# From the Dawn of Neutrino Astronomy to A New View of the Extreme Universe

C. A. Argüelles ID<EMAIL_ADDRESS>Department of Physics &
Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge,
MA 02138, USA  F. Halzen ID<EMAIL_ADDRESS>Department of Physics &
Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin,
Madison, WI 53706, USA  N. Kurahashi ID<EMAIL_ADDRESS>Department of
Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA

###### Abstract

Over the past decade, neutrino astronomy has emerged as a new window into the
extreme and hidden universe. Current generation experiments have detected
high-energy neutrinos of astrophysical origin and identified the first
sources, opening the field to discovery. Looking ahead, the authors of this
Perspective identify seven major open questions in neutrino astrophysics and
particle physics that could lead to transformative discoveries over the next
20 years. These multi-disciplinary questions range from understanding the
vicinity of a black hole to unveiling the nature of neutrino mass, among other
topics. Additionally, we critically review the current experimental
capabilities and their limitations and, from there, discuss the interplay
between different proposed neutrino telescope technologies and analysis
techniques. The authors firmly believe that achieving the immense discovery
potential over the next two decades demands a model of global partnership and
complementary specialized detectors. This collaborative neutrino telescope
network will pave the way for a thriving multi-messenger era, transforming our
understanding of neutrino physics, astrophysics, and the extreme universe.

##  I Introduction

Astronomy views the Universe at wavelengths of light, reaching from radio
waves to gamma rays. The spectacularly successful method of multi-wavelength
astronomy eventually fails at the smallest wavelengths or highest energies
where the Universe turns dark to light. Above the threshold for pair
production $\gamma+\gamma_{\rm cmb}\rightarrow e^{+}+e^{-}$, the gamma rays
interact with microwave photons, $$411\text{\,}\mathrm{cm}$^{-3}$, to produce
electron-positron pairs. These shower in the cosmic microwave background (CMB)
and in other background electromagnetic fields permeating the Universe to
reach our telescopes as multiple photons of lower energy. At some point, we
barely see the center of our own galaxy. In this extreme Universe known to
harbor powerful cosmic particle accelerators, weakly interacting neutrinos are
the only astronomical messengers.

Imagined more than half a century ago Spiering (2012), high-energy neutrino
astronomy became a reality when the IceCube project transformed a cubic
kilometer of transparent natural Antarctic ice one mile below the geographic
South Pole into the largest particle detector ever built Aartsen  _et al._
(2017a). It discovered neutrinos in the $$\mathrm{TeV}$\sim$\mathrm{PeV}$$
energy range originating beyond our galaxy, opening a new window for astronomy
Aartsen  _et al._ (2013a, 2014). The observed energy density of neutrinos in
the extreme universe exceeds the energy in gamma rays Fang  _et al._ (2022);
it even outshines the neutrino flux from the nearby sources in our galaxy
Abbasi  _et al._ (2023a). The galactic plane only appears as a faint glow at
the ten percent level of the extragalactic flux, in sharp contrast with any
other wavelength of light where the Milky Way is the dominant feature in the
sky. This observation implies the existence of sources of high-energy
neutrinos in other galaxies that are not present in our own Fang  _et al._
(2024).

After accumulating a decade of data with a detector with gradually improved
sensitivity, the first high-energy neutrino sources emerged in the neutrino
sky: the active galaxies NGC 1068, NGC 4151, PKS 1424+240 Abbasi  _et al._
(2022a); Privon  _et al._ (2023), and TXS 0506+056 Aartsen  _et al._ (2018a,
b). The observations point to the acceleration of protons and the production
of neutrinos in the obscured dense cores surrounding the supermassive black
holes at their center, typically within a distance of only $10\sim 100$
Schwarzschild radii Abbasi  _et al._ (2022a). TXS 0506+056 had previously been
identified as a neutrino source in a multimessenger campaign triggered by a
neutrino of $290\text{\,}\mathrm{TeV}$ energy, IC170922, and by the
independent observation of a neutrino burst from the same source in archival
IceCube data in 2014 Aartsen  _et al._ (2018a, b).

With indications that neutrinos originate in the vicinity of the central black
hole of active galaxies, which can only be reached by radio telescopes,
neutrino astronomy represents an extraordinary opportunity for discovery. This
includes resolving the century-old problem of where cosmic rays originate and
how they reach their phenomenal energies. Since neutrinos originate from the
decay of charged pions, only sources accelerating cosmic rays that interact
with radiation fields or gas surrounding the accelerator to produce pions can
be neutrino sources. With energies exceeding those produced with earthbound
accelerator beams by one million, cosmic neutrinos also present a remarkable
opportunity for studying the neutrinos themselves.

In contrast with its exceptional discovery potential, neutrino astronomy faces
the evident lack of statistics for future progress, not only in neutrinos but
also in identified sources, a handful in a decade. A weakness in the current
status represents a future challenge and opportunity. The sensitivity of
IceCube has recently been significantly enhanced by progress in the
characterization of the optics of ice, and by exploiting the rapid progress in
machine learning to collect larger data samples that are reconstructed in
neutrino with improved energy and angular resolution. The observations of NGC
1068 and the galactic plane directly resulted from these improvements.

Efforts to upgrade the performance of IceCube continue. The IceCube project
has instrumented a cubic kilometer of natural Antarctic ice with 5160 light
sensors to configure a Cherenkov detector. IceCube is comprised of 10-inch
photomultiplier tubes deployed like beats on 86 one-kilometer-long electric
cables separated by $125\text{\,}\mathrm{m}$. This instrumentation maps the
secondary muon tracks and showers initiated by neutrinos interacting inside or
near the detector to reconstruct their direction, energy, and flavor. Further
progress requires a second-generation instrument with a sensitivity superior
by one order of magnitude. The design for such an instrument exists Aartsen
_et al._ (2021a) and its construction has been strongly endorsed by both the
astronomy and particle physics communities.

In parallel, instruments the size of IceCube are under construction in Lake
Baikal Shoibonov (2019), the Mediterranean sea Sanguineti (2022), and the
Pacific Ocean Bailly  _et al._ (2021) off the coast of Canada. Pioneered by
the DUMAND Roberts (1992) and ANTARES Ageron  _et al._ (2011) projects, these
new initiatives introduce multiple advantages: as complementary instruments
using deep ocean water as the Cherenkov medium, by collectively adding to the
growth of statistics of IceCube, and by improving our global field of view of
the neutrino sky because of their different geographic locations. Projects in
China aim for larger detectors, one matching the next-generation IceCube
detector Ye  _et al._ (2022) and one envisioning a volume of
$$30\text{\,}\mathrm{km}$^{3}$ Huang  _et al._ (2023). Additionally,
specialized detectors aim to find astrophysical tau neutrinos with high purity
in the energy range of IceCube observations are also currently being
developed; notably, TRINITY Otte  _et al._ (2023) using Cherenkov telescopes
and TAMBO Thompson  _et al._ (2023) using particle detectors. As we will
discuss in this Perspective, these small, relatively low-cost experiments will
serve as an essential complement to the larger optical neutrino telescopes.

In the future, we anticipate rapid progress with the collection of larger
statistical samples of neutrinos with superior directional pointing covering a
larger energy range. Further progress will be made possible by multiple
instruments able to cross-check individual results, an advantage that has been
demonstrated over time by the deployment of several complementary detectors at
a single accelerator. Eventually, we anticipate that data from the multiple
instruments will be combined in real-time, as is already routinely done for
the observed strains of the gravitational wave detectors LIGO, Virgo, and
KAGRA.

In parallel, many diverse efforts are underway to develop novel techniques to
extend the IceCube spectrum to EeV energies, driven mainly by radio neutrino
detection techniques. Unfortunately, the steeply falling flux and the slow
growth of the neutrino cross-section at these energies require extremely large
arrays to obtain a handful of events for the most pessimistic flux
predictions. Given the lack of overlap in energy with the current observations
— and thus the discovery opportunities they represent — we will not comment
further on these efforts.

In this Perspective, we attempt to anticipate a broad brush description of the
future of the field, building on the present results and realizing that the
most important impact of the rapid expansion of neutrino astronomy will result
from unanticipated discoveries. We will start by reviewing the astronomical
discoveries made by the first generation of instruments and the important
measurements they contributed to neutrino physics. We will discuss how the
novel observation raises new scientific questions that are harder to resolve
and how we anticipate that the field will move from discovery into astronomy
in the future by deploying a new generation of instruments.

##  II Questions that can lead to transformational discoveries

In this section, we pose seven questions that we believe can be answered over
the following decades and yield discoveries that will significantly impact
physics and astronomy. At the end of each subsection, for each question, we
have written a short take-home message in italics preceded by the symbol ✒.
For a reader who wants a first glance at our vision of the future, we
encourage you to read these short answers and our parting words in Section IV.

