Astronomy Quiz: Stellar Mass And Lifetime
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Stellar Mass And LifetimeQuestion 1 of 20

In a close binary system, a 10 M☉ star and a 1 M☉ star form at the same time. The 10 M☉ star evolves first, expands, and transfers a significant amount of mass to its 1 M☉ companion. What is the most likely consequence for the companion star's subsequent main-sequence lifetime?

Its lifetime will be greatly extended because it has gained a large amount of fresh hydrogen fuel.
Its lifetime will be significantly shortened because the added mass will increase its core pressure and accelerate its fusion rate.
Its lifetime will be unchanged because its core fusion rate is determined by its original mass, not by mass added to its outer layers.
It will become unstable and immediately evolve off the main sequence, as main-sequence stars cannot gain mass.
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Astronomy Quiz

Astronomy Quiz: Stellar Mass And Lifetime

Practice Stellar Mass And Lifetime in Astronomy with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Stellar Mass And Lifetime, giving you a quick way to practice the rules, question types, and explanations that matter most for Astronomy.

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Question 1

In a close binary system, a 10 M☉ star and a 1 M☉ star form at the same time. The 10 M☉ star evolves first, expands, and transfers a significant amount of mass to its 1 M☉ companion. What is the most likely consequence for the companion star's subsequent main-sequence lifetime?

  1. Its lifetime will be greatly extended because it has gained a large amount of fresh hydrogen fuel.
  2. Its lifetime will be significantly shortened because the added mass will increase its core pressure and accelerate its fusion rate. (correct answer)
  3. Its lifetime will be unchanged because its core fusion rate is determined by its original mass, not by mass added to its outer layers.
  4. It will become unstable and immediately evolve off the main sequence, as main-sequence stars cannot gain mass.
Explanation: The correct answer is B. The added mass increases the total gravitational force of the companion star. This increased gravity compresses the star's core, raising its temperature and pressure. To maintain hydrostatic equilibrium, the core's fusion rate must increase dramatically. This accelerated fuel consumption will cause the star to evolve much more quickly and significantly shorten its remaining main-sequence lifetime. A is a classic misconception that more fuel equals a longer life, ignoring the much larger impact on the consumption rate. C is incorrect because the added mass affects the entire star's structure, including the core. D is incorrect; while the star's properties change, it will adjust to a new equilibrium on the main sequence corresponding to its new, higher mass, rather than becoming immediately unstable.

Question 2

In any stellar census of a galaxy, low-mass M-dwarf stars vastly outnumber high-mass O-type stars. While star formation physics produces more low-mass stars, what other critical factor related to stellar mass explains this profound observational imbalance?

  1. Low-mass stars have main-sequence lifetimes that are orders of magnitude longer than high-mass stars, so they accumulate in the population over cosmic time. (correct answer)
  2. High-mass stars are often obscured by the dense dusty nebulae in which they form, leading to a significant undercount in observational surveys.
  3. Low-mass stars fragment into multiple systems more often during formation, artificially inflating their numbers compared to single high-mass stars.
  4. High-mass stars have much stronger gravitational fields, causing them to quickly merge and reduce their numbers after forming in clusters.
Explanation: The correct answer is A. The question asks for a factor besides the initial mass function. The most significant factor is lifetime. M-dwarfs have lifetimes of trillions of years, longer than the current age of the universe. This means nearly every M-dwarf ever formed is still shining. In contrast, O-type stars have lifetimes of only a few million years. They are born and die out very quickly. Therefore, at any given moment, the population of stars is dominated by the long-lived, low-mass stars that have been accumulating for billions of years. B, C, and D describe real astronomical phenomena, but they are secondary effects compared to the overwhelming impact of the mass-lifetime relationship on the composition of the stellar population.

Question 3

Which of the following sequences best describes the causal relationship that determines a main-sequence star's lifetime?

