A2 H 54 A3 AstrophysicsCosmology

8/11/2019 A2 H 54 A3 AstrophysicsCosmology

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The Doppler Effect

A B C D EA B C D

As the ambulance travels

forwards:

The sound wave in front is

compressed

- decreasing its wavelength

- increasing its frequency

The sound wave behind is

stretched out:

- increasing its wavelength

- decreasing its frequency
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The Doppler Effect also occurs with light and radio waves.

With light waves:

In front of the moving object

decreasing wavelength and increasing frequency

makes the light BLUER

Behind the moving object

increasing wavelength and decreasing frequency

makes the light REDER


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v

Radial and tangential velocityConsider a galaxy movingrelative to the Sun at velocity v.

This velocity can be split into twocomponents:

radial velocity, vr

vr= vcos

and tangential velocity, vtvt= vs in

The Doppler Effect can beused to measure radialvelocities.

vr

vt
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Doppler effect equations

When the radial speed of the object, v isMUCH LESSthan the speed of light, c.

change of frequency = ob ject radial speedsou rce frequency speed of l igh t

f = vf c


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Also:

change of waveleng th = ob ject radial speed

sou rce waveleng th speed of l igh t

= - v

c

In either case, The Doppler Shift,zis given by:

z = f = - = v

f c

Remember: vMUST BE


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Question 2

The Andromeda Galaxy has a Doppler Shift of 0.000 5.

The observed wavelengths are also smaller than thesource wavelengths.

(a) Calculate radial velocity of the Andromeda Galaxyrelative to the Earth.

(b) What will be the observed wavelength of red light if thesource was 700.00 nm?

c= 300 000 kms-1


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Question 3

A hydrogen radio source emits waves of frequency 1420

MHz. A radio telescope observes these waves to have afrequency of 1430 MHz.

Calculate radial velocity of the source relative to the Earth.

c= 300 000 kms-1


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Doppler shift summary

Doppler

shift, z

in frequency

f

f

in wavelength

Colour shift

with light

Source

movestowards

observer

Source

moves away

from

observer

+vc

+vc

-vc

-vc

RED

SHIFT

BLUE

SHIFT


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400 500 600 700

wavelength / nm

Doppler shift in spectra

Stationary source

H

Receding source

RED SHIFT

H

Approaching sourceBLUE SHIFT

H


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Question

The hydrogen-alpha spectra line of a distantgalaxy occurs at a wavelength of 680 nm. In the

Sun this wavelength is 656 nm.

Calculate the recessional radial velocity of the

galaxy.

c= 300 000 kms-1


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The Doppler effect with binary stars

A binary star system consists of two stars in mutual orbitabout each other.

The two stars are often too close together to be resolved bya telescope as separate stars.

However, as they orbit each other they will be moving awayand towards the Earth.

The stars will produce both red and blue shifts which canbe measured.

This type of system is called a spectroscopic binary.From the Doppler shift measurements the orbital speeds ofthe stars can be found.


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Question

A spectral line of a certain spectroscopic binary

merges once every 4 years and splits to amaximum displacement of 0.036 nm and 0.015

nm from its laboratory wavelength of 656 nm.

Calculate:(a) the orbital speed of each star and

(b) the radius of the larger orbit.

c= 300 000 kms-1


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Hubbles Law

In 1929 after plotting the redshift calculated speeds ofabout thirty galaxies against their distances Hubble noticedthat a rough straight line through the origin was obtained.


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Hubbles law states that the speed of recession of agalaxy is proportional to the distance to the galaxy.

v d

inserting a constant of proportionality:

v = Hd

H = the Hubble constant = 65 km s-1Mpc-1

Notes:

(a) Mpc = megaparsec (= 3.26 million light years)

(b) Hubbles law does not work with some nearby galaxies(which are approaching us!)


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Question 1

Calculate or state the speeds expected forgalaxies at distances: (a) 1 Mpc; (b) 10 Mpc

& (c) 1 billion light years.

1 Mpc = 3.26 million light years


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Question 2

Calculate the distance, in light years, to agalaxy if its recessional velocity is 10% of

the speed of light.

c= 300 000 kms

-1

& 1 pc = 3.26 lyr


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The expansion of the Universe

Hubbles law tells us that distant galaxies arereceding from us and that the further they areaway the faster they are moving away from us.

Hence the Universe is expanding.

Balloon model of theexpanding Universe

The space between the

galaxies expands and so the

galaxies grow further apart


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Estimating the age of the UniverseHubbles constant tells us that the speed of a galaxy increases by65 kms-1for every Mpc or 3.26 million light years.

For a galaxy to be receding at the speed of light its distance wouldbe:

(300 000 kms-1) / (65 kms-1 Mpc-1)

= 4 615 Mpc

= 4 615 x 3.26 million light years= 15 billion light years

Galaxies cannot travel this fast.

Therefore light cannot have been travelling for this length of time.

Therefore the Universe must be less than 15 billion years old.

The current greatest length of time observed is about 13.5 billionyears.


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As can be seen in the above calculation, the maximum size of theUniverse, Dis given by:

D = c / H

But distance = speed x t ime

For a galaxy travelling at speed cfor the age of the Universe T.

