Simulation study of meteors for the Mini-EUSO experiment on the ISS

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Simulation study of meteors for the Mini-EUSO experiment on the ISS

John Sigvant

^∗

and Petter Bühlmann

^†

∗sigvant@kth.se, ^†buhlman@kth.se

SA114X Degree Project in Engineering Physics, First Level Supervisor: Christer Fuglesang

Department of Physics School of Engineering Sciences Royal Institute of Technology (KTH)

Stockholm, Sweden TRITA-FYS-2017

May 20, 2017

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Abstract

Mini-EUSO is an UV telescope developed by the JEM-EUSO collaboration and will be placed on the international space station in the end of 2017. Mini-EUSO is a precursor based on the same technology as the larger UV telescope known as JEM-EUSO. The primary objective of Mini-EUSO is to test the system to help to optimize the JEM- EUSO instrument. A secondary objective of this mission is to study UV phenomena such as Extreme Energy Cosmic Rays, transient luminous events, strange quark matter, space debris and meteors in the Earth’s atmosphere. In this bachelor thesis we focused on studies of meteors. The existing simulation software ESAF will be used to perform simulations and by analyzing the output data a trigger algorithm will be developed to be able to distinguish meteoric events and also investigate the faintest meteoric events that can be detected.

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Chapter 1 Introduction

1.1 Background

JEM-EUSO (Extreme Universe Space Observatory on board the Japanese Experiment Module) is an international collaboration between research institutes in sixteen coun- tries [1]. The main purpose of this collaboration is to put a telescope in space to detect and measure a physical phenomena known as Extreme Energy Cosmic Rays (EECRs).

EECRs are rare particles with energies above 5 × 10¹⁹ eV. When these particles enter the Earth’s atmosphere they interact with air molecules and creates a shower of particles. This phenomena is known as Extensive Air Shower (EAS) and could involve up to 100 × 10⁹ particles and extend to several hundred kilometers. A large amount of these particles are electrons which excite nitrogen molecules in the atmosphere. When the nitrogen molecules de-excite UV light is emitted. To detect these particles JEM-EUSO is under development to measure the emitted UV light in the range 290-430 nm. Mea- surements in this range also give the opportunity to study other UV phenomena such as transient luminous events (TLEs), strange quark matter, space debris and meteors.

As a precursor to this misson, Mini-EUSO is an instrument based on the same tech- nologies as JEM-EUSO but on a smaller scale. Mini-EUSO is planned to be put in orbit on the International Space Station (ISS) in late 2017. Mini-EUSO will be placed in the Russian Zvezda Module on ISS in a UV-transparent window facing the earth at all times. The Mini-EUSO project will help to optimize the JEM-EUSO instrument and also provide important observations of the mentioned UV phenomena.

In this bachelor thesis the existing software package ESAF (EUSO Simulation and Analysis Framework) [2] will be used to simulate different meteor events to get an insight on what data can be expected from such event. Based on these simulations an algorithm will be created on how to distinguish a meteor event from the collected dataset.

1.2 General information about Meteoric Phenomena

Meteoric Phenomena is the term used for the physical phenomena when a meteoric body enter a planetary atmosphere [3]. A meteoric body also known as meteoroid is defined as a cosmic body, origination from asteroids or comets, entering the atmosphere. When entering the atmosphere the meteoric body or meteoroid interacts with air molecules and is heated to very high temperatures and begins to melt and vaporize. This interaction

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produces luminosity from the vapor and the air and this phenomena is called a meteor.

Directly behind the meteor, a wake is created, the wake’s luminosity is caused by the same interaction as for a meteor. Along the path of the meteor the air is ionized which leaves a trail called a persistent train. The typical mass of the meteoroids varies approximately between 10⁻⁷ g to 10⁷ g. If a meteoroid reaches the planetary surface it is called a meteorite. Meteorites can originate from meteoroids with masses up to 10¹² g. The process when a meteor breaks up into smaller fragments is referred to as the fragmentation process, these smaller fragments can have masses as small as 10⁻¹² g. The process by which a meteor loses its mass is called ablation and is mainly due to vaporization, fragmentation and fusion. At the end of the meteor path, the meteor suddenly can break up into many fine fragments and in doing so a light-burst occurs. Meteoric bodies enter the atmosphere at a variety of speeds depending on their trajectories and the laws of gravitation. There are three main meteoroid types: Stone, iron-stone and iron [4].

