Question

A distant radio galaxy, $8 \mathrm{C} 1435+63,$ has a redshift of $z=4.25 .$ Assume WMAP values for this problem. (a) How old was the universe at this redshift? Express your answer both in terms of years and as a fraction of the present age of the universe. (b) What is the present proper distance (in $\mathrm{Mpc}$ ) to $8 \mathrm{C} 1435+63 ?$ (c) What was the proper distance (in Mpc) to $8 \mathrm{C} 1435+63$ when its light was emitted? (d) What is the luminosity distance to $8 \mathrm{C} 1435+63 ?$ (e) What is the angular diameter distance to $8 \mathrm{C} 1435+63 ?$ (f) The angular diameter of the nucleus of $8 \mathrm{C} 1435+63$ is about $5 "$. What is the linear diameter of the galaxy (in units of $\mathrm{kpc}$ )? (g) Suppose the galaxy's redshift were $z=1 .$ What would its linear diameter be [using the same angular diameter as in part (d)]? Further information about $8 \mathrm{C} 1435+63,$ which may be the progenitor of a cD elliptical galaxy, can be found in Spinrad, Dey, and Graham (1995).

          A distant radio galaxy, $8 \mathrm{C} 1435+63,$ has a redshift of $z=4.25 .$ Assume WMAP values for this problem.
(a) How old was the universe at this redshift? Express your answer both in terms of years and as a fraction of the present age of the universe.
(b) What is the present proper distance (in $\mathrm{Mpc}$ ) to $8 \mathrm{C} 1435+63 ?$
(c) What was the proper distance (in Mpc) to $8 \mathrm{C} 1435+63$ when its light was emitted?
(d) What is the luminosity distance to $8 \mathrm{C} 1435+63 ?$
(e) What is the angular diameter distance to $8 \mathrm{C} 1435+63 ?$
(f) The angular diameter of the nucleus of $8 \mathrm{C} 1435+63$ is about $5 "$. What is the linear diameter of the galaxy (in units of $\mathrm{kpc}$ )?
(g) Suppose the galaxy's redshift were $z=1 .$ What would its linear diameter be [using the same angular diameter as in part (d)]? Further information about $8 \mathrm{C} 1435+63,$ which may be the progenitor of a cD elliptical galaxy, can be found in Spinrad, Dey, and Graham (1995).

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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03/14/2023

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A distant radio galaxy, $8 \mathrm{C} 1435+63,$ has a redshift of $z=4.25 .$ Assume WMAP values for this problem. (a) How old was the universe at this redshift? Express your answer both in terms of years and as a fraction of the present age of the universe. (b) What is the present proper distance (in $\mathrm{Mpc}$ ) to $8 \mathrm{C} 1435+63 ?$ (c) What was the proper distance (in Mpc) to $8 \mathrm{C} 1435+63$ when its light was emitted? (d) What is the luminosity distance to $8 \mathrm{C} 1435+63 ?$ (e) What is the angular diameter distance to $8 \mathrm{C} 1435+63 ?$ (f) The angular diameter of the nucleus of $8 \mathrm{C} 1435+63$ is about $5 "$. What is the linear diameter of the galaxy (in units of $\mathrm{kpc}$ )? (g) Suppose the galaxy's redshift were $z=1 .$ What would its linear diameter be [using the same angular diameter as in part (d)]? Further information about $8 \mathrm{C} 1435+63,$ which may be the progenitor of a cD elliptical galaxy, can be found in Spinrad, Dey, and Graham (1995).

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00:01 Hello everyone for the first part of the question.

00:04 Let the age of universe be t, then t is equal to h0 rest of the power minus 1, whole divided 1 plus 2, then here h0 is equal to 70 km per second m -p -e.

00:31 Therefore h0 is equal to 2 .2 multiplied by 10 -d -pour -1.

00:37 Minus 13 per second.

00:41 Hence t is equal to 8 .66 multiplied by 10 to power 16 second or 2 .75 multiplied by 10 to power 9 year or 2 .75 beer.

01:04 Now for the second part the proper distance given as dp t0 which is equal to c divided by h0 z which is z where t not is present time therefore c multiplied by three multiplied by tenders to power 8 all divided by 70 multiplied by 4 .5 which is equal to 1 .93 multiplied by tenders to power 7 mp now for the seat part the proper distance when the light was emitted is d .p.

01:46 Te.

01:47 Therefore, d .p.

01:50 T .0 divided by 1 plus z.

01:55 Hence, where t .e is the time of emission, therefore it is equals to 3 .67 multiplied by 10 to power 6 mpe.

02:05 Now for the fourth part, the luminosity distance dl is equal to d .p.

02:13 T .0.

02:15 Multiplied by 1 plus z.

02:17 Therefore, the value is 10 .13 multiplied by tendous to power 7 m p.

02:26 Now for the fifth part, the angular diameter of the nucleus is 5 seconds...

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