Final answer:
The statement that the Sun has a mass-to-light ratio of 1 by definition is false; the mass-to-light ratio is a comparative value. The luminosity of a star with 1/12 the mass of the Sun would be calculated using the mass-luminosity relationship and would be (1/12)^3.9 times that of the Sun.
Step-by-step explanation:
Regarding the statement, "By definition, our Sun has a mass-to-light ratio of 1 solar mass per solar luminosity," the answer is False. The definition of the Sun's mass-to-light ratio does not assume a value of 1. In fact, the mass-to-light ratio is used to compare the mass of other objects, like stars and galaxies, to their luminosity in solar units. When it comes to the least massive true star, which is 1/12 the mass of the Sun, its luminosity can be calculated using the mass-luminosity relationship, which says that luminosity is proportional to the mass raised to the power of approximately 3.9. Therefore, for a star with a mass of 1/12 solar masses, its luminosity would be (1/12)^3.9 times that of the Sun's luminosity.