###  II.1 Where are the gamma rays produced together with the neutrinos?

The rationale for searching for cosmic-ray sources by observing neutrinos is
straightforward: in relativistic particle flows, for instance, onto black
holes, some of the gravitational energy released in the accretion of matter is
transformed into the acceleration of protons or heavier nuclei. These
subsequently interact with radiation and/or ambient matter in the vicinity of
the black hole to produce pions and other secondary particles that decay into
neutrinos. Both neutrinos and gamma rays are produced with roughly equal
rates; while neutral pions decay into two gamma rays,
$\pi^{0}\to\gamma+\gamma$, the charged pions decay into three high-energy
neutrinos ($\nu$) and antineutrinos ($\bar{\nu}$) via the decay chain
$\pi^{+}\to\mu^{+}+\nu_{\mu}$ followed by $\mu^{+}\to
e^{+}+\bar{\nu}_{\mu}+\nu_{e}$; see Fig. 1. Based on this simplified flow
diagram, we expect equal fluxes of gamma rays and muon neutrinos. The flow
diagram of Fig. 1 implies a multimessenger interface between the pionic gamma-
ray and three-flavor neutrino flux Ahlers and Halzen (2015):

$E_{\gamma}^{2}\frac{dN_{\gamma}}{dE_{\gamma}}\approx\frac{4}{K_{\pi}}\,\frac{1}{3}E_{\nu}^{2}\frac{dN}{dE_{\nu}}\Big{|}_{E_{\nu}={E_{\gamma}}/2},$
(1)

where $K_{\pi}$ is the ratio of charged and neutral pions produced, with
$K_{\pi}\approx 2(1)$ for $pp(p\gamma$) interactions.

This powerful relation relates neutrinos and pionic gamma rays with no
reference to the cosmic-ray beam producing the neutrinos; it simply reflects
the fact that a $\pi^{0}$ decays into two gamma rays for every charged pion
producing a $\nu_{\mu}+\bar{\nu}_{\mu}$ pair. Also, from the fact that in the
photo-production process 20% of the initial proton energy is transferred to
the pion111This is referred to as the inelasticity $\kappa_{p\gamma}\simeq
0.2$., we obtain that the gamma-ray carries one-tenth of the proton energy and
the neutrino approximately half of that.

Because high-energy photons inevitably accompany cosmic neutrinos, neutrino
astronomy is a multimessenger astronomy. Unlike neutrinos, gamma rays interact
with microwave photons and other diffuse sources of extragalactic background
light (EBL) while propagating to Earth. The gamma rays lose energy by
$e^{+}e^{-}$ pair production, and the resulting electromagnetic shower
subdivides the initial photon energy into multiple photons with reduced energy
reaching our telescopes.

Observing neutrinos as a signature for the acceleration of cosmic-ray protons
or nuclei is powerful because the alternative possibility to identify pionic
photons has turned out to be challenging because they must be isolated from
photons radiated by, or upscattered to high energy by inverse Compton
scattering, by high-energy electrons.

Figure 1: Flow diagram showing the production of charged and neutral pions in
$p\gamma$ interactions. The circles indicate equal energy going into pairs of
gamma rays and muon neutrinos and antineutrinos. Because the charged pion
energy is shared roughly equally among four particles and the neutral pion
energy among two photons, the photons have twice the energy of the neutrinos.
Unlike the weakly interacting neutrinos, the gamma rays and electrons may lose
energy in the target and will lose additional energy in the background light
(EBL) before reaching Earth.

After accumulating a decade of data, the observed flux of neutrinos reaching
us from the cosmos is shown in Fig. 2. It has been measured using two
different methods to separate the high-energy cosmic neutrinos from the large
backgrounds of cosmic-ray muons, 3,000 per second, and neutrinos, one every
few minutes, produced by cosmic rays in the atmosphere. The first method
identifies muon neutrinos of cosmic origin in samples of muon tracks produced
by upgoing muon neutrinos reaching the South Pole from the Northern
Hemisphere. The Earth is used as a passive shield for the large background of
cosmic-ray muons. By separating the flux of high-energy cosmic neutrinos from
the lower energy flux of neutrinos of atmospheric origin, a cosmic high-energy
component is isolated with a spectral index $\rm dN/dE\sim E^{-\gamma}$ with
$\gamma=2.37\pm 0.09$ above an energy of $\sim$100\text{\,}\mathrm{TeV}$$
Aartsen  _et al._ (2017b); see Fig. 2. Also shown are the results of a second
search that exclusively identifies showers initiated by electron and tau
neutrinos that interact inside the detector and can be isolated from the
atmospheric background to energies as low as $10\text{\,}\mathrm{TeV}$ Abbasi
_et al._ (2022b). Reaching us over long baselines, the cosmic neutrinos flux
has oscillated to a ratio $\nu_{e}:\nu_{\tau}:\nu_{\mu}$ of approximately
1:1:1.

Figure 2: Current all-sky measurements of the high-energy astrophysical
neutrino emission. The flux of cosmic muon neutrinos Aartsen  _et al._ (2017b)
inferred from the $9.5$-year upgoing-muon track analysis (solid line) with
$1\sigma$ uncertainty range (shaded) is compared with the flux of showers
initiated by electron and tau neutrinos Aartsen  _et al._ (2020), when
assuming standard oscillations. The measurements are consistent assuming that
each neutrino flavor contributes an identical flux to the diffuse spectrum.
Both are consistent with the flux derived from the observation of a single
Glashow-resonance event shown in red.

Additionally, IceCube has independently confirmed the existence of neutrinos
of cosmic origin by the observation of high-energy tau neutrinos Abbasi  _et
al._ (2022c) and by the identification of a Glashow resonant event where a
weak intermediate $W^{-}$ boson is produced in the resonant interaction of an
electron antineutrino with an atomic electron: $\bar{\nu}_{e}+e^{-}\rightarrow
W^{-}\rightarrow q+\bar{q}$ Aartsen  _et al._ (2021b). Found in a dedicated
search for partially contained showers of very high energy, the reconstructed
energy of the Glashow event is $6.3\text{\,}\mathrm{PeV}$, matching the
laboratory energy to produce a $W^{-}$ of mass $80.37\text{\,}\mathrm{GeV}$.
Given its high energy, the initial neutrino is cosmic in origin and provides
an independent discovery of cosmic neutrinos at the level of $5.2\sigma$.

As already discussed, unlike neutrinos, gamma rays interact with photons
associated with the extragalactic background light while propagating to Earth.
The $\gamma$-rays lose energy by $e^{+}e^{-}$ pair production, and the
resulting electromagnetic shower subdivides the initial photon energy into
multiple photons of reduced energy reaching Earth. This significantly modifies
the implications of the gamma-neutrino interface, which we illustrate Fang
_et al._ (2022) by first parametrizing the neutrino spectrum as a power law

$\frac{dN}{dE_{\nu}}\propto E_{\nu}^{-\gamma_{\rm astro}},\,E_{\nu,\rm
min}\leq E_{\nu}\leq E_{\nu,\rm max},\,$ (2)

for four recent measurements taken from Refs. Abbasi  _et al._ (2021a);
Aartsen  _et al._ (2020); Abbasi  _et al._ (2022d); Aartsen  _et al._ (2019).
Conservatively, the minimum and maximum energies are limited to the range of
neutrino energies the particular analysis is sensitive to. For each neutrino
flux measurement, we derive the accompanying gamma-ray flux from the fit to
the neutrino spectrum using the interface of Eq. 2. This pionic gamma-ray flux
is subsequently injected into the EBL, assuming that the sources follow the
star-formation (SFR) history in a flat $\Lambda$CDM universe (Hopkins and
Beacom, 2006). Figure 3 shows the diffuse neutrino fluxes and those of their
accompanying gamma-ray counterparts. As the values of the neutrino flux
spectral indices are comparable for the four measurements, the flux of the
cascades is essentially determined by the value of $E_{\nu,\rm min}$ where the
energy peaks. We conclude that when $E_{\nu,\rm
min}\lesssim$10\text{\,}\mathrm{TeV}$$, the showers initiated by the pionic
photons contribute up to $\sim 30-50\%$ of the diffuse extragalactic gamma ray
flux between $30\text{\,}\mathrm{GeV}$ and $300\text{\,}\mathrm{GeV}$ and
nearly 100% above $500\text{\,}\mathrm{GeV}$. The cascade flux exceeds the
observed gamma-ray flux above $\sim$10\text{\,}\mathrm{GeV}$$ when $E_{\nu,\rm
min}\leq$10\text{\,}\mathrm{TeV}$$, assuming that the measured power-law
distribution continues.

Figure 3: Gamma-ray-transparent sources? Cosmic neutrino spectra (black
curves) and $\gamma$-ray flux resulting from the accompanying gamma rays (red
curves). The data points are measurements of the diffuse cosmic neutrino flux
(Aartsen  _et al._ , 2017c; Abbasi  _et al._ , 2021a), the extragalactic
gamma-ray background (EGB), the isotropic gamma-ray background (IGRB)
(Ackermann  _et al._ , 2015) from $0.1\text{\,}\mathrm{GeV}$ to
$1\text{\,}\mathrm{TeV}$, and the diffuse MeV gamma-ray background
(Weidenspointner, 1999; Watanabe  _et al._ , 1999; Strong  _et al._ , 2004).
Neutrino spectra correspond to the best-fit single power-law models for the
different IceCube analyses. Fluxes below and above the sensitivity range for
the IceCube analyses are not constrained by the data and are shown as dashed
curves. Pionic gamma rays from hadronic interactions are assumed to leave the
sources without attenuation, propagate in the EBL, and cascade down to GeV-TeV
energies.

In the end, the room left to accommodate secondary photons from TeV-PeV gamma
rays and electrons is small, and it is difficult to avoid the conclusion that
the extragalactic gamma-ray flux accompanying cosmic neutrinos exceeds the
diffuse gamma-ray flux observed by Fermi, especially because blazars produce
$\sim 80\%$ of the latter at the highest gamma-ray energies that are not
sources of neutrinos Aartsen  _et al._ (2017d). There is no contradiction
here; we infer from the calculations that the pionic gamma rays already lose
energy in the target producing the neutrinos prior to propagating in the EBL.
As a result, pionic gamma rays emerge below Fermi threshold, at MeV energies
or below. The observed diffuse neutrino flux originates from $\gamma$-ray-
obscured sources. The analysis presented here reinforces the conclusions of
previous analyses; see Refs. Murase  _et al._ (2013, 2016); Capanema  _et al._
(2020, 2021).

