the corresponding photon’s energy) entering estimate (24) is a very hard technical problem, see Note 8. However, our generic claim that scale (24) must be dramatically smaller than scale (17) is a solid qualitative prediction of the framework as it is entirely determined by the differences in the photon’s mean free paths for two very different environments with similar X-ray energies. Estimate (24) shows the consistency of the entire framework when the scale of the BL phenomena is determined by the interaction of the $AQ{N}_s$ core with the environment, rather than by its internal structure. As we discussed in the previous section, Section 3.4, the internal size of the $AQ{N}_s$ core is dramatically smaller than scale (24).

The energy density injected at the instant when BL passes through a window glass of width $l\approx 2\mathrm{mm}$ can be estimated from (24) as follows:

$$\begin{array}{ccc}\hfill {ϵ}^{Si}& \equiv & {\displaystyle \frac{(\Delta B_{{\mathrm{AQN}}_{\mathrm{s}}}·m_p)}{{\left({\lambda }^{Si}\right)}^{2}l}}\approx {\displaystyle \frac{{10}^{2}J}{{\left(0.25\mathrm{mm}\right)}^2\left(2\mathrm{mm}\right)}}\approx {10}^3{\displaystyle \frac{\mathrm{kJ}}{{\mathrm{cm}}^3}},\hfill \\ \hfill \Delta B_{{\mathrm{AQN}}_{\mathrm{s}}}& =& \left(\pi R_{\mathrm{eff}}^{2}l\right)·n_{\mathrm{glass}}\approx {10}^{-3}{B}_{{\mathrm{AQN}}_{\mathrm{s}}},\hfill \end{array}$$

(25)

where $\Delta B_{{\mathrm{AQN}}_{\mathrm{s}}}$ is amount of antimatter being annihilated during the BL’s passage through the window glass of width $l\approx 2\mathrm{mm}$. In this estimate, we use the same $R_{\mathrm{eff}}\approx {10}^{-6}\mathrm{cm}$ which enters (20) from the previous section, Section 3.4. For numerical estimates, we use the baryon number density of glass $n_{\mathrm{glass}}={\rho }_{\mathrm{glass}}/m_p\approx 1.4·{10}^{24}{\mathrm{cm}}^{-3}$.

An important point here is that ${ϵ}^{Si}$ is dramatically greater than the similar estimate for BL propagating in air as given by (19). This enormous energy density is obviously more than sufficient to melt the glass in a small volume of size ${\left({\lambda }^{Si}\right)}^{2}l$. The process of the glass melting in the AQN framework can be thought of as an (almost) instantaneous event when the 12 keV photons radiate along the $AQ{N}_s$ path with an area of size ${\left({\lambda }^{Si}\right)}^2$ and length l. This (almost) instant process ends after the $AQ{N}_s$ passes through glass windows on the time scale $l/v_{BL}\approx 0.5\mathrm{ms}$, after which BL returns to its previous original size 20 cm observed for BL propagating in air. Such short changes in size in the time scale of order $0.5\mathrm{ms}$ of course cannot be noticed by the human eye (the threshold is about 20 ms). In fact, all witnesses report that no changes occurred during the course of BL passing through glass windows. A few comments are in order:

• In the AQN framework, the BL passing through glass windows (or any other surfaces) is a very natural effect. Indeed, the available energy density of the BL crossing a solid material could be very large according to (25). When the BL crosses the window, the emitted (from $AQ{N}_s$ core) photons will be localized on a scale of order (24). As a result of this “focusing” effect, the energy density assumes an enormous value (25) in the form of a very short pulse with time scale of order 0.5 ms. This enormous energy density is sufficient to melt essentially any material.
• This picture of passing BL through the window is consistent with the studies of ref. [10] where “one can assume that the heating of the glass was carried out by a powerful pulse of electromagnetic radiation” (this is a direct quote).
• The emergent scale of problem (24) is not related in any way to the internal structure of the BL itself, which was discussed in the previous section, Section 3.4. Rather, scale (24) emerges due to the interaction of the $AQ{N}_s$ with the environment (window glass) where the mean free path ${\lambda }^{Si}$ is relatively short. It should be contrasted with our discussions of the propagation of BL in air in Section 3.3 where a dramatically different scale (17) emerges.

