Question 1

When the Sun entered the main sequence, its core was approximately 75 percent hydrogen and 25 percent helium, by mass. What was the ratio of hydrogen nuclei to helium nuclei?

Accepted Answer

The mass of a hydrogen nucleus (proton) is roughly 1 atomic mass unit (amu), while the mass of a helium nucleus (alpha particle) is roughly 4 amu. Given the Sun's core composition of 75% hydrogen and 25% helium by mass, for every 4 amu of helium, there are 3 amu of hydrogen. Therefore, for every helium nucleus, there are $ \frac{3}{1} \times \frac{1}{4} = \frac{3}{4} $ hydrogen nuclei, which simplifies to 3 hydrogen nuclei for every 4 amu of mass. Since helium is 4 times heavier than hydrogen, you get 3 hydrogen nuclei for every 1 helium nucleus by mass, but considering the mass proportions (75% H, 25% He), you actually have 3 times as much hydrogen by mass, which translates to 3 times 4, or 12 hydrogen nuclei for every helium nucleus, making the ratio 12:1.

Question 2

The main-sequence lifetime of a star with half the mass of the Sun

Accepted Answer

The main-sequence lifetime of a star is primarily determined by its mass, with lower-mass stars burning their fuel more slowly and thus having longer lifetimes. A star with half the mass of the Sun would burn its nuclear fuel more slowly than the Sun, resulting in a longer main-sequence lifetime.

Question 3

The spiral galaxy of which Earth is a part is roughly 14 billion years old. Which of these statements about the stars that formed when the Milky Way Galaxy was very young (say, during the first billion years) is true?

Accepted Answer

Stars with less than 3/4 of the Sun's mass have long lifespans and can remain on the main sequence for billions of years, so they could still be on the main sequence today.

Question 4

Main-sequence stars can be divided into those with more than 75 percent of the mass of the Sun and those with less than this amount of mass. What is different about these two groups?

Accepted Answer

Stars in the more massive group have higher surface temperatures and luminosities than stars in the less massive group. This is because the more massive stars have a greater gravitational force, which causes them to contract more and become hotter. The higher temperatures in the more massive stars allow them to undergo nuclear fusion at a faster rate, which produces more energy and makes them more luminous.

Question 5

The star Zeta Pegasi (in the constellation Pegasus, the Flying Horse) has a spectral luminosity class of B8 V, which gives it a surface temperature of about 11,000 K. According to Table 13-2 in the text, the expected main-sequence lifetime of Zeta Pegasi is

Accepted Answer

Stars with a spectral class of B8 V are massive and have relatively short main-sequence lifetimes, typically around 500 million years.

Question 6

The present estimate of the age of the universe is about 14 billion years. How long will a half-solar-mass star spend on the main sequence, compared with the present age of the universe?

Accepted Answer

A half-solar-mass star will spend significantly longer on the main sequence than a star like our Sun because lower mass stars burn their fuel more slowly. Given the present estimate of the universe's age at about 14 billion years, a half-solar-mass star can spend well over 100 billion years on the main sequence, which is more than 10 times the current age of the universe.

Question 7

A star is observed to be on or close to the main-sequence region of the Hertzsprung-Russell diagram. What particular feature of stellar behavior can be inferred by this observation?

Accepted Answer

Main-sequence stars, like our Sun, are in a stable phase of their lifecycle where they generate energy through the fusion of hydrogen into helium in their cores. This process is what keeps them in the main-sequence region of the Hertzsprung-Russell diagram.

Question 8

Of all the low-mass red dwarfs (0.08 M < M < 0.4 M) that have formed since the Galaxy came into being 15 billion years ago, how many are presently on the main sequence?

Accepted Answer

Red dwarfs have extremely long lifetimes, much longer than the current age of the Universe (about 13.8 billion years), so all low-mass red dwarfs that have formed are still on the main sequence.

