As astronomers extend their distance ladder beyond \(30 \mathrm{Mpc}\) they change their measuring standard from Cepheid variable stars to Type Ia supernovae. Why is this change necessary? a. Type Ia supernovae are more luminous than Cepheid variables. b. Type Ia supernovae are less luminous than Cepheid variables. c. Type Ia supernovae vary more slowly than do Cepheid variables. d. Type Ia supernovae vary more quickly than do Cepheid variables.

Cepheid variables play a crucial role in measuring distances when it comes to nearby galaxies. These stars are unique because they have a predictable pattern of brightness fluctuations over time. The cycle of their brightness variation is closely tied to their intrinsic luminosity, which allows astronomers to determine their absolute magnitude. Once we know the absolute magnitude, we can compare it with the apparent magnitude observed from Earth and use the inverse-square law of light to calculate the distance to the Cepheid variable. This method helps determine distances within our own galaxy and to galaxies not far from the Milky Way.

Type Ia supernovae are extremely important for measuring astronomical distances well beyond our galaxy. These supernovae occur in binary systems where a white dwarf star accumulates material from its companion star until it reaches a critical mass and undergoes a catastrophic explosion. The key property that makes Type Ia supernovae valuable as standard candles is their consistent peak luminosity. They are about five billion times brighter than the Sun at their peak, which makes them visible across vast cosmological distances. This extraordinary luminosity allows astronomers to use them for distance measurements extending up to several hundred megaparsecs (Mpc). Historically, Type Ia supernovae have proven instrumental in uncovering the expansion of the universe and studying its rate of acceleration.

Luminosity is a fundamental concept in astronomy; it refers to the total amount of energy a star or another astronomical object emits per unit of time. Unlike apparent brightness, which varies depending on an object's distance from the observer, luminosity is an intrinsic property. Understanding luminosity helps astronomers determine distances and physical characteristics of celestial bodies. For standard candles like Cepheid variables and Type Ia supernovae, their known luminosity allows us to gauge how far away these objects are. By comparing the luminosity to the observed brightness using the inverse-square law, distances across the universe can be precisely calculated. This process is a cornerstone of the cosmic distance ladder, a series of methods by which astronomers measure distances to objects at different scales within our universe.