Master’s Thesis

Theoretical Physics

Studying The Local Interstellar Medium through Measurements of Interstellar Hydrogen Inside the Heliosphere

Frida Wikberg

November 9, 2020

Supervisors: Mika Juvela Erkki Kyrol¨ a¨ Examiners: Mika Juvela Erkki Kyrol¨ a¨ Karri Muinonen

UNIVERSITY OF HELSINKI

DEPARTMENT OF PHYSICS

P.O. Box 64 (Gustaf Hallstr¨ omin¨ katu 2a)

00014 University of Helsinki

Tiedekunta – Fakultet – Faculty Koulutusohjelma – Utbildningsprogram – Degree programme Faculty of Science Physical Sciences

Tekijä – Författare – Author Frida Wikberg

Työn nimi – Arbetets titel – Title Studying The Local Interstellar Medium through Measurements of Interstellar Hydrogen Inside the Heliosphere

Työn laji – Arbetets art – Aika – Datum – Month and year Sivumäärä – Sidoantal – Number of pages Level November 9, 2020 50 Master’s thesis ​ ​

Tiivistelmä – Referat – Abstract

The Interstellar Medium (ISM) incorporates all the matter that fills up the space between the stars of a galaxy. Interstellar matter consists mainly of hydrogen and helium gas, either in atomic or ionized form, as well as some heavier atoms, molecules and dust particles. It varies in temperature and density, forming structures and interacting with stars as a part of the stellar evolution.

The Sun’s magnetic field and solar wind forms the heliosphere, effectively shielding us from our interstellar surroundings as we travel through the interstellar medium. However, the neutral component of the ISM, mainly in the form of hydrogen atoms, are not directly affected by the Sun’s magnetic field and can therefore enter the heliosphere where they can be observed through their interactions with solar Lyman-alpha photons that then produce the Lyman-alpha background radiation in the heliosphere. The SWAN instrument, on the SOHO satellite, measures this radiation and can provide a good picture of the interstellar hydrogen inside the heliosphere.

In this work I introduce our current understanding of the Local ISM and ways of observing and modelling it. By modelling the intensity signal observed by SWAN, I also show an example of analysing interstellar parameters using SWAN observations of interstellar hydrogen inside the heliosphere.

Avainsanat – Nyckelord – Keywords interstellar matter, heliosphere, local interstellar medium, SWAN, Lyman-alpha

Säilytyspaikka – Förvaringställe – Where deposited

Muita tietoja – Övriga uppgifter – Additional information

Contents

1 Introduction 1

2 The Interstellar Medium 2

2.1 Origin and Structure ...... 2

2.1.1 The Origin of Matter ...... 2

2.1.2 Interstellar Constituents ...... 4

2.1.3 Interstellar Structures ...... 5

2.1.4 Observing the Interstellar Medium ...... 7

2.1.5 Interstellar Matter and Stellar Evolution ...... 9

2.2 The Local Interstellar Environment ...... 11

2.2.1 The Local Interstellar Bubble ...... 11

2.2.2 The Local Interstellar Cloud ...... 13

2.2.3 The Local Interstellar Magnetic Field ...... 16

2.2.4 The LIC-LB boundary ...... 16

2.2.5 Effect on Earth ...... 17

3 Interstellar Matter in the Heliosphere 19

3.1 The Solar Wind ...... 19

3.2 The Interplanetary Magnetic Field ...... 20

3.3 The Heliospheric Boundaries ...... 21

3.3.1 The Termination Shock ...... 22

3.3.2 The Heliopause ...... 23 CONTENTS 4

3.3.3 The Bow Shock ...... 24

3.4 The Interaction Between the Local Interstellar Medium and the Heliosphere ...... 25

3.4.1 Radiation and Gravity ...... 25

3.4.2 Charge Exchange and Pickup Ions ...... 25

4 The SWAN Instrument on SOHO 27

4.1 Solar Observations ...... 27

4.2 SOHO ...... 27

4.2.1 Scientific Objectives ...... 28

4.2.2 Success ...... 28

4.3 SWAN and the Lyman-α Method ...... 29

4.3.1 The Lyman-α method ...... 29

4.3.2 The SWAN Instrument ...... 31

4.3.3 A Typical SWAN Sky Map ...... 31

5 Modelling the Interstellar Matter in the Heliosphere 34

5.1 Challenges ...... 34

5.2 Early Models ...... 34

5.3 Multicomponent Models ...... 36

6 An Example Using Direct Simulation 37

6.1 Model for the intensity signal ...... 37

6.2 Parameters and data set used ...... 38

6.3 The Implementation ...... 38 6.4 Results ...... 39

6.5 Analysis ...... 42

7 Conclusions 45 1 INTRODUCTION 1

1 Introduction

The interstellar medium (ISM) incorporates all the matter that fills up the space between the stars in a galaxy. From our point of view, the ISM begins at the edges of the solar wind’s influence and ends at the edges of the Galaxy where it meets the intergalactic medium. Interstellar matter consists mainly of hydrogen and helium gas, either in atomic or ionized form. Heavier atoms and molecules, dust particles, and cosmic rays make up some of the other constituents of interstellar space. Magnetic fields play an important role in the dynamics and overall structure of the ISM. Temperature and particle density vary over several orders of magnitude in different regions and form a diverse and complex environment far from the “empty space” it was once thought to be. Chapter 2 provides an introduction to the current knowledge of the interstellar matter in general and findings about our local interstellar environment in particular.

The solar wind makes up nearly all the plasma content in interplanetary space. Eventually, far beyond the orbits of the planets, the solar wind comes to a stop and interstellar matter starts to dominate. This boundary marks the edge of the heliosphere. There are two very different types of plasmas interacting in this boundary region. On one hand we have the particles of the Local Interstellar Medium (LISM), particles of interstellar origin, and on the other there are the solar wind particles, ultimately originating from the protosolar cloud (PSC) that later became our solar system. Where these two plasmas meet, a dynamic and highly turbulent interface region is formed.

In Chapter 3 the focus is on how the interstellar matter interacts with the Sun. The neutral particles of the LISM are not directly affected by the Sun’s magnetic field and so they can enter the heliosphere. Chapter 4 describes the observations made by the SWAN instrument on board the SOHO satellite, which can be used to study the interstellar particles flowing through and interacting with the heliosphere.

Chapter 5 introduces the models used to describe these two multicomponent plasmas as well as their complex interactions. In Chapter 6, to exemplify this, I use a model of the interstellar H distribution in the heliosphere to simulate the Lyman-α observations made by SWAN in order to compare the two. The aim is to examine the behavior of the interstellar matter by looking at the characteristics and tendencies of the parameters when carefully varied. This is done using direct simulation. 2 The Interstellar Medium

As interstellar space is highly complex and variable, it is of great importance to study the Local Interstellar Medium. The first part of this chapter describes what we know of interstellar space; what it consists of, how it is linked to stars, and how to study it. The second part deals with our local interstellar environment; the interstellar cloud that the Sun is immersed in and the large interstellar bubble surrounding that cloud.

2.1 Origin and Structure

The widely accepted theory of cosmology describing the origin of the Universe can be summed up in the Big Bang model. Observations verify that we live in a Universe that was once extremely hot, dense, and concentrated to a single spot from where the Big Bang caused it to start expanding. Hydrogen and helium were formed only a few minutes after the bang and remain to this day the two most abundant elements in the known Universe.

Interstellar matter is inhomogeneously spread out. Approximately half of the interstellar mass in the Galaxy is situated in relatively dense structures, called interstellar clouds, taking up only 1 − 2% of the volume of interstellar space. Consequently, the low-density regions form massive cavities, bubbles, in the ISM.

In a clear sky, the ISM can be seen as darker regions, mainly along the Milky Way, where clouds of interstellar particles absorb the light from stars behind them. The main method for studying the ISM is spectroscopy. The chemical composition of stars as well as the matter surrounding the stars can be deduced by analyzing spectral lines of emission or absorption.

Stars interact with the ISM in several ways. A star is born as a result of a very dense cloud collapsing and during its life cycle it will itself emit matter into interstellar space. If it dies in a supernova it will end up having a profound effect on its surroundings.

2.1.1 The Origin of Matter

A few minutes after the Big Bang, 13.8 billion years ago, the process called primordial nucleosynthesis began. Nucleosynthesis is the fusion process in which free protons and neutrons are combined to form nuclei. This resulted in the two lightest, most elemental nuclei; that of hydrogen and helium, and some

2 2 THE INTERSTELLAR MEDIUM 3

of their isotopes. Very small amounts of beryllium (Be) and lithium (Li) nuclei are also thought to have formed at this point. Along with photons, they are the only particles in existence at this time in the early Universe.

At an approximate age of 105 years, due to the ongoing inflation, the density and temperature of the Universe reached values low enough to allow for the process of recombination, in which the nuclei capture electrons to form the first atoms. At roughly 109 years, the inhomogeneity of space finally resulted in the gravitational collapse of matter into stars. These first stars are categorized as population III stars. All elements, except for the ones created during the nucleosynthesis, are produced by stars. Galaxies and clusters develop later as an effect of gravitational collapse on a larger scale. At this point, stars that may contain traces of already star-processed material started appearing. They are population II stars, and later on, stars of population I arose. Population I stars are the youngest stars in the Universe today, with the highest content of heavy elements. Our Sun belongs to the category of population I stars. The oldest known stars in the Universe are of population II. The existence of population III stars are a direct consequence of the Big Bang theory but have not been observed. It is possible that they were all very massive and exhausted their fuel quickly.

Interstellar matter can be divided into two categories according to its place in relation to the stellar evolution. Primordial matter is the matter originating directly from the Big Bang nucleosynthesis, thus consisting of only hydrogen and helium (and traces of Li and Be). Stellar matter is produced in the fusion reactions in stars, which is where all the heavier elements - referred to as ‘metals’ in astronomy - originate. The matter created in supernova explosions is another component of stellar matter.

By measuring the abundances of elements and their isotopes in our close space environment we can learn more about stellar evolution in general and our local space environment in particular. In a stellar system like ours, where the star is of population I, the metallicity is high compared to other parts of the Universe. Our Sun was formed 4.5 billion years ago when a cloud of interstellar matter, the Protosolar Cloud (PSC), collapsed under its own gravity.

In addition to the two kinds of nucleosynthesis described here, primordial and stellar, the third way chemical elements can be formed is by high-energy cosmic rays, producing rare nuclei, such as beryllium and 6Li.

