# High-energy neutrino transients and the future of multi-messenger astronomy

Claire Guépin  Joint Space-Science Institute, University of Maryland, College
Park, MD 20742, USA  Kumiko Kotera  Sorbonne Université et CNRS, UMR 7095,
Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France  Vrije
Universiteit Brussel, Physics Department, Pleinlaan 2, 1050 Brussels, Belgium
Foteini Oikonomou  Institutt for fysikk, NTNU, Trondheim, Norway  e-mails:
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

The recent discovery of high-energy astrophysical neutrinos and first hints of
coincident electromagnetic and neutrino emission herald the beginning of the
era of multi-messenger astronomy. Due to their high power, transient sources
are expected to supply a significant fraction of the observed energetic
astroparticles, through enhanced particle acceleration and interactions. Here,
we review theoretical expectations of neutrino emission from transient
astrophysical sources and the current and upcoming experimental landscape,
highlighting the most promising channels for discovery and specifying their
detectability.

##  1 Introduction

Transient emissions are short (up to months), violent, and irregular
emissions, that could be isolated events or appear as a sudden activity
increase of an existing source. Many new classes of luminous transients have
been discovered recently, thanks to improved instrumental sensitivity, time
resolution, and fast follow-ups across the full electromagnetic spectrum. Many
more discoveries are expected with the launch of wide field instruments,
multi-instrument platforms and multi-messenger (MM) networks. In 2017, a MM
window opened on the high-energy (HE) transient sky, with the detection of
gravitational waves from the merger of two neutron stars (NS), GW170817,
jointly with electromagnetic counterparts[1]. HE ($\gtrsim 10^{15}\,$eV) and
ultra-high energy (UHE, $\gtrsim 10^{17}\,$eV) neutrino astronomy should be
the next window to open, likely with the MM observation of a flaring neutrino
transient source.

Because they can inject their huge amount of energy over short timescales,
powerful transients are the most promising sources capable of supplying enough
energy and flux to astroparticles at the observed level. The increase in
luminosity can be related to enhanced cosmic-ray acceleration, with subsequent
particle interactions and production of secondary emissions, such as HE and
UHE neutrinos and gamma-rays. Moreover, anisotropy, source-density, energetics
and magnetic-structure arguments strongly challenge steady-source scenarios
for UHE cosmic rays with light composition[2, 3, 4, 5, 6]. By observing the
transient sky at the highest energies, we thus naturally tackle the long-
standing enigma of the origin of the highest energy astroparticles.

HE and UHE neutrinos are expected to play a major role in precision time-
domain astronomy, as undeflected signatures of hadronic interactions. Their
deeper cosmological horizon compared to cosmic rays and gamma rays implies
that they can be observed from sources located at cosmological distances,
possibly in coincidence with gravitational waves. Neutrinos, like secondary
photons, can also exhibit time-variability signatures, which can be combined
with other wavelengths to probe the structure and evolution of the source and
its environment.

From an experimental point of view, the detection of a transient HE or UHE
neutrino event is favored, as time-dependent neutrino searches tend to reduce
the background (e.g., due to atmospheric neutrinos and muons in IceCube or
ANTARES[7, 8]). Real-time analysis and MM follow-up of alerts can also
drastically increase the statistical significance of associations. The
detection of several neutrinos from a single source (“neutrino point sources”)
is the ultimate goal of HE neutrino astronomy. What constitutes a detected
neutrino point source varies from detector to detector and depends on the
neutrino background at the energy and arrival direction of each individual
event. In general, an accumulation statistically inconsistent with an
accumulation of atmospheric or astrophysical neutrinos by chance is needed in
order to assertain the detection of a true astrophysical point source. From an
astrophysical perspective, the detection of neutrino point sources (or small
scale clustering referred to as “multiplets”) depends upon the overall number
density of sources[9]. At UHE, currently known powerful steady sources are too
rare to enable the detection of multiplets, whereas transient sources could
lead to a burst of neutrinos[6]. A guaranteed background for astrophysical
neutrino searches at UHE is the flux of neutrinos produced in the interactions
of ultra-high energy cosmic rays (UHECRs) [10], often referred to as
“cosmogenic” neutrinos. These two distinct diffuse astrophysical neutrino
populations (cosmogenic versus astrophysical neutrinos produced in source)
will be difficult to distinguish without exceptional statistics but will, once
discovered, give complementary information about the sources of UHECRs. Point
sources of UHE neutrinos, would reveal in-source neutrino production, as the
deflections and time-delays suffered by UHECRs make the detection of point
sources of cosmogenic neutrinos unlikely.

IceCube has been accumulating diffuse HE neutrino data since 2008[11, 12] and
has been sending and receiving alerts via large-scale networks [13]. These
searches have led to the detection of a neutrino of energy $\sim 0.1-1\,$PeV,
IceCube-170922A, in association with a flaring blazar, TXS 0506+056, observed
in multiple wavelengths, including in X-rays and gamma-rays[14]. The
theoretical and experimental interpretations of this association are still
under debate, and await confirmation with further observations. Several other
possible coincident detections have been discussed[15, 16, 17].

Theoretical models of time-variable neutrino emission from luminous transient
sources are being developed. The models are based on analytical and numerical
approaches, with various levels of complexity in modeling the parent cosmic-
ray acceleration and escape/interaction regions in and surrounding the
sources[18]. Thanks to theoretical and experimental progress, we are starting
to place strong constraints on the structure and energetics of powerful
sources that are not detected in HE neutrinos.

Many neutrino observatories from HE to UHE are in construction or planned,
with increased sensitivity, optimized fields of view, and for some of them,
excellent angular resolution. The diverse envisioned designs should help
tackle different aspects of the challenging detection of neutrino transients.
One of the goals of this review is to summarize the theoretical ingredients in
the numerous sources models as well as the characteristics of current and
future instruments, and to connect both ends to assess MM detection
performances. This could help refine models, optimize instrumental designs and
call for synergies between projects.

Figure 1: Maximum neutrino energy [19] (in eV) that could be produced by
various categories of transient sources, with variability timescale $t_{\rm
var}$ and bolometric luminosity $L_{\rm bol}$. We represent non-relativistic
sources with outflow Lorentz factor $\Gamma=1$ (top) and relativistic sources
with $\Gamma=10$ (bottom). Neutrinos directly produced through pion (muon)
decay are shown with dashed (solid) lines. Overlaid are the properties of
different categories of transient sources (colored regions).

##  2 Estimating neutrino fluxes from transient sources: methodologies

HE neutrinos are produced through the interaction of accelerated cosmic rays
with photon or baryon backgrounds. Various interaction channels are involved,
such as the production of charged pions, charged kaons or charm hadrons and
their subsequent decay (for instance $\pi^{+}\rightarrow\mu^{+}+\nu_{\mu}$ and
$\mu^{+}\rightarrow e^{+}+\bar{\nu}_{\mu}+\nu_{e}$), or nuclear decays. In the
following sections, we discuss how regions involved in HE neutrino production
are modeled (section 2.1), and how the interplay of acceleration and
interaction timescales (section 2.2) allows us to estimate neutrino fluxes
from transient sources from phenomenological (section 2.3) and numerical
(section 2.4) points of view.

###  2.1 Modeling cosmic-ray acceleration and interaction regions

In the case of transient sources, interactions leading to the production of
transient HE neutrino signals involve backgrounds located inside the sources
or in their vicinity. Therefore, most transient neutrino signatures are
governed by the interplay between typical timescales that characterize the
acceleration, interaction and escape of cosmic rays in these regions.
Transient source models usually involve one or more zones inside the source,
where different processes can take place. In one zone models, particles are
accelerated, propagate and interact in a region that produces all observed
emission. When this type of description is inadequate, for instance when one
zone models fail at explaining multi-wavelength or MM data[20], two zone
models can be adopted. For instance, acceleration can be treated prior to
interactions (first zone) and accelerated hadrons and leptons can be injected
in the interaction region (second zone) where they only propagate and
interact. Another example is the use of an external radiation background as a
target for interactions. The use of two-zone models should be well motivated
by a sufficient amount of available multi-wavelength or MM data, due to the
caveat that considering two or more zones allows for additional degrees of
freedom.

