# The mysterious diffuse UV radiation and Axion Quark Nugget dark matter model

Ariel Zhitnitsky  Department of Physics and Astronomy, University of British
Columbia, Vancouver, V6T 1Z1, BC, Canada

###### Abstract

It has been recently argued [1, 2, 3] that there is a strong component of the
diffuse far-ultraviolet (FUV) background which is hard to explain by
conventional physics in terms of the dust-scattered starlight. We propose that
this excess in FUV radiation might be result of the dark matter annihilation
events within the so-called axion quark nugget (AQN) dark matter model, which
was originally invented for completely different purpose to explain the
observed similarity between the dark and the visible components in the
Universe, i.e. $\Omega_{\rm DM}\sim\Omega_{\rm visible}$. We support this
proposal by demonstrating that intensity and the spectral features of the AQN
induced emissions are consistent with the corresponding characteristics of the
observed excess of the FUV radiation. If the future studies confirm the
puzzling characteristics observed in [1, 2, 3] it might unlock a much more
deeper and fundamental problem of modern cosmology– it may reveal the nature
of the dark matter.

###### keywords:

dark matter, axion, diffuse UV radiation

††journal: Journal of LaTeX Templates

##  1  Introduction and Motivation

The title of this work seemingly includes two contradicting terms: the first
one is “the radiation”, while the second term of the title is “the dark
matter” (DM) which, by definition, must decouple from the baryons and the
radiation. However, the main goal of this work is to argue that the puzzling
features observed in [1, 2, 3] in fact can be explained within a specific dark
matter model, the so-called axion quark nugget (AQN) dark matter model [4].
Therefore, the contradiction in the title is only apparent, while the DM in
form of the AQNs strongly couples to the baryons and can emit light.
Furthermore, if the future and more precise analysis confirms the puzzling
observations [1, 2, 3] it could serve as an extraordinary evidence revealing
the nature of the dark matter, see few additional comments at the very end of
this Introduction.

Before we proceed with our arguments we should, first of all, highlight the
mysterious properties of the observations [1, 2, 3] which are very hard to
understand if interpreted in terms of the conventional astrophysical
phenomena. Indeed, the widely accepted picture is that the dominant source of
the diffused ultraviolet (UV) background radiation is the dust-scattered
radiation of the UV emitting stars. However, the recent analysis carried out
in [1] and in subsequent papers [2, 3] disproves this conventional picture.
The corresponding refutal arguments are based on the following puzzling
features of the observations:

1. “uniformity puzzle”: The diffuse radiation is very uniform in both hemispheres, see Figs 7-10 in [1]. This feature should be contrasted to the strong non-uniformity in distribution of the UV emitting stars;

2. “galactic longitude puzzle”: The diffuse radiation is almost entirely independent of Galactic longitude. This feature must be contrasted with localization of the brightest UV emitting stars which are overwhelmingly confined to the longitude range $180^{0}-360^{0}$, which strongly suggests that the diffuse background radiation can hardly originate in dust-scattered starlight;

3. “galactic latitude puzzle”: The diffuse radiation increases in brightness toward lower galactic latitude at all galactic longitudes. This should be contrasted with conventional modelling [1] which predicts very low brightness at low Galactic latitudes. This observation also suggests that the recorded diffused emission has galactic, not extragalactic origin. Indeed, the extragalactic light cannot strongly vary toward lower galactic latitude. Due to the same reasons, the observations also conclusively suggest that this emission has celestial, and not terrestrial nature;

4. “non-correlation puzzle”: Conventional picture for the UV diffuse radiation suggests that it must be correlated with the 100 $\mu m$ thermal emission as both radiations are assumed to be related to the dust and its distribution in the galaxy. However, this conjecture dramatically fails as the 100 $\mu m$ thermal emission is highly asymmetric and explicitly shows a strong correlation with localization of the emitting stars, while UV diffuse emission is highly uniform and it is not correlated with the dust distribution, see Fig. 14 in [1].