About one quarter of all meteorites are iron meteorites, almost exclusively made up of nickel-iron. The other three-quarters are stony meteorites, or stone-iron meteorites [5].

Meteoroids can be divided into three groups. One-third are known as chondrites which is ordinary stones. The second group contains weaker carbonaceous chondrites and the third group consists cometary material, made of ice and snow and these are unable to reach the Earth’s surface. Meteoroids are made up from various elements. The elements with emission lines in the UV spectrum measured by Mini-EUSO are according to Ceplecha et al. [6] N, M g, Si, Ca, T i, Cr, M n, F e, Co, N i and Sr. Of these elements M g, Ca, F e and Cr are responsible for the strongest emission lines. M g are the strongest for slow velocities and Ca for fast velocities.

1.2.1 Derivation of meteor velocities

Earth’s orbital eccentricity is about 0.0167 according to NASA [7], which justifies the assumption that Earth’s motion around the sun is roughly circular. For circular motion the magnitude of the centripetal acceleration is given by a_c = v²/r where v is the speed and r is the radius of the motion circle. Newton’s second law of motion states that the magnitude of the resulting force on an object is F = ma where m is the mass and a is the acceleration of the object. The magnitude of the gravitation can be described by Newton’s law of universal gravitation F = GM m/R² where G is the gravitational constant, M and m are the involved masses and R is the distance between these masses.

According to equations of motion [5] the resulting force on the Earth due to gravitation from the Sun is given by

m⊕v_⊕²

R = GMm⊕

R²

⇒ v⊕ = r

GM

R . (1.1)

where m⊕, v⊕ are the mass and velocity of the Earth respectively and M is the mass of the Sun. To derive the minimum and maximum velocity of a meteoroid in Earth’s orbit the following reasoning was considered [5]. For the meteoroid the kinetic energy is given by Ek = mv²/2. The work done by the gravitational force from the Earth on the meteoroid from infinity to distance r between the masses is given by

E = Z r

∞

F dr⁰ = Z r

∞

GM⊕m

r⁰² dr⁰ = −GM⊕m

r . (1.2)

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If we consider the total energy for the meteoroid in Earth’s orbit and the total energy when the meteoroid is at a distance infinity large from the Earth the law of conservation of energy gives

E_k+ E = 0,

as the the velocity at infinity is zero which means that the kinetic energy is zero and the distance r is infinitely large which makes the gravitational energy equal to zero. This implies that

E_k = −E, (1.3)

in Earth’s orbit. To derive the minimum speed it was assumed that all other forces on the meteoroid were cancelled out. The expression for the kinetic energy and equation (1.2) inserted in equation (1.3) gives

mv²

2 = GM⊕m r

⇒ v_min = r

2GM⊕

r . (1.4)

To derive the maximum velocity for a meteoroid the same assumption that its kinetic energy is equal to the gravitational energy is made but this time due to the gravitation of the Sun to the distance to Earth’s orbit. This gives

mv²

2 = GMm r

⇒ v_max = r

2GM

r . (1.5)

To achieve the maximum speed relative to earth we assume that the meteoroid is pulled by the Sun in the opposite direction of the Earth which gives the maximum speed as the sum of Earth’s speed relative the Sun and maximum speed of the meteoroid. This analysis gives speeds varying from 11 km/s to 73 km/s. This result agrees with the result from the report written by Ceplecha et al. [6].

1.2.2 Fundamental equations

The study of meteors is mainly based on three fundamental equations [3]. The deceleration equation, the mass-loss equation and the luminosity equation. By assuming that the momentum lost of the meteoroid is proportional to the momentum of the resisting air flow the deceleration equation can be described as

Mdv

dt = −ΓSρv², (1.6)

where M is the meteoroid mass, v is the meteoroid velocity, Γ is the air drag coefficient, S is the maximum mid-sectional area of the meteoroid and ρ is the air density. Assuming that a portion of the kinetic energy flow Sρv³/2 is transferred to the ablation the mass- loss equation can be written

dM

dt = −ΛSρv³

2Q , (1.7)