###  2.2 Typical timescales involved in transient HE neutrino production

Acceleration and interactions of cosmic rays operate at microscopic scales
that are not accessible to macroscopic source models. The modeling of the
typical timescales characterizing these processes allows to evaluate how they
compete with each other and thus estimate key quantities such as the maximum
energy and flux of neutrinos. These timescales are usually calculated in the
comoving frame of the acceleration or interaction region. For various
categories of transient sources, the dominant processes are cosmic-ray
acceleration, synchrotron and adiabatic losses, and photopion production.
Other processes can thus often be neglected at first order. In the following,
quantities in the comoving frame are denoted by primed quantities. Other
quantities are in the observer frame.

A precise description of acceleration processes, such as shock acceleration
[21] or magnetic reconnection [22] for instance, requires the modeling of the
astrophysical plasma and the complex interplay between the charged particles
and the electromagnetic fields, at scales of the order of the plasma skin
depth. Detailed plasma simulations [23] and theoretical estimates [24] can be
used to derive estimates of the acceleration timescale $t_{\rm acc}$ and the
spectrum of accelerated particles, often modeled by a power-law with maximum
energy $E_{\rm max}$ and spectral index $\alpha$. Various acceleration
processes involve the scattering of charged particles on magnetic
inhomogeneities, thus the acceleration timescale can be related to the
particle Larmor time $t^{\prime}_{\rm L}=E^{\prime}/(cZeB^{\prime})$

$t^{\prime}_{\rm acc}=\eta_{\rm acc}^{-1}\,E^{\prime}(cZeB^{\prime})^{-1}\,,$
(1)

where $E^{\prime}$ and $Ze$ are the energy and charge of the particle, and
$B^{\prime}$ the mean magnetic field. In most cases $\eta_{\rm acc}^{-1}\gg 1$
[25] and $\eta_{\rm acc}^{-1}\sim 1$ could be achieved for a maximally
efficient energy dissipation mechanism.

The particles are typically confined in the transient source during a
dynamical timescale $t_{\rm dyn}$, which characterizes the evolution of the
radiation region. This is a central quantity in the modeling of flaring
transients and can be related to the observed variability timescale of the
emission $t_{\rm var}$ by a condition of causality

$t^{\prime}_{\rm dyn}=(1+z)^{-1}\delta\,t_{\rm var}\,,$ (2)

where $z$ is the redshift of the source and
$\delta=[\Gamma(1-\beta\cos\theta)]^{-1}$ is the Doppler factor, with $\theta$
the viewing angle of the emission, $\Gamma$ and $\beta c$ the Lorentz factor
and velocity of the outflow. Fore this estimate, we assume a homogeneous and
instantaneous emission, however it can be influenced by the structure of the
radiation region[26, 27]. In transient sources, the short dynamical timescale
of the system limits the particle escape timescale, and the diffusion of
cosmic-ray particles due to scattering on magnetic waves can be considered to
only intervene in the acceleration timescale.

The energy-loss and interaction processes at play include various
photohadronic and hadronic processes [28, 29], involving interactions with a
photon field of spectrum ${\rm d}n^{\prime}_{\gamma}/{\rm
d}\epsilon^{\prime}$. In the case of flaring sources, the dominant interaction
background to consider in the simplest case is the flaring radiation. First,
interactions with steady baryon or radiation fields in the source or in the
cosmic medium happen in most cases over a timescale $t\gg t_{\rm var}$, due to
the larger size of the source compared to the flaring region, and due to
magnetic diffusion of particles. In such a configuration, the neutrino
emission will be diluted over time and can be viewed as a steady emission
stemming from the quiescent source. Second, the flaring baryonic material is
usually optically thinner to HE-UHE neutrino production via hadronic
interactions [19]. However, the case of interaction backgrounds with high
opacity (for instance a dense supernova ejecta) needs to be modeled
specifically.

Photohadronic processes $X\gamma$, where $X$ is a nucleon or an atomic
nucleus, contribute to the production of HE neutrinos above the pion
production threshold. It corresponds to the minimum proton energy
$E_{p}^{\prime}\simeq 10^{17}\,{\rm eV}\,(1\,{\rm eV}/\epsilon^{\prime})$ for
a typical radiation field energy $\epsilon^{\prime}$. Their interaction
timescales are

${t^{\prime}}_{N\gamma}^{-1}=\frac{c}{2{{\gamma^{\prime}}^{2}}}\int_{0}^{\infty}\frac{{\rm
d}\epsilon^{\prime}}{{\epsilon^{\prime}}^{2}}\frac{{\rm
d}n^{\prime}_{\gamma}}{{\rm
d}\epsilon^{\prime}}(\epsilon^{\prime})\int_{0}^{2\gamma^{\prime}\epsilon^{\prime}}{\rm
d}\bar{\epsilon}\,\bar{\epsilon}\,\sigma_{N\gamma}(\bar{\epsilon})\,,$ (3)

where $\sigma_{N\gamma}(\bar{\epsilon})$ is the photodisintegration cross
section. Secondary particles produced through these processes, such as
electrons, pions, muons or high-energy photons, can experience energy-losses
and interactions before escaping the source. Moreover, charged secondaries can
be injected at shock fronts, or magnetically reconnecting regions, and be
accelerated by first order or second order acceleration processes [30, 31, 32,
33, 34]. In the case of secondary particles involved in HE and UHE neutrino
production, energy losses and acceleration can significantly impact the
neutrino spectrum and its flavor composition.

###  2.3  Phenomenological recipes to evaluate the maximum energy and flux of
HE neutrinos

The competition between the aforementioned timescales allows to estimate the
maximum energy of HE neutrinos. Several important assumptions usually need to
be made to constrain the source properties, for instance an assumption of
equipartition between the non-thermal electromagnetic energy density and the
magnetic energy density to estimate the mean magnetic field. Under these
assumptions, the maximum proton and neutrino energies can be estimated as a
function of the transient source properties $t_{\rm var}-L_{\rm bol}-\Gamma$,
as illustrated in Figure 1. In the same spirit as standard approaches designed
to identify possible production sides for UHE cosmic rays [35], such estimates
allow to identify promising categories of transient sources for the production
of HE neutrino signals. In Figure 1, several categories of transient sources
are represented, which are described further in section 3.1. We also give the
example of PS16cgx, an object consistent with a type Ic supernova, and
possibly a choked-jet or an off-axis GRB, that was identified by Pan-STARRS
[15] in a search conducted after the detection of a candidate cosmic neutrino
IceCube-160427A [36]. For deriving further properties of the source
environment, the balance between the different processes at play can also be
constrained using MM observations, with models dedicated to specific transient
source categories.

The total non-thermal electromagnetic (EM) energy $U_{\gamma}$ radiated during
the transient event is used as a proxy for the maximum energy channeled in HE
to UHE transient neutrinos. Typically, models consider
$U_{p}=\eta_{p}U_{\gamma}$, with $U_{p}$ the energy in accelerated protons and
$\eta_{p}$ a constant. The energy channeled in neutrinos
$U_{\nu}\simeq\eta_{\rm ch}\,f_{p\gamma}\,U_{p}$ depends on the efficiency of
photopion production $f_{p\gamma}=\min(1,\tau_{p\gamma})$ where
$\tau_{p\gamma}=t^{\prime}_{\rm dyn}/t^{\prime}_{p\gamma}$ is the opacity for
photopion production. The factor $\eta_{\rm ch}\simeq 3/8$ depends on the
channels involved in neutrino production (e.g., resonances, multi-pion
production). At first approximation, the neutrino spectrum can be described by
a power law between a minimum and a maximum energy, with an index
$\alpha_{\nu}$ depending on the proton spectrum (assumed to be a power-law of
index $\alpha_{p}$) and the photon background. For a hard radiation
background, for instance a power-law spectrum with a photon index $<1$ or a
blackbody spectrum, $\alpha_{\nu}=\alpha_{p}$ in the energy range where
photopion production dominates. A softer photon spectrum or significant
secondary energy losses can significantly modify the slope of the neutrino
spectrum. Similar to the study of steady HE neutrino sources [37], simple
detectability criteria can be calculated using the total energy channelled in
neutrinos and the properties of their spectrum, together with the
sensitivities of HE to UHE neutrino experiments [26, 19, 34, 38].