We should emphasize that the fact that powerful neutrino sources are gamma-ray
obscured should not come as a surprise. The photon and proton opacities in a
neutrino-producing target are related by their cross sections (up to a
kinematic factor associated with the different thresholds of the two
interactions; see Ref. Svensson (1987))

$\tau_{\gamma\gamma}\simeq\frac{\sigma_{\gamma\gamma}}{\kappa_{p\gamma}\sigma_{p\gamma}}\,\tau_{p\gamma}\simeq
10^{3}\,\tau_{p\gamma}\,,$ (3)

where $\kappa_{p\gamma}\sim 0.2$ is the inelasticity in $p\gamma$
interactions. For instance, we should not expect neutrinos to be significantly
produced in blazar jets that are transparent to very high-energy gamma rays.
In contrast, the highly obscured dense cores close to supermassive black holes
in active galaxies represent an excellent opportunity to produce neutrinos,
besides providing opportunities for accelerating protons.

✒ Understanding the production regions of neutrinos in astrophysical sources
requires the use of multimessenger data. This does not come as a surprise
since neutrino astrophysics is multimessenger astrophysics, as the production
of neutrinos is associated with the production of gamma rays. However, the
current data indicates that the intense neutrino sources are actually gamma-
ray opaque. We predict that up-coming sub-GeV gamma-ray instruments will find
correlations with high-energy astrophysical neutrino sources.

###  II.2 What does an improved observation of Galactic neutrinos tell us?

The Milky Way is an ideal observational target to answer many of the questions
raised in the previous decade of neutirno astronomy. Our own Galaxy is
expected to host high-energy sources of cosmic rays and thus neutrinos. Cosmic
ray propagation, a challenge to model and of long standing interest, will
enter a new era once diffuse Galactic neutrinos are measured accurately.
Neutrino-gamma-ray connections can be studied at much closer distances than by
studying extragalactic sources.

In 2023, IceCube announced the first observation of the Milky Way Galaxy in
neutrinos at a statistical significance of 4.5 $\sigma$ Abbasi  _et al._
(2023a), thus starting the field of Galactic neutrino astronomy. High-energy
neutrinos are produced when Galactic cosmic rays interact at their
acceleration sites and during propagation through the interstellar medium. The
Galactic plane has, therefore, long been hypothesized as a neutrino source.
IceCube’s observation of the diffuse Galactic Plane represents the first non-
electromagnetic image of our Galaxy as a whole and the first high-energy
neutrino observations from our Galaxy (MeV-scale neutrinos have been observed
for decades from the Sun and more recently in lower energies).

The high-energy neutrino observations from our Galaxy open a new door to
search for Galactic PeVatrons, sources capable of cosmic-ray acceleration to
PeV energies Bustamante (2023). While gamma rays have led the search for
PeVatrons, there is a large chance that their interactions in the Galaxy
obscure searches. Using future neutrino observations, together with cosmic-ray
and gamma-ray observations, we will be able to identify Galactic PeVatrons.

With the Galactic Plane observed, the Galactic Center (GC) emission also
becomes interesting. The GC is a region that promises high activity based on
the presence of a supermassive black hole (SMBH) at the position of Sgr A*.
SMBHs can be sources of cosmic-ray emissions and their secondaries, neutrinos,
and gamma-rays. Because of the density of matter in the GC region, future
neutrino observations may be able to probe deeper than any other observations
in cosmic rays, gamma rays, or any other electromagnetic wavelengths, thanks
to their large interaction length (ie ”neutrino depth”).

The pressing question regarding the observed diffuse flux is how much
individual Galactic point sources, below the current detection threshold,
contribute to it. Identifying many types of individual Galactic sources
remains a challenge. Future detectors with better capabilities will provide a
more complete answer Ambrosone  _et al._ (2024). This is a great opportunity
for the upcoming KM3NeT neutrino observatory in the Mediterranean, which is
currently under construction.

The 2023 observation of the diffuse Galactic Plane was based on testing
templates generated from diffuse neutrino models. Because the models Ackermann
_et al._ (2012); Gaggero  _et al._ (2015), which generate both spatial
distribution and energy spectrum templates used in the neutrino analysis, use
models of matter distribution in the galaxy, galactic cosmic-ray production,
and their propagation, in addition to a template of neutral pions, when the
observation of the Galactic Plane in neutrinos is refined, in turn, it can
provide constraints on those input models. Currently, the observational limit
in neutrinos means we are constrained to testing existing models based on
gamma-ray and cosmic-ray observations. Once neutrino observations become more
sensitive, they then inform the modeling of gamma-ray production and cosmic-
ray propagation.

Beyond model testing, a model-free observation of the spatial distribution of
the neutrino flux in the Galaxy provides a comparison to the gamma-ray data to
shed light on the gamma-ray-neutrino connection, as described in II.1. The
model-independent observation of the energy spectrum is also a pressing
question for the field. This can only be answered by collecting larger
statistical and sensitive observations of the Galactic plane. It remains to be
seen whether there is any energy region where the Galactic diffuse flux
outshines the extragalactic diffuse flux in neutrinos.

✒Galactic neutrino astronomy provides an opportunity to study sources of the
closest distance, the closest black hole, and discover Galactic PeVatrons.
Detailed observations of the Galactic neutrino diffuse flux, and comparison to
the counterpart gamma-ray flux, will lead to understanding the gamma-ray-
neutrino connection, cosmic-ray production and propagation, and matter
distribution in the Galaxy.

###  II.3 What will we learn from probing the black hole environment with
neutrinos?

The identification of the first cosmic-neutrino sources confirms that cosmic
neutrinos originate in sites that are opaque to gamma rays. The gamma rays
accompanying the neutrinos emerge from the source at energies below the Fermi
threshold, at MeV energies, or below. The multiwavelength observations of the
active galaxy NGC 1068 represent an interesting case study. The neutrino flux
measured by IceCube is shown in Fig. 4 along with the gamma-ray data. Note
that the MAGIC telescope’s upper limits exclude the presence of the
accompanying pionic gamma-ray flux by more than one order of magnitude in the
TeV energy range; the source is indeed gamma-ray obscured.

Figure 4: Multimessenger spectral energy distribution of NGC 1068. Dark and
light green points indicate gamma-ray observations at 0.1 to
$100\text{\,}\mathrm{GeV}$ Ajello  _et al._ (2020); Abdollahi  _et al._ (2020)
and $>$200\text{\,}\mathrm{GeV}$$ Acciari  _et al._ (2019), respectively.
Arrows indicate upper limits and error bars are $1\sigma$ confidence
intervals. The solid, dark blue line shows our best-fitting neutrino spectrum,
with the dark blue shaded region indicating the 95% confidence region. We
restrict this spectrum to the range between 1.5 and $15\text{\,}\mathrm{TeV}$,
where the flux measurement is well-constrained (26). Two theoretical
predictions are shown for comparison: The light blue shaded region and the
gray line show the NGC 1068 neutrino emission models from Refs. Inoue  _et
al._ (2019), Inoue  _et al._ (2020), and Murase  _et al._ (2020),
respectively. All fluxes are multiplied by the energy squared $\rm E^{2}$.

Dimensional analysis is sufficient to show that the observations point to the
production of neutrinos in the obscured dense core surrounding the
supermassive black holes at their center. A conceptual version of the neutrino
source in Fig. 5 shows the dense core of X-rays confined to a radius $\rm R$
that converts protons accelerated near the supermassive black hole into
neutrinos. Astronomers refer to the gamma-ray-obscured core emitting X-rays as
a “corona.”

Figure 5: Cosmic neutrinos cradle. The core of an active galaxy combines the
ingredients to produce neutrinos, with protons accelerated by the black hole
and/or by the accretion disk and a target (corona) with a large optical depth
in both gamma rays and hydrogen that converts them into neutrinos.

The opacity of the X-ray target to protons is

$\rm\tau_{p\gamma}\simeq\frac{\kappa_{p\gamma}R_{escape}}{\lambda_{p\gamma}}\simeq\kappa_{p\gamma}\rm
R_{escape}\,\sigma_{p\gamma}\,n_{\gamma},$ (4)

which is determined by how often the proton interacts in a target of size $\rm
R_{target}$ given its interaction length $\lambda_{p\gamma}$. With each
interaction, the proton loses a fraction $\kappa_{p\gamma}$ of its energy, the
inelasticity. The interaction length is determined by the density of target
photons $\rm n_{\gamma}\simeq n_{X}$ and the interaction cross section
$\sigma_{p\gamma}$:

$\rm n_{X}=\frac{u_{X}}{\epsilon_{X}}=\frac{1}{4\pi
R^{2}c}\,\frac{L_{X}}{\epsilon_{X}}\,,$ (5)

and therefore,

$\rm\tau_{p\gamma}=\frac{\kappa_{p\gamma}\sigma_{p\gamma}}{4\pi
c}\,\frac{1}{R}\,\frac{L_{X}}{\epsilon_{X}}.$ (6)

We here determined the target density in X-rays from the energy density of
X-rays $\rm u_{X}$ divided by their energy $\epsilon_{X}$ and, subsequently,
identified the energy flux $\rm cu_{X}$ with the measured luminosity of the
source $\rm 4\pi R^{2}\,L_{X}$. In the end, the opacity of the corona to
protons is proportional to the density of target photons, i.e., to the X-ray
luminosity $\rm L_{X}$, and inversely proportional to the radius $\rm R$.