The authors of [1] conclude, I quote “the source of the diffuse FUV emission
is unknown –that is the mystery that is referred to in the title”. I keep the
same term “mysterious radiation” in the title of the present work.
Furthermore, the authors of [1] argued that this “exotic” mysterious component
of emission is unknown but must be galactic origin, and might be due to the
interaction of the DM with the nuclei of the interstellar medium. In addition,
the authors of [1] also suggested that if the DM particle is electrically
neutral but represents a composite system, than such DM particles may
contribute to the “exotic” diffuse UV component. In fact this proposal had
been advocated even earlier in [5].

In the present work we offer a specific DM model, the so-called AQN dark
matter model which is capable to produce the required “exotic” diffuse UV
radiation as mentioned in previous paragraph. The AQN model was invented long
ago [4] for drastically different purpose (unrelated to the present studies)
to explain the observed similarity between the dark matter and the visible
matter densities in the Universe. The original motivation [4] for the AQN
model can be explained in two lines 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 $\cal{CP}$ violation effects, realizing three famous Sakharov’s
criteria [6]) evolved into a state with a net positive baryon number, which
represents the idea of baryogenesis. In the AQN framework the baryogenesis is
actually a charge segregation (rather than charge generation) process in which
the global baryon number of the universe remains zero at all times. This
scenario should be considered as an alternative path which is qualitatively
distinct from conventional baryogenesis. The AQN construction in some respects
is similar to the Witten’s quark nuggets, see [7, 8, 9]. This type of DM is
“cosmologically dark” not because of the weakness of the interactions with the
visible SM particles, but due to their small cross-section-to-mass ratio,
which scales down many observable consequences of an otherwise strongly-
interacting DM candidate.

The main distinct feature of the AQN model which plays absolutely crucial role
for the present work is that nuggets can be made of matter as well as
antimatter during the QCD transition as a result of this charge segregation
(rather than charge generation) process. In this scenario the DM density,
$\Omega_{\rm DM}$ representing the matter and anti-matter nuggets, and the
visible density, $\Omega_{\rm visible}$, will automatically assume the same
order of magnitude densities $\Omega_{\rm DM}\sim\Omega_{\rm visible}$ as they
are both proportional to one and the same fundamental dimensional parameter of
the theory, the $\Lambda_{\rm QCD}$. Therefore, the AQN model, by
construction, actually resolves two fundamental problems in cosmology without
necessary to fit any parameters of the model. For the present studies we take
the agnostic viewpoint regarding the questions on formation mechanism of the
AQNs, and assume that such nuggets made of antimatter are present in our
Universe, see [10] for a short overview on specific questions related to the
nugget’s formation, generation of the baryon asymmetry, and survival pattern
of the nuggets during the evolution in early Universe with its unfriendly
environment. This assumption is consistent with all available constraints as
long as the average baryon charge of the nuggets is sufficiently large
$\langle B\rangle\geq 3\cdot 10^{24}$.

The presence of the antimatter nuggets in the system implies that there will
be annihilation events leading to large number of observable effects on
different scales: from galactic scales to the terrestrial rare events. In
fact, there are many hints suggesting that such annihilation events may indeed
took place in early Universe as well as they are happening now in present
epoch. In particular, the AQNs might be responsible for a resolution of the
“Primordial Lithium Puzzle” [11] during Big Bang Nucleosynthesis (BBN) epoch.
The AQNs may also alleviate the tension between standard model cosmology and
the recent EDGES observation of a stronger than anticipated 21 cm absorption
feature as argued in [12]. The AQNs might be also responsible for famous long
standing problem of the “Solar Corona Mystery” [13, 14] when the so-called
“nanoflares” conjectured by Parker long ago [15] are identified with the
annihilation events in the AQN framework. The AQNs could be also responsible
for mysterious and anomalous Cosmic Ray (CR) like events such as mysterious
bursts [16] observed by the Telescope Array collaboration or Multi Modal
Clustering anomalous events [17] observed by the HORIZON 10T collaboration.
Sufficiently large (and vary rare) AQNs with $B>10^{27}$ entering the Earth’s
atmosphere could produce infrasound and seismic acoustic waves as discussed in
[18] when the infrasound and seismic acoustic waves indeed have been recorded
by dedicated instruments while a synchronized all-sky camera network (visible
frequency bands) ruled out a conventional meteor source.

