Master's Thesis

MASTER'S THESIS

Titan’s Atmospheric Composition from the Analysis of Cassini/UVIS Stellar Occultation

Ivan Lehocki 2014

Master of Science (120 credits) Space Engineering - Space Master

Luleå University of Technology Department of Computer Science, Electrical and Space Engineering

Titan’s atmospheric composition from the analysis of Cassini/UVIS stellar occultation

Ivan Lehocki

Luleå University of Technology, Sweden

Paul Sabatier University, France

Thesis carried out in:

Laboratoire Interuniversitaire des Systèmes Atmosphériques, Créteil, France

Supervised by:

Professor Yves Bénilan

University Paris-Est Créteil, France

Dr. Fernando Javier Capalbo

University Paris-Est Créteil, France

Examined by:

Dr. Mathias Milz

Luleå University of Technology

Kiruna, Sweden

Abstract

One of the fundamental questions concerning each and every human being is: are we alone in this Universe? This deceptively simple question, with potentially profound implications for the trajectory of civilization's development (regardless of the answer), is one of the principal driving forces for exploration of the Solar System and beyond.

One of the primary candidates for the study of the origin of life beyond Earth is Titan, Saturn's largest moon. Unlike other natural satellites revolving around the Solar System's planets, Titan has an atmosphere. This atmosphere is thick and mostly dominated by molecular nitrogen (N2) and methane (CH4) to a lesser degree. The aforementioned molecules, coupled with the Sun's electromagnetic radiation (EMR) in the far ultraviolet (FUV) part of the spectrum (~110-190 nm), as well as charged particles stemming from Saturn’s strong magnetic field, are giving rise to higher complexity organic molecules, molecules that are very interesting from an astrobiological point of view.

Identification of some of the molecules existing in Titan's upper atmosphere through the detection of well-defined absorption features, in an altitude range between 400-1400 km (above Titan's surface), is now possible with the Ultraviolet Imaging Spectrograph (UVIS) onboard Cassini. Its spectral resolution surpasses that of similar instruments in preceding missions (Vervack et al., 2004). Moreover, laboratory work providing higher spectral resolution absorption cross section (ACS) data can be used together with measured transmission spectra to further aid the identification of molecules. Beyond the detection, spatial distribution of species, their abundances as a function of altitude as well as temperature profiles, are deductible parameters from UVIS altitude-dependent transmission spectra.

The interpretation of data is aided by the radiative transfer equation which describes the propagation of electromagnetic (EM) waves through a medium, for example an atmosphere. It serves as a link between measured and deduced quantities.

Researchers throughout the world are trying to decipher UVIS data with their in-house softwares. One such software package was developed in the Space Organic Physicochemistry group

(Groupe de PhysicoChimie Organique Spatiale – GPCOS) of Inter-universittary Laboratory of Atmospheric Systems (Laboratoire Interuniversitaire des Systèmes Atmosphériques – LISA) in Créteil, France (Capalbo, 2014). The software incorporates several modules, one of which is called MPFIT (Markwardt, 2009). This is the heart of the software as it performs spectral inversion in order to obtain column densities from measured (altitude dependent) transmission spectra. Therefore, the outputs of the MPFIT routine, namely column densities of 8 species (CH4,

C2H2 (acetylene), HCN (hydrogen cyanide), C2H4 (ethylene), C4H2 (diacetylene), HC3N

(cyanoacetylene), C6H6 (benzene) and aerosols), were studiously examined in synthetic modelling tests where they were compared to input "true" column densities. Thus, the characterization of the MPFIT routine, i.e. the dependence of the final solutions on the initial guess factor multiplying the initial column densities, was one of two main tasks of this work.

This was followed by in-depth search of Outer Planetary Universal Search (OPUS)1 online database with the aim of creating a stellar occultation list from which an occultation for further analysis was chosen. Finally, the retrieved abundances of T41 II occultation were compared to previously published results of T41 I occultation which was occurring on the same day, but some 6 hours earlier and on different latitude-longitude coordinates.

The ultimate goal of this thesis was to contribute knowledge towards comprehending complex organic chemistry taking place in Titan’s atmosphere. By studying Titan, we are studying Earth and its atmosphere in its prebiotic stage of evolution.

1 OPUS search tool website: http://pds-rings.seti.org/search

Contents

List of Figures ...... V List of Tables ...... IX 1. Introduction ...... 1 1.1. Titan and its atmosphere ...... 1 1.2. Photochemical models ...... 4 1.3. Observation and exploration ...... 5 1.3.1. Cassini-Huygens mission...... 6 1.3.2. UVIS instrument ...... 8 1.3.2.1. UVIS data ...... 10 1.4. Project description ...... 11 1.5. Report outline...... 12 2. Theory and methods ...... 13 2.1. Stellar occultation ...... 13 2.2. The equation of radiative transfer ...... 15 2.3. Methods for analysis of stellar occultation data ...... 20 2.3.1. Column density and number density retrieval ...... 20 2.3.2. Synthetic modeling ...... 21 2.3.2.1. Retrieval matrices ...... 23 2.3.3. Methods applied in real data analysis ...... 28 2.3.3.1. Ancillary data ...... 29 2.3.3.2. Procedure ...... 31 2.3.3.3. Uncertainties ...... 35 3. Results ...... 38 3.1. Synthetic modelling – retrieval matrices ...... 38

3.1.1. CH4 ...... 39

3.1.2. C2H2 ...... 40 3.1.3. HCN ...... 41

3.1.4. C2H4 ...... 42

3.1.5. C4H2 ...... 43

3.1.6. HC3N ...... 44

III

3.1.7. C6H6 ...... 45 3.1.8. Aerosols ...... 46 3.2. Real data analysis - T41 II stellar occultation ...... 47 Conclusions ...... 57 Acknowledgments ...... 60 Appendix A – Influence of initial guess factor on column density calculation ...... 62 Appendix B – Softwares and tools used ...... 67 Bibliography ...... 68 Acronyms ...... 72

List of Figures

FIGURE 1.1: DIONE PASSING BEHIND TITAN, BOTH IN FRONT OF THE PLANET SATURN AS SEEN BY CASSINI ON MAY 21, 2011. (IMAGE

CREDIT: NASA/JPL/SPACE SCIENCE INSTITUTE, 2011)...... 2

FIGURE 1.2: TENTATIVE TEMPERATURE PROFILE OF TITAN’S ATMOSPHERE AS FOUND IN YELLE ET AL. (1997) AND DIVISION BY LAYERS. THE

RECOMMENDED (REC), MINIMUM (MIN) AND MAXIMUM (MAX) MODELS ARE SHOWN. IN ADDITION, EXTENSIONS OF THE IONOSPHERE

(SOLID DOUBLE ARROWS) AND THE HOMOPAUSE (DASHED DOUBLE ARROW) ARE DENOTED...... 3

FIGURE 1.3: SCHEMATIC OF THE PHOTOCHEMISTRY OF N2 AND CH4 IN TITAN’S ATMOSPHERE (ATREYA ET AL., 2006). MOLECULES IN BLACK

BOLDED ELLIPSES (LEFT) AND RECTANGLES (RIGHT) ARE SPECIES USED IN CALCULATIONS OF ABUNDANCES IN THIS WORK (SEE CHAPTER

3 FOR DETAILS)...... 4

FIGURE 1.4: CASSINI ORBITS SATURN (ARTISTIC DEPICTION). SOURCE: MICROSOFT, 2006...... 6

FIGURE 1.5: SCHEME OF UVIS FUV CHANNEL. FROM ESPOSITO ET AL. (2004)...... 9

FIGURE 2.1: PRINCIPLE OF STELLAR OCCULTATION. SPECTRA SHOWN ARE MEASURED SPECTRA FOR T41 II OCCULTATION (THAT WILL BE

THOROUGHLY ANALYZED IN SECTION 3.2). SOURCE SPECTRUM I0 IS THAT OF THE ADHARA STAR (KNOWN AS Ε CANIS MAIORIS IN

BAYER DESIGNATION). AT 1200 KM HEIGHT ABOVE TITAN’S SURFACE (LEFT POINT ON LINE 2), THE SPECTRUM IS NEGLIGIBLY

MODIFIED (ONLY) IN SHORTER WAVELENGTH RANGES CORRESPONDING TO THE START OF ABSORPTION BY METHANE MOLECULES.

LASTLY, AT 650 KM ABOVE TITAN’S SURFACE (LEFT POINT ON LINE 3) THE SPECTRUM IS SIGNIFICANTLY MODIFIED SINCE ALMOST ALL

OF THE STAR’S LIGHT (IN THE FUV PART OF THE SPECTRUM) IS ABSORBED BY ATOMS AND MOLECULES PRESENT IN LOS BETWEEN THE

UVIS INSTRUMENT AND ADHARA. SIZES OF TITAN AND UPPER ATMOSPHERE CONTOURS ARE DRAWN TO SCALE. TWO CIRCLES

DENOTING THE UPPER ATMOSPHERE ARE AT 400 AND 1400 KM ABOVE TITAN’S SURFACE. TAKEN FROM ESA (2014) AND

SUBSTANTIALLY ALTERED FOR THE PURPOSES OF THE THESIS...... 14

FIGURE 2.2: SCHEME OF SPHERICALLY SYMMETRIC ATMOSPHERIC LAYERS CREATED FOR THE ANALYSIS. LAYER I HAS A NUMBER DENSITY NI.

THE DISTANCE FROM TITAN’S CENTER TO THE UPPER END OF THE LAYER I IS RTOP,I. DI,J CORRESPONDS TO THE DISTANCE RADIATION

TRAVERSES ACROSS THE LAYER I WHEN PROBING THE TANGENT ALTITUDE AMIDST LAYER J AND IS REFERRED TO AS THE OPTICAL PATH.

FURTHERMORE, THE UVIS PROBING REGION (400-1400 KM) AND IGNOROSPHERE (500-950 KM) ARE DENOTED. SIZES OF TITAN

AND THE UPPER ATMOSPHERE CONTOURS ARE DRAWN TO SCALE. TAKEN FROM CAPALBO (2014) AND MODIFIED FOR PURPOSES OF

THIS THESIS...... 18 2 FIGURE 2.3: ABSORPTION CROSS SECTION (CM ) VS. WAVELENGTH (NM). ONLY ACS-S OF SPECIES USED IN CALCULATIONS ARE SHOWN.

ACS WAVELENGTH-DEPENDENCY OF AEROSOLS IS SHOWN SEPARATELY IN THE UPPER RIGHT CORNER OF THE LOWER SUBPLOT.

RECTANGLES IN BOTH SUBPLOTS DEFINE THE RANGE OF ESTABLISHED BINS (WHICH ARE PRESENTED IN TABLE 2) AND ARE COLORED

ACCORDING TO SPECIES. NOTE THE OVERLAP OF SPECTRAL FEATURES AMONG SPECIES. THIS IS ALSO REFLECTED IN BINNING. FOR

EXAMPLE, BINS OF SIX SPECIES OVERLAP IN THE NARROW 139.4-145 NM WAVELENGTH RANGE...... 27

FIGURE 2.4: WORKFLOW DIAGRAM. TRANSMISSION AS A FUNCTION OF ALTITUDE IS CALCULATED FROM MEASURED UVIS DATA COMBINED

WITH ANCILLARY DATA. SIMULTANEOUSLY, ABSORPTION CROSS SECTIONS, PUBLISHED MODEL PROFILES AND THE UVIS INSTRUMENT

FUNCTION ARE COMBINED TO GENERATE A SIMULATED TRANSMISSION. THEN, MPFIT SEARCHES FOR AN OPTIMAL SET OF COLUMN

DENSITY PROFILES. THESE CAN FINALLY BE INVERTED FOR NUMBER DENSITIES. FROM CAPALBO (2014)...... 29

FIGURE 2.5: GEOMETRY OF AN OBSERVATION. THIS ANCILLARY INFORMATION IS PROVIDED BY NAIF. CREDITS: NAIF/NASA (2014). .... 30

FIGURE 2.6: LEFT SUBPLOT: RAW LIGHT CURVE VS. TIME INDEX FOR T13 AND T41 II FLYBYS. NOTE THAT THERE IS A PLETHORA OF

MEASUREMENT POINTS ABOVE TOA FOR THE T41 II STELLAR OCCULTATION. THIS IS NOT THE CASE FOR THE T13 OCCULTATION,

THEREFORE ITS FURTHER ANALYSIS IS IMPOSSIBLE. NOTE ALSO THAT T13 WAS INGRESS AND T41 II WAS EGRESS OCCULTATION. RIGHT

SUBPLOT: THE STAR’S X- AND Y-COORDINATES IN THE FOV OF THE UVIS/FUV LOW RESOLUTION SLIT AS A FUNCTION OF TIME INDEX

FOR THE T52 STELLAR OCCULTATION. THE UNSTABLE POINTING REFLECTED IN A VARIATION OF OFFSET FROM THE FOV CENTER IN THE

X-DIRECTION (WOBBLING OF INSTRUMENT) RENDERS DATA OF THIS OCCULTATION USELESS...... 32

FIGURE 2.7: STAR’S X- AND Y-COORDINATES IN THE FOV OF THE UVIS/FUV LOW RESOLUTION SLIT AS A FUNCTION OF TIME INDEX FOR THE

T41 II FLYBY. THE POINTING IS STABLE FOR THE WHOLE TIME OF OCCULTATION IN BOTH X- AND Y-DIRECTIONS...... 33

FIGURE 2.8: THE LEFT SUBPLOT DEMONSTRATES 5 SPECTRA TAKEN DURING 5 INTEGRATION TIMES (OF DURATION 1.75 S). IN ADDITION, THE

3D AXIS REPRESENTS THE 3D SPATIAL-SPECTRAL CUBE, WHERE ROWS = I, COLUMNS = Λ AND TIME INDEX = TG ALTITUDE. ROWS

WERE SUMMED IN ORDER TO GET A SINGLE SPECTRUM FOR ANY TANGENT ALTITUDE PLOTTED. THE UPPER RIGHT SUBPLOT ILLUSTRATES

LIGHT CURVES CORRESPONDING TO 130 AND 170 NM BEFORE (BLACK) AND AFTER AVERAGING. THE PLOT IS ZOOMED TO 2037-

2065 (KM) AND 9-33 (COUNTS/PIXEL/S) BOX IN ORDER TO SHOW THE NUMBER OF POINTS BEING AVERAGED (DENOTED BY X) AND

THE PLACES OF NEW AVERAGED POINTS (MARKED BY GRAY DIAMONDS). THUS, THE SNR RATIO IS INCREASED AT THE EXPENSE OF

ALTITUDE RESOLUTION DECREASE (TO ~10 KM). THE LOWER RIGHT SUBPLOT SHOWS MEASURED SPECTRA (IN BLACK) OVERLAIN BY

(BOXCAR) FILTERED SPECTRA FOR TWO DIFFERENT TANGENT ALTITUDES (800 AND 2000 KM). THE SIGNAL WAS ADDED TOGETHER

OVER THE SPATIAL PIXELS SO AS TO OBTAIN A SINGLE SPECTRUM FOR EACH TANGENT ALTITUDE...... 33

FIGURE 2.9: TANGENT ALTITUDE-TRANSMISSION RELATION MEASURED WITH UVIS FOR 4 WAVELENGTH BINS SPECIFIED IN THE PLOT.

