Modelling the Sensitivity of the
KM3NeT/ARCA and

KM3NeT/ORCA
to Neutrinos from Quiescent

Blazars

A Dissertation submitted to the Faculty of Science at the University
of the Witwatersrand, Johannesburg, in fulfillment of the

requirements for the degree of Master of Science in Physics.

By
Bhuti Nkosi

bhutilindankosi@outlook.com

Supervised by
Prof. Andrew Chen

Johannesburg, South Africa
December 2022



Declaration

I, Bhuti Nkosi, student number [1602018], declare that this Dissertation is my own,

unaided work. It is being submitted for the Degree of Master of Science in Physics

at the University of the Witwatersrand, Johannesburg. It has not been submitted

before for any degree or examination at any other University.

(Signature of candidate)

4th day of September 20 23 in Johannesburg

i



Abstract

Blazar jet emission has been modelled using two families of models, leptonic and

hadronic, to explain the double-peaked SED. In hadronic models, the higher energy

peak is explained by proton interactions with the jet material and external fields.

Lepto-hadronic models are a type of blazar emission model that accounts for both

leptonic and hadronic processes in the jet. In these models, the low-energy bump

of the spectral energy distribution SED is produced by synchrotron radiation from

primary electrons, while the high-energy bump is produced by a combination of

radiation from protons and secondary particles. Lepto-hadronic models can explain

the variability and spectral features of blazars in different states, such as flaring

or quiescent. In this project, we used a one-zone lepto-hadronic model to simulate

the blazar jet and calculate the neutrino emission and detection prospects with

KM3NeT.

ii



For Sifiso, he believed in me before I knew that I had potential. For Paul, who

ensured that potential is utilized by supporting me throughout. For everyone who

supported me throughout.

iii



Acknowledgements

The financial assistance of the National Research Foundation (NRF) towards this

research is hereby acknowledged, UID 145143. Opinions expressed and conclusions

arrived at, are those of the author and are not necessarily to be attributed to the

NRF.

I would like to acknowledge the National Institute for Theoretical and Computa-

tional Sciences (NITheCS) South Africa for also financially supporting this research.

I would like to acknowledge my supervisor, Prof. Andrew Chen for all the guidance

and advices. I would like to acknowledge the KM3NeT Collaborators for their

technical support and making this research possible.

iv



Contents

Declaration i

Abstract ii

Dedication iii

Acknowledgements iv

List of Figures vii

List of Tables ix

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Blazars, Neutrinos and KM3NeT 4

2.1 Blazars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Properties of blazars . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Relativistic Jets . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.3 Blazar jet modelling . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.4 Quiescent Blazars . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Invisible messengers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.3 Properties of neutrinos . . . . . . . . . . . . . . . . . . . . . . 12

2.3 A new window on our Universe . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

v



2.3.2 KM3NeT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.3 KM3NeT detection technology . . . . . . . . . . . . . . . . . . 15

3 A closer look: OneHaLe and CALCRATE 22

3.1 Blazar jet simulation using OneHaLe . . . . . . . . . . . . . . . . . . 22

3.1.1 Particle distribution evolution . . . . . . . . . . . . . . . . . . 23

3.1.2 Radiative evolution . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 CALCRATE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.1 Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.2 Discovery and Sensitivity . . . . . . . . . . . . . . . . . . . . . 33

4 Methodology 37

4.1 SED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 CALCRATE methods . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.2.1 Rates, sensitivity and discovery . . . . . . . . . . . . . . . . . 40

5 Results 43

5.1 Results of OneHaLe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.2 Results of CALCRATE . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2.1 Neutrino Sensitivity, Discovery and Rates . . . . . . . . . . . 45

6 Conclusion 50

6.1 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6.1.1 Some neutrino fluxes at the end of the tunnel . . . . . . . . . 51

6.2 Main findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

vi



List of Figures

2.1 Schematic illustration of the unified AGN model. [1] . . . . . . . . . 4

2.2 From left to right, the HESS [2] and VERITAS telescopes[3] . . . . . 5

2.3 Blazar jet composition and the particle interactions inside the jet.Image

from [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 DOM on the left, a DU in the middle and DOM being installed in

the sea by the KM3NeT Collaboration.[5] . . . . . . . . . . . . . . . . 15

2.5 Configuration of the ARCA and ORCA detectors. . . . . . . . . . . . 16

2.6 Visualization of the reconstructed tracks.[6] . . . . . . . . . . . . . . 18

2.7 Reconstruction of the track event from the PMTs.[6] . . . . . . . . . 19

4.1 An early fit of the 3C 279 SED using the ’fit-by-eye’ method ’ to 3C

279 archival data found on NED. . . . . . . . . . . . . . . . . . . . . 39

5.1 SED ’fitted-by-eye’ to 3C 279 archival data found on NED. Solid

line represents the total neutrino flux, and the dotted lines represent

neutrinos produced from the different neutrino processes. Some of

the input parameters are displayed. . . . . . . . . . . . . . . . . . . . 44

5.2 Neutrino fluxes corresponding to the SED in Figure 5.1. . . . . . . . . 44

5.3 Histogram showing MDP binned by effective energy and the viewing

angle. The bin centred at (4,5) has the optimized MDP and MRF,

the MDP is 644.50 and the MRF is 1649.24. . . . . . . . . . . . . . . 48

5.4 MRF and MDP for combined signal detected through the track and

shower channel. Effective energy and the cone viewing angle are set

to be at 1◦ and logE = 5 for track events. In shower events, the

effective energy and the cone viewing are set to be at 4◦ and logE = 5 48

vii



5.5 Signal and background rates, for the optimized MRF and MDP for

both shower and track events. Blue line is for the signal rates and

the orange line is for background rates. The above plots illustrate

that the source is background-dominated in all observable directions.

Apparent fluctuations in the background signal are due to changes

in the optimum energy threshold rather than intrinsic changes in the

background or instrument sensitivity. . . . . . . . . . . . . . . . . . . 49

viii



List of Tables

3.1 The functions g0 and g1 for νµ and νe . . . . . . . . . . . . . . . . . . 27

4.1 List of OneHaLe free parameters with units . . . . . . . . . . . . . . 38

4.2 Table showing the list of input options used for CALCRATE . . . . . 40

5.1 The optimized simulated discoveries and sensitivities for a νµ detected

using the track channel. . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.2 The optimized simulated discoveries and sensitivities for a νe detected

using the track channel. . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3 The optimized simulated discoveries and sensitivities for a νe detected

using the shower channel. . . . . . . . . . . . . . . . . . . . . . . . . 45

5.4 The optimized simulated discoveries and sensitivities for a νµ using

the shower channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.5 The optimized simulated discoveries and sensitivities for combined

νµ, νe using the track channel. . . . . . . . . . . . . . . . . . . . . . . 46

5.6 The optimized simulated discoveries and sensitivities for combined

νµ, νe using the shower channel. . . . . . . . . . . . . . . . . . . . . . 46

5.7 Simulated discoveries and sensitivities for combined νµ, νe through the

shower channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.1 Calculated upper flux limits and minimum flux needed for a discovery

in each channel. The results were calculated using Equation 3.37,

where Φ(E, θ) = 1.75368 × 10−12 ergs/cm2/s for energies 10 GeV to

108 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

ix



Chapter 1

Introduction

1.1 Motivation

The detection of a high-energy neutrino by the IceCube observatory in spatial and

time coincidence with a gamma-ray flare from the blazar TXS0506+056 in 2017

(event IceCube-170922A) was a breakthrough event in multi-messenger astronomy[7].

This event suggested a possible link between blazars and very high energy cosmic

rays, as both gamma-rays and neutrinos could be produced by the same process:

the acceleration of protons or heavier nuclei in the relativistic jets of supermassive

black holes (SMBH) and their subsequent interactions with photons or matter.

One of the most promising ways to study the blazar jet environments and their vari-

ability is to use neutrino astronomy. Neutrinos are neutral and weakly interacting

particles that can travel long distances without being affected by magnetic fields or

radiation [8]. This means that neutrino carries the information of the environment

in which they were made. Blazars are Active Galactic Nuclei (AGNs) with relativis-

tic jets oriented in our line of sight[9]. They have a double-peaked spectral energy

distribution (SED) that can be explained using two different types of models, the

hadronic models and the leptonic models. In both models the lower energy peak is

explained by electron synchrotron radiation. However, the higher energy peak can

be explained using processes such as inverse-Compton and pair production in the

case of leptonic models, but for hadronic models the higher energy peak is explained

in terms of proton synchrotron and other proton processes[9].

The hadronic models predict that blazars can produce high-energy neutrinos through

1



interactions of protons with photons or matter in the jet. These neutrinos can be

detected by telescopes, which uses a large volume of ice or water as a target for

neutrino interactions. By measuring the direction, energy and flavor of the neutrinos,

we can identify neutrino sources and test the hadronic model. On the other hand,

the leptonic models do not predict significant neutrino emission from blazars, as

electrons do not produce neutrinos directly. Therefore, neutrino detection from

non-flaring blazars can help to discriminate between the two models and constrain

the physical parameters of the blazar jets, such as magnetic field strength, jet power

and particle acceleration mechanisms.

1.2 Aim

The detection of neutrinos from blazars in non-flaring state is a challenging but

rewarding task for astrophysics. Non-flaring blazar flares are less luminous and

more difficult to detect and measure their spectra.

The goal of this project is to investigate the detectability of neutrinos from blazars

in quiescent state with the KM3NeT/ARCA. KM3NeT/ARCA is a large-scale un-

derwater neutrino telescope under construction in the Mediterranean Sea, which

will have a high sensitivity to neutrinos in the TeV-PeV range[10]. By using a

multi-messenger approach that combines multiwavelength electromagnetic data and

neutrino data, we aim to constrain the hadronic models of blazar emission and test

the hypothesis that blazars are neutrino accelerators.

1.3 Outline

The structure of this dissertation is as follows. Chapter 2 provides a comprehensive

overview of the theoretical framework that underpins this research, including the

relevant concepts and equations of relativistic astrophysics and high-energy physics.

Chapter 3 introduces the lepto-hadronic model that we adopted to explain the multi-

wavelength emission from blazars, and the software tool (CALCRATE, unpublished

tool from KM3NeT) that we used to perform numerical simulations and data anal-

ysis. Chapter 4 introduces the approach and methodology used in this research.

Chapter 5 presents the main results of this project, which include the spectral mod-

eling of several blazar sources, the parameter estimation and uncertainty analysis,

and the comparison with other models and observations. Chapter 6 discusses the

implications and limitations of our findings, and offers some suggestions for future

2



work in this field.

