Thursday, December 20, 2018

Speed of Light from Galaxies [Solved]

December 20, 2018
Speed of light from galaxies.Astronomers theorize that cold dark matter (CDM) caused the formation of galaxies. The theoretical CDM model requires an estimate of the velocity of light emitted from the galaxy. The Astronomical Journal (July, 1995) published  a study of galaxy velocities. One galaxy, named A1775, is thought to be a double cluster, that is, two cluster cluster of galaxies in close proximity. Fifty-one velocity observations (in kilometers per second, km/s) from cluster A1775 are listed in the table.

22,922
20,210
21,911
19,225
18,792
21,993
23,059
20,785
22,781
23,303
22,192
19,462
19,057
23,017
20,186
23,292
19,408
24,909
19,866
22,891
23,121
19,673
23,261
22,796
22,355
19,807
23,432
22,625
22,744
22,426
19,111
18,933
22,417
19,595
23,408
22,809
19,619
22,738
18,499
19,130
23,220
22,647
22,718
22,779
19,026
22,513
19,740
22,682
19,179
19,404
22,193





Source: Oegerle, W.R., Hill, J.M., and Fitchett, M.J., "Observations of high dispersion clusters of galaxies: Constraints on cold dark matter." The Astronomer Journal, Vol. 110, No. 1, July 1995, p. 34 (Table 1). p. 37 (Figure 1)
1. Use a graphical method to describe the velocity distribution of galaxy cluster A1775.
The graph used in this case is histogram. The histogram is made based on frequency distribution table. The table with 7 classes is shown as follows.

Class Interval
Frequency
18,000 – 19,000
3
19,000 – 20,000
15
20,000 – 21,000
3
21,000 – 22,000
2
22,000 – 23,000
18
23,000 – 24,000
9
24,000 – 25,000
1

    The histogram is shown as follows.

2. Examine the graph, part a. Is there evidence to support the double cluster theory? Explain.
Based on the histogram in part 1, it appears that the data is centered on 2 intervals, i.e. the 18,000 - 21,000 and 20,000 - 25,000 intervals. The visualization supports the double cluster theory, that is, two cluster cluster of galaxies in close proximity. 

3. 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.
Here the formula to calculate mean and standard deviation. Let and s respectively denote mean and standard deviation of sample data x, and n mean the number of data points,
 
Let a and b denote the data of galaxy velocities in cluster A1775A and 1775B respectively.

= (18499 + 18792 + 18933 + 19026 + 19057 + 19111 + 19130 + 19179 + 19225 + 19404 + 19408 + 19462 + 19595 + 19619 + 19673 + 19740 + 19807 + 19866 + 20186 + 20210 + 20785)/21 ≅ 19462

sa = sqrt(((18499 - 19462)2 + (18792 - 19462)2 + (18933 - 19462)2 + (19026 - 19462)2 + (19057- 19462)2 + (19111 - 19462)2 + (19130- 19462)2 + (19179- 19462)2 + (19225- 19462)2 + (19404- 19462)2 + (19408- 19462)2 + (19462- 19462)2 + (19595- 19462)2 + (19619- 19462)2 + (19673- 19462)2 + (19740- 19462)2 + (19807- 19462)2 + (19866- 19462)2 + (20186 - 19462)2 + (20210- 19462)2 + (20785 - 19462)2)/20) ≅ 532

with the same way for the data in cluster b, it can be obtained
≅ 22838
sb ≅ 561

4. Suppose you observe a galaxy velocity of 20,000 km/s. Is this galaxy likely to belong to cluster A1775A or A1775B? Explain
A galaxy velocity of 20,000 km/s is likely belong to cluster A1775A because it is in interval 18,000 - 21,000 km/s which is belong to cluster A1775A.

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