Asteroseismology and Stellar Seismology primarily rely on measuring the variations in stellar brightness, known as stellar pulsations, to infer information about the star's internal structure and dynamics.

Asteroseismology studies various types of stellar pulsations, including radial pulsations (where the star expands and contracts uniformly), non-radial pulsations (where different parts of the star pulsate in different ways), and mixed-mode pulsations (a combination of radial and non-radial pulsations).

Analyzing stellar pulsations allows astronomers to determine the star's mass and radius, its age and evolutionary stage, and its internal structure and composition, including the distribution of density, temperature, and chemical elements within the star.

Asteroseismology is primarily applied to main-sequence stars, which are stars that are fusing hydrogen in their cores and are in a stable phase of their evolution.

The helioseismic technique involves studying the Sun's oscillations to probe its internal structure and dynamics, providing valuable insights into the Sun's core, convection zone, and outer layers.

Asteroseismic observations provide valuable constraints on stellar models and theories, allowing astronomers to test and refine our understanding of stellar evolution, including the processes of star formation, nucleosynthesis, and stellar death.

The Kepler space mission was specifically designed for asteroseismic studies, with the primary goal of detecting exoplanets by observing stellar brightness variations caused by planetary transits. However, Kepler's data also provided a wealth of information about stellar pulsations and asteroseismology.

Helioseismology is the specific branch of Asteroseismology that focuses on studying the Sun's oscillations and internal structure.

Stellar pulsations typically occur in the microhertz (µHz) to millihertz (mHz) frequency range, which corresponds to periods of hours to days.

The fundamental mode of stellar pulsation is the mode with the longest period and the largest amplitude. It corresponds to the star's overall expansion and contraction.

The pulsation frequency is proportional to the square root of the star's density. This relationship is known as the pulsation equation and is a fundamental tool in Asteroseismology.

The presence of noise and contamination in the data is a major challenge in interpreting asteroseismic data. This can arise from various sources, such as instrumental noise, stellar activity, and background stars.

Asteroseismic observations can help in detecting exoplanets by measuring the variations in stellar brightness caused by planetary transits. When a planet passes in front of its host star, it blocks a small amount of starlight, causing a periodic dimming of the star's brightness.

The future of Asteroseismology and Stellar Seismology lies in continued observations with existing and upcoming space missions, the development of new theoretical models and data analysis techniques, and the application of asteroseismic techniques to study a wider range of stars, including evolved stars, binary stars, and variable stars.