Question 9

Red dwarfs are fully convective. In this, they are like

Accepted Answer

Red dwarfs and brown dwarfs are both fully convective, meaning that energy is transferred from the core to the surface by convection throughout the entire star or object, unlike in the Sun where only the outer layer is convective.

Question 10

A low-mass red dwarf (0.08 M < M < 0.4 M) experiences which of these fusion reactions as the last fusion reaction in its core?

Accepted Answer

Low-mass red dwarfs, with masses between 0.08 and 0.4 times that of the Sun, do not have sufficient mass and, consequently, core temperatures and pressures to fuse elements heavier than hydrogen. Therefore, the last fusion reaction in their cores is hydrogen fusion, after which they become dim white or black dwarfs without going through the helium or heavier element fusion stages.

Question 11

What is unique about a low-mass red dwarf star compared with stars at other stages of evolution, such as main-sequence stars?

Accepted Answer

Convection occurs throughout the interior of a low-mass red dwarf star, which is unique compared to other stars. This process allows the star to mix its materials from the core to the surface, preventing the formation of distinct core and outer layer regions and contributing to the star's longevity.

Question 12

The total lifespan of the Sun is believed to be

Accepted Answer

The total lifespan of the Sun is believed to be about 10 billion years, with it currently being about halfway through its life cycle.

Question 13

It is now believed that MOST stars are

Accepted Answer

The answer of It is now believed that MOST stars...

Question 14

Some protostars, when they evolve onto the main sequence, are fully convective and use convection to transport material all the way from the core to the surface. Which stars show this characteristic?

Accepted Answer

Only the smallest stars, of less than about 0.4 solar mass, are fully convective throughout their entire structure. This means that they transport material and energy from the core to the surface entirely through convection.

Question 15

How long does a star of 3 times the Sun's mass live compared with the lifetime of the Sun?

Accepted Answer

The lifetime of a star is inversely proportional to its mass raised to a certain power (roughly 2.5 to 3 for stars of this size). Therefore, a star with 3 times the mass of the Sun will have a significantly shorter lifespan, approximately 1/20 as long.

Question 16

What is unusual about main-sequence stars that are about 75 percent the mass of the Sun?

Accepted Answer

Main-sequence stars that are about 75 percent the mass of the Sun have lifetimes much longer than the current age of the universe, meaning none of these stars has yet evolved off the main sequence.

Question 17

How long ago was the Sun a ZAMS star?

Accepted Answer

The Sun was a Zero Age Main Sequence (ZAMS) star approximately 5 billion years ago, marking the start of its main sequence phase where it began fusing hydrogen into helium in its core.

Question 18

If one were able to visit Earth one million years into the future, which of these views of the sky would be MOST likely?

Accepted Answer

Over a million years, the positions of nearby stars would change due to their own motion through the galaxy. Some blue stars, which are typically very hot and massive, may evolve over this timescale, changing color as they age. However, since a million years is relatively short in astronomical terms, the overall structure of the sky wouldn't be vastly different.

Question 19

The final stage in the evolution of a red dwarf star is

Accepted Answer

A red dwarf star is a star with a mass less than about half the mass of the Sun. Red dwarf stars are the most common type of star in the Milky Way galaxy. They are also the longest-lived stars, with some red dwarfs expected to live for trillions of years.Red dwarf stars spend most of their lives on the main sequence, fusing hydrogen into helium in their cores. However, once they exhaust the hydrogen in their cores, they begin to evolve off the main sequence. The final stage in the evolution of a red dwarf star is a star of pure helium that no longer generates energy by nuclear fusion. This type of star is known as a helium white dwarf.

Question 20

The end of the life of a red dwarf star is predicted to be a sphere of almost pure helium. But no such spheres have been detected. What do astronomers believe is the reason?

Accepted Answer

The evolution rate for red dwarfs is extremely slow, meaning that none has yet reached its final evolutionary stage, which is why we haven't observed any end-stage red dwarf remnants.

Quiz 13: The Lives of Stars From Birth Through Middle Age