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where Λ is the portion of the kinetic energy flow to ablation and Q is the heat of vaporization or fusion of the meteoroid including the energy needed to heat dM from initial temperature to its vaporization or melting temperature. All other less energy consuming events are included in Λ. The luminosity equation is based on the fact that most of the radiation comes from the emission of its evaporating atoms. Assuming that the radiation intensity I of the meteor is proportional to the kinetic energy of the mass dM evaporated in the time dt the luminosity equation is given by

I = τ

−dM dt

v²

2, (1.8)

where τ is the luminosity coefficient which generally depends on the velocity, mass and composition of the meteoroid. These fundamental equations can also be used to derive other quantities such as flux density and absolute magnitude. For isotropic radiation from an object of spherical shape the flux density is [5]

F = πI. (1.9)

From the flux density (1.9) the total flux at a distance r can be described as

L = 4πr²F = 4π²r²I, (1.10)

if the flux is assumed to be distributed evenly on a spherical surface whose area is 4πr². A quantity measuring the intrinsic brightness of a luminous object is the absolute magnitude. By definition an object with absolute magnitude M = 0 corresponds to a total flux L₀ = 3.0 × 10²⁸ W. An objects absolute magnitude over all frequencies is given by

M = −2.5log L L₀

. (1.11)

By inserting equation (1.8) and (1.10) in (1.11) the following expression for the absolute magnitude can be achieved

M = −2.5log

−dM dt

2τ (πrv)² L0

. (1.12)

Based on observations, for instance made by photometry or radar [6], it is possible to determine the parameters in these equations.

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1.3 The Mini-EUSO instrument

Figure 1.1: A CAD representation of the Mini-EUSO instrument. The main sub-systems are shown: the two double-sided Fresnel lenses, the PDM and the readout electronics.¹

The Mini-EUSO instrument weighs about 30 kg and measures 37 × 37 × 62 cm³ [8].

The instrument consists of mainly three systems, an optical system, a Photo Detector Module (PDM) and a data acquisition system. The optical system includes two Fresnel lenses, each with a thickness 11 mm and a diameter of 25 cm, referred to as Front lens and Rear lens in Figure 1.1. Fresnel lenses can be made thinner and lighter and collect more oblique incoming light than comparable conventional lenses. The Fresnel lenses used have a field of view (FoV) of 19^◦, which is the angle from the nadir axis, to focus the incoming light on the PDM. It is going to be the first time the Fresnel lens will be used in space.

The PDM consists of 36 multi-anode photomultiplier tubes (MAPMTs) referred to as the Focal surface in Figure 1.1. Each photomultiplier tube consists of 64 pixels covering about a 25 km² area per pixel on Earth’s surface assuming that the ISS is 400 km above ground. That makes a total of 2304 pixels and a total ground area of ∼ 58000 km². The data acquisition system receives photon pulses from the PDM which are digitized and then sent to the CPU for data management and stored on the memory unit. Due to limitations on data storage a multi-level trigger system is implemented to capture interesting events at higher time resolution. The power consumption of Mini-EUSO is 30 W and it gets its power supply from the ISS.

1Picture taken from the report, “The integration and testing of the Mini-EUSO multi-level trigger system”, Advances in Space Research (January 3, 2017) by A. Belov et al.

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1.3.1 The multi-level trigger system

The duration of the different UV events spans from micro seconds for EECRs and TLEs up to seconds for meteors. In order to optimize the data output of the instrument a multi-level trigger system is implemented. The lowest time resolution is set to 40,96 ms per gate time unit (GTU) which is the time the MAPMTs counts the number of photons before reset. This resolution is enough to observe meteoric events in great detail. This resolution is referred to as level three and functions as an continuous readout. In the event of a TLE the second level should be triggered and a resolution of 320 µs per GTU starts.

The highest resolution is 2.5 µs per GTU and starts when the first level is triggered.

The first level is mainly made for EECR-like events This multi-level trigger system is implemented in order to maximize the scientific output of the instrument [9].

1.4 Objective

The main purpose of this thesis was to investigate the faintest meteoric event that could be detected by a custom-made trigger algorithm. The existing simulation software ESAF was used to reconstruct different meteoric events. Based on the output data from these simulations a trigger algorithm was created on how to distinguish a meteoric event from a collected dataset.

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Chapter 2 Methodology

2.1 Determine parameters

In ESAF it is possible to vary a number of parameters. The most important ones for the purpose of this thesis are the velocity and the absolute magnitude of the meteoroid. The mass and volume of the meteoroid were set automatically, using a simple meteor model in the software, on what magnitude, density and velocity that were chosen.