ERROR BARS ARE SUPERIMPOSED. FOR CLARITY, ONLY EVERY FIFTH POINT WAS PLOTTED...... 34

FIGURE 2.10: LOCAL MINIMUM: ONE OF THE MPFIT STOPPING CRITERIA. BY CHANCE, THE LOCAL MINIMUM FOUND MAY COINCIDE WITH

THE GLOBAL MINIMUM. SOURCE: MATLAB (2012)...... 36

FIGURE 2.11: ANOTHER POSSIBLE STOPPING CRITERION FOR MPFIT. SOURCE: MATLAB (2012)...... 36

FIGURE 3.1: RELATIVE ERROR-(LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR CH4 BEFORE (UP) AND AFTER (BELOW) FILTERING...... 39

FIGURE 3.2: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR C2H2 BEFORE (UP) AND AFTER (BELOW) FILTERING...... 40

FIGURE 3.3: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR HCN BEFORE (UP) AND AFTER (BELOW) FILTERING...... 41

FIGURE 3.4: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR C2H4 BEFORE (UP) AND AFTER (BELOW) FILTERING...... 42

FIGURE 3.5: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR C4H2 BEFORE (UP) AND AFTER (BELOW) FILTERING...... 43

FIGURE 3.6: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR HC3N BEFORE (UP) AND AFTER (BELOW) FILTERING...... 44

FIGURE 3.7: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR C6H6 BEFORE (UP) AND AFTER (BELOW) FILTERING...... 45

FIGURE 3.8: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR AEROSOLS BEFORE (UP) AND AFTER (BELOW) FILTERING. ... 46

FIGURE 3.9: SPECTRUM OF Ε CMA MEASURED BY UVIS. THE WAVELENGTH AT WHICH MAXIMUM INTENSITY IS EXPECTED FROM WIEN’S

LAW IS MARKED. THE CALCULATED (EXPECTED) INTENSITY AT THAT WAVELENGTH IS ALSO SHOWN...... 47

FIGURE 3.10: UPPER SUBPLOT: MEASURED (BLACK) AND MODELED TRANSMISSION SPECTRA AS A FUNCTION OF WAVELENGTH FOR THREE

ALTITUDES (500 KM – GRAY, 800 KM – LIGHT GRAY, 1000 KM – LIGHT). LOWER SUBPLOT: RESIDUAL PLOT, I.E. THE DIFFERENCE

BETWEEN MEASURED AND MODELED TRANSMISSION AS A FUNCTION OF WAVELENGTH. NOTE THE OVERESTIMATION OF ABUNDANCES

AT THE 500 KM TANGENT ALTITUDE IN THE 134-144 NM WAVELENGTH INTERVAL...... 48

FIGURE 3.11: TEMPLATES CREATED FROM SYNTHETIC MODELING (THIN LINES) USED FOR IDENTIFICATION OF SPECIES THAT POTENTIALLY

HAVE ALTITUDE INTERVALS OF BIASED MPFIT RETRIEVAL. THERE ARE 9 CONSTANT INITIAL GUESS LINES. STARTING FROM LEFT TO

RIGHT, THESE ARE: 1/10, 1/6, 1/4, 1/2,1, 2, 4, 6 AND 10. THESE CONSTANT INITIAL GUESS LINES THAT ROUGHLY ENCLOSE THE

NINIT/NFILT CURVE OBTAINED FROM REAL DATA INVERSION (THICK BLACK LINE) ARE MARKED WITH RED (LEFT) AND ORANGE (RIGHT),

RESPECTIVELY. IN ADDITION, INITIAL GUESS VALUES FOR THESE LINES ARE SHOWN FOR EASIER INTERPRETATION. FOR EXAMPLE, IN THE

CASE OF CH4, THE NINIT/NFILT RATIO TOGETHER WITH (HORIZONTAL) 1-ΣM ERRORS, BOTH OBTAINED FROM SPECTRAL INVERSION OF THE

T41 II FLYBY DATA, ARE ENCLOSED BY CONSTANT X = 1 AND X = 4 INITIAL GUESS LINES...... 50

FIGURE 3.12: NUMBER DENSITY PROFILE OF 8 SPECIES USED IN THE RETRIEVAL FOR THE T41 II STELLAR OCCULTATION (FIRST 3 SUBPLOTS).

ALSO MARKED ARE THE SPECIES AND INTERVALS WHERE SPECTRAL INVERSION MIGHT HAVE SERVED UNRELIABLE COLUMN DENSITIES

(ACCORDING TO TABLE 6). NOTE THAT THIN VERTICAL LINES AT THE LIMITS OF THE FIRST 2 SUBPLOTS DENOTE ZONES OF POOR

RELIABILITY (WHERE R = 0.5-1 IN SYNTHETIC MODELING) AND THICK LINES DENOTE POTENTIAL ZONES OF BAD RELIABILITY (R > 1

ACCORDING TO R-MATRICES). RELIABILITY OF THE RETRIEVAL IN GENERAL IS CAPTURED BY 2 NUMBERS: NAMELY Q-UNCERTAINTY AND 2 2 REDUCED Χ (EXPLAINED IN SUBSECTION 2.3.3.3). THESE ARE PRESENTED IN SUBPLOT 4. REDUCED Χ VALUES ARE PLOTTED FOR

BOTH INVERSION STEPS. FINALLY, THE NUMBER OF ITERATIONS OF MPFIT WITHIN THE 2-STEP ITERATION SCHEME IS PRESENTED

(SUBPLOT 5)...... 53

FIGURE 3.13: RATIO OF NUMBER DENSITIES TOGETHER WITH THEIR UNCERTAINTY BARS FOR TWO FLYBYS THAT TOOK PLACE ON THE SAME

DAY. HIGHLIGHTED ZONES ARE THOSE WHERE THE RATIO, TOGETHER WITH THE UNCERTAINTY BARS OF AT LEAST ONE OF THE SPECIES

(SHOWN IN ANY OF THE SUBPLOTS), DO NOT CROSS THE NT41 II / NT41 I = 1 LINE...... 56

FIGURE 0.1: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 1/10 BEFORE (UP) AND AFTER

(BELOW) FILTERING...... 62

FIGURE 0.2: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR = 1/6 BEFORE (UP) AND AFTER

(BELOW) FILTERING...... 63

FIGURE 0.3: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR = 1/4 BEFORE (UP) AND AFTER

(BELOW) FILTERING...... 63

FIGURE 0.4: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 1/2 BEFORE (UP) AND AFTER

(BELOW) FILTERING...... 64

FIGURE 0.5: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 1 BEFORE (UP) AND AFTER (BELOW)

FILTERING...... 64

VII

FIGURE 0.6: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 2 BEFORE (UP) AND AFTER (BELOW)

FILTERING...... 65

FIGURE 0.7: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 4 BEFORE (UP) AND AFTER (BELOW)

FILTERING...... 65

FIGURE 0.8: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 6 BEFORE (UP) AND AFTER (BELOW)

FILTERING...... 66

FIGURE 0.9: RELATIVE ERROR (LEFT) AND Σ-(RIGHT) RETRIEVAL MATRICES FOR INITIAL GUESS FACTOR= 10 BEFORE (UP) AND AFTER (BELOW)

FILTERING...... 66

VIII

List of Tables

TABLE 1: TABLE SHOWING THE CRITERIA FOR INTERPRETATION OF THE R- AND Σ-RETRIEVAL MATRICES AND EVALUATING THE RESPONSE OF

MPFIT TO DIFFERENT INITIAL GUESSES...... 24

TABLE 2: CHARACTERISTIC ABSORPTION BINS IN THE FUV PART OF THE SPECTRUM FOR SPECIES USED IN THE RETRIEVAL...... 26

TABLE 3: ABSORPTION CROSS SECTIONS AND EXTINCTION (AEROSOLS) OF SPECIES INCLUDED IN THE RETRIEVAL. RESOLUTION AND

TEMPERATURE AT WHICH THE MEASUREMENTS WERE CONDUCTED ARE ALSO INCLUDED. LASTLY, ALTITUDE RANGE WHERE SPECIES ARE

EXPECTED TO BE RETRIEVED ARE INCLUDED AND COMPARED AGAINST EXPECTED ALTITUDE RANGES OBTAINED BY KOSKINEN ET AL. (2011)...... 28

TABLE 4: LIST OF STELLAR OCCULTATIONS BUILT FROM THE OPUS DATABASE. THE FIRST COLUMN DENOTES THE FLYBY NAME, THE SECOND

REPRESENTS THE DATE WHEN THE FLYBY TOOK PLACE AND THE THIRD IDENTIFIES THE NAME OF THE STAR (ACCORDING TO THE BAYER

CLASSIFICATION) BEING OBSERVED BY UVIS. OCCULTATION ANALYZED IN THIS WORK IS BOLDED...... 31

TABLE 5: CHARACTERISTICS OF TWO STELLAR OCCULTATIONS. T41 I WAS ANALYZED BY KOSKINEN ET AL. (2011) AND CAPALBO (2014),

WHILE T41 II WAS EXTENSIVELY ANALYZED IN THIS WORK AND COMPARED AGAINST THE FORMER. NOTE THAT THE LAT-LON RANGE

PROBED IS NARROW IN BOTH CASES. THEREFORE, COLUMN DENSITY PROFILES CAN SAFELY BE CONVERTED TO LOCAL NUMBER DENSITY

PROFILES (KOSKINEN ET AL., 2011)...... 48

TABLE 6: QUANTIFICATION OF INITIAL GUESS FACTOR FROM LINKING THE SYNTHETIC MODELING AND REAL DATA INVERSION RESULTS

ACCORDING TO EQ. 3.2. FOR ANY GIVEN SPECIES, X IS DETERMINED WITH THE PROCEDURE ELABORATED ABOVE FOR THE GIVEN

ALTITUDE RANGE. THEN, R-MATRICES FROM SECTION 3.1 ARE CONSULTED IN ORDER TO QUALITATIVELY ESTIMATE THE RELIABILITY OF

NFILT INVERTED FROM REAL DATA (COLUMN 5). FINALLY, EITHER A GENERAL REMARK OR A REMARK SPECIFIC FOR A GIVEN ALTITUDE

RANGE IS GIVEN FOR ALL THE SPECIES. ZONES OF POOR (THIN LINES) AND BAD RELIABILITY (THICK LINES) ARE PLOTTED IN SUBPLOT 1

AND 2 OF FIGURE 3.12...... 52

1. Introduction

Saturn is a jewel in a vast family of celestial objects orbiting the Sun. Being the second largest planet in the Solar System at about 30 astronomical units (AU) distance from its parent star, it is easily recognizable by its magnificent system of rings. To date, 62 moons, more than half of which are less than 5 km in diameter, are known to orbit this fascinating world (Howell, 2014). One of these moons is of particular interest to scientists and is captivating the attention of space scientists worldwide.

The main focus of this thesis is the study of a mesmerizing celestial object, in many ways reminiscent of our own. More particularly, the focus is on the analysis of the upper part of its atmosphere, a zone where the interplay of sunlight and simple molecules (like methane and molecular nitrogen) gives rise to complex organic molecules not unlike those in the atmosphere of young Earth that might have given rise to life itself. Therefore, Titan is a moon considered as a prime candidate in the search for life in the Solar System.

In this introductory chapter several broad topics will be briefly touched upon. First, Titan and its atmosphere are described. Then, the observation and exploration of Titan’s atmosphere are presented with particular focus on the Cassini-Huygens mission. This is followed by a simplified explanation of the photochemistry giving rise to Titan’s complex organic chemistry. Finally, project objectives are defined and the project outline is put forward.

1.1. Titan and its atmosphere

After Jupiter’s Ganymede, Titan is the second largest moon in the Solar system with a diameter of about 5150 km (larger than the planet Mercury). It was discovered in 1655 by Dutch astronomer Christiaan Huygens who believed that Titan was the biggest satellite of all. Therefore it was named after the Titans, a family of giants in Greek mythology.

Chapter 1: Introduction

Titan circles Saturn at a distance of about 1.22 million km, closing an orbit about once every 16 Earth days. Much like many other moons (including our own), Titan is tidally locked. That is to say, the time that Titan rotates about its axis equals the time of its revolution around Saturn. The eccentricity of Titan’s orbit and its inclination to Saturn’s equator are virtually zero.

In comparison to our Moon, its diameter is approximately 50% larger. However, it is comprised of less dense material, predominantly rocks and water ice (ESA, 2005). In terms of surface gravity, this translates roughly to Titan having about 80% of the Moon’s gravity. Titan exhibits an extended atmosphere reaching a few thousand kilometers above its surface.

Figure 1.1: Dione passing behind Titan, Similarities with Earth are plentiful. For example, molecular both in front of the planet Saturn as nitrogen and methane are the main components of Titan’s seen by Cassini on May 21, 2011. substantial atmosphere (Brown et al., 2010). Analogously, the (Image credit: NASA/JPL/Space Science Institute, 2011). dominant constituents of Earth’s atmosphere are nitrogen and oxygen. The atmospheric surface pressure on Titan is about 1.5 times the atmospheric pressure at sea level of Earth. Furthermore, similar atmospheric and geologic processes are taking place, albeit with different materials in completely different environments. The roles of liquid water and rocks on Earth are replaced by methane and water ice on Titan, respectively. On Earth, water circulates in a so-called water cycle; on Titan methane circulates in a methane cycle.

Titan’s atmosphere is divided into 5 distinct layers according to a model of atmospheric temperature variation published in 1997 by Yelle et al. (see Figure 1.2). The lowermost layer, namely the troposphere, extends from the surface to about 50 km which corresponds to a temperature drop from 94 K to 70 K at the tropopause. From that boundary onwards the temperature increases in a layer called the stratosphere, reaching 180 K at a maximum height of 300 km. The temperature then decreases to 135 K in a layer called the mesosphere. The thermosphere follows with average (recommended) temperatures peaking at 175 K around 925 km. According to the model, temperature variation is 0 in a subsequent layer known as the exosphere. Thus, the average expected temperature throughout the exosphere is 175 K.

Chapter 1: Introduction

The atmosphere has other distinctive layers and boundaries in the previously discussed altitude domain which do not depend on temperature. The homosphere is the region of atmosphere where all major constituents

(N2, CH4, H2 and inert, noble gases) are expected to be well mixed (Brown et al., 2010). It extends from the surface to a boundary called the homopause at 750 km (pressure ~2x10-3 Pa around 750 km) (e.g., Wilson et al, 2003; Wilson and Atreya, 2004), 850 km (according to Yelle et al., 1997) or even to 1000 km (Vervack et al., 2004). The heterosphere follows, a zone where gases form layers depending on molecular weight.

Figure 1.2: Tentative temperature profile of Titan’s Titan’s atmosphere also has two main layers where atmosphere as found in Yelle et al. (1997) and gases are ionized by radiation. According to several division by layers. The recommended (rec), authors (e.g., Fulchignoni et al., 2005; Gronoff et al., minimum (min) and maximum (max) models are shown. In addition, extensions of the ionosphere 2009), the ionosphere can be identified roughly between 2 (solid double arrows) and the homopause (dashed 50-200 km and 700-1200 km altitude ranges (Figure double arrow) are denoted. 1.2).

The complexity of Titan’s atmospheric composition was first exposed by Voyager infrared data 3 (Hanel et al., 1981). The presence of N2 , CH4 and H2 was detected in the troposphere, while in the stratosphere CH4, C2H2, C2H6, C2H4, C3H8, C4H2, HCN, HC3N, CO2 were discovered, to mention a few. This motivated the creation of photochemical models that would attempt to recreate the observed composition.

Some of the most recent findings about Titan’s atmosphere suggest that source of nitrogen in its atmosphere must have originated as ammonia ice in the protosolar nebula, thus before its parent planet was formed (Mandt et al., 2014). However, this idea was already proposed much earlier (for example, Atreya et al., 1978).

2 The ionization processes in this region would be by cosmic rays and not by radiation. 3 The presence of N2 was already unambiguously detected from UV spectroscopy.

Chapter 1: Introduction

1.2. Photochemical models

A trace composition of Titan’s upper atmosphere can be modeled and reproduced by one- dimensional photochemical models. These models describe how UV photons dissociate into the main atmospheric components, N2 and CH4, producing radicals that are the seeding elements for the production of more complex nitrile and hydrocarbon molecules (see Figure 1.3 below), ultimately leading to the generation of aerosols (for example, Atreya, 1986; Wilson and Atreya, 2004).

Figure 1.3: Schematic of the photochemistry of N2 and CH4 in Titan’s atmosphere (Atreya et al., 2006). Molecules in black bolded ellipses (left) and rectangles (right) are species used in calculations of abundances in this work (see Chapter 3 for details).

The strong N2 bond can be broken as a response to excitation by energetic EUV photons (λ<100 nm) so that the nitrogen molecule dissociates into N4S and N2D via light-stimulated chemical 4S decomposition called photolysis. HCN is formed from the reaction of N with CH3 radicals.

Later, HCN can decompose into CN. This CN can combine with C2H2 to produce HC3N.

Hydrocarbon chemistry is initiated with photolysis of CH4 in its stratosphere, mesosphere and thermosphere. Byproducts of this reaction are CH3 (methyl), CH2 and CH radicals (Figure 1.3).

