Evaluating the depth dependence
of atmospheric muons with the
first string of the KM3NeT/ORCA
detector
THESIS
submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
in PHYSICS
Author : Jeroen van Doorn
Student ID : s1267930
Supervisor : Dorothea Samtleben
2ndcorrector : Jan van Ruitenbeek
Evaluating the depth dependence
of atmospheric muons with the
first string of the KM3NeT/ORCA
detector
Jeroen van Doorn
Huygens-Kamerlingh Onnes Laboratory, Leiden University P.O. Box 9500, 2300 RA Leiden, The Netherlands
November 26, 2018
Abstract
KM3NeT is a international collaboration focused on neutrino telescopy. Its main goals are to detect high energy cosmological objects through neutrino detection and reveal the neutrino mass hierarchy. For this it uses
two detectors, the ARCA detector which is constructed on the coast of Italy and the ORCA detector which had its first two detection strings deployed in the fall of 2017. In this thesis we focus on measuring the background produced by muons generated in atmospheric events. This
will allow us to gain an estimation of the expected background from which we obtain an indication of the performance of the detector. We have used two methods of filtering uncorrelated backgrounds such as the
signals produced by decay of40K in the ocean to extract atmospheric signals. Through the two methods we have found two halving lengths of
muons flux in the water of the Mediterranean. A halving length of 239 meters for the method filtering low energy hits and a halving length of
267 meters for signals extracted by correlations between DOMs. The results give a good estimation of the order of magnitude of muon
decay through increasing depths, however we have found systematic artifacts in the DOMs, which are expected to be caused by differences in
the DOM efficiencies. For this reason further research is required to obtain a definitive result.
Chapter
1
Introduction
High energy cosmological sources emit high energy radiation (HER). HER contains a lot of information about its source in the form of ultra high en-ergy particles and gamma rays. Most of the HER is nearly undetectable with traditional telescopes. Cosmological dust, will absorb a significant part of the signal and the surviving radiation will get absorbed by the atmosphere [7]. Space telescopes outside of the atmosphere are able to de-tect HER directly, however due to their limited size space telescopes can-not measure enough signal to accurately distinguish high energy sources from the background.
In order to observe high energy objects we must leave behind the tradi-tional method of direct observation. One way to observe high energy sources is by observing neutrinos. Neutrinos are a form of HER which interacts with environment generating detectable high energy particles. Neutrinos are fundamental particles which only interact via weak inter-actions. They are near massless and have a neutral charge [13]. As a re-sult neutrinos are very inert. A bundle of neutrinos travels through bar-riers nearly unperturbed, even the earth is not a significant blockade [8]. Because of this high energy neutrinos are perfect information carriers to observe high energy sources. Despite the low interaction probability it has been shown that enough neutrinos do interact within certain media to be accurately detected [12]. A detector within an optically transparent medium, like the deep ocean or ice, covering a large volume will be able to identify enough of these interactions to clearly separate cosmological signals from atmospheric backgrounds. This generates a method of in-direct HER detection and enables us to observe high energy objects. An advantage of neutrino telescopy over the the detection of other forms of
6 Introduction
allows us to only observe the surface of an object, but neutrinos will have a high chance of being emitted even if they are generated inside a source. Because of this neutrinos open a new window for all cosmological objects. Over the past decades multiple projects have been launched to detect cos-mic neutrinos. ANTARES, a deep sea detector having finished construc-tion in 2008, has given a proof of concept for our method of neutrino de-tection [1]. And IceCube a detector which has been built in the antarctic ice. Being larger than its predecessors it has succeeded in detecting mul-tiple cosmological neutrinos by 2013. KM3NeT, is the newest iteration of neutrino telescopes combining the strengths of its predecessors. The Ice-cube detector was built on the South Pole using ice as interaction medium for neutrinos. Despite ice being a rigid base for the detector the light pro-duced by neutrino interactions is scattered around more as opposed to water. This extra scattering lowers the angular resolution which lowers the efficiency for the reconstruction of the neutrinos propagation direc-tion. KM3NeT is built in the Mediterranean Sea giving it higher accuracy over its competitors. Additionally, the IceCube detector having been built on the South Pole is focused on deep space. KM3NeT on the other hand will be aimed more in the plane of our galaxy, which has a lot of objects of interest [2]. Antares was built in the Mediterranean as well, but is a rela-tively small size and is therefore restricted to low energy regimes.
KM3NeT is a combination of two detectors. The first detector is called the Astroparticle Research with Cosmics in the Abyss detector or ARCA de-tector. The ARCA detector is a large detector in the Mediterranean close to the Italian coast. Its main goal is to detect neutrinos in the TeV regime from cosmological sources [2]. Its counterpart is the oscillation Research with Cosmics in the Abyss detector (ORCA). ORCA is a denser detector, mak-ing it sensitive to particles in the low GeV regime, located on the french coast near Toulouse. It improves on Antares by obtaining a higher reso-lution through improvements in the detector modules, while also being larger and therefor obtaining more data [2]. In contrast to the ARCA de-tector ORCA focuses on atmospheric neutrinos. Atmospheric neutrinos are less energetic than the neutrinos emitted by high energy sources and the denser instrumentation of the detector will make ORCA more sensi-tive to these particles. Its goal is to deduce the mass hierarchy of neutrinos through studying of the neutrino oscillations. In this thesis we will focus on the performance of the ORCA detector. ORCA is still under construc-tion and at the moment of writing the first funcconstruc-tional string has been in the water for several months. We will discuss the functionality of the working string using measurements of well understood atmospheric signals to test the performance of the string, and to identify and explain certain caveats. 6
Chapter
2
Detection concepts
In order to detect neutrinos we make use of the Cherenkov technique. With the cherenkov technique signals from the products of a neutrino in-teraction are detected. When a neutrino interacts with water it produces a shower of particles [10].The shower will consist out of a multitude of different particles with various charges. Due to the high energy of the pri-mary neutrinos, we expect high velocities for the collision products. Light enough particles will obtain velocities higher than the speed of light in the medium. This speed is called the Cherenkov limit.