For NGC 1068, with a black hole of approximately $10^{7}$ solar masses, the
above result can also be written as

$\rm\tau_{p\gamma}\simeq
10^{2}\,\left[\frac{R_{s}}{R}\right]\,\left[\frac{$1\text{\,}\mathrm{keV}$}{\epsilon_{X}}\right]\left[\frac{L_{X}}{L_{\rm
edd}}\right]\simeq 10^{-3}\,\tau_{\gamma\gamma}\,,$ (7)

with $\rm L_{X}\sim 10^{43}\,\rm erg/s$ at keV energy, or $\rm L_{X}\simeq
10^{-2}\,L_{\rm edd}$.

Even for a relative modest opacity of $\tau_{p\gamma}\gtrsim 0.1$, the above
result requires that the X-rays be confined to a radius of $\rm R\simeq
10\,R_{s}$. Importantly, this will automatically guarantee the suppression of
the pionic photon flux by more than one order of magnitude relative to
neutrinos by Eq. 3.

Detailed modeling of the accelerator and target reinforce the conclusion that
neutrinos originate within $\rm\sim 10^{-4}\,pc$ of the supermassive black
hole. Producing neutrinos, even at the base of the jet at a distance, will
fail to yield the neutrino flux observed for NGC 1068 and suppress the
appearance of a TeV gamma-ray flux at TeV energy and below.

Interestingly, high densities of both radiation Bauer  _et al._ (2015);
Marinucci  _et al._ (2016); Ricci  _et al._ (2017) and matter Rosas  _et al._
(2022); et al. (2016) are associated with the core of NGC 1068 and therefore
neutrinos are efficiently produced in both $p\gamma$ and $pp$ interactions. A
second look at the multiwavelength data shown in Fig. 4 leads us to conclude
that $\tau_{pp}>\tau_{p\gamma}$ because the $p\gamma$ threshold for producing
neutrinos on a target of keV-energy photons at the $\Delta$-resonance, is at
PeV energy. Instead, the typical energy of the neutrinos observed by IceCube
from the direction of NGC 1068 is closer to $\sim$10\text{\,}\mathrm{TeV}$$;
see Fig. 4. These neutrinos are predominantly produced in $pp$ interactions,
with a reduced threshold for producing multiple pions, which results in
neutrinos of lower energy.

From Eq. 4, we calculate the opacity to protons of the large matter density
close to the black hole

$\rm\tau_{pp}\simeq\frac{\kappa_{pp}\,R}{\lambda_{pp}}\simeq\kappa_{pp}\,\rm
R\,\sigma_{pp}\,n_{p}\simeq\kappa_{pp}\,\sigma_{pp}\,N_{H},$ (8)

where we have introduced the line-of-sight density $\rm N_{H}=R\,n_{p}$, which
is sufficiently large for NGC 1068 to achieve an opacity $\rm\tau_{pp}\gtrsim
1$. In Fig. 4, two such models are compared to the flux observed by IceCube
from NGC 1068. Accelerated protons interact in the corona with both the dense
gas in $pp$ interaction and with the X-ray photons by $p\gamma\rightarrow
pe^{+}e^{-}$, the Bethe-Heitler process. The latter channels the energy stored
in the flux of relativistic protons to relativistic pairs with extended
distributions. Contrary to accelerated leptons, whose maximum energy is
limited by radiative losses, the maximal energy of pairs is determined by the
kinematics of the process and, in this case, populates the MeV energy region.

From Eq. 8, one may be tempted to conclude that, with the production of
neutrinos in $pp$ interactions only depending on the line-of-sight density
$N_{H}$, we can evade the constraint on the size of the production region $\rm
R\lesssim 100\,R_{s}$. This is not the case because a high density of X-rays
in the corona is still required to suppress the flux of pionic gamma rays
produced in $pp$ interactions to evade the strong upper limits from the MAGIC
telescope shown in Fig. 4. The suppression of the $\gamma$-ray flux by over
one order of magnitude cannot be achieved with interactions with protons only.
Although produced by different mechanisms, the gamma rays accompanying the
neutrinos still emerge at MeV energies, the characteristic energy at which the
X-ray corona becomes transparent to photons. For a more detailed review of the
models, see Refs. Murase (2022); Kheirandish  _et al._ (2021); Eichmann  _et
al._ (2022); Anchordoqui  _et al._ (2021).

Do cosmic neutrinos (and cosmic rays) originate in the obscured cores of
active galaxies? Some do, and with NGC 1068 and NGC 4151, we have identified
the first sources of high-energy cosmic rays since their discovery more than a
century ago. Instead, modeling the multiwavelength spectrum of TXS 0506+056
represents an unmet challenge. The source is different: it emits neutrinos in
bursts with Eddington luminosity characterized by a harder neutrino spectrum,
close to $\rm E^{-2.2}$. The gamma-ray obscured spectra at the time of
neutrino production Halzen (2021) may indicate that the neutrinos are produced
in the vicinity of the core as is the case for NGC 1068 but in association
with catastrophic events hinted at by the observation of a strong optical
flare in 2017 Lipunov  _et al._ (2020).

✒While any conclusions regarding the origin of the highest energy cosmic rays
may be premature, we feel that with more and larger instruments, the
revelation of a multitude of sources and the resolution of the puzzle is
within reach. The emission of neutrinos from the few sources we have
identified indicates that they are produced near supermassive black holes.
Thus, neutrino observations, and their comparison to gamma-ray observations,
provide information about the matter and radiation density around the black
hole.

###  II.4 What will we learn about stellar collapse and neutrino physics from
galactic and extragalactic supernovae?

A core-collapse supernova radiates the vast majority of the binding energy of
the resulting compact remnant in the form of neutrinos of all flavors.
Information on the astrophysics of the collapse and subsequent explosion, and
about the physics of the neutrinos themselves, is encoded in the time, energy,
and flavor structure of the neutrino burst. When supernova 1987A exploded,
only a couple of tens of events provided sufficient information to not only
probe the physics of the explosion but also to shed new light on neutrino
properties such as their mass, magnetic moment, and lifetime. Neutrino
oscillations produce significant modifications of the neutrino spectra. Matter
transitions in the expanding remnant modify the time- and energy-dependent
profiles of the spectra of neutrinos and antineutrinos, which depend on the
neutrino mixing parameters and the presently unknown neutrino mass ordering.
Additionally, depending on the type of supernova, “collective” effects
resulting from neutrino-neutrino interactions can result in additional
modifications of the spectra.

Although designed as a high-energy Cherenkov detector with a nominal threshold
of $100\text{\,}\mathrm{GeV}$ ($\sim$5\text{\,}\mathrm{GeV}$$ in IceCube-
DeepCore), IceCube can identify with high significance the interactions of
below-threshold MeV neutrinos produced by the passage of the flux resulting
from a Galactic supernova. It is observed as a collective increase in all
photomultiplier counting rates over their very low dark noise in
radioactivity-free ice. The rate increase is caused by the Cherenkov light
from shower particles produced by supernova electron antineutrinos interacting
in the ice, predominantly by the inverse beta decay reaction. The secondary
positron tracks of about $$0.6\text{\,}\mathrm{cm}$\times(E_{\nu}/{\rm MeV})$
length radiate $178\times(E_{e^{+}}/{\rm MeV})$ Cherenkov photons in the
$300-$600\text{\,}\mathrm{nm}$$ wavelength range. From the approximate $E^{2}$
dependence of the neutrino cross section and the linear energy dependence of
the track length, the light yield per neutrino scales with $E^{3}$. With
absorption lengths exceeding $100\text{\,}\mathrm{m}$, photons travel long
distances in the ice, so each DOM effectively monitors several hundred cubic
meters of ice.

Although the rate increase in a single light sensor, for this discussion
IceCube’s Digital Optical Module or DOM, is not statistically significant, its
significance increases when recorded collectively in multiple independent
sensors. It reaches over $10\sigma$ for a supernova at
$10\text{\,}\mathrm{kpc}$ producing one million photoelectrons, producing a
detailed movie of the time evolution of the neutrino signal. Whereas DOMs
overwhelmingly record single photons, the frequency of two-photon coincidences
can be used to measure the average energy of the neutrinos . With a two-
megaton effective volume for supernova neutrinos, IceCube is the most precise
detector for analyzing their neutrino light curve Abbasi  _et al._ (2011a).
This has been demonstrated by establishing a limit on the frequency of
supernovae using more than ten years of data Abbasi  _et al._ (2023b).

Besides continuously monitoring the highly stable noise rate in the DOMs
Abbasi  _et al._ (2023c), IceCube additionally buffers for several days the
information from all photomultiplier hits, with every photon in every DOM
recorded with a resolution of $2\text{\,}\mathrm{ns}$ Heereman von Zuydtwyck
(2015). This low-level data, saved when a supernova occurs, provides several
advantages: the complete detector information is available over the duration
of the supernova, and the data—buffered at an early stage of the data
acquisition system on the so-called string hubs—will be available in the
unlikely case that the data acquisition fails or saturates, for instance in
the case of an extremely close supernova. The automatized hitspooling has been
working reliably for several years, including the automatic data transfer in
case of potentially interesting alarms to the North.

The excellent sensitivity to neutrino properties such as the neutrino
hierarchy, as well as the possibility of detecting the neutronization burst, a
short outbreak of anti- $\nu_{e}$ released by electron capture on protons soon
after collapse are discussed in references Abbasi  _et al._ (2011a, 2023c). In
Fig. 6, we illustrate the sensitivity of IceCube to the neutrino mass
hierarchy for a supernova at the most likely distance of
$10\text{\,}\mathrm{kpc}$. On the astrophysics side, the characteristic “SASI”
oscillations of the standing accretion shock will leave clear signatures in
the high-statistics IceCube observations, as will the collapse of the star to
a black hole.