In this thesis, ‘matter’ is used synonymously with ordinary matter, or baryonic matter. Baryonic matter (a term used loosely to describe normal atomic matter, also including electrons that are not actually baryonic) is the matter that makes up the known Universe. It is now suspected that baryonic 2 THE INTERSTELLAR MEDIUM 4

matter might make up as little as 4.6% of all the matter in the Universe. More than 95% of the energy density in the Universe is of another nature entirely - dark matter and dark energy - of which we are yet to form a coherent understanding.

2.1.2 Interstellar Constituents

Interstellar space consists of gas (molecular, atomic or ionized), dust, cosmic rays and magnetic fields. The vast majority of interstellar particles are hydrogen atoms or ions (∼ 90%) while the rest is helium, and a small amount (< 1%) of heavier elements. The figures do not significantly differ from the overall cosmic composition.

The coldest and most dense form of interstellar gas is molecular and includes molecules such as + 6 CH, CH , CN, CO, and H2. The temperature can be as low as ∼10 K and the density as high as ∼10 particles per cm3. (This is still 13 orders of magnitude less dense than the Earth’s lower atmosphere that has ∼1019 particles per cm3). This so-called molecular gas is necessary for star formation.

Table 1: Parameters of different components of interstellar gas [12].

Component T (K) n (cm−3) Molecular 10 − 20 102 − 106 Cold atomic 50 − 100 20 − 50 Warm atomic 6000 − 10000 0.2 − 0.5 Warm ionized ∼ 8000 0.2 − 0.5 Hot ionized ∼ 106 ∼ 0.0065

Neutral (atomic) hydrogen can be in rough thermal pressure equilibrium at low temperatures of ∼102 K and at warmer temperatures (and lower densities) of ∼104 K. This is why atomic hydrogen can be considered a two-phase medium with two phases coexisting over a narrow range of pressures [55].

When interstellar gas is ionized it results in free ions and electrons and is essentially a plasma. The overwhelming majority of the matter in the Universe is in plasma state, and so is most of the volume of the ISM. Interstellar plasma can be up to ∼106 K hot and have a density that is 8 orders of magnitude smaller than molecular gas. The ionized part of the ISM is often separated into two categories: warm ionized gas and hot ionized gas. In a somewhat simplified explanation, the warm ionized gas can be described as warm neutral gas that has been ionized by the UV radiation from massive, hot stars while hot ionized gas has been generated by supernovae. Table 1 shows densities and temperatures of the 2 THE INTERSTELLAR MEDIUM 5

different components of interstellar gas.

Approximately 1% of the mass of interstellar matter is not in the form of gas or plasma but of solid particles. Interstellar dust starts as a clustering of molecules in stellar outflows and supernovae and continues to develop in the ISM. The dust grains consist mostly of graphites, carbonates, silicates, water molecules and some of their compounds. Most of the heavier elements in interstellar space are located in dust grains. The radius of a dust particle can vary from nanometers up to a few micrometers, and their temperatures are usually similar to that of molecular gas. Interstellar dust plays an important role in the formation of H2 molecules in cold gas clouds.

Cosmic rays are electrically charged, high-energy particles that hit the Earth’s atmosphere with velocities close to the speed of light. The concept of cosmic rays includes three different phenomena: (1) energetic particles ejected from the Sun through solar flares, (2) galactic cosmic rays (GCRs) and (3) anomalous cosmic rays (ACRs). Type 2 and 3 originate from interstellar space. ACRs are a product of the processes in the interface region at the edge of the Sun’s influence and will be further described in Chapter 3. GCRs, on the other hand, originate elsewhere in the Galaxy. Most of the particles are protons, but some are helium or heavier nuclei, and electrons. Supernova remnants are the likely cause of the acceleration of GCRs [1]. After the initial acceleration, the rays continue to travel in the ISM and are governed by its magnetic fields.

Magnetic fields play an important part in the overall structure of the ISM. Apart from being intimately linked to the cosmic ray particles, the interstellar (or galactic) magnetic field (ISMF) also controls the ionized part of the interstellar gas. Neutral particles are in most regions closely linked to ionized particles and are therefore indirectly affected by the magnetic field. The only parts of the ISM that are not strongly affected by the ISMF are dense molecular clouds with a low ionization degree. There are a variety of ways in which magnetic fields act on interstellar matter, for example by working against gravity and providing a pressure balance for interstellar clouds, or by causing matter to pile up along ripples in field lines [12]. Both examples are crucial phenomena in the formation of stars and interstellar structures.

2.1.3 Interstellar Structures

Interstellar matter is highly inhomogeneous and prone to structure formation. The two main categories are the so called clouds and bubbles. Clouds are dense and cold and consist of atomic or molecular gas while bubbles are large and hot cavities of ionized matter. 2 THE INTERSTELLAR MEDIUM 6

The definition of an interstellar cloud is ’a collection of gas moving with the same bulk velocity’ [36]. Clouds can be difficult to distinguish from each other, especially since they often move in clusters. The properties of a cloud can also differ significantly from its edges to its middle. There are several different kinds of collections of interstellar matter that count as clouds and they often hold a mix of the interstellar constituents described in chapter 2.1.2. Molecular clouds are generally very cold (∼10 K), with a high density and a low ionization degree, diffuse clouds are made up of neutral atomic gas (at ∼102 K) and the term translucent clouds refers to clouds that are composed of a mix of neutral and molecular gas and show a combination of these characteristics [12]. Clouds of partly ionized matter are referred to as warm clouds.

The bubbles, on the other hand, are considered a ‘hot’ medium. The density is typically of the order 10−2 particles per cm3 and the temperature can be up to 106 K. These regions form large cavities in interstellar space and can be hundreds of parsecs across. They are essentially more of an absence of matter than a collection of matter.

The formation of a bubble is strongly linked to massive stars, as both their ionizing radiation, stellar winds and supernova explosions can cause bubbles in the interstellar medium. The shock front produced by a supernova explosion will clear up a large region and leave it much less dense than its surroundings. The clouds that are found inside bubbles are most likely formed from the bubble’s shell material, i.e. the piling up of material at the edges of a bubble. There is a larger concentration of massive stars along the spiral arms in the Galaxy, leading to a higher frequency of supernova explosions in those regions. The resulting cluster of bubbles are called superbubbles, and the shells supershells.

When a cloud is immersed in a bubble, its outer layers are exposed to a very different medium, resulting in the process of conduction at these boundaries. The energy from the hot material in the surroundings causes ionizing radiation in the cloud. Large radiative losses cause condensation while small radiative losses cause evaporation. As particles from the cloud evaporate into the bubble, the cloud will shrink at a rate of

−5/6 7/6 M/dM = 0.65np4 rpc Myr (2.1)

4 −3 where n is the particle density of the cloud, p4 is the thermal pressure in units of 10 cm K and rpc is the radius of the cloud in parsecs [27]. This is a highly simplified model of cloud evaporation. There are several factors which can significantly alter the situation. Magnetic fields, for example, can prevent conduction and are an important factor in cloud stability. 2 THE INTERSTELLAR MEDIUM 7

The interstellar medium is inhomogeneous and dynamic. In some cases it might be more enlightening to look at the different structures as phases instead of regions. The different phases the interstellar medium can be subjected to are then typically described by these four: the cold phase, the warm neutral phase, the warm ionized phase and the hot ionized phase. The hot ionized phase is thought to be predominant and makes up for over 80% of interstellar space [11].

2.1.4 Observing the Interstellar Medium

Parts of the interstellar medium can be observed with the naked eye. In a clear sky, dense clouds can be seen as dark regions, seemingly devoid of stars or as an especially bright nebula (from Latin: ‘cloud’). The term ‘nebula’ refers to dense molecular clouds of gas and dust but has historically been used more loosely to refer to diffuse astronomical objects.

It is the dust that causes the phenomenon known as obscuration or extinction, where interstellar clouds can be seen as dark regions in the sky. Starlight is absorbed and scattered by the dust particles in the cloud and as a result, the stars from behind that region are not visible. Blue light is more strongly obscured, causing a reddening effect.

The main method for observing the interstellar medium is spectroscopy. The study of absorption lines from nearby stars is what gave the first indications of an inhomogeneous and complex medium. When distances to stars are known, the light from them can be analyzed in order to detect the density of the medium which it has to travel through. Differences in velocity in the surrounding interstellar structures can lead to turbulence and make it difficult to deduce accurate velocities for the interstellar structures [14]. It can be particularly difficult to distinguish individual clouds. In a region with many small clouds moving with similar velocities, in order to separate them, one will require a high spectral resolution in the equipment. Different formations of interstellar matter move with different velocities in different directions relative to stars causing Doppler effects that need to be taken into consideration when analyzing the data. UV spectroscopy (or absorption spectroscopy) is mainly used to detect molecular gas and hot ionized gas. The UV spectrometer on the Copernicus satellite, launched in 1972, contributed significantly to the initial understanding of these two components.

The transitions between energy levels for the electron correspond to different spectral lines caused by the emission (or absorption) of a photon of a specific wavelength. The Ly-α emission line, at wavelength 1.216×10−7 m and the strongest line in the hydrogen spectrum, is the result of the electron falling from its first excited state to its ground state (from the n = 2 orbital to the n = 1 orbital, n being 2 THE INTERSTELLAR MEDIUM 8

the principal quantum number) and emitting a photon in the process. The interstellar Ly-α is the main source of information on interstellar neutral hydrogen. Warm ionized gas, on the other hand, can be detected from its Balmer-α (H-α) emission, which is produced by electrons falling from n = 3 to n = 2.

Another important emission line is the 21 cm hydrogen line. It is caused by the difference in energy between a hydrogen atom where the spins of the proton and electron are parallel and one where they are antiparallel. The antiparallel state has slightly lower energy and so the ones with parallel spins will eventually switch to antiparallel. The resulting energy emission can be observed at radio frequencies as the 21 cm line.

In addition to studying the spectral qualities of light, one can look at its photometric aspects, such as the flux (energy per unit time and area) or intensity (flux per unit area, unit time, and solid angle). A photometric detector - a photometer - is essentially a photon counting device.

Depending on the situation, one might make use of pulsars with known parallaxes. If there is a pulsating star in the vicinity, it presents a straightforward way to measure the density in the nearby interstellar medium by sampling of pulsar dispersion measures [6]. The dispersion measure, DM = neD, of the pulsar depends on the electron density ne and the distance D between the pulsar and the observer. Furthermore, the radio waves from the pulsar will show signs of scattering caused by inhomogeneities in the interstellar medium, giving a good picture of the variations in the medium on a smaller scale.