Methyl radicals recombine into ethane (C2H6). Ethane can further produce C2H4 which in turn can form C2H2 through photodissociation. This C2H2 can form C4H2. Formation of higher-order hydrocarbons, such as C6H6, can be initiated from the C3H3 radical.

Formation of even more complex molecules from hydrocarbon-nitrile photochemistry ends with the production of haze. This gives the characteristic reddish color to Titan and obscures a direct

Chapter 1: Introduction view of its surface in the visible range of the electromagnetic spectrum. These macromolecular organic compounds made from C, H and N are the main constituents of Titan’s atmospheric aerosols.

While photochemical models of Titan’s stratosphere and lower thermosphere greatly facilitate the understanding of chemical processes that lead to the creation of rich nitrile and hydrocarbon chemistry in the aforementioned regions, it is important to emphasize that some species (for example, HC3N) show a discrepancy of one order of magnitude or more between the calculated and predicted abundances (Brown et al., 2010). Furthermore, models coupling photochemistry and dynamics (Hourdin et al., 2004) shed additional light on the shortcomings of 1-D photochemical models which fail to quantitatively reproduce the composition, as well as the latitudinal and seasonal variability of Titan’s stratosphere.

1.3. Observation and exploration

The first observation of Titan’s atmosphere occurred in 1908 when José Comas Solà observed limb darkening on Titan (Comas Solà, 1908). However, it was not until 1944 that the existence of an atmosphere on Titan was unambiguously proven by Gerald Kuiper (Kuiper, 1944). During the winter of 1943-1944, Kuiper made spectrographic studies of Titan where he observed two absorption bands of methane at 619 and 725 nm, which led him to conclude that Titan has a thick atmosphere with methane as one of the main constituents.

15 years after the advent of the space age in 1957, the first missions to the systems of the outer planets were sent off (Pioneer 10 and 11). The first envoy to Titan was Pioneer 11. However, the first close look at Titan’s atmosphere was taken by Voyager 1 in 1980. This mission gave some valuable insights into the chemistry and physics of Titan’s atmosphere. With the aid of an ultraviolet spectrometer (UVS) onboard Voyager 1, light was shed on its bulk composition: 90% molecular nitrogen and 1-8% methane (for example, Broadfoot et al., 1981; Smith et al., 1982).

Many other trace elements in the form of hydrocarbons (C2H6, C2H4, C2H2, to mention a few), nitriles (HCN, HC3N, etc.) and oxygen compounds (CO and CO2) were detected (Hanel et al., 1981). Furthermore, Voyager infrared (IRIS) data allowed the discovery of a plethora of other

Chapter 1: Introduction gases in Titan’s stratosphere and gave the first glimpse into the surface conditions prevalent on Titan: the surface temperature was constrained to be in the range between 94 and 97 K (Samuelson et al., 1981).

In addition to Voyager data, Earth-based observation methods of Titan became more sophisticated, spectroscopic techniques more refined, and new theoretical models emergent. Yet, many questions still remained unanswered with new questions arising. Thus, an in-depth exploration of this fascinating world was necessary.

In 1982 the Cassini-Huygens mission was conceived. As opposed to previous missions that only performed flybys of planets, the goal of Cassini was to be inserted into Saturn’s orbit and perform flybys of the moons so as to gather as much scientific data as possible. This data would then be used by space scientists worldwide to illuminate through the thick haze of mysteries covering Titan.

1.3.1. Cassini-Huygens mission

Cassini-Huygens is a very ambitious and highly specialized planetary mission specifically designed to carry out a detailed study of Saturn as well as its rings, magnetosphere moons. It was successfully launched from Cape Canaveral, Florida, on 15 October 1997 as a joint effort of the American National Aeronautics and Space Administration (NASA) and the European Figure 1.4: Cassini orbits Saturn (artistic depiction). Source: Space Agency (ESA). After 7 years of a Microsoft, 2006. journey on a highly complicated interplanetary trajectory gravitationally aided by Venus, Earth and Jupiter, it was finally inserted into Saturn’s orbit on July 1, 2004 (NASA, 2014). Thus, in contrast to its predecessor flyby missions, namely Pioneer and Voyager, Cassini is orbiting the ringed planet and performing

Chapter 1: Introduction flybys of its moons in order to collect as much as scientific data as possible. It does so in a highly autonomous fashion because it is at the distance of 1.5 light-hours from Earth.

The Cassini-Huygens spacecraft is the largest and most complex outer planetary spacecraft ever built. This fact is clearly reflected in its price tag which came to 3.26 billion dollars. Being 6.7 m tall and 4 m wide, its launch mass was 5712 kg, more than half of which was propellant (3130 kg) (ESA, 2013). Its large mass was the reason why the spacecraft was sent on the aforementioned circuitous path, rather than being directly injected into a Saturn-approach trajectory.

The Cassini orbiter is equipped with 12 scientific instruments. In addition, onboard Cassini was the ESA-operated probe, known as Huygens, that descended to Titan’s surface through its dense atmosphere from a parachute, in January 2005. Equipped with 6 instruments, it gathered data about the state of the atmosphere and recorded astounding images of Titan’s surface. Indeed, Huygens unveiled to us a brand new world, very different from our own, yet surprisingly similar in many aspects (see Section 1.1).

The nominal Cassini mission lasted for 4 years, but was prolonged twice. As of now it is planned to be terminated in 2017. It is worth mentioning that in the final stage of its mission, Cassini is planned to be sent into a death orbit to Saturn’s atmosphere so as not to potentially contaminate its moons with bacterial life from Earth.

The general scientific objectives of Cassini mission are the study of:

 Saturn and its rings  Saturn’s magnetosphere  Icy satellites, with particular focus on Titan

The scientific objectives of Cassini with regard to Titan are to:

 Determine the atmospheric composition  Investigate energy sources for atmospheric chemistry  Measure winds and global temperature distribution  Study aerosol properties  Determine properties of surface and infer internal structure

Chapter 1: Introduction

 Investigate the upper atmosphere and ionosphere

After Cassini-Huygens’ nominal mission, we have good first order knowledge of the composition and thermal structure of Titan’s atmosphere, except for the altitude region in the range of ~500- 950 km, also known as the ignorosphere or agnostosphere (Brown et al., 2010).

The focus of this work is an investigation of Titan’s upper atmosphere using an instrument known as an Ultraviolet Imaging Spectrograph, or UVIS.

1.3.2. UVIS instrument

UVIS (McClintock et al., 1993; Esposito et al., 2004) is an instrument onboard the Cassini spacecraft complementing the Composite InfraRed Spectrometer (CIRS) and the Ion Neutral Mass Spectrometer (INMS). It can detect molecules using their absorption features in the region known as the ignorosphere (altitude range: ~500-950 km). UVIS also probes regions below and above the ignorosphere, from 400 km to 1500 km in altitude, a zone of high interest for exploration since prodigious photochemistry occurs there (Shemansky et al., 2005, Koskinen et al., 2011).

The Ultraviolet Imaging Spectrograph observes ultraviolet light:

 Absorbed during solar or stellar occultations by Titan’s atmosphere  Reflected from the gas and aerosols in Titan’s atmosphere  Emitted from atomic and molecular species

UVIS scientific objectives have focused on the investigation of (Esposito et al., 2004):

 Chemistry, aerosols, clouds and the energy balance of the Titan and Saturn atmospheres  Deuterium-to-hydrogen ratio for Titan and Saturn  Neutrals in the Saturn magnetosphere  Structure and evolution of Saturn’s rings  Surface properties of Saturn’s moons

Chapter 1: Introduction

UVIS has two moderate resolution spectrographs, each sensitive to different wavelength ranges:

N2, CH4 and other hydrocarbon species can be detected from 850 to 3500 km altitude with solar occultations at extreme ultraviolet wavelengths (EUV: 56-118 nm). In the FUV part of the spectrum (110-190 nm), UVIS is a valuable tool for detecting and identifying molecules constituting Titan’s upper atmosphere (~300-1200 km). Two other channels of UVIS are a Hydrogen Deuterium Absorption Cell (HDAC) and a high speed photometer (HSP). The latter is used for high signal-to-noise ratio (SNR) stellar occultations by atmospheres and rings and HDAC is used for measurements of relative abundances of hydrogen and deuterium from their Lyman-α emission.

Figure 1.5: Scheme of UVIS FUV channel. From Esposito et al. (2004). The scheme of the FUV spectrograph is presented in Figure 1.5. An optimal tradeoff between instrument size, image quality and spectral resolution was achieved in its design. The telescope consists of an off-axis section of a parabolic mirror with a focal length of 100 mm. It is equipped with a sunshade and baffle system to minimize scattered light background during limb scan measurements. 133 mm in front of the mirror is an aperture of dimensions 20x20 mm2. Furthermore, the FUV spectrograph has three entrance slits switchable by the slit changer mechanism. The width of these slits is 0.075 mm (high resolution), 0.15 mm (low resolution), and 0.8 mm (occultation slit). Radiation then travels to a toroidal grating with a 300 mm horizontal radius of curvature where the spectrum is formed. Spectrograph images from a slit are mapped onto a 25.6x6.4 mm2 2D CODACON (Coded Anode Array Converter) microchannel

Chapter 1: Introduction plate detector with one axis giving spectral information and the other giving spatial information. Broader 2D spectral images are constructed by scanning perpendicular to the slit axis as the spacecraft changes attitude. The detector format is 1024x64 (spectral by spatial) with a pixel size of 25x100 µm2 and a width of 0.078 nm in the spectral dimension. The CODACON detector is enclosed in a vacuum housing with a MgF2 window. The output electronics are informed by CODACON which pixel was impacted by each detected photon. The photon counts are accumulated in external memory to build a picture which is periodically read out for transfer to the spacecraft memory and eventually to ground. For a thorough description of the instrument, interested reader may refer to Esposito et al. (2004).

In summary, the enhanced capabilities of the UVIS instrument (higher sensitivity, higher spectral resolution) in comparison to the Voyager and Galileo UVS/EUV instruments greatly aided in revealing the composition and thermal structure characteristic of the ignorosphere and will continue to do so until the mission is terminated.

1.3.2.1. UVIS data

An observation is a sequence of data taken while the instrument configuration is unchanged. For example, changing the channel of the instrument from EUV to FUV marks the end of one observation and the beginning of a new one. Each observation has a unique identifier.

UVIS data measured in FUV channel mode are a time series of 2-dimentional matrices of detector counts. Thus, FUV mode UVIS observation is a spatial spectral cube of a time ordered sequence of 1024x64 matrices and each element of the matrix is the number of counts taken at an individual detector pixel during a fixed time interval. These raw observation data are stored in binary format. All raw observation data are accompanied by calibration data which convert detector counts into Rayeighs. Moreover, ancillary data defining geometry and time of observation, as well as other information relevant for the observation of interest are also available for download and further usage in the processing of the data. For more details on ancillary data, the reader is referred to Subsection 2.3.3.1. For a detailed description of the UVIS data format see the Planetary Data System (PDS) documentation (PDS, 2014).

Chapter 1: Introduction

1.4. Project description

The internship was conducted in the Space Organic Physicochemistry group (GPCOS) at Inter- universittary Laboratory of Atmospheric Systems (LISA) in Créteil, France, as part of the Joint European Master program in Space Science and Technology. This group’s latest focus is on the analysis of UVIS stellar and solar occultation observations in order to deduce composition, elements distribution and temperature profile of Titan’s upper atmosphere. For this purpose they developed flexible software in the IDL environment in which a robust, well tested and widely used Levenberg-Marquardt algorithm (see for example Press et al., 1996) is implemented in routine called MPFIT (Markwardt, 2009) for efficient calculation of column densities.

Since the detection depends on the absorption cross section of the molecules and aerosols, the GPCOS group conducts laboratory measurements of absorption cross sections for different species both at low temperatures (representative of Titan’s upper atmosphere) and room temperatures. Results of measurements provide valuable inputs for computations, thus reducing uncertainties in calculated quantities.

The Levenberg-Marquardt minimization algorithm employed in the MPFIT routine is robust in the general sense, but can converge slowly or become stuck at an unwanted local minimum (Capalbo, 2014). This motivated extensive synthetic modeling to thorougly test the behavior of the MPFIT routine4. Specifically, the dependence of final (calculated) column densities on initial column density guesses (which were multiplied by factors spanning from 1/10 to 10) was studied and compared against „true” column densities. For a simple visual representation of the results of synthetic modeling, retrieval matrices (Capalbo, 2014) were created.

4 It is important to underline that one of two main goals of this thesis was to test the behavior of the MPFIT routine and not to test the Levenberg-Marquardt algorithm itself (which is widely tested algorithm). To clarify the subtle difference, an analogy from physics is drawn. Kinematics is a branch of physics that deals with the motion of a body or system without reference to force and mass. Dynamics, on the other hand, is the branch of mechanics that deals with motion and the way in which forces produce motion. In this work the goal is to describe the “kinematics of MPFIT routine”, while the dynamics of it is neglected. More closely, the “motion of MPFIT” (effect) is studied while the “forces producing motion” (cause) are ignored.

Chapter 1: Introduction

This was followed by the creation of a list of stellar occultation events, giving potential candidates for real data analysis. After careful inspection of the data, one stellar occultation event was chosen to be studied with scrutiny.

In summary, the key research goals of the study at hand were twofold:

1) Analyze and characterize the outputs of MPFIT routine, 2) Study Titan’s upper atmosphere from the analysis of one stellar occultation event recorded by the UVIS instrument onboard the Cassini spacecraft

1.5. Report outline

This report is structured as follows:

Introduction mostly focuses on providing sufficient background information for placing the work into a context. Additionally, a brief description of the thesis objectives is put forth.

Theory and methods is a chapter devoted to introducing the essential theoretical concepts and methods used in this work.

Results summarizes the results of synthetic modeling and discusses the limitations of algorithms used in calculations. Furthermore, a carefully chosen real stellar occultation dataset is analyzed and the most important results are reported.

Conclusions recapitulates the work done together with the obtained results and puts forward ideas on how to potentially improve the herein presented algorithms.

2. Theory and methods

The composition of the atmosphere at any particular height can be inferred from a measurement of an absorption spectrum of a mixture of gases. The vertical distribution of atmospheric constituents can be obtained by repeatedly measuring absorption spectra as a function of height. Since many gases are strong absorbers of UV light, instruments operating in that part of the electromagnetic spectrum are designed for probing the upper parts of an unknown atmosphere. The UVIS onboard Cassini is one such instrument that is sensitive to the FUV part of the spectrum (see Subsection 1.3.2 for more details on the UVIS instrument).

In this chapter the concept of stellar occultation is first defined. This is followed by the introduction of basic physical laws governing the interaction of the electromagnetic radiation with medium it traverses. Finally, the description of methods together with online resources used in this work are detailed.

2.1. Stellar occultation

Stellar occultations provide a powerful technique for the study of planetary atmospheres (e.g., Smith and Hunten, 1990). Already at the dawn of the 20th century it was realized that an optical occultation of a star by a planet could give useful information (Pannekoek, 1904). Generally, occultation occurs when an object hides a source of light from an observer (Elliot, 1979). A solar eclipse is one example where the Sun is occulted by the Moon.

The concept of stellar occultation will now be explained with the aid of Figure 2.1. The Cassini UVIS instrument is pointed towards the star of interest so that the Line Of Sight (LOS), i.e. the line connecting the UVIS longitudinal axis and the star is well above the atmosphere (line 1 and spectrum 1 in the figure) so that the star’s original spectrum (I0) is recorded. As the spacecraft progresses along its trajectory to the endpoint of line 2, the LOS cuts through a small part of the uppermost region of the upper atmosphere. Therefore, the original spectrum gets slightly modified at shorter wavelengths by molecules present at these heights. Next, the spacecraft-star LOS plunges deeper into Titan’s atmosphere and many spectra are recorded along the way. For

Chapter 2: Theory and methods example, the left point on line 3 is at 650 km above Titan’s surface. At this point the spectrum has nearly vanished. The reason for this is that the starlight traverses many atmospheric layers (denoted by thin concentric circles), each of which absorbs part of the spectrum. Which part of the spectrum will be absorbed, and to which degree, depend on species present and their abundances, respectively.