Figure 6:  Supervanoe neutrino events in a neutrino observatory. Simulated
photoelectrons in IceCube from the interactions of electron antineutrinos
produced by the collapse of a 13 solar mass progenitor
$10\text{\,}\mathrm{kpc}$ from Earth Nakazato  _et al._ (2013). Different bin
sizes are chosen to illustrate time features in different phases of the star’s
collapse: (left) the deleptonization peak, (center) a $\sim 0.5$ second
plateau as matter accretes onto the core forming a proto-neutron star, and
(right) $\sim 10$ second of exponential decay as the proto-neutron cools.
Contrasted are the results assuming neutrino oscillations for normal and
inverted hierarchy of the masses.

IceCube supernova data will also represent an extraordinary opportunity for a
multimessenger analysis with the gravitational wave signal Takiwaki  _et al._
(2021). The gravitational wave strain of a supernova burst is proportional to
the second time derivative of its moment of inertial $I$, which we can rewrite
in terms of its mass, radius, and characteristic frequency

$h\sim\rm\frac{d^{2}I}{dt^{2}}\sim MR^{2}f^{2}.$ (9)

An asymmetry in the shock, required for a non-vanishing strain, develops
because of the rotation of the star and also results from the SASI
oscillations. The same frequency is visible in the IceCube data and is
revealed by transforming the high statistics time dependence data into the
frequency domain.

Icecube observations also represent an opportunity to search for the super-
luminous extragalactic interaction-powered Type IIn supernovae where particles
can be accelerated to relativistic energies by the ejecta of the star
interacting with the dense circumnuclear medium Lincetto  _et al._ (2023).

✒Neutrino telescopes are in a position to make crucial and complementary
observations to MeV-to-keV-scale neutrino detectors for Galactic core-collapse
supernovae. Such observations can not only tell us about the supernovae
themselves but become a particle physics laboratory to measure phenomena such
as neutrino mass hierarchy. Extragalactic Type IIn supernovae are neutrino-
bright source candidates in neutrino astronomy.

###  II.5 What will we learn about the nature of dark matter with neutrino
telescopes?

A neutrino observatory is a powerful tool for searching for the particle
nature of dark matter and provides unique capacities to study dark matter
complementary to Earth-based experiments. For example, if “weakly” interacting
massive particles (WIMPs) make up the dark matter, they have been swept up by
the Sun for billions of years as the Solar System moves about the galactic
halo. Though interacting weakly, they will occasionally scatter elastically
with nuclei in the Sun and lose enough momentum to become gravitationally
bound. Over the Sun’s lifetime, a sufficient density of WIMPs may accumulate
in its center so that an equilibrium is established between their capture and
annihilation. The annihilation products of these WIMPs represent an indirect
signature of halo dark matter, their presence revealed by neutrinos, which
escape the Sun with minimal absorption for sub-100 GeV masses. The neutrinos
are, for instance, the decay products of heavy quarks and weak bosons
resulting from the annihilation of WIMPs into
$\chi\chi\rightarrow\tau^{+}\tau^{-}$, $b\bar{b}$, or $W^{+}W^{-}$. Neutrino
telescopes are sensitive to such neutrinos because of their relatively large
neutrino energy, reflecting the mass of the parent WIMP, making them distinct
from neutrinos produced in nuclear process in the Sun.

The beauty of the indirect detection technique using neutrinos originating in
the Sun is that the astrophysics of the problem is understood. The source in
the Sun has built up over solar time, sampling the dark matter throughout the
galaxy; therefore, any unanticipated structure in the halo has been averaged
out over time. Other astrophysical uncertainties, such as the dark matter
velocity distribution, have little or no impact on the capture rate of dark
matter in the sun Choi  _et al._ (2014); Danninger and Rott (2014). Given a
WIMP mass and cross section (and the assumption that the dark matter is not
exclusively matter or antimatter), one can unambiguously predict the signal in
a neutrino telescope. If not observed, the model will be ruled out; see, e.g.,
Fig. 7 for a recent result. This is in contrast to indirect searches for
photons from WIMP annihilation, whose sensitivity depends critically on the
structure of halo dark matter; observation requires cuspy structure near the
galactic center or clustering on appropriate scales elsewhere; observation
necessitates not only appropriate WIMP properties but also favorable
astrophysical circumstances.

There are two other unique ways in which neutrino telescopes can search for
dark matter. First, if dark matter is very heavy, e.g., when its masses are
above 100 TeV, the photons produced from the decay or annihilation of dark
matter in our halo do not reach Earth unscattered. Instead, they interact with
the extragalactic light or the cosmic microwave background Berezinsky and
Kalashev (2016); Skrzypek  _et al._ (2023). In this scenario, neutrino
telescopes provide the most direct and effective probe of very heavy dark
matter annihilation and decay Argüelles  _et al._ (2021, 2023a). Neutrino
telescope can look for this signal by looking for neutrinos from
concentrations of WIMPs in the Milky Way Aartsen  _et al._ (2017e, 2015a,
2016); Abbasi  _et al._ (2011b); Aartsen  _et al._ (2015b) and nearby galaxies
Aartsen  _et al._ (2013b). These searches are especially important since
neutrinos are the final channel to test the WIMP miracle, where dark matter
interaction with the Standard Model is at the weak scale. Second, neutrinos
can interact with dark matter from their sources to Earth. Interactions
between neutrinos and dark matter are motivated by scotogenic neutrino mass
generation mechanism Blennow  _et al._ (2019), where the neutrino mass is
produced by these interactions, and recent cosmological observations Hooper
and Lucca (2022). The study of the opacity of the universe to high-energy
neutrinos yields constraints on the neutrino-dark matter interaction Argüelles
_et al._ (2017); Kelly and Machado (2018); Ferrer  _et al._ (2023); Abbasi
_et al._ (2023d) that are comparable with cosmological studies. Additionally,
the intensity of neutrino emission from the sources provides information about
the hadronic environments where these neutrinos are produced. This observation
can place constraints on the proton-dark matter interaction, which is probing
the same coupling as direct detection experiments at Earth Herrera and Murase
(2023).

Figure 7: Upper limits at 90% confidence level on the spin-dependent
neutralino-proton cross section assuming that the neutrinos are produced by
$b\bar{b}$ and $W^{+}W^{-}$ annihilation Aartsen  _et al._ (2013c). Limits
from the Super-Kamiokande and direct detection experiments are shown for
comparison. The shaded region represents supersymmetric models not ruled out
by direct experiments. To be updated with the latest result.

✒Neutrino telescopes, given their broad energy range, from tens of GeV to
multiple PeV, offer a unique way to discover dark matter. They are the most
effective probes for very heavy dark matter, and they offer a way to test the
one of the last remaining channels of the WIMP miracle: dark matter
annihilation to neutrinos. Additionally, Universe’s transparency to high-
energy neutrinos allows for the potential discovery of neutrino-dark matter
interactions.

###  II.6 What will astrophysical neutrinos tell us about the nature of
neutrino mass?

The discovery of non-zero neutrino masses has been one of the most significant
observations of the last century. This measurement implies that the Standard
Model particle content is incomplete and that new physics is responsible for
the neutrino masses. So far, we have only been able to learn about neutrino
masses by studying the change in neutrino flavors over long distances. In
fact, two naturally occurring neutrino sources were used to discover this
phenomenon: solar neutrinos and neutrinos produced in cosmic-ray collisions in
Earth’s atmosphere. As we will discuss in this section, the study of high-
energy astrophysical neutrinos with neutrino telescopes can address three
fundamental questions in neutrino physics: the nature of neutrino masses, the
lifetime of the neutrino, and the unitarity of the neutrino mixing matrix. Of
these three questions, the latter two require new physics beyond the existence
of massive neutrinos to yield observable signatures in neutrino observatories;
however, the first question is already invited by the observation of non-zero
neutrino masses.

Shedding light into the origin of neutrino masses.— With more than twenty
years of measurements using natural and anthropogenic neutrino sources, the
parameters that dictate neutrino flavor transition have now been measured to
the few-percent level Esteban  _et al._ (2020). Despite these improved
measurements, we still do not know the mechanism responsible for neutrino
masses. Models that aim to explain neutrino masses can be broadly organized
into scenarios where neutrinos are Majorana particles and where they are
predominantly Dirac fermions. Much attention has been placed on the former
scenario, where the Weinberg operator describes neutrino masses at low-energy
scales. This operator can be UV completed to high-energy scales by introducing
additional heavy neutrino states in what is known as the see-saw mechanism,
where the smallness of neutrino masses is explained by the smallness of the
Dirac-like mass term compared to the larger Majorana-like term associated with
these heavy neutrinos. A prediction of this scenario is that neutrino-less
double beta decay should be observed, pending accidental cancellations of
neutrino Majorana phases. This has led to a vibrant experimental program
aiming to observe this process.

The other possibility is that neutrinos are Dirac-like in nature. In this
case, new, right-handed neutrinos are added to the Standard Model particle
content. These can yield neutrino masses similarly to the case of charge
lepton through $y\bar{L}\tilde{H}N_{R}$, where $H$ is the Higgs double, $y$
the Yukawa couplings, and $N_{R}$ the new, right-handed neutrino field. In
this case, to achieve the right scale for the neutrino masses, the Yukawa
couplings are distinctly small compared to those associated to other fermions.
The lack of an explanation for the smallness of the Yukawa in this scenario
and the lack of experimental signatures to promptly confirm this have
generally made this scenario less appealing. However, recent advancements in
quantum gravity Ooguri and Vafa (2017); Gonzalo  _et al._ (2022), within the
Swampland program, point to the fact that neutrinos should be Dirac-like in
nature Vafa (2024). This coupled to the recent discovery of high-energy
astrophysical neutrino sources, which, as we will discuss, provides new
avenues to discover Dirac-like neutrinos, makes revisiting this scenario
timely.