  1. High Luminosity → Faster Fusion Rate → High Core Temperature → High Mass → Shorter Lifetime
  2. High Mass → Stronger Gravity → Higher Core Temperature/Pressure → Faster Fusion Rate → Higher Luminosity → Shorter Lifetime (correct answer)
  3. Stronger Gravity → High Mass → Higher Luminosity → Faster Fusion Rate → Shorter Lifetime
  4. Faster Fusion Rate → High Mass → Shorter Lifetime → High Luminosity → Stronger Gravity
Explanation: The correct answer is B. This sequence correctly identifies mass as the primary independent variable. A star's initial mass determines the strength of its self-gravity. Gravity dictates the core conditions (temperature and pressure) needed to achieve hydrostatic equilibrium. These conditions, in turn, set the rate of nuclear fusion. The fusion rate determines the star's energy output, or luminosity. Finally, the lifetime is the result of how much fuel the star has (related to mass) divided by how quickly it is consumed (luminosity). All other options present an incorrect or illogical causal flow.

Question 4

An astronomer observes two open star clusters, Cluster A and Cluster B. In Cluster A, the most massive stars still on the main sequence are G-type stars. In Cluster B, the most massive stars still on the main sequence are B-type stars. Based on the principles of stellar evolution, what is the most direct conclusion? (Recall the spectral sequence O-B-A-F-G-K-M from hottest to coolest).

  1. Cluster B is significantly older than Cluster A.
  2. Cluster A is significantly older than Cluster B. (correct answer)
  3. Cluster B is much more distant than Cluster A, making only its brightest stars visible.
  4. Cluster A and Cluster B formed with different proportions of high-mass stars.
Explanation: The correct answer is B. All stars in a cluster form at roughly the same time. The most massive stars evolve the fastest and leave the main sequence first. The point on the H-R diagram where stars are just now leaving the main sequence is called the 'main-sequence turnoff point,' and its position indicates the cluster's age. B-type stars are much more massive and have shorter lives than G-type stars. Since Cluster B still has massive B-type stars on its main sequence, it must be relatively young. In Cluster A, all stars more massive than G-type have already evolved off the main sequence, indicating it is much older. A is the reverse of the correct logic. C is incorrect because distance affects apparent magnitude, not the evolutionary state of the stars. D is a distractor; while the initial mass function can vary, the turnoff point is a direct measure of age based on the stars that did form.

Question 5

A main-sequence star is in hydrostatic equilibrium, where the inward force of gravity is balanced by outward thermal pressure from nuclear fusion. How does a star's mass dictate the terms of this equilibrium and consequently affect its lifetime?

  1. A higher mass requires a much greater outward pressure to counteract gravity, which in turn demands a much higher fusion rate, rapidly consuming the star's fuel. (correct answer)
  2. In high-mass stars, gravity slightly overwhelms pressure, causing the star to contract and heat up continuously, which shortens its life.
  3. The equilibrium is maintained by different fusion reactions (p-p chain vs. CNO cycle), and the CNO cycle in high-mass stars is inherently less stable, leading to a shorter life.
  4. A higher mass increases the star's fuel reservoir and its fusion rate by the same proportion, so the equilibrium itself does not explain the shorter lifetime.
Explanation: The correct answer is A. This statement correctly describes the chain of reasoning. More mass means more gravity. To prevent collapse, the outward pressure must be higher. This pressure is generated by the energy from fusion. To generate more energy, the fusion rate in the core must be much higher. A higher fusion rate means the available fuel is consumed much more quickly, leading to a shorter lifetime. B is incorrect; a main-sequence star is, by definition, in equilibrium, not contracting. C is a subtle distractor; the switch to the CNO cycle is a consequence of the high core temperature required for equilibrium in massive stars, not an independent cause of instability. The high temperature and resulting high fusion rate are the direct cause. D is incorrect because the fusion rate increases much more steeply than the mass (fuel).

Question 6

An astronomer is studying a globular cluster, which is known to be very old (over 10 billion years). Which of the following stellar populations would the astronomer least expect to find within this cluster?