Figure 2.1: Principle of stellar occultation. Spectra shown are measured spectra for T41 II occultation (that will be thoroughly analyzed in Section 3.2). Source spectrum I0 is that of the Adhara star (known as ε Canis Maioris in Bayer designation). At 1200 km height above Titan’s surface (left point on line 2), the spectrum5 is negligibly modified (only) in shorter wavelength ranges corresponding to the start of absorption by methane molecules. Lastly, at 650 km above Titan’s surface (left point on line 3) the spectrum is significantly modified since almost all of the star’s light (in the FUV part of the spectrum) is absorbed by atoms and molecules present in LOS between the UVIS instrument and Adhara. Sizes of Titan and upper atmosphere contours are drawn to scale. Two circles denoting the upper atmosphere are at 400 and 1400 km above Titan’s surface. Taken from ESA (2014) and substantially altered for the purposes of the thesis.

5 Note that the coloring of spectra in the figure was chosen in such a way to qualitatively reflect the height of the observation, i.e. the tangent altitude being probed (for definition of tangent altitude, see Section 2.2). It goes from light gray above TOA to dark grey in the optically thick part of the atmosphere. This convention will be followed throughout this work.

Chapter 2: Theory and methods

2.2. The equation of radiative transfer

Light is a supreme carrier of information. Its interaction with matter creates fingerprints (i.e. unique spectra) with which the atoms and molecules can be identified and its abundances inferred. Physics of radiation propagation in a three dimensional absorbing, scattering and emitting medium can be modeled using the radiative transfer equation which takes the following general form (Rees, 2001):

dLT, f ,,   T, f   T, f  LT, f ,, R f   T, f  J  f   T, f  BT, f  Eq. 2.1 dD a s s a where

 W  LT, f ,, – spectral radiance   of specific frequency6 f (Hz) spreading in ,  m2  sr Hz direction

dD– distance in the direction of propagation (m)

 a T, f  ,  s T, f  – temperature T (K) and frequency dependent absorption and scattering

1 coefficients (units: ), respectively. The sum of these two quantities is interchangeably referred m to as attenuation or extinction.

R f  – differential refractivity

 W  J  f  – radiation scattered in the direction of propagation from other directions    m2  sr Hz

 W  BT, f  – spectral radiance   of black-body radiation at the appropriate T coming  m2  sr Hz from emission from the medium

6 It is reminded that the simple, yet profound relation between frequency and wavelength of the electromagnetic wave holds: c = λ f, where c = 299 792 458 m/s (speed of light in vacuum), λ – wavelength of the wave (m). Therefore, instead of frequency dependence, the wavelength dependence will be discussed from this point on.

Chapter 2: Theory and methods

The first term on the right side of the equation corresponds to the original radiation (stemming from the source) attenuated due to extinction. The second term accounts for the emitted radiation that accumulates along the path. Finally, the third term represents emission of the atmosphere.

Solving Eq. 2.1 analytically in all its generality is virtually impossible and numerical methods are to be invoked in order to make progress. Alternatively, a few assumptions can be postulated which greatly simplify the general equation.

From now on the inspection of Eq 2.1 is restrained to occultation of Vacuum UV (VUV) radiation, corresponding to the 10-400 nm wavelength range. Assuming the medium through which the radiation propagates is a homogeneous, non-scattering and non-refracting atmosphere (for the validity of last two assumptions, see Smith and Hunten, 1990), substantial simplifications to the right side of the equation can be made. In this case only absorption plays a significant role.

Mathematically:  s = 0, R = 1 and B = 0, thus Eq. 2.1 simplifies to:

dLT,   T, L Eq. 2.2 dD a

Note that direction , is not specified because it does not change since there is no scattering. If

 a varies with position D, the solution of Eq. 2 is:

LT,, D LT,,0expT,, D Eq. 2.3 where

D  T,, D   T,, D '  dD'  a   Eq. 2.4 0

This quantity is called the optical thickness of the path from 0 (surface) to D (thus, the whole path of the radiation through the atmosphere) and is dimensionless as the equation suggests.

Next, using the relation linking spectral radiance and intensity I (measured in Rayleighs),

1010 L  I  Eq. 2.5 4

Eq. 2.3 is rewritten:

Chapter 2: Theory and methods

IT,, D  exp T,, D T,, D Eq. 2.6 I 0 T,

where I 0 and I are the incident and transmitted intensities, respectively, and  is the transmission (also referred to as transmittance) calculated from measured intensities. This is the basic equation for absorptive occultations, also known as the Lambert-Beer law (Vervack et al., 2004).

2 Optical depth (for one species) is defined as a product of the absorption cross section  a (cm ) and the column density/abundance N (cm-2) (Smith and Hunten, 1990):

 T, a T, N Eq. 2.7

On the other hand, the absorption coefficient can be expressed as a product of the absorption cross section and number density n (cm-3) of all the gas species present in the atmosphere (each of which is responsible for attenuation of part of the spectrum):

 a T, a T, n Eq. 2.8

Calculations can further be simplified by considering L spherically symmetric layers (Figure 2.2). In each layer every species considered in calculations is assumed to have a constant and uniform density (Capalbo, 2014). The closest distance between the line of sight from the UVIS instrument to the occulted star and Titan’s surface is called the tangent altitude (Capalbo, 2014) or impact parameter (Koskinen et al., 2011). In Figure 2.2 the signal travels through three layers to the UVIS and the tangent point can be thought of as the point where the measurement takes place (corresponding to layer 3 being probed). Generally, the distance Dij passed through the layer i by the signal when probing the tangent altitude in the middle of layer j can be expressed by invoking Pythagoras’s theorem:

 2 2 2 2  D  2 r  r  r  r  ; for i  j i, j  top,i mid, j top,i1 mid, j 

2 2 Di, j  2 rtop,i  rmid,i for i  j Eq. 2.9

Chapter 2: Theory and methods

where rtop,i denotes the distance from Titan’s center to the upper end of the layer i and rmid , j is the distance from Titan’s center to the middle point of layer j (which equals the sum of Titan’s radius and the tangent altitude).

Figure 2.2: Scheme of spherically symmetric atmospheric layers created for the analysis. Layer i has a number density ni. The distance from Titan’s center to the upper end of the layer i is rtop,i. Di,j corresponds to the distance radiation traverses across the layer i when probing the tangent altitude amidst layer j and is referred to as the optical path. Furthermore, the UVIS probing region (400-1400 km) and ignorosphere (500-950 km) are denoted. Sizes of Titan and the upper atmosphere contours are drawn to scale. Taken from Capalbo (2014) and modified for purposes of this thesis.

Substituting Eq. 2.4 and Eq. 2.8 into Eq. 2.6 and decomposing integrals into sums in order to obtain a numerical solution, the following equality is obtained:

L S L S Il T,, D ln   T,, D    ' T, n '  D '    ' T, N '  l ,s l ,s l ,l  l ,s l ,l,s Eq. 2.10 I0 T, l' l s1 l' l s1

The negative logarithm of  T,,D is called the optical depth. Note that when comparing with Eq. 2.7, Eq. 2.10 is more general as the inner summation runs over S species (where S is a positive integer) while Eq. 2.7 contains only the case when S = 1. The outer summation runs over L atmospheric layers through which radiation passes. Radiation crosses D distance in a layer l' ,l denoted by l’ and column abundances for species s considering this distance are symbolized by

N . Both quantities refer to the tangent altitude in the middle of layer l. l' ,l,s

Chapter 2: Theory and methods

The solution of Eq. 2.10 requires knowledge of the absorption cross section’s dependence on temperatures in the VUV part of the spectrum. For most of the species involved in the retrieval procedure, these data are unavailable, especially at low temperature regimes present in Titan’s upper atmosphere (Capalbo, 2014). Therefore, it will be assumed that absorption cross sections are altitude (consequently temperature)-invariant. This hypothesis can be validated when taking into consideration that the temperature variations in Titan’s upper atmosphere (from a height of 500 km onwards) are minute, with amplitudes of variations being equal to ~10-20 K (e.g. Fulchignoni et al., 2005). As pointed out by Capalbo (2010), these variations will not affect the retrieval appreciably. Eq. 2.10 can now be rewritten so that absorption cross sections are taken outside of the outer summation7:

I , D S  ln l  , D    N I   s totl,s Eq. 2.11 0   s1 where

L N  N totl,s  l',l,s Eq. 2.12 l'l

Eq. 2.11 is used in the retrieval procedure. Absorption cross sections at a constant temperature are used and initial abundances are iteratively changed until the difference between calculated and measured transmission spectra is acceptably small (ideally zero).

In order to simplify calculations, Eq. 2.11 could be linearized. However, according to a study published by Kyrola et al. (1993), linearization does not give a satisfactorily good representation of the measurements. Therefore, Eq. 2.11 is not altered and nonlinear minimization algorithms are utilized to search for an optimal set of column densities (Subsection 2.3.1).

7 Note that in order to take absorption cross sections outside of the summation over distances, the order of summation must first be swapped.

Chapter 2: Theory and methods

2.3. Methods for analysis of stellar occultation data

In Section 2.2 the theory of absorptive occultations was explained. In this Section methods applied in the analysis of stellar occultation data will be introduced. First, the mathematical procedure of column densities retrieval will be described. This will be followed by a description of the most important steps involved in synthetic modeling. The purpose of synthetic modeling is to test the reliability of the MPFIT routine. Finally, procedures employed in the analysis of real data will be presented.

The workflow closely followed in this work is developed by Capalbo (2014).

2.3.1. Column density and number density retrieval

The UVIS dataset gives insight into the state (dynamics and temperature profiles) of Titan’s upper atmosphere. However, in order to extract physical quantities that are easy to interpret (column or number densities, temperature), clever processing and inversion of data involving sophisticated mathematical algorithms have to be employed. The standard technique used to solve nonlinear least squares problems8, called the Levenberg-Marquardt minimization algorithm, is utilized for the determination of the optimal set of column densities from the equation:

   2  2  meas, mod,  2 Eq. 2.13   meas, where  2 is the quantity/cost function to be minimized (giving the most likely set of column densities), meas, is wavelength and tangent altitude dependent measured transmission (the UVIS

2 dataset),  meas, corresponds to uncertainties in the measured transmission and mod, is the transmission calculated from the forward model analogous to Eq. 2.11:

 S    exp   exp   N  mod l  s totl,s Eq. 2.14  s1 

8 Fitting a (nonlinear) parameterized function to a set of measured data points by minimizing the sum of the squares of the errors between the data points and the function defines the (nonlinear) least squares problem.

Chapter 2: Theory and methods

In this equation l refers to the layer being probed (which contains the tangent point) (see Figure N 2.2), while totl,s is the sum of the column abundances of species s over all traversed layers.

The Levenberg-Marquardt algorithm is implemented in the IDL routine MPFIT (Markwardt, 2009) and was the main focus of investigation in synthetic modelling (see next Subsection and Section 3.1 for more information). It is an iterative procedure that provides a numerical solution to a nonlinear least squares fitting problem.

Number density profiles can be inverted from the optimal set of column densities. This is called spatial inversion. The equation to be inverted:

N  D  n  N Eq. 2.15

-2 where N and  N represent column densities and their uncertainties (cm ) respectively, D (cm) is the distance matrix (see Eq. 2.9 and Figure 2.2) and n stands for number densities (cm-3).

This inversion problem (Eq. 2.15) is ill-conditioned9, i.e. a small amount of noise in the measured quantities is amplified which results in the retrieved quantities becoming highly distorted (Capalbo, 2014). In order to control the growth of the errors, the Tikhonov regularization technique is used in the inversion (for details on this technique, see Tikhonov and Arsenin, 1977).

2.3.2. Synthetic modeling

Synthetic modeling10 is a standard procedure in all branches of (computational) science to test the reliability of algorithms employed in the estimation of the sought quantity (or quantities). In the inversion of transmission spectra, the sought quantity is column density. The algorithm employed is known as the Levenberg-Marquardt algorithm and is coded into the IDL routine called MPFIT (see Subsection 2.3.1). The goal of synthetic modeling was to extensively test the outputs of MPFIT (raw/unfiltered column densities) by comparing them to input “true” column densities.

9 Whether the problem is well-conditioned or ill-conditioned can be diagnosed by the condition number which measures how sensitive the function is to errors in the input. In the case of a small condition number, the problem is said to be well-conditioned. In the case of a large condition number, the problem is ill-conditioned. 10 For details on how the synthetic dataset was created, the reader is referred to Capalbo (2014).

Chapter 2: Theory and methods

The motivation of this exhaustive testing was to test the performance of MPFIT which, despite being a generally well-behaved and robust algorithm, sometimes converges slowly or to an unwanted minimum when using an inadequate initial guess (Capalbo, 2014).

The procedure for characterizing the MPFIT routine follows. “True” abundances ( NT ) of all species were multiplied by different factors (denoted by x) in order to create initial guesses ( Ninit ) for MPFIT. Mathematically:

Ninit  x  NT Eq. 2.16

The multiplying factors were: 1/10, 1/6, 1/4, 1/2, 1, 2, 4, 6 and 10. For example, “true” column densities remained unbiased when the guess factor was 1 and served as the initial column densities used in the spectral inversion. In all the other cases, initial column densities were smaller (multiplying factor < 1) or larger than the “true” column densities.

Previous simulations showed that, taking into account the trade-off between improvements of the results and the processing time, two iterations are sufficient for retrieving column densities reasonably well (Capalbo, 2014) (for explanation of the 2-iteration MPFIT scheme, the reader is referred to Subsection 2.3.3.3). Thus, unfiltered (raw) column densities retrieved after the second iteration were compared against the “true” column densities. The comparison was visualized through retrieval matrices introduced by Capalbo (2014) (see Section 3.1 and subsequent Subsections). The rows of the matrix represent each altitude studied while the columns stand for the initial guesses used. In Appendix A – Influence of initial guess factor on column density calculation, species (columns)-altitude (rows) matrices are shown.

The MPFIT routine outputs two numbers for each species at each altitude where calculations are performed. These numbers are the calculated (unfiltered) column density ( Nc ) and its uncertainty

(  m , where the m index refers to MPFIT). The first number was compared against using the well-known formula for the calculation of relative error:

N c  NT r  Eq. 2.17 NT where r spans values between 0 and infinity (indeed, sometimes the retrieval can give infinite column densities and these points need to be filtered out – see below for details on how the

Chapter 2: Theory and methods filtering is implemented). Note that the absolute value is taken because it is not important to know for this part of the analysis which number is larger, N c or NT . It is only the deviation from each other that is to be quantified. The relative error is plotted as the third dimension in one of two different retrieval matrices.

However, it is not sufficient to characterize the retrieval by comparing how close the retrieved value is to the true value. Every measured quantity is accompanied by inherent measurement uncertainties. These map into the calculations and it is essential to obtain a number quantifying uncertainties in the retrieved parameters. That number is  m and has the same units as the column densities (cm-2). It is calculated from the covariance matrix between fitted (column density) parameters by taking the square root of the elements in the main diagonal of the matrix.

In order to check how well the uncertainties “captured” deviations of from , the following formula is used:

N c  NT   Eq. 2.18  m

This quantity serves as a color coding parameter for the second retrieval matrix and will be referred to as  -uncertainty or simply . The next subsection gives a detailed description of retrieval matrices and their interpretation.

2.3.2.1. Retrieval matrices

A critical part of this work was the characterization of the MPFIT routine. The motivation to do so was that it can sometimes converge slowly or to an unwanted minimum if a poor initial guess is used (Capalbo, 2014). Photochemical models providing initial column densities for retrieval may sometimes be far from the optimal set of column densities (Bénilan, personal communication, 2014). In addition, uncertainty estimates (given by MPFIT) for some species and altitude ranges seem not to capture uncertainties correctly. For example, Capalbo (2014) performed an exhaustive Monte-Carlo simulation to characterize the output uncertainties and found that they are highly underestimated, for example, for methane. All this necessitated an in-depth investigation of MPFIT performance.

Chapter 2: Theory and methods

A synthetic dataset was created as described in Capalbo (2014). Two quantities were used for the characterization of MPFIT, namely relative error (r) and  -uncertainty ( ), both of which are defined in Subsection 2.3.2. These were plotted in so called “retrieval matrices” (Capalbo, 2014), which serve as a visual aid for the interpretation of the results. The rows of the matrix represent each altitude studied and the columns are the initial guesses used. The third, colored dimension of the matrices is either r or . This color gives the key information about performance of the MPFIT routine and is used for the interpretation of routine’s dependence on the initial guesses. Matrices will be referred to as r-retrieval matrices or -retrieval matrices (or, abbreviated, r- matrix and -matrix).

