STOCKHOLM SWEDEN 2016,
Statistical analysis of the electric field measurements
from the Rosetta spacecraft in the plasma environment of comet
67P/Churyumov-Gerasimenko
GUILLAUME DICKELI
KTH ROYAL INSTITUTE OF TECHNOLOGY
Statistical analysis of the electric field measurements
from the Rosetta spacecraft in the plasma environment of comet 67P/Churyumov-Gerasimenko
KTH R OYAL I NSTITUTE OF T ECHNOLOGY
Department of Space and Plasma Physics
Author
Guillaume D ICKELI
Examiner Tomas K ARLSSON
July 2016 — December 2016
A BSTRACT
Comets are a key to understanding the early stages of the solar system. They were here at its formation and have not evolved ever since, which means they are our best shot at learning the processes that led to the formation of the solar system as we know it today. Yet, our knowledge about these bodies is very limited. They are far from the Earth and small, which makes it complicated and expensive to reach them. But the study of the chemistry and geology of comets is not the only goal of the scientific com- munity. The plasma environment of these astronomical bodies could also give answers to many questions regarding the science of plasma physics, such as the interaction of the solar wind with plasmas. Answering some of these questions was an objective of the Rosetta Mission. Before its launch, only three space missions out of eight tar- getting comets had plasma instruments onboard. Rosetta carried several instruments designed to analyse the plasma environment of comet 67P/Churyumov-Gerasimenko.
We were able to perform a statistical analysis of the electric field spectrum in the vicin- ity of comet 67P/Churyumov-Gerasimenko. This allowed us to determine two regions of high spectral activity using the two probes of the LAP instrument and to propose several theories about the physical processes that were active.
Kometer är en nyckel till att förstå solystemets tidiga stadier. De var här under dess
tillkomst och har inte utvecklats sedan dess, vilket innebär att de är en av våra bästa
möjligheter att lära oss om de processer som ledde till bildandet av solsystemet. Ändå
är vår kunskap om dessa kroppar väldigt begränsad. De är långt från jorden och små,
vilket gör det komplicerat och dyrt att nå dem. Men studier av kometers kemi och
geologi är inte det enda målet för det vetenskapliga samfundet. Plasmamiljön hos
dessa astronomiska kroppar kan också ge svar på många frågor om vetenskapen om
plasmafysik, såsom växelverkan mellan solvinden och plasman. Målet för Rosetta-
strument. Rosetta hade flera instrument ombord för att analysera plasmamiljön hos
kometen 67P/Churyumov-Gerasimenko. Vi kunde utföra en statistisk analys av det
elektriska fältets spektrum i plasmamiljön runt kometen. Detta tillsammans med an-
vändningen av de två sonderna på LAP-instrumentet gav oss möjligheten att bestämma
två regioner med hög spektral aktivitet, samt möjligheten att föreslå flera teorier om de
fysikaliska processerna som var aktiva.
C ONTENTS
Abstract i
Contents iii
Abbreviations v
1 Introduction 1
1.1 Comets . . . . 1
1.2 The Rosetta mission . . . . 3
1.2.1 Brief history of the mission . . . . 4
1.2.2 67P/Churyumov-Gerasimenko . . . . 4
1.2.3 Instruments . . . . 5
1.2.4 The LAP instrument . . . . 6
1.3 Objectives . . . . 7
2 Methodology 8
2.1 Obtaining the electric field . . . . 8
2.1.1 Acquisition and calibration of the probe potentials . . . . 8
2.1.2 Calculation and detrending of the electric field . . . . 10
2.2 Calculation of the electric field dynamic spectrum . . . . 15
2.2.1 Determination of Rosetta’s position around the comet . . . . 15
2.2.2 Calculation over one day . . . . 17
2.2.3 Statistical analysis – calculation over several months . . . . 18
3 Results 21
3.1 Spatial analysis of the spectra . . . . 22
3.2 Analysis of the time series . . . . 26
3.3 Observations . . . . 28
3.3.1 February to May 2015 . . . . 29
3.3.2 September 2015 to March 2016 . . . . 31
3.3.3 April to June 2016 . . . . 34
4 Discussion 35
4.1 Lower hybrid waves . . . . 36 4.2 Interpretation of the dynamic spectra . . . . 38 4.3 Plasma instabilities and creation of density gradients . . . . 41
5 Conclusion 42
Appendices 44
Acknowledgments 50
Figures 51
Tables 53
Bibliography 54
A BBREVIATIONS
PSD Power Spectral Density LAP Langmuir Probe
67P 67P/Churyumov-Gerasimenko CSO Comet-Solar Orbital
LHDI Lower Hybrid Drift Instability
1.
I NTRODUCTION
1.1 Comets
Ten million years after the formation of the solar system, particles started to conglom- erate. Some of these agglomerates – the biggest – kept on growing by attracting more particles and by colliding with others, creating gaseous and rocky planets. The others remained small and untouched. These small bodies, ranging from a hundred meters to tens of kilometers, are called comets if their nucleus is made of ice, and asteroids otherwise. Although their central body is small, comets can usually be detected eas- ily thanks to their much bigger coma (also called tail ). This visible atmosphere forms when the comet passes close to the Sun, by an outgassing from the icy nucleus due to the increasing temperature, and is precisely what distinguishes comets from asteroids.
This outgassing also creates the plasma environment around the comet. The neutral gas
emitted from the comet is photoionized and locally increases the plasma density. But
outgassing is not the only impact the Sun has on comets. Stars are known to constantly
eject a solar wind made of charged particles from their upper atmosphere – mostly pro-
tons, electrons and α particles. When they reach a comet, these particles modify the
environmental electric and magnetic fields as well as the environmental plasma den-
sity. The photoionized particles originating from the nucleus are picked up by the solar
CHAPTER 1. INTRODUCTION
wind and accelerated by the solar wind electric field until they reach its speed. This process is called mass loading or ion pickup.