Charged particles breaking the Cherenkov limit in a di-electric medium will generate Cherenkov radiation [6]. A charged particle propagating through a di-electric medium will polarize it. This creates an ordered state which almost immediately becomes disordered, a process which produces a weak radial electromagnetic (EM) pulse. When a charged particle trav-els above the Cherenkov limit it will overtake the EM pulse it produces and create a new pulse with its origin ahead of the first pulse. These two waves will superimpose amplifying the intensity in a certain direction. When this effect continues over a long distance the superpositions of all waves generate a coherent wavefront from which we can reconstruct the particles track. (Figure 2.1)
As Cherenkov radiation is emitted the loss of energy will decrease the ve-locity of the particle, which will eventually be under the Cherenkov limit. As the particle slows down the angle θ decreases a little bit, but the change in θ will be small enough that we do not take this into account and we are able to assume all light particles to travel at light speed. The angle of Cherenkov radiation is estimated by the formula:
8 Detection concepts
Figure 2.1:A schematical drawing of the overlapping radial pulses generated by the relaxation of a medium back into its groundstate. The yellow arrows show the direction of the Cherenkov wavefront [6].
Where θc is the Cherenkov angle β is the fraction between the speed of the particle and the speed of light. We assume the muon velocity to be equal to the speed of light we say β = 1, and n is the refractive index of the medium, in our case n = 1.34 [6]. This gives us a Cherenkov angle of 41.73◦.
By correlating the signals received by the interaction products of a neu-trino, we are able to reconstruct the direction and energy of the primary neutrino.
The wavelength of the emitted Cherenkov radiation is derived using the Frank-Tamm formula [4]. The Frank-Tamm formula gives the amount of photons emitted over a length of water per frequency for a superluminal particle.
∂2N ∂x∂ω =q
2 µ
4πsin(θc) (2.1)
with q being the charge of the emitter and µ the permeability of the medium the source propagates in. For relativistic muons, with a Cherenkov angle of 41◦, it was estimated that 250 photons per centimeter traveled will be produced in the optical regime (wave lengths between 300 nm and 500 nm) [11]. This is good news for our detector. Water is very absorbent out-side of the visible regime. If radiation gets absorbed more easily we expect a greater loss in signals resulting in a less sensitive observation technique. The estimated intensity of charged particle radiation is enough for our de-tector to measure, and thus can we focus on the optical regime of light with our detector to detect the light produced by neutrino interaction products.
8
Chapter
3
The ORCA detector
The ORCA detector is an array consisting out of 2070 Digital Optical Mod-ules (DOMs) in a cylindrical volume with a radius of 106 meters and a height of 200 meters. The DOMs are distributed over 115 strings such that each string contains 18 DOMs, which are distributed over the detector area with an average spacing of 20 meters. (Figure 3.1)
Figure 3.1: Top view of the ORCA detector. The 115 red dots indicate strings, which have an average spacing of 20 meters. The circle indicates the boundary of the system with a radius of 106 meters [2]
10 The ORCA detector
A detector string has a buoy attached to its top end, and the bottom end is mounted on the sea floor. This results in a taut string perpendicular to the ocean floor. (Figure 3.2)
Figure 3.2:Left: a schematical drawing of a detection string. The yellow sphere at the top is a buoy keeping two strings taut. The black spheres are the DOMs. Only 8 of the 18 DOMs of the string are shown for clarity. Right: A mounted DOM as seen from the side.
A string consists out of two identical cables on which the DOMs are mounted. Due to technical constraints the DOMs are mounted with unequal dis-tances between each other. These differences follow a recurring pattern such that the intervals between DOM 1 through 7 resemble those between DOM 7 through 13 and again between DOM 13 through 18. In Table 3.1 the intended position of each DOM on a string is given as the height from the sea bottom, also the DOM separation is shown.
DOMs are glass spheres on which 31 Photon Multiplier Tubes (PMTs) are mounted. A PMT is a device which absorbs a single photon and using the energy of the photons produces a cascade of electrons amplifying the weak deep sea signals. The PMTs are located within 5 rings around the zenithal axis. Each ring consists out of 6 PMTs. The first ring is located at a 60◦angle from the zenith angle and subsequent rings are each placed 30◦from the previous one. A single PTM is added the bottom of the DOM (zenith angle = 180◦).
The DOM has a radius of 21.6 cm, while the PMTs have an effective diame-ter (including detector rings) of 85 mm giving the entire DOM an detection area of 227 cm2. The distribution of the PMTs will result in only 12 of 31 PMTs being directed up. (zenith angle of less then 90◦.) This distribution 10
11 positions 1 2 3 4 5 6 7 8 9 10 28.3 37.98 46.89 56.57 65.48 75.17 86.39 96.07 104.98 114.67 11 12 13 14 15 16 17 18 buoy 123.58 133.26 144.48 154.17 163.08 172.76 181.67 191.35 197.53 separation 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 9.68 8.91 9.68 8.91 9.69 11.22 9.68 8.91 9.69 8.91 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-buoy 9.68 11.22 9.69 8.91 9.68 8.91 9.68 6.18
Table 3.1: blueprint height of DOM x from the bottom of the sea. And the sepa-ration between the DOM pairs. The distances are given in meters.
was chosen because of our interest in upward going signals. Figure 3.2 shows a picture of a DOM.