Depending on the magnitude of r (calculated for each height and each species considered), criteria were established for the estimation of the goodness of retrieval. The relative error gives information on how far off the calculated column densities are from the “true” column densities, the ideal case being when r = 0 (corresponding to N c = NT case). -uncertainty, on the other hand, quantifies how well MPFIT captures uncertainties in calculations through its  m parameter, the optimal case being when ≤ 1. Referring to Eq. 2.17, this simply means that the magnitude of deviation of from is smaller than or equal to  m . That is to say, is within or just at the boundary of the ± interval. The criteria for coloring retrieval matrices are presented in Table 1.

Color r Retrieval goodness σ Retrieval goodness

Dark green No Value not retrieved No Value not retrieved Green [0-0.2)11 Good [0-1) Good Orange [0.2-0.5) Acceptable [1-2) Acceptable

probably highly Red [0.5-1] Marginally acceptable [2-5] underestimated Pink > 1 Unacceptable > 5 Unacceptable

Table 1: Table showing the criteria for interpretation of the r- and σ-retrieval matrices and evaluating the response of MPFIT to different initial guesses.

11 In mathematics, a square bracket indicates that the number on the (square bracketed side of the) interval is included in the interval. A round bracket, on the other hand, means that the number is not part of the interval. The same convention is followed in this work.

Chapter 2: Theory and methods

In the case of the r-matrix, it follows from the table that full green (0 ≤ r < 0.2) and full orange (0.2 ≤ r < 0.5) matrices signify a flawless and acceptable retrieval technique, respectively. Red (0.5 ≤ r ≤ 1) and pink (r > 1) matrices mean a marginally acceptable or unacceptable retrieval, respectively. Lastly, a full dark green r-matrix means that MPFIT did not retrieve N c in any of 15 -2 the niches studied (it returned Not-a-Number – NaN). For example, assuming NT = 8  10 cm 15 -2 and inverted Nc = 3 10 cm , r = 0.63 is obtained from Eq. 2.17. This means that the particular altitude and species studied will have red color signifying a marginally acceptable retrieval. 15 -2 Assuming Nc = 17 10 cm and the same NT as before, r equals 1.1, and according to Table 1, this means an unacceptable retrieval (pink color). Finally, in Nc = NaN, it follows that r = NaN. In this case, the niche is dark green since the value was not retrieved.

The  -matrix can be interpreted analogously to the r-matrix (and with the aid of Table 1 and Eq.

15 -2 15 -2 15 2.18). For example, assuming NT = 8  10 cm , Nc = 3 10 cm and  m = 2 10 , = 2.5 is obtained. According to Table 1, this means that is underestimated and that the particular (altitude, initial guess and species dependent) niche in the -matrix is colored in red. The - matrix will have dark green niches (meaning not retrieved values, i.e. = NaN) in 3 cases (Eq. 2.18):

1. If Nc = NaN (as for r-matrix)

2. If = 0

3. If ≥ Nc

Note that cases 1 and 2 may occur simultaneously. As for case 3, a simple example with real values is given later in this subsection after the introduction of types of filters applied in “cleaning” the retrieved parameters and their uncertainties from unrealistic values.

Apart from characterizing the performance of MPFIT, synthetic modeling has a further purpose. It can be used to estimate the altitude ranges for which the density profiles of different species can be obtained (Koskinen et al., 2011). In Table 3 the last two columns show these estimations obtained from this work and Koskinen et al. (2011). It should be noted that the synthetic model was created in a similar manner and from the same dataset in both cases.

Chapter 2: Theory and methods

The retrieved abundances and their  m uncertainties may contain clearly incorrect values. For example, the retrieved abundances may take on infinite values or uncertainties may equal zero. Thus, they are treated as unacceptable and are filtered out in the several steps described below.

Refer to Eq. 2.6. For the case when incident and transmitted intensities are equal, transmission is mathematically equal to 1. In reality, transmission is close to 1 when UVIS measures high in the

(thin part of the) atmosphere when the first FUV light begins to be absorbed by CH4 molecules (close to the top of the atmosphere (TOA) where the tangent altitude takes values of ~1400 km). On the other end of the range, the measured intensity normalized by the source intensity equals 0. This happens when the atmosphere is so thick that no FUV photons pass through it (all of the light is absorbed along the path – the corresponding tangent altitudes being equal to ~400 km). This lack of signal naturally decreases SNR. As a result, the retrieval procedure determines “optimal” column densities with large uncertainties. In order to “clean up” the final column densities from these “edge-effects”, a criterion is established which determines the valid altitudes for a particular profile (Capalbo, 2014):

    0.99 and     0.01 Eq. 2.19

In words, the sum and the difference of the transmission (  ) and its uncertainty (   ) should be smaller than or equal to 0.99 and larger than or equal to 0.01, respectively, for each wavelength

Species Wavelength bins (nm) bin. This will be referred to as altitude filtering.

CH4 [120, 145] Unfortunately, the ACS-s for different species overlie each

C2H2 [139.5, 155], [160, 180] other (see Figure 2.3). Therefore, some bins were defined HCN [134, 154] as “characteristic bins” for a particular species and Eq. 2.19

C2H4 [135, 190] was used for the quantification of pairs of limiting altitudes

C4H2 [138, 148], [151, 175] for each bin. In this case species was binned more than

HC3N [138, 163] once, the median among the lower limits was set as the

C6H6 [165, 185] lower limiting altitude and the median among the upper AER [185, 190] limits as the upper one (Capalbo, 2014). The bins used for

Table 2: Characteristic absorption bins in the the species retrieved are shown in Table 2 (left). FUV part of the spectrum for species used in the retrieval. 26

Chapter 2: Theory and methods

Figure 2.3: Absorption cross section (cm2) vs. wavelength (nm). Only ACS-s of species used in calculations are shown. ACS wavelength-dependency of aerosols is shown separately in the upper right corner of the lower subplot. Rectangles in both subplots define the range of established bins (which are presented in Table 2) and are colored according to species. Note the overlap of spectral features among species. This is also reflected in binning. For example, bins of six species overlap in the narrow 139.4-145 nm wavelength range.

After altitude filtering, column density profiles were additionally filtered, this time with the purpose of eliminating outliers. Thus, a median filter was applied and those values which differed from their median in two standard deviations or more were interpolated. Furthermore, column densities that had uncertainties larger than or equal to the retrieved values (σm/Nc ≥ 1) or those with uncertainties equal to zero (σm = 0) were interpolated assuming a function decreasing exponentially with altitude. The same was done for infinite column densities. Lastly, uncertainties whose ratios with corresponding column densities were smaller than 0.01 (i.e. where σm/Nc < 0.01), were recalculated so that the ratios equaled 0.01. This was done to circumvent numerical problems in the spatial inversion in order to obtain more reliable number density profiles (Capalbo, 2014).

A few simple examples may elucidate some of the filtering applied. It is assumed that the 12 -2 12 -2 retrieved value Nc =8  10 cm and its uncertainty σm = 9 10 cm for a given species at a certain tangent altitude point. In this case σm/Nc = 1.1. Therefore, this Nc value is interpolated as 10 -2 12 -2 described above. Next, assuming σm = 4 10 cm with the same Nc (=8 10 cm ), σm/Nc = 0.005 12 10 -2 is obtained. Thus, it is recalculated from σm/ 8 10 = 0.01. Recalculated, σm equals 8 10 cm .

Chapter 2: Theory and methods

The (experimentally obtained) absorption cross sections spectra used in this work (Figure 2.3) are shown in Table 3. Altitude ranges in which species are expected to be retrieved according to Eq. 2.19 are also included.

Alt. range Wavelength range Alt. range (this Species Resolution (nm) T (K) Reference (Koskinen et (nm) work) (km) al., 2011) 120-142 0.06 150 Chen and Wu (2004) CH4 570-1380 550-1300 143-152 0.1 295 Lee et al. (2001)

C2H2 117-210.9 0.005 150 Wu et al. (2001) 400-1070 400-1200 HCN 115-190 0.06 255 Bénilan (unpublished) 400-900 600-1000

C2H4 115-190 0.005 140 Wu et al. (2004) 400-1150 400-1200 135-169.8 0.05 173 Ferradaz et al. (2009) C4H2 400-1090 400-1000 170-195 <0.08 295 Fahr and Nayak (1994) 113-163 0.05 203 Ferradaz et al. (2009) HC3N 400-1000 500-1000 165-230 0.05 298 Ferradaz et al. (2009) 172-191 0.1 215 Capalbo (2014) C6H6 400-900 400-850 115-205 0.1 298 Capalbo (2014) (see Koskinen et al., AER 120-200 - - 430-900 400-900 2011) Table 3: Absorption cross sections and extinction (aerosols) of species included in the retrieval. Resolution and temperature at which the measurements were conducted are also included. Lastly, altitude range where species are expected to be retrieved are included and compared against expected altitude ranges obtained by Koskinen et al. (2011).

2.3.3. Methods applied in real data analysis

Steps taken in the analysis of real data will now be introduced with the aid of Figure 2.4. When performing flybys, the Cassini UVIS instrument in FUV mode measures the intensity of radiation between 110-190 nm coming from the direction of the star whose light is to be studied. The intensity is measured outside of the atmosphere in order to obtain a source spectrum (I0) and repeatedly while the UVIS-star LOS is occulted by Titan’s atmosphere (I). In order to calculate (wavelength and) tangent altitude dependent transmission spectra, ancillary information is required which defines the time and geometry of observation. It contains information on spacecraft time, position, velocity vector, and attitude, angles, with respect to Saturn and the Sun,

Chapter 2: Theory and methods to mention a few. Combining all this information gives “measured”12 transmission spectra as a function of tangent altitudes.

Figure 2.4: Workflow diagram. Transmission as a function of altitude is calculated from measured UVIS data combined with ancillary data. Simultaneously, absorption cross sections, published model profiles and the UVIS instrument function are combined to generate a simulated transmission. Then, MPFIT searches for an optimal set of column density profiles. These can finally be inverted for number densities. From Capalbo (2014).

On the other hand, for the calculation of modeled transmission spectra, it is crucial to have accurate laboratory measurements of absorption cross sections at temperature ranges representative of Titan’s upper atmosphere. This, combined with the UVIS instrument function (see, for example, Capalbo, 2014) and model profiles, gives calculated transmission spectra. With all this information, Eq. 2.13 can be solved for optimal column densities by employing the MPFIT routine.

2.3.3.1. Ancillary data

Occultation data can be freely downloaded from the archive of the PDS (2014). These 3D spatial spectral cubes data are recorded when Cassini performs Titan flybys (see Subsection 1.3.2.1 for more information on FUV UVIS data). Raw measurement data are downloaded to Earth and

12 It is intensity that is measured and transmission is calculated from it.

Chapter 2: Theory and methods organized according to PDS standards. They cannot be interpreted without additional information, namely calibration and ancillary data. Instrument calibration data are necessary for the conversion of raw data counts into geophysical units (in this case Rayleighs).

Ancillary data, on the other hand, provide all the necessary information concerning the positions and orientations of the spacecraft, instrument, planets, the sizes and shapes of these, as well as the times when observations took place (Figure 2.5). These data are crucial

Figure 2.5: Geometry of an observation. This ancillary information is for placing the measurement into provided by NAIF. Credits: NAIF/NASA (2014). context: e.g. the tangent altitude could not be calculated without them.

Observation geometry data are provided by NASA’s Navigation and Ancillary Information Facility (NAIF) and is called SPICE (abbreviated from Spacecraft Planet Instrument “C-Matrix” Events). The SPICE system focuses on solar system geometry (Figure 2.5) and includes software to read SPICE data files into many computing environments and to compute the necessary observation geometry (for example, pointing geometry). In the present work, a toolkit called ICY was utilized for deriving essential geometry related quantities (like tangent altitudes) from the SPICE ancillary data.

The main SPICE data sets are called “kernel files” or simply “kernels”. They are composed of navigation and other ancillary information. SPICE kernels also include metadata. These provide descriptive information that might be of need during the geometry analysis. For more information and tutorials on SPICE, refer to NAIF/NASA (2014).

Chapter 2: Theory and methods

2.3.3.2. Procedure

Flyby Date Star The analysis of stellar occultation was carried out by UVIS Tb I 12/13/2004 α Vir analysis software. First, a database of stellar occultation Tb II 12/13/2004 λ Sco T13 04/30/2006 β Ori candidates for the study was built from the OPUS online T16 07/22/2006 β Ori catalogue. This resulted in obtaining a list of 18 candidates T21 12/12/2006 α Eri T23 01/13/2007 η UMa (see Table 4 on the next page). Then, a candidate was chosen T40 01/05/2008 ε CMa and all of the observation and ancillary data were T41 02/22/2008 η CMa T41 I 02/23/2008 ε CMa downloaded from resources described in Subsection 2.3.3.1. T41 II 02/23/2008 ε CMa Initially, raw data, such as spectra and light curves as a T47 I 11/19/2008 η UMa 13 T47 II 11/19/2008 β CMa function of time index , were inspected. Already this step T48 12/05/2008 ε CMa exluded two occultations from further analysis. T52 04/03/2009 α Eri T53 04/19/2009 α Eri The first dataset of occultation, tagged T13, was loaded. All T56 06/06/2009 η UMa 14 T58 07/08/2009 η UMa rows and all columns of (1024x64xtime index) the spatial T70 06/21/2010 α Vir spectral cube were added together (leaving the time index Table 4: List of stellar occultations built from dimension intact), which had an effect of compressing 3D the OPUS database. The first column data into 2D data. The corresponding plot is shown in the left denotes the flyby name, the second represents the date when the flyby took subplot of Figure 2.6. When comparing with T41 II raw light 15 place and the third identifies the name of curves , the main message of the plot is that the number of the star (according to the Bayer points measured outside of the atmosphere at the T13 flyby is classification) being observed by UVIS. insufficient (if any). Consequently, I0 cannot be determined, Occultation analyzed in this work is bolded. and thus Eq. 2.11 cannot be employed for the calculation of abundances. It is also apparent that UVIS collected many more data points (more than 3000) when performing the T41 II flyby than on the T13 flyby (less than 400). As a result, the further analysis of the latter flyby was discarded.

13 It should be noted that the multiplication of the time index with the integration time (defined in a file downloaded from PDS) gives the time elapsed from the start of the observation. 14 In reality, only few detector rows (5 to 9 pixels) contain useful data and only these spatial lines are added together. The reason for this is twofold: 1) the pointing attitude of the spacecraft, 2) the point spread function of the instrument (Capalbo, 2014). Which lines should be added is specified in the header of the data downloaded from PDS. 15 Light curve is defined as transmission as a function of tangent altitude (Koskinen et al., 2011). 31

Chapter 2: Theory and methods

Other type of problem may appear and this is illustrated in the right subplot of the same figure (Figure 2.6) on data of the T52 flyby. In this case, the pointing of the spacecraft was not stable, which resulted in starlight oscillating around the center of the FOV in instrument’s x-direction. Koskinen et al. (2011) note that pointing drift is associated with wavelength shift. Thus, in order not to distort the results of the spectral inversion, this stellar occultation was not analyzed further.

The stellar occultation labeled T41 II did not have any of the problems detailed above. UVIS measured a sufficient number of times above TOA, therefore the I0 value was calculable (left subplot of Figure 2.6). Furthermore, its pointing was stable for all time indices in both directions (Figure 2.7). Therefore, this occultation was chosen to be analyzed in detail.

Figure 2.6: Left subplot: raw light curve vs. time index for T13 and T41 II flybys. Note that there is a plethora of measurement points above TOA for the T41 II stellar occultation. This is not the case for the T13 occultation, therefore its further analysis is impossible. Note also that T13 was ingress16 and T41 II was egress occultation. Right subplot: The star’s x- and y-coordinates in the FOV of the UVIS/FUV low resolution slit as a function of time index for the T52 stellar occultation. The unstable pointing reflected in a variation of offset from the FOV center in the x-direction (wobbling of instrument) renders data of this occultation useless17.

16 In the case of ingress occultation, the outermost of Titan’s layers are first probed, and as Cassini progresses along its trajectory, the deeper (lower tangent altitude) layers are probed. The opposite is true in the case of egress occultations. 17 This is not completely true. As Koskinen et al. (2011) point out, a calibration algorithm could be developed that correlatse the wavelength shift and the flux variations with the position of the star in the slit.

