title: Millimetre-continuum diagnostics and non-LTE radiative transfer modelling of solar prominences
Creators: name: Rodger, Andrew
Publisher: name: University of Glasgow
Year: 2019
Subjects: subject: Solar physics, solar prominences, radiative transfer, radio astronomy, Millimetre continuum.

description: With the advent of solar observing capability the Atacama Large Millimeter/sub-millimeter Array (ALMA), solar physicists now have access to high spatial resolution imaging of the millimetre-continuum emission from the solar atmosphere for the first time. The radiation in the wavelength range of ALMA is formed primarily through collisional processes, which, along with lying within the Rayleigh-Jeans Limit, results in a linear relationship between the brightness temperature and the electron temperature of the emitting plasma. Therefore, it is expected that millimetre observations have the potential for strong temperature diagnostics as well as other internal plasma parameters such as the emission measure. However, until ALMA the usefulness of millimetre-continuum observations has been hampered by low spatial resolutions. In this thesis I address the potential for the plasma diagnostics of solar prominences using ALMA. Solar prominences are an extreme example of natural magnetic confinement, where relatively high density, low temperature plasma is suspended within the sparse, extremely high temperature energetic solar corona. The term solar prominence generally refers to these structures when viewed off the solar limb, however, they are also observable, often as dark absorption features known as filaments, against the disk. These structures are maintained for long periods of time ranging from days to weeks through detailed energy balance. However, once this balance is broken solar prominences can erupt violently leading to dramatic events, often including Coronal Mass Ejections (CMEs). Understanding the formation, structure and energy balance of solar prominences is therefore an integral part in understanding solar atmospheric activity as a whole. To understand the formation of the millimetre-continuum from solar prominences I used the 2D non-Local Thermodynamic Equilibrium (non-LTE) cylindrical prominence code C2D2E of Gouttebroze &amp; Labrosse (2009). This code considers a plasma consisting of both hydrogen and helium, with their ionization equilibrium. The use of a non-LTE model is important because, although the millimetre-continuum is formed from LTE processes, the ionization populations of the hydrogen and helium will be determined by non-LTE processes caused by incident ionizing and energising UV radiation. Considering sets of both isothermal–isobaric and multi-thermal prominence models including an ad-hoc prominence-to-corona transition region (PCTR) I calculated the emergent brightness temperature expected from solar prominences using the output from the C2D2E models. The results from the isothermal–isobaric models found that, whilst the optical thickness of a given millimetre wavelength is approximately &gt; 4 - 5, the brightness temperature from the prominence at said wavelength equaled the constant electron temperature of the particular model. For the multi-thermal models it was found that the brightness temperature, whilst the plasma was optically thick, was representative of the electron temperature of a given formation layer within the particular line of sight (LOS). The formation layer was defined as the region/regions of each LOS with 70% the maximum contribution function for that LOS. When the material is optically thin the emergent brightness temperature is not representative of any unique layer within the prominence structure, but rather an integration across the entire temperature distribution within the LOS, with this integration also being affected by the optical thickness of the particular LOS. Therefore, in order to make assertions into the temperature structure from a solar prominence using millimetre-continuum diagnostics it is important to first have some understanding of the optical thickness regime of the emitting plasma. From the multithermal prominence models, of radius 1Mm, it was found that ALMA Band 3 produced a maximum optical thickness greater than 1 for pressures approximately &gt; 0.1 dyn/cm^2, whilst Band 6 required pressures approximately &gt; 0.5 dyn/cm^2. The millimetre-continuum prominence code was then altered to simulate the emergent brightness temperature from an on-disk filament observation. Again both isothermal–isobaric and multi-thermal PCTR filament models were considered, however, with the inclusion of various different background brightness temperatures from the solar disk. Using these models the visibility of filaments at ALMA Bands 3 and 6 is investigated by analysing their contrast against the background brightness temperature, with the inclusion of a discussion into how this may change with the inclusion of a “coronal cavity” above the overlying filament structure. A possible method to estimate the optical thickness of a plasma is by using coordinated observation of the same structure but in a different wavelength regime. I investigate correlations between the millimetre-continuum optical thickness and the integrated intensity from the important Lyman and Balmer lines of neutral hydrogen as well as the He I D3 line of neutral helium. The most important factor in determining the optical thickness of the millimetre-continuum is the charge squared weighted electron–ion emission measure. In this work a clear power-law relationship is found between the electron–proton emission measure and the integrated intensity of the Balmer lines, and between the electron–first ionized helium emission measure for the integrated intensity of the He I D3 line for isothermal–isobaric models. The brightness temperature of the millimetre–continuum is also found to produce a similar result to the colour temperature of the Lyman continuum when both are formed in near to overlapping formation regions. Other methods to determine the optical thickness of the millimetre-continuum investigated in this thesis include using analysis of the millimetre-continuum spectra. A relationship between the gradient of the logarithmic brightness temperature spectrum and the optical thickness of the millimetre-continuum at band-centre is derived. This relationship is then tested using sets of isothermal and multi-thermal 2D prominence models. A case study into using the gradient of the brightness temperature enhancement observed in a sub-band, science verification ALMA observation of an on-disk plasmoid eruption is presented. The method proves to be a strong candidate for estimating the optical thickness of the millimetre-continuum. However, it relies on a good understanding of the uncertainty into the brightness temperature measurement as well as the gradient of the background brightness temperature spectrum, which, due to the current state of understanding into the uncertainty of absolute brightness temperature measurements with ALMA, needed to be estimated in this study. In the final chapter of my thesis I present some preliminary results from the first high resolution interferometric observation of a solar prominence with ALMA. Coordinated observation with H alpha spectral imaging from the MSDP telescope in Białkow is used to estimate the optical thickness regime of prominence in the millimetre-continuum. A discussion into the morphology of the brightness temperature images of the prominence is provided as well as the correlations found between the brightness temperature distribution and the intensities from co-aligned images in each AIA band.