3.6. How Does BL Emerge (Inthe Form of the AQN_s) After Spallation?

As we mentioned in Section 2.3, the parent AQN may disintegrate when one or several smaller pieces consisting of the original AQN material (in the form of the anti-quark-matter) get separated. The question we address in this subsection is as follows. How long does it take for $AQ{N}_s$ to slow down from its typical velocity ${10}^{-3}c$ to essentially zero velocity at the Earth’s surface when BL is normally observed? To estimate the corresponding length scale L (when stopping occurs), we observe that the elastic head-on collision of $AQ{N}_s$ with a single baryon charge leads to a decrease in the initial $AQ{N}_s$ momentum by an amount of $\sim 2m_p{10}^{-3}c$. In case of annihilation or non-head-on collision, the decrease in momentum is numerically smaller. However, for a simple estimation, we can assume that the amount of material from the air in a cylinder of radius $R_{\mathrm{eff}}$ and length L must be of the same order of magnitude as the baryon charge $B_s\approx {10}^{15}$ for the $AQ{N}_s$ to lose its huge initial velocity, i.e.,

$$\begin{array}{c}\hfill B_s\sim \left(\pi R_{\mathrm{eff}}^2\right)·n_{\mathrm{air}}·L\to L\sim 3\mathrm{km},\end{array}$$

(26)

where $R_{\mathrm{eff}}\approx {10}^{-6}\mathrm{cm}$ is the internal effective size of the $AQ{N}_s$ which has been used previously in Section 3.4. A few comments are in order:

• We consider the numerical value for L to be a very reasonable estimate. Indeed, scale (26) corresponds to the typical size of the thunderclouds. Therefore, the $AQ{N}_s$ can reach the Earth’s surface after spallation in thunderclouds by losing its huge original velocity to become BL with very low velocity at the surface where it is normally observed. A typical stoppage time ${\tau }_s$, when $AQ{N}_s$ loses its 99% of its momentum, can be estimated as ${\tau }_s\approx 2\mathrm{s}$; see Appendix B for an estimate. It is slightly shorter than BL’s life time $\tau$ from (22). At this velocity, the BL becomes observable in visible frequency bands.
• One can explicitly see that very small $AQ{N}_s$ with $B_s\ll {10}^{15}$ cannot survive a several-kilometre journey from the thunderclouds to the Earth’s surface as they get completely annihilated long before they reach the surface. This could be a simple explanation (within the AQN framework) for the well-established feature that BL has a lower energetic bound (1). In the AQN framework, this bound emerges as a result of identification (13) when two entities (energy $E_{\mathrm{BL}}$ and baryon charge $B_s$) are tightly linked in our proposal: $E_{\mathrm{BL}}\approx B_s\left(2\mathrm{GeV}\right)$.
• Estimate (26) also shows why extremely large $B_s\gg {10}^{15}$ have never been observed as BL events. Indeed, the observed maximum for $E_{\max }$ is, at most, two orders of magnitude above the average value according to (1). In the AQN framework, this feature is explained as follows. Very large values of $B_s\gg {10}^{15}$ imply that the stoppage distance L must be much longer in comparison with our estimate (26). Therefore, the secondary $AQ{N}_s$ with very large $B_s\gg {10}^{15}$, if they are formed, will hit the Earth’s surface with very high velocities and get completely annihilated only in deep underground regions, in contrast with BLs which assume very low velocity near the surface. As a result, such energetic events with $B_s\gg {10}^{15}$ are less likely to be observed in comparison with the typical BL9.
• One should emphasize that spallation is not a mechanism of the production (formation) of anti-quark material powering BL. Anti-quark nuggets had been produced during the QCD transition in the early Universe and survived until present epoch; see review in [23]. Spallation is a secondary phenomenon when a small portion of this anti-quark material disintegrated from the original antimatter AQN. In other words, spallation is not a production of the engine powering the BL. Rather, this engine, in the form of antimatter (we observe today in the form of BL), had been produced during the QCD transition in the early Universe.

