--------- #1259 - Distant Quasars and the Early Universe?
- Quasars are distant galaxies that are extremely active because they have massive Blackholes at their centers. The spinning Blackholes have rotating accretion disks of high energy material that emits enormous amounts of radiation energy. These active galaxies are so bright they can be seen over astronomical distances. Astronomers are using them to see the early evolution of the Universe.
- How can astronomers tell how far the galaxies are away from us?
- What can they tell us about the birth of the Universe?
- The answers come from the same way we can tell how fast a car is moving with its horn stuck:
- The method used in these calculations is called the Doppler Effect. When an emitting source is approaching you the waves appear compressed to a higher pitch, or a higher frequency. When the emitting source is moving away from you they appear as stretched out, or redhifted, to longer wavelength, and lower frequency. The cops use radar reflections and the Doppler effect to catch the speeding cars. The illustration we will use first is the car with the horn stuck.
- The sound of the car’s horn coming towards us will be higher pitched than when it passes us and is moving away from us. The sound wave is traveling at a constant speed of 330 meters per second. (738 miles per hour ). The frequency of the sound coming towards a stationary listener is 853 cycles per second. The frequency of the sound when the car’s horn is moving away from us is 741 cycles per second.
- The equation is simple to learn the actual frequency of the horn. Simply take the average of the two frequencies.
-------------------------- fo = ½ ( f hi + f lo)
------------------------- fo = ½ ( 853 cps + 741 cps)
------------------------- fo = 797 cycles per second is the frequency of the horn.
- To learn the velocity of the car we take the ratio of velocity, “v”, to the velocity of sound, “c”, equal to the ratio of the difference of the high - low frequencies and the sum of the high - low frequencies:
------------------------ v / c = f hi - f lo / f hi + f lo
------------------------- v / c = ( 853 - 741 ) / ( 853 + 741 )
------------------------- v / c = 112 / 1594
------------------------ v = ( 330 m/sec ) * ( 112 / 1594 )
------------------------ v = 23.2 metes / sec
----------------------- v = 52 miles per hour.
- The Doppler Effect formula for sound is different then the Doppler Effect formula for light. When dealing with the electromagnetic spectrum’s waves and frequencies you must us the Theory of Relativity because speeds are nearing the speed of light, distances contract and time slows. The same Doppler phenomena occurs when astronomers view the spectrum of light coming from the distance galaxies. Because the Universe is expanding the galaxies are ceding at higher velocities the more distant they are. The light wavelengths get stretched, or redshifted, just like the car horn sound moving away from us.
- Light leaves the Quasar galaxy at a wavelength of 121 nanometers, in the ultraviolet spectrum. It passes over billions of light years through space that is expanding. The wavelength gets stretched out, redshifted. When it arrives at the astronomers telescope it is 358 nanometers wavelength. ( The reason the source wavelength of 121 nm is known is because the same element’s spectrum can be measured here on Earth, in the laboratory. We assume the physics is the same in the distant cosmos.)
- The relativistic formula for the Doppler Effect uses the ratio of the measured wavelength to the original wavelength squared :
------------------ ( w / wo ) ^2 = (1 + v/c) / (1 - v/c)
------------------ “w” is the wavelength measured, 358 nanometers
---------------- “wo” is the original wavelength from the source , 121 nanometers
---------------- “v” is the receding velocity of the galaxy
----------------- “c” is the speed of light , 3 *10^8 meters / second
- The wavelength of the spectrum has been redshifted by 237 nanometers to a longer wavelength at a lower frequency because the galaxy velocity is receding away from us.
“ v / c” is the ratio of the velocity of the galaxy to the speed of light. Rearranging the above equation to solve for “ v / c “ :
------------------- ( v / c ) = ( w / wo)^2 - 1 / ( w / wo )^2 + 1
------------------- ( v / c ) = ( 358 / 121)^2 - 1 / ( 358 / 121 )^2 + 1
------------------- ( v / c ) = 8.75 -1 / 8.75 +1
------------------- ( v / c ) = 0.79
- The velocity of the galaxy is receding at 79% the speed of light. That is the reason relativistic formulas needed to be used. The galaxy is not actually moving at that velocity where it resides. It is the amount of space in between us that is expanding. The more expanding space between us the faster we separate.
