Question

In: Physics

Suppose that you have obtained spectra of several galaxies and have measured the observed wavelength of...

Suppose that you have obtained spectra of several galaxies and have measured the observed wavelength of the H-alpha line (rest wavelength = 656.3nm) to be:

Galaxy 1: 659 nm. Galaxy 2: 666.5 nm. Galaxy 3: 676.6 nm.

10. [4pt] Calculate the redshift, z, for each of these galaxies.

11. [4pt] Calculate the radial velocity of each of these galaxies.

12. [4pt] Assuming a Hubble Constant of 69.6 km/s/Mpc, cal- culate the distance to each of these galaxies (answer in Mpc).

Solutions

Expert Solution

10. redshift z = /

where = rest wavelength

= observed wavelength - rest wavelength

for Galaxy 1:   = 659-656.3 = 2.7nm

z1 = 2.7nm / 656.3 = 0.0041

for Galaxy 2   = 666.5-656.3 = 10.2 nm

z2 = 10.2nm / 656.3 = 0.0155

for Galaxy 3:   = 676.6-656.3 = 20.3nm

z3 = 20.3 / 656.3 = 0.031

11. Velocity and redshift relation = v/c = ((z+1)2 -1 )/ ((z+1)2 +1)

For Galaxy 1 :

(z1+1)2 = 1.00412 = 1.008

v/c = (1.008 - 1) / (1.008+1) = 0.008/2.008 = 0.0039

v1=0.0039c = 0.0039*3*108 = 1.2x 106 m/s

For Galaxy 2 :

(z2+1)2 = 1.0152 = 1.03

v/c = (1.03- 1) / (1.03+1) = 0.03/2.03 = 0.0147

v2=0.0147c = 0.0147*3*108 = 4.4x 106 m/s

For Galaxy 3 :

(z3+1)2 = 1.032 = 1.061

v/c = (1.061- 1) / (1.061+1) = 0.061/2.061 = 0.0296

v3=0.0296c = 0.0296*3*108 = 8.8x 106 m/s

12. according to Hubble's law, v = HD

H= Hubble constant =69.6 km/s/Mpc = 0.0696m/s/Mpc

D= distance of galaxy from observer

v= velocity of galaxy

Hence, D= v/H

Distance of galaxy1 = D1 = v1/H = 1.2 x106 / 0.069 Mpc = 17.39 x 106 Mpc

Distance of galaxy2 = D2 = v2/H = 4.4x126 / 0.069 Mpc = 63.7 x 106 Mpc

Distance of galaxy3 = D3 = v3/H = 8.8x106 / 0.069 Mpc = 127.5 x 106 Mpc


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