3



Chapter 2

Blazars, Neutrinos and KM3NeT

2.1 Blazars

Figure 2.1: Schematic illustration of the unified AGN model. [1]

Blazars are a fascinating and unique category of celestial objects that have captured

the attention of astronomers in recent decades. These objects are a subcategory of

AGN, which are galaxies that contain a central SMBH that emits significant amounts

of radiation. However, blazars are distinguished by their unusually strong emission

of high-energy gamma-ray radiation, which makes them some of the brightest ob-

jects in the sky. Blazars also exhibit other unusual characteristics that make them

4



particularly interesting. For example, they can vary significantly in brightness over

relatively short periods of time, sometimes fluctuating by factors of 10 or more in

just a few hours. This variability is not well understood.[11]

Blazars are also notable for their large redshifts, which indicate that they are located

very far away. This makes them important tools for cosmologists to study the

early universe, as the distant blazars allow us to look back in time and observe the

conditions of the host galaxy when the light we see was emitted. There are a number

of theories about how blazars form and what powers their intense radiation. Most

models suggest interactions inside the jet; only the radio emission has substantial

contribution from the intergalactic medium. [12]

The study of blazars is an active area of research in astronomy, with many telescopes

and observatories dedicated to observing and studying these fascinating objects. The

Fermi Gamma-Ray Space Telescope[13], for example, is a satellite-based observatory

that has been designed to search for blazars and other sources of high-energy gamma-

ray emissions. On the ground, telescopes like the Very Energetic Radiation Imaging

Telescope Array System (VERITAS)[3] and the High Energy Stereoscopic System

(HESS)[2] are also used to study the properties of blazars.[14]

Figure 2.2: From left to right, the HESS [2] and VERITAS telescopes[3]

Overall, blazars are some of the most intriguing and unique objects in the universe,

offering a valuable window into the early history of the cosmos and the physics of

extreme phenomena like black holes and relativistic particle jets.

2.1.1 Properties of blazars

Here are some of the properties of blazars:

� High Luminosity: One of the key properties of blazars is their high luminosity,

which can range from 1043 to 1047 erg/s in γ-rays. This is often attributed to

relativistic beaming of the jet material in our line of sight.[15]

5



� Jets: Blazars are also characterized by highly collimated and relativistic jets of

plasma, which are powered by the same black hole accretion process. These jets

can extend up to several millions of light-years in distance and emit radiation

across the electromagnetic spectrum.[16, 17]

� Variability: Blazars exhibit rapid and unpredictable variations in their bright-

ness levels, especially in the gamma-ray and X-ray bands. This variability is

thought to be linked to instabilities in the accretion disk and jet, as well as

to changes in the properties of the surrounding gas and dust[18]. It can also

be associated with changes in the viewing angle of the emitting region[19],

these changes in the viewing angles affects the apparent fluxes observed and

the variability time scales. This can be explain by using Doppler boosting.

� Polarization: Another unique property of blazars is the high degree of polar-

ization in their radiation, especially in the optical band. This is believed to

result from the intense magnetic fields that are generated by the jet plasma.[9]

Blazars are likely to be sources of multimessenger emission, which means they pro-

duce radiation across multiple wavelengths and also emit high-energy neutrinos (e.g.

TXS0506+056) and cosmic rays. This makes them important targets for astronomy

and astroparticle physics studies.[7, 17, 20]

2.1.2 Relativistic Jets

Figure 2.3: Blazar jet composition and the particle interactions inside the jet.Image
from [4]

Blazar spectra are dominated by non-thermal emission, with a double-peaked SED

with one in the lower energies (radio to soft X-ray) and one in the X-ray to gamma-

ray regime or higher energies. This highly variable gamma-ray emission makes

blazars a valuable tool in studying high-energy astrophysics.[21, 22, 23]

6



In addition to their high-energy emission, blazars have also been observed in other

bands of the electromagnetic spectrum, including radio, optical, and X-ray. These

observations have enabled the study of the structure and evolution of these objects

in detail and have provided important insights into the physics of active galactic

nuclei and the growth of supermassive black holes. Blazars can be classified using

two subcategories, BL Lacs (BL Lacertae objects) and FSRQ (flat-spectrum radio

quasars). However, they have distinct characteristics that differentiate them.

BL Lacs are characterized by their absence of defined emission lines in their optical

spectra, indicating a lack of hot material in their vicinity. This implies that BL Lacs

are almost ”naked” black holes, with little or no surrounding gas or dust. FSRQs,

on the other hand, have prominent spectral lines in their emissions, indicating the

presence of gas and dust in the vicinity of the central black hole. They peak in the

MeV-GeV range rather than the GeV-TeV range.[24]

In summary, BL Lacs are characterized by lack of prominent emission lines, while

FSRQs have clear spectral lines.[24]

2.1.3 Blazar jet modelling

Two competing types of models, leptonic and hadronic, are commonly used to ex-

plain the origin of the observed emission from blazars.

Leptonic models:

The leptonic models assume that the non-thermal radiation from blazars arises from

the acceleration and synchrotron emission of high-energy electrons in a relativistic

jet. The electrons lose energy through inverse Compton scattering with photons in

the jet, resulting in high-energy gamma-ray emission. This model can explain the

observed spectral energy distribution of blazars, which typically exhibits a peak in

the range of gamma-rays.[9, 25, 26, 12]

Hadronic models:

The hadronic models, on the other hand, assume that the non-thermal emission

is due to the interactions of high-energy protons in the jet. These protons interact

with photons or matter in the jet, producing charged pions that eventually decay into

gamma-rays. This model can explain the low-frequency radio emission observed in

some blazars, which cannot be easily explained by the leptonic model.[9, 25, 26, 12]

7



Both models have their strengths and weaknesses and have been applied to different

sources depending on the observed properties. However, a growing body of evidence

suggests that both mechanisms may be operating simultaneously, making it difficult

to distinguish between them [22, 9]. This is called the lepto-hadronic model. In these

models, it is assumed that both ultrarelativistic electrons and ultrarelativistic pro-

tons are present in the jet material and both contributes a similar (in theory) amount

to the fluxes. The presence of ultrarelativistic protons mean that the interactions

inside the jet include proton-induced electromagnetic (EM) cascades, neutral pion

decay, Bethe-Heitler (BH) pair production and proton synchrotron radiation[25].

The interaction of protons with the jet material and target photons can lead to

photopion interactions. Photopion interactions can happen in two basic channels:

(a) p+ γ → p+ π0

(b) p+ γ → n+ π+

which are equally probable. The neutrons can either escape the jet emission re-

gion or interact with the target photons leading to the following interactions, which

are also equally probable

(c) n+ γ → n+ π0

(d) n+ γ → n+ π−.

The neutrons can also decay into protons with a half-life of τ = 881.5± 1.5s

(e) n → p+ e− + ν̄e.

Following the photopion production, pion decay and muon decay can occur to pro-

duce neutrinos; these processes are defined by the following equations

(f) π± → µ± + νµ(ν̄µ) for pion decay

(g) µ± → e± + ν̄µ(νµ) + νe(ν̄e) for muon decay.

The electrons (positrons), muons, protons and pions (charged) can undergo syn-

chrotron radiation to produce γ-rays which will then escape the jet emission region.

Furthermore, the electrons can interact with positrons to create γ-rays. Neutral

8



pions will decay into γ-rays. BH pair production also increases the population of

electrons; the interaction process is given as follows:

(h) p+ γ → p′ + e+ + e−, where p′ is the proton in the lab frame.

Photons and neutrinos escape, with neutrinos having little to no interactions, hence

carrying the information about the environment in which they were created.[9, 25,

26, 12]

2.1.4 Quiescent Blazars

When a blazar is in a quiescent or non-flaring state, the blazar exhibits little to no

flares in fluxes over the period of observation[27]. A blazar would normally remain

in that state for an extended period of time that could go to up to years, then

suddenly have a huge increase in the flux that could be by factors of more than 100.

This sudden increase could go to time-scales of several years, 3.5 years in the case

of S5 1803+ 78 [28], from a time-scale of less than an hour, around 33 minutes in

the case of NRAO 530 [29]. This makes it hard to explain what causes blazar flares

due to varying time-scales. In the absence of neutrinos from a flaring blazar, both

leptonic and hadronic models can be used to explain the observed spectra. However,

if neutrinos coincides with the blazar flare spatially and in time, hadronic models are

favoured over the purely leptonic models. After the flare, the blazar could go back

to the initial non-flaring state or obtain a new non-flaring state. With everything

considered, explaining the flare becomes a troublesome task, since the two types of

blazar jet models used imply different blazar environmental conditions[22]. We then

need to constrain the types of models that could be used so that a blazar emission

mechanism can be fully understood.

Here is what makes observations of blazars in quiescent state very important:

� Blazars can remain in non-flaring state for a long time, which allows for longer

studies of a source.

� Observational data from non-flaring blazars can be used to characterize and

classify blazars.

� Some studies suggest that the flare could be due to external factors[30] and

others changes in the inter jet environment[31], so studying quiescent blazars

9



could help understand the environment surrounding the blazar.

Detection of neutrinos from blazars in quiescent state would suggest that blazars

fundamentally have substantial contribution from protons/neutrons even without a

flare. This would rule out the purely leptonic models when fitting observed spec-

tra, and use either lepto-hadronic models which are slightly dominated by leptonic

interactions over hadronic interactions or models which are dominated by hadronic

processes. Since neutrinos weakly interacts with matter, they are more likely to con-

tain information such as the energy and direction of the location where they were

created. We can use that information together with multi-messenger observations of

the same source to find the distance from the SMBH in which the jet was collimated

and the initial conditions in which neutrinos were made.

10



2.2 Invisible messengers

2.2.1 Introduction

Neutrinos are subatomic particles with no electrical charge and very low mass. These

ghostly particles are difficult to detect because they interact very weakly with matter,

which makes them travel through the universe almost completely unimpeded. First

proposed by Wolfgang Pauli in 1930[8], neutrinos were discovered in 1956 by Clyde

Cowan and Frederick Reines, for which they were awarded the 1995 Nobel Prize in

Physics. Since then, neutrinos have become the subject of intense research, not only

because of their elusive nature, but also because they offer valuable insights into the

properties of matter and the structure of the universe.

2.2.2 Neutrinos

Neutrinos are elementary particles. There are three types of neutrinos known as

electron neutrino, muon neutrino, and tau neutrino. According to the Standard

Model of particle physics, each type of neutrino is associated with a charged particle:

electron neutrinos are emitted during beta decay, muon neutrinos are produced when

muons decay, and tau neutrinos are generated when tau leptons decay. Neutrinos

have no electric charge and very little mass, which means they are almost as massless

as a photon[7]. In fact, neutrinos were long thought to be massless, but experiments

conducted in the late 1990s and early 2000s have shown that they do have mass,

albeit very small. These experiments also showed that neutrinos have the unique

property of oscillation, which means they can change from one type to another as

they travel through space[32].

Neutrinos are notoriously difficult to detect because of their feeble interactions with

matter. Neutrinos can pass through dense materials like lead, concrete, and even the

entire Earth with minimal disruption. However, when a neutrino does interact with

matter, it can produce a secondary particle that can be detected. There are several

methods used to detect neutrinos, such as the Cherenkov radiation, scintillation,

and liquid argon detectors. The Cherenkov radiation method involves measuring

the flashes of light produced when a neutrino interacts with water or ice, and the

charged particles produced by the neutrino interactions travel faster than the speed

of light in the medium[33]. The scintillation method uses materials like organic liquid

scintillators, which emit photons when a neutrino interacts with it. The liquid argon

detector uses liquid argon as the detection medium that uses the ionization energy

11



by the neutrinos to produce a signal.[14]

Neutrinos have played a significant role in astrophysics and particle physics. Neutri-

nos have been detected from several natural sources, such as the Sun[34], supernovae,

and AGN, with prospects of detection in gamma-ray bursts[35]. These detections

provide insights into the stellar phenomena, nuclear reactions, and the evolution

of the universe itself. Neutrinos have also contributed to our understanding of the

structure of matter. In 1983, the discovery of the W and Z bosons at CERN’s

proton-antiproton collider, made possible through the indirect detection of neutri-

nos using momentum conservation, confirmed the electroweak theory that unified

the electromagnetic and weak forces[36]. The discovery of neutrino oscillation in

1998 demonstrates that neutrinos have mass and that the Standard Model must be

extended to explain their behavior[37].