2.1.1 Velocity

The velocity of the meteor was set as vector, ~v = (v_x, v_y, v_z), in a cartesian coordinate system. The ISS was assumed to travel with a velocity of 7.7 km/s according to European Space Agency [10] set in the x direction in ESAF. The speed of the meteor was calculated as the norm of the velocity vector

k~vk =q

v²_x+ v²_y + v²_z. (2.1) The angle of incidence was defined relative to the nadir axis of the instrument and calculated with elementary trigonometry as

φ = arctan

sv²_x+ v²_y v²_z

!

. (2.2)

To get different photon concentrations on the focal plane several meteoric trajectories were chosen and speeds ranging from 11 km/s to 73 km/s, as derived in section 1.2.1.

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2.1.2 Absolute magnitude

The published paper on meteors for JEM-EUSO [1] states that the JEM-EUSO telescope are able to detect meteors up to absolute magnitude M = +7 and the Mini-EUSO telescope up to absolute magnitude M = +5 under dark conditions based on simple estimates. To find the limit for detectable meteoric events, using a custom-made trigger algorithm for Mini-EUSO, meteors ranging from M = +5 and up were chosen to simulate.

The flare also known as burst was set to have a absolute magnitude of M = +3 and to last for 0.5 s to match the simulations made by Abdellaoui et al. [1] for comparison.

2.1.3 Density

The meteoroids density were of less importance for our purpose since ESAF by default calculate the mass and the volume of the meteoroid to match the chosen value for absolute magnitude. Due to this the density was set fixed to 3.55 g m⁻³ as assumed by Abdellaoui et al. [1]. This value also match the mean density for meteoroids according to Flynn [4].

2.1.4 UV Background

According to Adams et al. [11] the UV background without moon is about

500 photons/m²/ns/sr which corresponds to 1 count/pixel/GTU. The UV Background was superimposed onto the simulated data assuming a Poisson distribution of background events centered on 1 count/pixel/GTU [9]. This condition is referred to as optimal dark background.

2.2 The trigger algorithm

The output data from ESAF were able to get as a text file containing matrices including information from the simulated event. The elements in one matrix represented all the 48 × 48 pixels of the MAPMTs on the focal plane, where each element contained the sum of photons who reached that specific pixel in a time frame of 40.96 ms. To create the algorithm the software Matlab from Mathworks were used. First the output text file were loaded into Matlab. For each matrix the standard deviation, σ, and mean value, µ, of the including elements were calculated. The algorithm then divided each matrix in to smaller units corresponding to the MAPMTs and went through each element and searched for elements containing values bigger than µ + 4σ. This value is referred to as the threshold value. If such element was found the algorithm recorded which MAPMT was triggered and which matrix the element belonged to. At the end of the event a mesh plot of the total sum of photons on the focal plane was presented. For better visual presentation of the event a signal amplifier was created. The amplifier added a value of 5000 photons to all the elements that were containing values bigger than the threshold value. The effect of this amplifying function is illustrated in Figure 2.2-2.3.

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2.3 Simulations

ESAF is a numerical simulator consisting of two packages, a simulation package and a reconstruction package [12]. ESAF is written in C++ and based on the ROOT framework. The simulation has been divided in two main subsystems, the light generation, taking care of all the physical phenomena occurring outside EUSO that can produce photons on the entrance of the detector, and the detector, where the photons are traced through the telescope and the response of the electronics is simulated. The simulator did not take any deceleration of the meteor into account. For all simulations made in this project the beginning height of the event was set to 95 km and the duration of the event was set to 2 s. The simulations was performed in order to Setting 1-5 in Table 2.1 for absolute magnitudes from M = +5. After each simulation UV background was added to the simulation output. Then the trigger algorithm was run on the output data and then the procedure was repeated for an increase in absolute magnitude of one integer.

All simulations were performed three times each for statistical reasons.