Chapter 2: Theory and methods

Next, utilizing the ICY toolkit and SPICE kernels downloaded for the time interval in which T41 II occurred, raw spectra and light curves (i.e. spectra and light curves as a function of time) were transformed into spectra and light curves as a function of tangent altitude. In order to obtain a single spectrum for a given tangent altitude (equivalent to time index), rows

Figure 2.7: Star’s x- and y-coordinates in the FOV of in the spatial spectral cubes were added together, thus the UVIS/FUV low resolution slit as a function of time creating a wavelength-intensity relation (black lines in index for the T41 II flyby. The pointing is stable for the the lower right subplot of Figure 2.8). whole time of occultation in both x- and y-directions.

Figure 2.8: The left subplot demonstrates 5 spectra taken during 5 integration times (of duration 1.75 s). In addition, the 3D axis represents the 3D spatial-spectral cube, where Rows = I, Columns = λ and Time index = Tg altitude18. Rows were summed in order to get a single spectrum for any tangent altitude plotted. The upper right subplot illustrates light curves corresponding to 130 and 170 nm before (black) and after averaging. The plot is zoomed to 2037-2065 (km) and 9-33 (counts/pixel/s) box in order to show the number of points being averaged (denoted by x) and the places of new averaged points (marked by gray diamonds). Thus, the SNR ratio is increased at the expense of altitude resolution decrease (to ~10 km). The lower right subplot shows measured spectra (in black) overlain by (boxcar) filtered spectra for two different tangent altitudes (800 and 2000 km). The signal was added together over the spatial pixels so as to obtain a single spectrum for each tangent altitude.

18 More precisely, they are not equal, but interchangeable.

Chapter 2: Theory and methods

In order to see how intensity changes as a function of tangent altitude for one wavelength, the 3D spatial-spectral time series matrix is sliced along the constant wavelength channel. The resulting light curves for 2 wavelengths bins19 are shown in upper right subplot of Figure 2.8.

It should also be mentioned that the count rate at channels 1015-1024 of the 1024-channel detector was found to be very low (close to zero). Therefore, these channels were excluded from the analysis as it is more plausible to assume that those pixels where this sharp drop (as compared to the rest of the spectrum) was observed are “bad”, than to assume that the star’s spectrum falls sharply at the right end of the FUV spectrum (Capalbo, personal communication, 2014).

Before calculating the transmission, the raw data were further manipulated in order to improve SNR. This is also illustrated in Figure 2.8, particularly in the zoomed subplots. All the spectra were smoothed using a boxcar filter. Furthermore, light curves were averaged every 13 tangent altitude points (as illustrated in the zoomed plot of the upper right subplot of Figure 2.8) in order to increase SNR at the expense of decreasing the altitude resolution (from 0.8 km to 10 km).

Thereafter, I0 was determined from all the tangent altitudes higher than TOA where the atmosphere is so dilute that it can be considered transparent. TOA in the case of the T41 II stellar occultation was set to be 1600 km.

At this point all the data were ready for calculating transmission (as “seen” by UVIS) using Eq. 2.6. It was not necessary to perform an absolute intensity calibration since relative intensity is sufficient to obtain transmission (and optical depth).

In order to solve Eq. 2.13, the modeled transmission

Figure 2.9: Tangent altitude-transmission relation also had to be determined. For that, knowledge of the measured with UVIS for 4 wavelength bins absorption cross section wavelength and temperature specified in the plot. Error bars are superimposed. dependence is important. The ACS data used in this For clarity, only every fifth point was plotted. work are summarized in Table 3 and the binning applied

19 Size of 3D spatial-spectral cube may be reduced by windowing and/or binning of the spatial and/or spectral dimensions. For more information, refer to PDS data documentation.

Chapter 2: Theory and methods in the retrieval is shown in Table 2. Lastly, column densities used as the initial guess in the retrieval came from a photochemical model (Capalbo, 2014).

The column density retrieval was described in Subsection 2.3.1. The same conditioning for raw column densities was applied as described in 2.3.2 in order to “clean” them from unrealistic values. Finally, these values were used to invert for the number densities (using the procedure outlined in Subsection 2.3.2.1), profiles of which can be seen in Figure 3.12.

2.3.3.3. Uncertainties

Measurement uncertainties are inherent to all the measurements, regardless of how sophisticated the instrument at one’s disposal is, i.e. regardless of its accuracy. In the case of the UVIS instrument, this means a possible error in the count of photons which can be statistically modeled by the Poisson distribution. This source of error is mitigated by averaging a certain number of altitude points where measurements took place. More earthly experimental uncertainties are those related to measurements of absorption cross sections. In addition, the obtained absorption cross section data for some species are not measured at temperatures representative of Titan’s upper atmosphere which potentially means usage of erroneous ACS-s in the forward modelling20.

Another source of uncertainties comes from the assumptions behind the model. Data error is often unimportant in relation to errors arising from uncertainties about the assumptions behind the model (Gubbins, 2004). There are several assumptions made in order to simplify calculations and these are discussed in Section 2.2. For example, idealizing Titan’s (upper) atmosphere as concentric circles might be a good first order approximation. However, subtle features in abundances might stay unresolved unless more a complex model is assumed (ellipsoids). Our calculations are as good as the assumptions behind the models21.

20 The absorption cross section for a given species is dependent on both the ambient temperature and wavelength (range of the flux) of photon(s). However, the ACS-s of some species show small variation with changing temperature, and thus can be considered temperature-invariant. 21 Gubbins (2004) aptly points out: “The inversion excludes any radically different interpretation. For example, if we invert the seismic arrival times for the depth of a pair of horizontal reflectors we would never discover that they really come from a single, dipping reflector”.

Chapter 2: Theory and methods

Uncertainties in the column density retrieval are characterized by the Q-probability and the reduced χ2. The Q-probability is the probability that χ2 is bigger than the one obtained by chance (Press et al., 1996). It takes on values between 0 and 1, the former representing a very untrustworthy retrieval, the latter denoting a perfectly trustworthy retrieval.

The reduced χ2 is defined as follows (Capalbo, 2014):

 2  2  Eq. 2.20 reduced k where χ2 is defined by Eq. 2.13 and k is the number of degrees of freedom. The latter is equal to the number of wavelength channels in the spectrum contributing to χ2 minus the number of

2 parameters involved. In case of good fits, reduced takes on value of around 1. Both the Q-probability and are plotted in Figure 3.12 and serve as indicators of zones where the retrieval can(not) be Figure 2.10: Local minimum: one trusted. of the MPFIT stopping criteria. By chance, the local minimum found The retrieval of column densities in the MPFIT routine of UVIS may coincide with the global analysis software (2014) is wrapped in a 2-iteration scheme. These minimum. Source: MATLAB will be referred to as large iterations. The routine itself performs (2012). many “small” iterations until a stopping criterion is reached (see subplot 5 in Figure 3.12). One potential stopping criterion is that the solver might locate a point that seems to be a local minimum22 of the sum of squares (Figure 2.10). Another potential stopping criterion is illustrated in Figure 2.11. In this case, MPFIT stops iterating if a certain threshold (called the tolerance) is crossed. TolX is a lower bound on the size of a step, meaning the norm of (x – x ). If the Figure 2.11: Another possible i i+1 stopping criterion for MPFIT. solver attempts to take a step that is smaller than TolX, the iterations Source: MATLAB (2012). end. TolFun is a lower bound on the change in the value of the

22 According to documentation in Optimization Toolbox in MATLAB software (MATLAB, 2012), local minimum of a function is a point where the function value is smaller than at nearby points, but possibly greater than at a distant point. In the same source, global minimum is defined as a point where the function value is smaller that at all other feasible points.

Chapter 2: Theory and methods

objective function during a step. If |f(xi) – f(xi+1)| < TolFun, the iterations end.

Whether the MPFIT routine will be called once or twice for the given tangent altitude (in a 2- iteration scheme) is decided based on the reduced χ2 parameter (Capalbo, 2014). When the stopping criterion is reached (after, for example, 30 “internal” or “small” iterations), MPFIT will

2 be called again if reduced is larger than a certain threshold (set arbitrarily to 15 in the software). Furthermore, if is smaller than the threshold, but some column density values or their associated σm uncertainties were not properly retrieved (for example, if the obtained σm is NaN), the retrieval is repeated with a new initial guess for badly retrieved parameters (species) while the properly retrieved parameters and their σm uncertainties remain unchanged. In other cases, if < 15 and all the parameters (for the given tangent altitude) were properly retrieved, the routine exits after the first “large” iteration. If the routine is called for the second time, the new initial guesses (new initial column densities) are calculated simply by dividing by 2 the column densities that served as the initial guess in the first (large) iteration. Note that in subplot 5 of Figure 3.12 MPFIT performs only 1 “large” iteration in the 430-750 km altitude interval with about 10-20 small iterations at each altitude point.

3. Results

After the introduction of the theory and methods used in this work (Chapter 2), the present chapter deals with the results obtained from the analysis of the data. First, the performance of the MPFIT routine (see Subsection 2.3.2) was thoroughly tested through the creation of synthetic datasets where the “true” column densities were known. The results are presented in Section 3.1 and subsequent subsections.

In Table 4 the list of potential candidates for the analysis was created from the OPUS database (OPUS, 2014) and the T41 II stellar occultation was chosen for further analysis. The results of this analysis are presented in Section 3.2.

3.1. Synthetic modelling – retrieval matrices

In following subsections the r- and  -retrieval matrices will be plotted for a given species as a function of the initial guess at each altitude studied. r-matrices are plotted on the left side and - matrices on the right side. Furthermore, the upper plots illustrate r- and -matrices before filtering, and the lower plots portray the same matrices after filtering. Types of filters used in “cleaning” the retrieved values are detailed in Subsection 2.3.2.

Chapter 3: Results

3.1.1. CH4

Figure 3.1: Relative error-(left) and σ-(right) retrieval matrices for CH4 before (up) and after (below) filtering.

Methane is one of two molecules from which the photodissociation in Titan’s upper atmosphere starts, the other one being N2 (Figure 1.3). It is the second most abundant species in Titan’s atmosphere and the most abundant species used in the retrieval with the column density values several orders of magnitudes larger than other (minor) species for the given altitude.

Figure 2.3 reveals a broad feature in ACS of CH4 without appreciable structure. It was one of the only two species known to be present in Titan’s atmosphere prior to the Voyager flybys (Brown et al., 2010).

At first glance at relative error the matrix reveals a good, “clean” retrieval, meaning that the calculated (Nc) values were well retrieved (within 20% of Nt) independently from the initial guess factor. The same cannot be said for the σ-matrix where the values are between 2 and 5 from 1000 km onwards and even larger than 5 between the 800-1000 km altitude range. This hints towards

σm being highly underestimated for this species. Note also that after filtering, the 400-600 km altitude range is lost. Therefore, it is not expected to retrieve CH4 below heights of 600 km in the real data analysis.

Chapter 3: Results

3.1.2. C2H2

Figure 3.2: Relative error (left) and σ-(right) retrieval matrices for C2H2 before (up) and after (below) filtering.

Acetylene forms via photolysis (with solar photons) from ethylene (Brown et al., 2010). Similarly to methane, acetylene has a “clean” r-matrix between 400 and 1160 km before filtering and between 400-1070 km after applying the altitude-filter (Eq. 2.19). Thus, according to simulations, acetylene’s true column density values are expected to be well retrieved in the 400-1070 km altitude range, unless a poor initial guess is used in which case the abundances in the lower altitude ranges might be lost or badly retrieved (between 400 and 600 km).

In the case of the σ-matrix it can be generally be said that the “true” profile is retrieved within 2-σ uncertainties. In the case of a poor initial guess factor and altitude ranges between 400-600 km, σ-values are either not retrieved (initial guess factor = 1/10) or poorly retrieved (σ larger than 2 and mostly larger than 5). Therefore, σm uncertainties are too small in comparison to the deviation of Nc from Nt in this region and for these initial guesses (Eq 2.18).

Chapter 3: Results

3.1.3. HCN

Figure 3.3: Relative error (left) and σ-(right) retrieval matrices for HCN before (up) and after (below) filtering.

The most abundant nitrile species in Titan’s atmosphere, detected at all latitudes, is HCN (Brown et al., 2010). In order for this species to form, strong N2 bonds break with photons with wavelengths below≈100 nm. The retrieval of HCN is more uncertain as it relies on a few sharp absorption lines near 141 nm in ACS that overlap with absorption by other species (Figure 2.3).

The filtered r-matrix of the HCN species does not look too good. Two particularly poorly retrieved layers, where r > 1 (the percentage error23 is more than 100%), are observed at approximately 500-600 km and 840-870 km altitude intervals. None of the abundances above 900 km is retrieved, except for the initial guess factor = 6, in which case the relative errors are 0.5 or larger. Only the altitude range 730-800 km can be trusted as the r-values are not larger than 0.5.

The σ-matrix, on the other hand, looks much cleaner. Apart from a few places where the initial guess factors are equal to or larger than 4 and around 600 km height, it can be stated that the true abundances are retrieved within 2-σ uncertainties.

23 Percentage error is relative error multiplied by 100.

Chapter 3: Results

3.1.4. C2H4

Figure 3.4: Relative error (left) and σ-(right) retrieval matrices for C2H4 before (up) and after (below) filtering.

The reaction of methylene (CH2) with methyl radical leads to the formation of ethylene (Brown et al., 2010). This in turn leads to acetylene formation (see Subsection 3.1.2).

This species also reveals a “clean” r-matrix. Nc-s are calculated with merely 20% or less deviation (percentage error) from Nt, with the exception of two thin layers around a 1000 km altitude where r is between 0.2 and 0.5. After filtering, the altitude-range in which Nc is obtained is 400-1150 km.

The σ-matrix also looks good, most of σ-uncertainties being smaller or equal to 2 (or equivalently, the “true” column density values are mostly recovered within 2-σ uncertainties). There are few thin layers (at around 660, 860 and 980 km) of larger uncertainties where σ-values between 2 and 5 are observed for all the initial guess factors.

Chapter 3: Results

3.1.5. C4H2

Figure 3.5: Relative error (left) and σ-(right) retrieval matrices for C4H2 before (up) and after (below) filtering.

Together with HC3N and C6H6 (excluding aerosols), C4H2 is the least abundant species used in this retrieval.

The raw (unfiltered) r-matrix of diacetylene is essentially flawless up till 800 km for all initial guess factors and starts to deteriorate from that point on. The σ-matrix is also within the acceptable level, mostly being smaller or equal to 2 with a few thin altitude ranges where σ- uncertainties are between 2 and 5. After filtering, the altitude range above 1100 km is lost and between 1000 and 1100 km the r-values become larger than 1. Note that the layer in this altitude- range was not retrieved before filtering for both r- and σ-values and then apparently became retrieved after filtering. The explanation for this is that the values between two thin r > 1 (and σ ≤ 1) lines (at 1000 and 1100 km heights) were interpolated according to the procedure described in Subsection 2.3.2.

Another interesting point to note is that if Nc is far away from NT in the absolute sense (corresponding to a large relative error), which is the case for the abovementioned altitude interval, then in order for σ-uncertainties to be at a small (acceptable) level (σ ≤ 2), σm has to be large (i.e. close to the absolute difference between Nc and NT). 43

Chapter 3: Results

3.1.6. HC3N

Figure 3.6: Relative error (left) and σ-(right) retrieval matrices for HC3N before (up) and after (below) filtering.

HC3N is a photochemical product in the thermosphere and upper atmosphere. 1-D photochemical models do not reproduce this nitrile very well and the disagreement between the calculated and predicted abundances can reach an order of magnitude or even more (Brown et al., 2010).

Together with C4H2 and C6H6, it is the least abundant species used in this retrieval.

Spectral features of HC3N overlap with those of C4H2 (Figure 2.3). It is a delicate species with hidden features in its spectrum which makes its abundances difficult to retrieve. Its r-matrix proves that point. Nc values above a 1000 km altitude were not retrieved or were filtered out while those around 1000 km and just above 400 km were either filtered out (initial guess factor = 1/10) or badly retrieved (r > 1). Moreover, as the initial guess factor increased from 4 to 10, both relative error and sigma values became successively worse. Nonetheless, apart from the aforementioned problematic regions and initial guess factors, the r-retrieval matrix looks reasonably good in the 450-900 km altitude range (r ≤ 0.5). Similarly, the σ-matrix has mostly σ <= 2 values between 450-900 km.