2.2.3 Properties of neutrinos

The properties of neutrinos can be summarized as follows[38]

� Neutrinos have very little mass: Neutrinos are one of the lightest known parti-

cles in the universe. Their mass is on the order of 10−35 kg, which is less than

a millionth of the mass of an electron.

� Neutrinos are electrically neutral: Unlike protons, electrons, and other par-

ticles that have electric charge, neutrinos are electrically neutral. They do

not interact with electromagnetic forces and cannot be deflected by magnetic

fields.

� Neutrinos are able to travel great distances: Neutrinos are able to travel

through matter with very little interaction, making them able to travel great

distances through space. This allows them to be detected from sources many

light-years away.

� Neutrinos have three different types or flavors: Neutrinos come in three differ-

ent flavors: electron neutrinos, muon neutrinos, and tau neutrinos. They can

change from one flavor to another, a phenomenon known as neutrino oscilla-

tion.

� Neutrinos are extremely abundant: Neutrinos are one of the most abundant

particles in the universe. It is estimated that more than a trillion neutrinos

12



pass through a human body every second.

� Neutrinos are produced in a variety of astrophysical processes: Neutrinos are

produced in many astrophysical processes, such as nuclear reactions in stars,

supernova explosions, and black hole accretion disks.

� Neutrinos may have played a role in the evolution of the universe: Neutrinos

may have played an important role in the evolution of the universe, helping to

drive processes such as nucleosynthesis and even the formation of galaxies.

Neutrinos are an essential particle in particle physics and astrophysics. Their prop-

erties of small mass, zero electric charge, and weak interactions with matter make

them challenging to detect, but their detection has contributed significantly to our

understanding of the universe’s structure and the behavior of matter. [39]

13



2.3 A new window on our Universe

2.3.1 Introduction

Neutrino astronomy is an emerging field of study that aims to detect and observe

neutrinos emitted by astrophysical sources in space. These include supernovae,

gamma-ray bursts, and black holes, among others. In recent years, numerous neu-

trino observatories have been established around the world to study these elusive par-

ticles, including the IceCube observatory in Antarctica and the Super-Kamiokande

observatory in Japan[14, 40]. However, none of these facilities can match the angular

resolution of the KM3NeT[41] underwater neutrino observatory, which promises to

revolutionize the field of neutrino astronomy alongside IceCube-Gen2[42].

2.3.2 KM3NeT

KM3NeT (Kilometer Cube Neutrino Telescope) is a multi-national research consor-

tium that aims to construct a kilometers-scale neutrino detector of unprecedented

sensitivity for the study of astrophysical neutrino sources. The observatory will be

built at the bottom of the Mediterranean Sea, at depths ranging from 2 to 4 km.

The KM3NeT has two main detectors, namely: ARCA and ORCA. ARCA is an

acronym for Astroparticle Research with Cosmics in the Abyss and ORCA is an

acronym for Oscillation Research with Cosmics in the Abyss. The detection units

of the ARCA telescope will be anchored at a depth of about 3500 m and ORCA

around 2500 m.[41, 43, 10]

The main scientific objectives of the KM3NeT project are to[41]:

� Study the sources and properties of cosmic neutrinos with energies up to several

PeV.

� Search for new and exotic astrophysical phenomena, such as dark matter,

magnetic monopoles, and cosmic rays.

� Study the properties of neutrinos themselves, including their mass, mixing,

and oscillation patterns.

The KM3NeT observatory is expected to have a profound impact on the field of

neutrino astronomy and astrophysics. The ability to detect and study high-energy

neutrinos with unprecedented sensitivity will allow exploration of the properties and

14



sources of these elusive particles and advance our understanding of the universe. The

observatory will also serve as a platform for testing and advancing the technology

and techniques used in the detection of neutrinos, paving the way for future inno-

vations in the field. By advancing our understanding of neutrinos and their sources,

KM3NeT will make significant contributions to the fields of astrophysics, particle

physics, and cosmology.

2.3.3 KM3NeT detection technology

Figure 2.4: DOM on the left, a DU in the middle and DOM being installed in the
sea by the KM3NeT Collaboration.[5]

The ARCA and ORCA telescopes consist of vertical strings of light sensors, called

detection units (DUs), that are anchored to the seabed and connected to shore

stations by cables. Each DU has 18 digital optical modules (DOMs) that contain

31 photo-multiplier tubes (PMTs) each. The PMTs amplify and record the faint

flashes of Cherenkov light that are emitted by charged particles produced in neutrino

interactions with the water molecules.[5]

The ARCA telescope will have two detector blocks, each consisting of 115 vertical

detection units (in total 230 DUs) that are about 700 m high and equipped with

light sensor modules, see Figure 2.5. These modules will detect the faint Cherenkov

light produced by the charged particles from neutrino interactions inside or near the

telescope. The ARCA telescope will use its high angular resolution to study the

cosmic neutrino flux and its properties, such as origin, energy spectrum and flavour

composition. The ARCA telescope will also map 87% of the sky, including most of

the Galaxy and the Galactic Center, where some unexplained phenomena have been

observed by other astroparticle detectors. The low scattering of the sea water will

allow precise measurement of the neutrino direction, which is crucial for identifying

15



Figure 2.5: Configuration of the ARCA and ORCA detectors.

the sources of these elusive particles[43], as well as confirming previously discovered

sources including NGC1068[44] and TXS0506+056[7].

The ORCA detector uses the high flux of atmospheric neutrinos, which are created

by cosmic rays interacting with the Earth’s atmosphere, to probe the fundamental

properties of these elusive particles. One of the main goals of ORCA is to determine

the neutrino mass hierarchy, which is the unknown ordering of the three neutrino

mass eigenstates. This can be done by studying how neutrinos change their flavour

as they travel through matter, a phenomenon known as neutrino oscillation. The

neutrino mass hierarchy affects the oscillation patterns of different neutrino flavours

as a function of their energy and path length through the Earth. By measuring

these patterns with high precision, ORCA can reveal the nature of the neutrino

mass spectrum.[45]

Event reconstruction

The reconstruction of neutrino events in KM3NeT involves several steps. The first

step is to identify the hits or signals produced by the PMTs in each optical module.

This is done by applying suitable filters that remove noise and other spurious signals.

Then, the time and charge information for each hit is recorded and sent to a central

data processing unit (DPU), where the event reconstruction takes place.

The goal of the event reconstruction algorithms is to infer the neutrino’s path and

16



energy from the hits recorded by all the optical modules that were activated by the

same neutrino interaction. This is a challenging task because the number of hits can

be very large and the neutrino energy is not known beforehand. Some of the most

commonly used algorithms include the likelihood fit method. These algorithms take

into account various factors such as the arrival time of the neutrino, the direction

and length of the muon track (if a muon was produced), and the spatial distribution

of the hits in the detector. Shower events are reconstructed using the energy of the

shower and the angular size of the shower.

Once the event reconstruction is complete, the resulting data is analyzed and com-

pared with theoretical models to extract useful information about the properties of

neutrinos and their sources. This information can help us better understand the

mysteries of the universe and the nature of the fundamental particles that make it

up.

Cherenkov radiation

A type of electromagnetic radiation called Cherenkov radiation is emitted when a

medium is traversed by a charged particle that moves faster than the speed of light

in that medium. The radiation forms a shockwave in the shape of a cone along

the path of the particle. The color and brightness of the radiation are determined

by the particle’s energy and speed, as well as the medium’s refractive index. In

nuclear reactors, Cherenkov radiation causes a blue glow in the water around the

fuel rods. Cherenkov radiation has various applications, such as detecting high-

energy particles, studying the characteristics of cosmic rays, and imaging biological

tissues.[33]

When a charged particle (such as an electron) travels faster than light in a certain

medium (such as water) with a refractive index n, the atoms in the medium get

disturbed and release photons in a form of a shock wave of visible light. This

light is usually blue because the photons released have high frequencies and short

wavelengths. The angle θC between the direction of the particle and the direction

of the photon emission depends on n and the speed of the particle v, and it can be

calculated by

cos θC =
1

βn
(2.1)

where β = v/c and c is the speed of light in vacuum. The number of Cherenkov

photons N that a particle with charge Ze emits per unit wavelength interval dλ and

17



per unit distance travelled dx, is given by:

d2N

dxdλ
=

2παz2

λ2

(
1− 1

β2n2(λ)

)
(2.2)

where λ is the wavelength of the photon and α is the fine structure constant. In

water, which is transparent from 300 nm to 600 nm in wavelength, this results in a

blue or violet glow that can be seen in some nuclear reactors. Cherenkov radiation

is used to detect high-energy charged particles and cosmic rays or gamma rays.

Track reconstruction

Figure 2.6: Visualization of the reconstructed tracks.[6]

We consider muons with energies above Eµ ≳ 100 GeV that can pass through the

detectors, since the atmospheric muon fluxes are low at those energies. The effects of

multiple scattering and finite energy on the muon trajectory and velocity are small

enough to be neglected. The muon position at a given time t0 is denoted by

P⃗ ≡ (px, py, pz)

and its normalized direction is given by

d⃗ ≡ (dx, dy, dz)

, which can be written in terms of the polar and azimuthal angles θ and ϕ as

d⃗ ≡ (sin θ cosϕ, sin θ sinϕ, cos θ).

18



The goal of the reconstruction algorithm is to estimate the five parameters px, py, pz, θ, ϕ

and a quality parameter for the quality of the track fit that can be used to discard

events with poor reconstruction. The muon energy is not directly calculated by any

algorithm, but for the analysis on point-like sources, the number of selected hits is

used as a proxy for the energy. A key quantity used in the reconstruction is the

so-called ”time residual”, which is the difference between the actual hit time ti and

the expected time of arrival tth of the photon on the PMT. The time residual is com-

puted assuming that the event starts at a time t0, the muon follows a straight line

with speed c and the Cherenkov light is produced at a Cherenkov angle θC ∼ 42◦

relative to the muon direction with a speed c/n, where n is the refractive index

in the medium (n ∼ 1.35) Figure 2.7 illustrates the track description used in the

reconstruction. Let v⃗ be the vector from the point P⃗ to the hit position Q⃗i, i.e.

Figure 2.7: Reconstruction of the track event from the PMTs.[6]

v⃗ = Q⃗i − P⃗ , where a photon reaches a PMT. We can decompose v⃗ into two compo-

nents: l, which is the projection of v⃗ onto the muon direction d⃗, and k, which is the

length of the vector perpendicular to d⃗. Then we have l = v⃗ · d⃗ and k =
√
|v⃗|2 − l2.