  1. A large population of K- and M-type main-sequence stars.
  2. Numerous white dwarfs.
  3. A well-populated red giant branch.
  4. Several B-type main-sequence stars. (correct answer)
Explanation: The correct answer is D. B-type stars are high-mass stars. Their main-sequence lifetimes are extremely short, typically in the range of 10 to 100 million years. In a cluster that is over 10 billion years old, any B-type stars that formed with the cluster would have exhausted their fuel and died long ago. A is incorrect because K- and M-type stars are low-mass stars with lifetimes much longer than the age of the universe, so they would be expected. B is incorrect because stars like our Sun would have had plenty of time to evolve and die, leaving behind white dwarfs. C is incorrect because stars slightly more massive than the Sun, which are just now ending their main-sequence lives, would be evolving onto the red giant branch.

Question 7

A star with an initial mass of 7 M☉ and a star with an initial mass of 9 M☉ are near the dividing line between stars that end as white dwarfs and those that go supernova (approx. 8 M☉). How will their evolution and lifetimes most significantly differ?

  1. The 9 M☉ star will have a significantly shorter lifetime and will likely end in a core-collapse supernova, while the 7 M☉ star will have a longer life and end as a massive white dwarf. (correct answer)
  2. Both stars will end their lives as white dwarfs, but the 9 M☉ star will have a much shorter main-sequence lifetime before reaching that stage.
  3. The 7 M☉ star and 9 M☉ star will have comparable lifetimes, but the 9 M☉ star will fuse heavier elements, leading to a different type of planetary nebula.
  4. Both stars will undergo a core-collapse supernova, but the remnant from the 7 M☉ star will be a neutron star while the 9 M☉ star will form a black hole.
Explanation: The correct answer is A. The mass of a star determines not only its lifetime but also its ultimate fate. There is a critical mass threshold, around 8 M☉, that separates these two paths. The 7 M☉ star is below this threshold; it will have a longer (though still short compared to the Sun) life, fuse elements up to carbon and oxygen, and end its life by shedding its outer layers to form a planetary nebula, leaving a carbon-oxygen white dwarf. The 9 M☉ star is above the threshold; it will have a much shorter life, be able to fuse heavier elements in its core up to iron, and end in a core-collapse supernova. B and D incorrectly state the fate of one or both stars. C incorrectly claims their lifetimes will be comparable; the 9 M☉ star will live for a much shorter time.

Question 8

Imagine a main-sequence star, Star X, with a mass of 5 M☉. If, through some external process, its mass were instantaneously doubled to 10 M☉ while it remains a main-sequence star, what would be the most immediate and significant consequence for its stellar lifetime?

  1. Its remaining lifetime would roughly double because its total hydrogen fuel supply has doubled.
  2. Its remaining lifetime would be cut approximately in half, as the doubled mass would create a proportionally higher fusion rate.
  3. Its remaining lifetime would decrease dramatically, as its luminosity and fuel consumption rate would increase by a factor much greater than two. (correct answer)
  4. Its lifetime would be unaffected, as a star's evolutionary track and lifespan are fixed by its initial mass at formation.
Explanation: The correct answer is C. A star's luminosity (and thus its fuel consumption rate) is related to its mass by approximately L∝M3.5L \propto M^{3.5}. Doubling the mass from 5 to 10 M☉ would increase its luminosity by a factor of roughly 23.5≈112^{3.5} \approx 11. While the fuel has doubled, the consumption rate has increased more than tenfold, leading to a dramatic decrease in its remaining lifetime. A reflects the common misconception that more fuel means a longer life. B incorrectly assumes a linear relationship between mass and fusion rate. D is incorrect because mass is the ongoing determinant of a star's structure and evolution; a change in mass would force the star to a new equilibrium with a new, much shorter lifetime.

Question 9

Star Vega (approx. 2 M☉) and the Sun (1 M☉) are both main-sequence stars. Given that Vega will have a total lifetime of about 1 billion years, what does this imply when compared to the Sun's 10-billion-year lifetime?