3.7. Summary: Consistency of Proposal (13) with Observed Features from Section 1.1

In Section 3.1, Section 3.2, Section 3.3, Section 3.4, Section 3.5 and Section 3.6 above, we argued that our proposal (13) is perfectly consistent with observed items from Section 1.1. However, all our explanations and estimates were scattered in the text. The goal here, for consistency and uniformity of presentation, is to summarize and collect all of the items in the same order, one by one, with precise reference to specific and detailed estimates given in the text. The observed features from Section 1.1 include the following:

(i)

BL’s association with thunderstorms is discussed in Section 3.2 and Section 3.6 with specific estimate (26) of the distance that BL propagates from the thunderclouds where it was formed to the surface where it is normally observed. The basic reason for thunderclouds to play a key role in BL formation is the generation of the AQN’s internal negative electric charge which dramatically increases the interaction with positively charged ions from the surrounding area during thunderstorms.

(ii)

The typical size of BL in visible frequency bands is discussed in Section 3.3 with specific estimates as given by (18) and (17). The life time of BL is discussed in Section 3.4 with the specific estimate for $\tau$ as given by (22). The arguments suggesting that there should be no strong time-variation of these parameters throughout the BL’s time evolution are presented in item 4 in Section 3.4.

(iii)

Most of the BL events are likely to occur in open air as BLs (in the AQN framework) propagate to the Earth’s surface from thunderclouds. However, BL can easily cross a glass or any other material and continue to propagate in enclosed spaces such as buildings or aircraft; see Section 3.5 with corresponding discussions and estimation for the cavity size for glass (24). Similar estimates are applicable for any other materials, including metals in the case of an aircraft.

(iv)

The average density of BL is the same as the surrounding air; see item 2 in Section 3.3. This is because the observed radiation from BL is not associated in any way with heating of the air inside the visible part of BL. The emission in visible frequency bands from BL has a dramatically different nature, as explained in detail in Section 3.3 with specific estimation (17) of the visible portion of BL.

(v)

The typical life time of BL is discussed in Section 3.4, with a specific estimate for $\tau$ as given by (22). This estimate assumes a smooth evolution. In some cases (resulting from some external impacts), the explosion may occur as mentioned in item 3 in Section 3.4.

(vi)

In case of a still evolution, the life time is determined by formula (22) from Section 3.4. This formula holds for the smooth propagation of BL in air when its entire original energy is released in a steady way in the form of X-rays and visible light without much damage to the surrounding area.

(vii)

The process of BL crossing through metal screens or glass is described in Section 3.5, with specific estimate (24) for the size of the cavity in the glass as a result of such passage. The typical time for such passage is estimated on the level of $0.5\mathrm{ms}$ such that this fast variation in BL’s size cannot be noticed by the human eye.

(viii)

The radiation from the $AQ{N}_s$ is very broad band in nature. In particular, it includes MeV photons along with X-rays; see item 6 in Section 3.3. Furthermore, the $AQ{N}_s$ carries an internal negative charge which could be much larger in value than the original initial charge (15) after spallation. The atomic photo-effects described in Section 3.3 may also ionize the surrounding air. All these phenomena may produce a number of effects described in (viii), including acrid odours and other phenomena due to ionizing radiation as reported in [3].

(ix)

In the AQN framework, the emergence of this new scale (0.24 mm) as reported in ref. [10] can be naturally explained; see Section 3.5. The main point is that scale (24) emerges due to the interaction of the $AQ{N}_s$ with the environment (window glass). This new scale is not related to the internal structure of the BL.

(x)

The spectrum contains soil components (Si I, Fe I, and Ca I) according to [11,12]. This is because the soil components have a much larger Z such that cross section (16) is much greater than for the dominant air components O and N. As a result, even a tiny amount of these soil components in air could produce strong intensity lines associated with these elements; see item 3 in Section 3.3.

(xi)

The direct observations explicitly show [13] that the spectrum from BL must include UV or/and X-ray emission. This observation is perfectly consistent with the picture of emission advocated in this work; see items 5 and 6 from Section 3.3.

