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Chapter 5: Q60P (page 1215)

.. Quasars,an abbreviation for quasi-stellar radio sources,are distant objects that look like stars through a telescope but that

emit far more electromagnetic radiation than an entire normal galaxy of stars. An example is the bright object below and to the

left of center in Fig. P36.60; the other elongated objects in this image are normal galaxies. The leading model for the structure

of a quasar is a galaxy with a supermassive black hole at its center. In this model, the radiation is emitted by interstellar gas and dust within the galaxy as this material falls toward the black hole. The radiation is thought to emanate from a region just a few light-years in diameter. (The diffuse glow surrounding the bright quasar shown in Fig. P36.60 is thought to be this quasar鈥檚 host galaxy.) To investigate this model of quasars and to study other exotic astronomical objects, the Russian Space Agency plans to place a radio telescope in an orbit that extends to from the earth. When the signals from this telescope are combined with signals from the ground-based telescopes of the VLBA, the resolution will be that of a single radio telescope in diameter. What is the size of the smallest detail that this arrangement could resolve in quasar , which is light-years from earth, using radio waves at a frequency of ? (Hint:Use Rayleigh鈥檚 criterion.) Give your answer in light-years and in kilometres. Figure P36.60

Short Answer

Expert verified

the size of the smallest detail that this arrangement could resolve

2.1 light-years

Step by step solution

01

Determine the Rayleigh's criterion

For a circular aperture, lens, or mirror, the Rayleigh criterion states that two images are just resolvable when the centre of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other

02

Determine the size of the smallest detail that this arrangement could resolve

IDENTIFY and SET UP:

This problem concerns resolving power of an arrangement of telescopes (a combination of a space radio telescope and the

VLBA)- We use Eq- (36.17) to ?nd the angular separation 0 of the smallest detail this arrangement could resolve in quasar 3C

405- Hence, the size of the smallest (resolvable) detail in the quasar is

EXECUTE:

From Eq- (36.17) the angular separation 0 of the barely resolved detail in the quasar is

where We used the relationship A = c/ f Substituting the known values of f and D, we ?nd

)

Hence, the size of the barely resolved detail in the quasar

EVALUATE:

The size of the smallest detail that the arrangement of telescopes in our problem could

resolve is about 2 light-years- This is a

huge size; To have a sense of how actually big this size is, you might know the size of our solar system extends over only 1-5

light鈥攜ears! However, this size is in the order of the size of the region, it is thought, from which the radiation of quasar is

emanated, and which is very small compared to the size of it's host galaxy. So this limit of resolution can actually help us

reveal more about the structure of the quasar.

Therefore the size of the smallest detail that this arrangement could resolve

2.1 light-years

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