###  2.4 Numerical methods

The full treatment of HE and UHE neutrino production in astrophysical
environments requires the simultaneous description of cosmic-ray propagation,
acceleration, energy-losses and interactions, and the full cascade of
secondary nucleons and nuclei, neutrinos and photons. Numerical simulations
allow us to study these different processes in great detail. However, self-
consistent simulations are challenging and computationally expensive, due to
the wide range of spatial and energy scales to be considered. Moreover, the
modeling of transient HE to UHE neutrino emission requires a time-dependent
description of backgrounds and structures in the source environment.

The description of propagation and acceleration of cosmic rays in the vicinity
of the sources requires a self-consistent treatment of the evolution of the
properties of the particles coupled with the evolution of the electromagnetic
fields, as the cosmic-ray energy density is not necessarily negligible when
compared with the electromagnetic energy density. This coupled and non-linear
description can be achieved for instance using particle-in-cell (PIC)
simulations [39], but on length scales well below the typical sizes of the
regions of emission inside the sources. These detailed simulations provide
analytical prescriptions and initial conditions, such as acceleration
timescales, particle spectra and energy densities, that can be used in larger
scale simulations. Studies of HE-UHE cosmic-ray acceleration accounting for
macroscopic source properties are emerging, with MHD and test-particle
simulations [40, 41, 42, 43], or fully kinetic simulations. For instance, the
study of cosmic-ray acceleration in pulsar magnetospheres and winds is
addressed in [44], by making simplifying assumptions about the energy range
and the energy-loss processes at play. Moreover, the addition of Monte Carlo
modules to PIC simulations paves the way for self-consistent simulations [45,
46, 47].

Simplifying assumptions can be considered to focus on specific aspects of
cosmic-ray propagation and interactions in the vicinity of compact sources.
Following interstellar and intergalactic propagation codes, such as GALPROP
[48], DRAGON [49], PICARD [50], CRPropa [51] or SimProp [52], the propagation
of cosmic ray densities at high energies can be treated by solving transport
equations, and at UHE, the numerical integration of the equation of motion of
single particles can be considered. These methods rely on the test-particle
assumption, ignoring the feedback of cosmic rays on the electromagnetic
fields. Recent work aims at unifying the simulation of cosmic-ray propagation
from HE to UHE, for instance in CRPropa [53].

Approaches tackling cosmic-ray interactions and the subsequent nuclear
cascades make use of Monte Carlo methods [54, 55, 56], while others solve
coupled sets of partial differential kinetic equations [57]. Interaction cross
sections and interaction products involved in HE and UHE neutrino production
can be obtained from analytical formulae [28] or numerical codes, such as
Sophia [58] for photopion production, Talys [59] for photonuclear interactions
and Epos [60] or Sibyll [61] for purely hadronic interactions. Some
uncertainties arise from the description of the interaction processes; for
instance in the case of photonuclear interactions, the standard approach
treating the nucleus as a superposition of nucleons can lead to an
overestimation of the neutrino flux [62]. The implementation of cosmic-ray
interactions generally relies on an analytical description of the populations
of leptons and/or the related radiation backgrounds. Therefore, the feedback
of accelerated and interacting hadrons and leptons on the radiation background
is only partially accounted for. The implementation of radiation backgrounds
as well as interaction processes can lead to significant uncertainties on the
computed neutrino fluxes [63, 57, 64]. Cosmic-ray propagation and interaction
codes have been developed to study steady emissions. However, they can be
adapted to study transient HE to UHE neutrino emissions by considering the
evolution of interaction backgrounds in successive time-bins [56, 65, 66, 67],
to identify time-dependent signatures and predict coincidences or delay
between emissions. Additional modules are developed, for instance in CRPropa,
descriptions of Fermi acceleration, or EM cascades with thinning procedures to
speed up the simulations [68]. Detailed studies of specific source classes can
be performed, as well as large parameter-space scans are now within reach[69,
70].

Another category of codes focuses on the radiation of accelerated leptons and
hadrons, traditionally for the multi-wavelength modeling of active galactic
nuclei spectra, for instance AM3 [71], ATHE$\nu$A [72], B13 [73] and LeHa-
Paris [74] which are compared in [75], and the publicly available agnpy [76],
NAIMA [77] and JetSet [78]. These codes include synchrotron, inverse-Compton,
$\gamma\gamma$ pair production or Bethe-Heitler processes, considering
internal (mostly produced by the synchrotron radiation of leptons) or external
radiation fields. Several of these codes can account for time-dependent
emission. Generally, from the hadronic side, only nucleons are considered
which is sufficient for most astrophysical environments where nucleons are
dominant. At ultra-high energies the existence of appreciable fractions of
other nuclear species is indicated by UHECR composition measurements [79].
This has led to the development of dedicated frameworks such as NeuCosmA [80,
81, 82] and CRPropa3 [68, 83]. Efforts are underway by several groups to
produce coupled versions of cosmic-ray interaction and time-dependent
radiative codes.

In addition to the prediction of HE-UHE neutrino production in the vicinity of
sources, the assessment of detection prospects for ground-based, sub-orbital
or space-based detectors requires a good understanding of their interactions,
mostly in the Earth, the ice, and the atmosphere, and the subsequent
production of observable signals, such as Cherenkov light, fluorescence light,
or radio waves. Several numerical packages have been developed to describe the
full chain between the neutrino flux arriving on Earth, the interactions and
propagation of the signals and the response of the detectors, with great
precision, e.g. [84, 85, 86, 87].

##  3 Sources and detectability

Various categories of EM transients are promising sources of transient HE to
UHE neutrino signals, due to their high bolometric luminosity, their powerful
non-thermal emissions and/or their dense interaction backgrounds. Although
they all present a common ingredient, which is a powerful plasma outflow,
their structure, evolution and observational characteristics are widely
different. We provide references to recent models (section 3.1). Moreover, we
discuss the theoretical questions that should be answered to assess their
detectability, such as predictions of the neutrino energy (section 3.2) and
the variation of the neutrino signal with time (section 3.3), and we discuss
the theoretical aspects required to better interpret observations
–associations in particular– through a careful modeling of theoretical
uncertainties (section 3.4). We also discuss the input of data on source
modeling, through non-detections or detections of multi-wavelength signals
(section 3.5), multi-wavelength or MM coincidences (section 3.6), and how
these data constrain source population models (section 3.7).

###  3.1 The transient zoo at very high energies

Several source classes can produce recurring transient emissions, such as
active galactic nuclei and in particular blazars, which produce a range of
flares at multiple wavelengths [71, 88, 89, 90, 91, 92, 93, 94, 95, 20, 96,
97, 98, 99, 100, 101, 102, 103]. NS and magnetars and their sub-classes of
anomalous X-ray pulsars and soft gamma-ray repeaters, as well as X-ray
binaries, can also produce a range of bursts and flares [104, 105, 106, 107,
108, 109, 110, 111]. One-time events encompass various classes of stellar-
related explosions [112], such as novae, supernovae (SNe) and hypernovae, or
super-luminous supernovae (SLSNe) [113, 114, 115, 116, 117, 44, 118, 119, 120,
121], and the potentially associated low-luminosity gamma-ray bursts [122,
123, 124, 125, 126, 127, 128, 129, 130] or long-duration gamma-ray bursts
(GRBs) [131, 132, 133, 134, 135, 136, 137, 138, 139, 56, 140]. Gravitational
wave detections by the LIGO and Virgo collaborations have raised the interest
for various compact object mergers, such as white dwarf mergers [141], NS-NS
mergers and the related short GRBs [142, 143, 65, 144, 67, 145], NS-black hole
(BH) mergers and BH-BH mergers [146, 147, 148], and also the disruption of
stars or white dwarfs by massive or stellar mass BH [149], namely tidal
disruption events (TDEs) [150, 151, 152, 153, 154, 155, 156, 157, 158, 159,
160, 66, 161, 162, 163, 164, 17], and micro-TDEs [165]. Supermassive BH
mergers [166] and various classes of explosions happening in disks of active
galactic nuclei [167] are also potential neutrino sources.