The photon is emitted at a point P⃗e along the muon track, such that

−→
Pe = l − k

tan θC
(2.3)

where θC is the Cherenkov angle. The photon travels a distance of

b =
k

sin θC
(2.4)

to reach the PMT. The theoretical arrival time of the photon at Q⃗i is then

tth = t0 +
1

c

(
l − k

tan θC

)
+

n

c

(
k

sin θC

)
(2.5)

19



where t0 is the time of emission of the muon, c is the speed of light in vacuum and

n is the refractive index of water. Given the measured time ti and position Q⃗i of

each hit, we can define the time residual ri = ti − tthi , which depends only on P⃗

and d⃗. Another relevant quantity is the expected angle of incidence θi of the photon

on the PMT, which is the angle between the photon direction and the normalised

direction, w⃗, of the PMT axis. Assuming that the photon is emitted at θC , setting

s⃗ =
[
v⃗ − d⃗

(
l − k

tan θC

)]
we can compute cos θi as

cos θi =
1

|s|
(s⃗ · w⃗) (2.6)

using the above equation we can then find θi which is the direction from which the

signal originates. Combining signals from multiple points along the muon track, the

muon track direction can then be determined.

Background sources

One of the challenges of detecting neutrino signals is to reduce the background noise

from other sources of radiation. There are three main optical background sources,

bioluminescence,40K decay, and atmospheric muons/neutrinos. Bioluminescence is

the emission of light by living organisms in the deep sea, which can interfere with the

detection of faint scintillation signals from neutrino interactions[46]. 40K decay is

the radioactive decay of potassium-40, a naturally occurring isotope that is present

in seawater and in some materials used to construct the detector. Atmospheric

muons/neutrinos are high-energy particles that are produced by cosmic rays hitting

the upper atmosphere and can penetrate deep into the ocean, mimicking cosmic

signals or creating secondary particles that can trigger the detector. These optical

background sources pose a significant challenge for KM3NeT and require careful

analysis and mitigation strategies.[47, 5, 43]

One of the ways to reduce the background noise from bioluminescence is to use a

time-coincidence technique, which requires that two or more optical modules detect

a signal within a short time window to be considered as a valid event. This re-

duces the chance of false positives from single flashes of light that are not related

to neutrino interactions. Another way to reduce the background noise from 40K

decay is to use a pulse-shape discrimination technique, which exploits the difference

in the shape of the scintillation signals from 40K decay and neutrino interactions.

The signals from 40K decay have a faster rise and fall time than the signals from

20



neutrino interactions, which allows them to be distinguished and rejected by apply-

ing a threshold on the pulse-shape parameter. Finally, one of the ways to reduce

the background noise from atmospheric muons/neutrinos is to use a directional re-

construction technique, which uses the information from multiple optical modules

to determine the direction of the incoming particle. This allows them to discrimi-

nate between upward-going neutrinos that originate from astrophysical sources and

downward-going muons/neutrinos that originate from cosmic rays. We are also left

with upward-going atmospheric neutrinos.[47, 5, 43]

21



Chapter 3

A closer look: OneHaLe and

CALCRATE

In this chapter, we present a simulation study of neutrino detection from a blazar

with the KM3NeT telescope. We used a time-dependent lepto-hadronic model,

called OneHaLe[25], to generate neutrino fluxes from a representative source, 3C279,

whose multiwavelength spectral data was obtained from the NASA Extragalactic

Database (NED)[48]. We then applied CALCRATE, a tool that computes expected

rates, sensitivities and discovery potentials for neutrino telescopes, using detector

response functions and fluxes as inputs. This simulation allowed us to estimate the

performance of KM3NeT in detecting neutrino events from 3C279 and other similar

sources.

3.1 Blazar jet simulation using OneHaLe

In this section, we present OneHaLe, a code developed by M. Zacharias that is

described in detail in [25],[26] and [12]. Here, we only give a brief overview of

the main features and assumptions of OneHaLe, as a detailed discussion is beyond

the scope of this study. OneHaLe assumes that protons and electrons/positrons

originate from the same location and are accelerated by a uniform magnetic field

co-moving with the jet. The primary particles then interact with the magnetic field

and external photon fields to produce secondary particles, such as e±, µ±, π±, π0,

photons and ν. The electrons and protons do not interact with each other in the

emission region.

22



We then discuss the key assumptions and calculations involved in OneHaLe, in-

cluding the geometry, the bulk flow of particles and fields (radiation and magnetic

fields), and the particle distributions after the interactions with external photon

fields, synchrotron photon fields and magnetic fields are solved using the Fokker-

Planck equation. We adopt the cosmology with Ωm = 0.3, ΩΛ = 0.7 and H0 = 70

km.s−1.Mpc−1.

3.1.1 Particle distribution evolution

A spherical region with a radius R and a distance z0 = 6GM0/c
2 from a SMBH

with mass M0 emits protons and electrons. The region moves with a constant bulk

Lorentz factor Γ and an angle θobs relative to the observer’s line of sight. The Doppler

factor can be expressed as,

δ =
1

Γ (1− βΓ cos θobs)
(3.1)

where βΓ =
√
1− Γ−1. The particles interact with both external and internal radi-

ation fields and magnetic fields with strength B.

The Fokker-Planck equations for protons, electrons, pions and muons describe how

the particle distribution changes with time t. The Fokker-Planck equation is

∂ni(χ, t)

∂t
=

∂

∂χ

[
χ2

(a+ 2)tacc

∂ni(χ, t)

∂χ

]
− ∂

∂χ
(χ̇ini(χ, t))+Qi(χ)−

ni(χ, t)

tesc
− ni(χ, t)

γt∗i,decay
(3.2)

where χ = γβ is the normalized momentum. Subscript i represents the particle

species mentioned above. The particle density is ni, a ratio of the shock to Alfvèn

speed, tacc(t) = ηacctesc(t) is the time-scale for energy-independent re-acceleration of

particles in the acceleration zone, momentum gain and loss rate is given by χ̇i =

|χ̇i,loss| − χ̇acc where the acceleration rate is parametrized as,

χ̇acc =
χ

tacc
(3.3)

t∗i,decay is the decay time-scale of the unstable particles in their rest frame and tesc(t) =

ηescR(t)/c is the time-scale in which a particle escapes the emission region. Qi(χ) is

the particle injection rate.

OneHaLe considers a scenario where electrons and protons are injected with a power

law spectrum in a region of size R as primary particles. These particles are pre-

23



accelerated and interact with various fields, such as magnetic fields and external

photon fields. These interactions produce secondary particles. The injection rate of

the secondary particles depends on the process that created them. We can write the

primary injection rate as

Qi(γ) = Qi,0γ
−qiH(γ; γmin, γmax) = Qi,0χ

−qiH(χ;χmin, χmax) = Qi(χ) (3.4)

where γ is the Lorentz factor of the particle, qi is the spectral index, and H is the

Heaviside function defined by

H(χ;χmin, χmax) = H(γ; γmin, γmax) =

1, if γmin ≤ γ ≤ γmax

0, otherwise

The normalization constants Qp,0 and Qe,0 are determined by the injection lumi-

nosity of protons and electrons (Lp,inj and Le,inj), the total energy density, and the

Eddington luminosity, LEdd. See Zacharias[25]

The sources of photons in the AGN jet are synchrotron radiation of electrons and pro-

tons, and the primary particles interacting with the fields present in the jet. Protons

interact with the internal and external radiation to produce secondary particles, such

as muons, pions, electrons and photons. Secondary electrons are created by Bethe-

Heitler pair production (BH pair production), when a photon and a proton collide.

The photons are created by synchrotron radiation of the secondary electrons and

protons, and inverse Compton processes such as Synchrotron Self-Compton (SSC).

The charged pions decay into muons, which then decay into neutrinos, while the

neutral pions decay into two photons.

Evolution of protons

The target fields in the jet environment cause protons to lose their momentum as

they interact with them. The magnetic fields also affect the protons via synchrotron

cooling. The magnetic density is given by uB = B2/8π. The protons can also

interact with radiation fields via BH pair production and pion production. Another

way that protons lose their momentum is through the adiabatic process. Since we

are studying blazars in quiescent state, the adiabatic processes contribution are not

that significant. The terms for the momentum loss rates, χ̇p,loss or − χ̇p,loss, are as

follows[25]:

24



−χ̇p,syn =
4cσT

3mec2
uB

(
me

mp

)3

χ2 (3.5)

for synchrotron cooling,

−χ̇p,adi =
3c tan(η0/Γ)

R

(
γ − γ−1

)
(3.6)

for adiabatic cooling,

−χ̇p,BH = αSr
2
ec
me

mp

∫ ∞

2

dκnph(
κ

2γ
)
Φ(κ)

κ2
(3.7)

for BH pair production where αS ≈ 1/137 is the fine structure constant, κ = 2γϵ

with ϵ = Eph/mec
2 is the normalized photon energy and re is the classical electron

radius, η0 is the jet opening angle (in radians), Γ is the bulk Lorentz factor and R

is the distance from the central engine. The term for pion production is given in

[12]. The total number of protons at any point is assumed to be not greater than

the initial number of protons injected into the jet since there was no explicit consid-

eration of neutrons, meaning that there are no interactions which convert protons

into neutrons, and vice versa, so that is not considered in the model. Equation 3.2

is then solved.

Pions

Pions are the product of the photo-pion production processes, and they lose mo-

mentum via adiabatic and synchrotron cooling. To simplify the calculation of the

cross-section for single pion production processes induced by neutrinos, the interac-

tion channels (ITs) are divided into three categories. It is assumed that pions lose

momentum through adiabatic and synchrotron cooling. The energy of each pion

flavor i is given by Eπi =
√
χ2 + 1mπic2, where mπi is the mass of the pion and χ is

a dimensionless parameter. The injection rate of pions from all ITs is then given by

Qπi = mπic2
∑
IT

np(
Eπi

ϵIT
)
mpc

2

Eπi

∫ ∞

ϵth/2

dy nph(
mpc

2yϵIT

Eπi

)M IT
πi f IT (y) (3.8)

where np is the proton distribution at the pion energy per each fraction of the mean

energy ϵIT at each daughter particle for each IT, nph is the photon distribution, mp is

25



the proton mass, ϵ = hv/mec
2 is the normalized photon energy, y =

√
χ2
p + 1 ϵ is the

integrating variable, χp is another dimensionless parameter, M IT
πi is the multiplicity

of pion production for each IT, and f IT (y) is a function that depends on the IT.

Neutral pions have a very short lifetime of t∗π0,decay = 2.8× 10−17s and they quickly

decay into gamma rays. Charged pions, on the other hand, have a longer lifetime

of tπi,decay = 2.6 × 10−8s before they decay into muons and neutrinos. During this

time, the pions can interact with the magnetic field and the expanding jet and

lose momentum through synchrotron cooling and adiabatic process. The rate of

momentum loss due to synchrotron cooling is proportional to the magnetic energy

density uB and the square of the pion momentum χ, as shown by

−χ̇πi,syn =
4cσT

3mec2
uB(

me

mπi

)3χ2 (3.9)

where c is the speed of light, σT is the Thompson cross section, me is the electron

mass and mπi is the charged pion mass. The rate of momentum loss due to adiabatic

process is proportional to the jet expansion speed and the Lorentz factor γ, as shown

by

−χ̇πi,adi =
3c tan(η0/Γ)

R
(γ − γ−1) (3.10)

where η0 is the jet opening angle (in radians), Γ is the bulk Lorentz factor and R

is the distance from the central engine. The equation of motion for pions can be

obtained by combining these two terms.

