\thesischapter{Introduction}
\label{thesis_intro}
%---------------------------------------------------------------------------------------------------------------------------------

\section{Solar Observations Throughout History}

The Sun has always been the most important celestial object in our sky, and remains so to this day. All the major ancient civilisations worshiped a Sun god in some form; the Egyptians worshiped Re, the Babylonians worshiped Shamash, the early Greeks worshiped Helios and later Pheobus Apollo. The study of the Sun, planets and stars led the Greek philosophers to the first big step in astronomy of removing the earth from the centre of the universe, and suggesting it, along with all the other planets, revolved around the Sun. Since then solar observations have played a central role in many major scientific achievements throughout the ages

Galileo used the Sun as the most obvious light source to test his new instrument in 1610. The development of this instrument, the telescope, would be a big breakthrough for physics and would be the main experimental driving force behind other important seventeenth century scientific advances. Kepler's observations of the Sun and planets would later lead to Newton's {\em Principia} (1687) and hence the theory of Gravitation was born. In his investigation of colours  Newton (1672) used sunlight directed through a prism to discover the colour constituents of white light. Wollaston (1802) used sunlight through a narrow slit to discover dark lines, which he incorrectly identified as the borders between colours. Fraunhofer (1817) used a more sensitive setup to discover hundreds of these dark absorption lines which would later be named after him (Figure~\ref{fraunhofer}). 

He made the important step of identifying the lines as a property of the sunlight itself, and not a property of the earth's atmosphere as previously thought (although some lines are due to absorption by oxygen molecules in the earth's atmosphere). His labelling system of the lines (Table~\ref{ident}) based on relative strengths, is still used today to some extent (e.g., the sodium D doublet and ionized calcium H and K lines). The positions of these dark lines were soon equated with similar bright lines from earth based experiments. The jump to inferring the existence of certain elements in the Sun from their corresponding dark lines was soon made. Indeed in 1868 one such line led to the discovery of `helium' (named after the Greek god Helios) in the Sun 30 years before it was discovered on earth. The following years saw many new scientific theories with solar observations at their centre: Kirchhoff's law for radiation was based on fully explaining the Fraunhofer lines; the explanation of the Doppler shift originated from studying the Fraunhofer lines at the solar limb; the solar eclipse of 1919 provided confirmation of Einstein's Theory of Relativity.   

\begin{figure}
\begin{center}
\epsfig{figure=spectrum.eps,width=5in}
\caption[The Fraunhofer lines]{The Fraunhofer lines on the solar spectrum}
\label{fraunhofer}
\end{center}
\end{figure}

\begin{table}
\begin{center}
\caption[Identification of Fraunhofer lines]{Identification of Fraunhofer lines. Most lines are of solar origin, but a few are due to absorption in the earth's atmosphere.}
\label{ident}
\begin{tabular}{lll} 
\hline
\hline
Fraunhofer Line	&Element	&Wavelength ({\AA}) \\
\hline
A - (band) 	&O$_2$ 		&7594 - 7621\\
B - (band) 	&O$_2$ 		&6867 - 6884\\
C 		&H 		&6563\\
a - (band) 	&O$_2$ 		&6276 - 6287\\
D - 1, 2 	&Na 		&5896 \& 5890\\
E 		&Fe 		&5270\\
b - 1, 2 	&Mg	 	&5184 \& 5173\\
c 		&Fe 		&4958\\
F 		&H 		&4861\\
d 		&Fe 		&4668\\
e 		&Fe 		&4384\\
f 		&H 		&4340\\
G 		&Fe \& Ca 	&4308\\
g 		&Ca 		&4227\\
h 		&H 		&4102\\
H 		&Ca 		&3968\\
K 		&Ca 		&3934\\
\hline
\end{tabular}
\end{center}   
\end{table}

The start of the twentieth century also saw the realisation of quantum physics and the atom. These theories would explain the origins of the dark Fraunhofer lines. The continuous solar spectrum was explained by Planck (1900), and further by Einstein (1905), by approximating the solar surface (photosphere) to a black body at a temperature of 5800~K (Figure~\ref{blackbody}). Bohr (1913), using Planck's ideas and Rutherford's atomic model, explained the atom in terms of discrete electrons orbit, where photons of light were emitted when any electron jumped from one orbit to another. Radiation from the photosphere with exactly the right amount of energy could be absorbed by an electron, exciting it to a higher orbit. The `flash spectrum' viewed during the initial stages of an eclipse could be explained as the re-emission of light as the electron decays to the lower orbit. Viewed against the brighter solar surface this would normally appear as dark lines in the solar spectrum. In the last few decades, the role of solar observations has moved into new areas. It still has a vital role to play in astronomy, as our only spatially resolvable star, in physics as the most stable and readily available example of plasma, the fourth state of matter, and in the commercial areas of military and communication.

\begin{figure}
\begin{center}
\epsfig{figure=blackbody.ps,width=5in}
\caption[Solar irradiance]{A blackbody curve at a temperature of 5800~K is overplotted on the solar irradiance curve.}
\label{blackbody}
\end{center}
\end{figure}

\section{The Solar Atmosphere}

\begin{figure}
\begin{center}
\epsfig{figure=solar_section.eps,width=5in}
\caption[A 3-dimensional view of the Sun]{A 3-dimensional view of the Sun showing the interior, photosphere, chromosphere and corona (Scientific American 2003)}
\label{cutaway}
\end{center}
\end{figure}