3.8. Concluding Comments on Proposal (13)

We conclude this section with the following very generic comments. The AQN model was suggested long ago to resolve some fundamental problems in cosmology; see Section 2. The corresponding AQN parameters (including spectral properties of radiation, etc.) were also worked out long ago to address many puzzles and mysteries, mostly related to the observed excesses of radiation at different frequency bands at different cosmological and astrophysical scales; see Section 6.2 for a brief review. The AQN model was not designed to address BL physics. In our estimates in this work, we use exactly the same set of parameters extracted from our cosmological studies to test the bold and unorthodox proposal (13) relating BL and DM physics.

We produced a number of estimates relating the observed BL parameters listed in Section 1.1 with AQN parameters. All our estimates in this section are based on a single input parameter (14), the baryon charge (or what is the same, the energy of BL) of the $AQ{N}_s$ identified with BL according to proposal (13). In particular, the visible size of BL (17), its typical life time (22), and the cavity size (24) are determined by incorporating this single input normalization parameter (14) with a variety of well-known physical observables, such as the photo-effect cross section for different atoms, the density of the environment, mean free paths, etc.

It is a highly nontrivial consistency check that all our estimates of the BL characteristics in this section assume very reasonable values, being consistent with observations relating BL and DM physics in the AQN framework. Indeed, the rate of annihilation determines the internal temperature of the $AQ{N}_s$ according to (A5), which consequently determines the spectrum, which (through the atomic photo-effect) determines the mean free path and the size of the BL in visible frequency bands (17) in the air. The same parameters determine the life time of the BL according to (22). It strongly supports the basic idea formulated as (13) that the antimatter nuggets, representing the DM objects in empty space, in fact become the engines powering BL physics and producing profound effects when these objects enter the Earth’s atmosphere.

This consistency check in fact extends to the next section, Section 4, where we demonstrate that the frequency of the appearance of BL is consistent with the flux of DM objects in the form of AQNs. In this case, the basic normalization factor is the dark matter density ${\rho }_{DM}=0.3GeV·{\mathrm{cm}}^{-3}$ extracted from numerous cosmological studies. It turns out that it is precisely this factor, ${\rho }_{DM}$, that determines the frequency of appearance of BL, which further strengthens proposal (13) relating BL and DM physics.

4. Frequency of Appearance

We start with an overview of the recent analysis [8,34] for the frequency of BL appearance. The corresponding lower bound flux has been estimated as [8]:

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{BL}}{dAd\Omega }}>1.75·{10}^{-24}{\displaystyle \frac{\mathrm{events}}{{\mathrm{cm}}^2·\mathrm{sr}·\mathrm{s}}}.\end{array}$$

(27)

The author of ref. [8] argues that the actual frequency of BL is in fact much greater than lower bound (27). However, it is hard to estimate. We would like to represent lower bound (27) using more appropriate (for rare events) units

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{BL}}{dA}}>4·{10}^{-6}{\displaystyle \frac{\mathrm{events}}{{\mathrm{km}}^2·\mathrm{year}}},\end{array}$$

(28)

where we insert factor $2\pi$ into (28) as the solid angle to account for all directions from the entire sky. One can formulate the following question. It is known that BLs are associated with lightning, see item (i) in Section 1.1. Therefore, one can argue that the lightning should play an important role in the formation of BL10. Then, why is rate (28) much lower than the average frequency of conventional lightning in the continental U.S., which is about $24{\mathrm{km}}^{-2}{\mathrm{year}}^{-1}$? We rephrase the same question in a different way: what is so special about very rare lightning events which produce BL (28) in comparison with the vast majority of lightning events which do not lead to BL?

Now we turn to another side of our story, dark matter. In the AQN framework, the corresponding AQN flux is proportional to the dark matter number density $n_{\mathrm{DM}}\propto {\rho }_{\mathrm{DM}}/\langle B\rangle$. It is convenient to represent the DM flux as given by (8) and (9) as follows:

$$\begin{array}{c}\hfill {\displaystyle \frac{d\Phi }{dA}}={\displaystyle \frac{\Phi }{4\pi R_{\oplus }^2}}=4·{10}^{-2}\left({\displaystyle \frac{{\rho }_{\mathrm{DM}}}{0.3\mathrm{GeV}{\mathrm{cm}}^{-3}}}\right)\left({\displaystyle \frac{v_{\mathrm{AQN}}}{220\mathrm{km}{\mathrm{s}}^{-1}}}\right)\left({\displaystyle \frac{{10}^{25}}{\langle B\rangle }}\right){\displaystyle \frac{\mathrm{events}}{\mathrm{year}·{\mathrm{km}}^2}},\end{array}$$