Chapter 3: Results

3.1.7. C6H6

Figure 3.7: Relative error (left) and σ-(right) retrieval matrices for C6H6 before (up) and after (below) filtering. Benzene is an aromatic hydrocarbon. It is one of the postulated precursors to aerosol production (for example, see Waite et al., 2007).

The retrieval matrices of benzene do not look too good. The raw r-matrix from 800 km onwards looks particularly bad and after filtering most of these values are removed. Similarly to C4H2, the altitude range between 900 and 1000 km was interpolated with abundances whose relative errors were larger than 1. However, again analogously to the C4H2 species, the corresponding σ-matrix for this altitude range looks quite good. Yet again, this implies that σm is of the size of NT or larger and of the size between 0.5 and 1 times Nc. Then, Eq. 2.18 gives σ-uncertainty values between 2 and 1, respectively. It is noted that NT can be expressed from Eq. 2.17 and substituted into Eq. 2.18 (or the other way around) to give the expression:

N r   c  Eq. 3.1  m 1 r

For example, in the case of r = 1 and Nc = 2 σm, σ = 1 is obtained. In the case of r = 5 and Nc = 1.6

σm, σ = 1.3. It can also be shown that in these cases, NT = σm and NT = 0.26 σm, respectively.

Chapter 3: Results

3.1.8. Aerosols

Figure 3.8: Relative error (left) and σ-(right) retrieval matrices for aerosols before (up) and after (below) filtering. The existence of aerosols was already deduced from remote-sensing observations at IR and UV wavelengths in the mid 1970-s (for example, see Danielson et al., 1973) and confirmed by Voyager 1 and 2. Danielson et al. (1973) realized that the photochemical chain of reactions occurring in Titan’s upper atmosphere is probably24 leading to the formation of these orange dark organic polymers.

Almost all the retrieved Nc values for this species are within 20% of the NT values (the r-matrix). Above 930 km the retrieved abundances and their uncertainties were either filtered out or nonexistent.

The σ-matrix is generally the best for an initial guess factor = 4. In the case of initial guesses of

1/4 or smaller and 6 or 10, σm values look underpredicted (σ >= 2) for a few altitude ranges.

Excluding these and also altitude range between 500-520 km (where 2 ≤ σ ≤ 5), σm captures the deviation of Nc from NT satisfactorily.

24 Photochemical models can recreate lighter molecular products with up to about 6 heavy atoms (Brown et al., 2010).

Chapter 3: Results

3.2. Real data analysis - T41 II stellar occultation

The extensive synthetic modeling was performed with the purpose of testing the MPFIT algorithm and to find out in which altitude ranges each of the species can be safely retrieved. Overall, most of the species were retrieved within 2-σ uncertainties.

The procedure of the analysis of stellar occultation data was described in Subsection 2.3.3.2. Table 4 contains the list of all the stellar occultation events that served as potential candidates for the study. Finally, the T41 II flyby was chosen as it was found to have stable pointing and enough points above the TOA to determine I0.

In this section the results of the real data analysis are presented and compared to results of previously studied T41 I stellar occultation (Koskinen et al., 2011; Capalbo, 2014).

The FUV Imaging Spectrograph (UVIS) was used to measure the attenuation of light from the star ε Canis Majoris as it passed behind Titan’s limb during the T41 II flyby. The FUV channel is used for observing stellar occultations. Occultation studied in this work was observed in a low resolution slit state which has a field of view of 1.5x60 mrad (see Subsection 1.3.2 for more information on UVIS slit states).

Characteristics of two stellar occultations compared in this work are shown in Table 5 (next page). Both products belong to the CO-S-UVIS-2-CUBE-V12 dataset and both were measured on 23rd February 2008. Moreover, the UVIS instrument was pointed towards the same star in both cases. In fact, this is a binary system, and the main star is of spectral type B2 II (SIMBAD database) and Bayer designation ε, even Figure 3.9: Spectrum of ε CMa measured by UVIS. The wavelength at which maximum intensity is though it is the second brightest star in the expected from Wien’s law is marked. The calculated constellation Canis Major. This spectral type (expected) intensity at that wavelength is also corresponds to a surface temperature of 22 200 K. shown. From Wien’s displacement law (for example, Feynman et al., 1963), one can calculate the wavelength at which the intensity peaks. It was

Chapter 3: Results found to be 130.5 nm for Adara (Figure 3.9). Expectedly, this star is a strong emitter of FUV photons.

Sc–tg. Atmosp. Altitudes Original Data product (FUV Lat Lon alt. min Flyby Star in probed sampling ) (deg) (deg W) distance shadow (km) (km) (km) T41 I FUV 2008_054_15_36 ε CMa -2 – -10 332–334 Yes 243-2028 0.4 4.7x105 T41 II FUV 2008_054_21_31 ε CMa -19– -30 171–177 No 72-3044 0.8 6.0x105

Table 5: Characteristics of two stellar occultations. T41 I was analyzed by Koskinen et al. (2011) and Capalbo (2014), while T41 II was extensively analyzed in this work and compared against the former. Note that the lat-lon range probed is narrow in both cases. Therefore, column density profiles can safely be converted to local number density profiles (Koskinen et al., 2011).

After completing all the steps described in Subsection 2.3.3.2, the transmission as a function of wavelength was calculated. The retrieval was initiated for the altitude range between 300 and 1300 km. From this and the information provided in Subsection 2.3.3.2., namely that the final altitude resolution obtained after the altitude averaging is ~10 km, it follows that the spectral inversion was performed exactly 100 times (i.e. in 100 tangent altitude points).

Figure 3.10: Upper subplot: Measured (black) and modeled transmission spectra as a function of wavelength for three altitudes (500 km – gray, 800 km – light gray, 1000 km – light). Lower subplot: Residual plot, i.e. the difference between measured and modeled transmission as a function of wavelength. Note the overestimation of abundances at the 500 km tangent altitude in the 134-144 nm wavelength interval.

The results of inversion at three tangent altitude points are presented in Figure 3.10 in the form of wavelength-transmission plots. In the upper subplot the modeled transmission nicely overlies the “measured” transmission in the case of the 800 and 1000 km tangent altitudes in the whole

Chapter 3: Results wavelength spectrum studied. This implies that the choice of species used in the retrieval is good and that MPFIT retrieved one set of column density values which together with the ACS-s of species used (Eq. 2.14) explain the observed transmission satisfactorily. Similar considerations are valid for the wavelength-transmission plot at the 500 km tangent altitude, except for the 134- 144 nm interval. There, the largest discrepancy between the modeled and transmission calculated from UVIS data is observed. In the lower residual plot, where the difference between the measured and calculated transmission has been taken, this discrepancy is more pronounced. The reason for the mismatch is that the abundances of species at that wavelength interval were overestimated, therefore the Гmeas - Гmod plot as negative values. Note also that, apart from the previously discussed deviation, the residuals oscillate around zero for all three tangent altitudes illustrated.

From the column density profiles, number density profiles may be obtained (for details on how to obtain number densities from column densities, see for example Capalbo, 2014). These will be discussed later. Before that, the results of the synthetic modeling will be used to detect which species and in which altitude ranges species might have been retrieved with biased values. It should be underscored that this exercise does not reveal the problematic species with biased zones: rather it reveals potentially problematic species with potentially biased zones.

The quest for potentially biased species starts by combining Eq. 2.16 and Eq. 2.17 into25:

N x init  Eq. 3.2 N filt 1 r where Ninit are the initial guesses of abundances, Nfilt are the retrieved and filtered abundances (calculated by MPFIT), x is the initial guess factor and r represents the relative error values calculated in the synthetic modeling.

Eq. 3.2 opens up the possibility for the creation of templates from the synthetic modeling for each species used in the retrieval. These templates can be utilized to identify species that may have altitude ranges in which MPFIT may not have performed in the optimal way. The explanation of the generation and usage of templates follows.

25 Ninit  By analogy,  x  can be obtained to search for a potentially biased σm after combining Eq. 2.16, Eq. 2.17  m r and Eq. 2.18. 49

Chapter 3: Results

Both sides of the Eq. 3.2 are known in the case of synthetic modeling. These are plotted as a function of altitude in Figure 3.11 for each species studied. Note that 9 curves are obtained on each plot corresponding to 9 initial guesses studied (Subsection 2.3.2).

Figure 3.11: Templates created from synthetic modeling (thin lines26) used for identification of species that potentially have altitude intervals of biased MPFIT retrieval. There are 9 constant initial guess lines. Starting from left to right, these are: 1/10,

1/6, 1/4, 1/2,1, 2, 4, 6 and 10. These constant initial guess lines that roughly enclose the Ninit/Nfilt curve obtained from real data inversion (thick black line) are marked with red (left) and orange (right), respectively. In addition, initial guess values for these lines are shown for easier interpretation. For example, in the case of CH4, the Ninit/Nfilt ratio together with (horizontal) 1-σm errors, both obtained from spectral inversion of the T41 II flyby data, are enclosed by constant x = 1 and x = 4 initial guess lines.

26 The word „lines“ is used, even though strictly speaking, it should be avoided as it is by definition „a special case of curve, namely a curve with null curvature“ (see, for example, Line (curve)).

Chapter 3: Results

In the case of real data inversion, however, only the left side of Eq. 3.2 is known. The goal is to use the Ninit/Nfilt from real data and x/(1+r) (or equivalently, Ninit/Nfilt) from synthetic modelling to identify zones where the MPFIT routine might have served flawed column densities. In order to do so, Ninit/Nfilt from synthetic tests is calculated for all the 8 species used in the retrieval. Every template of each species contains 9 lines corresponding to 9 initial guesses. It is known which initial guess factor creates which line.

Note that if, in Eq. 3.2, r = 0 for any initial guess, then Ninit/Nfilt = x. In other words, constant initial guess lines would not be distorted; they would be straight lines whose values coincide with labels in the horizontal direction. For example, in the case of CH4, the constant initial guess factor contours are only slightly distorted so that they match the values seen on the labels (in the horizontal direction) in the upper left subplot of Figure 3.11 (the only exception being the 550-

660 km altitude interval when x = 4). On the other hand, there are species like C6H6 for which constant initial guess contours are considerably distorted so that, for example, the contour line of x = 10 zigzags between 1/4 and 10 on the horizontal scale (the orange thin line in subplot 7 of Figure 3.11, counting from up and left). Therefore, it is important to have the contour lines from the synthetic modeling in order to make a correct connection between the real data results and the synthetic modeling results.

The procedure for linking the Ninit/Nfilt parameters stemming from the real data inversion and synthetic modeling follows. From Figure 3.11 the initial guess factor valid for a given altitude range is read off for each species. With this information (and for a given species), the relative error retrieval matrix (Section 3.1) is consulted in order to estimate the goodness of the retrieval.

For example, in case of methane, Ninit/Nfilt changes between x = 1 and x = 4 (Figure 3.11). Then, the retrieval quality is checked for the aforemntioned initial guess factors in the lower left subplot of Figure 3.1 (the r-matrix after filtering for CH4). Since the r-matrix looks good for these initial guesses over the whole altitude range studied, it can be stated that the reliability of the retrieval of the real data inversion for CH4 is expected to be good. In other words, the retrieval can be trusted for CH4, and inverted (and filtered) column densities obtained for CH4 probably represent the upper atmospheric true column densities well. Table 6 summarizes the results of applying this procedure and gives a simple qualitative estimate of goodness of the retrieval in the Reliability and Remark columns.

Chapter 3: Results

Alt. range Species x r Reliability Remark (km) 570-850 1

CH4 850-1200 2 0-0.2 Good Generally good retrieval 1200-1300 4 400-500 2

C2H2 500-950 1/2 0-0.2 Good Generally good retrieval 950-1050 1 400-470 1/4 0.5-1 Poor 470-650 1/4-2 > 1 Bad HCN 650-820 1/4 0-0.5 Good-Fair Erratic r-matrix 820-900 1/2 0.5 - > 1 Poor-Bad 400-550 2 550-680 1

C2H4 680-800 1/2 0-0.2 Good Generally good retrieval 800-950 1 950-1100 2 400-650 1 0-0.2 Good 650-770 1/2 0-0.2 Good

C4H2 770-850 1/4 0-0.5 Fair Good r-matrix up till 850 km 850-930 1/10-1/6 0-1 Good-Poor 930-1040 1/6-1/2 0 - > 1 Good-Bad 400-430 1/4 0.5- > 1 Poor-Bad 430-450 1/2 > 1 Bad 450-520 1 0.2-0.5 Fair

HC3N 520-720 1/2 0-0.5 Good-Fair 720-900 1/4 0-1 Good-Poor Mostly acceptable (0-0.5) 900-960 1/2 0.2-1 Fair-Poor 960-1000 1 > 1 Bad 400-570 10 0-1 Good-Poor Mostly acceptable (0-0.5) 570-620 2 0-0.2 Good

C6H6 620-700 1-1/4 0-1 Good-Poor 700-820 1/6 0.2- > 1 Fair-Bad r = 0.2-0.5 until 750 km 820-900 1/4-1/6 0- > 1 Good-Bad

AER 400-670 1/4-10 0-0.5 Good Ninit/Nfilt spans the whole range of x-s Table 6: Quantification of initial guess factor from linking the synthetic modeling and real data inversion results according to Eq. 3.2. For any given species, x is determined with the procedure elaborated above for the given altitude

range. Then, r-matrices from Section 3.1 are consulted in order to qualitatively estimate the reliability of Nfilt inverted from real data (column 5). Finally, either a general remark or a remark specific for a given altitude range is given for all the species. Zones of poor (thin lines) and bad reliability (thick lines) are plotted in subplot 1 and 2 of Figure 3.12.

Chapter 3: Results

The application of these templates in general could and should be questioned. For example, one of the caveats that should be mentioned is how representative these templates are for any given latitude range on Titan. Nevertheless, they serve as a good general guide for detecting species and delineating zones for which and where the retrieval might have failed to recover appropriate abundances.

As a final step of the stellar occultation analysis27, column density profiles were inverted for number densities according to the procedure described by Capalbo (2014). The resulting profiles, together with 1-σm uncertainties, are shown in the first three subplots of Figure 3.12 (below). In the case of some species (such as methane), these uncertainties are smaller than the thickness of the line representing number densities. As suggested in Subsection 3.1.1, this hints towards the uncertainties being (highly) underestimated. Note that in case of aerosols, the extinction profile was plotted.

Figure 3.12: Number density profile of 8 species used in the retrieval for the T41 II stellar occultation (first 3 subplots). Also marked are the species and intervals where spectral inversion might have served unreliable column densities (according to Table 6). Note that thin vertical lines at the limits of the first 2 subplots denote zones of poor reliability (where r = 0.5-1 in synthetic modeling) and thick lines denote potential zones of bad reliability (r > 1 according to r-matrices). Reliability of the retrieval in general is captured by 2 numbers: namely Q-uncertainty and reduced χ2 (explained in Subsection 2.3.3.3). These are presented in subplot 4. Reduced χ2 values are plotted for both inversion steps. Finally, the number of iterations of MPFIT within the 2-step iteration scheme is presented (subplot 5).

27 Actually, number densities can be carried further into the calculation of the temperature profile representative of regimes prevalent in Titan’s upper atmosphere.

Chapter 3: Results

Generally, a monotonic increase of number densities with decreasing altitude is observed. However, a few species exhibit deviation from this general trend in some altitude ranges (for example, C2H4 and C4H2 between 400-600 km). Small undulations in some profiles (e.g., C6H6 in the 700-850 km altitude range) might be due to the fact that the spatial inversion algorithm is ill- conditioned and amplifies noise in the data (Capalbo, 2014), rather than due to the real changes in number densities captured by inversion.

Subplot 1 and 2 in Figure 3.12 convey an additional piece of information obtained from Table 6. Species and zones of potentially unreliable altitude ranges are plotted. For example, in subplot 1, abundances of HCN are potentially flawed in the 400-470 (denoted by thin lines which mean poor reliability, i.e. the zone where r = 0.5-1 in the synthetic modeling), 470-650 and 820-900 km (thick lines, r > 1 in the synthetic modeling) altitude ranges.