The detector is located in the Mediterranean sea 40 kilometers away from the shore of Toulon, France. Here the Mediterranean Sea is 2450 meters deep. The data is transported by cable to the French shore where relevant data is saved to be evaluated. In the rest of this thesis we will evaluate so called L1 hits. L1 hits are signals obtained through postselection of the data. When a light source like a muon propagates past a DOM it is capable of exciting PMTs multiple times. We will attribute signals on any PMT on a single DOM with a time difference of less then 25 ns to be produced by the same source. Separate L1 hits on a single DOM will therefore always be at least 25 ns apart from each other, and we make sure a single source is not counted multiple times. Further improvement of source identification is possible. We have looked into the introduction of an angular cut, which adds the criterium of an L1 hit being confined to a 90◦ angle on the DOM. This has been done for one of our measurement. This can also be taken further by taking the exact PMT positions into account, but this has not yet been done at the moment of writing.
Chapter
4
Measurement effects and optical
backgrounds
In the rest of this thesis we will discuss the influence of the background generated by muons generated in the earth’s atmosphere. Relativistic at-mospheric muons are generated by HER entering the atmosphere collid-ing with air. These muons have enough energy and long enough penetra-tion depth to reach our deep sea detector and generate identical signals to those produced by neutrino collision products. These signals are unin-teresting for neutrino research and should be reduced from the final data. The most obvious method of distinguishing between atmospheric muons and neutrino collision generated ones is by looking at the direction of the muons. In contrast to muons created in neutrino collisions, atmospheric muons cannot come from below the detector. This is caused by muons not being able to travel through the earth nor the larger volume of water a muon has to travel though as the zenith angle of the muon increases. When we measure an upward going signal we know it to be produced in a neutrino collision from a neutrino having come through the earth. Thus, to filter muonic signals generated by other interactions then neutrino col-lisions we focus our attention on upward going signals.
Sadly, the easy premise of this technique is misleading. Cherenkov radia-tion is sent out in a cone [6]. We can rotate the direcradia-tion of the Cherenkov source in such a way that the opposite wavefront generated will have the same direction as the pre-rotated system. (figure 4.1) As a result some downward going muons will mimic signals from upward going muons and the reduction of the atmospheric muons is not as straight forward as it seems.
14 Measurement effects and optical backgrounds
Figure 4.1:Figure showing a comparison between Cherenkov light emitted by an upward going muon and one with a zenith angle such that the wavefronts on the right of each figure have the same direction. As a consequence the two muons generate an indistinguishable signal from each other for a detection string.
In order to obtain the neutrino generated signals in our data we must fil-ter out the signals generated by the atmospheric background. To do so we measure the intensity of the atmospheric muons and introduce directional cuts. When muons traverse through water they will lose energy and ei-ther decay or stop. Because of this we expect the muon flux to decrease exponentially with depth. We have used data from the ORCA detector to obtain an estimation of the depth dependence of muon flux. The depth dependence of muons can be compared to theoretical data to find the per-formance of the detector.
Beside these artifact we also discuss backgrounds. Signals received by Cherenkov light are very weak compared to daylight. At a depth of 2450 m no light from surface sources is present.This makes the bottom of the Mediterranean sea an ideal location for a neutrino detector. However other sources of light are also present during measurements for which we will discuss the effects on our measurements and solutions in the next chapters. First we consider the signals generated by the decay of an un-stable potassium isotope (40K) in the deep sea. 40K is an unstable atom found evenly distributed in the oceans. When 40K decays it produces a relativistic electron. This electron will generate a signal if the40K decays inside or near our detector. Due to the isotropic distribution and the con-stant decay over time we measure a concon-stant amount of low energy hits distributed evenly over the entire detector. These signals have been used to test time and efficiency calibrations. In the next chapter we will discuss two separate ways to identify the background produced by40K and omit it from our data, allowing us to extract the muon signals.
14
15
Secondly we look at bioluminescence. This is the light produced by bio-luminant organisms, which are common life on 2450 meters depth in the Atlantic [5]. The light they produce is very strong compared to signals generated by high energy particles. When a bioluminant organism passes by the detector and produces light we expect a period in which these sig-nals dominatet for a single DOM. Unusual irregular high peaks we have encountered in our data are expected to be caused by this effect.
Chapter
5
Identification of atmospheric muon
signals
The goal of our analysis is evaluating the intensity of the atmospheric muon signals as a function of depth, in order to verify the performance of the detector. Atmospheric muons are constantly generated in atmo-spheric collisions. By identifying downward going signals we are able to find the muon distribution and cross check the detectors consistency with known measurements. In order to do this we need to take the other back-grounds in consideration as well. In this chapter we will discuss in detail two methods of isolating the most predominant source of background,40K decay. The multiplicity method which uses coincidences on a single DOM, and the correlation method which correlates signals between DOMs. We present our data in runs, measurement windows in which we log the times at which PMTs are hit. We selected three runs which we will com-pare in our analysis. Run 2867, Run 2888 and Run 3010. The former two runs have a run time of exactly three hours (10800 seconds), the latter is nearly 15 minutes shorter at 10450 seconds. We will use run 3010 in this chapter to visualize the steps for each method. Furthermore, run 2888 was a run with a angular cut. This has no effect on our analysis except for a lower absolute amount of signals.