If the masses of neutrinos are predominantly due to a Dirac-like mechanism, as
suggested by recent work Ooguri and Vafa (2017); Gonzalo  _et al._ (2022), or
by plain similarity to how the other fermions acquire masses in the Standard
Model, then, in the context of quantum gravity, we expect that neutrinos are
Quasi-Dirac particles Valle and Singer (1983). This is because the value of
the right-handed neutrino mass term is proportional to the amount of lepton
number violation, which is expected to be broken at the Planck scale, as no
global symmetries are expected to be preserved by quantum gravity. In the
scenario of a small Majorana mass term compared to the Dirac mass term, one
produces ultra-small mass splitting between the left- and right-handed
neutrinos. As we will discuss below, this can produce the disappearance of
neutrinos with oscillation frequencies that scale like $L/E$ on galactic
Crocker  _et al._ (2002) or extragalactic scales Keranen  _et al._ (2003);
Beacom  _et al._ (2004); Esmaili (2010); Esmaili and Farzan (2012); Shoemaker
and Murase (2016); Carloni  _et al._ (2024). Finally, even when we ignore the
motivation of quantum gravity and pose that neutrinos are Dirac-like
particles, studying extremely long baseline oscillations is of fundamental
importance. This is because, in the Dirac-like scenario, the right-handed
neutrino mass term ($\frac{1}{2}m_{R}\bar{N}_{R}^{c}N_{R}$) presents a
fundamental, unconstrained parameter of the new Standard Model. Determining if
this parameter is non-zero but small would have profound implications in
fundamental physics as it proves new, ultra-small energy scales.

As proposed in Ref. Carloni  _et al._ (2024), one can use the observation of
multiple high-energy neutrino sources to search for the disappearance of
neutrinos in the Dirac-like scenario. This technique has the advantage over
prior proposals, see, e.g., Refs. Beacom  _et al._ (2004); Esmaili (2010);
Esmaili and Farzan (2012); Shoemaker and Murase (2016), in that it is within
experimental capabilities and mitigates the astrophysical source modeling
uncertainties by correlating neutrino observations from different sources at
the same $L/E$. The oscillation probability in this scenario is given by

$P_{\alpha\beta}=\frac{1}{2}\sum_{j=1}^{3}\left|U_{\beta
j}\right|^{2}\left|U_{\alpha j}\right|^{2}\left[1+\cos\left(\frac{\delta
m_{j}^{2}L_{\text{eff }}}{2E_{\nu}}\right)\right],$ (10)

where $L_{\text{eff }}$ is the effective distance to the source after
correcting for cosmic expansion, and $U$ is the mixing matrix measured in
terrestrial experiments. The disappearance is expected to be the same strength
for all flavors in the minimal model scenario. This has critical
phenomenological implications since this implies that the effect should be
present in tracks, produced predominantly by muon-neutrinos, and cascades,
produced by all flavors.

Figure 8: Neutrino oscillations at cosmic scales and the sensitivity to
extremely small energy differences. Left: Artistic rendition of ultra-long
baseline neutrino oscillations from astrophysical sources. Right: Expect
sensitivity of IceCube-Gen2 to quasi-Dirac neutrinos. Figures reproduced from
Ref. Carloni  _et al._ (2024).

Given the current experimental capabilities, this implies that
extraterrestrial sources will be restricted to searching for distortions in
the muon spectra energy distribution since we do not currently expect to
establish high-significance correlations between cascade and point-like
neutrino sources. The signature of this scenario is thus the disappearance of
muon neutrinos at sources that share the common value of $L/E$, see Fig. 8
(left). Figure 8 (right) shows the sensitivity that is expected from the
combination of multiple extraterrestrial neutrino sources as a function of the
ultra-small mass-square difference, $\delta m^{2}$ for IceCube-Gen2. As can be
noticed, the sensitivity can reach discovery-level significance due to the
combination of multiple sources that probe the same values of $L/E$ even when
the astrophysical fluxes are marginalized over all multiple shapes of the
neutrino spectra, see the dashed line in the figure. However, understanding
the neutrino fluxes of these sources would yield significant improvement in
the sensitivity. For example, if the fluxes were to be modeled by an unbroken
power-law in energy, the sensitivity would scale to match the shaded region
demarcated by the solid line. Thus, the change in significance between the
dashed and solid lines in this figure provides a proxy for the impact of
extraterrestrial astrophysical source modeling in this scenario. Additionally,
as noted in Ref. Crocker  _et al._ (2002), high-energy neutrinos produced in
the galaxy are also sensitive to mass-squared differences of the order of
$10^{-14}{\rm eV^{2}}$, which offers a complementary source to look for this
effect.

Probing the neutrino lifetime and the unitarity of the neutrino mixing
matrix.— Other properties of the neutrino can be studied by measuring high-
energy astrophysical neutrinos. These are the lifetime of the neutrino and the
number of neutrino species. The extremely long baselines that astrophysical
neutrinos travel made them especially sensitive to the neutrino lifetime.
Given the unknowns in the order of neutrino mass states, i.e., our lack of
understanding of which of the neutrinos is less massive, we can be in two
scenarios. In one scenario, the neutrino mass state with the most electron-
neutrino content is the lightest; this is known as the normal ordering, and in
the other, the neutrino with the least electron fraction is the lightest,
known as the abnormal or inverted ordering. The neutrino ordering problem is
expected to be resolved over the next years as new data is gathered from
terrestrial neutrino oscillation experiments. In particular, neutrino
telescopes are expected to be important in establishing neutrino ordering
Argüelles  _et al._ (2023b) by performing precise measurements of the
oscillation parameters using large data sets.

The Standard Model expectation is that all known neutrinos are stable over
cosmological distances Hosotani (1981); Pal and Wolfenstein (1982); Nieves
(1983); however, new physics scenarios Bahcall  _et al._ (1972); Chikashige
_et al._ (1980) can significantly reduce the heavier neutrino lifetime,
allowing them to decay into their lighter partners. This directly affects the
ratio of neutrino flavors on Earth Bustamante  _et al._ (2017); Song  _et al._
(2021); Abdullahi and Denton (2020); Liu  _et al._ (2023). The neutrino
ordering above leads to two extreme scenarios, where either the neutrino with
the most or least electron content remains at Earth. These two scenarios lead
to dramatically distinct fractions of electron neutrinos at Earth; in one
case, one expects $\sim 0.7\%$ of the neutrinos to be electron-flavored, while
in the other scenario, only $\sim 0.05\%$ are electron-flavored Bustamante
_et al._ (2017). Current observations by IceCube Aartsen  _et al._ (2015c);
Abbasi  _et al._ (2022b) already disfavor the large-electron fraction scenario
at the $2\sigma$ level, placing constraints on the lifetime of the neutrino
that is significantly stronger than Earth-based experiments under the
assumption of normal neutrino ordering, which is currently preferred by
neutrino oscillation measurements Esteban  _et al._ (2020). Thus, further
measurements of the fraction of electron neutrinos at Earth in the
astrophysical beam and their energy dependence Liu  _et al._ (2023) will help
to further constraint scenarios that reduce the neutrino lifetime. Finally,
the number of neutrino states can also affect the expected distribution of
astrophysical neutrino flavors at Earth Brdar  _et al._ (2017); Argüelles  _et
al._ (2020a). Currently, terrestrial neutrino oscillation experiments
constrain the unitarity of the neutrino mixing matrix to only $20\%$ at the
$3\sigma$ level Parke and Ross-Lonergan (2016); Ellis  _et al._ (2020),
leaving space for additional heavier neutrino states to exist. The existence
of additional neutrino states has been suggested by anomalies in accelerator
Athanassopoulos  _et al._ (1996); Aguilar-Arevalo  _et al._ (2013),
radioactive source Abdurashitov  _et al._ (1999); Hampel  _et al._ (1998);
Barinov  _et al._ (2022), and reactor neutrino experiments Serebrov  _et al._
(2022), though these have not been confirmed in other neutrino experiments
Argüelles  _et al._ (2022); Adamson  _et al._ (2019) with similar reach.
Beyond the experimental motivation, the search for additional neutrino states
is of significant interest in fundamental physics as it is predicted in
scenarios that aim to resolve the hierarchy problem, e.g., the dark dimension
solution Montero  _et al._ (2023). The current sensitivity of the
astrophysical neutrino flavor ratio is insufficient to shed light on the
existence of new neutrino states Argüelles  _et al._ (2020a); Song  _et al._
(2021), but future measurements could enable the indirect detection of these
additional neutrinos.

✒The observation of astrophysical neutrinos from galactic and extragalactic
sources can uncover the nature of neutrino masses. By observing the
transformation of neutrinos into new, invisible neutrino states, they can
establish that neutrinos are Dirac-like particles, which would have profound
implications in particle physics. Their detailed study can yield new insight
into the stability of neutrinos and additional neutrino states.

###  II.7 What fundamental and particle physics can be done with super high-
energy neutrino beams?

Two important features of high-energy astrophysical neutrinos make them unique
probes of new physics Argüelles  _et al._ (2020b): the extremely long lengths
traversed from neutrino emission to detection and their high energy.