The visible surface of the Sun is a thin layer of plasma known as the photosphere, denotes the top of the solar interior (Figure~\ref{cutaway}) and is the depth limit of direct observations. As such the photosphere is best defined using optical depth, $\tau$,
\begin{equation}
\tau_{\lambda} = \int_{-\infty}^{z} a_{\lambda} dz \ ,
\end{equation}
where a$_{\lambda}$ is the extinction coefficient at a wavelength $\lambda$ and z is a depth coordinate such that z$\rightarrow -\infty$ outside the Sun. The optical depth is essentially the number of mean free paths along the line of sight. For a large $\tau$, photons are absorbed and re-emitted numerous times along the line of sight, and so the plasma is described as optically thick. This applies to the deep lying layers of the Sun. Photons originating in the core pass through the radiative and convective zones, with the respective transport mechanism dominating in each zone, before reaching the photosphere (Figure~\ref{cutaway}). The photosphere has a small $\tau$, so most photons can travel directly to earth without being absorbed. The common definition of the photosphere is the layer from which the bulk of the visible photons are emitted, $0.1\leq \tau_\lambda \leq 3.0$. As optical depth is a function of wavelength, it is reasonable to refer to the visible photosphere, the infrared-red photosphere, {\em et cetera}. Hence for the Sun, where the majority of photons are emitted in the visible wavelength, the photosphere is often defined as the layer where light emitted at 5000~{\AA} (green) has an optical depth of 2/3, ($\tau_{5000} = 2/3$). The optical opacity of the photosphere and upper solar interior is mainly due to the negative hydrogen ion, where the second electron is only loosely attached. A photon with a large range of energies can hence remove the electron by absorption.

Above the photosphere the conditions change rapidly (Figure~\ref{solatm}). Moving up through the chromosphere the electron density drops off, while the temperature drops to a minimum of 4200~K then gradually increases again. At a height of about 2000~km above the photosphere the electron density decreases sharply, and temperature increases dramatically from 25,000~K to a coronal temperature of 10$^6$~K in a transition region only a few hundred kilometers thick. This layer acts as an interface between the cool chromosphere and the hot tenuous corona. The corona, only viewable from earth when the photosphere is blocked out by a total eclipse or coronagraph, extends out though the solar system past Earth and on to the gas giants. 

By careful comparison of atomic data with modelling of the solar atmosphere it is possible to estimate the height of formation of the Fraunhofer lines (Figure~\ref{solatm}). The VAL model (Vernazza, Avrett, \& Loeser 1981) is the most widely used and complete model of the origin of the absorption lines. This model is derived by semi-empirically inverting the observed extreme ultraviolet (EUV) line intensities. The cores of the stronger lines (Balmer lines, ionized calcium and magnesium) form mostly in the chromosphere, whereas weaker lines (e.g., G-band) originate from the low chromosphere/photosphere. The transition region mostly emits in ultraviolet (UV) wavelengths below 2000~{\AA}, which is strongly absorbed by the earth's atmosphere. The corona has increased UV, EUV and X-ray emission due to its high temperature. However the corona also emits a pair of visible continua, the K and F coronae. The low-intensity K corona, which dominates nearer the Sun, is due to electron scattered light. Doppler broadening due to the fast motion of the electrons removes the Fraunhofer lines from this continuum and polarizes the light. These scattering electrons must have extremely high temperatures ($\sim~2{\times}10^6$~K). The F corona comes from light scattered by dust particles and does contain the Fraunhofer lines. Several optical lines which could not be attributed to any element known on earth were detected in the eclipse of 1869. They were attributed to a new element, `coronium'.The brightest lines were the green line (5303~{\AA}) and the red line (6374~{\AA}), with a few dozen fainter lines also discovered. The actual source of these was finally explained by Edlin (1942) and Grotian (1939) as due to forbidden transitions in highly ionized iron (Fe~{\sc xiv} and Fe~{\sc x} respectively). The high temperatures necessary to create these ionisation states, and the low densities to ensure the forbidden transition from the metastable states, provided further evidence of the extraordinary conditions in the corona. 

\section{The Fraunhofer Lines}

\begin{figure}
\begin{center}
\epsfig{figure=val.eps,width=5in}
\caption[The VAL model]{Temperature stratification of the quiet Sun. Heights of formation of several Fraunhofer lines are indicated. (Vernazza, Avrett, \& Loeser 1981)} 
\label{solatm}
\end{center}
\end{figure}

\subsection{Photospheric Lines} 
\label{pl}

By the equation of radiative transfer,
\begin{equation}
\frac{dI_{\lambda}}{dx} = J_{\lambda} - K_{\lambda}I_{\lambda} \ ,
\end{equation}
the change in intensity, I, at any wavelength, $\lambda$, over a distance, $x$, is dependant on two processes, absorption and emission. The {\em{absorption coefficient}}, $K_{\lambda}$, is essentially the fraction of energy removed from a beam, either by absorption or scattering, per unit length. The {\em{emission coefficient}}, $J_{\lambda}$, is a measure of the amount of energy added to the beam. The {\em{source function}}, $S_{\lambda}$, is then the ratio of emission to absorption, 
\begin{equation}
S_{\lambda} = \frac{J_{\lambda}}{K_{\lambda}} \ .
\end{equation}
In an ideal situation, where the atoms and photons of a gas are completely interacting, the Sun can be equated to a black body and hence the source function can be equated to the Planck function. However for the Sun, where some radiation escapes, this can only be achieved through the local thermodynamic equilibrium (LTE) approximation. Here the source function is approximated to the Planck function at the local temperature value. This is equivalent to the `grey atmosphere' approximation where the absorption coefficient is independent of wavelength. The departure of the solar continuum curve from that of a black body (Figure~\ref{blackbody}) is due to the fact that the absorption coefficient is dependent on wavelength. For larger absorption coefficients, radiation is emitted from higher in the atmosphere, where the temperature is cooler (i.e., as far up as the temperature minimum). This applies to the wavelengths of the Fraunhofer lines. Conversely for other parts of the spectrum, radiation comes from lower in the atmosphere where the temperature is hotter. As a result of this temperature difference the total flux emitted from the Sun in the Fraunhofer lines is lower than the continuum, hence the lines appear dark. 
 