We model our results using an exponential fit: I = e(−c+λ∗h) where I is the intensity at a certain depth, e−c is the intensity at the sea bottom λ is the slope of the fit and h the distance to the seabottom. As this models the
18 Identification of atmospheric muon signals
5.1
The multiplicity method
The multiplicity method reduces the 40K signals by omitting the L1 hits with a low amount of activated PTMs on a DOM. The amount of PMTs which measure a specific L1 hit is called the multiplicity of the hit. Sig-nals generated by the 40K background, or other random signals like the intrinsic dark counts, are not strong enough to generate coincidences with a multiplicity higher than 7. Muons, and other high energy particles, do have the required energy to generate coincidences with higher multiplic-ities. In a previous study it was shown that the high multiplicity coin-cidences match the muon signature as seen in simulations [3]. We show these results in in figure 5.1.
Figure 5.1: Rates of multifold coincidences in a time window of 25 ns for the 3 DOMs, compared to the expected Monte Carlo rates. Symbols refer to data, histograms to Monte Carlo simulations. No normalisation factor is applied to Monte Carlo rates. (figure taken from: [3])
For low multiplicities the measured coincidence rate was several orders of magnitude higher than the expected amount of signals we would receive from atmospheric muons alone Comparing the high multiplicity rates of all DOMs, we find that the low multiplicity hits contain significant amounts of secondary sources for coincidences. Which was found to be dominated from40K decay products and other random coincidences. High multiplic-ity signals on the other hand were found to be dominated by atmospheric muons. By filtering the low multiplicity coincidences, and looking only 18
5.1 The multiplicity method 19
at coincidences with multiplicities higher than 7, we obtain data which is dominated by atmospheric muons. by comparing the high multiplicity rates between DOMs we can obtain an estimate for the muon depth de-pendence. The distribution of all coincidences for a DOM during run 3010 is shown in figure 5.2.
Figure 5.2:The amount of coincidences with multiplicity n for DOM 8 measured during run 3010.
The distribution of the hit multiplicity shows a rapid decline of an order of magnitude per multiplicity level for the first 6 multiplicities, after which the decline stagnates abruptly. This process is in exact agreement with the expectations we obtained from the simulations.
Signals are expected to be affected by the internal efficiencies of the PMTs, because of this we should consider the effectiveness of the each DOM be-fore we continue. PMTs have their own intrinsic effectiveness and have a safeguard build in which makes it turn off as a signal with a sufficiently high intensity is detected. The period a PMT is turned off is called a High Rate Veto (HRV).
A low efficiency of a DOM has high impact on the amount of signal mea-sured, but the overall efficiencies of PMTs are stable in the small time win-dows we use and predictable. The HRV however is highly variable inside the period of a single run. This can have strong implications for the effi-ciency off the DOM as a whole. Because of this we logged the HRV events for each DOM and compared it to the amount of received signal in the high multiplicity regime. Also DOMs with non functioning PMTs have
20 Identification of atmospheric muon signals
varying average functionality of PMTs we have found the variation of the PMTs to have no significant effect on the final results. We also checked whether a large amount of simultaneous HRV events showed a clear ef-fect, but also this was not the case.
Despite not having a specific correlation between the amount of broken PMTs and outlyers in the data, we expect the effectiveness of the DOM to be the cause low valued consistent coincidence rates. Further research toward the correlation of HRV and toward internal PMT efficiencies must be performed to obtain a better understanding of the systems shortcom-ings. Furthermore researching the directionality of the PMTs measuring hits and experiencing HRV events can reveal unconsidered sources and could be used to distinguished strong background signals.
We show a comparison between high multiplicity coincidences of four DOMs at different heights in figure 5.3. Small differences are visible in the amount of signal per DOM consistent over the multiplicities. These signals at multiplicities up to 18 show a decreasing amount of signal as the depth of the DOM increases.
Figure 5.3: The amount of hits with multiplicity n for DOM 1, DOM 8, DOM 13 and DOM 18 for multiplicities between 5 and 20. Note the consistent lower amount of signals for lower DOMs.
For each DOM we add all coincidences with a multiplicity higher than 7 as a function of the DOMs distance to the sea bottom figure 5.4. We see that Figure 5.4 supports the hypothesis of an lowering muon flux at increasing depths. We have fitted the data with an exponential fit. The decrease in signal at increasing depth is deduced, and the constant which scales the 20
5.1 The multiplicity method 21
Figure 5.4:The amount of hits per second with multiplicity n>8 on each DOM as a function of distance to the sea bottom. The data points have been fitted using a exponential fit
data to match its starting point. At this moment we don’t have a good absolute calibration of pure muon signals at any depth, as a result the nor-malization and other nornor-malizations in this thesis’ fits are not verified. We evaluate the data shown in figure 5.4 with the discussed features in mind, and to test the robustness of our method we compare our three dif-ferent runs. Furthermore we repeat the data collection for each run 5 times each time omitting an additional multiplicity level. This allows us to check for consistent absorption at higher muon energy levels (figure 5.5).
22 Identification of atmospheric muon signals
(a)Run 2867
(b)Run 2888
(c)Run 3010
Figure 5.5:The hitrate of each DOM as function of distance to the sea bottom for 3 runs. Each subfigure contains 5 different multiplicity omissions. From top to
bottom each multiplicity under 8 till 12 have been omitted. The slopes of each fit is found in table 5.1
22
5.1 The multiplicity method 23
We see a clear upward trend in the signal with increasing DOM height strongly suggesting the acquired signal is dominated by signals with a decreasing intensity as depth increases. Some features are visible as well such as the amount of signal received by DOM 16 which shows consis-tent low rates as compared to the fit. Less visible are the low intensities measured at the top two DOMs. All data points seem to have increasing intensities as their height increases, but this trend breaks down at high DOMs. We expect this to be caused by priorly mentioned DOM efficien-cies. Other low valued DOMs are found in DOM 3 and DOM 6, in run 2867 and 2888. We find these outliers to be consistent over the runs and at different multiplicity cut offs.