Setting v_x v_y v_z k~vk φ

1 2.2 km/s 0 km/s -12.0 km/s 12 km/s 10^◦ 2 7.7 km/s 0 km/s -44.0 km/s 45 km/s 10^◦ 3 -9.0 km/s 7.0 km/s -4.1 km/s 12 km/s 70^◦ 4 -30.0 km/s 30.0 km/s -15.5 km/s 45 km/s 70^◦ 5 -47.0 km/s 50.0 km/s -25.0 km/s 73 km/s 70^◦

Table 2.1: Simulation schedule of settings with velocity parameters and the calculated speed and incidence angle according to formula (2.1) and (2.2).

.

Gtus 0-799739 Hits on screen: 80293

X [mm]

−100 −50 0 50 100

Y [mm]

−100

−80

−60

−40

−20 0 20 40 60 80

Counts

0 5 10 15 20 25 30

(a) Incident angle 70^◦ from nadir axis with velocity 45 km/s.

Gtus 0-799741 Hits on screen: 52027

X [mm]

−100 50

− 0 50 100

Y [mm]

−80

−60

−40

−20 0 20 40 60 80 100

Counts

0 5 10 15 20 25 30

(b) Incident angle 10^◦ from nadir axis with velocity 45 km/s.

Figure 2.1: Simulated focal plane view of meteoric event with absolute magnitude M = +5 with a burst of M = +3. The duration of the event was set to 2 s.

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3.05 0 50

5 45 3.1

10 40 15 35 3.15

20 30

Y position X position

25 25 10⁵

Photon counts

20 3.2

30 35 15

40 10 3.25

5 45

0 50 3.3

(a) With amplified meteor signal.

3.09 0 50

5 45 3.1

10 40

35 3.11

15 20 30

25 3.12

25

Photon counts

10⁵

30 20 3.13

35 15 40 10 3.14

5 45

0 50 3.15

(b) Without amplified meteor signal.

Figure 2.2: Sum of photon counts on the focal plane of meteoric event with absolute magnitude M = +6 with a burst of M = +3. The duration of the event was set to 2 s with background signal. The velocity was set to 45 km/s with incident angle 70^◦ from nadir axis. Threshold value was set to µ + 4σ. This event was defined as detectable according to conditions stated in Chapter 3.

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3.2 0 50

45 3.3

5 10 40 3.4

15 35 20 30 3.5

25 25

Photon counts

10⁴

3.6

30 20 35 15 3.7

10 40

3.8

5 45

0 50 3.9

(a) With amplified meteor signal.

3.22 0 50

5 45 3.24

10 40

35 3.26

15 20 30

25 3.28

25

Photon counts

10⁴

30 20 3.3

35 15 40 10 3.32

45 5 50 0 3.34

(b) Without amplified meteor signal.

Figure 2.3: Sum of photon counts on the focal plane of meteoric event with absolute magnitude M = +6 with a burst of M = +3. The duration of the event was set to 2 s with background signal. The velocity was set to 45 km/s with incident angle 10^◦ from nadir axis. Threshold value was set to µ + 4σ. This event was defined as undetectable according to conditions stated in Chapter 3.

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Chapter 3 Results

As each pixel was looked at as independent and the fact that all pixels were identically Poisson distributed their sum tends to an normal distribution according to the central limit theorem [13]. The probability that a UV background value exceeds the threshold value in one pixel integrated over 40.96 ms was calculated to 3.167×10⁻⁵ thus for all 2304 pixels the probability becomes 7.3 %. A two seconds event makes up about 48 GTUs for 40.96 ms this means that approximately less than four GTUs are triggered because of UV background. Therefore a limit of five triggered GTUs was set as a condition for detectable. A second condition was set that the triggered pixels had to be in the same MAPMT or in neighboring MAPMTs. In Table 3.1-3.5 the # GTUs corresponds to the number of GTUs containing triggered pixels, # Focal plane hits corresponds to the total number of photons that reached the focal plane without UV background of the event, # Pixels (Detectable) corresponds to the number of pixels defined as detectable according to the conditions and # Pixels (Total) corresponds to the total number of triggered pixels.

All values in Table 3.1-3.5 corresponds to the arithmetic mean value with the standard deviation of the three simulations. The absolute magnitude is referred to as M .

M # Focal plane hits # GTUs # Pixels (Detectable) # Pixels (Total)

+5 71971 ± 80 42 ± 2 44 ± 3 44 ± 3

+6 31123 ± 212 3 ± 1 0 3 ± 1

Table 3.1: Results from simulation of Setting 1 in Table 2.1: The velocity was set to 12 km/s for an angle of incidence of 10^◦ from nadir axis.

