Question

Consider the following table consisting of the observed wavelengths of the Lyman-? emission line and the strength of the line in ten galaxies. This emission line is an indicator of active star formation in a galaxy. We will assume that the strength of the line in these particular galaxies tracks the overall star-formation rate in the Universe at past times. Galaxy Observed Wave- length of Ly ? (nm) Strength of Emission line

		Strength of Emission line
1	168.6	34.5
2	384.1	213.3
3	576.5	544.4
4	693.6	439.0
5	761.2	634.4
6	981.5	698.8
7	1020.5	576.6
8	1092.7	392.1
9	1203.2	270.8
10	1346.0	194.2

a) Calculate the redshift of each galaxy assuming that the rest (emitted) wavelength of the Lyman-? line is 121.6 nm. Plot the line strength (y-axis) as a function of redshift (x-axis).

Answer 1

Redshift (z) is given by the formula:

where, and are the observed wavelength of Lyman-? line and rest wavelength (as seen by an observer at the galaxy) of Lyman-? line.

Redshift calculated from data given

No.	Wavelength Observed (in nm)	Strength of Emission line	Redshift
1	168.6	34.5	0.387
2	384.1	213.3	2.159
3	576.5	544.4	3.741
4	693.6	439.0	4.704
5	761.2	634.4	5.26
6	981.5	698.8	7.072
7	1020.5	576.6	7.392
8	1092.7	392.1	7.986
9	1203.2	270.8	8.895
10	1346.0	194.2	10.069

And here is the plot of "Strength of emission line vs Redshift":

The plot is generated by a python script, which is given below:

import matplotlib.pyplot as plt
import numpy as np
plt.style.use('ggplot')

## Variable declaration
wavelength = np.array([168.6, 384.1, 576.5, 693.6, 761.2, 981.5, 1020.5, 1092.7, 1203.2, 1346.0])
strength = np.array([34.5, 213.3, 544.4, 439.0, 634.4, 698.8, 576.6, 392.1, 270.8, 194.2])
rest_wavelength = 121.6

# Calcualting redshift
redshift = (wavelength - rest_wavelength)/rest_wavelength
print("Redshift of given data:")
for i in range(len(redshift)):
    print(wavelength[i], strength[i], round(redshift[i],3))

# Plotting
plt.plot(redshift, strength)
plt.scatter(redshift, strength)
plt.xlabel("Redshift")
plt.ylabel("Strength of emission line")
plt.grid(True)
plt.show()

END OF CODE