Question 1

Use the Hertzsprung-Russell diagram (Figure 10-7)and the mass-luminosity relation (Figure 10-14)in Comins,Discovering the Essential Universe,6th ed.,to estimate the mass of Vega,an AO V main-sequence star with a surface temperature of about 10,000 K.

Accepted Answer

Vega, being an A0 V main-sequence star, falls into the category of stars with masses between 1.5 and 5.0 solar masses according to the mass-luminosity relation and its position on the Hertzsprung-Russell diagram.

Question 2

The object you are observing through a telescope appears visually to be a single star,but you know by looking at its spectrum that it is a binary system.Which spectral feature might NOT characterize it as a binary?

Accepted Answer

Option D is the correct choice because it describes a phenomenon known as "line doubling," which is commonly observed in binary stars where one component is significantly brighter than the other. This effect is caused by the periodic variation of the spectral lines from one spectral type becoming brighter and the lines from the other spectral type becoming dimmer. Therefore, it is the only option that does not directly characterize the system as a binary. Options A, B, and C all describe characteristic features of binary systems in which multiple spectral types are present and are moving periodically with respect to each other.

Question 3

In the case where a large number of stars of different masses all form at the same time (e.g.,in a cluster of stars),what does the phrase initial mass function mean?

Accepted Answer

The initial mass function refers to the distribution of masses of stars that form in a cluster or in a certain region at the same time. It describes the number of stars that form at different mass ranges, and it can be shown as a histogram or a mathematical equation that characterizes the typical mass range of stars in the population. Options A, B, and C do not accurately capture the meaning of the initial mass function.

Question 4

A simple relationship exists between mass and luminosity for:

Accepted Answer

The answer of A simple relationship exists between mass and...

Question 5

What would be the mass of a main-sequence star that has a luminosity 1000 times greater than that of the Sun? (See Figure 10-15,Comins,Discovering the Essential Universe,6th ed.)

Accepted Answer

According to the mass-luminosity relation for main-sequence stars, luminosity is approximately proportional to the mass raised to the power of 3.5. A star with a luminosity 1000 times that of the Sun would have a mass around 5 solar masses.

Question 6

The radial velocity curve of a star in a binary star system is a plot against time of the:

Accepted Answer

The radial velocity curve of a star in a binary star system is a plot of the variation of Doppler shift of the star's spectral lines and hence of its speed toward or away from us. This curve provides important information about the mass, orbit, and distance of the binary system.

Question 7

What particular and very important phenomenon frequently occurs in binary star systems where the stars are very close together?

Accepted Answer

Mass transfer is a common phenomenon in close binary star systems, where material from one star can be pulled onto its companion, often through an accretion disk. This process can significantly affect the evolution of both stars and is a key area of study in astrophysics.

Question 8

According to the mass-luminosity relation shown in Figure 10-14 of Comins,Discovering the Essential Universe,6th ed.,what is the mass of the star Regulus (α Leonis,the brightest star in the constellation Leo)? See also the Hertzsprung-Russell diagram in Figure 10-7.

Accepted Answer

Regulus is a B7V star, which corresponds to a mass of between 2.5 and 5 solar masses.

Question 9

Using the Hertzsprung-Russell diagram and the mass-luminosity relationship for main-sequence stars (Figure 10-14 of Comins,Discovering the Essential Universe,6th ed.),determine which type of main-sequence stars would have the highest mass.

Accepted Answer

According to the mass-luminosity relationship, more massive stars are also more luminous. Therefore, the main-sequence star with the highest mass would also be the brightest. The Hertzsprung-Russell diagram shows that O-type stars are the most luminous of the main-sequence stars, indicating that they have the highest mass. Therefore, the best choice is option C.

Question 10

Which is NOT needed to determine individual masses in a binary star system?

Accepted Answer

The absolute magnitude of at least one star is not needed to determine individual masses in a binary star system. The distance to the binary system is needed to determine the scale of the system and the relative sizes of the orbits of the two stars are needed to determine the ratio of the masses. The plane of the orbit of the two stars is needed to determine the inclination of the orbit, but this can be determined through spectroscopic observations of the orbital motion. However, the absolute magnitude of at least one star is not needed for any calculations related to determining the masses of the stars in a binary system.

