Suppose a main-sequence star suddenly started burning hydrogen at a faster rate in its core. How would the star react? Discuss changes in size, temperature, and luminosity.

The process of energy production in a star begins in its core through nuclear fusion. For main-sequence stars, this typically involves the fusion of hydrogen atoms into helium. When a star increases its hydrogen burning rate, often due to changes in its internal conditions or external influences, the rate at which hydrogen nuclei fuse accelerates. This process, known as the stellar fusion rate, greatly influences the star's overall behavior.
Higher fusion rates lead to an increase in the energy output from the core. As more hydrogen nuclei fuse together, more energy is released in the form of light and heat. This increment in energy production is a critical trigger for subsequent changes in the star's characteristics.

Core pressure is the force exerted by the particles in the star's core as they interact and fuse together. When the fusion rate increases, the core of the star produces more energy, causing the pressure to rise due to the heightened activity.
This increased core pressure acts as a counterforce to the gravitational pressure pushing inwards. To maintain stability, the star responds to this imbalance. The core pressure is crucial because it dictates whether the fusion reactions can continue at their heightened rate or whether they will slow down. If the internal pressure becomes too high, the star must adjust in order to return to equilibrium.

In response to the increased core pressure, the outer layers of the star begin to expand. This expansion occurs because the excess energy and pressure from the core need to be balanced, causing the star to swell.
As the star expands, its volume increases, which can have a range of impacts on its overall structure. The expansion is a mechanism for the star to distribute the added pressure and maintain a state of equilibrium. As the star grows larger, the density of the outer layers decreases, contributing further to the star's overall size adjustment.

When the outer layers of a star expand, its surface area increases, which has a direct effect on its surface temperature. As the surface area grows, the energy from the core now needs to spread over a larger area. This causes the surface temperature of the star to decrease.
Think of it like spreading butter over a larger toast: the same amount of butter covers more space but creates a thinner layer. Similarly, the dispersed energy results in a cooler surface. This decrease in temperature doesn't mean the star is producing less energy; it indicates that the same amount of energy is now spread over a larger surface.

Despite the decrease in surface temperature due to expansion, the luminosity, or the total amount of energy the star emits per second, typically increases. This seeming paradox happens because the core's increased energy production outweighs the spread of energy over a larger area.
Luminosity depends on both the temperature and the surface area of the star. So, even if the surface temperature drops, the overall energy output can rise if the increase in surface area is significant, and more energy is being generated in the core. Thus, a star that has increased its fusion rate will shine brighter, which means it becomes more luminous.