\subsection{Chromospheric Lines}
\label{ch}

\begin{figure}
\begin{center}
\epsfig{figure=profiles_ha_ca.eps,width=5in}
\caption[Line profiles of Ca~{\sc ii}~K and {\ha}]{Line profiles of (a)~Ca~{\sc ii}~K and (b)~{\ha}. The K$_3$ core, K$_2$ peaks, and K$_1$ wings of the Ca~{\sc ii}~K are also noted in (a). The solar spectrum was obtained from the BASS2000 database and is normalised to continuum intensity.}
\label{lineprof}
\end{center}
\end{figure}

Although this simple explanation works well for weak and medium strength lines, as well as for the wings of stronger lines, the cores of the stronger lines must be explained differently. These lines are formed above the temperature minimum in the mid and high chromosphere (Figure~\ref{solatm}). At these increased temperatures, the local temperature, describing the speeds of atoms and ions, can be several hundred degrees higher than the the radiation temperature. Hence the source function cannot be equated to the Planck function and the LTE approximation cannot be assumed. Lines here fall into one of two categories, either photoelectrically or collisionally controlled. The Balmer {\ha} line is a good example of a photoelectrically controlled line. As such, the {\ha} line strength is dominated by photon excitations, and hence is governed by radiation from the photosphere, rather than the local temperature. Moving out from the photosphere, the source function steadily decreases, resulting from the increasing amount of radiation escaping into space (and hence decreasing emission coefficient). The line profile of {\ha} (Figure~\ref{lineprof}b) is purely in absorption at line centre (formed around 1500~km) and moving away from line centre corresponds to moving down through the atmosphere, where the emission coefficient, and hence source function, is higher. The ionized calcium (Ca~{\sc ii}) H and K lines are good examples of collisionally controlled lines. Here the line is dominated by electron collisions with the atom and hence reflects the local temperature. As the temperature increases moving out through the chromosphere, the source function also increases (due to increased emission). Around a height of 1900~km the source function decreases again, due to scattering. Hence the line core, denoted K$_3$, is formed at 1900~km, the self reversed peaks on either side (K$_2$) are mid-chromosphere, and the line wings (K$_1$) are formed around the temperature minimum (Figure~\ref{lineprof}a). 

\begin{figure}
\begin{center}
\epsfig{figure=magnat.ps,width=5in}
\caption[The magnetic canopy effect]{Diagram of the magnetic canopy effect as the field lines spread out. When the field lines from neighbouring network regions meet, the entire atmosphere is magnetic. Also shown are p-modes and the formation of acoustic shocks, discussed in Chapter~2. (Schmieder 2001)}
\label{magdia}
\end{center}
\end{figure}

\subsection{Magnetograms}
\label{mag}
\hspace{1cm}
Magnetic fields exist throughout the solar atmosphere and can be imaged and measured using the Zeeman splitting of Fraunhofer lines. The Zeeman splitting comes from the interaction of the external field with the magnetic field created by the electron motion, resulting in a small positive or negative energy transfer to the photons emitted. As such, a single Fraunhofer line is split into two components, with the separation proportional to the field strength (discussed further in Chapter~3). Iron is the most popular choice for magnetograms, imaging the photospheric magnetic field, but other Fraunhofer lines can also be used to image magnetic fields throughout the solar atmosphere. The splitting increases linearly with wavelength, giving obvious benefits from imaging in the red and infrared wavelengths. Solar magnetic fields are most conspicuous as sunspots in white light images, but smaller scale magnetic features can also be viewed in the wings of {\ha} or line centre of the G-band (the molecular band head of the CH molecule). Typically sunspots have a field strength of 3000~G, and the smaller structures around 1000~G. These structures are in pressure balance with the surrounding environment, therefore the gas pressure inside must be smaller than the surrounding atmosphere, as the magnetic field exerts an additional pressure. Hence the structures are confined by the surrounding gas pressure and the photosphere is locally depressed within. For sunspots this is viewed as the Wilson depression. To compensate for the reduced gas pressure in the upper atmosphere the magnetic structures fan out (Figure~\ref{magdia}). Eventually around the high chromosphere neighbouring structures meet, and the entire atmosphere is magnetic (Kopp \& Kuperus 1968). Recent work by Schrijver \& Title (2003) question the validity of this type of canopy. They suggest an alternative whereby field lines from the network connect with weaker fields in the nearby internetwork.
  