Figure 2 illustrates the theoretically expected neutrino fluence for a number
of promising astrophysical source classes, and how these compare to the
sensitivity of existing and proposed neutrino facilities. The short transients
($<$ day) shown are (i) early GRB neutrino afterglow [136], and (ii) extended
emission from short GRBs based on the moderate model of [168]. The stacked
signal from 100 such events is shown. This corresponds to the mean expected
number of bursts within 1 Gpc in ten years. The long transients shown are: (i)
Stacked ten-year neutrino fluence from ten flat spectrum radio quasars (FSRQs)
at redshift $z=2$, weighted according to the gamma-ray activity. The neutrino
emission is dominated by the gamma-ray flaring states, based on the infrared
torus model of [100]. (ii) Stacked neutrino emission from $10\,000$ chocked-
jet TDEs assuming 100-day-long activity (internal shock model of [157]). For
comparison, LSST is expected to detect $1000$ TDEs per year starting in $\sim
2024$ [169]. (iii) Stacked neutrino signal from 1000 NS-NS-merger events
within 300 Mpc [65], which is the number expected in ten years based on the
observed rate of [170]. Several of the theoretical models will be tested by
the upcoming neutrino facilities.

Figure 2: All-flavor neutrino fluence from theoretically predicted short
($<$day, top panel) and long (bottom panel) astrophysical transients and
comparison to the sensitivity of existing and upcoming neutrino detectors (see
text). The experimental sensitivities are per decade in energy for an assumed
$E^{-2}$ neutrino spectrum. For Auger, IceCube [171], and IceCube-Gen2 [172]
the sensitivity to neutrino transients at the location of GW170817A is shown.
The projected sensitivity of GRAND to short transients at zenith angles
$86^{\circ}\leq\theta\leq 93^{\circ}$ and long transients at declination
$0^{\circ}\leq\delta\leq 45^{\circ}$ assuming a single GRAND array at latitude
$42^{\circ}$ North [173] is indicated with a pink band. The projected
sensitivity of POEMMA to short and long transients in ToO-dual and ToO-stereo
mode respectively is shown with a green shaded band [174].

###  3.2 At what energies are neutrinos typically produced?

As can be seen in Figure 2, the typical energy of neutrinos produced by the
various source classes has a decisive impact on their detectability with a
given observatory. At first approximation, transient neutrino production is
described by one-zone models that focus on one-time interval around the peak
of the EM emission. In these cases, as illustrated in Figure 1, the maximum
energy of neutrinos depends on cosmic-ray acceleration, and energy losses of
primaries and secondaries. Long duration transients such as SLSNe, blazar
flares or TDEs, which are marginally subject to energy losses (such as
synchrotron radiation) for primary hadrons or secondary particles, can produce
neutrinos up to the UHE range. Short duration luminous transients, such as
millisecond magnetars, magnetar bursts and flares, NS-NS mergers or GRBs, are
also good candidates for cosmic-ray acceleration to EeV energies and above
[175, 65]; however, due to their short duration and the related small
radiation zone, their intense magnetic fields and radiation backgrounds can in
specific cases significantly limit the maximum energies of transient neutrinos
to the HE-VHE range or below. Dense radiation or hadronic backgrounds can also
significantly reduce the efficiency of the acceleration processes.

###  3.3 How does the neutrino signal vary with time?

The hints of spatial association of HE neutrinos with transient sources, see
section 3.6 for concrete examples, combined with their detection after the
peak EM emission, motivates an accurate description of transient neutrino
spectra and lightcurves. This requires time-dependent modeling of acceleration
and energy-loss processes, which is of particular interest for specific
transient sources with intense MM follow-up [17]. For various source classes,
the peak fluxes and peak energies of transient photons and neutrinos can occur
at different times, as acceleration and energy-loss processes evolve through
the duration of the transient. For instance, models of non-relativistic shock-
powered transients show a delay between the peak flux of HE neutrinos and the
time when they are produced at a maximum energy [121], which can impact
detectability for HE to UHE neutrino detectors. Moreover, secondary energy
losses and interactions can significantly suppress HE to UHE neutrino
production during the early phase of the transient EM or MM emission, with a
neutrino energy and flux peaking at later times, for instance in the case of
NS mergers [65, 67]. Similarly, the interactions of VHE photons, for instance
through pair production processes, can suppress a part of the transient multi-
wavelength emission and induce delays between the emissions of neutrinos and
VHE photons. In some scenarios with high opacities, HE to UHE transient
neutrinos can appear as precursors of the VHE EM emission, for instance for
models of chocked GRBs [176, 128], despite potential strong flux and maximum
energy suppression due to meson cooling [177].

###  3.4 Model uncertainties

Several sources of uncertainties challenge the modeling of transient neutrino
signals. Different emission regions in winds or jets can usually explain the
EM emission of a given source, with significantly different parameters. The
magnetic field, Lorentz factor, and the parameters characterizing the
radiation and hadronic backgrounds cannot systematically be inferred from
observations and can be degenerate, which directly impacts the acceleration
and the energy losses of primary and secondary particles involved in the
neutrino production, and the efficiency of neutrino production. The luminosity
of the cosmic rays accelerated inside the source is loosely constrained, as
well as their composition, which can strongly impact the neutrino spectrum due
to the photodisintegration of heavy nuclei, e.g. through giant dipole
resonance, and the production of secondary nucleons and nuclei. The
uncertainties on the interaction backgrounds also impact the opacity of the
source to EM radiation, and thus the estimate of the energy released during
the flare. Recent studies compare different emission models, e.g. [92, 178,
140] or systematically explore a fraction of the parameter space, e.g. [71,
89, 90, 179, 93, 70].

###  3.5 Learning from multi-wavelength data

Precise multi-wavelength and time-dependent data are decisive for
distinguishing between transients, such as jetted TDEs and AGN, or non-jetted
TDEs and SNe; and draw notable comparisons between the various source models.
The amount of data available and coverage of the EM spectrum differs between
transient categories, depending on the source locations and populations
(Galactic, extra-galactic) and the possibility of conducting multi-wavelength
follow-up campaigns. For instance, the small number of detections of short
GRBs and NS-NS mergers remains a limitation to characterize their properties
and their population. Specific EM constraints of the cosmic-ray component in
sources are starting to emerge. Some VHE EM emissions can be interpreted
hadronic emissions, however they can often also be explained by leptonic
emissions. The absence of detection of VHE EM emission can be a marker of
interaction backgrounds with a high optical depth and thus intense HE-UHE
neutrino production [180], accompanied by EM cascades of VHE photons. In
addition, EM cascades related to hadronic processes can provide strong
constraints for specific source classes, with dedicated observations in the
MeV-GeV energy range [91, 92]. However, intergalactic magnetic fields can
affect EM cascades and thus the arrival times of gamma rays [181, 182]. This
important effect can significantly impact correlation studies.

###  3.6 Learning from coincidences

The first hints of associations between EM emissions and HE neutrinos detected
by IceCube, from blazar flares[183, 184, 185, 186] TXS 0506+056 + IC170922A,
PKS 1502+106 + IC190730A, 3HSP J095507.9+355101 + IC200107A, and TDE[17]
AT2019dsg + IC191001A, or probable TDEs[187] AT2019fdr + IC200530A and [188]
AT2019aalc + IC191119A further motivate the on-going modeling effort for
predicting time-dependent MM and neutrino emissions from these sources. These
associations, if physical, imply extremely high proton luminosity, exceeding
the Eddington luminosity of the sources, and very high photo-pion induced EM
cascade flux in the keV-GeV energy range as a result. The cascade flux, and
thus the proton luminosity can be constrained by multi-wavelength
observations.