Because of their small size and long-period orbit, comets are very hard to study and our knowledge about these bodies is very limited. As proof of our limited knowledge about comets, only 5253 of them are known today
[1], while their total estimated population in the solar system is one trillion
[2]. Before Rosetta, only seven different comets have been investigated, all of them through brief fly-by’s (see Table 1.1). These missions usually aimed at studying the shape and geometry of the astronomical bodies, though some of them included plasma instruments.
Comet Mission(s)
21P/Giacobini-Zinner
ICE(American, 1978) 26P/Grigg-Skjellerup Giotto (European, 1985)
1P/Halley
Vega 1(Soviet, 1984)
Sakigake
(Japanese, 1985) Suisei (Japanese, 1985) Giotto (European, 1985) 19P/Borrelly Deep Space 1 (American, 1998)
Wild 2 Stardust (American, 1999)
9P/Tempel Stardust (American, 1999)
Deep Impact (American, 2005) 103P/Hartley Deep Impact (American, 2005)
Table 1.1: Investigated comets with the corresponding space missionsThe only cometary electric field measurements at our disposal comes from Vega, ICE and Sakigake which operated in the environments of comets 1P/Halley (Vega, Saki- gake, ICE) and 21P/Giacobini-Zinner (ICE). This material has been extensively studied by the scientific community. Regarding 1P/Halley, increases in the electric field power spectral density in the bow shock were detected by the Vega spacecraft at frequencies of a few Hz ([3], [4]) and in the mHz range behind the bow shock [5]. Sakigake de- tected wave activity up to 200 kHz upstream of the bow shock [6], while ICE observed fluctuations in the electric and magnetic fields around 100 Hz [7]. As for 21P/Giacobini- Zinner, ICE observed ion acoustic waves and electron plasma oscillations upstream of the bow shock [8], and lower hybrid and whistler modes in the cometosheath [7].
The process of pick up ions described previously was identified as the cause for the for-
mation of these waves both upstream and downstream of the bow shocks. The neutral gas of cometary origin is photoionized and picked up by the solar wind, leading to an unstable particle distribution in the cometary environment. This distribution is usually ring-shaped in ion velocity-space ([9], [10]) and generates the waves.
Even though their composition is quite well-known – icy core and dust-covered surface – the physical processes of formation and evolution of comets remain unclear. Yet, the study of these astronomical bodies is crucial if we want to have a bigger picture of the early stages of our solar system. Indeed, their structure has survived all the upheavals the solar system has been through during the last 4.5 billion years. Their extremely cold core (around -250
oC) allows them to maintain every molecule in a solid state, making them perfect witnesses of the evolution and early composition of the solar system.
But the comets could also be the key to another crucial question: the appearance of life on Earth, which is very tightly linked to the appearance of water on its surface.
There was no water on Earth in its early stages, and the collision of an icy comet with our planet could act as a triggering event to its appearance.
[11]Moreover, the organic materials they contain could also contribute to the creation of an atmosphere on certain planets after impact, which is necessary to regulate temperature, filter sunlight and maintain life-sustaining gases such as oxygen.
In this context, the Rosetta mission was a unique opportunity to learn more about these astronomical bodies. Unlike the other space missions listed in Table 1.1, Rosetta was designed to investigate the comet 67P/Churyumov-Gerasimenko in detail by orbit- ing it closely. Both its core and its coma were investigated, thus providing a deeper understanding about the formation and evolution of comets. Thanks to the specific equipment carried by the spacecraft, this mission was also a unique opportunity to investigate in depth the plasma environment of a comet.
1.2 The Rosetta mission
Rosetta is the name of a space mission designed by the European Space Agency whose
first goal was to obtain information about the core of comet 67P/Churyumov-Gerasimenko
and its interaction with the Sun. The mission was divided into two parts: the investi-
CHAPTER 1. INTRODUCTION
gation of the cometary surface, performed by the robot Philae, and the study of the environment of the comet performed by the orbiter. Rosetta also had two additional secondary goals: the study of asteroids Šteins and Lutetia.
1.2.1 Brief history of the mission
March 2, 2004 Rosetta was launched in a rocket Ariane 5 from Kourou, french Guyana March 4, 2005 First Earth swing-by to gain speed
February 25, 2007 Mars swing-by
November 13, 2007 Second Earth swing-by
September 1, 2009 Rendez-vous with asteroid Šteins November 13, 2009 Third (and last) Earth swing-by July 10, 2009 Rendez-vous with asteroid Lutetia June 8, 2011 The spacecraft was put in sleep mode January 20, 2014 Reactivation of the spacecraft
August 6, 2014 Rosetta was put in an orbit around 67P/Churyumov-Gerasimenko November 12, 2014 Philae landed on the comet
September 30, 2016 End of the mission
Table 1.2: History of mission Rosetta
1.2.2 67P/Churyumov-Gerasimenko
67P/Churyumov-Gerasimenko (which will be referred to as 67P from here on) is a Jupiter-class comet, which means its orbital period is shorter than 20 years and its in- clination is lower than 30
o. It was discovered by Soviet astronomers Klim Ivanovych Churyumov and Svetlana Ivanovna Gerasimenko in 1969. It is 4.3 km by 4.1 km in size and its particular shape (see Fig 1.1) suggests it results from the slow and gentle collision of two astronomical bodies.
Figure 1.1: Photograph of comet 67P/Churyumov-Gerasimenko taken by Rosetta[2]
67P has an elliptic trajectory about the Sun, with a quite large eccentricity of 0.6 and an orbital period of 6.45 years. Its perihelion was 4 AU up to 1840. Since then, two Jupiter encounters reduced it down to 1.29 AU, while its aphelion remained more or less constant around 5.68 AU
[2].
