Answer Key - Measuring the Hubble Constant

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Dec 6, 2023

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Measuring the Hubble Constant Introduction Flash back to the early 1900s --- astronomers are convinced that we live in a static universe. The universe, they felt, wasn’t getting bigger or smaller – it was always the same size! Indeed, Einstein was so convinced that the universe was static that he modified his theory of relativity to make sure it predicted a static universe. However, this view of the universe was all about to change! In the 1920s Edwin Hubble created a major stir in the astronomy community with his observation that distant galaxies were all moving away from the Milky Way. This led him to suggest that the entire universe was expanding! Hubble not only found that the distant galaxies were all moving away from the Milky Way. He also discovered that the farther away a galaxy was, the faster it was moving away! We can express this in what is now known as the Hubble Law: v = H o * d where v = Velocity of galaxy from Milky Way H o = Hubble constant d = Distance of galaxy from Milky Way In Hubble’s Law we express the velocity in km/s and the distance in megaparsecs (Mpc). 1 Mpc = 1,000,000 parsecs (pc) and 1 pc = 3.18 light years Finding the value of the Hubble constant has been extremely important to astronomers because we can use the Hubble constant to estimate the age of the universe! In today’s lab we will measure the Hubble constant using a set of 7 nearby galaxies. For each of these galaxies, you will measure its velocity as well as its distance! At the end we will see how old you find the universe to be! Measuring Distance To measure distance we will use the angular size of each galaxy. Question: What happens to the angular size of an object as it moves to greater and greater distances? Angular size decreases as the distance increases.

Questions: Imagine that you see two galaxies. Galaxy A has a larger angular size than Galaxy B. Can you determine which galaxy is the closest to us? If so, which galaxy is the closest? If you can’t, explain why you can’t determine which galaxy is closest. No --- angular size doesn’t tell you distance unless you know how the actual, physical size of the objects. You should not have been able to determine which galaxy was bigger based on what I told you in the question above. Now, assume that Galaxy A and Galaxy B have the same physical size. Can you determine which galaxy is the closest to us? If so, which galaxy is the closest? If you can’t, explain why you can’t determine which galaxy is closest. Yes – Galaxy A is closer because it has a larger angular size. For this lab, we will assume that every spiral galaxy has the same physical size. This will let us measure the distance! For each galaxy, complete the following steps to measure its distance. Record your numbers in the Table on the next page. 1) Measure the angular size in centimeters. Make sure to measure the galaxy along its largest axis – this may mean that you need to measure diagonally. 2) Convert the angular size from centimeters to degrees by: Angular size (in degrees) = 0.018354 * Angular size (in cm) 3) Calculate the distance to each galaxy in Mlyr using: Distance (in millions of light years) = 4.1 / Angular Size of Galaxy in degrees

Measuring Velocity To measure the velocity of each galaxy, we will take advantage of the Doppler shift. Emission and absorption lines from objects moving away from us will be shifted to longer wavelengths (called a redshift). The faster the object is moving away, the greater the redshift. If we know the redshift, we can calculate the velocity. For each galaxy, complete the following steps to measure its velocity. Record your numbers in the Table below. 1) Using the spectrum, record the wavelength corresponding to the Hα line. 2) Calculate the redshift (z) for each line by: ( ObservedWavelength − RestWavelength ) Rest Wavelength The rest wavelength for Hα is 6562.8 angstroms. 3) Calculate the velocity in km/s for each line by: v = 300,000 * z Galaxy Angular Size (in cm) Angular Size (in degrees) Distance (in Mlyrs) Observed Wavelength of Hα Redshift Velocity (in km/s) NGC 1832 2.0 0.0367 110 6607 .00673 2020 NGC 2276 2.2 0.0404 101 6615 .00780 2340 NGC 2903 10.0 0.184 22 6573 .00155 466 NGC 3147 1.7 0.0312 130 6620 .00872 2615 NGC 3627 5.8 0.106 39 6578 .00232 695 NGC 5248 3.0 0.0551 75 6585 .00338 1015 NGC 6643 2.8 0.0514 82 6591 .00430 1289

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Answer the following question: Which galaxy has the largest velocity? Which galaxy has the smallest velocity? Largest = NGC3147 Smallest = NGC2903 Look at the images of the two galaxies --- which one of these galaxies is larger? Is this what you would expect? Explain your answer. NGC2903 is larger – this is what I would expect because the galaxy with the smallest velocity will be the closest, which means that it will look the largest in the sky. Figuring out the Age of the Universe 1) Mark the location of each galaxy on the graph paper attached. The distance will be along the horizontal axis and the velocity will be on the vertical axis. Be very careful with this step!!! 2) Your data points should roughly lie in a straight line. Starting from the bottom left corner of the graph (0 km/s and 0 Mlyrs) draw a straight line that best fits the points on the graph. 3) Find where the line you have drawn reaches 90 Mly. Velocity at 90 Mlyr = 1780 km/s 4) Calculate the Hubble constant by: HubbleConstant = 3.26 × Velocity at 90 Mlyrs you wrote ∈ step above 90 Hubble constant = 64.5 5) Now that you have the Hubble constant you can estimate the age of the universe! Age of universe ( ¿ billionsof years ) = 977.85 HubbleConstant Age of universe = 15.1 billion years. 6) Answer the following question: Our Sun is approximately 5 billion years old. The oldest stars in the Milky Way are around 13 billion years old. Given these ages, does your age of the universe make sense? Explain. Yes – the universe should be older than the Sun or the oldest stars in our galaxy!

Velocity (km/s) 00 1000 1500 2000 2500 3000 3500 0 30 60 90 120 150 180 Distance (Mlyrs – Millions of Light Years) x x x x x x x

Answer Key - Measuring the Hubble Constant

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