Speed of light from galaxies. Refer to The Astronomical Journal study of galaxy velocities,… 1 answer below »

Speed of light from galaxies. Refer to The Astronomical Journal study of galaxy velocities, presented in Exercise 2.186 (p. 101). A second cluster of galaxies, named A1775, is thought to be a double cluster—that is, two clusters of galaxies in close proximity. Fifty-one velocity observations (in kilometers per second, km/s) from cluster A1775 are listed in the table on the next page. The data are saved in the GALAXY2 file.

a. Use a graphical method to describe the velocity distribution of galaxy cluster A1775.

b. Examine the graph you created in part a. Is there evidence to support the double-cluster theory? Explain.

c. Calculate numerical descriptive measures (e.g., mean and standard deviation) for galaxy velocities in cluster A1775. Depending on your answer to part b, you may need to calculate two sets of numerical descriptive measures, one for each of the clusters (say, A1775A and A1775B) within the double cluster. d. Suppose you observe a galaxy velocity of 20,000 km/s. Is this galaxy likely to belong to cluster A1775A or A1775B? Explain.

Exercise 2.186

Speed of light from galaxies. Astronomers theorize that cold dark matter caused the formation of galaxies and clusters of galaxies in the universe. The theoretical model for cold dark matter requires an estimate of the velocities of light emitted from galaxy clusters. The Astronomical Journal (July 1995) published a study of observed velocities of galaxies in four different clusters. Galaxy velocity was measured in kilometers per second (km/s), using a spectrograph and high-power telescope.

a. The observed velocities of 103 galaxies located in the cluster named A2142 are summarized in the accompanying histogram. Comment on whether the empirical rule is applicable to describing the velocity distribution for this cluster.

b. The mean and standard deviation of the 103 velocities observed in galaxy cluster A2142 were reported as  = 27,117 km/s and s = 1,280 km/s, respectively. Use this information to construct an interval that captures approximately 95% of the velocities of the galaxies in the cluster.

c. Recommend a single velocity value to be used in the CDM model for galaxy cluster A2142. Explain your reasoning.