{"knowledge_schema": {"broad_category": "Astronomy \u2192 Stellar Properties \u2192 Luminosity", "refinement": "This problem involves understanding the relationship between a star's temperature, radius, and luminosity, particularly using the Stefan-Boltzmann Law.", "specific_scope": "The focus is on comparing the luminosity of different stars based on their temperature and radius, given that they all have the same apparent magnitude.", "goal": "Identify which star has the highest luminosity based on the provided parameters."}, "summary": "This problem is centered on the concept of luminosity in stars, which is influenced by both temperature and radius. According to the Stefan-Boltzmann Law, luminosity increases with the fourth power of temperature and the square of the radius. The task is to compare the luminosity of four different stars with varying temperatures and radii to determine which one has the highest luminosity, given that they all have the same apparent magnitude. The correct answer is the star with a temperature of 6000 K and a radius of 2 solar radii, as it has the highest combination of temperature and radius, leading to greater luminosity."}