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Chapter 10: Problem 11

Which is more massive, a red main-sequence star or a blue mainsequence star? Which has the greater radius? Explain your answers.

Short Answer

Expert verified
In summary, a blue main-sequence star is both more massive and has a greater radius than a red main-sequence star. This is due to the fact that blue main-sequence stars have higher temperatures and luminosities, leading to increased mass. Additionally, the difference in luminosity outweighs the difference in temperature, resulting in a larger radius for blue main-sequence stars.

Step by step solution

01

Understanding Red and Blue Main-Sequence Stars

Red main-sequence stars are cooler and smaller than blue main-sequence stars. They mainly fuse hydrogen into helium in their cores, producing lower amounts of energy than more massive stars. Blue main-sequence stars, on the other hand, are hotter and larger, also fusing hydrogen into helium in their cores but doing so at a faster rate due to their larger mass, producing more energy as a result.
02

Comparing Mass

To know which is more massive, we need to understand that the mass of a star correlates with its luminosity (amount of energy it emits per unit of time) according to the Mass-Luminosity relation: \[L \propto M^3\] L is the star's Luminosity and M is its Mass. The more massive a star is, the more luminous it will be. Because blue main-sequence stars are hotter and more luminous than red main-sequence stars, it is clear that blue main-sequence stars have greater mass.
03

Comparing Radius

To know which has the greater radius, we can use the radius-luminosity-temperature relation: \[\frac{R}{R_\odot}=\left(\frac{L}{L_\odot}\right)^{1/2}\left(\frac{T_\odot}{T}\right)\] Where \(R\) is the star's radius, \(T\) is its temperature, and subscript \(\odot\) denotes the values for the Sun. Since blue main-sequence stars are more luminous than red main-sequence stars, they will have a greater radius if their temperatures (expressed in Kelvin) are not significantly higher. Blue main-sequence stars have a higher temperature than red main-sequence stars, but the difference in temperature is not enough to offset the difference in luminosity, thus blue main-sequence stars have a greater radius.
04

Conclusion

In conclusion, as a blue main-sequence star is more massive and has a greater radius than a red main-sequence star. The blue main-sequence star's higher temperature and luminosity results in a greater mass, and the difference in luminosity outweighs the difference in temperature also resulting in a larger radius.

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Most popular questions from this chapter

The star Zubenelgenubi (from the Arabic for "scorpion's southern claw" ) has apparent magnitude \(2.75,\) while the star Sulafat (Arabic for "tortoise") has apparent magnitude \(3.25 .\) Which star appears brighter? From this information alone, what can you conclude about the luminosities of these stars? Explain your answer.

If a red star and a blue star both appear equally bright and both are the same distance from Earth, which one has the larger radius? Explain why.

If a red star and a blue star both have the same radius and both are the same distance from Earth, which one looks brighter in the night sky? Explain why.

What is the inverse-square law? Use it to explain why an ordinary lightbulb can appear brighter than a star, even though the lightbulb emits far less light energy per second.

Why is the magnitude scale called a "backward" scale? What is the difference between apparent magnitude and absolute magnitude?
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