The results of figure 5.5 is summarized in table 5.1, in which we show the reliability of each fit. Here it should be directly noticed that the values of the χ2 are very high. With only 17 degrees of freedom the obtained χ2 is too high to verify the exponential depth dependence of muons. This, however, is expected to be a direct consequence of the low top data points, and the fact our error margin was solely based on the influence of Poisson noise. The mean of the slopes is 0.0029±0.00004, comparing this to all val-ues we find a χ2of 18.8 (degrees of freedom = 15) which makes the results consistent between runs and multiplicities , validating the consistency of our method and features. This gives us reason to believe the artifacts to be rather constant over each run, which allows us to generate an estimate of the muons survival length. With a slope of 0.0029±0.00004 we find a halving length of 239±3 meters. To obtain a better estimate, a model for DOM efficiency must be made.
multiplicity run 2867 χ2 run 2888 χ2 run 3010 χ2
n≥8 0.0024 ± 0.0002 101.55 0.0028 ± 0.0002 77.83 0.0028 ± 0.0002 55.82 n≥9 0.0027 ± 0.0002 99.14 0.0030 ± 0.0002 60.37 0.0028 ± 0.0002 45.40 n≥10 0.0027 ± 0.0002 81.29 0.0034 ± 0.0003 55.66 0.0027 ± 0.0002 26.86∗ n≥11 0.0031 ± 0.0003 62.27 0.0031 ± 0.0003 39.75 0.0028 ± 0.0003 24.44∗ n≥12 0.0030 ± 0.0003 57.33 0.0036 ± 0.0003 20.58∗ 0.0029 ± 0.0003 35.14
Table 5.1:Values of the slopes (λ) for the exponential fit (I = e(−c+λ∗h)) of each run
for each multiplicity. The asterices show the fits that coincide with an exponential function with a 95% probability.
24 Identification of atmospheric muon signals
5.2
The correlation method
The multiplicity method gives a good estimate of the expected reduction of muon intensity, however the reduction of the background also filters the most abundant muon data. As a subsequent test we reduce the back-ground with a method which conserves low multiplicity hits. To achieve this we analyze the correlations between DOM pairs. As explained in the physical concepts, when a high energy muon travels past a string, the light it produces will be detected by different DOMs on the string at different moments. By analyzing the time differences between these hits (correla-tion times), we are able to characterize the background and identify signals generated by a single source (correlated signals).
40K decay, and other less abundant backgrounds as dark counts, will gen-erate correlations between DOMs with arbitrary time difference (uncorre-lated signals). Due to the isotropy of these signals, we expect to measure a constant amount of correlations over the entire detector at all possible correlation times.
The distribution of time correlations for a typical DOM pair is shown in figure 5.6. At both high positive and high negative correlation times we detect the expected constant amount of correlations. At time differences close to zero we measure a signal which stands out from the background. These are correlated signals caused by a single source.
We extract the correlated signal by averaging over the values outside of the muon regime (the tails of the histogram), and subtracting the average from all entries in the histogram. With the uncorrelated signals removed we are able to read of the amount of correlated signals. For this analysis we have collected the L1 hits for each DOM and we compared correlations between each DOM with all other DOMs, for three hour measurements. Figure 5.7a shows the correlations between DOM 10 and all of its neigh-bors for run 3010.
In figure 5.7a a clear signature of correlated signals is visible exceeding the background value. DOMs which are located below the measurement DOM have a high intensity at positive correlation times, while DOMs lo-cated higher than the measurement DOM have a high intensity at nega-tive time differences. The direction of the signature shows a predominant amount of downward going signals. Figure 5.7b shows the y projection of the three slices to the right of the white bar in figure 5.7a. This results in three graphs showing the correlations between DOM 10 and its three up-per neighbors in the form of the data in figure 5.6 The shape of the peaks is in agreement with the expected shape of a muonic signal [3], and the 24
5.2 The correlation method 25
Figure 5.6: Histogram showing the number of correlations with correlation time dt between DOM 10 and DOM 11 for run 3010.
location of the peak at negative time differences agrees with downward going signals. From this we find the correlated signals to be dominated by muons.
As the distance between the DOMs in a pair grows, the peak of the sin-gle source signals moves toward larger time differences and by integrat-ing over the all signals in all y slices of figure 5.7a we have found that the amount of correlations decreases. This reduction of correlation inten-sity should not be confused with a depth dependent effect, for the mea-surement DOM is at a constant depth. The larger separation results in a narrower range of angles of the incoming muons the pair is sensitive to. Muons coming in from a large angle will not hit every DOM due to the increasing distance between the muon track and the detection string at different heights. Furthermore larger distances between correlation points heighten the chance of the muon to slow down enough to get under the cherenkov limit.
Before we continue the analysis of the muon depth dependence, we will first evaluate the shape of the direct neighbor peak shown in figure 5.6. We approximate the time difference between the hits of two DOMs as fol-lowed:
dt = ∆hcos(θ)
vwater
here dt is the time between hits between different DOMs measured in sec-onds, ∆h the distance between DOMs, θ the zenith angle of the
propa-26 Identification of atmospheric muon signals
(a)2D histogram containing the L1 correlations between DOM 10 and
all of its neighbors. The x axis shows the name of each DOM the deepest one being on the left. The white bar shows the correlations of
DOM 10 with itself and is left empty.
(b)Here the three slices to the right of the white bar in figure 5.7a are shown. We measure the correlation times with
the bottom DOM as the base (t=0).
