Lab 2 Cosmology 2 (Hubble's Law)

Transcription

1 The 8 supernovae used in this lab were observed in the mid 1990's. You will use photometry and spectrometry data to test Hubble's Law. This lab contains equal parts for analysis and explanation, involving the testing of Hubble's Law. It will require the use of a spreadsheet, and cannot be completed without reading the recommended background for each section. The lab should take about 2 hours to complete. Part A Background Carrol & Ostlie Chapter Read the chapter and answer the following questions. i. What is Hubble's Law? ii. What are its implications with regard to the evolution of the universe? Part B Measuring Redshifts Carrol & Ostlie Chapter The absorption spectra of 8 supernovae are shown in the appendix of this handout. They show the flux as a function of wavelength of light (a light curve) recorded by a spectrometer. You will determine the redshift by measuring how far the Si II line is shifted from its 'rest frame' value (at a redshift of 0) of 6150 Angstroms. i. On the spectra, the red line represents the value of 6150 Angstroms. The actual Si II line is the dip or trough on, or to the right of the red line. By measuring the difference between these two, calculate the redshift for each supernova. ii. From the redshift, calculate the relative velocity of each supernova relative to the Sun. iii. What are some typical uncertainties in the determination of a galaxy's redshift? How do these compare to your uncertainties? What factors contribute to this?

2 Part C Measuring Distance (Zeilik & Gregory) Chapter 22-3 Parts A and B Resources: It is split into two parts in the procedure, but this is the general formula for the apparent magnitude/distance relation. Here, m is the apparent magnitude, M is the absolute magnitude for type Ia supernovae (-19.12), and d is the distance in pc m " M = 5log 10 ( d) +c i. From the paper listed under Resources, find the photometry tables for the 10 supernovae used in Part A. Using the apparent magnitudes from the V column, find the minimum value for each supernova (the brightest the supernova reached) and record this. ii. Calculate the distance modulus, D, for each supernova. The distance modulus is given by D=m-M. From these values, use the equation given here to find the distance, d, to each supernova in Mpc. d =10 D+5 5 " 6 Mpc iii. What is special about type Ia supernovae that allows astronomers to use this distance/brightness generalisation? iv. How could we have improved the accuracy of this calculation? Part D Analysis and Conclusions (Zeilik & Gregory) Chapter 22-3 Part C Note: You will be required to submit graphs produced as part of your solutions. i. Plot a scatter graph of distance to each supernova (in Mpc) on the x axis, and the velocity of each supernova on the y axis. Perform a best fit to this data. ii. What is the value of the gradient of the line of best fit? iii. What does this constant represent? iv. What is unusual about the expected value? Give some explanations for its unusual nature. v. Is your value compatible with the Hubble's Law? ie. does it fall within the range of accepted uncertainty? vi. Derive a value for the Hubble time.

3 Appendix Data for Redshifts Figure 1 -- Supernova 1994ae

4 Figure 2 -- Supernova 1996X

5 Figure 4 -- Supernova 1995E Figure 3 -- Supernova 1995D

6 Figure 6 -- Supernova 1995bd Figure 5 -- Supernova 1995al

7 Figure Figure Supernova 1995ac 1996bo Figure Figure Supernova Supernova 1996bl 1994S