(29)

where we assumed the standard halo model with the local dark matter density being ${\rho }_{\mathrm{DM}}\simeq 0.3\mathrm{GeV}{\mathrm{cm}}^{-3}$ and canonical galactic wind $v_{\mathrm{AQN}}\simeq 220\mathrm{km}{\mathrm{s}}^{-1}$. The number density of the AQNs is very tiny, $n_{\mathrm{AQN}}\simeq \left({\displaystyle \frac{{\rho }_{\mathrm{DM}}}{m_p\langle B\rangle }}\right)$, as it is suppressed by factor $B^{-1}$. This should be contrasted with the canonical type of WIMPs with typical mass ∼${10}^2\mathrm{GeV}$ in comparison with AQN mass ∼${10}^{25}\mathrm{GeV}$. Conventional DM detectors designed for WIMP searches are obviously useless to study DM in the form of AQNs as there will not be any events for millions of years. The cosmic ray (CR) labs, on other hand, may record the AQN-induced events, and we shall comment on this in relation to recording some unusual CR-like events during the thunderstorms in Section 6.1.

Now we are ready to estimate the flux for BL within the AQN framework when AQN hits a thunderstorm area, which consequently leads to spallation and the formation of BL, according to proposal (13). Assuming that every AQN which hits the area under thunderclouds (where ionization is high and spallation is likely to occur) produces a single secondary $AQ{N}_s$, we arrive at the following estimate for the BL flux within the AQN framework:

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{BL}^{AQN}}{dA}}\approx {\displaystyle \frac{d\Phi }{\mathrm{d}\mathrm{A}}}·\mathcal{F}\approx 4·{10}^{-2}\mathcal{F}\left({\displaystyle \frac{{\rho }_{\mathrm{DM}}}{0.3\mathrm{GeV}{\mathrm{cm}}^{-3}}}\right){\displaystyle \frac{\left(\mathrm{BL}\mathrm{events}\right)}{\mathrm{year}·{\mathrm{km}}^2}},\end{array}$$

(30)

where parameter $\mathcal{F}$ describes the fraction of time when the area $\mathrm{dA}$ has been under thunderclouds.

We present two different estimates for parameter $\mathcal{F}$ below. The first estimation of parameter $\mathcal{F}$ is based on a compilation of the annual thunderstorm duration from 450 air weather systems in the USA, as described in [35]. The corresponding estimates suggest that on average, the thunderstorms last about $1\%$ of the time of the year in each given area [35]. If we adopt this estimate, we arrive at conclusion that

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{BL}^{AQN}}{dA}}\approx 4·{10}^{-4}\left({\displaystyle \frac{{\rho }_{\mathrm{DM}}}{0.3\mathrm{GeV}{\mathrm{cm}}^{-3}}}\right){\displaystyle \frac{\left(\mathrm{BL}\mathrm{events}\right)}{\mathrm{year}·{\mathrm{km}}^2}},\mathcal{F}\approx {10}^{-2}\end{array}$$

(31)

The second (independent) estimation of parameter $\mathcal{F}$ has been used in our analysis [25] of mysterious CR-like events, the so-called Telescope Array bursts. This estimate is based on the number of detected lightning events during a period of 5 years (between May 2008 and April 2013) in the area. The corresponding number of lightning events is 10,073 [36,37]. Assuming that a typical thunderstorm lasts one hour and produces ${10}^2$ lightnings [38] one can infer that the total time when the relevant area was under a thunderstorm is 10,073 × ${10}^{-2}$ h ≃ ${10}^2$ h over the 5 years of recording. This represents approximately a fraction of $\mathcal{F}\simeq 0.25·{10}^{-2}$. As a result, we arrive at our second estimate for the frequency of the BL events:

$$\begin{array}{c}\hfill {\displaystyle \frac{d{\Phi }_{BL}^{AQN}}{dA}}\approx {10}^{-4}\left({\displaystyle \frac{{\rho }_{\mathrm{DM}}}{0.3\mathrm{GeV}{\mathrm{cm}}^{-3}}}\right){\displaystyle \frac{\left(\mathrm{BL}\mathrm{events}\right)}{\mathrm{year}·{\mathrm{km}}^2}},\mathcal{F}\approx 0.25·{10}^{-2}.\end{array}$$