Figure 5.7
This approximation holds for plane waves, and naturally is only true for a single cherenkov wavefront. The formula reveals a maximum time dif-ference which relates to an angle for which the cherenkov wavefront is perpendicular to the measurement string. The edges of this boundary are approximated as:±v∆h
water where∆h is the DOM separation and vwateris the
speed of light in water. For direct neighbor DOM pairs we find the muon regime to be constraint between by dt≈ ±40 ns.
In figure 5.8 the background reduced histogram of the data in figure 5.6 is shown.
The correlation time for downward going Cherenkov radiation perpendic-ular to the detection string is indicated by the red line. At this correlation time the signal rises sharply, which is in agreement with the discussed the-ory for correlated signals. The yellow line shows the correlation time for a muon traveling parallel to the detection string to be dt ≈ ∆hc seconds. Here we have assumed the muons to travel at the speed of light. At this correlation time we find the highest amount of correlations. From this we expect an abundance of muons traveling parallel to our string.
The slow reduction of signals after the peak is caused by the increasing distance muons have to travel through water as the zenith angle grows. Most muons with a large zenith angle will already have decayed before reaching the detector. At dt = 0 we see a stagnation of this reduction. This stagnation is expected if upward going signals are present in the detector. 26
5.2 The correlation method 27
Figure 5.8: The background reduced correlations. The red line indicates the cor-relation time of cherenkov wavefronts perpendicular to the string at -39.9ns. The yellow line in figure 5.8 indicates correlation time of muons propagating parallel to the string at -29.7ns
dt = 0 is the correlation time where cherenkov wavefronts will be parallel to the detection string hitting both DOMs at the exact same time.
Lastly we focus on the slow increase of signal for negative time differences outside of the muon regime. Previous argumentation suggests that muon signals will exclusively have correlation times between ±40 ns, however we also measure a signal which exceeds the uncorrelated background, for correlation times lower than -40 ns. These signals are retarded muon sig-nals. Scattering in water will lengthen the travel path of radiation and we obtain a spread out signal.
Figure 5.7b shows this effect increasing at larger DOM separation. As the distance light has to propagate through water grows, the peaks will spread out more. For correlations between DOM 10 and DOM 13 (red graph in figure 5.7b), the sharp rise in signal indicating the boundary of the muon regime is no longer visible. This spread needs to be considered while quantifying the background, but has no effect on the amount of cor-related signals we measure.
The quantification of the uncorrelated background is done by finding the expected amount of correlations in the tails. The efficiencies of each DOM differs, so the amount of background signals measured is unique per DOM. Because of this we evaluate the background per pair separately. We
av-28 Identification of atmospheric muon signals
and over the amount of correlations between 200 ns and 2500 ns. These timewindows will ensure that we measure well outside the muon regime for both first and second neighbor (±70ns) pairs, in order to conserve the retarded signals as well.
To test whether we have no residual correlated signals or systematic back-grounds we compare the average amount of correlations in both the pos-itive and negative tails. Uncorrelated backgrounds are isotropic and we obtain errors only from Poisson noise. As a result when comparing the average rate of coincidences in each tail of a single DOM pair we expect them to be separated by only the differences generated by shot noise. This implies that when we look at the distribution of these differences in terms of the amount of the expected value of the standard deviation of the neg-ative tail (σ) the value of both tails should be equal, but due to random fluctuations we expect the differences between the average intensity of the backgrounds in both tails to be distributed like a Gaussian with a width of
√
2σ. We have compared the tails for each DOM pair in each run used in this thesis. The obtained results are shown in figure 5.9
Figure 5.9:Histogram obtained from subtracting the background signal at nega-tive correlation times from background signals at posinega-tive correlation times. The fit is a gaussian with a mean at -0.6σ and a width of 1.47 σ. σ is the standard deviation of the expected value from the tail of negative correlation times, taken separately for each measurement
The histogram contains the data of 6 measurements with either 17 or 16 data points generating 99 data points. The Gaussian is a very high quality 28
5.2 The correlation method 29
fit having a chi square of just 0.6, but the parameters are not as expected. The mean is located at 0.60σ±0.17σ away from the center with a width of 1.47σ±0.12σ. So we have found a Gaussian misplaced from the expected mean, but the width is as expected. This implies a remainder of some cor-related signals with negative time correlations (downward going signals). We have tested the effects of the offset for each run and have found the impact on our end result to be negligible. However, to prevent ghost sig-nals we evaluate and reduce the contributions of both tails separately. The source of the offset has not been investigated further.
After the amount of uncorralated signals for each DOM pair is found and subtracted from the total number of correlations for each pair, we obtain a histogram with an expected value of 0 for high correlation times as seen in figure 5.8. The results of multiple DOM pairs in a single run are shown in figure 5.10. At high positive and high negative correlation times the num-ber of correlations is now averaged at 0, indicating a successful reduction of uncorrelated signals. This allows us to evaluate and compare the corre-lated events for DOM pairs at varying depths. In figure 5.10 4 histograms, corresponding to DOM pairs: 1-2, 7-8, 13-14 and 17-18 are compared.
Each peak in figure 5.10 resembles the expected shape for muon data
sim-Figure 5.10: The background reduced correlations between DOM 1 (blue), DOM 6 (red), DOM 12 (yellow) and DOM 17 (green) and their respective direct upper neighbors.
ulated in Monte Carlo simulations [3]. The sharp rise of the peak at dt≈
-40 dt is consistent, small deviations in DOM pair separation will deviate the maximum correlation time by 10 ns. Additionally the gradual reduc-tion of signal as dt→0 is in compliance with muon signals as well. The
30 Identification of atmospheric muon signals
ficient to assume a muon signature for now.