  1. Vega's core must be proportionally hotter, causing it to fuse its greater fuel supply at a rate roughly 20 times that of the Sun. (correct answer)
  2. Vega must have formed with a significantly smaller fraction of hydrogen fuel compared to the Sun, leading to its shorter life.
  3. The Sun's fusion process is far more efficient at converting mass to energy, allowing it to shine longer with less fuel.
  4. Vega's higher mass leads to a fusion rate that is only slightly higher than the Sun's, but it has a less stable structure.
Explanation: The correct answer is A. To have a lifetime 1/10th of the Sun's with twice the fuel, Vega's fuel consumption rate (luminosity) must be approximately 2 / (1/10) = 20 times that of the Sun. (Observed luminosity is actually ~40 L☉, but the logic holds). This massively increased consumption rate is a direct consequence of the higher core temperature and pressure needed to support its 2 M☉ mass. B is incorrect; stars form with roughly the same composition (~75% H). C is incorrect; the fusion process (p-p chain and CNO cycle) has a fixed efficiency based on physics, it is not a property that varies independently. D is incorrect as it vastly underestimates the difference in the fusion rate needed to explain the lifetime difference.

Question 10

An analogy is often made between a star's main-sequence lifetime and a car's journey, where initial mass is the engine size and fuel is the gasoline. Which statement best completes the analogy to explain why high-mass stars have short lives?

  1. A car with a massive engine has a much larger gas tank and therefore travels for a significantly longer time than a small car.
  2. A car with a massive engine has a huge gas tank, but it burns fuel so inefficiently and powerfully that it runs out of gas much faster than a small, efficient car. (correct answer)
  3. All cars, regardless of engine size, have the same size gas tank, so the one with the biggest engine naturally runs out of gas first.
  4. A car with a massive engine travels faster, but its heavier weight causes more wear and tear, leading to a shorter overall lifespan of the car's parts.
Explanation: The correct answer is B. This analogy correctly captures the core concept. A high-mass star (massive engine) does have more fuel (a huge gas tank). However, its fuel consumption rate, or luminosity, is disproportionately higher (it burns fuel inefficiently and powerfully). The net result is that it exhausts its large fuel supply much more quickly than a low-mass star (a small, efficient car). A represents the common incorrect intuition. C is based on a false premise, as high-mass stars do have more fuel. D shifts the analogy from fuel consumption to mechanical failure, which is not the correct physical reason for a star's lifetime limit.

Question 11

Star A has twice the mass of Star B, and both are on the main sequence. Based on the approximate stellar relationship that lifetime is proportional to M−2.5M^{-2.5}, which statement most accurately describes their relative main-sequence lifetimes?

  1. The lifetime of Star A will be approximately half the lifetime of Star B.
  2. The lifetime of Star A will be approximately double the lifetime of Star B.
  3. The lifetimes will be roughly equal, as the increased fuel in Star A is balanced by a proportionally increased fusion rate.
  4. The lifetime of Star A will be significantly less than half the lifetime of Star B. (correct answer)
Explanation: The correct answer is D. The relationship between mass (M) and lifetime (T) is a steep power law, approximately T∝M−2.5T \propto M^{-2.5}. If Star A has twice the mass of Star B (MA=2MBM_A = 2 M_B), its lifetime will be TA∝(2MB)−2.5=2−2.5TBT_A \propto (2 M_B)^{-2.5} = 2^{-2.5} T_B. The value of 2−2.52^{-2.5} is approximately 1/5.6. Therefore, Star A will have a lifetime that is about 1/5.6 times that of Star B, which is significantly less than half. A assumes a linear inverse relationship (T∝M−1T \propto M^{-1}). B reflects the misconception that more mass means a longer life. C incorrectly assumes a perfect balance, which would imply a linear relationship between fuel and consumption rate, contrary to observations.

Question 12

A 10 solar mass (M☉) star and a 1 M☉ star both begin their lives on the main sequence. The 10 M☉ star has ten times the hydrogen fuel as the 1 M☉ star. Why, then, does the 10 M☉ star have a main-sequence lifetime that is hundreds of times shorter?