(32)

If the efficiency of spallation which produces the secondary $AQ{N}_s$ from the original AQN is less than 100%, the corresponding estimates (31) and (32) decrease correspondingly. If the original AQN produces (as a result of spallation) more than one $AQ{N}_s$, then the corresponding estimates (31) and (32) increase correspondingly.

With all these theoretical uncertainties mentioned above, we consider our estimates (31) and (32) perfectly consistent with lower bound (28). In fact, it is amazing that such different estimates, which include dramatically different environments and physical systems (from thunderstorms and lightning events to dark matter density ${\rho }_{\mathrm{DM}}$ and galactic wind velocities explicitly entering all the estimates), are so close to each other.

Precisely, estimates (31) and (32) answer (within the AQN framework) the question formulated in the first paragraph of this section: why are the BL events so rare? The proposed answer is that the rareness of BL events is a consequence of the rareness of the AQN events with very tiny DM flux (29).

We conclude this section with the following comment. The consistency of our estimates (31) and (32) with lower bound (28) along with the multiple consistency checks summarized in Section 3.8 further strengthen proposal (13) relating BL and DM physics.

5. On the Possible Relation Between BL and Pseudo-Meteorite Events

There are many reports in the literature describing meteor-like events which (after detailed studies by professionals) turned out not to be meteorites. The corresponding events are classified as “pseudo-meteorite events”; see [39] with a large number of references and details. In this work, we want to focus on a single event which took place in the U.S. town of Elma (Washington State) on 15 July 2003 as described in [39]. Many other similar events discussed in [39,40] shall not be mentioned here, and we think they likely have the same nature, and are originated from the same physics.

The key elements of the Elma event are as follows [39]: 1. after the event (fireball), the glassy black rocks had been found; 2. the rocks were very hot (one of the witnesses had burned a thumb and a finger by collecting the rocks); 3. an analysis of the discovered stones by the University of Washington concluded that the glassy rocks were not meteorites (see pictures in [39]); 4. security cameras did not record any suspicious images; and 5. a cloud of dust went up in the active area.

Our original comment is as follows. The Elma event is very similar to BL events discussed in Section 3 with the only difference being that the $AQ{N}_s$ must be much larger in size, $B\gg {10}^{15}$, in comparison with a typical BL event. In this case, as we discussed in item 3 in Section 3.6, the $AQ{N}_s$ cannot efficiently slow down, and it is likely to hit the Earth’s surface with a high speed. As a result, the $AQ{N}_s$ gets annihilated in deep underground regions (not in air, which is typical for BL events) by heating the surrounding rocks along its path. In many respects the heating of the surrounding material is similar to phenomena of BL passing through a glass window when the internal $AQ{N}_s$ temperatures could reach enormous values due to the much higher density of the soil in comparison with air; see our estimates in Section 3.5. It explains the hot glassy rocks found in the area. Furthermore, for the $AQ{N}_s$ moving with a high speed, the radiation in visible frequency bands is suppressed in contrast with the slow-moving BL discussed in Section 3.3. It explains the absence of any images by security cameras. Therefore, we speculate that the “pseudo-meteorite events” are identified as BL events. In other words, both types of events represent profound manifestations of the same DM physics.

6. Concluding Comments and Future Developments

The presence of the antimatter nuggets11 in the system implies, as reviewed in Section 2, that there will be annihilation events leading to an enormous energy injection into the surrounding region. As a result of these annihilation events, one should anticipate a large number of observable effects on different scales: from the Early Universe to the galactic scales, to the Sun and the terrestrial events.