The soft X-ray background has been observed by satellites for some time now. Many objects are sources for this emission, including stars, quasars and the magnetospheres of planets as well as the boundary region between our interplanetary space and the surrounding interstellar medium. A large part of the soft X-ray background emission is generated in this interesting boundary region.

Interstellar magnetic fields and dust cause a phenomenon that can be observed as polarization of starlight, in which paramagnetic dust grains align along the magnetic field. Spinning dust grains tend to orient their short axis of rotation with the magnetic field and, as a result, the light passing through the dust will be polarized in the direction of the magnetic field. Observations of the polarization can therefore reveal the direction of the magnetic field.

There are three methods generally used to obtain the magnetic field strength: one can look at (1) the amplitude of the Zeeman splitting of the 21 cm hydrogen line (or, in denser regions, the spectral lines of molecules such as OH or CN), (2) the Faraday rotation of pulsar signals, and (3) radio synchrotron emission from relativistic electrons [12]. 2 THE INTERSTELLAR MEDIUM 9

In some locations on Earth, interstellar dust particles can be observed, such as for the rare isotope of Iron, 60Fe, that was recently found in Antarctic snow in such a concentration that it was concluded to be of interstellar origin [30]. By then studying the presence and abundance of isotopes in older ice cores, a historical record of the interstellar surroundings the Solar System has encountered during its lifetime can be produced.

Neutral interstellar particles are unaffected by the Sun’s magnetic field and can travel into interplanetary space where in situ measurements can be performed by satellites. The particles do react with solar particles on the way, however, and so in one way or the other the Sun has an impact on all observations made in its region of influence. The IBEX (Interstellar Boundary Explorer) mission, an Earth orbit satellite launched in 2008, is studying what happens at the boundary region between the interstellar medium and the solar wind. It does this by detecting energetic neutral atom (ENA) emissions.

A milestone in space exploration was reached when Voyager 1, launched in 1977, was the first man- made object to enter interstellar space in 2012 [21]. Its twin spacecraft, Voyager 2, entered interstellar space in 2018. The Voyagers will be sending data for a few more years providing unprecedented information from the local ISM.

2.1.5 Interstellar Matter and Stellar Evolution

A star is formed when the internal pressure of a molecular cloud is no longer able to overcome the gravitational pressure. For a system in equilibrium, with kinetic energy T and gravitational potential energy U, the virial theorem states that

1 < T >= − < U > (2.2) 2

From the virial theorem it can be concluded that the potential energy of the internal gravitational force is required to be at least twice as big as the kinetic energy of the gas pressure in order for a collapse to take place. The Jeans criterion gives the condition for the collapse of a cloud:

Gmc RT > (2.3) r µ 2 THE INTERSTELLAR MEDIUM 10

where R is the gas constant, G is the gravitational constant and µ, mc, r and T are cloud parameters (mass per particle, cloud mass, radius and temperature respectively). If the cloud is massive enough, i.e. if mc is large enough, it will collapse and in the process a protostar is formed.

However, in addition to the purely thermal pressure, magnetic fields provide a balancing force against gravity and star formation as they affect the flowing gas and can prevent it from being drawn in by gravity. Turbulence is another factor that can work against star formation by creating a pressure that counterbalances gravity.

During a star’s lifetime it will influence the ISM in two important ways: through its radiation and through its wind. Stellar radiation causes ionization and heating of the surrounding interstellar gas. The most massive stars (those of class O and B) are the main contributors with their high-energy UV photons. All stars emit some sort of stellar wind, which releases matter from its upper atmosphere to its surroundings and eventually mix with interstellar matter. The velocity, temperature and density of the wind depend on the characteristics of the star.

At one point late in the life of a typical medium-sized star, it will turn into a planetary nebula. Planetary nebulae are clouds of ionized gas, which consist of material produced by the star, including heavier elements, back into interstellar space. The Sun will eventually become a planetary nebula following its red giant phase.

When a star dies as a supernova, the explosion creates a massive hot void in space as the shock wave sweeps particles out of the way and throws stellar material far into interstellar space leaving a large region much less dense than its surroundings, thus creating a bubble. A dense shell is generally formed around the bubble, where matter has piled up. Only 1% of stars are massive enough (M > 8Msun) to die as a supernova, the rest will end as white dwarfs.

It is through the interactions between stars and the ISM that new structures are created in a galaxy. Molecular clouds collapse to form stars, matter is processed in the stars, then released into interstellar space, by means of stellar wind or supernova explosion, slowly increasing the metallicity of the ISM and again, eventually, new stars are formed. Obtaining information about all stages in this cycle is crucial for developing a deeper understanding on matter and energy in the Universe.

It is possible that the interstellar magnetic field originated in the early Universe. This seed field would then have been sustained and amplified by the dynamo effect, converting mechanical energy into magnetic energy [51]. 2 THE INTERSTELLAR MEDIUM 11

2.2 The Local Interstellar Environment

Interplanetary space is dominated by the wind and radiation from the Sun. The region of solar influence, the heliosphere, is blocking out the interstellar medium. By using spectroscopy we can obtain information about the parameters of the interstellar structures surrounding the heliosphere.

However, neutral interstellar particles can and do enter the heliosphere and they provide a valuable source of information. In situ measurements of interstellar hydrogen and helium are possible and these have confirmed the results from spectroscopic measurements. And for the first time in history, there are now, since 2012, in situ measurements from outside the heliosphere, from the two Voyager spacecraft [21].

We know that the Sun is located inside a region of warm gas - the Local Interstellar Cloud (LIC), which is itself immersed in a larger, more diffuse cavity - a superbubble, called the Local Bubble (LB). The diameter of the bubble is up to 200 pc at its largest place. (The disk of our galaxy has a radius of about 30 kpc and a thickness of about 500 pc.) The size of the LIC is about 2.5 pc.

2.2.1 The Local Interstellar Bubble

The Sun is currently traveling through a bubble of high temperature (∼ 106 K) and low density (∼ 0.001 cm−3) plasma. The LB is a very diffuse region compared to the rest of the ISM in the Galaxy, which has an average density one order of magnitude larger than that of the LB. The LB is not bubble-shaped but shaped rather like an hourglass or a peanut, with an approximate diameter ranging from 50 pc to 200 pc. It is at its narrowest in the galactic plane and gets wider where it extends above and below the disk. Furthermore, it appears to be open-ended at the ‘top’ and ‘bottom’ where it opens up into the galactic halo.

Simulations show that bubbles with equal thermal and magnetic pressures expand fairly spherically during the early stages but become asymmetrical and elongated along the ISMF later on in the expansion process [22]. The bubble will contract at the equator (axis parallel to the ISMF) and continue to expand at the poles. This asymmetry is due to the magnetic pressure supporting the equatorial region while the thermal pressure supports the polar regions. Since the thermal pressure inside the bubble is larger than that of the ISM in general, it will continue to allow for expansion while the magnetic pressure eventually will cause a contraction along the equator. This also explains why the shell is thicker along the equator. In situations with a weak magnetic field, the expansion is more spherical. 2 THE INTERSTELLAR MEDIUM 12

The particle density will also affect the formation of a bubble. The previously mentioned study [22] also shows a significantly shorter time-scale for bubble expansion and contraction for an interstellar medium with a particle density of 1 cm−3 as opposed to 0.2 cm−3.

Massive stars shape their surroundings during their lifetime as well, through the stellar winds that create bubbles on a smaller scale of ∼10 pc, into which the supernova will expand [53].

The LB was first described in the 1970s, when background X-ray radiation on rocket flights indicated the existence of a volume of hot, dilute gas surrounding the Sun. Soft X-ray images have later provided a better picture of the superbubble and of the neighboring superbubble, the Loop I Bubble, which is pushing into the LB. Loop I and the LB are both the products of strong stellar winds and successive supernova explosions during the last few million years. The Scorpius-Centaurus (Sco-Cen) Association (the nearest association of OB stars), is the likely origin of the stars creating these two bubbles, as indicated by elemental abundances, kinematics and magnetic fields of local interstellar matter [20].

The superbubble shell of Loop I, which is pushing into the LB is an important actor in the local ISM. Expansion models place the Sun close to or inside this shell. The shell is divided into two subshells, S1 (outer) and S2 (inner), that have different magnetic pole directions. The simulations of the expanding shells give a magnetic field direction at S1 that matches the direction of ISMF (from polarization data) close to the heliosphere [16]. These models place the heliosphere in the rim of the S1 shell. The expansion of S1 is a likely explanation for the flow of clouds in the solar neighborhood, one of which

Figure 1: An artist’s conception of the Local Bubble, credits: NASA 2 THE INTERSTELLAR MEDIUM 13

the Sun is currently immersed in.

Figure 1 shows an artist rendering of the LB and the Loop I Bubble. The Sun and Beta Canis Majoris, a star in the Canis Majoris constellation, are both located inside the peanut-shaped and open- ended LB. The distance from the Sun to Beta Canis Majoris is roughly 150 pc. Betelgeuse is roughly 200 pc from the Sun and situated outside of the Bubble, whereas Antares, a star in the Scorpius constellation, is immersed in the Loop I Bubble.

Simulations of the LB estimate its age to about 14.5 million years [7]. The same study predicts a merging of the LB with Loop I Bubble in 3 million years from now when the shell that separates them will eventually dissolve.

2.2.2 The Local Interstellar Cloud

For the last 104-105 years the Sun has been traveling through a denser and colder part of the LB, known as the Local Cloud or sometimes the Local Fluff. Models suggest that the cloud can be described as a quasi-spheroid with a diameter of ∼ 2.5 pc and a mass that is ∼ 0.32 times the solar mass [17]. The Sun could be in an interface region on this scale as well, near the edge of the LIC and close to another cloud - the G cloud. With this in mind, the interstellar matter surrounding the heliosphere, i.e. our immediate surrounding cloud neighborhood, while still probably inside the LIC, is more clearly defined as the Circum-Heliospheric Interstellar Medium (CHISM or CISM). CHISM is simply the heliosphere’s (ever-changing) surroundings. The CHISM is at the very edge of the LIC, and might be showing some interface characteristics and the effect of the interactions with the adjacent cloud. The properties of the CHISM are similar to that of a typical interstellar cloud in this region of the LB [15]. In agreement with the definitions in section 2.1.2, the CHISM can be described as a warm gas, it is partially ionized and two orders of magnitude denser than the hot gas of the LB.

