Which of these is NOT a good estimate of the age of the universe?

* Decay times of 238U and 232Th in metal-poor stars.

* Isochrone fits for globular clusters.

* Ages of the faintest white dwarfs.

* Ages of the hottest main-sequence stars in distant galaxies.

To determine which of these options is NOT a good estimate of the age of the universe, let's go through each one and understand how they are used to estimate the age:

1. Decay times of 238U and 232Th in metal-poor stars: This method involves measuring the abundance of uranium-238 and thorium-232 isotopes in metal-poor stars and comparing it to their decay rates. By calculating the time it would take for the observed abundance of these isotopes to decay, scientists can approximate the age of the stars and, by extension, the universe.

2. Isochrone fits for globular clusters: Globular clusters are groups of tightly bound stars that have a similar age and composition. By plotting the properties of stars in a globular cluster on a graph called a color-magnitude diagram and fitting theoretical isochrones (curves of star evolution) to the observed data, scientists can estimate the age of the globular cluster, which provides a lower limit on the age of the universe.

3. Ages of the faintest white dwarfs: White dwarfs are the remnants of low-mass stars that have exhausted their nuclear fuel. By studying the faintest white dwarfs and analyzing their cooling rates, researchers can estimate their age. Since white dwarfs take a long time to cool down, the age of the faintest white dwarfs provides an upper limit on the age of the universe.

4. Ages of the hottest main-sequence stars in distant galaxies: Main-sequence stars are in the phase of their lives where they are steadily burning hydrogen fuel and are considered relatively young. By measuring the temperature and luminosity of the hottest main-sequence stars in distant galaxies and comparing them to stellar evolution models, scientists can estimate their ages. These ages give an indication of the age of the universe, assuming that the stars formed shortly after the universe's inception.

From this analysis, it can be concluded that the answer to the question is: *Decay times of 238U and 232Th in metal-poor stars* is NOT a good estimate of the age of the universe. This is because the decay rates of uranium-238 and thorium-232 in stars provide information about the ages of the stars themselves, but not necessarily about the overall age of the universe.