Muons

We can write the particle injection term for muons as

Qµi =
nπi

γt∗π±,decay

. (3.11)

where nπ± is the number density of pions and t∗π±,decay is their decay time. Muons

are produced by pion decay and have a lifetime of t∗µ±,decay = 2.2 × 10−6s. They

then decay into electrons, positrons and neutrinos. Muons lose momentum due to

synchrotron and adiabatic processes. The rate of synchrotron cooling is

−χ̇µ±,syn =
4cσT

3mec2
uB(

me

mµ±
)3χ2 (3.12)

where c is the speed of light, σT is the Thomson cross section, me is the electron

mass, mµ± is the muon mass, uB is the magnetic energy density and χ is the Lorentz

26



Function νµ νe
g0(y) 5/3− 3y2 + 4y3/3 2− 6y2 + 4y3

g1(y) 1/3− 3y2 + 8y3/3 −2 + 12y − 18y2 + 8y3

Table 3.1: The functions g0 and g1 for νµ and νe

factor. The rate of adiabatic cooling is

−χ̇µ±,adi =
3c tan(η0/Γ)

R
(γ − γ−1). (3.13)

We can solve equation 3.2 for muons using these rates.

Neutrinos

Muon neutrinos are created from pion decay. Electron neutrinos and muon neutrinos

are created from muon decay processes. Due to neutrino oscillations, the distribution

of the flavours is equal in the observer’s frame. The production rate from pion decay

for muon neutrinos is given by

Qπ
νµ(Eνµ) =

1

mµc2

∫ ∞

Eνµ

mπc2(1−rM )

dγµ
γπ

Qµ±(γµ)

1− rM
(3.14)

with rM = (mµ/mπ)
2.

From muon decay, the production rate of muon neutrinos and electron neutrinos is

given by

Qµ
ν± =

1

mµc2

∫ 1

0

dy
Qµ

e (Eνi/y)

y

dn

dy
(3.15)

where y = Eνi/Eµ and Qµ
e = n′

µi(χ)/(γt′µi,decay), with primed reference frame being

in the laboratory frame. The neutrino production rate in the lab frame is given by

dn

dy
≈ g0(y) + g1(y) (3.16)

where g0 and g1 are functions summarized in Table 3.1. Neutrino power in the

observer’s frame is assumed to be equally distributed across the flavours due to

neutrino oscillations with the antineutrinos and neutrinos not distinguished.

27



Evolution of electrons

Primary electrons are injected using Equation 3.4, then lose momentum due to syn-

chrotron, adiabatic and inverse-Compton. Unlike protons, electrons are also created

from secondary processes such as BH pair production, γ − γ pair production and

muon decay. Secondary electrons also lose momentum from the processes mentioned

above for primary electrons. Electrons are stable particles so the decay term from

Equation 3.2 will be 0. Fokker-Planck for electrons is then solved.

3.1.2 Radiative evolution

This section provides a summary of how we handle the radiation terms in OneHaLe.

We use the radiative transfer equation (RTE) to compute the photon distribution at

equilibrium. The RTE is a differential equation that describes the change of radiance

(L) along a ray of light in a medium. The radiance is the energy flow per unit area

per unit solid angle per unit time. The RTE can be written as

∂nph(v, t)

∂t
=

4π

hv
jv(t)− nph(v, t)

(
1

tesc,ph
+

1

tabs

)
(3.17)

where jv is the emissivity for all radiation processes, tesc,ph is the photon escape

time-scale from a slice of size ∆z, tabs is the absorption time-scale due to synchrotron

self-absorption and pair production. The spectral luminosity in the observer’s frame

is then obtained by

vobsLobs
vobs = δ3

hv2Vco

tesc,ph
nph(v, t) (3.18)

where nph is the photon number density, Vco is the co-moving volume, and δ is the

Doppler boost. The absorption time scale is given by

tabs =
∆z

c (τSSA(v) + τγγ(ϵ))
(3.19)

where τSSA and τγγ are the opacities for synchrotron self-absorption and pair pro-

duction, respectively. We evaluate the emissivity from various radiation processes

such as synchrotron, inverse Compton with external photons, neutral pion decay,

28



inverse-Compton from isotropic photon fields and synchrotron self-Compton using

the equations given in [12].

External photons

The AD, the BLR, the DT and the CMB are four sources of external photons that

can interact with the jet of a blazar. We assume that the jet is powered by a fraction

of the accretion power onto a supermassive black hole, so that L̂AD = leddLedd, where

Ledd is the Eddington luminosity and ledd is the Eddington ratio. The Eddington

luminosity depends on the mass of the black hole M0, the proton mass mp, the speed

of light c, and the Thomson cross-section σT , as Ledd = 4πGM0mpc/σT . We adopt

a thin-disc model for the AD, which extends from the innermost stable orbit to a

maximum radius where the disc becomes unstable due to self-gravity. This radius

is given by

R̂AD,max = 1680Rg

(
M0

109M⊙

)−2/9

α2/9l
4/9
edd

(
ξ

0.1

)−4/9

cm (3.20)

where α is the disc viscosity parameter, and ξ is the mass-to-radiation conversion

efficiency. The temperature of the AD as a function of its radius r̂AD is given by

T̂AD(r̂AD) =

(
3GM0L̂AD

8πξc2σT r̂3AD

)1/4

. (3.21)

A grey body radiator is used to model the BLR and DT, which are imperfect radi-

ators that partially absorb and emit incident electromagnetic radiation. The tem-

perature of the BLR and DT is denoted by T̂BLR and T̂DT , respectively. The radius

of each radiator is given by the following equations:

R̂DT = 2.5× 1018
(

leddLedd

1045erg s−1

)1/2

cm (3.22)

R̂BLR = 1017
(

leddLedd

1045erg s−1

)1/2

cm (3.23)

where ledd is the Eddington ratio and Ledd is the Eddington luminosity. The lumi-

nosity of each radiator in the galaxy frame, assuming isotropy, is calculated as a

function of the distance z from the galaxy, as follows:

L̂BLR =
0.1leddLedd

(1 + z/R̂BLR)3
(3.24)

29



L̂DT =
0.1leddLedd

(1 + z/R̂DT )4
(3.25)

OneHaLe is a code that takes some input parameters and outputs the spectral fluxes

for all particles and fields in the observer’s frame. It also outputs other properties

that are not relevant for our purpose, such as light curves. The input parameters

for OneHaLe are listed in Table 4.1.

3.2 CALCRATE

CALCRATE is a software tool developed for KM3NeT. It allows users to estimate

neutrino and background rates, as well as discovery potential and sensitivity, for

different types of neutrino sources. It employs a cut-and-count method, where the

rates, discoveries and sensitivities are computed for various combinations of energy

and angular cuts. It can handle both point-like and diffuse neutrino sources, and ac-

counts for the background from atmospheric muons and neutrinos, bioluminescence

and K40-decay. The signal and background rates are used to evaluate the sensitivity

and discovery criteria based on statistical methods.

3.2.1 Rates

In general the neutrino rates are calculated using

Rate(E, θ) =

∫ ∫ ∫
Aeff (E

′, cos θ′)F (E ′)D(E ′, E, cos θ)P (E ′, cos θ′, cos θ)dE ′dΩ′dt

(3.26)

To predict the neutrino rate in each energy bin, one needs to account for the de-

tection efficiency of the instrument and the selection criteria applied to the data.

The instrument response function (IRF) is used to calculate the effective area of

detection, Aeff (E
′, cos θ′), which depends on the energy and direction of the incom-

ing neutrinos. This is multiplied by the neutrino flux, F (E ′), which is the intensity

of neutrinos per unit area and energy. Then, it is multiplied by ∆E, which is the

width of each energy bin, and T , which is the duration of the observation of the

neutrinos and the angular bin size Iθ = 2π · [cos(θmax)− cos(θmin)], where θmax and

θmin are the maximum and minimum angle of generation. Finally, it is multiplied

by D(E ′, E, cos θ) and P (E ′, cos θ′, cos θ), which are correction factors that account

for the energy dispersion and point spread function of the detector. The resulting

30



expression for the neutrino rate is

Rate(E, θ) = T
∑
E′

∑
cos θ′

Aeff (E
′, cos θ′)∗F (E ′)∗∆E∗D(E ′, E, cos θ)∗P (E ′, cos θ′, cos θ)∗Iθ

(3.27)

Background rate estimates used are from atmospheric muons and neutrinos using

Monte Carlo simulations.

Instrument response function

The KM3NeT is not yet fully operational, so Markov-Chain Monte Carlo (MCMC)

simulations are used to generate events that mimic the instrument response function.

One year of observation time is assumed. Three different sources of neutrinos to

are used to simulate the events: atmospheric conventional neutrinos, atmospheric

prompt neutrinos and cosmic neutrinos. The atmospheric conventional neutrinos

are based on the Honda model [49], which uses a virtual detector to calculate the

neutrino fluxes. The atmospheric prompt neutrinos are based on the ERS model

[50], which accounts for the charm production in the atmosphere due to cosmic rays.

Both models are adjusted for the cosmic-ray spectrum knee used by Gaisser[51]. The

cosmic neutrinos are assumed to follow a diffuse flux given by

Φνi+ν̄i = 1.2× 10−4E−2
νi+ν̄i

(GeV −1m−2s−1sr−1) (3.28)

where Eν is the neutrino energy. More realistic cosmic neutrino spectra are not yet

implemented in CALCRATE (KM3NeT internal document, 2023, Combined track

and cascade selection with ARCA115v9 ).

Track reconstruction

To reconstruct an event in a Cherenkov detector that is working properly, the tracks

of the particles that produce Cherenkov light are used. The most important track

is the one from the muon with the highest energy in the event, which will generate

at least one Cherenkov photon that hits two different DOMS. This track is used to

select events that are suitable for studying the detector response. The quality of the

reconstructed track depends on two criteria:[52]

� The number of DOMS that detect Cherenkov photons from the highest energy

muon must be at least two.

31



� The angle between the direction of the highest energy muon and the recon-

structed track must be less than 10◦.

To optimize the selection of neutrino events, four kinds of cuts are applied: track,

direction, background-like and signal-like cuts. I will explain each of them briefly.

Track cuts: Only events with a reconstructed track that has a positive likelihood,

positive length and energies above 10 GeV are accepted by this cut.

Direction cut: This cut selects tracks that are upgoing or horizontal, meaning that

they have a reconstructed angle θrec between 0◦ and 100◦.

Background-like cut: This cut removes tracks that are poorly reconstructed and

belong to a region where the signal is negligible.

Signal-like cut: This cut reduces the background contamination by applying a sep-

arate criterion for events with a reconstructed neutrino energy Etrack,rec higher than

106 GeV or Etrack,rec > 106 GeV. This is the energy above which we expect the

cosmic neutrino flux to be higher than the atmospheric neutrino flux. These events

are also the most likely to be well reconstructed.

