Understanding the Relationship
* Luminosity and Temperature: A star's luminosity (total energy output) is directly related to its temperature. The relationship is described by the Stefan-Boltzmann Law:
* L = σAT⁴
* L = Luminosity
* σ = Stefan-Boltzmann constant
* A = Surface area
* T = Temperature
* Flux and Luminosity: Flux is the amount of energy received per unit area. If a star's luminosity increases, its flux at a given distance also increases.
Solving the Problem
1. Flux and Luminosity: Since the flux increased by a factor of 625, the star's luminosity also increased by a factor of 625.
2. Stefan-Boltzmann Law: We know L is proportional to T⁴. If luminosity increased by a factor of 625, we can set up a proportion:
* 625 = (T₂/T₁)^4
3. Solving for Temperature Change:
* (625)^(1/4) = T₂/T₁
* 5 = T₂/T₁
* T₂ = 5T₁
Conclusion
The temperature of the variable star increased by a factor of 5.
Important Note: This is a simplified model. In reality, the temperature change in a variable star is more complex and depends on the type of variability (e.g., pulsating, eruptive) and other factors.