Many spatial and temporal correlation studies between detected HE neutrinos
and individual or population of sources are conducted. For instance, hints for
correlations have been found between intermediate and high-energy peaked
blazars and HE neutrinos [189] and radio-selected blazars [190]; these
associations being individually compatible with statistical fluctuations.
Among other examples, time-dependent searches are performed by IceCube for
increased X-ray activity of magnetars [191], using the McGill Online Magnetar
Catalog [192], X-ray binaries [193], using their X-ray lightcurves,
gravitational wave detections of LIGO/Virgo [194], supernovae [195], GRBs
[196, 197], blazar flares [198], minute-scale transients in general [199].
General searches for associations with optical transients and resulting limits
have been presented in [200, 201].

Associations are expected to significantly increase in the next decades, with
the multiplication of observations of transient sources, and in particular
observations of compact object mergers [18]. As an example, in the past three
years, the Zwicky Transient Facility has discovered $>1500$ core-collapse
supernovae, $>100$ hypernovae and $>30$ tidal disruption events (among other
transients). The modeling of possible coincidences will require a precise
description of spatial properties, to correctly assess emissions directed
towards the observer; for instance, in the case of GW170817, to correctly
predict coincident photons and neutrinos that are not emitted in the direction
of the relativistic jet (off-axis emissions) [202, 203].

Finally, in coincidence studies, a careful consideration should be given to HE
neutrino backgrounds. The contribution of all HE neutrino production regions
along the line of sight from the Earth, not necessarily located in the
vicinity of transient sources [204, 205, 206], should be accounted for. This
irreducible astrophysical neutrino background must be accounted for when
calculating the significance of the detection of HE neutrinos from transient
sources. The impact of this astrophysical background on the significance of
observed associations depends on the precision of temporal and spatial
coincidences, instrument properties, neutrino emitting source population, and
the energy of the neutrinos.

###  3.7 Constraints on source populations

The contribution of observed GRBs to the diffuse HE neutrino flux detected by
IceCube is strongly constrained by time-dependent searches [196, 207, 208].
The contributions of known source populations to the total cosmic neutrino
flux detected by IceCube, constrained through stacking analyses [209, 210],
are the following: prompt phase of GRBs ($<1\%$) [196], blazars ($<17\%$)
[211], non-jetted TDEs ($<26\%$) and jetted TDEs ($<1\%$) [212], ultraluminous
infrared galaxies ($<10\%$) [213], Galactic sources ($<14\%$) [214], SNe IIn
($<55.2\%$), SNe IIP ($<79.6\%$) and SNe Ibc ($<28.6\%$) [195], microquasars
($<7.3\%$) [193], galaxy clusters out to redshift 2 (<5%) [215], and radio
galaxies ($<30\%$) [216]. Recently, a $2.6\sigma$ excess of neutrinos from the
directions of non-jetted AGN weighted by their soft X-ray flux has been
reported [217]. If this is a genuine signal, it implies that 27% to 100% of
neutrinos at 100 TeV come from non-jetted AGN.

Uncertainties related to the relation between the electromagnetic flux at a
specific wavelength and the neutrino flux of the sources as well as the exact
shape of the emerging neutrino spectrum significantly impact these estimates.

Figure 3: Comparison of the local density and implied neutrino energy output
of transient extragalactic neutrino sources to the sensitivity of upcoming UHE
neutrino detectors. The green band indicates the neutrino energy output / and
local number density range that is compatible with the total observed diffuse
neutrino flux in the IceCube energy range extrapolated to $10^{18}$ eV using
the best-fit parameters of [218] for sources whose redshift evolution ranges
from negative to positive and equal to the redshift evolution of the star
formation rate. The grey shaded area indicates the parameter space that will
be constrained by upcoming detectors in the absence of detection of point
sources.

A luminosity dependent lower limit on the number density of neutrino sources
can be derived from the absence of significant small scale clustering
(multiplets) and neutrino point sources in the IceCube data. Their absence
disfavours rare and very bright astrophysical sources as the sources of the
bulk of the neutrino flux in the IceCube energy range [219, 220, 9, 221, 222,
223]. A similar constraint will be possible to derive at ultra-high energies
with planned neutrino facilities if a UHE neutrino flux is detected. The
expected capabilities of GRAND, IceCube-Gen2-Radio, and POEMMA assuming their
planned limiting sensitivity $F_{\rm lim}=0.1$GeV/cm2 at $10^{18}$ eV are
shown in Figure 3. The neutrino flux at energy exceeding $10^{16}$ eV has been
estimated extrapolating the parameters that best describe the IceCube diffuse
flux at lower energies, as derived by [218]. The width of the green band
corresponds to the uncertainty introduced by the unknown redshift evolution of
neutrino sources for which we considered the range considered by [6]. The
assumed rates of the transient events considered are according to the observed
rates quoted in Table 2 of [224], except for NS-NS mergers for which we have
used the updated estimate of[170]. For the observed duty cycle of FSRQ flares
we have taken the mean of the estimates of[225] and [226]. In some instances,
most demonstrably jetted TDEs, the power in cosmic rays must exceed the EM
power of the objects so as for them to account for the bulk of the high-energy
neutrino flux. This calculation is conservative in the sense that it doesn’t
take into account the possibility of an additional UHE neutrino emitting
source population above $10^{16}$ eV, which would lead to enhanced neutrino
flux in the considered energy range with respect to what is expected based
simply on an extrapolation of the TeV-PeV astrophysical neutrino flux. For an
independent calculation assuming different benchmark scenarios see [227].

The non-detection of joint gravitational waves and neutrino events [228] also
starts to set constraints on the population density of powerful and high-rate
transients capable of producing copious gravitational wave signals, such as
short gamma-ray bursts [229].

##  4 Instruments to detect and identify high-energy neutrino transients

Further constraints on source modeling and the actual identification of
neutrino transients will be achieved by adequate and powerful neutrino
detectors, combined with EM follow-up telescopes and gravitational wave
detectors via efficient networks. We discuss the performances of such current
and up-coming instruments in the following, focusing on neutrino and EM
observatories. Because of the pointing capabilities of EM instruments compared
to neutrino and gravitational-wave detectors, a joint neutrino-gravitational-
wave detection would be detected by correlating neutrino and EM signals on the
one hand and with EM-gravitational-wave campaigns on the other. Various
reviews cover the latter subject [230, 231], hence we concentrate on the
former.

###  4.1 Neutrino detectors

Neutrino detection requires large target volumes because of their low
interaction probability with matter. At very high energies (up to $\sim 10$
PeV), large volumes of ice (for IceCube) or water (for ANTARES) have been
instrumented, in order to detect the Cerenkov light emitted by up-going
neutrinos crossing the Earth or down-going neutrinos arriving at small zenith
angles. The successful detection of PeV neutrinos with IceCube [232, 233] has
triggered several international efforts to build larger detectors following
the same principles [234]: KM3NeT-ARCA [235], Baikal-GVD [236] and P-ONE [237]
deep underwater, and IceCube-Gen2 [172] in ice. Note that several of the
projected instruments are based on detection techniques that have not been
fully tested. For example, the success of BEACON, GRAND, POEMMA, TAMBO, or
Trinity rely on reconstructing air-showers in Earth grazing configurations, or
from above the atmosphere. GRAND also requires to perform efficient self-
triggering on radio signals, which still needs to be validated, although
promising preliminary studies exist [238].