Figure 9: Quantum gravity effects on the flavor triangle and constraints from
IceCube. Left: Trajectories in the astrophysical neutrino flavor triangle for
different dimension six, flavor operators. Right: Constraints on dimension six
operators that parameterize the interaction of neutrinos with a Lorentz-
violating field. Figures reproduced from Ref. Abbasi  _et al._ (2022e).

The extremely long distance from production to detection makes high-energy
astrophysical neutrinos one of the longest naturally occurring
“interferometers” Aartsen  _et al._ (2018c) available to search for new
phenomena. This can be exploited by studying the relative ratio of
astrophysical neutrino flavors Learned and Pakvasa (1995); Argüelles  _et al._
(2015a); Bustamante  _et al._ (2015). The power of the astrophysical neutrino
flavor composition as an observable comes from two distinct angles. On the one
side, it is an observable that is well-predicted within the Standard Model
with massive neutrinos and is robust under various production mechanisms, thus
unambiguously observing new physics when deviations are observed Song  _et
al._ (2021). On the other side, the long lever arm from production to
detection serves as an extremely long lever arm interferometer allowing for
the observation of extremely small effects Argüelles  _et al._ (2015a).
Namely, as neutrinos travel from their sources to us they can coherently
interact with the medium they traverse, leaving an imprint on the observed
flavor ratio at Earth. For example, in some theories of quantum gravity,
Lorentz symmetry is spontaneously broken at high scales leaving a remnant
Lorentz-violating field throughout space. Neutrinos can interact with this
field modifying their flavor composition, see Fig. 9 (left). The strength and
type of this hypothetical interaction are unknown, but it is usually described
by a theory known as the Standard Model extension, which includes effective
Lorentz-violating terms Colladay and Kostelecky (1998). Within this framework,
the interactions of neutrinos with this field are expected to be suppressed by
powers of the Planck scale. Currently, high-energy astrophysical neutrinos
provide the best way to search for these minute interactions, which accumulate
as the neutrinos travel from their source to us. This yields constraints on
the coupling strengths of these new, space-time forces that are well beyond
the Planck scale Abbasi  _et al._ (2022e), see Fig. 9, right. Though, for most
of the parameters, they are dependent on the flavor structure of the
interaction and the flavor composition at the source. Other effects that can
be probed by studying astrophysical neutrino flavor are coherent interactions
between neutrinos and dark matter de Salas  _et al._ (2016); Capozzi  _et al._
(2018); Farzan and Palomares-Ruiz (2019) and extremely long-range forces
Bustamante and Agarwalla (2019); see Argüelles  _et al._ (2024) for a recent
recast of these constraints in various scenarios. Additionally, the study of
neutrino flavor can provide us information about the dense environments in
which neutrinos are produced Dev  _et al._ (2023) and information on new,
secret neutrino-nucleon interactions Gonzalez-Garcia  _et al._ (2016).

The high-energies and extremely large detectors required to measure high-
energy astrophysical neutrinos comprise a second opportunity for discovery.
These large detectors measure a large fraction of high-energy astrophysical
neutrinos, which can achieve statistics on the order of hundreds of thousand
Abbasi  _et al._ (2024a, b). These high-energy atmospheric neutrinos have been
shown to be one of the most sensitive probes of light sterile neutrinos Abbasi
_et al._ (2024a, b), Lorentz symmetry breaking Aartsen  _et al._ (2018d),
decoherence and fundamental tests of quantum mechanics Coloma  _et al._
(2018); Stuttard and Jensen (2020); Jones and Seidel (2024); Abbasi  _et al._
(2023e), and non-standard neutrino-nucleon interactions Salvado  _et al._
(2017); Abbasi  _et al._ (2022f). Additionally, neutrino interactions at
energies above an EeV probe increasingly inelastic regimes where the proton
structure function has yet to be studied. These high-energy neutrinos probe
regions within the proton where the number of partons is increasingly large,
and color-shadowing is expected Block and Halzen (2011), yet directly
unobserved in collider experiments to date. The so-called darkening of the
proton at high energies is expected to reduce the neutrino-nucleon interaction
cross-section Argüelles  _et al._ (2015b). The deeply inelastic component of
the neutrino-nucleon cross-section can be measured by studying the
transparency of Earth to neutrinos Aartsen  _et al._ (2017f); Bustamante and
Connolly (2019); Abbasi  _et al._ (2020), while the mostly elastic component
can produce new morphological features Garcia Soto  _et al._ (2023). Finally,
new particles can be discovered at these high energies by their impact in the
neutrino cross section Alvarez-Muniz  _et al._ (2002); Dey  _et al._ (2018);
Babu  _et al._ (2020).

✒The study of the relative flavor of neutrinos at Earth allows us to measure
the smallest interactions, having sensitivity to Planck-scale physics.
Potentially enabling the observation of Planck-scale physics for the first
time. Additionally, the measurement of Earth’s transparency to high-energy
neutrinos through various layers of the Earth will provide insights into
uncharted depths of the proton, potentially allowing us to observe gluon
shadowing.

##  III Enabling technologies

The fundamental challenge of neutrino astronomy is the enormous number of
background particles, the neutrinos and muons created in the Earth’s
atmosphere, that the neutrino telescopes encounter. The overburden of water or
ice above the detector is usually of order $\sim$\mathrm{km}$$. Thus,
atmospheric muons penetrate through to the detector to produce many orders of
magnitude more events as compared to neutrinos. Atmospheric neutrinos, while
lower in rate compared to muons, are background events that are larger in rate
than astrophysical neutrinos, and in almost all cases indistinguishable from
them at an event-by-event level.

To combat the disproportionate background rate, many statistical techniques
are deployed. They are usually in the form of data filtering, which aim to cut
out background events while retaining as many signal events as possible. While
every event observed in a detector usually corresponds to a single particle
detection, noise and multiple particles in the detector at the same time can
make event classification challenging. Furthermore, classifying events as
”signal” or ”background” is a statistical process. It is usually not possible
to definitively distinguish each event as one or the other so only
probabilistic statements can be made based on the event’s characteristics.
This can be as simple as using the particle’s estimated energy as a
characterstic to cut on, as it accounts for the fact that atmospheric
components have a softer spectrum, or filtering for earth-penetrating events
to reduce muon rates. More sophisticated techniques, such as veto-based event
selections, which aim to keep only events with neutrino interaction vertices
contained within the detector and targeting unique interactions or flavors,
such as showers, identifiable tau events, or Glashow events, as discussed in
Section II.1 are also used. Generally, a combination of many techniques leads
to a final analysis-ready event sample.

In every case, though, the final event samples, while higher in signal-to-
noise ratio, become statistically limiting in astrophysical neutrinos. Either
they are still background dominated or become an extremely reduced event
samples with a handful of events. Thus, the main key to unlocking more results
in neutrino astronomy in the coming decades is statistical power. More
astrophysical neutrinos are obtained by collecting more data, and more data
are collected faster with more detectors around the globe. This means more
deployed PMTs in water and ice. Thus, the metric of success, to first order,
for the next generation of detectors is more instrumented volume around the
world.

Beyond this crude metric, optimization of new neutrino telescopes that are
coming online and their complementarities to each other and existing
telescopes become important. While the original neutrino telescopes imagined
decades ago aimed for one globally optimized design, in the last decade, with
multiple discoveries emerging, it has become clear that different detector
configurations are becoming important in targeting different fluxes of
astrophysical neutrinos. We have entered the era of divergent detector needs.
This is to be celebrated as a sign of a maturing field.

###  III.1 Astrophysical Neutrino Fluxes

Figure 10: Different detector technologies and their dominant energy region.
The colored lines in this figure show the different neutrino components of
interest as a function of energy, where the ranges should be taken as order of
magnitude estimations. The leading technologies for high-energy astrophysical
neutrino detection are illustrated: water-Chrenkov, ice-Cherenkov, Earth-
skimming, and radio. As discussed in this Perspective, The former three
detection methods are synergic as they provide complementary information on
the same galactic and extragalactic neutrino sources. On the other hand, radio
is expected to reach out towards new, unexplored energy domains.

In the TeV to EeV range, the neutrino fluxes can be described by four
principal components, as shown in Fig. 10. Here, we reduce the discussion to
describing each component as described in Eq. 2, a single power-law flux
spectral index $\gamma_{\rm astro}$ to focus on broader observational needs.
It is clear from recent observations that the diffuse fluxes and the sources
that possibly contribute to the fluxes could have more complicated energy
spectra.

Starting from the lowest of this energy range, the atmospheric neutrino flux
dominates with a level that is many orders larger than any astrophysical
fluxes. This is the background neutrinos to any astrophysical observations and
have the softest spectrum at a spectral index of $\sim 3.7$.

The next observable component in energy is the diffuse Galactic flux. As
described in II.2, it is possible that within a narrow energy range, this flux
dominates in the Galactic Plane region of the sky. While this spectral index
is expected to be harder at $\sim 2.7$, the discrimination of this flux
against the atmospheric background using energy measurements of events will
not be so effective since the fluxes have the closest spectral indices. The
crucial observational metric for targeting Galactic neutrinos is thus angular
resolution. Localizing the diffuse plane or Galactic point sources with good
angular resolution allows discrimination against a directionally uniform
background, where energy has limited discrimination power.

Neutrinos of extragalactic origin are expected to have spectral indices of
$\sim 2$. The flux is now much harder compared to the atmospheric background,
so angular resolution requirements can be loosened by relying more on the
observed energy of the events. The distribution of energies of the signal
events is different enough to the background in identifying sources.