Although the CHISM may show some characteristics of a cloud transition zone, IBEX observations have confirmed that the Sun resides close to the edge but remains fully within the boundaries of the LIC, which it is estimated to leave sometime in the next few hundred or thousand years. The LIC and its surroundings are shown in Figure 2, as viewed from the North Galactic Pole. The G-Cloud is approaching from the direction of the Galactic Center. Alpha Centauri, one of our closest stars at a distance of roughly 1.3 pc from the Sun, lies on the other side of the G cloud, which has a more elongated shape. The LIC lies in the middle of a group of clouds of different shapes and sizes. The clouds often get their names from the constellations or star clusters towards which they are observed, as 2 THE INTERSTELLAR MEDIUM 14

for Aquila (Aql) and Hyades. Also shown in the image is the binary star Sirius, close to the edge of the large Blue cloud.

The parameters of the LISM presented in Table 2 are inferred from in situ measurements of helium by IBEX [39]. The assumption is that neutral helium is almost unaffected by the heliospheric interface and therefore a good indicator of CHISM parameters. The analysis in that study suggests these parameters as ”working values” for the undisturbed interstellar matter which they have defined as 1000 au to be outside of the solar influence. The values are based on six years of IBEX data, and are also consistent with previous Ulysses data.

The relative velocity between the Sun and the CHISM creates an interstellar wind that flows around and - for the neutral component - through the heliosphere. This flow direction, based on the He atom flow in the heliosphere, is given in Table 2 as the heliospheric nose direction in ecliptic coordinates.

The difference in the wind directions measured by IBEX to that measured previously by Ulysses

Figure 2: Artist’s conception of local interstellar clouds and their relative motions in the Galactic Plane (1 light year ≈ 0.3pc), credits: NASA 2 THE INTERSTELLAR MEDIUM 15

[54] has raised some interesting questions. By analyzing data from several spacecraft from the last 40 years a study indicated that a change in the wind flow direction is likely; during these 40 years, the longitude component of the wind shows an increase of 6.8 ± 2.4◦. [18]. This result has led to some debate as the statistical method used to infer the change in longitude was criticized and it was argued that there is no evidence for a change in flow direction [35]. After some adjustments the temporal longitude variation suggested by the original study was corrected to 5.6 ± 2.4◦ [19]. Determining the hydrogen flow using data from the SWAN instrument on board SOHO however, has indicated a stable longitude component [31].

Hydrogen atoms are subjected to various processes while entering the heliosphere so the H atom density can not be directly inferred from in situ data within the heliosphere. It can be obtained indirectly by using the estimated interstellar hydrogen to helium ratio, R(H/He)LIC, and the measured He atom density in the heliosphere, nLIC(He), again assuming negligible filtration of He atoms. The estimated H atom density in the LIC is then given by [25, p. 72]:

nLIC(H) = R(H/He)LICnLIC(He) (2.4) and the result is 0.2 ± 0.05 cm−3. Of the neutral gas particles that enter the heliosphere, almost 9% are helium. The total particle density of the CHISM is estimated to be n(H + He + e) ≈ 0.35 cm−3 [27].

As seen in Figure 2, the LIC is part of a group of clouds, sometimes referred to as the CLIC, for “cluster of local interstellar clouds”. This refers to clouds within roughly 30 pc of the Sun. There is a good overview of the dynamics and morphology of 15 clouds within 15 pc, that was put together using absorption lines towards 157 stars [46]. With the help of spectroscopic observations, it has been shown that the individual clouds in the CLIC have similar velocities and temperatures. So much so, in fact, that they can be described by a single flow vector [17]. The fact that the CLIC moves together suggests that they have a common origin. They are moving in a direction outwards from the center of Loop 1 (and away from the Sco-Cen association), inside the S1 subshell, which makes the expanding

Table 2: Local Interstellar Parameters based on IBEX data of interstellar helium [39]

Parameter Working values Sun/CHISM relative velocity 25.4 kms−1 Local interstellar temperature 7500 K Sun/CHISM ecliptic longitude 255.7◦ Sun/CHISM ecliptic latitude 5.1◦ 2 THE INTERSTELLAR MEDIUM 16

superbubble model a good model for the origin and driving force of the local clouds [15]. It is evident that studies of superbubble (and shell) evolution is a key to understanding the past and future of local clouds surrounding the Sun.

2.2.3 The Local Interstellar Magnetic Field

The interstellar - or galactic - magnetic field is commonly referred to with the acronym ISMF, not to be confused with the interplanetary magnetic field: IMF.

Modelling the field using IBEX data, gives the following parameters for the undisturbed ISMF; ecliptic longitude: 227.28◦ ± 0.69◦, ecliptic latitude: 34.62◦ ± 0.45◦, and a magnitude of: 2.93 ± 0.08 µG [59]. These parameters are consistent with Voyager 1 data from the very local ISMF, the first ever in situ measurements of the ISMF. The interstellar magnetic field has a west to east polarity, which is the opposite of the planetary motions along the ecliptic. A recent study used high precision measurements of the polarization of starlight to map the ISMF [43] discovering magnetic filament structures in both the upwind and downwind directions of the interstellar flow.

As Voyager I entered interstellar space in 2012, the magnetic field direction, surprisingly, did not change much indicating that the solar magnetic influence was still noticable in this region. However, studies show that it is slowly changing towards our estimated direction as Voyager is moving farther and farther away from solar reach [8]. The interstellar magnetic field strength average as directly measured by Voyager I during its first couple of years in interstellar space is 4.9 µG. When Voyager 2 entered interstellar space in 2018, it observed a significantly larger magnetic field strength than Voyager 1 [9] so it is possible that the ISMF is significantly stronger than previously expected.

As mentioned in Chapter 2.2.1, the S1 shell model prediction for the magnetic field is consistent with the one obtained from starlight polarization. Since Loop I is the driving force of the local interstellar matter, an understanding of the magnetic fields governing Loop I is crucial.

2.2.4 The LIC-LB boundary

The boundary region between the LB and the LIC is subject to much speculation. The LB model constructed from soft X-ray measurements presented a thermal pressure value of P/k ∼ 15000 cm−3K in the bubble while the thermal pressure in the LIC is only P/k ∼ 2500 cm−3K (with a total particle density of 0.35 cm−3 and a temperature of 7000 K) [27]. This discrepancy has been thoroughly investigated 2 THE INTERSTELLAR MEDIUM 17

and the most likely solution is that the LB pressure is actually significantly lower and that there has been a foreground contamination of the X-ray data due to photons emitted in charge exchange reactions between solar and interstellar wind particles [27]. This resulted in an overestimated thermal pressure. The new estimate for the LB pressure puts the two media roughly in pressure equilibrium. A more recent study combining the magnetic field observations by Voyager 1, with the charge exchange effects from the solar wind, and improved mapping of three-dimensional interstellar structures, indicated a thermal pressure of P/k ∼ 10700 cm−3K for the LB [49], which would allow for pressure equilibrium with the LIC, considering the magnetic field pressure present in the cloud that makes up for the difference.

Another puzzling observation is the relatively high ionization fraction of helium (∼ 38%) compared to that of hydrogen (∼ 24%) in the LIC [17]. There are not enough strong stellar extreme ultraviolet sources to produce this kind of ionization nor is it enough to heat the LIC to its high temperature. The solution seems to be an additional - interstellar - source of radiation. Models of the boundary region between the warm gas in the LIC and the hot gas in the LB depict an evaporative interface that produces a significant amount of ionizing radiation [48]. The new and lower thermal pressure will affect this, however, since the higher P/k value was used in these models [27].

Learning more about this boundary region will shed light on the evaporation of LIC and thus its lifetime. The Sun being at the edge of the LIC makes it even more important, and since there have been no direct way of observing it, several significant unknowns remain. Depending on what the magnetic fields at the boundary look like, they might effectively be keeping the cloud from evaporating. The group of clouds in the CLIC might also be intervening by shielding each other slightly from the effect of the LB. Turbulence is also a factor that could affect the evaporation.

2.2.5 Effect on Earth

In spite of the fact that our most local interstellar environment - the LIC - is slightly more dense than the LB as a whole, it is still an exceptionally dilute part of the interstellar Galaxy. This position of the Sun in a region of relatively low density is not insignificant. There is a considerable optical transparency towards our surroundings that would not have been possible in a denser environment.

As our Sun orbits the galactic center (every 240 million years) it encounters regions of very different density and radiation. Throughout this journey, the heliosphere works as a barrier, preventing a large part of the radiation from ever entering this bubble. But the shape of the heliosphere is dependent on the characteristics of the interstellar gas it is moving through. Simulations have shown that a cloud 2 THE INTERSTELLAR MEDIUM 18

with an H atom density of 10 cm−3 (i.e. about 50 times more dense than the LIC) would cause a compression of the heliosphere by a factor of 10 (from ∼100 au to ∼10 au) [56]. The heliosphere is sensitive to the local ISM and even small variations could potentially show radical changes in our conditions on Earth. 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 19

3 Interstellar Matter in the Heliosphere

The Sun affects its surroundings in several different ways; through gravity, radiation, and by ejecting 1 million tons of matter every second in the form of a solar wind. The solar wind makes up nearly all the plasma content in interplanetary space. Eventually, far beyond the orbits of the planets, the solar wind comes to a stop and interstellar matter starts to dominate. This boundary marks the edge of the heliosphere.

When interstellar plasma encounters the solar wind, it is forced to travel around the heliosphere due to the Sun’s magnetic field. The neutral particles, however can enter the heliosphere. These particles - mainly hydrogen atoms - will be affected by the Sun in other ways. This chapter deals with the processes at the interface region and all the way through the heliosphere.

3.1 The Solar Wind

Each second, the Sun is emitting 1 million tons of matter from its surface. These particles, mainly hydrogen and helium ions and electrons, are streaming away from the Sun at a supersonic speed. The solar activity varies with the solar cycle, which has its maximum approximately every 11th year. There are approximately 6 solar wind particles per cm3 at 1 au.

The processes involved in the heating of the corona and the subsequent acceleration of the solar wind is one of the biggest areas of study in solar physics. It is clear that the source is magnetic in nature but exactly how the magnetic energy is converted into heat (to a temperature of the order of 106 K, while the photosphere is only a few thousand kelvins) is yet to be fully explained. Currently there are two categories of explanations, the wave theory (as descibed in [28]) and the nanoflare theory (as described in [40]).