The International Astronomical Union identified five different kinds of regions on its surface, depending on their structure: dust covered, rock-like, pitted and brittle mate- rial, smooth, and large-scale depression
[2]. However the composition of a comet varies a lot from one perihelion to another, which means the surface of 67P evolved a lot throughout the mission and these structures were not fixed to particular areas on the comet’s surface
[2]. Indeed, a comet is mostly composed of ice – mainly frozen water but also other substances such as methane or carbon dioxide – and dust. When the comet approaches the Sun, its ice is sublimated into a gas, forming the coma. The Sun’s radiation pressure pushes the particles away from the nucleus and form a tail. When the comet is far enough from the Sun, its coma becomes ice again and the tail disappear.
1.2.3 Instruments
The orbiter carried 11 different scientific instruments, which are described in Table 1.3 and illustrated in Fig 1.2.
[12]Figure 1.2: Scientific instruments embedded on the orbiter[2]
CHAPTER 1. INTRODUCTION
ALICE
an ultraviolet spectrometer for analysing the coma and tail of the comet
CONSERT
a radiofrequency probe for analysing the internal structure
COSIMA
another spectrometer for analysing the dust grains ejected in order to find out whether they are organic or not
GIADA
measures the amount of ejected dust grains as well as their mass, speed and direction
MIDAS
measures the size and volume of the particles at the vicinity of the comet
MIRO
a radiotelescope measuring the surface temperature and finding the right spot to land on the comet
OSIRIS
two optical cameras used to determine the rotation of the core
ROSINAa spectrometer for analysing the structure of the atmosphere and
ionosphere of the comet
RPC
the Rosetta Plasma Consortium is composed of 5 plasma analysers and 2 Langmuir probes. It is used to study the interaction between the comet and the solar wind
RSI
measures the main properties of the core (mass, density)
VIRTISa spectrometer measuring the surface temperature
Table 1.3: List of the scientific instruments on Rosetta
This paper focuses on the Rosetta Plasma Consortium (RPC), and more precisely the Langmuir probes (LAP).
1.2.4 The LAP instrument
The LAP device was composed of two sensors (probes LAP1 and LAP2). Both probes
were titanium spheres of 2.5 cm radius and weighing 40 g. They had a coating made
of titanium nitride, which is robust and chemically inert. The probes were mounted on
15 cm long arms and attached to the upper and lower booms of the spacecraft (as illus-
trated on Fig 1.2), about 2 m away from the spacecraft. The distance between the probes
was 5 m. These distances were very short which means the data could be disturbed by
the spacecraft in two ways : first because of the equipment embedded on Rosetta which
might cause unwanted interactions with the sensors ; second the spacecraft itself might
modify the plasma in the vicinity of the two sensors.
[12]Figure 1.3: One of the LAP sensors on board Rosetta[13]
LAP had 5 main scientific goals.
• Extend our knowledge about the cometary plasma environment (formation and structure) by measuring plasma density, electron temperature and flow speed.
• Provide a detailed understanding of the inner coma region by studying the space and time variations of the fluid parameters in its vicinity.
• Measure the plasma density structures.
• Study the electric field.
• Study different kinds of plasma waves.
1.3 Objectives
As a step towards the last two goals, a statistical study of the electric field using the LAP instrument has been performed in this thesis. To carry out this task, different steps were needed: retrieval of the data sent by Rosetta, calculation and detrending of the electric field, and finally spectral analysis.
In Chapter 2 we present the realisation of these three steps and the methods used. In
Chapter 3 we go through the results obtained for the identified time periods in 2015 and
2016 when the electric field data is available and of good quality. Chapter 4 contains a
discussion of the methods used and the results obtained. Finally, Chapter 5 summarizes
the work.
2.
M ETHODOLOGY
2.1 Obtaining the electric field
2.1.1 Acquisition and calibration of the probe potentials
The LAP instrument can be used in two different ways: with a bias voltage or a bias current, with a possibility of operating each mode with and without sweeping.
The bias voltage mode is used to measure electron density and temperature. In this mode, the probe voltage is either swept or kept fixed and the current collected by the probes is measured.
The other operation mode is using a bias current. In this situation the probe current is chosen such as to minimize asymmetries in the impact of the plasma on the probe potentials. The potentials of both probes with respect to the spacecraft (V
1and V
2) are recorded. When recording the potentials, the bias current is usually kept constant. For example for high density plasmas, I
bias= 0.
One could expect V
1and V
2to be almost equal, given the short distance between the
probes. However when retrieving the data from Rosetta one can often notice a quite
large offset between those potentials. This error is due to the above mentioned asym-
metries caused by the short boom length (about 2 meters) of the LAP probes. Both the
spacecraft (by shadowing or perturbing the environmental plasma flow) and its equip- ment (by causing spurious electric fields) can disturb the probes’ measurements . Fig 2.1 below illustrates this situation.
Figure 2.1: Non calibrated probe potentials for the time interval 2015/02/27 01:40 - 01:42
In this figure, the blue dots represent the data retrieved by each LAP probe. Ideally these points should be close to the red line, which corresponds to V
2= V
1. The sys- tematic offset can be removed by a cross-probe calibration : a linear fit is applied to the relation between the probe signals and the offset is then subtracted. The result of this procedure is shown in red in Fig 2.2.
Figure 2.2: Calibrated probe potentials for the time interval 2015/02/27 01:40 - 01:42
CHAPTER 2. METHODOLOGY
2.1.2 Calculation and detrending of the electric field
Once the probe potentials are calibrated, the small difference that remains between the individual probe signals can be used to determine the electric field with the simple Eq (2.1) (assuming the probes separation is short enough to consider that the field is constant in that domain):
E = V
1− V
2d (2.1)
where d is the distance between LAP1 and LAP2. One should notice that what is calcu- lated here is the electric field component in the direction of the probe separation.
For the date and time used earlier (27 February 2015 between 01:40:00 and 01:42:00
UTC
), the individual probe signals (top panel) and the electric field calculated with Eq (2.1) (bottom panel) are plotted in Fig 2.3.