The main result we are interested in is the decreasing amount of signal as a DOM pair is located deeper in the sea. The reduction of the signal at lower DOMs is in agreement with our expectation, as lower amount of muons at large depths will decrease the number of correlations and as a result lower the peak for a deeper positioned DOM pair.
We obtain the amount of correlated signal for each DOM pair by integrat-ing over all correlation times for each DOM pair and averagintegrat-ing over time. Figure 5.11 shows the amount of correlated signals as a function of the depth of the bottom DOM in each DOM pair for a direct neighbor analy-sis. We have fitted the data using an exponential fit. The margin of error is
Figure 5.11:The amount of correlated signals as a function of the depth of a DOM pair. The fit is an exponential function: I = e(−0.3+0.0026∗h)
calculated by combining the Poisson errors of the average amount of the background correlations and the Poisson error of the amount of correla-tion in the measurement window. With this we have found an indicacorrela-tion of the reduction in correlations as a function of depth. To test the consis-tency of our technique and the validity of our estimates we have used this technique on the three runs for both the direct neighbor correlations and the second neighbor correlations.
When comparing the results in figure 5.12, we note a unexpected low val-ues for the top three DOM pairs for direct neighbors is consistent across each run. This was also visible in figure 5.10 where upon close inspection the green graph does not take on a higher value then the yellow graph. These consistent outliers are visible in the second neighbor correlations as well. DOM pair 16-18 is consistently over 1σ below the expected value. 30
5.2 The correlation method 31
DOM pair 15-17 does not appear to show any loss of data and seems to be in agreement with the fit. Other features include the low correlation frequency for DOM pair 6-7 and the low correlation frequency of DOM pair 6-8. DOM pair 6-7 is in agreement with our expectation for run 3010, and only -2σ away for the other runs. On its own this would not be rele-vant, however comparing this to the deviations for all runs in DOM pair 6-8 which shows deviations of -1σ, -2σ and>-3σ, and the amount of coin-cidences in the high multiplicity events give us adequate reason to suspect a lower efficiency within this specific DOM.
Due to these low efficiencies causing a lower measured correlation fre-quency we expect a reduction in the steepness of the slope for muon in-tensity as a function of depth. This results in the seemingly consistently high data correlation frequency measured in the DOM pairs 13-14, 14-15, 13-15. These pairs show a consistent 1σ deviation from the fit. Efficiency checks show no reason to assume a higher efficiency at these DOM pairs and our current expectation is that the slope of the fit is higher than pre-sented, due to low performing DOMs. The last noticeable outlier is DOM pair 8-10, which is always higher than expected with a single outlier>3σ. With the each data points sufficiently evaluated we will evaluate the re-sulting depth reduction over all runs. The fit parameters for the function I =eI0+λh, which is the earlier exponential function with h the height from
the seabottom, are shown in table 5.2.
run
I
0λ
χ
2Run 2867 first neighbor
-0.35 ± 0.01
0.0025 ± 0.0001
62.62
Run 2867 second neighbor
-0.46 ± 0.02
0.0025 ± 0.0001
73.05
Run 2888 first neighbor
-0.44 ± 0.02
0.0025 ± 0.0001
29.73
Run 2888 second neighbor
-0.61 ± 0.02
0.0028 ± 0.0002
29.31
Run 3010 first neighbor
-0.30 ± 0.01
0.0026 ± 0.0001
38.82
Run 3010 second neighbor
-0.40 ± 0.02
0.0025 ± 0.0001
39.18
Table 5.2: The fit parameters of each run individually. I0 is the expectedfre-quency of coincidences for a pair with measurement DOM on the seabottom, and λis the slope of the exponential function and the χ2 is given for each fit, direct neighbor data has 16 degrees of freedom and second neighbor results 15 degrees of freedom. Here we find the data to be inconsistent with an exponential, see text for discussion
The values of I0 are the normalization constants of each measurement. Since the detector is not yet calibrated correctly at the moment of writing
32 Identification of atmospheric muon signals
(a)run 2867 direct neighbor correla-tions
(b)run 2867 second neighbor corre-lations
(c)run 2888 direct neighbor correla-tions
(d)run 2888 second neighbor corre-lations
(e)run 3010 direct neighbor correla-tions
(f) run 3010 second neighbor corre-lations
Figure 5.12: The data obtained by using the method discussed in this paragraph for three of our runs. The Left figures show the correlations between DOMs and their direct upper neighbor as a funtion of the depth of the bottom one. The right side pictures show correlations between second neighbors. Fit parameters are also shown in table 5.2
32
5.2 The correlation method 33
the constants should be consistent with each other, but due to the angu-lar cut of 2888 the normalization lies lower for run 2888, and due to higher sensitivity the second neighbor measurements have a lower normalization as well. rn 2867 and 3010 seem to be consistent with each other for both first neighbor and second order neighbor measurement. These differences are noted, but the reduction of signal per unit of distance is only affected by λ. For this reason we continue to focus on the slopes. In this case the ex-ponential fit has also turned out to be a poor model for the obtained data, but as was the case in the multiplicity method, this is likely caused by in-efficiencies in specific DOMs. Further evaluation of the slope values show that the values of the slopes are consistent with each other and we can again estimate the reduction of muon signal as if the exponential is a good model, since the artifacts are consistent through all measurements. The average slope over our measurements is 0.0026±0.00004. Checking with the fit we find the χ2 of 5.5 for 5 degrees of freedom, giving a strong in-dication of the results to be consistent among the different measurements. From this we find a muon halving length of 267±4 meters.