  1. Its core temperature and pressure are much higher, leading to a disproportionately faster rate of nuclear fusion. (correct answer)
  2. The stronger stellar winds in the massive star eject a large fraction of its hydrogen fuel into space before it can be fused.
  3. Its larger radius means the fuel is less concentrated at the core, making fusion less efficient over its entire volume.
  4. It has significantly more fuel, but it exhausts it at a rate only slightly higher than the lower-mass star due to radiative energy transport.
Explanation: The correct answer is A. A star's lifetime is determined by the ratio of its fuel supply to its fuel consumption rate (luminosity). While a 10 M☉ star has 10 times the fuel, its luminosity is thousands of times greater than a 1 M☉ star. This is because its greater mass leads to immense gravitational pressure on the core, which must be counteracted by higher temperatures and pressures, causing nuclear fusion to proceed at a tremendously accelerated rate. B is incorrect because while stellar winds are significant in massive stars, the core fusion rate is the dominant factor determining lifetime by orders ofmagnitude. C is incorrect because high-mass stars have extremely dense and hot cores where fusion is highly efficient. D is incorrect as it mischaracterizes the fusion rate, which is vastly higher, not 'slightly higher'.

Question 13

An astronomer observes two open star clusters, Cluster A and Cluster B. In Cluster A, the most massive stars still on the main sequence are G-type stars. In Cluster B, the most massive stars still on the main sequence are B-type stars. Based on the principles of stellar evolution, what is the most direct conclusion? (Recall the spectral sequence O-B-A-F-G-K-M from hottest to coolest).

  1. Cluster B is significantly older than Cluster A.
  2. Cluster A is significantly older than Cluster B. (correct answer)
  3. Cluster B is much more distant than Cluster A, making only its brightest stars visible.
  4. Cluster A and Cluster B formed with different proportions of high-mass stars.
Explanation: The correct answer is B. All stars in a cluster form at roughly the same time. The most massive stars evolve the fastest and leave the main sequence first. The point on the H-R diagram where stars are just now leaving the main sequence is called the 'main-sequence turnoff point,' and its position indicates the cluster's age. B-type stars are much more massive and have shorter lives than G-type stars. Since Cluster B still has massive B-type stars on its main sequence, it must be relatively young. In Cluster A, all stars more massive than G-type have already evolved off the main sequence, indicating it is much older. A is the reverse of the correct logic. C is incorrect because distance affects apparent magnitude, not the evolutionary state of the stars. D is a distractor; while the initial mass function can vary, the turnoff point is a direct measure of age based on the stars that did form.

Question 14

Star A has twice the mass of Star B, and both are on the main sequence. Based on the approximate stellar relationship that lifetime is proportional to M−2.5M^{-2.5}, which statement most accurately describes their relative main-sequence lifetimes?

  1. The lifetime of Star A will be approximately half the lifetime of Star B.
  2. The lifetime of Star A will be approximately double the lifetime of Star B.
  3. The lifetimes will be roughly equal, as the increased fuel in Star A is balanced by a proportionally increased fusion rate.
  4. The lifetime of Star A will be significantly less than half the lifetime of Star B. (correct answer)
Explanation: The correct answer is D. The relationship between mass (M) and lifetime (T) is a steep power law, approximately T∝M−2.5T \propto M^{-2.5}. If Star A has twice the mass of Star B (MA=2MBM_A = 2 M_B), its lifetime will be TA∝(2MB)−2.5=2−2.5TBT_A \propto (2 M_B)^{-2.5} = 2^{-2.5} T_B. The value of 2−2.52^{-2.5} is approximately 1/5.6. Therefore, Star A will have a lifetime that is about 1/5.6 times that of Star B, which is significantly less than half. A assumes a linear inverse relationship (T∝M−1T \propto M^{-1}). B reflects the misconception that more mass means a longer life. C incorrectly assumes a perfect balance, which would imply a linear relationship between fuel and consumption rate, contrary to observations.