Figure 2.3: Individual probe measurements and corresponding electric field signal for the time interval 2015/02/27 01:40:00 - 01:42:00UTC
Several observations can be drawn from this figure. First, the peaks of electric field
happen at the same time as large gradients in V
1and V
2, which are a proxy for plasma
density. Then, one can notice that the mean of the electric field is not zero, which charac-
terizes the presence of trends. Such trends are usually caused by events with time scales
longer than the ones of the record pictured in Fig 2.3 and can therefore affect the low
frequencies of the spectrum. In Fig 2.4, it is clear that the very low-frequency peaks (0 –
1 Hz) are much greater than the rest of the spectrum and possibly non-physical. Several methods can be used to eliminate the trends in the electric field signal and therefore re- duce these distortions in the spectrum. These methods are described in detail in [14], we will adapt them to our problem.
Figure 2.4: PSD of the signal without detrending for the time interval 2015/02/27 01:40:00 - 01:42:00UTC
Removing running average
The first method that can be applied to the signal is to remove its running average. It is also the easiest because it simply consists in taking a moving average of the data points and subtracting it to the original signal. It is very effective when it comes to reducing the trends, as Fig 2.5 obtained during the time interval 2015/04/16 11:35:30 - 11:36:10
UTC
illustrates. One may notice the data gap located around 11:35:42
UTC. As will be
further discussed, this kind of gap in the data might induce disturbances in the electric
CHAPTER 2. METHODOLOGY
field spectrum.
Figure 2.5a: Original electric field signal. Figure 2.5b: Electric field with running av- erage removed.
One may also consider using linear fitting as an alternative to running average removal.
This method consists in applying a linear fit to the data and then subtracting it from the signal. This is particularly efficient if the trends are more or less linear. If they are more complicated one can use quadratic or even sinusoidal functions.
One can notice that the mean of the electric field with its running average removed (Fig 2.5b) is a lot closer to zero, which means the trends have been efficiently reduced.
However further treatment, namely windowing, needs to be applied to further sup- press them.
Windowing
The distortion in the spectrum can be due to other causes, such as discontinuities in the
electric field signal. Indeed, when computing the Fourier transform, it is assumed that
the signal is periodic (the same at the beginning and the end of the time interval that
is considered to compute the Fourier transform). However, this is not always the case
in practice: the example of Fig 2.5a is obvious, but actually even in Fig 2.5b the electric
field is not the same at the beginning and the end. One way to address this issue is to
apply a window to the signal in order to force it to be equal to zero at the beginning
and the end. Usually the Hann window is used because it has a very low impact on the
spectrum, but one can also consider using gaussian or triangle windows.
Figure 2.6a: Electric field signal without window.
Figure 2.6b: Electric field signal with win- dow.
Now that the electric field is detrended and that a window has been applied, a spectral analysis is possible. We first compute the Fourier transform, which can be done using the Fast Fourier Transform algorithm in MATLAB. The power spectral density can then be estimated by plotting the Fourier transform magnitude squarred.
Figure 2.7: Power spectral density for the time interval 2015/02/27 01:40:00 - 01:42:00UTC
Fig 2.7 shows an example of such a plot comparing the power spectral densities ob-
tained with and without the different detrending methods evoked earlier. One can
notice that the distortions observed at very low frequencies (around 1 Hz) were con-
sequently reduced by applying these methods. As expected, the window decreased
the height of the very first peaks, while the fact of removing the running average sup-
pressed them up to 2 Hz. The spectral activity around 2 to 10 Hz, however, is more
CHAPTER 2. METHODOLOGY
interesting and physically correct. The nature and possible causes for the peaks located in this frequency range will be further discussed in Chapter 4.
Fig 2.8 below shows an example of an electric field dynamic spectrum for the time inter- val 12:00:00 – 12:10:00
UTCon 28 May 2015. The figure contains three panels: the probe potentials, the electric field deduced from these potentials, and the electric field’s spec- trum calculated over the time interval. The dynamic spectrum is obtained by dividing the signal into short segments of a few seconds and then calculating the power spectral density of each time segment, which typically gives a result similar to the middle panel of Fig 2.8. More details about the method used to calculate this dynamic spectrum will be given in section 2.2.2.
We will see in the upcoming sections that these results can be used to obtain the dy- namic spectrum of the electric field over longer periods of time and eventually realize a statistical analysis.
Figure 2.8: Recording from the LAP device for the time interval 28/05/2015 20:10:00 – 20:20:00
UTC. From top to bottom: individual probe potentials against time (V), electric field spectrum against frequency and time (colorbar in (mV/m)2/Hz), electric field deduced from first panel against time (mV/m).
2.2 Calculation of the electric field dynamic spectrum
We saw in the previous section how to correctly detrend the electric field and how to obtain its spectrum over a short period of time (a few minutes). At first sight the electric field spectrum seems to present regions of increased activity in the lower hybrid frequency range (around 5 Hz) as already observed in a limited number of cases by [15].
In order to confirm these obervations, a further analysis over longer time intervals is needed.
This section will apply the methodology described above to obtain the power spectrum density of the electric field signal as a function of the frequency and the position of the spacecraft over several days. The goal is twofold : to determine the frequencies for which the activity is highest, and to determine which regions of the comet are the most active with regards to the electric field oscillations.
2.2.1 Determination of Rosetta’s position around the comet
As detailed above, the point of this section is to make a PSD map for every frequency and position of Rosetta. The first thing to do is therefore to define the coordinate sys- tems that will be used to acquire this position. Two systems will be used:
• the comet-solar orbital (CSO) system has its origin at the center of 67P. The x-axis points towards the center of the Sun, the y-axis is its perpendicular on the orbital plane of the comet, and the z-axis completes the orthogonal system. This system will be used to determine the relative position of 67P to the Sun.
• the fixed system has the same origin as the CSO system. The z-axis is in the direction of rotation of the comet, while x is its perpendicular on the orbital plane and y completes the system. This system will be used to determine the position of Rosetta around the comet. This should enable us to find out which regions of 67P are associated with high electric field activity.