------------------ v = ( 3 * 10^8 meters / second ) * 0.79
-------------------- v = 238,000,000 meters per second
-------------------- v = 523,000,000 miles per hour.
- The galaxy is receding from us ate 523 million miles per hour. To calculate how far away it is we use Hubble’s Constant for expansion of the Universe. The Hubble Constant, “ H”, is 0.047 miles per hour per lightyear. The further the galaxy is away from us the faster it is receding. A galaxy is has a receding velocity of 0.047 mph for every lightyear distant it is.
---------------------- Distance = v / H
----------------------- Distance = 532,000,000 mph * lightyear / 0.047 mph
---------------------- Distance = 11,319,000,000 lightyears
- The Quasar is 11 billion lightyears away from us. The Universe is only 13.75 billion years old since the Big Bang. This Quasar being viewed is when the Universe was only 2.75 billion years old.
- The summary below is a table of seven distant objects measured in this way. The redshift is measured as the change in wavelength over the reference wavelength. For the galaxy we just measured the redshift was:
--------------------- Redshift = w - wo / wo
-------------------- Redshift = 358 - 121 / 121
------------------- Redshift = 237 / 121
--------------------- Redshift = 2.0
- The Redshifts in the table range from 5.3 to 10, an amazing distance away from us.
---------- Redshift -- Billion years ago --- Million years after Big Bang ---------
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------------ Infinity ----- 13.75 --------------0 --------- Big Bang occurs
------------ 10 --------- 13.2 --------------500 ------ Galaxy fragments forming
------------ 8.6 --------- 13.1 --------------600 ------- Galaxy fragments forming
------------ 8.2 --------- 13.07 --------------630 ------ Supernova
------------ 7.6 --------- 13.0 --------------700 ------- Star forming galaxy
------------ 6.9 --------- 12.88 --------------820 ------ Galaxy formations complete
------------ 6.4 --------- 12.7 --------------1000------ Super massive Blackhole
------------ 5.3 --------- 12.6 --------------1100 ------ Galaxy Clusters formed
- Astronomers use this distance data to develop theories on the evolution of the Universe. It looks like the first galaxies started about 500 million years after the Big Bang. It took another 320 million years before complete galaxies formed from these galaxy fragments. Complete galaxies were found 820 million years after the Big Bang.
- Quasars are created by super massive Blackholes that are 500,000,000 times the mass of the Sun. Their formations did not occur until 1 billion years after the Big Bang. It took 500 million years after the first galaxy fragments first formed before massive Blackholes came into existence.
- It took 600 million years after the first galaxy fragments first formed before Galaxy Clusters arrived.
- Note that no objects have been discovered before 500 million years after the Big Bang.
- Astronomers are able to study pictures of the birth of the Universe. Like archeologists digging up bones, astronomers keep looking at stuff back in time. Star light travels very fast, but, it has a lot of space to cover before it reaches us. We can not see things as they are now, but, as they were a long time ago.
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(1) H is often shown as 74.2 kilometers per second per mega parsec.
One mega parsec is 3.0857 * 10^19 kilometers.
Therefore H can also be shown as 74.2 / 3.0857 = 24 * 10^-19 sec^-1
(2) The reciprocal of H is the age of the Universe.
Age = 1/ 24 * 10^-19 sec^-1 = 0.0416 * 10^19 seconds
One year is 3.16 * 10^7 seconds
Age of the Universe = 0.0416 / 3.16 * 10^12 years
Age of the Universe = 13 billion years
(3) Distance to the galaxy Quasar can also be calculated in meters using:
------------ Distance = v / H
------------ Distance = 2.38 * 10^8 meters / second / 2.4 * 10^-18 seconds
------------ Distance = 0.99 * 10^26 meters
---------- The radius of the Observable Universe is 1.3 * 10^26 meters. This galaxy is 76% to the edge of the Observable Universe.
(4) These calculations are rough and used to illustrate and learn how distant galaxies are measured. They assume the expansion of the Universe was linear and at a Constant Hubble expansion rate. Today we think that the Universe expansion was slowing down due to the pull of gravity for the first 7 billion years. This expansion deceleration slowed down as masses separated in the expansion and Dark Energy took over reversing deceleration to acceleration pushing the expansion at an ever increasing rate. So, the Hubble Constant has not been “ constant”. The equations work because today’s number is a good average.
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