Question 15

In any stellar census of a galaxy, low-mass M-dwarf stars vastly outnumber high-mass O-type stars. While star formation physics produces more low-mass stars, what other critical factor related to stellar mass explains this profound observational imbalance?

  1. Low-mass stars have main-sequence lifetimes that are orders of magnitude longer than high-mass stars, so they accumulate in the population over cosmic time. (correct answer)
  2. High-mass stars are often obscured by the dense dusty nebulae in which they form, leading to a significant undercount in observational surveys.
  3. Low-mass stars fragment into multiple systems more often during formation, artificially inflating their numbers compared to single high-mass stars.
  4. High-mass stars have much stronger gravitational fields, causing them to quickly merge and reduce their numbers after forming in clusters.
Explanation: The correct answer is A. The question asks for a factor besides the initial mass function. The most significant factor is lifetime. M-dwarfs have lifetimes of trillions of years, longer than the current age of the universe. This means nearly every M-dwarf ever formed is still shining. In contrast, O-type stars have lifetimes of only a few million years. They are born and die out very quickly. Therefore, at any given moment, the population of stars is dominated by the long-lived, low-mass stars that have been accumulating for billions of years. B, C, and D describe real astronomical phenomena, but they are secondary effects compared to the overwhelming impact of the mass-lifetime relationship on the composition of the stellar population.

Question 16

An astronomer is studying a globular cluster, which is known to be very old (over 10 billion years). Which of the following stellar populations would the astronomer least expect to find within this cluster?

  1. A large population of K- and M-type main-sequence stars.
  2. Numerous white dwarfs.
  3. A well-populated red giant branch.
  4. Several B-type main-sequence stars. (correct answer)
Explanation: The correct answer is D. B-type stars are high-mass stars. Their main-sequence lifetimes are extremely short, typically in the range of 10 to 100 million years. In a cluster that is over 10 billion years old, any B-type stars that formed with the cluster would have exhausted their fuel and died long ago. A is incorrect because K- and M-type stars are low-mass stars with lifetimes much longer than the age of the universe, so they would be expected. B is incorrect because stars like our Sun would have had plenty of time to evolve and die, leaving behind white dwarfs. C is incorrect because stars slightly more massive than the Sun, which are just now ending their main-sequence lives, would be evolving onto the red giant branch.

Question 17

A star with an initial mass of 7 M☉ and a star with an initial mass of 9 M☉ are near the dividing line between stars that end as white dwarfs and those that go supernova (approx. 8 M☉). How will their evolution and lifetimes most significantly differ?

  1. The 9 M☉ star will have a significantly shorter lifetime and will likely end in a core-collapse supernova, while the 7 M☉ star will have a longer life and end as a massive white dwarf. (correct answer)
  2. Both stars will end their lives as white dwarfs, but the 9 M☉ star will have a much shorter main-sequence lifetime before reaching that stage.
  3. The 7 M☉ star and 9 M☉ star will have comparable lifetimes, but the 9 M☉ star will fuse heavier elements, leading to a different type of planetary nebula.
  4. Both stars will undergo a core-collapse supernova, but the remnant from the 7 M☉ star will be a neutron star while the 9 M☉ star will form a black hole.
Explanation: The correct answer is A. The mass of a star determines not only its lifetime but also its ultimate fate. There is a critical mass threshold, around 8 M☉, that separates these two paths. The 7 M☉ star is below this threshold; it will have a longer (though still short compared to the Sun) life, fuse elements up to carbon and oxygen, and end its life by shedding its outer layers to form a planetary nebula, leaving a carbon-oxygen white dwarf. The 9 M☉ star is above the threshold; it will have a much shorter life, be able to fuse heavier elements in its core up to iron, and end in a core-collapse supernova. B and D incorrectly state the fate of one or both stars. C incorrectly claims their lifetimes will be comparable; the 9 M☉ star will live for a much shorter time.

Question 18

Star Vega (approx. 2 M☉) and the Sun (1 M☉) are both main-sequence stars. Given that Vega will have a total lifetime of about 1 billion years, what does this imply when compared to the Sun's 10-billion-year lifetime?