\section{Photospheric Features}

\begin{figure}[t]
\begin{center}
\epsfig{figure=gran.ps,width=5in}
\caption[Photospheric granulation]{Granulation of the solar photosphere taken by the Dunn Solar Telescope, Sacramento Peak. This image, taken in a broad band visible light filter, covers an area of $30\arcsec$ by $30\arcsec$ on the solar disk. Typically, granules have a diameter of $\sim1.5\arcsec$, corresponding to 1100~km}
\label{gran}
\end{center}
\end{figure}

\subsection{Granulation}
\label{phgr}
Viewed in white light or in the wings of strong Fraunhofer lines the photosphere is covered in an irregular polygonal pattern known as granulation (Figure~\ref{gran}). The granular formation is due to the convective motion of the gas in the sub-photospheric layers, with the bright centre as upward flows and the dark lanes as downward flows. This overturning fluid carries heat bodily to the solar surface. As the hot opaque gas approaches the photosphere it is exposed to the interstellar vacuum, cools suddenly and becomes transparent. This loss in energy corresponds with a rise in density and the vertical motion is decelerated and diverted into a horizontal motion. Further radiation of energy leads to further increases in density and eventually gravity pulls the parcel back down, along the intergranular lanes. In response to this, hot gas flows up to replace it, and so the convective cycle is complete. This convective flow is dominated by the cooling at the photosphere. The increased density at the bottom of the convective zone, 10$^6$ greater than at the photosphere, means the acceleration of convective flow here is 10$^6$ times less than at the photosphere. This is unlike normal convection (e.g., boiling water), where the top and bottom of the flow contributes equally.

Granules vary in size from 150~km (current ground based limit of observation) to 2500~km, with the majority around 1100~km diameter. Ground based observations require careful selection of observation sights, using realtime frame selection (taking a burst of hundreds of images and selecting the best images) or by speckle interferometry. The convective motion exhibits vertical flows (measured by Doppler shifts) of around 2~km~s$^{-1}$ peak to peak. The centre of the granules are typically 30\%  brighter than the intergranular lanes, which corresponds to $\sim$400~K temperature difference by the Stefan-Boltzmann law. Granules are born from fragments of other larger granules or from the merging of smaller granules. After expansion, they die either by fragmentation, merging, shrinking or dissolution. and have a typical lifetime, birth to death, of around 8--20 minutes (Spruit, Nordlund, \& Title 1990).

Larger scale convective cells have been the topic of much debate (Hathaway {\etal} 2000). A second, larger, supergranular cell was discovered by Hart (1954) and later associated with convection by Leighton, Noyes, \& Simon (1962). It was discovered in the Doppler shifted velocity images of Fraunhofer lines. These images suggested horizontal velocities parallel to the surface of around $0.4$~km~s$^{-1}$, leading to large cells of around 30,000~km with a lifetime of about one day. Recent work by Hagenaar, Schrijver, \& Title (1997) suggest this may be overestimated, and propose a typical cell diameter of around 15,000~km. These larger cells carry the smaller granules like flotsam carried along a river, and hence the horizontal flows can be viewed by measuring the granular motion. This motion also carries magnetic flux tubes, which meet at the supergranular boundaries and fall. Some flux remains which moves along the boundaries to vertices, where the downflow is concentrated into small plumes, often with a vortex motion. Due to this concentration of magnetic flux, supergranular cells are spatially related to high chromospheric structure (Section~\ref{chnet}), but theory places their origins below that of granulation. Simon \& Weiss (1968) suggested different cell sizes on the Sun are each excited by various ionisation/recombination layers. Granulation was attributed to recombination of hydrogen at a depth of 1,000~km below the surface and supergranules attributed to recombination of helium at a depth of 15,000~km. Two further cells sizes were predicted, a 5000~km cell due to recombination of helium at 5,000~km depth and a much larger cell due to recombination of metals at 200,000~km depth (the base of the convection zone). These were later found as {\em mesogranules} (November {\etal} 1981) and {\em giant cells} (Beck, Duvall \& Scherrer 1998). The mesogranular flow can be observed as regions of converging and diverging horizontal flow of around 5,000 to 10,000~km. Bright, long-lived, rapidly expanding granules, normally with dark centres, are preferentially found in upflowing mesogranular centres, where horizontal flows diverge. Small, faint, short-lived granules are preferentially found in downflowing mesogranular boundaries, where horizontal flows converge. New observations and simulations suggest cells are more 'pancake shaped' with structure depth to around 1/4 to 1/2 of their diameter (Simon 2001). As such, granules are formed around 100~km depth and supergranules around 5000 -- 10,000~km. Some authors (e.g., Roudier {\etal} 1999) argue that the the fact that mesogranular parameters (e.g., velocity, lifetime) are dependant on the chosen filters suggests that mesogranulation may purely be an artifact of the data reduction. Hathaway {\etal} (2000) have further suggested that mesogranules are simply large granules (or small supergranules) and giant cells are large supergranules. The driving mechanism behind these large convection cells, and factors determining their size (or various sizes) remain unanswered.      

\subsection{Magnetic Structure}
\label{magstr}
The sunspots which blemish the solar surface are areas of high magnetic flux, and can be classified according to their appearance, complexity and magnetic structure. They are cooler than the surrounding photosphere so appear dark on images taken in the visible continuum.  A record of the monthly total number of sunspots led to the discovery of the well known eleven--year active--cycle of the Sun. Sunspots are part of a group of larger areas known as {\em{active regions}}. Active regions comprise all phenomena associated with emergent flux and many active regions exist without producing sunspots. Sunspots and active regions generally occur at low latitudes, whereas shorter lived, smaller scale, magnetic areas known as {\em{ephemeral}} active regions are evident over a higher latitude spread. The organisational quality of the supergranular flow tends to concentrate the magnetic field into the cell boundaries. But the finite efficiency of this process means there is some remnant field. This left over field eventually reaches an equilibrium with the convective and turbulent motions and this creates a third scale of magnetic field known as the {\em{intranetwork}} or {\em{internetwork}}, studies of which can only be achieved with deep magnetograms which have high spatial resolution and long exposure times. Unfortunately the small structures also evolve over short timespans so further progress in this field will require achieving the desired spatial resolution without trading off temporal resolution. 