In the present work, we focused on manifestations of these annihilation events on the possible resolution of the mysterious BL physics. In the next section, Section 6.1, we suggest specific tests which could support or refute the proposed resolution of these BL-related mysteries. In Section 6.2 we overview other manifestations of the same AQN framework at dramatically different scales: from the early Universe to galactic scales, to the solar scale and the Earth scale, where similar mysterious puzzles have been known for decades (even centuries), and could be also related to the same antimatter nuggets (representing DM objects) within the same AQN framework. We emphasize that the parameters of the model were fixed long ago irrespective of the BL physics which represents the topic of the present work.

6.1. BL as a Manifestation of AQN_s Events: Possible Future Tests of Proposal (13)

We already formulated the basic results demonstrating the consistency of proposal (13) with observed BL features in Section 3.8. We do not need to repeat these results again. Instead, we focus here on possible future tests of proposal (13). Before we formulate the basic idea for the test, we would like to make a few comments on the observed anomalous and mysterious cosmic ray (CR)-like events which are very hard to explain within the conventional framework and modelling. These events are strongly associated with thunderstorm and lightning events in the area, similar to BL events discussed in this work.

In particular, the Telescope Array (TA) collaboration [36,37] reported the observations of mysterious bursts when at least three air showers were recorded within 1 ms, which cannot occur with conventional high-energy CR (it should be days or even months for two or more consecutive energetic CR events to hit the same area). These TA mysterious bursts are associated with lightning events in the area. We proposed in [25] that these puzzling events could be related to the AQN-induced events. In fact, in ref. [25] we used the same Formula (29) for the estimation of the rate of TA mysterious bursts which was used for the estimation of the BL frequency of appearance in (32). We explained the rareness of these TA mysterious bursts precisely in the same way as the rareness of BL events.

Similar “Exotic Events” recorded by the AUGER collaboration [41,42,43] are also associated with thunderstorm activity in the area. These events also cannot be explained by canonical CR modelling. At the same time, these “Exotic Events” recorded by the AUGER collaboration can be explained within the AQN framework as argued in [26]. Furthermore, the rareness of these “Exotic Events” is also explained in the AQN framework by the same formula (29) and it is consistent with the counting of the “Exotic Events” by the AUGER collaboration.

We mentioned these two studies on unusual CR-like events to propose to test hypothesis (13) as follows. If one can install all sky cameras, similar to the ones used in analysis [11], to monitor the entire sky in the same area where TA or AUGER detectors (or any other CR labs) are located, one can record the BL events with a frequency of appearance similar to the mysterious bursts recorded by the TA collaboration or “Exotic Events” recorded by the AUGER collaboration12. Indeed, in all cases, the basic formula describing the rate for all these events is (32). This formula is shown to be consistent with the TA mysterious bursts (10 events recorded over 5 years) and the AUGER “Exotic Events” (23 events recorded over 13 years). The same formula is also consistent with the lower bound for BL events (28) as discussed in Section 4. Therefore, we predict (within the AQN framework) that the rate for BL events in the area will be similar to the observed TA mysterious burst events and the AUGER “Exotic Events” because all these events are different manifestations of the same DM physics.

Furthermore, we also predict, within the same AQN framework, that TA mysterious bursts will be correlated in time with observations of the BL in the same area under thunderstorms. In other words, the installation of all sky cameras, similar to the ones used in the analysis in [11], and the study of the correlations with TA bursts would be a very strong and unambiguous argument supporting the entire idea about the nature of BL as a profound manifestation of DM physics, as advocated in this work. The same comment obviously applies to AUGER “Exotic Events”.

6.2. Other (Indirect) Evidence for DM in the Form of AQN

There are many hints suggesting that the annihilation events and consequent energy injection into space (which is an inevitable feature of this framework) may have indeed taken place in the early Universe, during the galaxy formation as well as in the present epoch. We would like to mention (for completeness of the presentation) a number of mysterious puzzles at different scales which could be also related to the additional energy injection induced by the AQN annihilation events with the surrounding material.

