Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 24, Problem 26Q

(a)

To determine

The speed at which the blazar seems to be drifting away from us when a blazar at z=1.00 faces variation in brightness that lasts 1 week (168 hour) as seen from Earth.

(a)

Expert Solution
Check Mark

Answer to Problem 26Q

Solution:

v=1.8×108m/s.

Explanation of Solution

Given data:

Red shift of the blazar is z=1.

Formula used:

The expression for Hubble’s Law red shift is written as,

z=1+vc1vc

Here, z is the red shift, v is the speed of the blazar, and c is speed of the light.

Explanation:

Write the expression for Hubble’s Law for red shift.

z=1+vc1vc

Rearrange this for v.

v=c[(z+1)21(z+1)2+1]

Substitute 1 for z and 3×108m/s for c.

v=(3×108m/s)[(1+1)21(1+1)2+1]v=1.8×108m/s

Conclusion:

Therefore, the speed of the blazar is v=1.8×108m/s.

(b)

To determine

The time period for which the variation in brightness lasted as measured by an astronomer within the blazar’s host galaxy by using the idea of time dilation if a blazar at z=1 goes through fluctuation in brightness that lasts 1 week (168 hour) as seen from Earth.

(b)

Expert Solution
Check Mark

Answer to Problem 26Q

Solution:

Δt=134h.

Explanation of Solution

Given data:

Red shift of the blazar is z=1.

Speed of the blazar is 1.8×108m/s

Formula used:

The expression for time dilation in relativity is written as,

Δt'=Δt1v2c2

Here, Δt is the time interval for an observer, Δt' is the time interval for the person moving with speed v, c is speed of the light and v is the relative velocity between the observer and moving object.

Explanation:

Write the expression time for dilation in relativity.

Δt'=Δt1v2c2

Rearrange this for Δt.

Δt=Δt'(1v2c2)

Substitute 1.8×108m/s for v, 168h for Δt' and 3×108m/s for c.

Δt=(168h×3600sh)(1(1.8×108m/s)2(3×108m/s)2)=483840s×1h3600s=134h

Conclusion:

Therefore, the fluctuation lasted for Δt=134h.

(c)

To determine

The maximum size (in au) of the region of the blazar that emits energy.

(c)

Expert Solution
Check Mark

Answer to Problem 26Q

Solution:

The maximum size of the region of the blazar that emits energy is 2.06×102au.

Explanation of Solution

Introduction:

Blazars are an example of AGN. All the AGNs are powered by the material which falls into the black hole at the center of a host galaxy. This black hole generates a large amount of energy from the gas and dust.

Explanation:

Blazars emits energy from the surface. This surface is small with respect to the quasar. This is, approximately, 103parsecs, and 1parsec=2.06×105au. So, the maximum size of the region of the blazar that emits energy is found out as follows:

103parsecs=(2.06×105au)103=2.06×102au

Conclusion:

Therefore, the maximum size of the region of the blazar that emits energy is 2.06×102au.

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