At higher energies, the fluxes are lower, and more cost-effective detection
techniques have to be utilized to instrument even larger volumes. Earth-
skimming tau-neutrinos can interact with the Earth and produce tau leptons
which can decay and lead to air-showers [239]. These air-showers can be
observed via their particle (Auger [240], TAMBO [241]) their air-fluorescence
or beamed optical Cerenkov (Auger, POEMMA [242], Trinity [243], Ashra-NTA
[244]) or radio (GRAND [173], BEACON [245]) emissions. Radio-detection
techniques can also be used to search for the coherent, impulsive radio
signals that are emitted by electromagnetic particle cascades induced by
neutrinos interacting with ice [246], in ice (ARA [247], ARIANNA [248], RNO-G
[249], IceCube-Gen2 Radio [172]) or with balloon experiments (ANITA [250],
PUEO [251]).

In light of the previous sections, future neutrino observatories should meet
specific requirements in order to optimize the probability of detecting HE and
UHE transients. A fluence sensitivity improvement of one (two) order(s) of
magnitude in the PeV (EeV) range, should be aimed for, in order to reach the
levels of the fluxes of the most powerful transient source categories. A
maximal coverage of the energy range from PeV to EeV is desirable, with an
energy resolution of $\Delta E/E\lesssim 0.5$ to distinguish between different
source spectra. For efficient follow-ups, coincident searches, and source
identifications sub-degree angular resolution will be necessary, as well as
wide instantaneous (or daily, or monthly –depending on the type of transient)
field of view (FoV), and a multi-instrument network that enables full sky
coverage. Finally, being able to send and receive alerts is a key requirement.

Current and future neutrino detectors are listed in Table 1 together with
their timeline and their indicative characteristics. To give an idea of the
span of the energy range of the experiment, we quote the minimum energy –for
most experiments this either corresponds to an operational energy, or is
defined as the energy above which the sensitivity is competitive with the
IceCube limits (above PeV) over the lifetime of the project– and the “peak”
energy, where the instrumental sensitivity is best. Projected differential
sensitivity limits to the diffuse neutrino flux are quoted at this peak
energy. Although fluence sensitivities would be better suited to assess
transient source detectability, they are less convenient to quote due to
dependencies on declination and time integration. The sensitivities listed
here can serve for comparison between instruments. We caution that for many of
the projected instruments, these numbers are preliminary, based on simulations
and/or extrapolations from existing measurements111For example, for Baikal-
GVD, the predicted sensitivity is for a full detector of 112 strings,
extrapolated from the current instrument of 64 strings. For some experiments,
we quote the existing upper limits in brackets, and the measured flux for
IceCube. The instantaneous field of view (iFoV) and the daily sky coverage
(dFoV) are given as percentage of visible sky (the observable band is also
quoted for some experiments in square degrees in parenthesis). For the very
high-energy instruments ($<10\,$PeV), geometrical FoVs are listed, that do not
fold in any cut on the acceptance of the instrument222For example, with a 90%
cut on the acceptance, the FoV of P-ONE would drop to 22% (instantaneous) and
24% (daily average).. For the UHE instruments, a cut at 95% acceptance was
taken into account for the FoV calculations of ANITA, PUEO, ARA, POEMMA
fluorescence, Auger, GRAND, and Trinity. For proposed instruments, the FoV
could change depending on the final chosen site. The FoV and angular
resolution also depend on the neutrino energy and on the nature of the event.
In this table, the best performances are quoted, usually around the peak
energy. For very high-energy instruments, when the data is available, a
distinction is made for up-going muons tracks (denoted ‘up’) and cascade
events (marked in parenthesis), or for combined (‘up+casc.’) events when
specified333Muon tracks are elongated signals from muon neutrino interactions
in or near the detector. Electron or tau neutrinos rather deposit most of the
neutrino energy in a small region, resulting in nearly spherical ‘cascade’
events, from which it is more difficult to infer the arrival direction..

The table indicates that thanks to their complementary strengths and
locations, the projected experiments have a good potential of fulfilling most
of the requirements listed above for successful transient neutrino detection.
The planned PeV energy-range telescopes observe different parts of the sky and
their different techniques will enable to precisely study systematic effects.
Moreover, their characteristics indicate that they will have complementary
strengths: IceCube-Gen2 will accumulate the largest statistics, while KM3Net
will achieve a an angular resolution more than 3 times better, thanks the less
diffusive water-medium, compared to ice. For UHE instruments, in-ice radio,
optical and particle detectors reach lower energy thresholds, which ensures a
continuous energy coverage from the PeV range. In-ice radio experiments also
provide a wide instantaneous FoV, ideal for transient monitoring. For these
instruments however, although the angular resolution on the arrival angle of a
signal is of sub-degree order, the reconstruction of the direction of the
incident neutrino is more complex, as it is dominated by the resolution on the
orientation of the signal polarization [252, 253]. Hence, the angular
resolution is expected to be $>1^{\circ}$. On the other hand, radio-air shower
detectors and some optical instruments will naturally provide angular
resolutions of $<1^{\circ}$. The combination required for neutrino astronomy
as discussed above (a sensitivity improvement of 2 orders of magnitude, sub-
degree angular resolution and wide field of view) is projected for two
instruments: GRAND and Ashra-NTA.

We have not quoted energy resolutions in Table 1. Reaching good energy
resolutions might be challenging for all detectors observing muon and tau
neutrinos. Although the energy of the air-shower resulting from the lepton
decay could be resolved within $10\%$, the uncertainty on the energy rate
received by the lepton is the limiting factor ($\Delta E/E\sim 0.3-0.5$) [254,
255], but this could suffice to differentiate between source spectra.

The last column of Table 1 lists the neutrino alert programs that detectors
have or are planning to set up. Current networks and alert systems are
indicated in roman style. Most instruments (marked as “planned”) are planning
to send alerts. When network names are specified in italics, the corresponding
instruments have started to implement alert programs or are working on
extensions of existing structures. For some instruments like ARA, ANITA and
PUEO, implementing an alert system requires fundamental changes in data
handling, hence there are no immediate plans to be part of an alert system.

###  4.2 The power of multi-messenger networks

The IceCube observatory has provided us with a first view of the neutrino sky.
From the absence of clearly detected point sources and of small scale
clustering, we have learnt that the sources of high-energy neutrinos are
relatively abundant as discussed in Sec 3. In light of the fact that the
sources are relatively numerous and unlikely to lead to clear detection with
neutrinos alone, a promising method to identify neutrino sources is by
association of a neutrino with an electromagnetic signal accompanying a
transient event responsible for its generation. The required temporal
coincidence in addition to a spatial association increases the sensitivity and
the significance of a potential discovery.

The power of such EM+neutrino associations is harnessed by several ongoing
programs. These programs are based on two main observation strategies: A) EM
network follow-up on neutrino alerts [256, 13], and B) neutrino telescopes
following up on EM transient alerts [257, 258].

As part of A), the IceCube realtime alert system [13] rapidly communicates the
arrival direction of neutrinos with a high-probability of being astrophysical,
via a Gamma-Ray Coordinates Network (GCN) alert[259], to allow for follow-up
with steerable telescopes. IceCube generates approximately ten "Gold" alerts
per year[260]. Such neutrinos have $\sim 50\%$ chance of being astrophysical
as opposed to atmospheric, meaning that about half of these alerts point to
truly astrophysical neutrinos. Additional alert classifications exist with a
larger fraction of background neutrinos. X-ray, optical, and gamma-ray
instruments typically have a number of hours, or pointings allocated to such
follow-up, as part of their target of opportunity (ToO) programs (Table 2).
Non-steerable detectors including Auger, ANTARES perform archival searches for
similar emission [261, 258].

