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Chapter 20: Problem 54

Material ejected from the supermassive black hole at the center of galaxy M87 extends outward from the galaxy to a distance of approximately 30,000 pc. M87 is approximately 17 Mpc away. a. If this material were visible to the naked eye, how large would it appear in the nighttime sky? Give your answer in degrees, recalling from Chapter 13 that 1 radian \(=57.3^{\circ}\) b. Compare this size with the angular size of the Moon.

Short Answer

Expert verified
The material would appear approximately 0.101 degrees in the sky, much smaller than the Moon's size of about 0.5 degrees.

Step by step solution

01

- Convert units to the same scale

Distance to M87 is given as 17 Mpc, and ejection distance as 30,000 pc. Convert both distances to the same units. Note that 1 Mpc = 1,000,000 pc, so 17 Mpc = 17,000,000 pc.
02

- Calculate the angular size in radians

The angular size \theta can be found using \theta = \frac{D}{d}, where D is the ejection distance (30,000 pc) and d is the distance to M87 (17,000,000 pc). \[\theta = \frac{30,000}{17,000,000} = 0.00176\, \text{radians}\]
03

- Convert the angular size from radians to degrees

Use the conversion factor where 1 radian = 57.3 degrees: \[\theta \text{ in degrees} = 0.00176 \, \text{radians} \times 57.3 \, \text{degrees/radian} = 0.101\, ^\circ\]
04

- Compare with the angular size of the Moon

The angular size of the Moon is approximately 0.5 degrees. Compare the calculated angular size (0.101 degrees) with that of the Moon: \[\text{Moon} = 0.5 ^\circ \] \[\text{M87 ejecta} = 0.101 ^\circ\] Therefore, the ejecta's angular size is much smaller than that of the Moon.

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Key Concepts

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

Supermassive Black Hole
A supermassive black hole is an immensely large black hole that can be found at the center of most galaxies. These black holes have masses ranging from hundreds of thousands to billions of times the mass of our Sun. For example, the supermassive black hole at the center of M87 galaxy is one of the largest known, and it gained fame when the Event Horizon Telescope captured its image.
Supermassive black holes have such strong gravitational pulls that not even light can escape from them. They often have significant effects on their surroundings, such as accreting material and ejecting jets of particles into space.
Angular Size
The angular size of an object is a measure of how large that object appears to an observer. It is an angle formed by lines drawn from the observer’s eye to each end of the object. This angle tells us how much of our field of vision the object occupies.
To calculate the angular size, we use the formula \(\theta = \frac{D}{d}\), where \(D\) is the actual size of the object, and \(d\) is the distance from the observer to the object. The result is in radians. For more practical use, we also often convert this measure to degrees, noting that 1 radian equals approximately 57.3 degrees.
M87 Galaxy
M87, also known as Messier 87, is a giant elliptical galaxy located in the Virgo Cluster. It is about 53.5 million light-years away from Earth. The supermassive black hole at its center is approximately 6.5 billion times the mass of our Sun. This galaxy is large and near enough that astronomers can study its properties in great detail.
One notable feature of M87 is the jet of energetic particles that is being ejected by its central black hole. This jet extends to a distance of about 30,000 parsecs, which is a substantial distance when considered in the context of the galaxy’s overall size.
Unit Conversion
Unit conversion can often be a necessary step in astronomical calculations. In the given problem, the distances are initially given in different units: parsecs (pc) and megaparsecs (Mpc). To compare or use these values in equations, we need to convert them to the same unit.
1 Mpc is equal to 1,000,000 pc (or 1 million parsecs). So, converting 17 Mpc to parsecs gives us 17,000,000 pc. It is crucial to perform these conversions correctly to ensure accurate results in any further calculations.
Astronomical Calculations
Astronomical calculations often involve working with very large distances and utilizing specific formulas to derive meaningful results. In the example problem, we calculated the angular size of an ejection from a supermassive black hole.
First, we converted all measurements to compatible units and used the formula for angular size in radians. Then, we converted this angular size into degrees to make it more intuitive for our comparison with familiar objects like the Moon. Such calculations are fundamental in the field of astronomy, providing insights into spatial relationships and dimensions in the universe.

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Most popular questions from this chapter

If a luminous quasar has a luminosity of \(2 \times 10^{41} \mathrm{W}\), or \(\mathrm{J} / \mathrm{s}\), how many solar masses \(\left(M_{\circ}=2 \times 10^{30} \mathrm{kg}\right)\) per year does this quasar consume to maintain its average energy output?

A quasar has a luminosity of \(10^{41}\) watts \((\mathrm{W}),\) or \(\mathrm{J} / \mathrm{s}\), and \(10^{8} M_{\circ}\) to feed it. Assuming constant luminosity and 20 percent conversion efficiency, what is your estimate of the quasar's lifetime?

T/F: AGNs are small but extremely luminous.

a. Go to the website for the Fermi Gamma-ray Space Telescope (http://fermi.gsfc.nasa.gov). Scroll down to click on "Full 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 NASA Swift Gamma-Ray observatory (http://heasarc.nasa.gov/docs/swift/swiftsc.html), which studies gamma-ray bursts. Click on "Latest Swift News" and look for a story about supermassive black holes.

Name and describe a common, everyday object that appears so dissimilar when viewed from different angles that from these different views you might think it was actually a different object.
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