Chapter
6
Discussion
In the previous chapter we discussed two separate ways of extracting sig-nals generated by atmospheric muons and obtained two separate results for their absorption rate in water. The two results are in the same order of magnitude being estimated only 29 ± 7 meters apart. This suggests the merit of both methods, but there is still a significant difference in the found halving lengths. We will evaluate these differences by discussing the strengths and weaknesses of both methods and comparing the gener-ated artifacts.
The multiplicity methods largest downside has been mentioned. In or-der to filter uncorrelated backgrounds we must also omit all low multi-plicity coincidences generated by correlated signals. This can potentially effect the acceptance of the detector for signals of specific energies and an-gles. From previous Monte Carlo studies we have found over a third of all signals to be in this low multiplicity regime [3]. Furthermore the mul-tiplicity method’s need for high mulmul-tiplicity data will make vulnerable to underachieving PMTs, and external sources like bioluminescence. In the data presented in this thesis no significant effects generated by biolumi-nescence events have been quantified and effects have not been taken into account. We have not found evidence of a strong impact of bioluminescent fauna’s effects.
The features in the multiplicity method are partly compensated for by ing the correlation method. Reducing the uncorrelated backgrounds us-ing comparison between DOMs allows us to accurately extract the low multiplicity muon hits as well, giving us access to another regime of sig-nals from atmospheric products. The low multiplicity method makes each DOM much more robust to less efficient PMTs and HRV events. This is
36 Discussion
values of the correlation method generally have a higher reproducibility. On top of that the chances of two simultaneous bioluminence events at different two DOMs in a pair is negligible compared to a single life gen-erated signal which will dominate the data in the multiplicity method for a short period. Yet, the correlation method does have its limitations as well. The need for pairs reduces the amount of data points obtained in our measurements. Direct neighbor measurements will reduce will obtain 17 data points, and second neighbor measurements only 16 as opposed to the multiplicity methods 18 points. Pairs only observe events as both DOMs get hit, this makes the amount hits more dependent on angles, with a still unknown effect.
Despite the lesser impact of a DOM with a moderate efficiency loss, a DOM with a strong loss in efficiency reduce the efficiency of two DOM pairs and hence two data points.
comparing figure 5.4 and 5.11 we find a lot of similarities. The multiplicity shows low hit rates at DOM 6 and the top three DOMs. These low hit rates are also impacting the data shown in the correlation method. All DOM pairs containing one of the low functioning DOMs have a low amount of correlations in this method with the noticeable exception of the DOM pairs 5-6 and 4-6, which appear to be fitted correctly. The set of low hit rates at the top of the string lowers the slope of the graph considerably, making our estimation of the muon’s halving length in water several meters too low. To obtain a better estimation this shortcoming should be addressed. This low estimation also has an effect on the comparison of the obtained halving lengths. The correlation method has estimated a halving length of 29 meters more than the halving length of the multiplicity method, and we should also consider the enforced effect of the low hit rates at the cor-relation method due to the reduction of data points.
In order to obtain a better estimation of the muon depth dependence more research has to be done to find the effects of efficiency on the data. With such a model compensating for the losses in both methods. When this is succeeded we will expect to find a signal which is consistent with an ex-ponential fit and we’ll be able to evaluate the decreasing halving length as a function of the hit’s multiplicity as well. To further the understanding research should also be done to the angular distribution of the incoming muons. The angle at which an atmospheric muon enters the detector will determine the length it had to travel through water. This will effect the abundance of the amount of signal coming from each direction and the energy of the muons as can be seen in figure 5.5 where the angular dis-tribution is visible. cross referencing our results with the known angular distribution of atmospheric signals will allow us to make better estima-36
37
tions of the amount of signal as well as allow us to generate a good esti-mate of the amount of muons mimicking the upward going signals, and the intrinsic efficiency of each DOM in the string.
Chapter
7
Conclusion
In this thesis we have evaluated the performance of the KM3NeT’s ORCA detector by evaluating the consistent background produced by atmospheric muons. By comparing measured signals to models we can find the perfor-mance of each datapoint in the first deployed string of the detector. In order to extract the muon signals we have used two separate methods to reduce the signals generated by uncorrelated signals such as the decay of 40K and dark counts. One method omits data with low multiplicity on our DOM. Previous research has found that only high multiplicity data consists of mostly atmospheric muon signals. This method has the weak-ness that it is more vulnerable to external sources such as bioluminescence and is expected to feel a stronger effect of inefficiencies in the detector, as opposed to the alternative method. Additionally it omits the low multi-plicity muon signals as well. The correlation method compares the signals obtained between two DOMs in order to identify its source. This method is much more robust to singular events and is much more robust compared to the former method, but it is much more dependent of the propagation angle of the incoming particles, and we obtain less data points for each run.
After obtaining the muon signals we have considered remarkable features. We have found the exponential reduction of atmospheric muons as a func-tion of depth to be inconsistent with the found data, which we expect to be caused by low efficiency in specific DOMs. Some causes of these low effi-ciencies have been tested but as of yet no definitive cause has been pinned down. To reveal the effects of the PMT efficiency on the DOMs the PMTs on the DOMs should be evaluated further.
sig-40 Conclusion
3 meters and the correlation method gives us a halving length of 268± 4 meters. The results are in the same order of magnitude as each other and are agree with previous data, but still we obtain different results. These difference is caused by intrinsic differences in the methods and should be evaluated further to obtain a better result. To improve on the obtained results the efficiency of each DOM should be evaluated in depth to ob-tain a possibility to calibrate further. For full calibration a normalization measurement must be done, and for future research should look into the angular distribution of incoming atmospheric signal as a further test. Once all calibration are made an accurate measurement of the exact atmospheric flux can be made.
40
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