The list with numerous deviations from the standard cosmology at different
scales which could be explained in terms of the same antimatter nuggets within
the same framework as mentioned above is already quite long, but definitely is
far from being complete. Our comment here is that the presence of the
antimatter nuggets directly impacts all these (seemingly unrelated) fields of
physics, from baryogenesis (replaced by charge segregation) and the
“Primordial Lithium Puzzle” in early Universe to excess in diffuse FUV
background and rare CR-like anomalous events at present time. If the future
observations and more precise data confirm these hints on deviations from the
standard astrophysics and cosmology it will be an extraordinary evidence
revealing the nature of the dark matter.

##  2  The AQN Dark Matter model

The typical baryon number density of such dense objects is the same order of
magnitude as the conventional nuclear matter density $n\sim 10^{40}\rm
cm^{-3}$, while typical baryon charge of the nugget is around $B\sim 10^{25}$
which implies that the mass of a typical nugget is around $M\sim 10$ g, while
its size $R\sim 10^{-5}$ cm, see below with more specific and technical
details.

If the AQNs enter the regions of the surrounding material (such as stars,
planets or interstellar medium) the annihilation processes start and the
internal temperature of the nuggets $T$ starts to rise. A typical internal
temperature of the AQNs for the galactic environment of density $n$ can be
estimated from the condition that the radiative output, the surface emissivity
$F_{\text{tot}}(T)$ must balance the flux of energy due to the annihilation
processes [19], i.e.

$\displaystyle 4\pi R^{2}\cdot F_{\text{tot}}(T)\approx\kappa\cdot(\pi
R^{2})\cdot(2~{}{\rm GeV})\cdot n\cdot v_{\rm AQN},$ (1)

where the left hand side accounts for the total energy radiation from the
AQN’s surface per unit time while the right hand side accounts for the rate of
annihilation events when each successful annihilation event of a single baryon
charge produces $\sim 2m_{p}c^{2}\approx 2~{}{\rm GeV}$ energy. In Eq. (1) we
assume that the nugget is characterized by the geometrical cross section $\pi
R^{2}$ when it propagates in environment with local density $n$ with velocity
$v_{\rm AQN}\sim 10^{-3}c$. The factor $\kappa$ is introduced to account for
the fact that not all matter striking the AQN will annihilate and not all of
the energy released by an annihilation will be thermalized in the AQNs by
changing the internal temperature $T$. In particular, some portion of the
energy will be released in form of the axions, neutrinos, and also in form of
the x-rays from the so-called hot spots, see details below. The high
probability of reflection at the sharp quark matter surface lowers the value
of $\kappa$. The ionization of the AQNs, on the other hand, may induce the
negative charge of the AQNs, and as a consequence may increase the value of
$\kappa$ by effectively increasing the cross section (1). Furthermore, the
density of the galactic environment $n({\bf{r}})$ changes dramatically from
region to region, which implies that the temperature of the nuggets also
varies correspondingly, which also introduces a large uncertainty.

One can dramatically reduce all these numerous uncertainties in the estimation
for the effective temperature $T_{\rm eff}$ by normalizing the intensity of
the emission to some specific observations which can be identified with the
AQN annihilation events in interstellar medium. In fact, it has been argued in
[20] that the diffuse x ray emission analyzed in [21] cannot be explained in
terms of any conventional astrophysical sources but can be naturally explained
in terms of the AQN annihilation events. The combination of the arguments from
[19, 20] then suggest that the effective temperature of the AQNs in the
central region of the galaxy could be very high $T_{\rm eff}\geq(2.5-5)~{}\rm
eV$, see estimate below. Such high temperature for $T_{\rm eff}$ implies that
these nuggets could be very strong UV emitters, which is precisely the topic
of the present work.