Question 11

Where are the MOST massive stars to be found in the main sequence of a Hertzsprung-Russell diagram?

Accepted Answer

The upper left end of the main sequence on a Hertzsprung-Russell diagram represents the most massive stars. This is because they have a large amount of fuel (hydrogen) in their cores, causing them to burn brighter and hotter, and thus they appear towards the upper left. The lower right end of the main sequence represents less massive stars that burn cooler and dimmer.

Question 12

Using the Hertzsprung-Russell diagram in Figure 10-7 of Comins,Discovering the Essential Universe,6th ed.,and the mass-luminosity relationship for main-sequence stars shown in Figure 10-14,which list is the CORRECT sequence of stars in increasing order of mass?

Accepted Answer

From the Hertzsprung-Russell diagram, we can see that the sequence of stars in increasing order of luminosity (and therefore mass) on the main sequence goes:

Barnard's Star < Sun < Altair < Regulus

Using the mass-luminosity relationship for main-sequence stars shown in Figure 10-14, we can confirm that this is the correct sequence of stars in increasing order of mass. Therefore, the correct choice is C.

Question 13

The equation for the luminosity of a star in terms of its surface temperature is L = (surface area)σT⁴,where σ is the Stefan-Boltzmann constant.This suggests that,when a plot is made of luminosities versus temperature:

Accepted Answer

The equation shows that the luminosity depends on the surface area of the star in addition to its temperature. Therefore, stars with the same temperature but different radii will have different luminosities and occupy different points on the plot. This means that option A is the correct choice. Option B is incorrect because not all stars will plot along the same line. Option C and D are also incorrect because there is no direct relationship between the size of the star and its temperature.

Question 14

As you move along the main sequence,the masses of stars:

Accepted Answer

As you move along the main sequence from cooler to hotter stars, the mass of the stars increases with increasing temperature. This is because hotter stars are more massive and have higher luminosities.

Question 15

Absorption lines in the spectra of some binary stars are seen to change periodically from single to double lines and back again.Explain.

Accepted Answer

As the binary stars orbit around each other, they move toward and away from Earth. This causes the light from these stars to be Doppler shifted when motion is towards or away from Earth and no shift when they are moving perpendicular to the line of sight. This results in the periodic change of absorption lines from single to double and back again in the spectra of these stars.

Question 16

Which sentence describes the relationship between mass and luminosity of stars on the main sequence?

Accepted Answer

The larger the stellar mass, the larger is the luminosity. This relationship is known as the mass-luminosity relationship and is applicable to main sequence stars.

Question 17

Two stars in a binary system orbit around a common point that is:

Accepted Answer

The center of mass of a binary system is closer to the more massive star. This is because the more massive star exerts a stronger gravitational force on the system, causing the center of mass to be pulled closer to it.

Question 18

Suppose we observe the light curve of a totally eclipsing binary like that in Figure 10-13 in Comins,Discovering the Essential Universe,6th ed.The brightness falls gradually from magnitude 5 to magnitude 9 and remains there for 12 hours before increasing gradually to magnitude 5.Then after a while it drops gradually to magnitude 6,remains there for 8 hours,and returns to magnitude 5.What conclusion can be drawn from this light curve?

Accepted Answer

The answer of Suppose we observe the light curve of...

Question 19

The light curve made of a pair of eclipsing binaries will exhibit dips in intensity.The bottoms of these dips can have different shapes.How do we interpret this?

Accepted Answer

The answer of The light curve made of a pair...

Question 20

Is there a relationship between the mass of a main sequence star and its luminosity?

Accepted Answer

There is a relationship between the mass of a main sequence star and its luminosity, but it is not a simple linear one. The mass-luminosity relationship follows a power law, meaning that stars with larger masses have more than twice the luminosity of stars with half their mass. This relationship was first quantified by the astronomer Ejnar Hertzsprung and is known as the Hertzsprung-Russell diagram.

Quiz 10: Characterizing Stars

Use the Hertzsprung-Russell diagram (Figure 10-7) and the mass-luminosity relation (Figure 10-14) in Comins,Discovering the Essential Universe,6th ed.,to estimate the mass of Vega,an AO V main-sequence star with a surface temperature of about 10,000 K.