Images in the cores of weak lines, especially the G-band, show small features associated with increased magnetic field. A pattern of strings of small bright points can be found strung along intergranular lanes. These {\em{filigree}} can be found in the quiet Sun at supergranular boundaries, and in active regions as {\em{faculae}}. Each bright point can be spatially associated with a magnetic element of nearly the same size. Magnetic tubes of around 1000~G are concentrated by compression of converging granules in a diameter of around 400~km. This results in a large flux of 10$^{17}$Mx. Because of this strong interaction with energetic granules, filigree are unstable with a mean lifetime of around five minutes, and usually appearing in a dark junction of several granules, concentrating the field further. The gas inside the filigree is heated by the gas outside, due to its higher pressure. A combination of this along with the fact that deeper layers are viewed creates the brightness. The strong correlation with magnetic elements means filigree can be used to track chaotic flux. Magnetic waves, transverse to the field, are generated by this chaotic motion at the top of the convection zone and move up through to the corona with an exponential growth of amplitude. Dissipation of energy by these magnetohydrodynamic waves is suggested as a possible coronal heating mechanism.  
\begin{figure}
\begin{center}
\epsfig{figure=multi_wave.ps,width=5in}
\caption[Imaging in {\ha}]{Imaging throughout the solar atmosphere. All images were taken by the Dunn Solar Telescope, Sacramento Peak and are of the same region at disk centre with a field of view of 120$\arcsec$ by 120$\arcsec$. Images in the core of the {\ha} line are chromospheric. However moving away from disk centre, images are increasingly photospheric. At 1{\AA} into the blue wing, granulation dominates the images, similar to images taken in the continuum}
\label{multiwaveimage}
\end{center}
\end{figure}

\section{Chromospheric Features}
\subsection{Fine Structure}
\label{cfs}
The most useful lines for imaging the chromosphere are {\ha} and Ca~{\sc ii} H and K. As explained in Section~\ref{ch}, moving from line centre to the wings of these lines corresponds to imaging different heights in the atmosphere (Figure~\ref{multiwaveimage}). Images in K$_3$ show a series of bright and dark patches over the surface. The bright features are known as {\em{mottles}}. These are areas of large brightness contrast which link together to form a quasi-regular pattern around and above supergranules. The larger features are coarse mottles, also known in literature as {\em{flocculi}}. They combine to form the chromospheric network (Section~\ref{chnet}). Each mottle consists of several bright fine mottles, around 7000~km long and 700~km in diameter. Images in {\ha} contain additional contribution from higher levels (due to higher excitation energy). In {\ha} line centre, fine mottles can be bright (low-lying) or dark (height$\sim3000$~km), the latter sometimes showing fragmentation. In the wing of this line (Figure~\ref{multiwaveimage}), fine mottles are always dark. {\em{Rosettes}} are formed when alternate dark and bright fine mottles radiate from a common centre, where the common centre makes up part of the network. Typical fine mottles have a lifetime of 12-20 minutes. They are sites of upward and downward motions which can be regarded as cylinders   less than 1000~km thick, with a temperature in the range of 5000 -- 15000~K. The dark/bright contrast is due to an increase in gas pressure. {\em{Spicules}} are limb structures of $\sim$10,000~K, up to 1500~km across which extend 10,000~km into the corona, with a typical upward velocity of 20~km~s$^{-1}$. This upflow could fill the corona in three hours, and so requires a mass flow back down into the chromosphere. Often spicules, and the downflow corresponding to them, are attributed to mottles on the limb. In the centre of each cell smaller features can be found. The {\ha} violet wing shows small (1000~km) dark features associated with upward flow. In  Ca~{\sc ii} lines, {\em{bright grains}} are found which increase and decrease in brightness periodically over a few minutes. In the network, these are found to be spatially coherent with small magnetic elements which collide and reconnect. The brightness may be due to heating after magnetic reconnection, where magnetic flux is turned into heat (Chapter~2).

\subsection{Active Regions}
Across the solar disk, bright {\em{plages}} are found in a granular structure in the vicinity of active regions. These are areas of higher temperature and density than the surrounding areas, caused by the enhanced magnetic field of the active region. Fine dark {\em{fibrils}} are found arranged in a radial or spiral pattern around sunspots, with a clockwise rotation in the southern hemisphere, and a counter-clockwise pattern in the northern hemisphere. These are much longer ($\sim$20,000~km) than quiet-Sun mottles. The fibrils have been shown to connect areas of opposite magnetic polarity, and are aligned with the local magnetic field. On the other hand, long dark {\em{filaments}} mark lines of magnetic inversion. They can be found winding throughout active regions, often with one end close to a sunspot. An active region starts as a brightening in the network mottles, followed by plage filling in the network cell. Sunspots and flares follow within a few days. Newly emerging bipolar regions are connected by low-lying arch filaments. The arch filaments bring up the denser material from the lower atmosphere. At the ends of these loops the material is pulled back down, due to gravity. This is viewed as small bright {\em{Ellerman bombs}} which show up in the wing of {\ha} (with the rapid changes associated with quiet and active region chromospheric fine structure it is important to remember many of the structures will be Doppler shifted to the wings of absorption lines). Shearing and twisting of flux tubes in and around active regions also sets up currents along field lines. On a larger scale, the differential rotation of the Sun induces an extended current system. A third system of currents is due to the large conductivity of the atmosphere such that field structures cannot relax to a current free state. 