This is illustrated in Fig 2.9 below.
CHAPTER 2. METHODOLOGY
Figure 2.9: Coordinate systems – green : comet-solar orbital, blue : fixed. The Z axis for both systems is the same.
Once these coordinate systems introduced, the position of the spacecraft is defined by its latitude and longitude around 67P. The definition of these two angles with respect to the fixed axes X
F IX, Y
F IXand Z
F IXis detailed in Fig 2.10 below. In this figure, R represents the location of Rosetta around 67P. The two red vectors are its projection on the planes (X
F IXY
F IX) and (Y
F IXZ
F IX) and allow the definition of the two coordinate angles (longitude and latitude respectively).
Figure 2.10: Latitude and longitude of Rosetta around 67P.
When one looks at the data sent by Rosetta, one can notice the latitude stays almost constant over a day, which means the position of the spacecraft will be only described by the longitude as a first approximation for time intervals shorter than one day. The variation in longitude comes from the fact that the comet rotates around the axis Z
F IXwith a rotational period of about 12 hours
[2].
2.2.2 Calculation over one day
We saw in the previous section how to analyse the spectrum of the electric field for very short periods of time (about 30 seconds). However what is really interesting is to perform this analysis over longer intervals, at least one day, in order to have a wider understanding of the wave activity in the cometary plasma.
The first step is therefore to calculate the dynamic spectrum of the environmental elec- tric field over a full day. In order to do so, the electric field data for the day is divided in small windows of several seconds. Several window lengths were used (10 to 30 seconds) but they all gave similar results. An arbitrary duration of 10 seconds was therefore chosen. For calculations sakes, it was decided that the spacecraft would be assumed to be stationary during these 10 seconds. In other words, each window cor- responds to a specific position of Rosetta around 67P and to a unique latitude and lon- gitude. The PSD of every window is then computed and stored in a table, along with the corresponding position of Rosetta (latitude and longitude with respect to 67P). The matrix is then plotted, each element of the matrix corresponding to an average of the electric field spectral density over the considered couple (latitude, longitude).
Several plotting possibilities were tried, but the most relevant for the time interval du-
ration considered is to plot the PSD against the longitude for every frequency. Indeed,
as discussed earlier, the latitude of Rosetta can be considered constant over a day, which
means it is not very interesting to plot it.
CHAPTER 2. METHODOLOGY
2.2.3 Statistical analysis – calculation over several months
Figure 2.11: Dynamic spectrum averaged over October 2015 and duration of acquisition
Once the data is acquired for every day of a month, it can be compiled into one single file for a month, which allows a wider view on the behaviour of the comet’s plasma environment. If the same position of the comet was investigated by Rosetta at different dates in the same month, the results are weighted by the duration of the acquisition over this specific area. Comparing the results between different months will allow a statistical analysis of this behaviour. The plot of the dynamic spectrum for October 2015 is given in Fig 2.11 to illustrate the process.
The duration of acquisition of the PSD for each longitude of the spacecraft is given along with the dynamic spectrum. It is obvious that some regions of the comet are not covered as long as others. The regions of longer acquisition were traversed several times by Rosetta, which means the results for these areas are more reliable.
However, if for one day it was enough to plot the PSD against frequency and longi-
tude, there is now information missing about Rosetta’s latitude. This element could be considered constant for time intervals of about a day, but now it has to be taken into account.
Two solutions were implemented to fix this problem. The first one was to separate the results into two subplots : one for the positive latitudes (Northern hemisphere of the comet) and the other for the negative latitudes (Southern hemisphere). This is illus- trated in Fig 2.12 below.
Figure 2.12: Dynamic spectrum for October 2015 divided into Northern and Southern hemi- spheres
This result is interesting because it allows a comparison of the wave activities of both hemispheres. However it is not enough if one wants to have further information about the dynamic spectrum’s dependency in latitude. In such case another solution is to calculate the integral of the PSD along the frequency, in order to get rid of this variable.
This allows a plotting of the results against latitude and longitude (see Fig 2.13).
One can nonetheless notice that the latitude range is not very wide (75 degrees in this
example). Given this narrow latitudinal range, the plot in Fig 2.12 will give enough
information about the dependency of the spectrum against Rosetta’s latitude around
67P in most cases.
CHAPTER 2. METHODOLOGY
Figure 2.13: Integral of the dynamic spectrum along frequency for October 2015
3.
R ESULTS
In this chapter we will present in detail the results obtained for the relevant identified time intervals. By relevant we mean the time intervals that led to usable and useful con- clusions. Not all the data received from Rosetta was of good enough quality to use. A large part of the data had a sampling frequency lower than 1 Hz (less than one measure per second), which made it unusable. For some other days, large gaps in the poten- tial data made the calculation of the electric field impossible because of discontinuities.
Moreover, the LAP device was not always used in electric field mode. This mode would typically be run only two 12-hour period every second week. Consequently, most of the data from 2014 was not usable for the purpose of this thesis. This is the reason why this study will focus on the results obtained for different events in 2015 and 2016.
This chapter will be divided into three parts. The PSD of the electric field will first be
spatially analysed, then temporally. Finally a short examination of the results obtained
will be performed. The spatial analyses will be performed over time intervals lasting
one month in order to have a general view of the spectral behaviour of 67P’s environ-
ment. We will then have a closer look at time series for several intervals within the most
interesting months.
CHAPTER 3. RESULTS
3.1 Spatial analysis of the spectra
The following figures show the spatial variation of the electric field power spectral density between February 2015 and June 2016 monthly.
2.34 AU
1.88 AU
1.65
AU
1.36 AU
1.42 AU
1.65
AU
CHAPTER 3. RESULTS
2.11 AU
2.34 AU
2.57
AU
2.80 AU
3.23 AU
Figure 3.1: Dynamic spectra over 2015 and 2016 and corresponding approximate heliocentric distances of 67P in AU
One can already notice two very different behaviours between the period September 2015 – March 2016 and the rest of the data. At first sight, the first three and last two months of acquisition present a much higher spectral activity than the others and this intense spectrum seems to be localized on different regions of comet 67P. This will be further discussed at the end of this chapter.