In addition to bilateral collaboration programs, dedicated networks focus on
specific types of associations, as part of observation strategy B). Since 2005
the SuperNova Early Warning system (SNEWs) has been running with the aim to
alert the astronomical community at the time of next galactic supernova, by
requiring an online coincidence among several world-wide distributed neutrino
detectors [262]. The Astrophysical Multimessenger Observatory Network (AMON)
is a cyberinfrastructure network which connects ANTARES, Auger, FACT, Fermi-
GBM, Fermi-LAT, H.E.S.S., HAWC, IceCube, LCGOT, LIGO-Virgo, LMT, MASTER,
Swift, VERITAS, ZTF and focuses on coincidences among two or more of these
instruments in what would be subthreshold events in one individual detector
[263, 264]. In addition, the AMON infrastructure is used as a pass-through for
the aforementioned IceCube high significance alerts. Other instruments are at
the time of this publication in the process of joining AMON. The increasing
rate of astrophysical transients which are detected with astronomical surveys,
particularly optical ones, has lead to alternate approaches complementary to
those of MM networks. The Alert Management, Photometry and Evaluation of
Lightcurves (AMPEL) system [265], processes astronomical data according to
user defined criteria, in order to produce sub-samples of events, relevant to
a particular MM search. AMPEL is particularly useful for processing the data
acquired with surveys such as ZTF.

###  4.3 Electromagnetic follow-up instruments

The entire EM spectrum is today covered for coincident searches, with a
combination of wide field survey instruments (e.g., LHAASO [266], HAWC [267],
ASAS-SN [268], ATLAS [269], PanSTARRS [270], ZTF [271], Vera Rubin Observatory
[272]), high angular resolution pointing telescopes (e.g., CTA [273], H.E.S.S.
[274], Kanata/HONIR [275, 276], MAGIC [277], MASTER [278], VERITAS [279], XMM-
Newton [280], Athena [281], TAROT [282]), multi-platform satellites (e.g.,
Fermi [283], INTEGRAL [284], Swift [285], SVOM [286]) large field-of-view
imaging radio facilities (e.g., VLA [287], MWA [288], MeerKAT [289], SKA
[290]), and spectroscopic programs to measure the source redshift (e.g.,
GEMINI GMOS [291], GTC OSIRIS [292], Keck LRIS [293, 294], VLT X-shooter
[295]). Table 2 compiles indicative experimental characteristics –detailed
below– of a non-exhaustive list of actual or potential neutrino follow-up EM
instruments. The majority of the listed experiments have a dedicated ToO
follow-up program, and all of them, except for ATLAS, have participated in the
follow-up of at least one neutrino alert.

Although they are not listed in Table 2, future gamma-ray observatories in the
MeV range such as AMEGO [296] with capabilities beyond INTEGRAL and Fermi-GBM,
will fill an important gap and enable new types of studies. They will extend
the flux measurements of HE gamma-ray sources to lower energies, connecting
with X-ray observations, in an energy range where gamma-rays are not absorbed
by the extragalactic background light.

####  4.3.1 Field of view

Coincident observations of a neutrino and a transient counterpart require that
the field of view (FoV) of the telescope be comparable to the angular
resolution of the neutrino detector. The FoV depends on the energy/wavelength
and on the observation mode of the facilities. We quote the FoV at or in a
range around the best sensitivity of the instruments.444For ASAS-SN, combining
the 4 sites, the FoV is of 360 square degrees. However, when responding to a
ToO, the best single unit of 4 cameras is triggered, leading to a narrower FoV
of 72 square degrees [268, 297]. The figure for this latter observation mode
is quoted.

####  4.3.2 Slew speed and survey speed

The efficiency of an early follow-up program further depends upon the fast
response and slew speed of the telescopes after receiving the alert. The
indicated response delay corresponds to the time between the instant when a
neutrino or ToO alert is received by an instrument, and when it starts the
follow up. It can range from seconds or minutes for gamma-ray experiments in
particular, to days for wide field instruments that require Earth rotation to
reach the required field of view in the sky. For spectrographs, the slew rate
is given in terms of typical time $t_{\rm slew}$ between the pointing of two
objects in the visible sky, as “obj. / $t_{\rm slew}$”. HAWC and LHAASO do not
have a response delay, as they do not point to particular directions of the
sky. They can follow up on any source that falls in the visible sky within a
24-hour rotation of the Earth, but their exposure depends on the zenith angle,
such that some short transients in some specific position of the sky might not
be detected. For survey-type instruments, transient detection probability also
crucially depends on survey speed or cadence (quoted in brakets for normal
survey mode), i.e., the mean time between visits to the same piece of sky.

####  4.3.3 Differential sensitivity limits

For high-energy experiments, the differential sensitivity limit quoted in
Table 2 corresponds to the minimum flux needed by an instrument to obtain a
5-standard-deviation detection (4$\sigma$ for XMM-Newton) of a point-like
source, for the indicated observation time, as available in the literature.
The relative scalings can differ of a factor of order unity between the
experiments, due to different energy binning, detection criteria and
calculation methods. For optical telescopes, a typical depth in magnitude over
the different bands, and for radio observatories, the sensitivity for a
characteristic frequency (e.g., the dipole resonance frequency) and bandwidth,
with the instrument in its best configuration, are quoted. For ASAS-SN and
ZTF, the sensitivity indicated is for dedicated ToO images with longer
exposure time compared to the normal survey.

####  4.3.4 Angular resolution

The best or typical (in the given energy range) angular resolutions at FWHM,
are indicated for each instrument. For the four listed optical spectrographs,
the angular size of the pixels has been referenced.

####  4.3.5 Follow-up programs

The final column gathers information on the neutrino follow-up programs of
these instruments. Most high-energy instruments have dedicated neutrino or
more generally ToO follow-up time. The indicated neutrino follow up rates (in
hours per year) should be taken with great caution, as these number change
every year in the internal proposal evaluation processes. Besides, the time
allocated to a certain program does not necessarily reflect how many
observations are actually being performed. Each collaboration has different
priorities and complementary ways of running follow-up programs. For example
H.E.S.S. aims at deep and long-term follow-ups of a few selected events while
MAGIC covers as many neutrinos as possible but with short exposures [298].

In the same column, in brakets, we also indicate the number or percentage of
neutrino alerts that have been followed up. The alerts are either published
GCN alerts by IceCube or ANTARES, or IceCube Gold alerts. The fraction of
followed alerts depends on the accessible sky and reflects the internal
strategies and cuts set by each program. For instance, thanks to the numerous
sites positioned around the globe, MASTER follows 99% of the published GCN
neutrino alerts. ASAS-SN, TAROT and ZTF follow most accessible IceCube
neutrino alerts, that are not behind the sun or below the horizon.
Interestingly, these do not represent a large fraction of the observing time
for these telescopes (< 5%). On the other hand, MWA prioritizes immediate
triggering rather than late follow up (if an alert is not issued in a portion
of sky that is not currently in the field of view of MWA, it will not follow
up later, once the Earth has rotated). Its large FoV however provides a
reasonable chance to get late-time follow-up “for free” enabling the array to
derive interesting constraints on the radio emissions in the direction of
ANTARES neutrinos [299]. Instruments such as Fermi-LAT and HAWC have a wide
FoV that enables one to get information about any position in the sky almost
continuously, resulting in almost 100% of followed alerts. Very recent or
planned instruments such as LHAASO, CTA or Rubin Observatory are elaborating
their follow-up programs, and the allocation times will be adjusted over the
next few years.

For some instruments which have only followed up a limited number of neutrino
alerts, we give in the same column (in italics) specific examples of sources
or events that were studied: TXS 0506+56 [300, 301, 302, 303], IC190331A
[304], SN PTF12csy [305], and few ANTARES events for VLA [306, 307]. VLT
spectrographs X-Shooter and FORS2 as well as GTC spectrograph OSIRIS have also
participated in the spectroscopy of a sample of blazars that are neutrino
source candidates [308]. For XMM-Newton, we also quote a few follow-up
examples. Its relatively slow slewing speed compared to Swift and the limits
on the solar panel orientation with respect to the Sun (which reduces
significantly all-sky visibility), make it not ideal for fast repointing on
ToOs. As a consequence, XMM-Newton has only a limited history of neutrino
follow ups, e.g., the “Kloppo” PeV IceCube event [309], or PKS 1502+106 [310,
311, 99, 100].

####  4.3.6 Timeline

On the left-hand side of the table is given a tentative timeline of the
experiments. The termination date of instruments marked with a fading gradient
corresponds to their current funding expiry date, but many of them have a good
probability of being prolonged beyond. Upgrades are foreseen for several of
these facilities or their follow-up programs and we have quoted the improved
numbers when available.