To further reduce the events that are not signal-like but are background-like, a final

cut is applied based on a Boosted Decision Tree (BDT). The BDT is a machine

learning algorithm that combines multiple weak learners (such as shallow trees) in a

sequential way, where each learner tries to correct the error of the previous one. The

BDT uses the Gradient boosting method, which adjusts the weights of the learners

according to their performance. The BDT score is a measure of how signal-like an

event is, and it depends on the direction of the track. For up-going tracks, the BDT

score must be greater than 0.4, and for horizontal tracks, it must be greater than

0.9.

Cascade/Shower reconstruction

For cascade channel, the signal is defined as:

� The event must contain a νµ particle.

� The interaction vertex must be inside the detector.

32



� The angle between the reconstructed shower and the most energetic muon

must be less than 10◦.

Four cuts to the reconstructed showers are applied, namely: reconstruction status,

containment, Cherenkov hits and total number of hits. In addition, a BDT is used

to select events with short showers. Here is a brief explanation of each cut,

Reconstruction status: Only select events that have both a track and a shower

reconstruction. The cascade selection uses information from both reconstruction

algorithms and we note that no signal events are lost by also selecting for a completed

track reconstruction.

Containment: Only events that have a vertex far from the edge of the detector and

have a reconstructed vertex R > 500 m are selected. Events are required that the

height Z < 650 m.

Cherenkov hits: These are hits that are produced by Cherenkov radiation near a

detector. The hits that has at least NCherenkov > 10 are selected, to ensure that the

event is consistent with a cascade hypothesis.

Total number of hits: Each event must have a minimum number of hits given by

log10(Nhits) > 2.6.

For events with short showers (l < 300 m), a BDT cut is applied based on the

reconstructed shower energy. The BDT cascade score must satisfy

BDT cascade score > −0.7 log10(Eshower,rec) + 2.9 (3.29)

The events which are selected after the cuts using a likelihood test are then used

to calculate Aeff (E, cos θ), D(E ′, E, cos θ) and P (E, cos θ′, cos θ). These are also

known as instrument response functions (IRFs).

3.2.2 Discovery and Sensitivity

In a counting experiment, the main aim is right in the name which is to count the

number of events detected by a detector during the observation period. In neutrino

counting experiments atmospheric neutrinos are the most abundant, and a detected

event usually has a source and background signal. However, we are interested in

33



counting the number of cosmic neutrino events, thus, atmospheric neutrinos will

be part of the background events. Event detection is claimed if it can be proven

that the event is significantly different from the background, hence reducing what is

called chance detection. If an event cannot be significantly distinguished from the

background, the best detection setting is established.

We define a discovery as the rejection of the background-only hypothesis with a high

level of confidence. Subsequently, sensitivity is defined as the average upper limit

on the source flux in which detection can be claimed. In this section, we will be

discussing how the source discovery and sensitivity were calculated.

Discovery

Discovery potential is found using the total number of detected events, nα, with

a probability α or less to originate from a pure background source in (1 − β)% of

all hypothetical experiments1. Suppose we want to make a 5σ detection, then the

chance probability is α ≈ 3× 10−7 or 1 in 3.5 million that the detection occurred by

chance. To calculate nα, we find the least detectable signal mean µ or n0 which is the

number of observed events needed to deviate from the background-only hypothesis

at the given α, and this is given by

∞∑
nobs≡n0

P (nobs|nb) ≤ α (3.30)

where nobs = ns + nb with ns being the signal mean and background mean nb.

The critical number of observed events to deviate from the background is given by

nα. The probability of deviating from the background in (1 − β)% of hypothetical

experiment by 5σ is given by

P5σ =
∞∑

nobs≡n0

P (nobs|nb + nα) = 1− β (3.31)

thus, the minimum flux needed for discovery is

Φα(E, θ) = Φ(E, θ)
nα(nb)

ns

, (3.32)

where nα

ns
is the model detection potential (MDP).[53]

1β is the discovery power and 1− β is the statistical power

34



Sensitivity

Suppose the source is not significantly detected, an average upper limit is imposed on

the flux and it is found using the 90% confidence level. Using the Feldman-Cousins

method[54], the 90% confidence level for the signal mean is given by

µ̄90(nb) =
∞∑

nobs=0

µ90(nobs, nb)
(nb)

nobs

nobs!
exp(−nb) (3.33)

µ90(nobs, nb) is calculated assuming that there is no source detected (ns = 0).

Determination of µ90(nobs, nb)

Assuming the event counting with a known background rate b is given by

P (X = n|µ) = L(µ|X) = (µ+ b)n
e−(µ+b)

n!
(3.34)

where µ is the signal mean rate. Confidence level (α) is defined as the probability

that an estimator of a population parameter has the same location as the estimated

parameter. For instance, if a confidence interval was calculated at 95% confidence

level for a given sample, then there is a 95% chance that the population mean rate

parameter lies within the calculated interval. Therefore, the probability for a subset

member2 of µ, represented by x, in the confidence interval [x1, x2] to be an estimator

(µ̂) of a population mean rate, µ, is α. This can be written as

P (x ∈ [x1, x2]|µ) ≥ α, (3.35)

with the ”≥” used for avoiding under-coverage of events. For an event counting

experiment with a required 90% confidence level, Equation 3.35 becomes

P (n ∈ [n1, n2]|µ) ≥ 0.9 (3.36)

with the sample now being the number of detected events. Using Equation 3.34 and

Equation 3.36 we can solve for µ90(nobs, nb).

Equation 3.33 is for a single experiment, however, to impose an average upper limit

on the flux an average µ̄(nb) is needed and it can be found by using a statistical

ensemble. The result of the ensemble is denoted by just n̄90. Hence, the upper limit

2This is also called a ”sample”

35



flux is given by

Φ̄90(E, θ) = Φ(E, θ)
n̄90

ns

(3.37)

where n̄90

ns
is called the model rejection factor (MRF).

36



Chapter 4

Methodology

We will now show how the results in this project were obtained. We used OneHaLe to

estimated the neutrino fluxes by first fitting the simulated blazar with archival data

for 3C 279. We used the neutrino fluxes to then estimate the KM3NeT neutrino

detection potential and sensitivity. We then compared the upper limit flux with

those of existing telescopes such as IceCube.

4.1 SED

We present the results of our spectral energy distribution (SED) obtained from

simulating a blazar jet with OneHaLe, a code that calculates the fluxes, light-curves

and other distributions of photons, electrons and protons in a jet. We focus on

the neutrino emission from different processes involving these particles. We use the

parameters listed in Table 4.1 for our simulation.

OneHaLe requires two types of input parameters: those that depend on the source

and those that do not. The source-dependent parameters are obtained from observa-

tions of the specific source, such as z, M, ledd, R̂BLR, T̂BLR, L̂BLR, R̂DT , T̂DT and L̂BLR.

For 3C 279, which we use as an example, we adopt similar values for these parameters

as in [25].

The source-independent parameters are determined by the physical processes that

occur in the blazar jets. The magnetic field is one of the most important free

parameters, but we assume it is constant. We show the results in Figure 5.1 and

perform a qualitative fit due to the high number of free parameters (about 36 in

37



Value Symbol Description Units

120 B Magnetic field of the homogeneous region G

8.65× 1016 R Blob radius cm

20 ηesc Ratio of the acceleration to escape time scales

0.536 z Redshift to the source

25 Γ Bulk Lorentz factor for the blob

5.67× 10−2 θobs Observing angle relative to the axis of the BH jet rad

1.01 γmin,p Minimum Lorentz factor for the proton injection spectrum

2.00× 109 γmax,p Maximum Lorentz factor for the proton injection spectrum

1.60 qp Proton injection index

1.0× 1044 Linj,p Injection luminosity for the proton spectrum erg s−1

5.01 γmin,e Minimum Lorentz factor for the electron injection spectrum

2.01× 105 γmax,e Maximum Lorentz factor for the electron injection spectrum

2.40 qe Electron spectral index

1.10× 1042 Linj,e Injection luminosity for the electron spectrum erg s−1

20 ηR/c Multiplicative factor of the light travel time s

6.0 M Mass of the supermassive black hole 1.0× 108M⊙
1.18× 10−2 ledd Eddington ratio

7.70× 1017 R0 Initial location of the blob along jet axis cm

7.61× 1016 R̂BLR Radius of the BLR cm

5.0× 103 T̂BLR Effective temperature of the BLR K

2.30× 1044 L̂BLR Effective luminosity of the BLR ergs

5.23× 1018 R̂DT Radius of the DT cm

1.5× 103 T̂DT Effective temperature of the DT K

9.0× 1044 L̂DT Effective luminosity of the DT ergs

Table 4.1: List of OneHaLe free parameters with units

total) and the computational challenges of modelling them.

To find the neutrino fluxes, we used OneHaLe. We used OneHaLe because it is

a purely theoretical model which also allows us to estimate the neutrino fluxes.

Another reason why we used a lepto-hadronic model was to set up a parameter space

study in the modelling of blazars and AGNs in general. However, the use of 3C 279

as an illustrative source was partly based on the lack of neutrinos from blazars in

quiescent state and also due to the intensive study of 3C 279 in literature. OneHaLe

takes in an input file with free parameters that are used to find the geometry of the

blazar jet and the jet material including interactions.

We ran a simulation with the parameters listed in Table 4.1. When the simulation

was complete, fluxes in observer’s frame were found in the output and plotted. A fit-

by-eye technique was used to fit to plot due to the level of computational complexity

and power one would need to fit all free parameters from OneHaLe.

To perform the fit-by-eye, we started with the base parameters used by M. Zacharais

in [25]. The initial parameters did not fit the archival data, so we had to change the

38



parameters, which were not source dependent such as the magnetic field, injection

luminosities, spectral indexes and Lorentz factors (both maximum and minimum).

We changed the parameters, one at a time, to ensure that we understood the sen-

sitivity of the fit to changes in the parameters. However, as seen in Table 4.1,

the magnetic field and the proton injection spectrum produced by this manually

perturbative process were incorrect.

An early fit using the magnetic field of 0.25 G, shown in Figure 4.1, could not fit

the data. A similar study by C. Diltz[9] using the previous version of OneHaLe,

suggested that a magnetic field of around 150 G was needed to fit 3C 279, also using

a ”fit-by-eye” technique. This prompted the increase of the magnetic field from 0.25

G to 150 G. After several iterations of the magnetic field to fit better the high energy

data, a magnetic field of 120 G and proton injection index of 1.60 provided us with

a fit which was deemed to be a bit sufficient.

Figure 4.1: An early fit of the 3C 279 SED using the ’fit-by-eye’ method ’ to 3C 279
archival data found on NED.

The parameters which depend on observations of relativistic effects in the jet such as

the bulk Lorentz factor, acceleration to escape timescales and multiplicative factors

of light travel time were allowed to match that of [12].

OneHaLe outputs the simulated SED, as well as neutrino fluxes, so once an approx-

imate fit was done the neutrino fluxes were assumed to be correct.