In order to understand what kinds of physical processes can be the source to this dif-
ferent spectral activity, it is interesting to complete these spatial results with an analysis
of the times series recorded by the LAP instrument.
CHAPTER 3. RESULTS
3.2 Analysis of the time series
As explained in the introduction of this chapter, the temporal analysis will not be per- formed over the whole time period because it is difficult to summarize the large amount of data in a reasonable way. It was rather decided to work on short time intervals (10 to 30 minutes) for each month, in order to have a good picture of the plasma wave activity for each month. Fig 3.2 below depicts the temporal wave activity in 2015 and 2016 with the same format as Fig 2.8.
a. b. c.
d. e. f.
g. h. i.
CHAPTER 3. RESULTS
Figure 3.2: Recordings from the LAP instrument for several time intervals in 2015 (panels a to e) and 2016 (panels f to j). Same format as Fig 2.8.
These results will be analysed in the upcoming section. However before investigating them into detail one can notice the presence of vertical uniform lines in the spectrum.
It is the case for example on 15/11/2015 around 12:25:30
UTCand several times on 07/06/2016 around 05:04:45
UTC, 05:07:30
UTCand 05:09:45
UTC. The comparison be- tween the middle and bottom panels of these plots shows a correlation between these lines and very large and impulses in the electric field signal. These impulses are obvi- ously non-physical due to their extremely short duration. They are actually caused by gaps in the probe measurements.
One may also notice that the period February – May 2015 presents a very different behaviour from the other months, with a very intense spectral activity that also seems to come back in April and June 2016. This observation will be further discussed later on.
3.3 Observations
The plots in Fig 3.1 show the dynamic electric field spectrum against frequency and longitude of the spacecraft in the same format as Fig 2.11. As discussed earlier the latitude of the spacecraft is relatively constant over time intervals of one month long, therefore it is assumed that the single longitude of the spacecraft is enough to accurately represent its location around the comet. The plots divided into Northern and Southern hemispheres can nonetheless be found in Appendix 1 and give a little more information
j.
about the latitude of the spacecraft. The data seems to be divided into three periods:
February to May 2015, September 2015 to March 2016 and April to June 2016.
3.3.1 February to May 2015
Even though the electric field spectrum intensity is very uneven during this time (much higher in February than in April for instance), it seems clearly focused over two regions of the comet: longitudes -180
o/-15
o, and 15
o/180
o. This appears even more distinctly after averaging the three spectra:
Figure 3.3: Average of the spectrum obtained between February and May 2015 (no data for March)
The electric field spectrum reaches its minimum around 0
oand maximizes around -90
oand 70
olongitude.
As observed earlier, the spectrum over this period shows a higher PSD than for other
times, which can interestingly be put in parallel with the temporal analysis detailed
in Fig 3.2. One can notice after observing the panels for February and May 2015 a
fluctuation of the individual probe potentials (top panels) that seems to be made of
two different variations, one slow corresponding to large-scale gradients in the plasma
density, and one fast corresponding to faster ones. Fig 3.2 shows clearly a correlation
between the gradients in plasma density and the electric field amplitude. This will be
CHAPTER 3. RESULTS
discussed in Chapter 4.
Fig 3.2 also indicates that these gradients are linked to the existence of regions of in- creased activity in the spectrum: the spectral peaks undeniably match the highest plasma density gradients. Therefore, these fast variations in the signal have a direct effect on the spectrum, which appears to be very intense in the middle panels. The nature of these very fast oscillations in the probe potentials is however still unclear and will be further discussed in Chapter 4.
It seems interesting to study the case of May 2015 a little further, since it presents the the strongest differences in its spectral activity outside and inside the region -15
o/+15
o. Fig 3.4 and Fig 3.5 below show two recordings from the LAP device for two intervals of 10 minutes in May 2015.
Figure 3.4: Recording from the LAP device for the time interval 28/05/2015 12:50:00 – 13:00:00
UTC(around -85olongitude), same format as Fig 2.8
Figure 3.5: Recording from the LAP device for the time interval 28/05/2015 21:45:00 – 21:55:00
UTC(around +15olongitude), same format as Fig 2.8
Fig 3.4 was acquired between 12:50:00 and 13:00:00
UTCon May 28, which corresponds to longitudes for Rosetta around -85
o. It is therefore located in the middle of the most active region in the dynamic spectrum for May 2015 (see Fig 3.1). This record shows very large and recurring plasma density gradients combined with much faster varia- tions which give rise to a very intense spectrum. On the other hand, Fig 3.5, which was acquired between 21:45:00 and 21:55:00
UTCon the same day and corresponds to the least intense spectral activity of the month (around +15
o), shows a very different behaviour. The fast variations in the individual probe potentials have disappeared and consequently the probe signals show less gradients. This is also reflected in the middle panel : the spectrum is less intense than previously observed and is concentrated to a much narrower frequency range.
To summarize the observations made between February and May 2015, we found two different spectral behaviours. The electric field spectrum was very low between -15
oand +15
oand very intense elsewhere. These spatial differences were correlated to dif- ferent phenomena in the temporal measurements made by the LAP instruments. The probes measurements presented regularly spaced big gradients for both cases, corre- sponding to gradients in the environmental plasma density; however these gradients were coupled to much faster fluctuations when the spectrum was more intense (be- tween -180
o/-15
oand +15
o/+180
o). It seems clear from these observations that the fast gradients are correlated with large amplitudes in the electric field signal which would be the cause for the increase in the electric field spectrum.
