1. Stars on the main sequence of the H-R diagram all are powered by the fusion of hydrogen nuclei into helium nuclei. The Sun will spend 10¹⁰ years = 10 billion years on the main sequence, until it has exhausted all of the hydrogen available for the fusion into helium in its core. The lifetime of another star on the main sequence depends on it mass (how much hydrogen is available for fusion into helium) and on its luminosity (how quickly the star uses its hydrogen for fusion into helium).

2. During a star’s life on the main sequence, it expands somewhat and becomes more luminous. Core hydrogen burning ends when all of the hydrogen in the star’s core has been exhausted. The star then has an inactive core of nearly pure helium, surrounded by a shell of active hydrogen burning. For a star like the Sun, the phase of hydrogen shell burning lasts about 1 billion years. During this phase, the inactive helium core shrinks while the stars outer layers expand and cool. The result is a red giant star.

3. Helium burning is the nuclear fusion of helium nuclei to form more massive nuclei, releasing energy in the process. The specific process of fusing three helium nuclei (also called alpha particles) into a carbon nucleus is called the triple alpha process. If a red giant star has less / more (circle one) than 2 or 3 solar masses, helium burning begins gradually. But if a red giant star has less / more (circle one) than 2 or 3 solar masses, helium burning begins explosively and suddenly in an event called the helium flash. This event takes place at the core of the star, and is cannot be seen from the outside. After the helium flash, a star like the Sun can burn helium in its core for only 100 million years.

4. Three H-R diagrams are shown below for the stars of three different star clusters.

a. For each cluster, identify the main sequence turnoff point (if there is one) by circling it on the diagram.

5. A Cepheid variable star is a pulsating star that expands and contracts with a pulsation period between 1 and 100 days. As the star expands and contracts, the star grows dimmer and brighter. The period - luminosity relation for Cepheid variables says that brighter stars take more/less (circle one) time to go through one bright-dim-bright cycle. If you measure the pulsation period of a Cepheid variable, you can use the period-luminosity relation to find M, the star’s absolute magnitude. Also, by observing a Cepheid variable in the sky, you can measure m, the star’s apparent magnitude. You can then find the distance to the star using the formula from Homework #10. For example, suppose you measure that the apparent magnitude of a Cepheid variable star is

m = 25

and that its pulsation period is 20 days. Using the period-luminosity relation below, the star’s absolute magnitude is

M = -5.

Now find the star’s distance:

[m - M + 5]/5 = [(25) - (-5) + 5]/5 = [35]/5 = 7,

and so

d = 10^{[m - M + 5]/5} = 10⁷ = 10 million parsecs.

6. Identify the final stages in the life of:

a. a low-mass star: the red giant star expels its outer layers to form a planetary nebula, while the star’s carbon-oxygen core slowly cools off as a white dwarf.

b. an intermediate-mass star: the supergiant star explodes as a Type II supernova; the star’s core may be left behind as a neutron star.

c. a high-mass star: the supergiant star explodes as a Type II supernova; the star’s core undergoes total gravitational collapse for form a black hole.

The Sun is a low-mass star, and will end its life as a white dwarf.

7. A white dwarf is the dead core of a low-mass star. Its core is composed primarily of carbon nuclei, oxygen nuclei, and electrons. As it cools, the star crystalizes. Because a diamond is crystalized carbon, these dead stars are like diamonds in the sky! Electrons supply the electron degeneracy pressure that supports a white dwarf against its own gravity. The tighter the electrons are squeezed together, the more electron degeneracy pressure they create. This means that more massive white dwarfs are actually larger / smaller (circle one) than less massive white dwarfs. However, if a white dwarf has more than 1.4 solar masses, the electron degeneracy pressure fails. The Chandrasekhar limit of 1.4 solar masses is the maximum mass possible for a white dwarf.

8. A Type II supernova occurs when the core of a massive star exhausts its nuclear fuel. Nuclei of iron and heavier elements cannot release energy through fusion reactions. When a massive star develops a core of iron nuclei, the source of the star’s central pressure and energy vanishes. The core can no longer support itself against the inward pull of gravity so the core will collapse, becoming super-dense. The star’s outer layers fall inward and then bounce outward from the super-dense core. When the resulting shock wave reaches the surface several hours later, the result is the explosion of a Type II supernova. The outward-moving gases are expelled into space to form a supernova remnant. Supernovas play four important roles in astronomy. A supernova

a. disperses elements up through iron that are created by fusion in the star's center

b. creates elements heavier than iron in the high temperatures and densities of the supernova explosion

c. makes neutron stars and black holes

d. produces a shock wave that can trigger the collapse of interstellar clouds to form new stars and planetary systems

9. In 1987, a Type II supernova was observed in the Large Magellanic Cloud. Three hours before the supernova appeared in the sky, a stream of "ghost particles" called neutrinos was detected. These neutrinos were created when the core of the supergiant star collapsed to form a neutron star. The outer layers bounced off the super-dense core of neutrons, and three hours later the resulting shock wave reached the surface to produce the supernova explosion.

10. If a white dwarf is a member of a close binary star system, its gravity may pull gas (mostly hydrogen) from its companion star. This gas will form an accretion disk around the white dwarf before spiraling down onto the white dwarf’s surface. The white dwarf may accrete enough gas that its mass gets close to 1.4 solar masses (the Chandrasekhar limit). As a white dwarf’s mass approaches the Chandrasekhar limit, its center gets so hot that the fusion of carbon nuclei will begin in the white dwarf’s core. This releases so much energy that the entire white dwarf explodes. This is called a Type Ia supernova.

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