\newpage
\begin{figure}[t]
\begin{center}
\epsfig{figure=ar.eps,width=6in}
\caption[Solar flares, CMEs, and aurora]{Top row\footnotemark[1]:{\soho} {\mdi} magnetogram and continuum image of active region NOAA 10486 - the magnetic mixing around (350,-350) means this region was assigned a $\beta\gamma\delta$ classification. Middle left\footnotemark[2]: {\goes} X-ray flux. The large X-class (X17.2) flare on 28 Oct 2003 came from NOAA 10486. Middle right \footnotemark[3]:{\soho} {\lasco}~C2 image of the CME associated with the X17.2 flare. Bottom left\footnotemark[4]: Aurora in Glengormley, N.Ireland as particles from the CME slammed into the earth's atmosphere.}
\label{sw}
\end{center}
\end{figure}
\footnotetext[1]{Images from {\soho} and courtesy of Peter Gallagher. (http://http://beauty.nascom.nasa.gov/arm/)}
\footnotetext[2]{Data from Space Environment Centre. (http://sec.noaa.gov/)}
\footnotetext[3]{{\soho} image. (http://sohowww.nascom.nasa.gov/)}
\footnotetext[4]{Image courtesy of A. Fitzsimmons.}

\newpage
\clearpage
The magnetic field above active regions extends into the corona, where reconnection between twisted field lines can lead to solar flares (Priest \& Forbes 2002), and occasionally to coronal mass ejections (CMEs). When earth-directed these can cause severe damage to satellites, astronauts and power grids, and cause the aurora in the earth's atmosphere. Figure~\ref{sw} shows how the Michelson Doppler Imager ({\mdi}; Scherrer {\etal} 1995) and Large Angle Spectroscopic Coronagraph ({\lasco}; Brueckner {\etal} 1995) on board the Solar and Heliospheric Observatory({\soho}; Fleck, Domingo, \& Poland 1995) can be used to study these explosive events.


\subsection{Chromospheric Network}
\label{chnet}
The chromospheric network is highly co-spatial with the photospheric supergranulation and dynamic over a timescale of hours. Evolution occurs by the appearance of new field in the centre, migration to the boundaries, further migration along the boundaries and eventual disappearance (Schrijver, Hagenaar, \& Title 1997; Hagenaar {\etal} 1999). The cell is dominated the appearance of many small, upflowing centres of magnetic field, known as the internetwork (Section~\ref{magstr}). Lites, Rutten, \& Kalkofen (1993) point out that the network viewed is not a mosaic of regular cells, instead it is a system of irregular patterns without actual well-defined insides. As such, the use of the terms `intranetwork', along with `cell boundary' and `cell interior', are not appropriate. However the use of these terms is still in common practice. On the granulation scale, granular buffeting moves these magnetic regions in a random walk. Across the supergranules the flow patterns have a longer lifetime, hence the magnetic regions are eventually collected in the network and move along it. Along the network these regions may interact; opposite polarities may meet and reconnect, and so vanish; some may split into two or more regions (fragmentation); two regions of the same polarity may meet and merge. 

The precise co-spatiality with the photospheric magnetic network can be used to find the polarity of the network regions in the chromosphere. They tend to be mixed in the quiet Sun and unipolar at the poles, near active regions, or near previous active regions. The K index (the strength of the central K$_3$ line in a 1~{\AA} band) is a measure of the intensity of regions in the chromosphere. In quiet regions the K index increases linearly with magnetic flux density. In the network regions (highly magnetized) the K index increases with magnetic flux density with an index less than unity. This is an indication of these regions spreading out horizontally with increasing height. (Figure~\ref{magdia}). Eventually the field lines form a canopy over internetwork regions at a height of 2000~km (Section~\ref{mag}). 

\section{The Chromospheric Heating Problem}
\label{hm}

The increase in temperature in the chromosphere, transition region and corona must be explained by some non-radiative form of energy. If radiation was the only energy being transported through the atmosphere, the temperature should decrease further out from the core, as more energy is escaping. An extra heating mechanism must exist, which will provide energy for atoms to become excited and decay. This process of absorption and decay acts as a thermostat for the lower chromosphere, and is mainly provided by hydrogen atoms (providing the red chromosphere during eclipse totality in {\ha}). When the supply of hydrogen atoms runs out the temperature increases sharply, marking the transition zone. A further thermostat is provided in the corona by the large number of highly ionized atoms. This provides a second temperature plateau. 

One of the most controversial areas in solar physics at the moment is the necessity of the existence of a temperature minimum at all (Figure~\ref{models}). The rise in temperature around 500~km is a direct result of the VAL model (Vernazza {\etal} 1981) and later in the FAL model (Fontenla, Avrett, \& Loeser 1993) to explain the chromospheric emission in EUV lines and was generally accepted for many years. Ulmschneider (1970) suggested short period ($\sim$~30~s) waves shocking in the chromosphere to explain this, but no observation evidence could be found. In contrast, previous stellar-like classical radiative equilibrium (RE) models (e.g., Gustafsson \& Jorgensen 1994), and the HOLMUL model (Holweger \& M\"{u}ller 1974) showed no need for a temperature rise. 