3.3.2 September 2015 to March 2016
These six months present a very similar behavior. Unfortunately September 2015 and March 2016 are hardly usable because of large gaps in the data (no information between -110
oand 5
ofor September 2015 and between -180
oand 105
ofor March 2016). However the data from October 2015 to February 2016 is enough to have a good estimate of the PSD for these time periods (see Appendix 2 for the durations of acquisition). We will therefore focus on these months.
The average of the spectrum between September 2015 and March 2016 is shown in Fig
3.6 below. It is most intense between -125
oand +60
olongitude, which is very close
CHAPTER 3. RESULTS
to the definition given by [16] of the neck region, and peaks at +10
oand -20
o. This is totally different from what was observed between February and March 2015.
Figure 3.6: Average of the spectrum obtained between September 2015 and March 2016
Another difference worth noticing is the intensity of the peaks. The spectral activity in this period is much weaker than during the first half of 2015, with a maximum value around 25 (mV/m)
2/Hz for the considered frequency range against more than 70 (mV/m)
2/Hz for the period February-May 2015. Furthermore, the regions of low spectral amplitude between September 2015 and March 2016 extend on a much larger longitudinal range than between February and May 2015. This eventually gives a much less intense spectrum over the whole longitudinal range -180
o/+180
o.
Below are given two samples acquired by the LAP device for two different times in October 2015. The first one was recorded on 25 October between 04:00:00 and 04:10:00
UTC
which corresponds to a longitude around -10
o, which means in the middle of the
highest spectral activity (see Fig 3.1). The second set of panels was recorded on 13
October between 06:20:00 and 06:30:00
UTC, which means around 75
olongitude, at the
lowest of the spectrum. Both samples last 10 minutes (same duration as in the previous
section).
Figure 3.7: Recording from the LAP device for the time interval 25/10/2015 04:00:00 – 04:10:00 UTC, around longitude -10o
Figure 3.8: Recording from the LAP device for the time interval 13/10/2015 06:20:00 – 06:30:00, around longitude 75o
Both plots present a similarity: there are more large-scale but less small-scale gradients in the potentials than in February and May, whether it is at the lowest or highest ac- tivity. However when one looks closer at these two figures, it seems that once again the regions of intense spectral activity show a combination of two types of gradients.
If Fig 3.7 only presents a few large-scale gradients, Fig 3.8 also shows small-scale gra-
dients within these large-scale fluctuations. Once again this combination of variations
induces more intervals of large amplitude in the electric field signal, which appear to
be much more numerous in Fig 3.8 than in Fig 3.7. The magnitude of these gradients,
however, seems to be more or less the same around 50 mV/m. Similar observations can
be performed between November 2015 and March 2016 (see Fig 3.2, panels e to h).
CHAPTER 3. RESULTS
3.3.3 April to June 2016
Figure 3.9: Average of the spectrum obtained between April and June 2016 (no data for May)
This last part of the data is a little bit harder to analyse than the previous ones. The range of longitudes covered by Rosetta during this period is smaller than previously observed, which is reflected in the dynamic spectra by large white gaps. However it is still possible to observe in Fig 3.1 a spectral behavior very similar to the one identified in section 3.3.1 for the period February – May 2015. As can be noticed in Fig 3.9 averaging the dynamic spectrum from April to June 2016, the spectral activity is again located outside the neck region and the spectral peaks easily exceed 35 (mV/m)
2/Hz.
These observations are confirmed by the plots of the integrated spectrum along fre-
quency against latitude and longitude (last two figures of Appendix 3). The plot for
June 2016 shows a clearly higher activity for longitudes under -100
oand over 65
o.
4.
D ISCUSSION
In this study we have performed a spectral and temporal analysis of the electric field signals sent by the spacecraft Rosetta orbiting comet 67P/Churyumov-Gerasimenko from January 2015 to the end of emission in August 2016. Although this long time in- terval allowed us to retrieve a large quantity of results, data was missing for rather long periods of time, sometimes exceding one month as it was the case during June/July 2015. This drawback was explained by several causes. The first obvious reason for the lack of electric field data was that the LAP device was not operated in the interesting mode during the periods concerned. However other phenomena – internal or external to the spacecraft – could disturb it and perturb the acquisition of the data. For exam- ple, the plasma density could be too low or the LAP sensors could have temporary failures. These events would typically result in gaps in the data or totally incoherent observations, such as sampling frequencies lower than 1 Hz.
In this chapter we will discuss the results obtained for the periods when the electric
field data was of good quality.
CHAPTER 4. DISCUSSION
4.1 Lower hybrid waves
One of the observations that were made in Chapter 3 concerned the intensity and fre- quency range of the electric field spectrum. We saw that it had two different behaviors depending on the period: the PSD was much higher during the first half of 2015 and April – June 2016 than during the rest of the mission. An increased activity means two things: the maxima are higher, but the frequency range is also a little wider. Typically, the periods of high activity show a spectrum ranging from 1 to 7 or 8 Hz (see Fig 3.3), against 3 or 4 Hz for the less active (Fig 3.6). Therefore, it seems that most of the spec- tral activity was located below 10 Hz. One can then wonder what kind of turbulences take place in the plasma environment of the comet and cause these fluctuations in the spectrum.
Let us assume the plasma is cold (no pressure gradient) and magnetized. In such case, the dispersion relation is given by Eq (4.1). We will not demonstrate this relation here because it is not the objective of this paper, however we will use the results obtained by [17] and [18].
1 − ω
pe2ω
2− ω
2ce− ω
pi2ω
2− ω
2ci= 0 (4.1)
In this equation ω
peand ω
piare respectively the electron and ion plasma frequencies, and ω
ceand ω
ciare the cyclotron frequencies:
ω
pe= s
ne
2m
e0ω
ci= eB/m
iω
pi= s
ne
2m
i0ω
ce= eB/m
eEq (4.1) has two solutions.
High frequency solution, ω ≈ ωpe
In this case, the ion term can be neglected, and the solution is:
ω
U H= q
ω
2pe+ ω
2ce(4.2)
This solution is called the upper hybrid mode.
