Question

If a galaxy's overall mass-to-light ratio is 100 solar masses per solar luminosity, and its stars account for only 5 solar masses per solar luminosity, how much of the galaxy's mass must be dark matter?

A) 5%
B) 10%
C) 95%
D) 90%

Answer 1

95% of the galaxy's mass must be dark matter, as the overall mass-to-light ratio of the galaxy is 100 and the stars account for only a ratio of 5.

Step-by-step explanation:

If a galaxy's overall mass-to-light ratio is 100 solar masses per solar luminosity, and its stars account for only 5 solar masses per solar luminosity, we can determine the proportion of mass that must be dark matter.

The mass-to-light ratio due to stars is 5, so subtracting this from the total mass-to-light ratio of 100 leaves us with 95 solar masses per solar luminosity that must be attributed to dark matter. To find the percentage of the galaxy's mass that is dark matter, we divide the mass attributed to dark matter (95) by the total mass-to-light ratio (100) and multiply by 100 percent:

(95 / 100) × 100% = 95%

Therefore, 95% of the galaxy's mass must be dark matter, which makes option C the correct answer.