Modelling of internetwork grains (Carlsson \& Stein 1992; 1995; 1997) suggested the temperature rise was purely a inversion technique artifact. They suggested that acoustic shocks in the internetwork may intermittently heat the chromosphere, without significantly increasing the average temperature. However, at UV wavelengths, they may be sufficiently bright to as to require a temperature rise when inverted as in the VAL and FAL models. The idea of a cool atmosphere with intermittent shocks also agrees with models derived from the CO line formation (e.g., Ayres 1981). Other authors (e.g., Kalkofen, Ulmschneider, \& Avrett 1999) question the validity of this model.  

\begin{figure}[t]
\begin{center}
\epsfig{figure=models.eps,width=5in}
\caption[Various models of the lower solar atmosphere]{Depiction of temperature stratification of various models of the lower solar atmosphere. Both the VAL and FAL models require a rise in temperature to account for excess EUV emission in the internetwork (IN). The HOLMUG, RE and CO models suggest a cool atmosphere. The network (NW) still requires a (deeper) temperature rise. (Rutten 1998)}
\label{models}
\end{center}
\end{figure}

\subsection{Network Heating}
Although the Carlsson \& Stein model explains the internetwork grains, it is still apparent the network requires an extra heating mechanism. Proposed heating mechanisms can broadly be divided into two categories, namely {\em alternating current} (AC) and {\em direct current} (DC). Direct current (DC) mechanisms involve current sheets with timescales longer than the dissipation time, whereby the energy stored in the magnetic field is directly dissipated. DC mechanisms can be further subdivided into those which dissipate energy by field aligned currents (Spicer 1991) and those where currents are perpendicular to the field (e.g., nanoflares - Parker 1988). AC mechanisms involve waves which are guided by the magnetic field and dissipated in timescales comparable to the period. These have three common factors, namely the generation, propagation and dissipation of waves. The various modes of waves and how they may influence the plasma through which they propagate are described in the next chapter (also see reviews by Rutten \& Uitenbroek 1991; Rutten 1999). 

\section{Outline of this Thesis}
The aim of the work for this thesis was to use multi-wavelength narrowband images of the chromosphere to search for the possible oscillatory signals of AC heating mechanisms. There are several reasons for specifically studying the chromosphere. From a theoretical perspective, it is the boundary between the interior (dominated by fluid motions and gas pressure) and the magnetically dominated corona. As an introduction to this background theory, Chapter~2 contains a summary of the equations which explain the various modes of waves possible in a stratified, magnetised plasma such as the chromosphere. A brief overview of the fundamental equations is provided, along with a description of wave propagation in homogeneous and inhomogeneous plasmas. 

From an observational aspect, the chromosphere provides several optical Fraunhofer lines, and UV continuum. Chapter~3 contains a description of the experimental set-up used in an observing run at Dunn Solar Telescope / National Solar Observatory, designed to observe the same region of the quiet Sun in as many optical wavelengths as possible, whilst still maintaining a sufficiently high cadence. As the earth's atmosphere absorbs UV continuum, it is necessary to use data from space-based instrument to observe the Sun in this part of the electromagnetic spectrum. Hence Chapter~3 also contains a description of the {\trace} spacecraft, and imaging in the UV.

Chapter~4 discusses novel image segmentation and statistical analysis techniques used to study oscillations in the chromospheric network imaged in {\cak}. Specifically the `contour and contrast' technique is used to separate oscillations in network bright points from those of other solar (e.g., internetwork), or of non-solar (e.g., earth's atmosphere) origin. This work is extended to search for oscillations at several heights in the chromosphere in Chapter~5. Wavelet analysis routines are used to search for correlated oscillations across all frequencies, which may result from waves travelling through the chromosphere. This is used to test several chromospheric heating theories. 

Chapter~6 uses an automated wavelet analysis technique to search for intensity oscillations in UV passband data. This extends previous Fourier analysis of this work into the time-localised domain. Differing oscillatory signals in the network and the internetwork at various atmospheric heights are found to be indicative of differing wave modes and heating mechanisms in these two regions. The recurrence of oscillations of various periodicities and lifetimes are discussed in terms of previous work.

Finally, Chapter~7 summarises the conclusions of this thesis, and suggests future directions of this project. 

%Longitudinal (e.g. sound waves) cannot directly heat the surrounding gas, instead they cause the gas atoms to vibrate. As it moves up through the stratified atmosphere the gas density, $\rho$ decreases and the wave amplitude, V, increases so $\rho$V$^2$ remains constant. In effect the sinusoidal form of the original acoustic wave is distorted such that compressed regions travel faster than rarefied regions. Eventually when the amplitude reaches the sound velocity, a shock front is formed (Figure \ref{magdia}). This shock front can heat the surrounding gas and this form of heating is found to be efficient in the lower chromosphere. 


%The best candidate for this heating mechanism is upwardly propagating waves, the best known of which is the five minute period wave, as discovered by helioseismology. This periodicity is created by sound waves (where pressure is the dominant restoring force), travelling inside cavities in the interior. However a period leading to a velocity smaller than the velocity of sound in the plasma, the acoustic velocity, is necessary for propagation through the temperature minimum region.

%\subsection{Wave modes}
%\label{Wave modes}
%Sound waves cannot directly heat the surrounding gas, instead they cause the gas atoms to vibrate. As it moves up through the atmosphere the gas density, $\rho$ decreases and the wave amplitude, V, increases so $\rho$V$^2$ remains constant. In effect the sinusoidal form of the original acoustic wave is distorted such that compressed regions travel faster than rarefied regions. Eventually when the amplitude reaches the sound velocity, a shock front is formed (Figure \ref{magdia}). This shock front can heat the surrounding gas and this form of heating is found to be efficient in the lower chromosphere. 