Low frequency solution, ωci
< ω < ω
ceIn this case, the solution is:
ω
LH= v u u t
1
1
ω2pi
+
ω 1ceωci
(4.3)
≈ √
ω
ceω
cifor high densities (4.4)
This solution, so-called the “lower hybrid” mode, is the one of interest because as dis- cussed in the previous section, the observed waves occur at low frequencies.
Given the typical values for a cometary plasma expressed in Table 4.1, we find a typical lower hybrid frequency following (4.5).
Parameter Value
Plasma density n ∼ 10
2/10
6m
−3Magnetic field B ∼ 10/50 nT
Table 4.1: Plasma parameters
2 Hz ≤ f
LH= ω
LH2π ≤ 7 Hz (4.5)
Of course this result is given only to have an idea of the frequency range of such waves but should be taken carefully. (4.4) shows that f
LHdepends on the ion and electron cy- clotron frequencies, which are highly dependent on the environmental magnetic field.
The values given in Table 4.1 for these parameters are only estimates and can vary a
lot depending on the nature of the plasma. However the range in (4.5) matches very
well the regions of spectral activity discussed earlier, which means these lower hybrid
waves could be the cause.
CHAPTER 4. DISCUSSION
More physically speaking, lower hybrid waves are longitudinal ions and electrons os- cillations propagating perpendicularly to the magnetic field. It is a very uncommon event in the sense that both ions and electrons play an equal role. Indeed, the frequency of such waves is located between the electron and ion gyroradius:
ω
ciω ω
ce(4.6)
i.e. both ion and electron dynamics are important components of the motion. This
“hybrid” behaviour gave its name to the wave. It also shows in the dispersion relation (4.4), where both gyrofrequencies ω
ciand ω
ceappear.
These lower hybrid waves are mostly powered by the lower hybrid drift instability (LHDI). This instability is produced by a combination of cross field current and inho- mogenities in the plasma and magnetic field as described by [19]. [20] and [15] explain that in the conditions of this study with large density gradients, the LHDI is the main source of electro-magnetic fluctuations in the range 1 – 100 Hz.
4.2 Interpretation of the dynamic spectra
As discussed in Chapter 3, the results could be clearly divided into two categories.
The first one, ranging from September 2015 to March 2016, showed a very “normal”
behaviour that was expected from the conclusions drawn by the litterature. Indeed,
the measurements of the distribution of 67P’s environmental plasma were extensively
studied all along the Rosetta mission. [16] states that the plasma density peaks over the
neck of 67P, the region located between the two main lobes of the comet, around 60
oand -120
olongitude ([16]). This would be due to the fact that this neck region would
be the consequence of the slow collision of the two main lobes. This transition region
would therefore present different chemical characteristics than the comet’s lobes, which
would induce a different outgassing and therefore a different plasma density distribu-
tion. These observations are confirmed by the measurements done by the ultraviolet
spectrograph ALICE (see Table 1.3). [21] and [22] both report higher H
2O emissions
in the neck region of the comet. The PSD plots for the period September 2015 – March
2016 clearly show an increase in the electric field spectral activity in this region, with a
spectrum both more intense and expanding towards higher frequencies – even though some variation is worth noticing between -170
oand +170
o). This is in agreement with the fact that a higher plasma density means larger gradients in the electric field and therefore more activity in the spectrum.
If the spectral activity during the period September 2015 – March 2016 showed a strong correlation with the neck of the comet, the behaviour between February and May 2015 was totally different. This surprising behaviour does not match the observations per- formed by [16] is the one of an abnormal solar activity. A temporary burst in the solar wind could cause the environmental plasma density to locally and momentarily rocket, inducing large gradients in the electric field signal and therefore a raise in the spectral activity. But there could be another cause to this kind of event, which was broadly in- vestigated by the scientific community ([23], [10]). These works observed the presence of localized wave packets in the lower hybrid frequency range and coincident with local plasma density depletions. Because of their frequency range these events were called Lower Hybrid Cavities. According to [10], these density depletions could either be a natural result of low frequency fluctuations, or be caused by non-linear effects cou- pled with lower hybrid waves. These cavities were found to have a strong effect on the propagation of lower hybrid waves and were accompanied with a large increase in the wave energy. Such cavities could have temporarily formed in the plasma environment of 67P outside the neck region during the first half of 2015 and caused the spectral be- haviour discussed earlier, however it is very difficult to say with certainty. In the work performed by [10] these cavities were accompanied by deep drops in the plasma den- sity and probe potentials, which is not exactly what was detected in our study. The individual probe potentials acquired by the LAP sensors onboard Rosetta rather show potential gradients alsmot all the time (see Fig ??). Further investigation needs to be performed to confirm these observations.
Finally, it is interesting to discuss the difference of amplitude in the dynamic spectra
for February – May 2015 and September 2015 – March 2016. We saw in Chapter 3
that in the first case the spectral activity was much more intense (peaking around 75
(mV/m)
2/Hz, against 20 (mV/m)
2/Hz for the latter) and expanded towards higher
frequencies (15 Hz against 8 Hz). [21] and [22] both studied the coma of 67P by mod-
elling the cometary outgassing and comparing it to the measures performed by several
CHAPTER 4. DISCUSSION
instruments onboard Rosetta (ALICE, VIRTIS and ROSINA ). This allowed them to find two regions of high gas production: the south of the main lobe for CO
2and the neck region for H
2O. The total outgassing varies depending on which side of the comet is illuminated by the Sun. This observation gives an explanation to the results found by [16] (larger plasma density in the environment of the neck) and to the increase of spec- tral activity in this area for the time period September 2015 – March 2016. [22] also provided a plot of the time evolution of the cometary H
2O and CO
2emissions:
Figure 4.1: Gas emissions acquired by [22]. Top panel: H2O emissions as measured by Rosetta (blue) and calculated with their model (black). Bottom panel: CO2emissions as measured by Rosetta (orange) and calculated with their model (black).