Homeworks 7

Homework 7 due on 10/26/09

Problem 1

Part 1

How long does it take a star with a mass of 1 M⊙ to form, from the beginning of its collapse from an gas cloud until its arrival on the main sequence? A star with a mass of 15 M⊙? Objects with masses less than 0.08 M⊙ never become hot enough in their cores to fuse hydrogen into helium. What happens to these low-mass objects?

Answer

We can use the following equation to find the free fall time: $Tff=(3\pi /32G\rho )$

Since we have the mass and volume $(R=5.56*10^{10})$, we can assume the shape of a spherical cloud, and determine $\rho$. From there, we can use the equation for the different masses to find $Tff$.

From Table 12.1 on page 427 of the textbook, we can see that the time it takes for a star with mass 1M⊙ to form is around 38.9 million years, whereas a star with mass 15M⊙ takes about only 117 thousand years to form. Objects with masses less than 0.08M⊙ do not have enough mass to initiate fusion after burning through their initial fuel. These objects are fated to become brown dwarves.

Part 2

What observations give direct evidence for the existence of the following kinds of interstellar material?

1. Dust.
2. Massive, dense clouds with many molecules (molecular clouds).
3. Clouds of ionized hydrogen with temperatures near 10⁴ K (HII regions).
4. Clouds of neutral hydrogen with temperatures near 100 K (HI regions).
5. Extremely hot gas with temperatures near 10⁶ K (intercloud coronal gas).

Problem 2

Two hot, high-luminosity blue stars are embedded in an interstellar cloud. A picture of the stars and the cloud at visible wavelengths shows just one of the stars. It also shows that some parts of the cloud are blue and some parts have a green or red color.

1. What is the most likely reason that one star cannot be seen at visible wavelengths?
2. Why does part of the cloud look blue?
3. Why does part of the cloud look red?

Answer

1. The most likely reason that one star cannot be seen at visible wavelengths is that it is being obstructed by a thick cloud of dust.
2. Part of the cloud looks blue because the cloud reflects some of the blue light from the unobstructed star.
3. Part of the cloud looks red because the light of the obstructed star must pass through the cloud, causing light in the infrared to optical (red) range of the electromagnetic spectrum to be emitted.

Problem 3

Why is the chemical composition of the Earth and the other terrestrial planets so different from that of the sun? Why is the chemical composition of Jupiter and the other Jovian planets more similar to the sun’s?

Stars are made of primarily hydrogen. When gas condenses around dust, the small particles grow larger as they collide with others. Over time, the dust grows into gravel and rocks which form the terrestrial planets and the cores of the Jovian planets. Terrestrial planets form in the hot, high density region of the protoplanetary disk and are too small and too close to the sun to attract gas molecules. However, the Jovian planets are further away from the sun in the cooler, high density area of the protoplanetary disk. Usually more massive, Jovian planets can attract more gas by gravity, thus creating a gaseous exterior.

Problem 4

Describe the evolution of a 1 solar mass star. Draw the HR-diagram and identify the significant phases of burning. Which events mark the ’transitions”? Provide the time scales for the various burning stages.

While the planetary nebula is evolving to form the star and its planets, an accretion disk which rotates around the central star. The regions closest to the star are highly dense. In this central region,dust and rocks bump into each other often. This accumulation eventually forms the inner, rocky planets. However, solar winds push the lighter gasses away from the star. There is still a small amount of rock in the outer region. This small amount slowly makes small clumps that eventually become the cores of the Jovian planets. These small cores attract the gasses that are pushed out by the solar winds, and eventually form the gas giants we see today. It is important to note that the solar winds are not strong enough to push the rocks and heavier materials out farther into the depths of the solar system.

The following website has some fun, interactive, guides to the evolution of a star: Interactive Stellar Evolution