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Chapter 19: Problem 4

If you observed a galaxy with an \(\mathrm{H} \alpha\) emission line that had a wavelength of \(756.3 \mathrm{nm}\), what would be the galaxy's redshift? Note that the rest wavelength of the H \(\alpha\) emission line is \(656.3 \mathrm{nm}\). a. 0.01 b. 0.05 c. 0.10 d. 0.15

Short Answer

Expert verified
The redshift is approximately 0.152, closer to 0.15. So, the correct answer is d. 0.15.

Step by step solution

01

Determine Redshift Formula

The formula for redshift (z) is given by: \[ z = \frac{\lambda_{observed} - \lambda_{rest}}{\lambda_{rest}} \] where \( \lambda_{observed} \) is the observed wavelength and \( \lambda_{rest} \) is the rest wavelength.
02

Identify Given Values

From the problem, the observed wavelength \( \lambda_{observed} = 756.3 \mathrm{nm} \) and the rest wavelength \( \lambda_{rest} = 656.3 \mathrm{nm} \).
03

Substitute Values into Formula

Substitute the given values into the redshift formula: \[ z = \frac{756.3 \mathrm{nm} - 656.3 \mathrm{nm}}{656.3 \mathrm{nm}} \]
04

Calculate the Difference

Calculate the difference in the numerator: \[ 756.3 \mathrm{nm} - 656.3 \mathrm{nm} = 100 \mathrm{nm} \]
05

Calculate the Redshift

Now, substitute this difference back into the formula: \[ z = \frac{100 \mathrm{nm}}{656.3 \mathrm{nm}} \approx 0.152 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

H-alpha emission line
The H-alpha emission line is a specific wavelength of light emitted by hydrogen atoms when an electron falls from the third energy level to the second energy level. This spectral line is significant in astronomy as it helps to identify regions with ionized hydrogen, such as star-forming regions and certain types of galaxies. The rest wavelength of the H-alpha emission line is exactly 656.3 nanometers (nm). Noticing shifts in this wavelength allows us to infer useful astrophysical data.
Wavelength shift
A wavelength shift occurs when the observed wavelength of light from an object differs from its rest wavelength. In the context of observational astronomy, this shift can be due to various phenomena like the Doppler effect or, most commonly, the cosmological redshift. For instance, in the given exercise, the observed H-alpha emission line wavelength is 756.3 nm, while its rest wavelength is 656.3 nm. The difference of 100 nm indicates a redshift, meaning the galaxy is moving away from us.
Cosmological redshift
Cosmological redshift happens because of the expansion of the universe. When light travels through space, which is constantly expanding, the wavelengths of the light stretch, causing a redshift. The further away a galaxy is, the faster it appears to be moving away and the more its light is redshifted. The redshift, denoted as 'z', is calculated using the formula \( z = \frac{\lambda_{observed} - \lambda_{rest}}{\lambda_{rest}} \). In our specific problem, this formula helps us calculate a redshift value of approximately 0.152.
Observational astronomy
Observational astronomy involves collecting and interpreting data from various celestial objects using telescopes and other instruments. It includes studying light from stars, galaxies, and other astronomical phenomena to deduce their properties and behaviors. One key technique is the analysis of light spectra, including emission and absorption lines like the H-alpha line. Observing wavelength shifts in these lines helps astronomers understand the movement and distances of celestial bodies, contributing to our knowledge of the universe's structure and expansion.

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Most popular questions from this chapter

a. Go to the website for the Fermi Gamma-ray Space Telescope (http://fermi.gsfc.nasa.gov). Scroll down to click on 鈥淔ull News Archive" and look for a story about dark matter. What has this telescope discovered about dark matter? b. Go to the website for the Alpha Magnetic Spectrometer (http://ams02.org), a particle physics detector located on the International Space Station to search for dark matter, including WIMPs. What are the latest results?

The quasar \(3 \mathrm{C} 273\) has a luminosity of \(10^{12} L_{\text {sun }}\). Assuming that the total luminosity of a large galaxy, such as the Andromeda Galaxy, is 10 billion times that of the Sun, compare the luminosity of \(3 \mathrm{C} 273\) with that of the entire Andromeda Galaxy.

a. Go to the website for the NASA Swift Gamma-Ray observatory (swift.gsfc.nasa.gov), which studies gamma-ray bursts. Click on "Latest Swift News" and look for a story about supermassive black holes. What has been discovered? b. Go to the website for NuSTAR (Nuclear Spectroscopic Telescope Array- http://www.nustar.caltech.edu), a space telescope launched by NASA in 2012 . This mission is studying active galaxies hosting supermassive black holes. What type of telescope is this (wavelengths observed, general design)? What has been discovered?

Describe what astronomers think is happening at the center of a galaxy that contains an AGN.

What accounts for the differences among various types of AGNs? a. the type of the host galaxy b. the size of the central black hole c. the amount of dark matter in the galaxy's halo d. our viewing angle
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