We start this list of (yet) unresolved puzzles from the early Universe epoch, more specifically, with BBN when the so-called “Primordial Lithium Puzzle” has been with us for decades. It has been argued in [44] that the AQNs during the BBN epoch do not affect BBN production for H and He, but might be responsible for a resolution of the “Primordial Lithium Puzzle” due to the Li large electric charge $Z=3$ strongly interacting with negatively charged AQN.

Another well-known puzzle is related to the galaxy formation epoch. The corresponding puzzles commonly are formulated as the “Core-Cusp Problem”, “Missing Satellite Problem”, and “Too-Big-to-Fail Problem”, to name just a few; see recent reviews [15,45] for the details13. It has been argued in [46] that the aforementioned discrepancies (and many other related problems referred to in Note 13) may be alleviated if dark matter is represented in the form of the composite, nuclear density objects within the AQN framework.

We now move from the early times in the evolution of the Universe to the present day observations. In this case, there is a set of puzzles which is related to the diffuse UV emission in our galaxy. In has been claimed in [47,48,49,50] that there are many observations which are very hard to understand if interpreted in terms of the conventional astrophysical phenomena; see also the very recent brief review [51]. The analysis [47,48,49,50,51] very convincingly disproves the conventional picture that the dominant source of the diffused UV background is the dust-scattered radiation of the UV-emitting stars. The arguments are based on a number of very puzzling observations which are not compatible with the standard picture. First, the diffuse radiation is very uniform in both hemispheres, in contrast to the strong non-uniformity in the distribution of the UV-emitting stars. Secondly, the diffuse radiation is almost entirely independent of the galactic longitude. This feature must be contrasted with the localization of the brightest UV-emitting stars which are overwhelmingly confined to the longitude range ${180}^{\circ }$–${360}^{\circ }$. These and several similar observations strongly suggest that the diffuse background radiation can hardly originate in dust-scattered starlight. The authors of [47] conclude that the source of the diffuse FUV emission is unknown—that is the mystery that is referred to in the title of the paper [47].

It has been proposed in [52,53] that this excess in UV radiation could be a result of the dark matter annihilation events within the AQN dark matter model. The proposal [52,53] is supported by demonstrating that the intensity and the spectral features of the AQN-induced emissions are consistent with the corresponding characteristics of the observed excess [47,48,49,50,51] of the UV radiation.

We move from the galactic to the solar scale. The AQNs might be also responsible for the renowned long-standing problem14 of the “Solar Corona Mystery”, when the so-called “nanoflares” conjectured by Parker long ago [56] were identified with the annihilation events in the AQN framework [54,55].

We move from the solar scale to terrestrial unusual events. We already mentioned mysterious CR-like events in Section 6.1. There are many other terrestrial unusual events when the conventional picture cannot explain the observed phenomena. In particular, ANITA observed two anomalous events with non-inverted polarity [57,58]. Such events correspond to very a large inclination angle when “something” crosses the Earth before exiting from the opposite side of the Earth at the moment of the recording by ANITA. Such events are very hard to explain within conventional physics, but could be explained within the AQN framework [59].

Finally, it has been recently argued in [60,61] that numerous enigmatic observations remain challenging to explain within the framework of conventional physics. In particular, these anomalies include unexpected correlations between temperature variations in the stratosphere and the total electron content of the Earth’s atmosphere (along with many other mysterious correlations), such that the entire globe can be thought of as one large detector. Decades of collected data provide statistically significant evidence for these observed correlations. However, no conventional explanations for such mysterious correlations have been offered. It has been argued in [23] that the recorded correlations can be generated by the AQN-induced processes.

We conclude this work with the following final comment. We advocate an idea that the BL known for centuries might be a profound manifestation of DM physics when DM is made of (anti)quarks and gluons of the standard model as reviewed in Section 2. The AQN dark matter model is consistent with all presently available cosmological, astrophysical, satellite, and ground-based observations. In fact, it may even shed some light on the long-standing puzzles and mysteries, as briefly reviewed above in Section 6.2. If validated through the proposed tests and experiments, this framework could revolutionize our understanding of DM and its role in the cosmos. The BL events as profound direct manifestations of DM on Earth (within the AQN framework) could play a key role in the direct study of DM in scientific labs, in contrast with indirect manifestations of the AQN-induced phenomena reviewed in Section 6.2.