Problem 12 - Astronomy: At Play in the Cosmos

Question

Which of the following is true of an object with a redshift of \(z=5 ?\) a. Its spectrum shows longer wavelengths than is expected for specific elements. b. It is receding faster than an object with \(z=6\). c. It is only a few light-years away. d. It may be significantly closer than a second object with \(z=5\). e. It is farther away than an object with \(z=7\).

Step-by-Step Solution

Answer

Option (a) is true.

Step 1: Understanding Redshift

Redshift, denoted by \(z\), is a measure of how much the wavelength of the light from an object has been stretched due to the expansion of the universe. A positive redshift indicates that an object is moving away from us.

Step 2: Analyzing Option (a)

Option (a) suggests that the spectrum shows longer wavelengths than expected. A higher redshift \(z=5\) means the spectral lines are shifted towards the red end of the spectrum, indicating longer wavelengths. Therefore, option (a) is true.

Step 3: Analyzing Option (b)

Option (b) states that the object is receding faster than an object with \(z=6\). In reality, an object with a higher redshift \(z=6\) is receding faster than an object with \(z=5\). So option (b) is false.

Step 4: Analyzing Option (c)

Option (c) suggests the object is only a few light-years away. Typically, an object with \(z=5\) is very distant, far more than just a few light-years away, as high redshift values generally correspond to greater distances due to the expansion of the universe. So option (c) is false.

Step 5: Analyzing Option (d)

Option (d) implies that the object may be significantly closer than another object with \(z=5\). If two objects have the same redshift \(z=5\), they are generally at similar cosmological distances, so option (d) is typically false unless some peculiar velocities are involved.

Step 6: Analyzing Option (e)

Option (e) states that the object is farther away than an object with \(z=7\). An object with \(z=5\) is less redshifted and thus closer compared to an object with \(z=7\). Therefore, option (e) is false.

Key Concepts

Expansion of the Universe

The concept of the universe expanding is a fundamental idea in cosmology. Imagine the universe as a giant loaf of raisin bread, where galaxies are like raisins spread throughout the dough. As the bread bakes, it rises and expands, causing the raisins to move away from each other. This is similar to what happens in our universe.

• As space itself stretches, light traveling through space also stretches, resulting in redshift.
• The more the universe has expanded since the light left its source, the more redshifted and stretched the light becomes.

In the context of redshift, this expansion is crucial because it allows astronomers to determine how fast and in which direction objects are moving relative to us. The further away an object is, the faster it appears to move away due to the ballooning space between us and distant galaxies.

Spectral Line Redshift

Spectral line redshift occurs when spectral lines in the light emitted or absorbed by an object shift toward longer wavelengths. This shift towards redder parts of the spectrum is a signature of an object moving away from us due to the expansion of the universe.

• Redshift is quantified by the parameter \( z \), which measures the change in wavelength.
• If a galaxy's spectral line shifts significantly to longer wavelengths, it indicates a high redshift value, meaning the galaxy is moving away quickly.

To measure this, scientists observe specific elemental spectra, like hydrogen or helium, and note how much these lines are moved from their expected positions.

Cosmological Distance Measurement

Measuring distances in the universe is a challenging task due to its vastness. However, redshift provides a pivotal tool for these measurements. Let's see how:

• Redshift correlates with distance through a relationship known as Hubble's Law, which states that the further away a galaxy is, the faster it moves away.
• This law implies a linear relationship: doubling the distance roughly doubles the redshift.

Using redshift, astronomers determine how far back in time they are observing. Since light takes time to travel, seeing a galaxy with a high redshift means viewing it as it was billions of years ago, helping paint a timeline of the universe's history and expansion.