To proceed with our estimates we need the expression for the spectral surface
emissivity due to the bremsstrahlung radiation from electrosphere at
temperature $T$. It has been computed in [19]:

$\displaystyle\frac{d{F}}{d{\omega}}(\omega)\approx\frac{4}{45}\frac{T^{3}\alpha^{5/2}}{\pi}\sqrt[4]{\frac{T}{m}}\cdot
f(x),~{}~{}~{}~{}x\equiv\frac{\omega}{T}$ (2)

where dimensionless function $f(x)$ with sufficient accuracy can be
approximated as follows:

$f(x)\approx\begin{cases}\left(1+x\right)e^{-x}\left(17-12\ln(x/2)\right)&x<1,\\\
\left(1+x\right)e^{-x}\left(17+12\ln(2)\right)&x\geq 1.\end{cases}$

The total surface emissivity entering (1) is given by:

$F_{\text{tot}}(T)=\int^{\infty}_{0}\\!\\!\\!\\!\\!d{\omega}\;\frac{d{F}}{d{\omega}}(\omega)\approx\frac{16}{3}\frac{T^{4}\alpha^{5/2}}{\pi}\sqrt[4]{\frac{T}{m}}.\\\
$ (3)

The most important feature of this bremsstrahlung radiation is that, in
contrast with black body radiation, it is very flat for $\omega\leq T$, while
it starts to diminish only for sufficiently high frequencies $\omega\gg T$.
Numerically, the intensity of radiation (3) is also much smaller than black
body radiation by factor $\sim 10^{-6}$ for relevant temperatures around
$T\sim$ eV.

To compute the observable flux $\Phi_{\Gamma}$ for a given frequency band from
all nuggets one should multiply (1) to the number density of the nuggets
$n_{\rm DM}\simeq\rho_{\rm DM}/(m_{p}B)$ and integrate along the line of sight
$\Gamma$, i.e.

$\Phi_{\Gamma}\propto\int_{\Gamma}d{l}\,n(l)n_{\rm DM}(l),$ (4)

where we assume that all other parameters, except density $n$, entering the
right hand side of (1) are approximately the same. The key point here is that
the comparison between observations for different frequency bands along the
same line-of-sight is possible because the local emission for any frequency
band depends only on the local rate of annihilation $\propto n({\bf{r}})n_{\rm
DM}(\bf{r})$ as the spectrum is fixed by (2). Therefore, the main
uncertainties (mentioned above and related to the AQN dynamics as well as to
the matter and DM distributions) will be cancelled out when comparing the
emissions from the same position in the sky.

##  3  The FUV diffuse emission

From the arguments outlined above one can represent the spectral emissivity
with frequency $2\pi\nu=xT$ produced by AQNs at arbitrary direction in sky
determined by path $\Gamma$ as follows

$\displaystyle\frac{d\Phi_{\Gamma}(x)}{dx}\approx\bar{\Phi}\left[\frac{f(x)}{\int_{0}^{\infty}f(x)dx}\right]\left[\frac{\int_{\Gamma}d{l}\,n(l)n_{\rm
DM}(l)}{\int_{\bar{\Gamma}}d{\bar{l}}\,n(\bar{l})n_{\rm
DM}(\bar{l})}\right]\left[\frac{1-g}{g}\right].~{}~{}~{}$ (5)

In expression (5) the parameter $g$ is unknown empirical factor of order of
one to be discussed below while the main normalization factor $\bar{\Phi}$ is
chosen as the excess of the diffused X-ray emission from the galactic core as
observed by Chandra and analyzed in [21]. This choice is based on the
following arguments [20]. The X-ray emissions from the galactic core provide a
puzzling picture: they seem to indicate that an 8 keV thermal plasma is being
maintained, but the source of energy fuelling this plasma is a mystery. After
subtracting known X-ray sources from the Chandra X-ray images of the galactic
core, one finds a residual diffuse thermal X-ray emission with a thermal
component well described by a hot 8 keV plasma with surface brightness
$\Phi_{\rm keV}=(1.8$ – $3.1)\times 10^{-6}$ erg/cm2/s/sr [21]. To sustain
this plasma, some $10^{40}$ erg/s of energy must be supplied to the galactic
core which is much more than the observed rate of supernovae, for example, can
explain [21].