%\subsection{Magnetohydrodynamics}
%\label{Magnetohydrodynamics}
%Higher up, these acoustic waves are evanescent, and the network field plays an increasingly important role. The magnetic field lines frozen into the gas are subject to wave motions, creating MHD waves (Section \ref{magstr}). MHD waves can be divided into two main types, \alf\ waves and magneto-acoustic waves. \alf\ waves arise from the fact that field lines, when displaced sideways, tend to reform to their original state. This sets up an oscillation which can travel up the field lines at the \alf\ speed. As the field lines are frozen into the plasma, these oscillations also make the surrounding plasma vibrate. For a imperfectively conducting plasma, the wave dissipates with height, heating the gas. \alf\ waves are not damped at the low chromosphere level if they travel up filigree regions. Magneto-acoustic waves are \alf\ waves which do not propagate in a perfect vertical direction, and hence have an acoustic component perpendicular to the \alf\ motion. Slow mode magneto-acoustic waves have a dominent acoustic component and tend towards the acoustic velocity. Fast mode waves have an initial displacement almost entirely perpendicular to \alf\ waves, and have a smaller acoustic component tending to the \alf\ velocity. The short periodicity needed for these mechanisms, which extend through the upper chromosphere to the corona, has recently been observed by Mckenzie \& Mullan$^{\cite{mck97}}$ and Williams {\em{\etal}}$^{\cite{wil00}}$. A further possible coronal heating mechanism is the release of energy following magnetic reconnection in flares and nano-flares$^{\cite{par88}}$
 
%\subsection{Oscillations}
%\label{osc}
%Solar oscillations refer to any periodic or quasi-periodic oscillations found in the atmosphere, hence including both standing and propagating waves, of which the five minute oscillation, discussed in Section \ref{hm}, is the best known standing wave. The oscillatory behaviour of chromospheric lines is markedly different in the network and internetwork regions. In the internetwork calcium emission is almost always absent. When it does appear, it is most easily viewed in the violet K$_2$, often preceded by a brightening in the K$_3$ wing. This cycle is often repeated several times with a three minute period. These quasi-periodic bright grains (Section \ref{cfs}) lead to the three minute oscillation found throughout the internetwork. These were originally linked to the presence of small flux tubes, but alignment was never proved. It is now known they are formed as a result of the formation of shock waves$^{\cite{eaa}}$ (Section \ref{hm}, Figure \ref{magdia}). The K$_2$ violet peak is only possible if a strong velocity gradient co-exists with the shock wave formation. This three minute oscillation is very close to the acoustic cutoff period (200 seconds in the chromosphere). Waves with a period close to the acoustic cutoff can be excited in various ways. The wakes of long period evanescent waves, merging of shorter period waves, short period pulses, and the tendency of longer period waves to fall off with height all tend to produce a three minute oscillation. Skartlien {\em{\etal}} $^{\cite{ska00}}$ show that small collapsing granules, where upflow turns to downflow in a timescale less than three minutes, may provide the excitation mechanism of these bright grains. The granular collapse could be due to mesogranular downflow, or squeezing by surrounding expanding granules. The reversal of upflow to downflow creates a rarefaction. This changes the granulation horizontal flow from outwards to inwards, producing a compression to follow the rarefaction.

%Some questions remain unanswered however. Unexpectedly some observations show that velocities inferred from different lines are in phase. This suggests a standing wave, in conflict with the propagating waves found in Ca observations. A possible chromospheric cavity could be formed between the photospheric temperature drop off and transition region temperature rise. Also, a second type of bright grain is found at higher temperature which, although fewer in number, may be associated with the internetwork.$^{\cite{wor99}}$

%The network is dominated by waves with much longer periods (eight to twenty minutes). Unlike the internetwork oscillations, which are well correlated with the photospheric five minute oscillation, these longer oscillations show no such correlation. A period of around six to seven minutes seems to exist throughout the atmosphere which could be due to pseudo-periodic mottle behaviour. A five minute period has also been found in the network, the origins of which are unclear. It may be a purely chromospheric manifestations of waves,$^{\cite{lit93}}$ or perhaps of photospheric origin. Example theories of the latter are: a stochastic buffering of magnetic flux tubes by granulation motion at the photosphere$^{\cite{kne85}}$; or upwardly propagating, internetwork, magneto-gravity waves falling back down in the network$^{\cite{lit93}}$.

%\section{Conclusions}
%Until recently almost all observations of the Sun were taken in the the visible part of the electromagnetic spectrum, with the earth's atmosphere acting as an effective blockade to other wavelengths. In the last couple of decades, the emphasis has moved onto the X-ray, UV and EUV regions with the successes of YOHKOH, SOHO and TRACE. However, earth-based optical observations still have an important role to play in solar physics. Ground based observatories are much cheaper to build and maintain, with a much longer lifetime than satellites. The telemetry rate is much quicker, neccessary for high cadence, high resolution images. Also, improvements in computer hardware and software have removed many of the earth based problems like atmospheric seeing. The developing role of adaptive optics in astronomy is particularly useful for solar physics, where a reference point is easy to obtain. In the past few years, questions like the origins of bright grains and coronal heating mechanisms$^{\cite{wil00}}$ have been best investigated using ground based investigations. Many important unanswered questions like the nature of the photospheric and chromospheric fine structure, the heating of the chromopshere and the role of small scale internetwork magnetic fields are unanswered and ground based optical observations have an important role to play in these future investigations. 
    