The solar wind can be divided into two types. The fast solar wind has a velocity of about 750 kms−1 and its origin is thought to be the coronal holes, a structure that is caused by the Sun’s magnetic activity. Coronal holes are often created around the poles so the fast wind is usually originating in the higher latitudes. The slow solar wind, around 350 kms−1, is denser and hotter than the fast wind. It originates from the structure known as the streamer belt situated around the solar equator. During minimum solar activity, the slow wind is emitted from the equatorial region but while approaching the solar maximum it will increase and be emitted from almost all latitudes. The fast polar wind remains more stable during a solar cycle. Coronal mass ejections (CMEs) are large chunks of plasma emitted from particularly active 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 20

parts of the Sun and have such a large effect on the wind that they can be considered a third type of solar wind.

3.2 The Interplanetary Magnetic Field

It is practically impossible to separate the concept of the solar wind from the magnetic field since they are so closely linked. The interplanetary magnetic field (IMF) most probably has its origin in the interstellar gas cloud that collapsed and formed the Sun. This field has then been sustained by the solar dynamo and continues to convert kinetic energy into magnetic energy. As the Sun rotates, and the magnetic field follows the solar wind, the magnetic field lines will take on a spiral pattern, known as the Parker spiral. The polarity of the field is opposite in the north and the south hemisphere - spiraling inwards in one and outwards in the other. The surface where the polarity switches from north to south is called the heliospheric current sheet. The sheet is “wavy” due to the angle between the Sun’s magnetic and rotational axis, which is why it looks somewhat like a ballerina skirt, shown in Figure 3. This is why the polarity at the Earth’s location changes a lot, as the Earth will sometimes be above and sometimes below the sheet. At the Earth’s location, the angle of the field lines and solar wind flow is approximately 45◦. Far away from the Sun the field will be toroidal, i.e. parallel to the latitude lines.

Figure 3: Artist’s Impression of the heliospheric current sheet. Image credit: Original painting, Werner Heil, NASA, 1977.

At solar minimum, the field looks poloidal and closely resembles that of the Earth, with closed 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 21

field lines at low latitudes and open field lines at the poles. Closer to maximum activity, however the situation is more complicated as the highly magnetic sunspots will distort the field. The differential rotation of the Sun (the Sun rotates faster at the equator than at higher latitudes) causes field lines to tangle and this phenomenon is what in turn causes the sunspots. All this activity will then dominate over the magnetic dipole field. During maximum activity, the heliospheric current sheet will fluctuate up to higher latitudes as opposed to staying closer to the equator during minimum. In other words, the angle between the rotational and magnetic axes is at its smallest at solar minimum. At some point during the solar maximum, the polarity changes.

3.3 The Heliospheric Boundaries

The solar wind and magnetic field together create the heliosphere, which were it not for the relative velocity to the interstellar medium, would be a fairly spherical bubble of roughly 1000 au in diameter. This is the so-called Stromgren¨ sphere of the Sun, describing the ionised region around a star. The radius of this sphere, R = ( 3Q )1/3, depends on the ionisation rate, Q, the density of the surrounding s 4παn2 medium, n, and the temperature of the surrounding medium in the form of the ”recombination coefficient”, α, which is a function of the temperature.

However, due to the relative velocity of roughly ∼ 25 kms−1 between the heliosphere and the interstellar medium, the heliosphere will be much more stretched on the downwind side than on the upwind side, where it is squashed. The heliopause describes the boundary where the solar wind plasma meets the interstellar plasma and it is commonly regarded as the edge of the heliosphere. The heliosphere extends to around 150-180 au on the upwind side while the downwind side can be up to several thousand au long. For comparison, Neptune orbits the Sun at approximately 30 au. The Solar System still extends far beyond the heliopause as for example the Oort cloud lies within the Sun’s gravitational dominance.

Inside the heliosphere, the termination shock is where the solar wind speed changes from supersonic to subsonic. The bow shock (or wave), on the other hand, is situated outside the heliosphere, where the first effects from the solar wind is felt by the interstellar plasma. The boundaries fluctuate on a smaller time scale with the solar cycle and on a larger time scale they will change significantly as we move through interstellar space and encounter different environments. 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 22

3.3.1 The Termination Shock

The termination shock marks the transition from supersonic to subsonic solar wind speed in the heliosphere. It is where the pressure of the surrounding interstellar medium is sufficient to slow down the solar wind to less than the speed of sound.

The termination shock is a magnetohydrodynamic reverse shock caused by the deceleration of the supersonic solar wind by interstellar plasma. Its location is highly dependent on solar wind velocity and density. It varies (over the 11-year solar cycle) so that its distance from the Sun can be expressed as 100 au ± 7 au [24].

The termination shock forms a roughly spherical bubble of supersonic flow around the Sun with negligible longitudinal asymmetries (the pink region in Figure 4). However, owing to the latitudinal asymmetry of the solar wind, the latitudinal variations of the distance to the shock will be significant. Magnetic effects are also contributing to the variations. This asymmetry is evident in the crossings of the termination shock by the two Voyagers. Voyager 1 crossed the termination shock at 94 au in December 2004 while Voyager 2 crossed it at 84 au in August 2007. The termination shock (and similarly the heliosphere) is squashed in the Voyager 2 direction due to the angle between the ISMF and the interstellar wind flow. A magnetic field strength larger than 4µG is sufficient to produce the 10 au difference in the crossings [44]. Furthermore, because of the fluctuations in the solar wind, Voyager 2

Figure 4: Artist’s conception of the heliosphere, where the boundaries are indicated. The existence of a bow shock / wave in front of the heliosphere has not been confirmed. Credits: NASA’s Goddard Space Flight Center/Conceptual Image Lab 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 23

crossed the boundary several times.

3.3.2 The Heliopause

The edge of the heliosphere, the heliopause, is the boundary where the solar wind finally reaches a pressure balance with the interstellar plasma and essentially comes to a stop at 171 au ± 2 au [24]. The heliopause is not so much a border as an interface region of turbulent character.

The asymmetry caused by the angle between the interstellar magnetic field and the wind flow is more significant for the heliopause than for the termination shock. This asymmetry causes a compression of the heliosphere so that its smallest diameter is not in the upwind direction (i.e. right to left in Figure 4) but at a slight angle to it.

The region between the termination shock and the heliopause (the blue region in Figure 4) is called the inner heliosheath (or sometimes just the heliosheath) and several interactions between the two plasmas take place in this highly turbulent region where the solar wind and magnetic field are being squeezed and slowed by the interstellar pressure.

As the interstellar matter flows towards the heliosphere the charged particles are caught by the solar wind and magnetosphere and will go around the heliosphere without entering. The neutral part of the LISM, however, can penetrate the heliopause and flow almost freely through the heliosphere. Interstellar helium can also to some extent cross the boundary as do part of the interstellar dust grains. Comets and global cosmic rays (GCR) are other examples of interstellar matter that enter the heliopause and provide us with direct information about the Universe outside of the heliosphere [25, p. 138].

Voyager 1 crossed the heliopause at 121.7 au in August 2012. This event was marked by a significant increase in particle density. However, the lack of change in the magnetic field direction implies that the IMF might somehow be linked to the ISMF and that there is no clear boundary between the two fields [21]. Voyager 1 data combined with MHD models suggest reconnections between the IMF and the ISMF and a mixing of the two plasmas resulting in a porous, layered heliopause [52] with interstellar flux tubes. As Voyager 2 entered interstellar space, it found the heliopause at 119.0 au to be thinner and more stable compared to that encountered by Voyager 1. The observations made by Voyager 2 seem to indicate a LISM with both a higher temperature and a stronger magnetic field than expected.

Before reaching the heliopause it also encountered a magnetic barrier, which is effectively shutting out cosmic rays [9]. The magnetic barrier is a product of the interaction between the IMF and ISMF. 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 24

It was expected from models of the heliosheath, where this type of magnetic ”wall” is present in both the northern and southern hemisphere. Their magnetic field is significantly stronger than that of the heliosheath in general but weaker than that of the ISMF. The barriers move dynamically along the heliosheath, switching polarity with the solar cycle.

Figure 4 shows only the ”upwind” part of the heliosphere. The ”downwind” side - the heliotail - is much longer, forming a long ”comet-shaped” heliosphere. Recent analysis using Voyager data, however has indicated a more squashed shape, showing a heliosphere that looks more like a croissant than a comet [42].

3.3.3 The Bow Shock

Analogous to the wave that forms in front of a ship as it moves through water, or the shock wave in front of an aircraft, it has been speculated that there is a bow shock in front of the heliosphere as it moves through interstellar space. In other words, it is where the interstellar wind first encounters the solar wind.

The expected bow shock produced by multifluid magnetohydrodynamic models of the heliospheric interface is a slow magnetosonic shock [58]. It is not situated symmetrically in front of the nose as for a ship in water but displaced to the side because of the magnetic field. Voyager 1 is expected to encounter the bow shock while Voyager 2 is traveling in a direction free of a shock.

At the bow shock, the ionized part of the interstellar wind will start to pile up to eventually go around the heliospheric bubble. The ions are decelerated and heated and through momentum transfer with the neutral particles it will cause a similar piling up of the neutrals in this region as well. This piling up of hydrogen has caused the phenomenon known as the hydrogen wall [25, p. 335]. The hydrogen wall scatters Lyα photons and absorbs part of the emission from nearby stars.

√ From the Alfven´ Mach number MA = v 4πρ/B that dictates the type of MHD shock, it is clear that the shape and type of the bow shock depends on the interstellar velocity and density, in addition to the magnetic field effects such as the charge exchange happening in this region.

As IBEX shows a lower velocity for the LISM than was previously expected from Ulysses data, it seems there might not be a shock at this boundary at all, but perhaps a ”bow wave”, where the interstellar matter is a bit denser due to meeting the solar wind plasma. More recent MHD-kinetic models have been used to show that a bow shock is unlikely [45]. 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 25

3.4 The Interaction Between the Local Interstellar Medium and the Heliosphere

There are several ways in which the interstellar particles interact with the heliosphere from where they first encounter it at the interface region and all the way to the Sun. These interactions change the dynamics of the heliosphere as well as produce new components that need to be taken into account.