In has been argued in [20] that the spectrum and the intensity of the AQN
induced X-ray emission fits the observations, which is the crucial argument
for our normalization111Another way to normalize the intensity (5) is to use
the observed excess in 511 keV line as it was done in the original paper [20].
However, in this case an extra uncertainty appears due to unknown relation
between 511 keV line emission which is due to $e^{+}e^{-}$ annihilation and
the baryon charge annihilation processes within AQN core. In fact it has been
recently claimed [22] that the mechanism for the $e^{+}e^{-}$ annihilation is
different from the original proposal [23, 24] as the annihilation of the
visible electrons with AQN’s positrons may occur far away from the nugget’s
location due to the strong ionization features of the AQNs. Alternatively, one
could normalize (5) in terms of DM and visible matter distributions as it was
done in [23]. However, it would bring an enormous uncertainty in
normalization, which we try to avoid by normalizing to the observed flux. in
terms of factor $\bar{\Phi}$ entering (5):

$\bar{\Phi}\approx(2.5-3.9)\cdot
10^{-5}\frac{\text{erg}}{\text{cm}^{2}\cdot\text{s}},~{}~{}~{}~{}[\rm
X-ray~{}observations]$ (6)

where we multiply by factor $4\pi$ the observed intensity $\Phi_{\rm keV}$
extracted in [21] as quoted above. As discussed in [20] the X-ray emission in
the AQN framework is originated from the so-called “hot spots” which represent
the very localized regions close to the nugget’s surface, where the
annihilation events take place. The corresponding portion of the energy
released from “hot spots” is parameterized by unknown factor $g\ll 1$ entering
(5). The dominant portion of the energy $(1-g)$ due to the annihilation will
be thermalized, and will be emitted with the spectrum determined by (2). It
explains the numerical factor $(1-g)/g$ entering (5). The last factor
$\bar{\Gamma}$ which requires the explanation represents a specific path
$\bar{\Gamma}$ in the direction to the galactic core where uniform X-ray
diffused flux (6) is recorded. We also use notations $\bar{l}$ for the
integration variable for the path $\bar{\Gamma}$ to be distinguished from
generic path $\Gamma$.

Now we want to argue that a typical temperature $T_{\rm eff}$ which implicitly
(through parameter $x\equiv\omega/T_{\rm eff}$) enters (5) indeed typically
assumes the values in the eV range such that the AQNs will be the source of
the diffuse UV radiation, which represents the main claim of this work.
Indeed, to avoid a large number of uncertainties mentioned above we can
estimate $T_{\rm eff}$ by comparing the excess of radiation observed by WMAP
collaboration and coined as the WMAP haze [25, 26, 27, 28, 29] and the X-ray
diffused radiation we already mentioned. Assuming that the observed WMAP haze
intensity is saturated222It has been argued in [26] that the WMAP haze can be
attributed to the spinning dust or the dark matter annihilation [27, 28]. As
the physical source of this excess of GHz emission remains to be a matter of
debate we assume in our estimates (7) that a finite fraction of this excess is
due to the AQN annihilation events as argued in [19]. by the AQN radiation as
advocated in [19] with the flat spectrum (2) extending from UV to GHz
emission, one arrives to the following estimate for $T_{\text{eff}}$ (quoted
above) in terms of the parameter $g$:

$\frac{\text{eV}}{T_{\text{eff}}}\cdot\frac{1-g}{g}\approx(2\text{--}4)~{}~{}~{}\Rightarrow~{}~{}T_{\text{eff}}\geq(2.5-5)\rm~{}eV,$
(7)

where for numerical estimates we use $g\simeq 0.1$. One should emphasize that
the uncertainty of parameter $g$ is not a deficiency of the AQN framework
itself. Rather, this inevitable uncertainty results from very complex
annihilation pattern of the baryons from visible material (confined hadronic
phase) with antimatter from the AQNs (colour superconducting phase).
Therefore, this parameter $g$ fundamentally cannot be computed from the first
principles and will be treated in what follows as empirical phenomenological
parameter.

The key point here is that both emissions, the WMAP haze as well as diffuse
X-ray emissions are originated from approximately the same region in the sky,
and both are related to the same annihilation processes of the baryon charge
within the AQN framework such that the only uncertainty in the estimate of the
$T_{\text{eff}}$ comes from parameter $g$ defined above333Of course a number
of uncertainties related to extracting WMAP haze intensity and the X ray
intensity remain. Our claim refers to the theoretical uncertainties related to
the AQN model itself and its interaction with environment..

It is very instructive to compare our estimates determined by (5) and (6) with
intensities of the diffuse FUV emission as recorded by [1, 2, 3]. To proceed
with such comparison we have to use the same units. The simplest way to
compare is to use the conversion worked out in [1] where, I quote “the
intensity of excess FUV radiation detected by GALEX over its bandpass
(1380-2500)$\rm\AA$ is
$10^{-5}{\text{erg}}~{}{\text{cm}^{-2}~{}\text{s}^{-1}}$, assuming a flat
spectrum with 300 photons ${\rm({cm}^{-2}~{}{s}^{-1}sr^{-1}\AA^{-1})}$.”

This implies that the magnitude of 300 photons which typically emerges in
analysis [1, 2, 3] corresponds to the intensity
$10^{-5}{\text{erg}}~{}{\text{cm}^{-2}~{}\text{s}^{-1}}$ which appears in our
prediction (5) with normalization factor $\bar{\Phi}$ defined by (6). Several
numerical factors modify this crude estimate. First, there is an intensity
suppression due to decreasing of the interstellar medium density $n(l)$
entering (5) for the path $\Gamma$ for FUV (where the excess with 300 photons
is measured) in comparison with path $\bar{\Gamma}$. This suppression factor
might be largely neutralized by the enhancement factor $1/g\sim 10$ entering
(5). The same factor $g^{-1}$ may also increase the effective temperature
$T_{\text{eff}}$ comparison with oversimplified estimate (7). Furthermore, the
$T_{\text{eff}}$ might assume somewhat higher values in the galactic core
regions, which also contribute to FUV measured at higher latitudes due to the
re-scattering from the dust. Important point here is that the observed FUV
intensity is consistent with the temperature range (7) as the spectrum given
by $f(x)$ is very flat and effectively starts to diminish only for
sufficiently high frequencies $2\pi\nu\geq T_{\text{eff}}$.

Precise portion of the emission in the FUV frequency band within the window
$\Delta\nu$ is determined by the parameter $\chi$ defined as follows:

$\displaystyle\chi\equiv\frac{\int_{x_{\rm min}}^{x_{\rm
max}}dxf(x)}{\int_{0}^{\infty}dxf(x)},~{}~{}~{}\left(\frac{2\pi\nu}{T_{\rm
eff}}\right)\in(x_{\rm min},x_{\rm max}).$ (8)

The suppression factor $\chi$ obviously dramatically depends on effective
internal temperature $T_{\rm eff}$ of the nuggets, which itself is determined
by the local interstellar medium density $n$ according to (1). As an
illustration let us consider a typical temperature $T_{\text{eff}}\simeq 5$ eV
as estimated in (7) and bandpass (1380-2500)$\rm\AA$ where the excess of FUV
radiation was detected by GALEX. The factor $\chi$ in this case is about
$\chi\simeq 0.2$, which implies that quite substantial portion of the energy
will be emitted by the AQNs in this relatively narrow frequency band.

