Radiative transfer of star formation and destruction regions

While star formation and destruction may lie at the opposite ends of a star's life cycle, they display remarkable similarities. Both star forming regions and pre-planetary nebulae can be detected by observing molecular transitions in the millimetre/submillimetre regime. During specific phases they also present us with similar morphologies, with a central disk or waist and bipolar outflow, embedded within a larger cloud of gas and dust. This thesis focuses on the development and use of a pipeline to model such sources, as observed with high resolution interferometers, in order to understand the physics common to both. In the past decade ALMA has revolutionized millimetre/submillimetre astronomy, initiated by the discovery of rings in the protoplanetary disk of HL Tau. More recently, it has been used to probe the chemistry of protoplanetary disks down to a scale of just $10~{\rm au}$ in an effort to better understand the conditions necessary for planet formation. It can also be used to answer other open questions, such as how bipolar jets are launched in protostellar cores by observing their fine inner structure. ALMA can also be employed to address questions regarding pre-planetary nebulae (PPNe) and planetary nebulae (PNe), such as why PNe are observed with a lower mass than the expected mass ejected from stars during the formation of said PNe, or even why an unexpectedly large fraction of non-spherical PNe are observed. However, to continue capitalizing on these complex data, software must be developed to simplify the modelling process and match newly observed species. The pipeline presented here combines the 3-D morpho-kinematic capabilities of {\sc shape} to create physical models, the 3-D non-LTE radiative transfer code {\sc mollie} to simulate the emission of light and the ability of {\sc casa} to reproduce the complex effects introduced by the use of interferometers. The potential of {\sc mollie} itself has been expanded in this thesis by the addition of the HCN isotopologues H$^{13}$CN and DCN, as well as the molecule SO to the catalog of species whose emission it can simulate. The 3-D modelling environment of {\sc shape} is perfectly suited to drawing the shape and defining the physical properties of the many substructures observed by ALMA. The addition of these new species in {\sc mollie} will allow a larger fraction of ALMA data to be modelled to better define the physics for the areas of interest that could answer the open questions. The pipeline is used to model both a star formation and destruction source, L1527 and the Boomerang Nebula, respectively. Previously, the full line profile of C$^{18}$O (2--1) ALMA data of L1527 had only been modelled with an outer radius of $1,000~{\rm au}$. Here, all of the matter that is responsible for the P-Cygni profile is included by extending the radius to $6,200~{\rm au}$ to better match single dish observations. This results in a disk with a density profile that is over an order of magnitude lower, which could slow the formation of planets within it. The bipolar outflow is modelled for the first time with ALMA C$^{18}$O (2--1) data. While it matches previous models of CS (5--4), the sensitivity of the data is too low for strong conclusions. Data of all three observed SO lines, SO (6$_5$--5$_4$), SO (7$_6$--6$_5$) and SO (7$_8$--6$_7$), are modelled together for the first time. Previously, only the SO (7$_6$--6$_5$) and SO (7$_8$--6$_7$) had been modelled together. The results, a thin SO ring with a thickness of $15~{\rm au}$ and temperature of $32~{\rm K}$, favour the previous lone modelling of SO (6$_5$--5$_4$). As the SO (7$_6$--6$_5$) and SO (7$_8$--6$_7$) lines both involve the $J = 7$ to $J = 6$ transition, they are not independent of each other and therefore do not provide as strong a constraint if they are just modelled together. It is advised that lines with different $J$ levels are selected for future modelling and observations of multiple lines of SO. Since the surprising discovery, in 1997, that the Boomerang Nebula is colder than the cosmic microwave background (CMB), it remains a unique object. CO (1--0), CO (2--1), CO (3--2) and $^{13}$CO (3--2) ALMA data of the Boomerang Nebula are modelled to create a complete model. Previously, the ultra cool shell of the nebula, composed of H$_2$, was modelled as a two stage adiabatic explosion. However, an analytic solution for a diatomic equation of state, required for H$_2$, does not exist, so a monatomic equation of state was assumed. Here a new, numerical, approach is employed to obtain the more accurate diatomic solution. The result is that a monatomic solution will cool the shell to a temperature that is three orders of magnitude lower than the `best fitting' proper diatomic model. A much shorter expansion time-scale of $\sim100~{\rm days}$ and higher mass of $5~{\rm M_{\astrosun}}$, compared to the previous values of $5.8$ to $17.6~{\rm yrs}$ and $\ge 3.3~{\rm M_{\astrosun}}$, respectively. The shorter time-scale matches previous modelling of common envelope merger, the source of the shell. The high mass may explain why a similar absorption signal is not detected in other sources, such a mass is not common. Alternatively, the bias of interferometers that will filter out the shell without support, the shell of the Boomerang having a less complex chemical composition than other shells, allowing it to cool more efficiently, or because the shell heats back up quickly. Regardless of the reason why the shell of the Boomerang Nebula is observed, it is concluded that all other PNe and PPNe have a similar, as of yet unobserved, shell that would account for the lower than expected observed mass of PNe