3.4.1 Radiation and Gravity

As the interstellar particles enter the heliosphere, they will experience both an attractive and a repulsive force from the Sun - gravity and radiation. The ratio between the radiation pressure and the gravitational force is defined as µ = Frad/Fgrav. In other words, it is the ratio between these two accelerations acting on the streaming particles. Since both forces act with the factor r−2, it is possible to use a stationary and spherically symmetric approximation for µ [47]. There will however be fluctuations depending on solar activity, as Frad is slightly changing with the solar cycle.

Another effect caused by the UV radiation is the Lyman-α scattering. The scattering of solar photons by hydrogen atoms lead to a Lyman-α background, a so called resonance glow, in the heliosphere. The distribution of H and He in the heliosphere can be detected by observing this background radiation.

A third effect caused by the radiation is the photoionization occurring near the Sun. An interstellar hydrogen atom hit by a photon results in a pickup ion and an electron:

H + ν → pPUI + e (3.1)

Photoionization however, is only responsible for about 20% of the ionization in the heliosphere - the rest is due to charge exchange [32].

3.4.2 Charge Exchange and Pickup Ions

Charge exchange processes occur throughout the heliosphere when interstellar hydrogen meets solar wind protons and create ions. 3 INTERSTELLAR MATTER IN THE HELIOSPHERE 26

H + p → pPUI + HENA (3.2)

These ions, that are created by the UV radiation and charge exchange processes are then “picked up” by the solar wind and magnetic field, hence the name, pickup ions. They turn out to be a non- negligible part of the solar wind. After being heated at the termination shock, the pickup ions dominate the internal energy of the heliospheric plasma, increasing its plasma beta (the ratio of the plasma pressure to the magnetic pressure) from a relatively low value to that of β ' 4 [57]. Turbulent heating of the outer heliosphere is another effect of the pickup process [23].

For the flux of neutral H, on the other hand, there is a significant loss of particles - a filtering - as they are picked up by the photoionization and charge exchange processes throughout the heliosphere. Charge exchange is also responsible for a reduction in bulk speed and an increase in temperature of the H flow [25, p. 143]. Some pickup ions can gain acceleration by repetitive collisions with the termination shock and will then eventually diffuse back towards the Sun as anomalous cosmic rays (ACRs).

Observing the energetic neutral atoms (ENAs), that are created in the charge exchange with solar protons or pickup ions, can provide insights into the interactions between neutrals and plasmas. The data from IBEX has shown a puzzling ribbon of ENAs [38]. 4 THE SWAN INSTRUMENT ON SOHO 27

4 The SWAN Instrument on SOHO

Ever since the dawn of the Space Age in the 1950s, spacecraft have provided us with information which has increased our knowledge about the Earth and its atmosphere as well as other parts of our solar system. When it comes to the Sun, the main advantages of space-based observations as opposed to Earth based observations are the loss of effects from the Earth’s atmosphere as well as the possibility of making non-stop day-and-night observations providing continuous data. The Solar and Heliospheric Observatory (SOHO) is one of the most successful spacecraft in the history of solar observations, having revolutionized our knowledge of solar physics since 1995.

4.1 Solar Observations

The first space observations of the Sun were by the Soviet Prognoz satellites, launched between 1972 and 1985. An important part of their mission was to study solar activity. Ulysses was launched in 1990 as a joint program between the National Aeronautics and Space Administration (NASA) and The European Space Agency (ESA). It carried instruments designed to detect electrons, ions, gas, dust and cosmic rays. Ulysses was unique in that it was sent to an orbit outside of the solar ecliptic plane, thus enabling it to observe the poles of the Sun. This gave the first evidence of the latitudinal variations of the solar activity; the solar wind varies in density and velocity according to solar latitude [37]. The Ulysses data also hinted at the large differences in Sun’s activity from solar minimum to maximum.

4.2 SOHO

SOHO was developed as a collaboration between ESA and NASA. ESA was responsible for the procurement, testing and integration of the spacecraft, and NASA provided the launcher, launch services and ground-segment system and is also responsible for the in-flight operations. There are twelve instruments on board the spacecraft, involving scientists from 39 institutes from 15 countries [13]. The mission was proposed in 1982, and launched in December 1995 for an intended 2 year mission. After a successful launch it has been able to operate for over 20 years. SOHO has fulfilled its mission and exceeded expectations in providing valuable data concerning the Sun and its dynamics for two complete solar cycles. SOHO is currently still operational in late 2020 [50].

SOHO is situated at one of the Lagrangian points of the Earth and the Sun, L1. The Lagrangian 4 THE SWAN INSTRUMENT ON SOHO 28

points are the five positions that exist around two massive bodies where an object can be situated in order for it to be stationary with respect to the other two. It is the position where the gravity of the two large bodies give exactly the centripetal force needed for the smaller object to orbit together with them. The first Lagrangian point, L1, is between the two masses on the straight line connecting them. For the Sun and the Earth, L1 is at a distance of about 1.5 × 106 km sunward from the Earth, which is a bit less than 0.01 au. SOHO is not stationary at the L1 point, but is orbiting it in a halo orbit, allowing the communications with Earth to run smoother since it is not in the exact same direction as the Sun [13].

4.2.1 Scientific Objectives

The scientific objectives of SOHO are to study aspects of the Sun and its dynamics using a variety of methods. The main areas of interest are those that are difficult to study from Earth - the innermost and outermost parts of the Sun [13].

SOHO consists of three helioseismological instruments; Global Oscillations at Low Frequencies (GOLF), Variability of Solar Irradiance and Gravity Oscillations (VIRGO) and The Solar Oscillations Investigation - Michelson Doppler Imager (MDI/SOI). The six instruments observing the solar atmosphere by spectrometric measurements and high-resolution UV images are Solar Ultraviolet Measurements of Emitted Radiation (SUMER), Coronal Diagnostic Spectrometer (CDS), Extreme ultraviolet Imaging Telescope (EIT), Ultraviolet Coronagraph Spectrometer (UVCS), Large Angle and Spectrometric Coronagraph (LASCO) and Solar Wind Anisotropies (SWAN). Their observations have provided a significantly higher precision than previous observations of the Sun. Solar wind in situ measurements are provided by the last three instruments: Charge, Element, and Isotope Analysis System (CELIAS), Comprehensive Suprathermal and Energetic Particle Analyzer (COSTEP) and Energetic and Relativistic Nuclei and Electron experiment (ERNE). Being situated outside of the Earth’s magnetosphere, SOHO is at an appropriate place for in situ observations without disturbances.

4.2.2 Success

The Michelson Doppler Imager, MDI, has proven to be one of the most productive of the instruments over the years. It shows oscillations of the whole Sun and has revealed large-scale streams of the subsurface dynamics of the Sun. In addition, MDI’s ability to produce far side images of the Sun has proven valuable in space weather forecasting. 4 THE SWAN INSTRUMENT ON SOHO 29

The study of the Sun’s UV output provides information about bright flares and other coronal behavior. EIT, SUMER and CDS have been successful in mapping these characteristics of the solar atmosphere. Using UVCS, SUMER and MDI data, it has been possible to describe the way the magnetic field determines how the solar wind escapes from the Sun.

Apart from increasing our knowledge about the Sun, SOHO has also proved to be an invaluable tool in monitoring the near-Earth space weather. The velocity and density of the solar wind as well as the occasional emissions of huge amounts of plasma in the form of coronal mass ejections (CMEs) seriously affect the geomagnetic activity, which in turn can have severe effects on space-based technology as well as technology on Earth, and can even lead to collapses in the power network, as was the case for the Hydro-Quebec´ system in 1989 [3].

Another direct use of SOHO is for the discovery of new comets. SOHO spotted its 4000th comet in 2020 [41].

Perhaps the most closely related descendant of the SOHO is the Solar Dynamics Observatory, SDO, a NASA mission launched in 2010. Its goal is to investigate how the Sun’s magnetic field is generated and how the magnetic energy is released into the heliosphere as solar wind or energetic particles.

4.3 SWAN and the Lyman-α Method

The Solar Wind ANisotropies instrument on SOHO was developed as a cooperation between Service d’Aeronomie in France and The Finnish Meteorological Institute in Finland. Its scientific objectives can be deduced from its name; SWAN aims to detect anisotropies in the solar wind flux, as it was already shown by analysis of Ulysses data that the solar wind is far from isotropic and exhibits a great deal of variation according to latitude [37].

SWAN makes use of the Ly-α background scattering present in the heliosphere. The Ly-α method is a valuable tool when studying the heliosphere since it does not only detect the presence and amount of hydrogen but also helps to indirectly deduce things about the Sun’s activity.

4.3.1 The Lyman-α method

The first evidence of the presence of interstellar particles in the heliosphere came from satellites measuring UV radiation. The data did not only show the predicted light from stars but also revealed 4 THE SWAN INSTRUMENT ON SOHO 30

a strong source of Ly-α radiation. This radiation is caused by interstellar hydrogen that enters and flows through the heliosphere and scatters the solar wind protons.

The Ly-α scattering occurs because the radiation from the Sun is of a sufficient wavelength to produce jumps in energy levels. When the electrons fall back to their ground states, they emit photons of a certain wavelength. The transitions between energy levels for the electron correspond to different spectral lines caused by the emission or absorption of a photon of a specific wavelength. The Lyman-α line, the strongest line in the spectrum, is the result of an electron falling from its first excited state to its ground state. The electron falls from the n = 2 orbital to the n = 1 orbital, n being the principal quantum number. This scattering of solar Ly-α photons by the interplanetary hydrogen occurs at a rate of one photon every 500 s for one H atom at 1 au [4]. Studying the light of this particular wavelength, 1.216 × 10−7m, is very valuable. This scattered light is sometimes called resonance glow of hydrogen and can be observed in all directions in interplanetary space.

There are two main ways of implementing the Lyman-α method: photometric and spectroscopic [25, p. 283]. Using photometry, we can obtain accurate mass-flux distributions of the solar wind and in the outer parts of the heliosphere, it can be used to investigate physical processes in the heliospheric interface. The spectroscopic method, on the other hand, is used to study the spectral properties of the radiating source as the radiation interacts with some specific material.

The Lyman-α method was first tested in the Prognoz observations in 1976-77, revealing an increase in Ly-α emission near the ecliptic poles, discarding the idea of an isotropic solar wind [4]. This was confirmed by Ulysses in 1994.