39



4.2 CALCRATE methods

This section presents the simulated detection rates, discovery potential and sensitiv-

ity for νµ and νe events. We use CALCRATE to perform these calculations, which

requires several input parameters. These parameters can be divided into two (2)

categories, but we will enumerate them all. Table 4.2 shows the list of parameters

used in our analysis. In this section, we will briefly review the different input options

Option Description

f RDF/ingredients ROOT files

m output-type

F neutrino flux expression [1/(GeV m2 s sr)]

g flux expression refers to gamma-rays

T livetime (s)

YR years of observation

t Neutrino flavour interactions

c observational channels

p point source mode (flux in /GeVm2s)

d declination(range) for point-mode (degrees)

a search cone radius(range) for point-mode (degrees)

e minimal log of reconstructed energy (range)

w source width (degrees)

u source shape (if width > 0); 0=disk, 1=gaus

z confidence level for limits

s significance level for discovery

b 1-b statistical power for discovery

Table 4.2: Table showing the list of input options used for CALCRATE

for our analysis, with an emphasis on those that are not based on statistical meth-

ods. The option ”f” specifies the detector file that contains the information needed

to compute the IRFs, which are used by CALCRATE to calculate the background

and signal rates. Options ”F” and ”g” are related to the neutrino fluxes, where

”F” is the neutrino flux given in the units shown on Table 4.2 and ”g” uses the

gamma-ray flux to infer the neutrino flux. The options ”t” and ”c” account for the

neutrino interactions and observation channels, respectively. The channels are track

and shower, which correspond to different types of events produced by neutrinos in

the detector.

4.2.1 Rates, sensitivity and discovery

The output file for neutrino fluxes were used to produce the rates, sensitivity and

discovery. We exported the file into the KM3NeT servers, and used CALCRATE

with following input parameters (refer to Table 4.2 for full description):

� m - mrf, opt, rates

� t - shower, track

� T - 1 year

40



� c - numuCC, nueCC

� a - 0:5:1

� e - 1:8:1

� w - 0

� u - not needed

� z - 0.9

� s - 5sigma

� b - 0.2

� d - declination (◦)

Options a and e can be summarized as start:end:step. To find the right ranges for

”e”, we calculated the neutrino rates across all the energy cuts to determine the

energies where the detector response is zero. Using this, we were able to find the

lower and upper energy cuts. For ”a”, the input parameters were set to the newly

obtained limits for ”e”, meaning that ”e” would be 1:8:1, and we searched for the

maximum cone search angle that would optimize the MRF for shower events. To do

this, the cone search angle was set to be 0:90:0 and the optimal MRF was found.

The optimal MRF was found to be located near 5◦; we then set the range for the

viewing angle using the above angle.

To find the initial results, the declination was set at the declination of the source

(3C 279). We found the optimized MRF and MDP within the ranges of energy cuts

and cone viewing angles. For individual particle detections, option ”t” was set to

just ”numuCC” or ”nueCC” in the appropriate channel ”c” of ”track” or ”shower”.

The input for combined signals was set as ”t - numuCC, nueCC”. In the case of

combined shower events, the cone viewing angle and minimum energy cuts at the

optimized MRF and MDP were inconsistent with what was expected. Hence, we

produced an MRF table to find the bin the where the optimal MRF and MDP are

likely to be located.

To find the results in all declinations, the declination was set at −90◦ < δ < 90◦.

41



Then we repeated the procedure in the first part to find the optimized MDP and

MRF. We then compared the uppper flux limit for the most sensitive flux with that

from literature.

42



Chapter 5

Results

5.1 Results of OneHaLe

Due to the quantum mechanical phenomenon of neutrino oscillation, which implies

that neutrinos have non-zero mass and can change their lepton flavor as they propa-

gate through space, the neutrino fluxes observed at Earth are equal for νe, νµ and ντ .

The neutrino spectrum shown in Figure 5.2 is based on an estimated SED, which is

not exact. This means that the neutrino spectrum in Figure 5.2 is also approximated.

Figure 5.1 illustrates a simulated blazar jet SED which is dominated by proton

emission at higher energies. However, the SED does not completely fit the NED

archival data of 3C 279 due to a few reasons. One possible reason is that the use

of a fit-by-eye technique does not allow us to find the best-fit of the model to data.

Another possible reason is that the SED does not account for the variability and

orientation effects as the blazar jet evolves, which can affect the observed radiation

across different wavelengths.

Neutrinos in the observer’s frame (see Figure 5.2) have a spectrum that cannot

be modelled by an analytic function, meaning that the input spectrum for CAL-

CRATE is provided as a table of differential fluxes as a function of energy rather

than an analytic function. The differences between the neutrino spectra found in

the literature[31] and our simulated fluxes could be due to the hard spectrum of the

injected protons with α = 1.6 and γmax = 2 × 109 used. There is a possibility that

all protons undergo proton synchrotron radiation due to the high magnetic fields.

43



Figure 5.1: SED ’fitted-by-eye’ to 3C 279 archival data found on NED. Solid line
represents the total neutrino flux, and the dotted lines represent neutrinos produced
from the different neutrino processes. Some of the input parameters are displayed.

Figure 5.2: Neutrino fluxes corresponding to the SED in Figure 5.1.

44



5.2 Results of CALCRATE

5.2.1 Neutrino Sensitivity, Discovery and Rates

We aimed to identify the optimal neutrino fluxes that can be detected, excluding

the ντ flavour. For this purpose, we needed to know the best detector configuration,

which we defined as the optimal directional and energy cuts. We used CALCRATE

to simulate the sample source 3C 279, which has a declination of −05◦47′22′′, and

we calculated the optimal configuration for different neutrino flavours and neutrino

interaction channels that would achieve a 5σ discovery, chance probability of 3×10−7,

with a statistical power for discovery of 0.2. We used 3C 279 as an illustrative source,

however, the discovery power is derived from the elusive nature of neutrinos, and

factoring in the possibility that astrophysical neutrinos sources may be dominated

by sources which may not necessarily be blazars or even AGNs. Since, the study

is also for all blazar sources, not necessarily 3C 279, we chose the 5σ discovery as

most of the blazar neutrino source are not well known so we want the source signal

to be as different as possible from the background. We used the optimized MRF

and MDP methods, and we assumed 1 year of observation time. The results are

shown below: We observed that shower events have larger cone viewing angles

decl(rad) cone(opt) minlogE(opt) total-sig total bg mean limit MRF n limit discovery MDP

-0.101043 0.363078 4.49694 0.0130742 0.00107118 2.30321 176.165 0.9 68.8378

Table 5.1: The optimized simulated discoveries and sensitivities for a νµ detected
using the track channel.

decl(rad) cone(opt) minlogE(opt) total-sig total bg mean limit MRF n limit discovery MDP

-0.101043 1.99699 0.585471 1.58903e-06 0.00624475 2.30625 1.45135e+06 1.6 1.0069e+06

Table 5.2: The optimized simulated discoveries and sensitivities for a νe detected
using the track channel.

decl(rad) cone(opt) minlogE(opt) total-sig total bg mean limit MRF n limit discovery MDP

-0.101043 1.99538 4.42582 0.000669623 0.413577 2.30321 3439.57 0.9 1344.04

Table 5.3: The optimized simulated discoveries and sensitivities for a νe detected
using the shower channel.

decl(rad) cone(opt) minlogE(opt) total-sig total bg mean limit MRF n limit discovery MDP

-0.101043 1.99526 4.50134 0.000120985 0.382902 2.30321 19037.2 0.9 7438.94

Table 5.4: The optimized simulated discoveries and sensitivities for a νµ using the
shower channel.

(in degrees) than track events, as expected. We also noticed that muon neutrinos

45



(νµ) are more likely to be detected than other neutrino flavours, because they have

the lowest values of MDP and MRF. On the other hand, electron neutrinos (νe) and

muon neutrinos from track and shower interactions, respectively, are less likely to be

detected. This implies that track-like events are mainly caused by muon neutrinos,

while shower-like events are mainly caused by electron neutrinos. However, both

neutrino flavours can contribute to both types of events.

We assumed that the background is uniform and that the events are independent

of each other. Based on these assumptions, we calculated the detector limits or

configurations using the tables above. However, these assumptions are not very

realistic, so we decided to refine our analysis. We considered that both muon and

electron neutrinos can be detected in both shower and track events (we used model

fitting to distinguish between them), so we included both neutrino flavours in each

interaction channel. The results are shown below.

decl(rad) cone(opt) minlogE(opt) total-sig total bg mean limit MRF n limit discovery MDP

-0.101043 0.363078 4.49728 0.013073 0.00107118 2.30321 176.181 0.9 68.8443

Table 5.5: The optimized simulated discoveries and sensitivities for combined νµ, νe
using the track channel.

decl(rad) cone(opt) minlogE(opt) total-sig total bg mean limit MRF n limit discovery MDP

-0.101043 1.99966 0.0928499 0.000817171 0.382902 2.51678 3079.87 4.4 5384.43

Table 5.6: The optimized simulated discoveries and sensitivities for combined νµ, νe
using the shower channel.

We observe a slight reduction in the total signal of both electron and muon neutrino

events, which leads to a slight reduction in the MDP and MRF. The reason for

this reduction is the higher background events due to the detector being sensitive

to both types of neutrinos. This also avoids the potential problems that could arise

from separating neutrino events such as significantly underestimating the signal or

missing about two thirds (2/3) of the flux from the same source. When we compare

Table 5.3 and Table 5.6, we see that in the latter, the optimal viewing angle size

matches that of a shower event from a point source, but the optimal effective energy

is even lower than that of individual neutrino species. When we compare the MRF

table for shower events and the optimal MRF table for the combined signal νµ, νe,

we see that the result is not as optimal as expected. The bin where we would expect

to find the optimal MDP and MRF is shown in Figure 5.3.

We have performed simulations of neutrino fluxes from 3C 279. Our results, shown in

46



cone minloge total-sig total-bg meanlimit MRF n limit discovery MDP

1 1 0.000298503 0.0957651 2.35812 7899.79 3 10050.1
1 2 0.000298503 0.0957651 2.35812 7899.79 3 10050.1
1 3 0.000298416 0.0706783 2.3437 7853.81 3.1 10388.2
1 4 0.000295213 0.00407538 2.30498 7807.83 1.6 5419.81
1 5 0.000279762 5.05159e-05 2.30261 8230.61 0.9 3217.02
1 6 0.000227152 3.09233e-07 2.30259 10136.7 0.3 1320.7
1 7 4.79665e-05 9.68961e-10 2.30259 48004 0.3 6254.36
2 1 0.000817171 0.383031 2.51685 3079.95 4.4 5384.43
2 2 0.000817171 0.383031 2.51685 3079.95 4.4 5384.43
2 3 0.000816928 0.282692 2.46268 3014.56 3.7 4529.16
2 4 0.000807518 0.0163003 2.31214 2863.26 2.3 2848.23
2 5 0.000762444 0.000202048 2.3027 3020.16 0.9 1180.41
2 6 0.000616306 1.23684e-06 2.30259 3736.11 0.9 1460.31
2 7 0.000139685 3.87555e-09 2.30259 16484.1 0.3 2147.69
3 1 0.00122227 0.861711 2.75867 2257 5.6 4581.63
3 2 0.00122227 0.861711 2.75867 2257 5.6 4581.63
3 3 0.00122189 0.635976 2.64786 2167.02 5 4092.02
3 4 0.00120688 0.036671 2.32401 1925.63 2.3 1905.73
3 5 0.00113586 0.00045455 2.30285 2027.4 0.9 792.348
3 6 0.000918214 2.78253e-06 2.30259 2507.68 0.9 980.163
3 7 0.000217955 8.71888e-09 2.30259 10564.5 0.3 1376.43
4 1 0.00151017 1.53166 3.05904 2025.62 7.5 4966.32
4 2 0.00151017 1.53166 3.05904 2025.62 7.5 4966.32
4 3 0.00150966 1.13042 2.88388 1910.29 6.2 4106.89
4 4 0.00148985 0.0651813 2.34053 1570.98 3.1 2080.74
4 5 0.00139644 0.000807946 2.30306 1649.24 0.9 644.497
4 6 0.0011274 4.94585e-06 2.30259 2042.39 0.9 798.298
4 7 0.000278844 1.54975e-08 2.30259 8257.61 0.3 1075.87
5 1 0.00167573 2.39267 3.39628 2026.75 8.5 5072.42
5 2 0.00167573 2.39267 3.39628 2026.75 8.5 5072.42
5 3 0.00167512 1.76588 3.15555 1883.77 7.3 4357.89
5 4 0.00165199 0.101823 2.36158 1429.54 3 1815.99
5 5 0.00154311 0.00126213 2.30333 1492.65 1.6 1036.86
5 6 0.00124259 7.72612e-06 2.30259 1853.06 0.9 724.293
5 7 0.000315619 2.42093e-08 2.30259 7295.46 0.3 950.514

Table 5.7: Simulated discoveries and sensitivities for combined νµ, νe through the
shower channel.