Our estimates presented above suggest that the AQN-induced FUV radiation may
naturally assume $\sim 10^{-5}{\text{erg}}~{}{\text{cm}^{-2}~{}\text{s}^{-1}}$
intensity range. However, those estimates were based on comparison with
emission in a different frequency band (X-ray emission) which is assumed to be
also the AQN-induced radiation. Now we want to support the basic normalization
factor (5) by independent direct estimates without referring to any other
observed diffuse radiation.

First, we estimate a total luminosity $L_{\rm AQN}$ from a single AQN by
multiplying (3) to the surface area:

$\displaystyle L_{\rm AQN}\approx 4\pi R^{2}\cdot F_{\text{tot}}(T)\approx
4.7\left(\frac{T}{5~{}\rm eV}\right)^{\frac{17}{4}}\rm\frac{erg}{s},$ (9)

where for numerical estimates we use $R\approx 2.2\cdot 10^{-5}\rm cm$ and
$B\approx 10^{25}$ as in our previous studies for other applications in this
model, see [10] for review. To estimate the total FUV intensity
$\Phi^{FUV}_{\rm AQN}$ produced by all AQNs one should multiply the luminosity
$L_{\rm AQN}$ to the nugget’s density $n_{\rm AQN}\sim\rho_{\rm DM}/(m_{p}B)$
and the mean free path ${\cal{R}}$ in the local interstellar medium, i.e.

$\displaystyle\Phi^{FUV}_{\rm AQN}\sim L_{\rm AQN}n_{\rm AQN}{\cal{R}}\chi\sim
5\cdot 10^{-5}\left(\frac{T}{5~{}\rm
eV}\right)^{\frac{17}{4}}\rm\frac{erg}{s\cdot cm^{2}},~{}~{}~{}~{}$ (10)

where for numerical estimates we take the conventional value for the DM
density $\rm\rho_{\rm DM}\simeq 0.3~{}GeV/cm^{3}$. We also used parameter
$\chi\simeq 0.2$ as estimated above. This relatively large value for $\chi$ is
a result of the “flatness” of the bremsstrahlung radiation as mentioned after
(3). We also adopted parameter ${\cal{R}}\simeq 0.6\rm~{}kpc$ used in [1]. It
represents the result of conventional estimates for the mean free path of the
FUV photons propagating in the galaxy.

It is instructive to compare the estimate (10) with analogous estimates for
WIMP- like DM particles performed in [1]. The authors of [1] claim that the
total FUV intensity produced by WIMPs cannot exceed $10^{-17}\rm{erg}/{(s\cdot
cm^{2})}$ which according to the authors of [1] represents a model-independent
upper limit for WIMP-like models. It should be contrasted with our AQN based
estimates which show a perfect consistency with the observed intensity on the
level $10^{-5}\rm{erg}/{(s\cdot cm^{2})}$ as well as with estimates (5), (6)
based on normalization to the X ray diffuse emission.