Backscattered solar Ly-α radiation caused by interstellar hydrogen flow was used to provide a unique insight into the ISMF when it showed a significant difference in the flow direction of hydrogen and helium. Helium atoms are almost unaffected by the magnetic effects at the heliospheric boundary region due to a much smaller charge exchange cross section. This means that their flow direction is very close to that of the undisturbed ISM [33] [34]. The deflection of the hydrogen flow direction is caused by the ISMF and thus provides an indirect way of determining characteristics of the ISMF. However, there are several other factors to be taken into account such as the solar radiation pressure, gravitation and ionization and kinetic non-Maxwellian properties of the hydrogen distribution [29]. 4 THE SWAN INSTRUMENT ON SOHO 31

4.3.2 The SWAN Instrument

The SWAN mission is based on the Ly-α method and aims to investigate the variations of the solar wind by mapping Ly-α emission. The SWAN instrument is composed of two sensor units, situated on opposite sides of the spacecraft. They map the north and the south ecliptic hemispheres respectively. The halo orbit of SOHO and the tilt of the solar rotation axis enable a slight overlap in the field of view of the sensors, allowing for mutual calibration. In the SOHO coordinate axis, the x-axis is pointing towards the Sun and the two sensors are defining the +z and the -z axes. The xz-plane includes the solar rotation axis [13]. As SOHO moves around the L1 point, it will deviate from the ecliptic with up to 1◦.

The sensor units consist of a system of two mirrors that are moved with motors to each cover half of the sky. The instantaneous field of view of a sensor is a square of 5 × 5◦ divided in 5 × 5 pixels of 1◦ square. The photons are then counted in each pixel of the detector for a typical duration of 13 to 45 s, producing an intensity distribution [13]. Thereafter it switches to the next viewpoint, making it possible to cover the whole sky in less than a day. This is the so-called photometric mode, which is mapping the intensity.

In addition to the photometric mode, the spectral content of the light can be exposed with a hydrogen cell. The hydrogen cell is filled with molecular hydrogen that is transparent to Ly-α light. A tungsten filament can be heated in order to dissociate the H molecules into atoms. The atoms in the cell will then interact with the radiation and provide a spectral profile.

One of the challenges for SWAN is the contamination of the data caused by stars, some of which can be very strong Ly-α sources. Other sources are the geocorona, the galactic background, the reflection of sunlight on the moon and on the satellite itself. Comets also show up on the data making SWAN one of the more successful comet spotting instruments.

4.3.3 A Typical SWAN Sky Map

A typical full-sky intensity map, in ecliptic coordinates, produced by SWAN is shown in Figure 5. It is color coded so that it covers a range of 200 to 800 counts per second, per 1◦ pixel. The unit is Rayleigh. The upper half of the map is detected by the +z sensor unit and the lower half by the -z unit. The line between the two halves is almost but not strictly representing the ecliptic plane, since the z-axis coincides with the projection of the solar rotation axis on the zy-plane. The z-axis may be inclined from the ecliptic polar axis by 7.2◦. 4 THE SWAN INSTRUMENT ON SOHO 32

Figure 5: A full-sky Lyman-α map by SWAN, showing 17th of March 1996, credits: NASA 4 THE SWAN INSTRUMENT ON SOHO 33

A maximum intensity is seen on the left side, which is the hemisphere where the interstellar wind is approaching from, i.e. the upwind side, and a minimum on the right side, the downwind side. The size of these maximum and minimum regions vary seasonally as the Earth’s position changes by 2 au every 6 months. The bright spots are the UV emission of the Milky Way and some isolated hot stars, most of them seen along the galaxy and on the south ecliptic hemisphere more than the north. The two blank areas in the corners are caused by the absence of data due to the Sun while the one in the middle of the map is where the reflection of the Sun on the satellite is.

This particular map, from 1996, is observed during a solar minimum dominated by the high speed wind from coronal holes on all solar latitudes. On the map, we see this as a spread out region of intensity whereas during a solar maximum, the high intensity area is more positioned around the equatorial region. 5 MODELLING THE INTERSTELLAR MATTER IN THE HELIOSPHERE 34

5 Modelling the Interstellar Matter in the Heliosphere

The effects of the interstellar particles traveling through the heliosphere can be observed through their interactions with the Sun in the form of the Lyman-α background radiation. Using these observations to ascertain properties of the local interstellar matter undisturbed by the Sun is challenging due to the multiple different factors in play. Chapter 3.4 described the numerous ways in which the Sun interacts with the LISM, so for the interstellar particles observed inside the heliosphere it is clear that they might have undergone changes. This chapter gives an introduction to the physical models describing interstellar matter inside the heliosphere.

5.1 Challenges

Like many other problems in Space Physics and Astronomy, the heliosphere-LISM interaction is a non- linear inverse problem, where we want to find the physical processes resulting in the situation we are observing. Typical of an inverse problem is that there are infinitely many models that will fit the data.

Another challenging aspect is the fact that we are observing the scattering medium - the hydrogen background radiation of the heliosphere - from the inside. In tomographic measurements, the medium is most successfully mapped from the outside and this interior tomography problem is hard to overcome since the detector does not move significantly when compared to the size of the medium [32].

Any model of interstellar hydrogen inside the heliosphere needs to be able to accurately describe both the solar wind plasma and the interstellar plasma. Further complicating the matter are the components that are created by the interaction between these two different plasmas, for example the pickup ions described in Chapter 3.4.2. This new component of the solar wind needs to be taken into account in models.

5.2 Early Models

In addition to his groundbreaking model of the solar wind, Parker also developed in 1961 the first model of the interaction between the solar wind and its local interstellar surroundings. Little was known about the interstellar parameters at the time. The first models that considered a supersonic interstellar wind flow as well as the neutral component of the wind was introduced by Baranov and Malama in the 1980s [2]. This model was able to predict the heliospheric boundaries described in Chapter 3.3. 5 MODELLING THE INTERSTELLAR MATTER IN THE HELIOSPHERE 35

One of the first models that described the interstellar hydrogen inside the heliosphere was the so-called cold model. It describes a hydrogen gas moving in bulk under the influence of the solar gravitational field, assuming that all the atoms have the same velocity far away from the Sun. These assumptions makes it possible to obtain a distribution of the number density of interstellar atoms in the heliosphere. It also included effects of solar radiation.

The cold model neglects the thermal character of the hydrogen gas, T ∼ 104 K, since it underestimates the local hydrogen density [47]. The first model to take the thermal aspect into account was the so-called hot model. In order to do this, the velocity cannot be assumed Maxwellian, it needs to be calculated. The hot model provides the so-called Danby-Camm solution for the velocity, which was originally solved for gas cloud particles moving in the gravitational field of a point mass [10]. The assumptions are that the velocity distribution at infinity is Maxwellian, there are no H-H collisions, and that the µ = Frad/Fgrav is stationary and spherically symmetric. The Danby-Camm solution for the velocity distribution can then be expressed as [10]:

1 βer2 1 − 2 f (~v,~r) − 0 ∆φ W(~v,~r) = e 2vT e v0|p| (5.1) 3/2 3 (2π) vT where

2 2 vz(v0 − vr) −V(r)cosθ f (~v,~r) = vb + v0 − 2vbv0 (5.2) v0(v0 − vr) −V(r)

p 2 p and v0 = v + 2V(r) and vT is thermal width vT = kT/m. V(r) is the central force potential given by:

GM V(r) = − (1 − µ) (5.3) r where G is the gravitational constant and M is the solar mass.

βer2 − 0 ∆φ The factor e v0|p| is added in order to account for the effects of photoionization and charge exchange on the velocity distribution [32]. Here it is assumed that also the ionization rate, β, is stationary and spherically symmetric and that βe is the ionization rate at r0 = 1 au. The impact parameter is denoted by p and the angle swept by the particle is denoted by ∆φ. 5 MODELLING THE INTERSTELLAR MATTER IN THE HELIOSPHERE 36

5.3 Multicomponent Models

A model of the heliosphere needs to be able to describe both the interstellar wind plasma with all its components - the plasma, the neutral part, the ISMF and GCRs - as well as the solar wind with all its components - solar particles, pickup ions, energetic particles and ACRs [25, ch4]. As these components need to be modelled both kinetically (hydrogen) as well as magnetohydrodynamically (the plasmas), the resulting models are kinetic-continuum models.

Several limitations of the earlier models have been dealt with in the newer, more complex models. One main improvement has been the inclusion of the interaction between the neutral hydrogen gas and the surrounding plasma. When charge exchange and ionization occurs, there are other effects than simply a loss of hydrogen atoms to ionization. Another important aspect is to consider the effect of the solar cycle variations, and non-stationary, self-consistent models have been successfully used for predicting the varying distances to the heliospheric boundaries [24]. 6 AN EXAMPLE USING DIRECT SIMULATION 37

6 An Example Using Direct Simulation

To illustrate the modelling described in the previous chapter, I have used SWAN data of the Ly-α background radiation to examine interstellar parameters through the interaction of interstellar hydrogen with the Sun. This was done by simulating a signal of the Ly-α intensity and comparing it to the signal observed by SWAN.

As the hydrogen absorption cell on SWAN is alternatively switched on and off, the observed counting rates can be compared for a given line of sight by the reduction factor (or transmission factor)

Ion RSWAN(Tcell,τcell) = (6.1) Io f f

where Ion is the transmitted intensity and Io f f is the total intensity. RSWAN will depend on the cell temperature, Tcell, and the cell optical depth, τcell.

6.1 Model for the intensity signal

Radiative transfer theory, essentially describing how radiation travels, is needed in order to obtain a model for the intensity signal. Assuming an optically thin and single-scattering medium, the intensity signal can be modelled using [5]:

2 4 3 2 8πα R ω φ0r Z P(θ(s))ds Z I(ω ) = d q 0 × dv W[Λ ,v ,~r(s)] (6.2) q 27cΓ r(s)2 ⊥ q ⊥

where W[Λq,v⊥,~r(s)] is the velocity distribution, α is the fine structure constant, Rd is the radial part of the dipole matrix elements, Γ is the decay constant, φ0 is the solar Ly-α flux at r = 1 au, and P(θ) is the scattering phase function as derived in [5]. In the velocity distribution function, Λq = c((ωq −ωα )/ωq), where ωα is the Ly-α frequency. The integration is over velocities transversal to the line of sight (v⊥).