Finally, at the highest energies or extremely high energy (EHE) region,
cosmogenic neutrinos, also known as GZK neutrinos, are expected to dominate.
Because this flux is at the tail end of steeply falling fluxes in power law,
cosmogenic neutrinos are exceedingly rare.

###  III.2 Ice and water optical neutrino detectors

An optimized neutrino telescope to the three fluxes described above will
naturally be three different detectors. In any steeply falling power-law flux,
the higher the energy one targets, the lower the expected number of neutrinos.
Thus the size of the detector will necessarily get larger for higher energy
fluxes. For the GZK flux, this necessitates such a large volume of detector
that optical signals become challenging to instrument. A neutrino telescope
must have sensors at a smaller spacing than the attenuation length of the
signal for requiring coincidence in multiple sensors. Therefore, signals that
travel further without attenuating, such as radio pulses, allow a larger
detector volume to be instrumented by using the same number of sensors but
spaced further apart. Many future radio-based neutrino telescopes are planned,
but this section will focus on optical-based detectors in keeping with the
motivations in II.

Neutrino telescopes with optical sensors collected Cherenkov photons from
charged particles that resulted from neutrino interactions. The optical
properties of the detector media therefore naturally informs the optimization
of its detector. Water generally has a shorter attenuation length to optical
and UV light, but a longer scattering length. Ice generally has the opposite.
Figure 11 compares a high-energy muon traversing the entire detector length
for detectors using ice and water as media. The Cherenkov photons are shown as
lines coming out of the muon track. Color denotes the time difference. The
photons in ice can be seen covering a larger volume around the track, owing to
the longer absorption length. However, the photons do not travel as straight
as those in water because of the short scattering length.

Figure 11: Difference between light emission in water and ice. A muon-
neutrino-induced muon traversing an ice (above) and water (below) detector.
Lines emitted from the muon track show the path of Cherenkov photons emitted
from the muon. Figure courtesy of C. Kopper (FAU Erlangen-Nürnberg, ECAP).

The non-direct path of photons in ice creates the largest systematic effect in
the reconstruction of the muon track, and thus the direction of the neutrino
that created the muon. Water, with all else held equal, is a superior media
for directional reconstruction of neutrinos in the sky.

Figure 12: Instantaneous regions of highest detection efficiency for various
existing and proposed water and ice-Cherenkov neutrino observatories. The
color regions show the largest source discovery potential when assuming an
unbroken $E^{-2}$ energy spectra. The edges of the bands are defined by the
discovery potential dropping by a factor of two with respect to its maximum
value. This is an instantaneous snapshot, and the bands move as the Earth
rotates. Figure courtesy of L. Schumacher (FAU Erlangen-Nürnberg, ECAP).

However, the length photons travel in water is a disadvantage, especially when
the event is not a high-energy muon track traversing the entire detector. When
the effective distance the photon traverses from the charge particle is
limited, the sensors must be placed closer in order to obtain coincidence
detection of many sensors. This means that for the same number of sensors, if
the same coincidence-level is required, the water detector must be made
smaller with shorter sensor distances.

This naturally points to ice-based detectors as better suited for higher
energy fluxes, such as extragalactic fluxes. The larger spacing of sensors
allows a larger instrumented volume which is more suitable for detecting lower
fluxes of neutrinos. The less-optimized directional resolution of the
neutrinos is better tolerated as the extragalactic flux is much harder than
background, as previously described. Conversely, the water-based detectors are
better suited for softer fluxes, such as Galactic neutrinos and extragalactic
sources with softer emission. By leveraging the superior directional pointing,
discriminating from the soft background becomes possible, and higher fluxes at
lower energies compensate for the relatively smaller instrumented volume,
again, as described previously.

###  III.3 Complimentarity in the Global Landscape

The need for differently optimized telescopes to target different
astrophysical neutrino fluxes is not surprising. Much like how electromagnetic
astronomy developed different telescopes targeting different wavelengths and
has matured into multi-wavelength astronomy, the field of neutrino astronomy
is maturing rapidly. Differently optimized detectors operating simultaneously
is the second key to a continuing boom in neutrino astronomy in the coming
decades, second only to the first metric of globally instrumented volume as
discussed earlier.

One can argue then that the third key in global optimization is the locations
of neutrino telescopes. Multiple telescopes operating at different locations
in the world, covering different areas of the sky at any given time, ready for
real-time multimessenger astronomy, is not a new concept in astronomy. This is
indeed also the case for neutrino astronomy, as shown in Fig. 12. The
optimized regions of the sky for telescopes in the Mediterranean, Pacific
Ocean, and at the South Pole show the complementary in instantaneous coverage
that together spans the entire sky.

A final optimization in the neutrino telescope ecosystem is the relative
signal-to-background ratio. Water and ice Cherenkov neutrino telescopes can
only differentiate between atmospheric and astrophysical neutrinos for very
specific events. For example, most of the muon neutrinos observed in these
experiments cannot be claimed to be of astrophysical origin since many of them
are produced in Earth’s atmosphere. This is not the case for tau neutrinos,
where their observation implies that they have a high probability of being
astrophysical in nature Soto  _et al._ (2022). Thus, the dominant sample of
neutrinos detected in these experiments has low astrophysical neutrino purity.
On the other hand, Earth-skimming tau-neutrino detectors have a high
astrophysical neutrino purity, though they suffer from high-energy thresholds
and, thus, limit sample sizes. Currently Earth-skimming experiments, such as
TAMBO or TRINITY, are been developed as individual neutrino telescopes.
However, the vision of the authors, is to think neutrino telescope development
within a network of telescopes, rather than in isolation. Thus, we envision
arrays of Earth-skimming neutrino telescopes, whose energy threshold can match
the energy range of current and future water/ice Cherenkov neutrino
telescopes. These will provide a high-purity astrophysical sample that can be
instrumental in finding neutrino sources.

If the last two decades of neutrino astronomy can be characterized as the race
for becoming “the” globally optimized telescope, then the key to continued
success in the next two decades are multiple complementary neutrino
telescopes, each targeting different neutrino fluxes and flavors, using
different media, in different locations around the world, all summing up to a
substantial increased instrumented volume globally, operating simultaneously
and cross-checking neutrino signals from the sky. Neutrino telescopes are
expensive. Neutrino astronomy deserves to be a strong partner in multi-
messenger astronomy, as discussed in the science cases presented above. One or
two neutrino telescopes alone cannot accomplish this. In contrast to the
competition of the previous decades, specialization, cooperation, and
complimentary of many telescopes are needed for a truly multi-messenger era.

###  III.4 Additional Supporting Technologies

The experiments discussed above, which are currently either being deployed,
constructed, or in design stages, will operate in an era where machine
learning and artificial intelligence will have more than a decade of well-
established techniques. Already in the last three years, we have significant
impact on the scientific performance of neutrino telescopes such as IceCube
Abbasi  _et al._ (2021b), Baikal-GVD Kharuk  _et al._ (2023), and KM3NeT Reck
_et al._ (2021), due to the use of artificial intelligence. For example, the
improvement in cascade reconstruction and selection efficiency by means of
convolutional neural networks transformed a statistical hint into a firm
observation of the galactic plane. These initial approaches were promptly
superseded by approaches that allow for general detector geometries Abbasi
_et al._ (2022g), improve the execution speed Yu  _et al._ (2023), or operate
on power-constraint environments Jin  _et al._ (2023). A recent Kaggle
challenge Eller (2023) on IceCube simulation brought our community’s problems
to the machine-learning ecosystem, leading to improved event reconstructions.
The advancement of these methods has also led to the synergistic development
of open-source simulation tools Lazar  _et al._ (2023) and common data formats
among experiments. All of these improvements and community-building activities
will have a significant impact in the development of next-generation neutrino
telescope simulation and reconstruction. We expect that the speed of
development will grow very rapidly. The steady growth in the capacity of
commercially available quantum computers heralds a new era of enhanced
simulations and event reconstructions. Demonstrated recently Lazar  _et al._
(2024), even today’s quantum resources are capable of facilitating the study
of neutrino events.

##  IV Conclusion and parting words

Neutrino astronomy needs more signal-above-background and more astrophysical
sources. A “neutrino sources catalog” is desperately needed in the near future
to make the transformational discoveries that we believe are possible within
the next decade. The potential discoveries will provide insight into the
Universe’s more extreme environments and also promise discoveries that can
significantly impact neutrino physics and, more broadly, particle physics.
This requires differently optimized telescopes, in different parts of the
world, using different approaches, making simultaneous observations of
sources, combining data, and making discoveries to push forward multi-
messenger astronomy and particle physics through astronomical neutrinos.
Currently, the neutrino telescope collaborations operate independently with
limited crosstalk. It does not make sense to reinvent techniques, tools, and
observational strategies. The authors strongly believe that a fundamental
partnership of many neutrino telescope collaborations, beyond what is imagined
within the current efforts, is the path to a thriving field in the next
decade.

###### Acknowledgements.

We thank Jean de Merit and Julia Book Motzkin for carefully reading the
manuscript. We also thank Claudio Kopper and Lisa Schumacher for their help
with figures eleven and twelve. Finally, we thank Matheus Hostert, Kiara
Carloni, and Pavel Zhelnin for their useful feedback on earlier version of
this manuscript. CAA are supported by the Faculty of Arts and Sciences of
Harvard University, the National Science Foundation, the Research Corporation
for Science Advancement, and the David & Lucile Packard Foundation. The
research of FH is supported in part by the U.S. National Science Foundation
under grants PHY-2209445 and OPP-2042807. NK is supported by the U.S. National
Science Foundation under grants PHY-1847827 and PHY-2209445.

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