We are now in position to explain how the puzzles 1-4 listed above are
naturally resolved within AQN framework. First of all the “uniformity puzzle”
is obviously resolved as the DM in form of the AQNs are uniformly distributed
in the galaxy. Similarly, the “galactic longitude puzzle” is resolved as the
DM particles are not sensitive to the galactic longitude, as the AQNs are not
correlated with locations of the UV emitting stars. The “galactic latitude
puzzle” is also naturally resolved as the increase in brightness toward lower
galactic latitude is a direct consequence of the AQN framework when the number
of annihilation events is proportional to interstellar matter density
according to (4) which obviously leads to the increase of the temperature $T$
and as the consequence to the brightness toward lower galactic latitude.
Finally, the “non-correlation puzzle” with the 100 $\mu m$ thermal emission is
resolved as the dominant fraction of the 100 $\mu m$ radiation follows the
locations of the emitting stars, in contrast with AQNs, which contribute very
little to the thermal 100 $\mu m$ radiation444Indeed, a typical observed value
for the 100 $\mu m$ emission line ranges in $(0.7-2.5)\rm MJy/sr$ depending on
location, see Figs. 12, 13 in [1]. This observed intensity is numerically much
larger than the AQN induced contribution to this frequency band as determined
by the spectrum (2) with normalization (5).. One should emphasize that a
conventional WIMP-type DM models are not capable to generate the required
intensity of the signal as it was already pointed out in [1], as it was
already mentioned. The AQNs, in contrast with WIMP-type particles, are the
macroscopically large objects made of strongly interacting quarks and gluons
of the Standard Model (SM). In this sense it is indeed a “composite system” in
terminology of [1].

##  4 Concluding comments

There are several profound consequences of our proposal identifying the
mysterious diffuse UV radiation [1, 2, 3] with the emissions by hot AQNs.
First of all this proposal may also shed some light on a long standing problem
related to the nature of the re-ionization of the Universe. Indeed, by
studying the variety of spectra the authors of [30] argued that the same DM
source which is responsible for FUV diffuse emission (which is the topic of
this work) must also emit, I quote: “a continuum of photons in the range $\sim
850\rm\AA$ to about 2000 $\rm\AA$”. This feature is obviously present in the
AQN framework as the spectrum (2) is very broad and for $T_{\rm eff}\geq 5$ eV
extends to the shorter wavelengths well beyond the cut off at the $912\rm\AA$
when the hydrogen atom can be ionized as this wavelength exactly corresponds
to the Rydberg constant $13.6$ eV. In different words, the same AQNs could be
the source of ionizing radiation which is known to be present well above the
galactic plane [30].

Furthermore, the same DM source in form of the AQNs may also contribute to the
resolution of another long standing problem related to the Extragalactic
Background Light (EBL). Indeed, it has been known for some time that the
conventional measurements cannot be explained by diffuse galaxy halos or
intergalactic stars. The discrepancy could be as large as factor $\sim(2-3)$
or even more, see e.g. recent review [31]. Our comment here is that the AQNs
may fulfill this shortage as the spectrum (2) is very broad and includes
optical and IR light.

There is a number of direct tests which can be performed in future to
substantiate or refute this proposal identifying the mysterious diffuse UV
radiation [1, 2, 3] with the emission by AQNs. Some specific suggestions for
future studies have been already discussed in [1, 2, 3, 30], and include such
instruments as the Alice UV spectrometer aboard the New Horizon mission, and
we have nothing new to add here. The only original comment we would like to
make is that the intensity and spectral features of the radiation in the AQN
framework are determined by the line of sight which includes both: the DM and
visible matter distributions according to (4). It should be contrasted with
conventional WIMP-like models when it is exclusively determined by the DM
distribution. Therefore, some specific morphological correlations with DM and
visible matter distributions can be explicitly studied in future.

It is quite amazing that the spectral features and intensities for “exotic”
sources which were required (anticipated) by analysis [1, 2, 3, 30] in form of
the “composite system” in terminology [1] to fit the observations are
automatically present in the AQN framework which was originally invented for
dramatically different purposes with very different motivation, see [10] for
review. One should also emphasize that in the present work we use the same
basic parameters which were previously used for very different applications in
drastically different environment without any attempt to modify these
parameters to better fit the observations. We consider this “miracle
coincidence” as a strong argument supporting this proposal.

If our interpretation on source of the excess of the diffuse FUV emission is
confirmed by future studies it would represent an extraordinary evidence
supporting the resolution of two long standing puzzles: it reveals the nature
of the DM and the matter-antimatter asymmetry of our Universe as these two
problems of the cosmology are intimately linked in the AQN framework.

## Acknowledgements

This research was supported in part by the Natural Sciences and Engineering
Research Council of Canada.

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