The intensity signal observed by SWAN will then be:

Z Iobs = nin f Isolar(ω)Tins(ω)I(ω)dω (6.3)

where I(ω) is obtained from equation (6.2), nin f is the density of the interstellar hydrogen before 6 AN EXAMPLE USING DIRECT SIMULATION 38

entering the heliosphere and Isolar is the solar intensity. Tins is the instrument function of SWAN and includes the noise effects from the instrument as well as the on-off variation of the hydrogen cell. Simulating the on-off effect is important because when it is switched on, the cell absorbs part of the radiation spectrum while when it is off there is no effect. Depending on where SWAN is facing compared to the H flow, the observed frequency of the radiation will be Doppler shifted, affecting the signal. This so-called Doppler scanning method provides information about the spectrum also in the photometric mode. Now the reduction factor can be simulated using (6.3) and compared with the reduction factor calculated from SWAN measurements (6.1).

6.2 Parameters and data set used

The relevant parameters are the direction, temperature and velocity of the interstellar particles, the ratio of the radiation pressure to the gravitational force of the Sun, the particle density at infinity, the ionisation rate, as well as the cell temperature and cell optical depth of the instrument.

The parameters that were kept constant are: the wind longitude (in ecliptical coordinates) at 254◦, the particle density at infinity 1.25 × 105 m−3, as well as the cell temperature and cell optical depth using known values from previous studies.

The parameters that were varied are the following: wind latitude, temperature, velocity, µ, and β. Two values were used for the temperature, 7500 K and 12000 K, two values were used for the velocity, 20.0 and 22.5 kms−1, and for the latitude the two values 7.5◦ and 10.5◦ were used. For µ the values 0, 0.75, 0.95 and 1.0 were used. For β the values 0, 3.5, 3.75, 4, 4.5, 5, and 6 (in units of 10−7s−1) were used.

The data used for comparison with the simulated values is the Lyman-α intensity data from early SWAN observations during the solar minimum between solar cycle 22 and 23. The data set is restricted to 29 line of sight directions chosen to minimize Lyman-α contamination from starlight.

6.3 The Implementation

The program used to simulate the intensity signal from SWAN and compare with the observed values is a modified version of the program used in [26] and [32]. It uses the Danby-Camm solution to model an intensity signal and reduction factor and compares it to the reduction factor obtained from SWAN. 6 AN EXAMPLE USING DIRECT SIMULATION 39

Similarly to [26], the comparison is done using a goodness of fit measure, χ2, to quantify which parameters yield the best fits with the data. In [26], a Levenberg–Marquardt algorithm is used to minimize χ2 and produce the best-fit parameter values. In this version, however, direct simulation is performed so that for each chosen set of parameters, the program will compare the reduction factor obtained from the modelled intensity with that of the SWAN data for the corresponding line of sight 2 direction. For each line of sight, χlos is

2 2 (Rmodel(los) − RSWAN(los)) χlos = 2 (6.4) RSWAN(los)

The method is similar to the one used in [32], where different initial parameters were varied one at a time in order to analyse the anisotropies of the solar wind. Here the aim is to see which interstellar parameters produce the closest fit with the data, as well as to get an indication of the sensitivity of the different parameters in this model.

6.4 Results

2 2 The first 24 case studies are described in Table 3, with the resulting χ values (an average of the χlos values for each case). 6 AN EXAMPLE USING DIRECT SIMULATION 40

Table 3: Parameters used and the resulting χ2 value

Case nr Latitude (in degrees) Temperature (K) Velocity (kms−1) µ β χ2 1 7.5 12000 20.0 0.95 4.0 0.534 2 7.5 12000 20.0 0.95 6.0 0.297 3 7.5 12000 20.0 0.95 0 6.369 4 7.5 12000 20.0 0.75 6.0 1.110 5 7.5 12000 20.0 1.0 6.0 16.446 6 7.5 12000 22.5 0.95 6.0 0.714 7 7.5 7500 20.0 0.95 4.0 8.897 8 7.5 7500 20.0 0.95 6.0 8.314 9 7.5 7500 20.0 0.95 0 14.296 10 7.5 7500 20.0 0.75 6.0 6.579 11 7.5 7500 20.0 1.0 6.0 25.867 12 7.5 7500 22.5 0.95 6.0 8.186 13 10.5 12000 20.0 0.95 4.0 0.288 14 10.5 12000 20.0 0.95 6.0 0.477 15 10.5 12000 20.0 0.95 0 4.113 16 10.5 12000 20.0 0.75 6.0 2.311 17 10.5 12000 20.0 1.0 6.0 12.552 18 10.5 12000 22.5 0.95 6.0 1.555 19 10.5 7500 20.0 0.95 4.0 7.661 20 10.5 7500 20.0 0.95 6.0 7.473 21 10.5 7500 20.0 0.95 0 11.152 22 10.5 7500 20.0 0.75 6.0 7.536 23 10.5 7500 20.0 1.0 6.0 20.709 24 10.5 7500 22.5 0.95 6.0 8.085 6 AN EXAMPLE USING DIRECT SIMULATION 41

Some are clearly extreme, cases 5, 9, 11, 17, 21 and 23 all have a χ2 > 10. They correspond almost entirely to the cases where µ = 1. Also the cases where β = 0, (3,9,15 and 21) produce high χ2 values. With a χ2 < 0.3, cases 2 and 13 clearly show the best fit with SWAN data. Both cases have µ = 0.95, v = 20.0 kms−1, and T = 12000 K.

Additional simulations were run with µ = 0.95 and T = 12000 K kept constant while varying mainly the ionization, but also trying different velocity and latitude values. The results are shown in Table 4.

Table 4: Parameters used and the resulting χ2 value

Case nr Latitude (in degrees) Temperature (K) Velocity (kms−1) µ β χ2 25 7.5 12000 20.0 0.95 5.0 0.361 26 10.5 12000 20.0 0.95 5.0 0.352 27 10.5 12000 20.0 0.95 4.5 0.309 28 10.5 12000 20.0 0.95 3.5 0.298 29 10.5 12000 20.0 0.95 3.75 0.289 30 10.5 12000 22.5 0.95 4.0 0.909 6 AN EXAMPLE USING DIRECT SIMULATION 42

6.5 Analysis

The cases showing the best fit with SWAN data were where the parameters µ = 0.95, v = 20.0kms−1, and T = 12000 K were used. The best results were from case 2 and case 13, shown in Figure 6 and 7 respectively.

If one compares case 2 (χ2 = 0.297) with case 5 (χ2 = 16.446) where the only difference is in µ (µ = 0.95 for case 2 and µ = 1.0 for case 5), yet the resulting χ2 values are very different, it is clear that µ is a sensitive parameter in this model. The higher temperature generally seems to provide better results than the lower, as can be seen when comparing case 13 (χ2 = 0.288) with case 19 (χ2 = 7.661) for example. The lower value for velocity generally produced better results, so for case 30 (Figure 8) the same parameters as in the (best fit) case 13 were chosen, only with the velocity set to 22.5 kms−1 instead of 20.0 kms−1, and this resulted in a significantly higher χ2.

The latitude does not at first glance seem to be a sensitive parameter, as both latitude values resulted in some good cases. To ascertain something about the effect of the latitude, a comparison can be made between case 13 (latitude: 10.5◦) and case 1 (latitude 7.5◦) (Figure 9), where case 13 produces a clearly better χ2 value. And while case 2 with a latitude of 7.5◦ provides a good fit with the data, when comparing the cases 1-12 (with latitude 7.5◦), with cases 13-24 (latitude 10.5◦), it seems that in general, the bad cases are worse when using the lower latitude.

Since β values of both 4 and 6 produced good results, the second round of simulations were run with ionization rates of 5, 4.5, 3.5 and 3.75 (cases 26-29) out of which case 29 with β = 3.75 had the best fit. However, case 13 with β = 4 was still slightly better.

When comparing the best fit parameters with the interstellar parameters inferred from IBEX data, shown in Table 2 (in Chapter 2.2.2), it is worth noting that for both the temperature and the velocity the results seem to be contradictory. The lower temperature used here (7500 K) matches the IBEX data but did not lead to a good fit with the SWAN data here. Similarly, a velocity of 20.0 kms−1 produced better results than 22.5 kms−1, while IBEX data sets the velocity as high as 25.4 kms−1.

When µ = Frad/Fgrav = 1, the Sun’s attractive and repulsive forces cancel out and do not affect the trajectories of the interstellar particles as they move through the heliosphere. Since µ fluctuates around 1, this special case approximation is not unreasonable although it clearly does not agree with the data or the model used here. The SWAN data used here is from a solar minimum, during which usually µ < 1. 6 AN EXAMPLE USING DIRECT SIMULATION 43

Figure 6: Case 2 with χ2 = 0.297. The upper frame plots the observed and modelled reduction factors for the 29 different lines of sight used. The lower frame shows the difference between the observed and the modelled reduction factors for each line of sight.

Figure 7: Case 13 with χ2 = 0.288. The upper frame plots the observed and modelled reduction factors for the 29 different lines of sight used. The lower frame shows the difference between the observed and the modelled reduction factors for each line of sight. 6 AN EXAMPLE USING DIRECT SIMULATION 44

Figure 8: Case 30 with χ2 = 0.909. The upper frame plots the observed and modelled reduction factors for the 29 different lines of sight used. The lower frame shows the difference between the observed and the modelled reduction factors for each line of sight.

Figure 9: Case 1 with χ2 = 0.534. The upper frame plots the observed and modelled reduction factors for the 29 different lines of sight used. The lower frame shows the difference between the observed and the modelled reduction factors for each line of sight. 7 CONCLUSIONS 45

7 Conclusions

In Chapter 6, I used the Danby-Camm solution for the velocity distribution of hydrogen in order to model the intensity signal from SWAN using different parameters for the interstellar particles. To expand on this, one could try similar case studies for other days. As there is now SWAN data available for two whole solar cycles, it remains a valuable resource for continuous observations. Especially µ would be interesting to follow throughout a solar cycle. Another improvement would be using more recent values for the interstellar parameters, as these are constantly being refined, and can be compared with data obtained using other methods and from other satellites.

In addition to the improvements considered in the newer models mentioned in Chapter 5.3, the inclusion of the effects from the turbulent heliospheric interface region would be highly beneficial for the model. The hot model approximation used in Chapter 6 can often be used for helium with greater success, as it is not affected by the interface region as much as hydrogen.

The interplanetary Ly-α background remains a powerful tool when investigating interstellar particles, and combined with other methods of observation, both inside and outside the heliosphere, it is crucial in forming an understanding of the interstellar medium. REFERENCES 46

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