D = c T

Therefore: c / H = c T

1 / H = T

Hence the maximum age of the Universe is given by:

T = 1

H

Note: All of the above assumes that the Hubble constant has notchanged during the lifetime of the Universe.


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Question 1

The unit of 1 / H must be one of time.Calculate the value of 1 / H in seconds.

1 Mpc = 3.1 x 1022m


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Question 2

In 2009 measurements from the Hubble

Space Telescope yielded a Hubble constantof 74.2 3.6 km s-1Mpc-1. What is the

maximum age of the Universe, in years,

based on this measurement?1 Mpc = 3.1 x 1019km


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The Big Bang theory

Hubbles law supports the idea that theUniverse started in some form of massive

explosion.

This idea is called the Big Bang theory.

This theory was not generally accepted

until 1965 before which an alternative

explanation for the expansion of the

Universe called the Steady State theory

was dominant.


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The microwave detector used

by Penzias and Wilson

Cosmic Microwave Background radiation.

CMB map of the whole Universe obtained

by the COBE satellite in 1989


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2. Relative abundance of hydrogen to heliumUsing the Big Bang model it is possible to calculate theratio of concentration of hydrogen to helium-4 by mass.

This depends on the ratio of photons to baryons, whichitself can be calculated independently from the detailedstructure of Cosmic Microwave Background fluctuations.

The ratio by mass predicted is about 4:1.

The measured ratio of abundance is 3:1 which is roughly inagreement.

Other ratios such as hydrogen to Lithium-7 or Helium-3also give roughly similar results.


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Revision Question

Calculate the wavelength and frequency

associated with a thermal temperature of 2.7K.


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Revision of supernovae as standard candles

Type 1a supernovae have a known peak luminosity

allowing them to be used as standard candles.

At their peak all of these supernovae have an absolutemagnitude, Mof -19.3 0.03.

By noting their apparent peak magnitude, msuchsupernovae can be used to determine this distances togalaxies using the equation:

m M = 5 log (d / 10)


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QuestionIn a distant galaxy a Type 1a supernova is observed to

have an apparent magnitude of + 21 and a recessionalspeed (from red-shift measurement) of 60 000 kms-1.

Calculate the distance to this galaxy (a) from the

magnitude measurement (b) using Hubbles law.

Assume Type 1a supernovae have an absolute magnitudeof19.

Comment on your answers


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Dark energy In 1998 astronomers discovered that very distant type 1a

supernovae were further away than expected. Measurement of their

red shifts (used to measure their velocities) and the use of HubblesLaw to obtain their distances shows that these supernovae arefainter than expected.

These mesurements indicate that the Universe is expanding fasternow than when the supernovae exploded as the light has had totravel further to reach us than expected by a constant rate ofexpansion (assummed to be the case with Hubbles Law).

These and further measurements have led astronomers to concludethat the expansion of the Universe has been accelerating for aboutthe past 5000 million years.

Before this discovery, the expansion of the Universe was expected tobe decelerating due to the attractive gravitational forces of galaxieson each other.

Therefore there appears to be some unknown repulsive force actingwhich is releasing some hidden potential energy which is currentlyknown as dark energy.


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The nature of dark energyis unclear. It is thought to be a form of

background energy present throughout space and time.

It is more prominent than gravity at large distances as gravity

becomes weaker with distance (inverse square law) whereas theforce associated with dark energy is thought to remain constant.

Current theories suggest that it makes up 70% of the total energy of

the Universe.

The idea of dark energy leads to the speculation that in the future

the force associated with dark energy will ultimately tear apart allgravitationally bound structures, including galaxies and solar

systems, and eventually overcome the electrical and nuclear forces

to tear apart atoms themselves, ending the universe in a "Big Rip".


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Dark energy controversy

It has been noted that if Newtons law of

gravitation:F = GMm/r2

became: F = GMm/r

at large, intergalactic distances,

then the acceleration of the expansion of theuniverse no longer requires the existence of DarkEnergy.

Other alternative ideas for dark energy have comefrom string theory, brane cosmology and theholographic principle.


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QuasarsQuasar stand for quasi-stellar radio source.

A quasar is a compact region in the centre of amassive galaxy surrounding a centralsupermassive black hole.

Its size is 10-10,000 times the Schwarzschildradius of the black hole.

The quasar is powered by an accretion discaround the black hole.

Quasars were first identified as being high

redshift sources of electromagnetic energy,including radio waves and visible light, thatwere point-like, similar to stars, rather thanextended sources similar to galaxies.

Infra-red image

of a quasar.

Artists impression of a quasar


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Quasars are among the oldest and most distantobjects in the Universe.

A quasar is characterised by: its very powerful light output, much greater than

the most massive of stars

its relatively small size, not much larger than astar

a large red shift indicating its distance is between5 and 10 billion light years away.

The first quasar discovered, 3C 273 producedstrong radio emissions. However, not all quasars

produce such emissions.


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Question

Light from a certain quasar was found to contain a spectral

line that had been red-shifted by 80 nm from its normalwavelength of 486 nm.

Calculate the recessional speed of this quasar.

c= 300 000 kms-1

A2 H 54 A3 AstrophysicsCosmology

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