  1. Vega's core must be proportionally hotter, causing it to fuse its greater fuel supply at a rate roughly 20 times that of the Sun. (correct answer)
  2. Vega must have formed with a significantly smaller fraction of hydrogen fuel compared to the Sun, leading to its shorter life.
  3. The Sun's fusion process is far more efficient at converting mass to energy, allowing it to shine longer with less fuel.
  4. Vega's higher mass leads to a fusion rate that is only slightly higher than the Sun's, but it has a less stable structure.
Explanation: The correct answer is A. To have a lifetime 1/10th of the Sun's with twice the fuel, Vega's fuel consumption rate (luminosity) must be approximately 2 / (1/10) = 20 times that of the Sun. (Observed luminosity is actually ~40 L☉, but the logic holds). This massively increased consumption rate is a direct consequence of the higher core temperature and pressure needed to support its 2 M☉ mass. B is incorrect; stars form with roughly the same composition (~75% H). C is incorrect; the fusion process (p-p chain and CNO cycle) has a fixed efficiency based on physics, it is not a property that varies independently. D is incorrect as it vastly underestimates the difference in the fusion rate needed to explain the lifetime difference.

Question 19

In a close binary system, a 10 M☉ star and a 1 M☉ star form at the same time. The 10 M☉ star evolves first, expands, and transfers a significant amount of mass to its 1 M☉ companion. What is the most likely consequence for the companion star's subsequent main-sequence lifetime?

  1. Its lifetime will be greatly extended because it has gained a large amount of fresh hydrogen fuel.
  2. Its lifetime will be significantly shortened because the added mass will increase its core pressure and accelerate its fusion rate. (correct answer)
  3. Its lifetime will be unchanged because its core fusion rate is determined by its original mass, not by mass added to its outer layers.
  4. It will become unstable and immediately evolve off the main sequence, as main-sequence stars cannot gain mass.
Explanation: The correct answer is B. The added mass increases the total gravitational force of the companion star. This increased gravity compresses the star's core, raising its temperature and pressure. To maintain hydrostatic equilibrium, the core's fusion rate must increase dramatically. This accelerated fuel consumption will cause the star to evolve much more quickly and significantly shorten its remaining main-sequence lifetime. A is a classic misconception that more fuel equals a longer life, ignoring the much larger impact on the consumption rate. C is incorrect because the added mass affects the entire star's structure, including the core. D is incorrect; while the star's properties change, it will adjust to a new equilibrium on the main sequence corresponding to its new, higher mass, rather than becoming immediately unstable.

Question 20

Imagine a main-sequence star, Star X, with a mass of 5 M☉. If, through some external process, its mass were instantaneously doubled to 10 M☉ while it remains a main-sequence star, what would be the most immediate and significant consequence for its stellar lifetime?

  1. Its remaining lifetime would roughly double because its total hydrogen fuel supply has doubled.
  2. Its remaining lifetime would be cut approximately in half, as the doubled mass would create a proportionally higher fusion rate.
  3. Its remaining lifetime would decrease dramatically, as its luminosity and fuel consumption rate would increase by a factor much greater than two. (correct answer)
  4. Its lifetime would be unaffected, as a star's evolutionary track and lifespan are fixed by its initial mass at formation.
Explanation: The correct answer is C. A star's luminosity (and thus its fuel consumption rate) is related to its mass by approximately L∝M3.5L \propto M^{3.5}. Doubling the mass from 5 to 10 M☉ would increase its luminosity by a factor of roughly 23.5≈112^{3.5} \approx 11. While the fuel has doubled, the consumption rate has increased more than tenfold, leading to a dramatic decrease in its remaining lifetime. A reflects the common misconception that more fuel means a longer life. B incorrectly assumes a linear relationship between mass and fusion rate. D is incorrect because mass is the ongoing determinant of a star's structure and evolution; a change in mass would force the star to a new equilibrium with a new, much shorter lifetime.