The fit quality of calculated transmission to “measured” transmission (Figure 3.10) is characterized by two numbers, namely Q-probability and reduced χ2 (explained in Subsection 2.3.3.3). Both Q-probability and reduced χ2 take on values ~1 in the altitude range of 1000-1300 km, which essentially coincides with the retrieval of only CH4 (compare subplot 1 and subplot 4 of Figure 3.10). This implies an optimal fit. Reduced χ2 values between 1 and 2 for 300-1000 km imply a somewhat worse, but still good, fit. Q-probabilities in this altitude range are essentially zero. This would suggest retrieval of a very untrustworthy model (Capalbo, 2014). However, as Capalbo (2014) notes, even Q-values much lower than 1 can be acceptable28.

In subplot 5 of Figure 3.10 the number of MPFIT iterations is shown after each iteration of the 2- iteration scheme. More closely, MPFIT itself iterates many times starting from the initial guess abundances until it reaches a stopping criterion (for example, a local minimum). However, as mentioned in Section 1.4 and Subsection 2.3.2, it can converge to an unwanted minimum that does not provide optimal abundances. For this reason, the final column densities of iteration 1 were multiplied by a factor of 2 and served as initial guesses for iteration 2 (Capalbo, 2014).

28 Capalbo (2014) writes: “This Q-probability value varies between 0 and 1 for a statistically very untrustworthy and a perfectly trustworthy retrieval. However, due to the fact that the formal assumptions for which this statistics applies (models linear in the parameters, measurement uncertainties normally distributed, etc.) are normally not rigorously fulfilled by the models, the latter can be considered acceptable even with Q values several orders of magnitude below 1.”

Chapter 3: Results

Two remarks can be made about subplot 5 of Figure 3.12. Firstly, the number of MPFIT iterations was larger in iteration 1 than in iteration 2. This is expected, as in iteration 1 the Levenberg-Marquardt algorithm converged to a (hopefully) correct minimum. Secondly, in the 400-800 km altitude range, the software skipped the second iteration. This coincides with the minimum number of iterations in the first one iteration. Perhaps this is an indication of MPFIT having initial guess abundances close to the retrieved abundances for all of the species. However, this does not imply that these retrieved abundances are close to true abundances representative of the part of Titan’s upper atmosphere measured during the T41 II flyby.

T41 I and T41 II occultations took place on the same day with only about 6 hours of time delay (T41 II having been measured later). Table 5 summarizes and compares characteristics of these two flybys. The UVIS FUV spectrograph was pointed towards the same star. Even though the time of measurement was very similar, there are 2 differences that should be pointed out. In the case of the T41 I flyby, the atmosphere was in the shadow during the measurement. This was not the case for the T41 II flyby where the Sun was illuminating the part of the atmosphere measured. Moreover, the longitude range covered by 2 flybys is quite different: the measurements essentially took place on 2 opposite sides of the planet.

Keeping the above described similarities and differences in mind, a figure of ratios of number densities for the two events together with ratios of 1-σm uncertainty bars was plotted and is presented in Figure 3.13 (next page). Before doing so, number densities (and extinction, in the case of aerosols) of one of the occultations had to be interpolated in order to match the altitude points of the other occultation. Number densities (and extinction) of the T41 II flyby were chosen to be interpolated. In most cases the ratios of number densities were around the value of 1, taking into consideration the uncertainty bars. However, for some altitude ranges this was not the case. For example, in subplot 1, two zones are highlighted in the 900-100 km and 650-715 km altitude ranges. In the first case, CH4 abundances are smaller for the T41 II flyby; in the second case HCN abundances are larger for the same flyby. In this altitude range, ratios of almost all species (except aerosols) are close to 2 and calculated uncertainty bars are very small (they are not extending to nT41 II / nT41 I = 1).

Chapter 3: Results

In the 480-650 km altitude range, nT41 II / nT41 I < 1 is calculated in the case of C2H2, C2H4 and

C4H2. Similarly, a ratio smaller than 1 was calculated for the 435-650 km altitude range, this time for HC3N.

Figure 3.13: Ratio of number densities together with their uncertainty bars for two flybys that took place on the same day. Highlighted zones are those where the ratio, together with the uncertainty bars of at least one of the species (shown in any of the subplots), do not cross the nT41 II / nT41 I = 1 line.

The discrepancy in the ratios calculated may be attributed to many sources. For example, the fact that the two flybys took place on opposite sides of the moon with different illuminating conditions (Table 5) might explain some of the differences. Furthermore, it might be possible that the assumption of a spherically symmetric upper atmosphere (Section 2.2) is a good first order approximation, but for more accurate calculations of abundances, ellipsoidal atmospheric layers have to be assumed. Perhaps the difference might arise simply from the fact that the MPFIT routine did not provide good 1-σm uncertainties. In either case, to say something with more certainty deeper investigation is necessary.

Conclusions

“We are still steeped in the profound ignorance of what's going on in the Universe.”

Neil deGrasse Tyson

Scientists have a good reason to believe that Titan may hold the secret to how life on Earth emerged. The reason for this is that the photochemistry taking place in the upper layers of Titan’s atmosphere is presumably similar to the photochemical processes that took place in the atmosphere of prebiotic Earth. Therefore, the Cassini-Huygens mission was sent off to investigate this intriguing moon in unprecedented detail.

Stellar occultation measurements conducted by the UVIS instrument (in the FUV part of the spectrum) onboard Cassini are the means by which the composition and structure of Titan’s upper atmosphere (400-1400 km altitude range) can be identified and delineated, respectively. Data from the UVIS instrument were used in this work to perform spectral inversion of the wavelength dependent transmission data for many tangent altitude points. Thus, a column density profile was created for the 8 species studied (CH4, C2H2, HCN, C2H4, C4H2, HC3N, C6H6 and aerosols). These were further inverted for number densities according to the procedure described by Capalbo (2014). As a result, number density profiles shown in the first three subplots of Figure 3.12 were obtained.

Spectral inversion of real data was preceded by in-depth investigation of how well the MPFIT routine implemented in the UVIS analysis software (2014) retrieves column densities as a function of initial guess factor (Section 3.1). As a result of spectral inversion, MPFIT outputs two numbers for the given species and altitude studied. These are the retrieved column abundances and the corresponding 1-σm uncertainties. Both these numbers were compared against the “true” abundances. For that purpose, r- and σ-retrieval matrices were created which served as a visual aid in the characterization of the MPFIT performance for each species studied. r-matrices illustrate relative deviation (relative error) of retrieved column density values from the “true”

Chapter 3: Results column densities for a given species, altitude and initial guess factor. σ-matrices, on the other hand, quantify how well MPFIT captures uncertainties in calculations through its σm parameter, the optimal case being when σ ≤ 1. It was found that most of the species were retrieved within 2-

σ uncertainties. An exception to that was, for example, CH4, for which the σ-matrix exhibits mostly large values (> 2) hinting towards a possible underestimation of σm-uncertainties for that species, irrespective of the initial guess factor. More thorough investigation of this behavior is necessary in order to make firm conclusions. Initial work in this direction was already done by Capalbo (2014).

Filtered r-retrieval matrices indicate that calculated (and filtered) column densities are within

50% of the “true” column densities for most species, the obvious exceptions being HCN, HC3N and C6H6. Therefore, zones of potentially bad retrieval were identified according to the procedure described in Section 3.2, summarized in Table 6 and plotted in the first 3 subplots of Figure 3.12. Moreover, a quality of how well modeled transmissions fit those obtained from UVIS data (Figure 3.10) for all the tangent altitude points, obtained after altitude averaging of the measured intensities (upper right subplot of Figure 2.8) and converting them to transmission according to Eq. 2.6, was captured by Q-probabilities and reduced χ2 (Subsection 2.3.3.3). These quantities are shown in subplot 4 of Figure 3.12. Both Q-probabilities and reduced χ2 have values of ~1 in the 1000-1300 km altitude range, implying a “perfect” fit. However, in the 300-1000 km altitude ranges the two numbers diverge from each other, but can still be interpreted as indicators of a good fit of modeled (wavelength-dependent) transmissions to transmissions calculated from UVIS data.

Finally, a comparison of the ratios of inverted number densities and their 1-σm uncertainties from

T41 I and T41 II was carried out and nT41 II / nT41 I was plotted as a function of altitude as shown in Figure 3.13. Zones are highlighted where the ratio of species together with their uncertainties was not equal to 1. The reason for the observed discrepancies may come from many sources and requires a deeper investigation.

This work could be improved in many ways. Perhaps the most important of all would be the one concerning mathematics of retrieval. In order to get a better understanding of the uncertainties in calculations, the classical least-squares approach should be abandoned as it is very sensitive to the outliers in the data (for example, Tarantola, 2006). Moreover, even in case of careful

Chapter 3: Results

conditioning of data, this approach deduces only one “best model” and assigns 1-σm uncertainties to the retrieved values which often underestimate real uncertainties (Lomax, personal communication, 2014). According to Tarantola’s philosophy (Tarantola, 2006), the data should be used to falsify models and not to derive any particular model. In order to make the shift to this approach, sophisticated algorithms have to be constructed that can efficiently scan trough high dimensional parameter space (8-dimensional space in this work corresponding to the 8 species used in the retrieval). As of now, this approach would mean a much longer processing time and most likely memory issues due to the large dimensionality of the spaces involved (Milz, personal communication, 2014) and is thus deemed impractical.

Furthermore, additional laboratory work is necessary in order to obtain absorption cross sections as a function of temperature (especially for the temperature regimes characteristic of Titan’s upper atmosphere) for those species used in the retrieval for which this procedure has not been done.

Photochemical models from which abundances serving as initial guesses in the retrieval of real data are calculated might need to be reviewed. Indeed, more recent models, coupling photochemistry and dynamics (Hourdin et al., 2004), have shown that 1-D photochemical models cannot reliably reproduce the composition of Titan’s stratosphere, let alone its latitudinal and seasonal variability.

Obviously, more data would be invaluable. In order to increase the chances of observing stellar occultations, it would be optimal to have the orbiter specifically dedicated to studying Titan and its atmosphere (as opposed to the Cassini mission which is collecting data from the whole Saturnian system and only performs Titan flybys).

Perhaps only by taking into account the four crucial points for the improvement of results listed above, could the ignorosphere be renamed into sciosphere29.

29 Latin: Ignorare – to not know. Scire – to know.

Acknowledgments

Yet another chapter of my life has come to its very end. And what a ride it was! On occasions the road got very bumpy, but all the difficulties have been surpassed, all the problems solved. I will attempt to acknowledge most of the people that helped me to successfully finish this race as well as those who have enriched my life.

Firstly, I would like to extend sincere appreciation and gratitude to my supervisor professor Yves Bénilan for guiding me through this work. Moreover, his selfless help and prudent words greatly facilitated my life in France while his University access card ensured me peaceful working conditions. Merci beaucoup, professor!

Furthermore, I thank Dr. Fernando Capalbo for his continuous support during my internship in Créteil. Nothing of what is reported here would have been possible without software developed by him. Without his precise navigation through this vast field and his codes, I would have lost course many times. Gracias, Fernando.

I would also like to thank Dr. Mathias Milz and professor Anthony Lomax for their correspondence and their succinct and constructive replies to questions I posed. In addition, I would like to acknowledge all the people referred to in this work.

Very special thanks goes to professor Victoria Barabash, the academic coordinator of the SpaceMaster program, for leading this exciting program, a program that has changed my life thoroughly!

I am also indebted to Mrs. Anette Snällfot-Brändström and particularly Mrs. Maria Winnebäck, the education administrators at LTU, who supported me and other students from day one of the SpaceMaster program. Maria’s prompt replies to copious amounts of my mails made the administration part of this program absolutely painless. Tack så mycket, Maria!

On the same line of thought, I sincerely thank Mrs. Ursula Shahmary, the international student advisor in Würzburg, for navigating me through German bureaucracy. Vielen dank, Ursula!

Thanks also goes to people at GPCOS lab, especially Anaïs, Vassilissa and Fabien, for supporting me whenever support was asked for. Merci!

I cannot omit mentioning professor Per Avseth, a central figure of the last seven years of my life! His passion for science fuels me with ceaseless energy. It is not difficult to run the extra mile when surrounded by witty, inspiring people like him. Takk skal du ha, Per!

The list of acknowledgments would be incomplete if I omitted all the great people I have met while moving from Germany to Sweden and finally France. Danny boy (thank you for proofreading!), DJ Anis, Maxime, Lucas, Alexandru, Charles and all the other SpaceMaster students of Round 8, our studies are finished, but our friendship has just begun! All of you have transformed me into citizen of the world. Thank you, guys!

A very special moment in my life was a birth of a beautiful princess on September 6th, 2013. The mere thought of my little niece makes my heart filled with warmth and joy. Thank you for existing, little Barbara.

I sincerely thank my closest family members, sister, mother and father for their support and encouragement throughout this program. I would like to single out my father, a hard-working man, who truly is my role model. He wordlessly taught me one of the most important lessons in my life: work industriously in silence and never give up, no matter how difficult the task or situation at hand! Köszönöm, apám!

Finally, I thank a special girl for letting me live my dreams full-heartedly. Hvala ti, T.

Appendix A – Influence of initial guess factor on column density calculation

In Section 3.1 and the following subsections, the r- and σ-retrieval matrices were plotted as a function of the initial guess factor. In this appendix, the initial guess factor will be constant for the given retrieval matrix and instead, species will be plotted on the horizontal axis as the changing variable. Note that this merely means a permutation of already shown retrieval matrices and no new information is added. The purpose is merely to observe the results from a different point of view.

The same convention for coloring is followed as defined in Table 1 (Subsection 2.3.2.1).

Figure 0.1: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 1/10 before (up) and after (below) filtering.

Figure 0.2: Relative error (left) and σ-(right) retrieval matrices for initial guess factor = 1/6 before (up) and after (below) filtering.

Figure 0.3: Relative error (left) and σ-(right) retrieval matrices for initial guess factor = 1/4 before (up) and after (below) filtering.

Figure 0.4: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 1/2 before (up) and after (below) filtering.

Figure 0.5: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 1 before (up) and after (below) filtering.

Figure 0.6: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 2 before (up) and after (below) filtering.

Figure 0.7: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 4 before (up) and after (below) filtering.

Figure 0.8: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 6 before (up) and after (below) filtering.

Figure 0.9: Relative error (left) and σ-(right) retrieval matrices for initial guess factor= 10 before (up) and after (below) filtering.

Appendix B – Softwares and tools used

ICY Deriving geometry related quantities (tailored for IDL usage)

IDL All the calculations

MATLAB Creation of all of the figures (except those taken from internet)

Microsoft Word Report writing

UVIS analysis software Software written in IDL by F. J. Capalbo for analysis of UVIS data (2014)

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Acronyms

List of abbreviations used in the report

In case of an instrument or instrument part, the spacecraft carrying it is also denoted in brackets.

ACS – Absorption Cross Section

AU – Astronomical Unit

CODACON – Coded Anode Array Converter

CIRS – Composite InfraRed Spectrometer (Cassini)

EMR – ElectroMagnetic Radiation

ESA – European Space Agency

EUV – Extreme UltraViolet

FOV – Field Of View

FUV – Far UltraViolet

GPCOS – Groupe de Physico-Chimie Organique Spatiale

HDAC – Hydrogen Deuterium Absorption Cell (HDAC)

HSP – High Speed Photometer (Cassini UVIS)

INMS – Ion Neutral Mass Spectrometer (Cassini)

IRIS – InfraRed Interferometer Spectrometer and radiometer (Voyager 1)

LISA – Laboratoire Interuniversitaire des Systèmes Atmosphériques

LOS – Line Of Sight

NAIF – Navigation and Ancillary Information Facility

NaN – Not-a-Number

NASA – National Aeronautics and Space Administration

OPUS – Outer Planetary Universal Search

PDS – Planetary data System

SPICE – Spacecraft Planet Instrument “C-Matrix” Events

SNR – Signal-to-Noise Ratio

TOA – Top Of the Atmosphere

UVIS – UltraViolet Imaging Spectrograph (Cassini)

UVS – UltraViolet Spectrometer (Voyager 1)

VUV – Vacuum UltraViolet

Names of molecules

CH4 – methane

C2H2 – acetylene

C2H4 – ethylene

C4H2 – diacetylene

C6H6 – benzene

HCN – hydrogen cyanide

HC3N – cyanoacetylene

N2 – molecular nitrogen