+5 52334 ± 380 23 ± 3 21 ± 1 23 ± 3

+6 23268 ± 68 2 ± 1 0 2 ± 1

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+5 89760 ± 304 37 ± 3 53 ± 3 54 ± 4

+6 38242 ± 89 16 ± 1 14 ± 1 16 ± 1

+7 17833 ± 106 2 ± 1 0 2 ± 1

+5 80193 ± 141 36 ± 0 50 ± 1 50 ± 1

+6 34414 ± 197 16 ± 2 16 ± 1 17 ± 2

+7 16329 ± 70 2 ± 0 0 2 ± 0

+5 72961 ± 91 34 ± 1 44 ± 2 46 ± 2

+6 31574 ± 74 13 ± 2 12 ± 1 14 ± 1

+7 15147 ± 57 2 ± 1 0 2 ± 1

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Chapter 4 Discussion

4.1 Analysis

4.1.1 Evaluation of the simulation

In order to limit the total amount of simulations, simulations of borderline cases were focused on. To get a high photon concentration on the focal plane, a narrow incidence angle of 10^◦ was chosen and to achieve a more scattered distribution of photons the incidence angle of 70^◦ was chosen, a result of this can be seen in Figure 2.1. In both cases it was desired to get both a high and low speed in the range of meteror velocities. In the case of the narrow angle about 45 km/s was the maximum velocity because otherwise the meteor would hit the Earth’s ground which was impossible to simulate. To be able to do a comparison with the scattered distribution the velocity of 45 km/s was also simulated for the incidence angle of 70^◦. For the narrow angle of 10^◦ the velocity in the x direction was chosen as close as possible to the ISS. For Setting 1 in Table 2.1 the velocity, v_x was set to the only possible maximum of 2.2 km/s in order to maintain the incidence angle.

Yet again to limit the amount of simulations the absolute magnitude was set to only integer values. Due to the objective in section 1.4, to find how faint meteors can be and still be detected, only optimal UV background was simulated. According to Adams et al. [14], by taking into account the motion of the ISS and anthropogenic light sources (like cities), and natural phenomena such as lightnings and Moon phase, the UV background condition used in this report are met on the average of 20 % of the time.

4.1.2 Evaluation of the trigger algorithm

According to Abdellaoui et al. a meteor signal of a magnitude M = +5 would exceed 3σ − 4σ over the UV background. The same statistical analysis as in Chapter 3 for the probability that a UV background value exceeds the threshold value shows that three pixels per GTU of 40.96 ms would be triggered if the threshold value was set to µ + 3σ. This threshold value was considered to be to low because to many pixels would be triggered by the UV background. In that case the possibility to distinguish a meteoric event from UV background would decrease drastically. To increase the probability that in fact a meteoric event has been detected the threshold value was chosen to µ + 4σ.

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4.2 Conclusions

The results indicates that it was possible to detect meteor events with absolute magnitude M = +6 according to the detectable conditions for 60 % simulated velocities. The meteor events with M = +6 that wasn’t detectable had an incidence angle of 10^◦. A possible explanation for this might be that the atmosphere reflects the largest fraction of photons of all the simulations because for this incidence angle the meteor penetrates the atmosphere deepest of all simulations. It is also observable in Table 3.1-3.5 that the

# Focal plane hits are decreasing with the meteor depth in the atmosphere which justifies this theory. It might be possible to distinguish fainter meteoric events if the detectable conditions are lowered but this of course also implicates a higher risk for UV background to be mistaken for a meteoric event. The trigger algorithm was developed to handle any time resolution. This could be suitable for similar studies to this thesis on other levels of the multi-level trigger system described in section 1.3.1. A conceivable improvement of the trigger algorithm might be to divide the focal plane into pixel level instead of MAPMTs and do a further investigation of new conditions taking different meteoric trail patterns on the focal plane into account. An interesting use of the actual output data from Mini-EUSO could be to combine the data with the fundamental equations in section 1.4.4 to increase knowledge of the meteoric phenomena.

4.3 Acknowledgements

We would like to thank Francesca Capel for tributing with an tremendous amount of help and support and our supervisor Christer Fuglesang for his guidance and encouragement through this project.

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Simulation study of meteors for the Mini-EUSO experiment on the ISS