##  5 The future of multi-messenger astronomy: challenges and opportunities

The detection and identification of a neutrino transient source is expected to
be the next giant leap for the field of MM astronomy. This could be achieved
by the 2030s, thanks to theoretical and experimental progress.
Phenomenological models already enable us to assess the detectability of
sources, to optimize experimental design and direct the follow-up efforts of
steerable telescopes. Improvements on this aspect will come from the high-
cadence observations, which will help model the interaction backgrounds
responsible for neutrino production. More detailed constraints on source
content and structure require finer microscopic modeling with numerical
methods, that are being developed, with increasingly complete and self-
consistent codes. The main challenges are to account for the wide energy and
spatial scales at play, to accurately describe the time variabilities, and to
pin down the relevant source properties.

The observational prospects are promising: several HE neutrino observatories
are already in construction and should be in full operation by the beginning
of the 2030s, drastically improving the sensitivity to transients [312], and
with sub-degree pointing resolution for up-going muon neutrinos. At UHE, a
first generation of experiments with the sensitivity to detect the first UHE
neutrinos is planned to be fully deployed around 2025-2030. One may note that
current experiments such as ARA will remain competitive with this generation.
It is not expected that these instruments reach sub-degree angular resolution,
except for BEACON ($0.3^{\circ}-1^{\circ}$ resolution) and for the first sub-
array for the GRAND experiment (GRAND10k), corresponding to $1/20$th of the
full array, which will have few arcminute pointing accuracy. The next
generation, to be completed in the 2030s, will be better armed for neutrino
astronomy, thanks to an order-of-magnitude better sensitivities, to detect
(possibly stacked) short and longer transients, and with a handful of
experiments achieving sub-degree angular resolution. For several of these
instruments, technical challenges, in terms of air-shower reconstruction and
radio detection techniques, will have to be overcome for successful operation.
This will require experimental prototyping, cross-calibration between various
detection techniques, and common efforts in the community to understand the
signals emitted by air-showers arriving with non-standard geometries. On the
EM side, several wide-FoV instruments are planned for 2025 and beyond, with
great potential for serendipitous discoveries and excellent neutrino follow-up
capabilities, owing to shorter response times and fast slew or survey speeds.

In the future, with the improvement of EM and neutrino instruments, as well as
the development of MM networks, coincident detections and false positive
associations will become extremely common. To give a sense of the scale of the
problem in its current incarnation the Gold alert stream of IceCube transmits
neutrinos with a $\sim 50\%$ probability of being astrophysical. In addition,
within the angular uncertainty region of each individual muon neutrino it is
common to identify $\sim 10$ optical transients with the ZTF and several
Fermi-LAT identified sources e.g.[313]. The problem of random coincidences
will increase in proportion to the sensitivity increase of future survey and
follow up telescopes. In order to distinguish the most plausible associations,
theoretical vetoes –simple analytical criteria that can reject a possible
association, e.g. [26, 19, 168, 38] – could be implemented within alert
programs. From an observational point of view, narrowing down the search area
in the sky will require a precise reconstruction of the neutrino arrival
direction. As mentioned several times, sub-degree pointing will be naturally
achieved for a few UHE detectors in the 2030s. For cascade events in HE
neutrino telescopes, machine learning techniques are being explored to improve
the angular resolution [314, 315].

Machine learning and deep learning will take an important part in the search
for transient neutrino events, and more generally in transient multi-messenger
astronomy [316]. Techniques such as convolutional neural networks and graph
neural networks have recently attracted attention, due to their ability to
extract and treat spatial features in data [317, 318, 319, 320, 321, 322, 323,
324, 325]. These methods can be used for different purposes. For instance,
they can be used to improve source identification using multi-wavelength or MM
data [326, 327, 328]. Moreover, these techniques can serve to perform joint
analysis of MM signals, for instance by combining time series and images in
neural networks, to reconstruct the source properties [329]. Machine learning
is also used to increase the sensitivity of detectors and improve real time
searches [330], for instance by detecting GW signals earlier before the
compact object merger and thus improve alerts to perform multi-messenger
observations [331, 332]. To summarize, these techniques show promising
results, with improvements in the treatment of noisy data sets, signal
classification, and thus are promising for the reconstruction of neutrino
properties, the identification of neutrino point sources and coincident
detections.

Synergies and communication will be key to discoveries in the field of
transient MM astronomy: between theory and observations, and between the
different instruments.

## Acknowledgements

Many thanks to our numerous colleagues for providing detailed input on the
cited experiments, sometimes performing new calculations and discussing with
us about the relevant numbers to quote: Markus Ackermann, Jaime Alvarez Muñiz,
Carlos Arguelles, Jean Ballet, Didier Barret, Michel Boer, Sara Buson,
Mauricio Bustamante, Ken Chambers, Alexis Coleiro, Alan Coleman, Amy Connolly,
Frédéric Daigne, Cosmin Deaconu, Mathieu de Naurois, Krijn de Vries, Damien
Dornic, Christian Haack, Clancy James, Albrecht Karle, Mansi Kasliwal, Claudio
Kopper, Marianne Lemoine, Vladimir Lipunov, Olivier Martineau-Huynh, Miguel
Mostafa, Nepomuk Otte, Nahee Park, Luigi Piro, Simon Prunet, Elisa Resconi,
Andres Romero-Wolf, Marcos Santander, Makoto Sasaki, Lisa Schumacher, Fabian
Schüssler, Ben Shappee, Robert Stein, Olga Suvorova, John Tonry, Michael
Unger, Nick van Eindhoven, Aaron Vincent, Stephanie Wissel, Josh Wood, Yi
Zhang. We thank Alexis Coleiro, Shigeo Kimura and Fabian Schüssler for
insightful feedback that helped improve the manuscript.

C.G. is supported by the Neil Gehrels Prize Postdoctoral Fellowship. KK is
supported by the APACHE grant (ANR-16-CE31-0001) of the French Agence
Nationale de la Recherche.

## Author contributions

The authors contributed equally to all aspects of the article.

## Competing interests

The authors declare no competing interests.

Table 1: Indicative experimental characteristics of current and future
neutrino detectors targeting energies above (light blue band) and below (dark
blue band) $10\,$PeV. The left-hand side of the table indicates the timeline
of each instrument (green: current, yellow: up-coming, gray: under
construction). The following columns from left to right reference the minimum
neutrino energy, the peak energy where the differential sensitivity is best,
the differential sensitivity to diffuse neutrino flux [or measured flux or
measured upper limits in brackets], the instantaneous (iFoV) and daily
averaged (dFoV) fields of view in sky percentage and in square degrees in
brakets, and the angular resolution. The final column provides information on
alert programs set up or planned to be set up (in italics) by the instrument.
For instruments targeting $<10\,$PeV energies, the numbers in parenthesis are
for ‘cascade events’ (see text for definition), and the others for muon
tracks, unless otherwise indicated. Question marks indicate the yet unknown
values for up-coming experiments. References are given in the text. Table 2:
Indicative experimental characteristics of a non-exhaustive list of actual or
potential neutrino follow-up EM instruments. The left-hand side of the table
indicates the timeline of each instrument (green for current and yellow for
up-coming). Unclear termination dates are indicated with a fading gradient.
The following columns from left to right reference the band width
(characterized by either energy, wavelength or frequency range, depending on
conventions), the differential sensitivity limit (definition depends on the
type of instrument, see 4.3.3), the field of view (FoV), the angular
resolution, the slew speed and survey speed in brakets, the response delay to
a neutrino or ToO alert. The final column provides elements of the neutrino or
ToO follow up program of each facility, with a neutrino alert follow up rate
(“$\nu$ foll. rate", in hour/year) when available, percentage or number of
neutrinos followed in brakets, and specific followed source or event names in
italics. Question marks indicate the yet unknown values for up-coming
experiments. References are given in the text.

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