Question

9. The Hubble Law and Standard Candles. An elliptical galaxy called A lies at a distance of 20 Mpc (megaparsecs).

1. What would the velocity inferred from the redshift of its spectral lines be for galaxy A? Assume a Hubble constant of 73 km/s/Mpc
2. An identical elliptical galaxy called B with exactly the same luminosity as A is found to have a redshift exactly three times that of A. How does the measured brightness of B compare to that of A? (In other words, what is the ratio B_B/B_A?)

       c. Suppose a Type I (white dwarf) supernova explodes in galaxy B and has a maximum luminosity of 5 x 10⁴⁵ W. If the brightness of the supernova is measured to be 1 x 10^-4 W/m², determine the distance to Galaxy B in pc and explain whether its distance is what you expect assuming 10% error in the observations.

Answer 1

9a) lets consider hubble's law,

V = h*D

V = 73 * 20 = 1460 km/s of galaxy A

Velocity of galaxy, V = c*Z, where Z=redshift.

redshift of galaxy A, Za =1460 / (3*10^8) = 4.867*10-6

9b) luminosity of galaxy A =luminosity of galaxy B => La = Lb

redshift of galaxy B = 3 * redshift of galaxy A = 3 * 4.867*10-6 = 1.46 * 10-5

brightness of a galaxy,

we know, Da = 20Mpc

to know, Db, we use the redshift Zb

Vb = c * Zb = 3*10^8 * 1.46 * 10-5

Vb = 4380 km/s

Db = Vb / h = 4380 / 73 = 60 Mpc

9c)

luminosity of white dwarf, Lw = 5*1045 W

brightness of white dwarf, Bw = 1*10-4 W/m2

we know,