Figure 5.2, indicate that the detection of neutrinos from this source is unlikely given

our choice of parameters since MRF and MDP are above 1 for all tested energies. To

explore the possibility of detecting neutrinos with similar fluxes from other sources,

we have scanned the across all declinations for optimal MRF and MDP values for

combined shower and track signals. The results of this scan are presented in Figure

5.4.

As shown in Figure 5.5, our signals were dominated by background noise. The

source signal was weaker than the background for all optimized MRF and MDP in

all declinations. This suggests that the source was either too dim or too distant. The

47



Figure 5.3: Histogram showing MDP binned by effective energy and the viewing
angle. The bin centred at (4,5) has the optimized MDP and MRF, the MDP is
644.50 and the MRF is 1649.24.

Figure 5.4: MRF and MDP for combined signal detected through the track and
shower channel. Effective energy and the cone viewing angle are set to be at 1◦

and logE = 5 for track events. In shower events, the effective energy and the cone
viewing are set to be at 4◦ and logE = 5

background shown in these figures is the detector specific background, hence showing

the performance of the detector at different declinations. It shows that at extreme

declinations, the detector may have lower performance. Another reason could be

that the event reconstruction algorithm used does not perform that well around

−90◦ and 90◦. We explore the potential causes of this result and its implications for

future research in Conclusion.

48



Figure 5.5: Signal and background rates, for the optimized MRF and MDP for
both shower and track events. Blue line is for the signal rates and the orange line
is for background rates. The above plots illustrate that the source is background-
dominated in all observable directions. Apparent fluctuations in the background
signal are due to changes in the optimum energy threshold rather than intrinsic
changes in the background or instrument sensitivity.

49



Chapter 6

Conclusion

6.1 Summary of results

A brief discussion of OneHaLe parameters

OneHaLe requires a redshift for the source, so we chose 3C 279 as an example be-

cause it has a known redshift of 0.536 and it has been extensively studied in different

wavelengths. We used archival data from various telescopes and instruments to fit

the SED of 3C 279 in its non-flaring state, assuming that the emission is dominated

by synchrotron radiation from relativistic electrons and protons and their interac-

tions with photons and magnetic fields.

We obtained a reasonable fit to the data with OneHaLe, but we also encountered

some challenges and limitations. One of them was the choice of the magnetic field

strength (B) and the initial location of the blob (R0). We found that a high value

of B (120 G) and a large value of R0 (7.7× 1017 cm) were needed to reproduce the

observed SED. However, these values are difficult to justify physically, as they imply

a very powerful central engine and a very distant acceleration site for the particles.

Moreover, they are incompatible with shock acceleration mechanisms, which are

commonly invoked to explain the particle spectra in blazar jets. Another challenge

was the choice of the spectral indices for the electrons (pe) and protons (pp), which

determine the shape of the injected particle distributions. We used values of qe =

1.60 and qp = 2.40, where the proton index is inconsistent with previous studies of

3C 279, due to reasons previously discussed in the above chapters, and those of other

blazars. These values imply that the jet is dominated by non-thermal particles.

50



6.1.1 Some neutrino fluxes at the end of the tunnel

Rather than fit the shape of the neutrino spectrum to an analytical expression, we

used the directly tabulated numerical values as input to CALCRATE to calculate

the minimum flux to which KM3NeT/ARCA is sensitive as a function of direction.

Flavour + channel MDP cone search minlogE opt Upper Flux Limit (ergs/cm2/s)

track νµ 68.8378 0.363078 4.49694 1.20719 ×10−10

shower νe 1344.04 1.99538 4.42582 2.35701 ×10−9

track νµ, νe 38.078 0.363078 4.49728 6.67765 ×10−11

shower νµ, νe 644.50 4.0000 5.00000 1.13024 ×10−9

Table 6.1: Calculated upper flux limits and minimum flux needed for a discovery
in each channel. The results were calculated using Equation 3.37, where Φ(E, θ) =
1.75368× 10−12 ergs/cm2/s for energies 10 GeV to 108 GeV.

The results of this project are summarized in Table 6.1, which shows the expected

fluxes of neutrinos from different types of point sources that can be detected by

KM3NeT/ARCA in one year of observation. The upper flux limit for each channel

and neutrino flavour will be optimal at different declinations, as shown in Figure 5.4.

The first two rows are for 3C 279, and the last two rows are for any source having

the same flux as the one in Figure 5.2 in all sky directions. The most likely to be

detected neutrinos are track νµ. The minimum flux needed for a 5σ discovery is

given by the sensitivity, because for all optimized neutrino interactions and channels

the MDP is lower than the MRF. This could be due to the low discovery power of

20%.

The main goal of this project was to determine if KM3NeT telescopes would be able

to detect neutrinos from blazars in quiescent state, but this was not fully achieved

due to some limitations and choices. Firstly, we decided not to scale the simulated

observational time to get fluxes for more than a one year of observations, reasoning

that discovery of a background-dominated source would not significantly improve

with longer exposure. Secondly, we were limited by the archival data used to estimate

the fluxes did not include lightcurves to verify if the sources were in a flaring state

or not. These factors could affect the accuracy and reliability of the flux estimates.

However, this project was still valuable as it provided a first estimate of the sen-

sitivity of KM3NeT/ARCA to neutrino point sources using the OneHaLe model.

This could help to optimize the search strategies and selection criteria for future ob-

servations. Moreover, this project also demonstrated the feasibility of a specialized

study of sources using OneHaLe and estimating the neutrino fluxes. This is also not

surprising as ANTARES also produced an upper flux limit, for BL Lacs in quiescent

51



state, as E2dϕνµ/dEν ≈ 4− 10× 10−8 GeV cm−2s−1 for track [27] and our findings

for similar interaction channel and neutrino type is E2dϕνµ/dEν ≈ 4.16786 × 10−8

GeV cm−2s−1.

6.2 Main findings

In summary, it is found that:

� Simulated events are very useful, running a simulation before the actual ex-

periment can help with the expected data. By simulating the neutrino flux

from a blazar source and the detector response of KM3NeT, we can estimate

the sensitivity and discovery potential of the observatory for different scenarios

and assumptions.

� Blazar jet models still rely heavily on getting the model to fit the data, this

is why there is a degeneracy when it comes to purely leptonic and purely

hadronic models. Both models can explain the observed SEDs with differ-

ent combinations of parameters, but they have different implications for the

neutrino production and detection.

� All the simulations for KM3NeT were run at 5σ discovery and 20% statistical

power for discovery. This is an indication that the KM3NeT observatory has

great potential to detect neutrino signals from quiescent blazars, if they do

exist, considering that we used the final expected configuration of the KM3NeT

for 1 year and still got some promising results, as it has been shown that

it has better sensitivity for non-flaring blazars than IceCube in its current

configuration.

� If we extend the observation time, we may increase the chances of detection

and discovery. Moreover, if we combine KM3NeT data with other neutrino

observatories, such as IceCube, we may improve the sensitivity and angular

resolution of the neutrino sources.

� Archival data from NED is multi-wavelength, however, not ideal to use when

modelling blazars because the data is not timestamped and may introduced

some inconsistencies in the models.

52



6.3 Future work

Since we used a ’fit-by-eye’ approach, the first thing to do for future study would be

studying known candidate neutrino sources. This would greatly improve accuracy of

the parameters used. One challenge would be the computational requirement to fit

more than 26 free parameters that is used by OneHaLe, so we will use models similar

to OneHaLe in order to get the to model those sources. One such neutrino candidate

would be TXS0506+056 studied in both flaring and non-flaring state, because it has

neutrino fluxes for flaring state. A comparison of the two sets of parameters could

be used to help in constraining some of the OneHaLe parameters such the proton

index.

OneHaLe is a powerful model that can fit the observed spectra of some blazars and

predict their neutrino fluxes. However, it also has some limitations and uncertain-

ties, such as the dependence on several free parameters that are not well constrained

by observations. To test and improve OneHaLe, more observational data and the-

oretical developments are needed. Radio analysis of blazars and AGNs in general

could assist in constraining the model and also lead to new insight about these highly

energetic objects. These radio observations could be used to find the location of col-

limation of blazar jets which can be used to introduce a lower limit as to where the

emission region is located from the central SMBH. Knowing the such limits could

allow us to put a limit on the size of the emission region. In turn, the correct or

approximate values could be used for the R and R0 parameters used in OneHaLe.

Applying OneHaLe model to not just blazars but all the AGNs which have jets,

would further assist in constraining OneHaLe and reducing the free parameters too.

This type of application could be used to estimate the size of the jet if it was to be

applied to fit Radio Galaxies.

For sources with sufficiently high real event rates, data from KM3NeT and IceCube

could be combined to improve the total sensitivity. KM3NeT and IceCube could

complement each other very well since they are located in opposite hemispheres,

hence covering the whole sky with little to no blind spots. For example, down-going

events for IceCube would be up-going events for KM3NeT, allowing the background

rejection and directional and angular reconstruction of neutrino interactions to be

improved.

Other extragalactic sources besides AGNs that are worth studying include Gamma-

53



Ray Bursts, Supernovae and Tidal Disruption Events, all of which may produce

detectable neutrino signals. By combining multi-messenger observations of these

sources with theoretical models, we can hope to unravel the mystery of the origin of

the highest energy cosmic rays.

54



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Special Topics, vol. 231, no. 1, pp. 27–66, 2022.

[2] R. Simoni, Studies of supernovae and their remnants based on gamma-ray ob-

servations with HESS. PhD thesis, 2022.

[3] A. Abeysekara, W. Benbow, A. Brill, J. Buckley, J. Christiansen, A. Chrome