Stellar evolution is the life cycle that a star will take as it evolves over time. The different evolutionary stages of a star is heavily dependent on the mass of the star. For my research, I look at stars between 0.8 to 8 solar masses. These stars will start of as main sequence stars and will make their way to a white dwarf where the star will continue to cool off until it no longer emits light or heat. Within the stellar evolutionary cycle, I am specifically interested in the planetary nebula phase and the asymptotic giant branch or AGB phase. 

The AGB phase is the phase right before planetary nebula. You can think of an AGB star as a specific type of red giant.  Due to their stellar winds, AGB stars will lose 50 to 70 percent of their mass. These stars are also variable stars. Meaning, the star has a cycle of expansions and contractions in increments of time known as pulsations. The most interesting thing about the AGB stars are the maser emissions that are found in the atmosphere. Masers are very similar to lasers. Lasers stands for light amplification by stimulated emission of radiation. which is fundamentally a laser but in microwaves instead of visible light. SiO, H2O, and OH masers are fairly common in AGB stars and have unique characteristics.  

The planetary nebula or PN phase is the last phase before the star becomes a white dwarf. In this phase, the star has ejected the majority of its mass and there isn't enough fusion reactions in the core to overcome the effects of gravity. Therefore the core will condense and increase in temperature. The core becomes hot enough to ionize the gas and dust around it, BUT the interesting thing is that there are clumps of molecular hydrogen in these ionized regions of the PNe. More defined clumps are called cometary knots, based on their comet like shape. Trivially, they shouldn't be there but somehow these molecular "clumps" are optically thick enough to survive harsh, ionized regions. 

The coefficient of determination (R^2) is a statistical measure used to describe the strength of a relationship between two variables. It represents the proportion of variation in one variable that is explained by its linear relationship with another variable. R^2 ranges from 0 to 1, with values closer to 1 indicating a stronger linear relationship.   

The p-value is a statistical measure used to evaluate the significance of an observed relationship. It represents the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. Smaller p-values provide stronger evidence against the null hypothesis

Principal Component Analysis (PCA) is a statistical technique used to reduce the dimensionality of a dataset while retaining as much of the original variation as possible. It transforms a set of correlated variables into new, uncorrelated variables called principal components (PCs). Each principal component represents a different amount of the total variance, with the first component (PC1) explaining the greatest amount, followed by PC2, PC3, and so on.