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--------------------------------- 2371 - The Farthest Galaxy in Our Universe
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- Astronomers have found a galaxy believed to be the farthest detected as 2004. As we leaned from Edwin Hubble in 1920 the further away a galaxy is the faster it is receding, or moving away from us. (See Review 20 - The Runaway Universe).
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- The light from a galaxy that is moving away from us has its wavelength stretched out. This is called the Doppler effect. The light’s wavelength appears longer and the light’s frequency appears lower. It is called a redshift because the frequency, or the color, is shifted toward the red end of the spectrum.
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- The astronomers have measured this galaxy to have a redshift equal to 10. A redshift is defined to be the shift of the spectral lines to longer wavelengths caused by the recessional velocity of the galaxy.
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-------------- Redshift = Observed wavelength - Actual wavelength / Actual wavelength
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------------------------------ Z = wo - wa / wa
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- According to Einstein’s Special Relativity the radial velocity inferred from the redshift is:
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------------------------------ ( 1 + z )^2 = (1 + v/c ) / ( 1 - v/c )
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------------------------------ Where z is the redshift
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- “v” is the velocity of the galaxy moving in the radial direction away from us.
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- “c” is the velocity of light
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- “v/c” is the ratio of the galaxy’s radial velocity to that of light.
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------------------------------- ( 1 + 10 )^2 = (1 + v/c ) / ( 1 - v/c )
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------------------------------- 11^2 = 121 = (1 + v/c ) / ( 1 - v/c )
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------------------------------- v/c = 120 / 122
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------------------------------- v/c = 98.36% the speed of light.
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- This redshift of 10 would mean that the galaxy is traveling at 98% the speed of light and the light left the galaxy 460,000,000 years after the Universe was born.
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- For the first 300,000,000 years no light escaped from the Universe because all the atomic particles were too hot and were ionized. As the protons and electrons cooled they formed into atoms and became neutral. As space became neutral it allowed light photons to escape for the first time.
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- This first 300 million year period is called the Dark Age that followed the Big Bang. This particular galaxy formed just 160 million years after the Dark Age and at that time it was only 3.5% the present age of our Universe.
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- If Abell is traveling 98.36% the speed of light that means its radial velocity is 2.9488* 10^8 meters / second.
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- If Hubble’s constant is truly constant and linear over these great distances then:
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----------------------------- Distance = Velocity / Ho
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----------------------------- Distance = 13.36 * 10^9 lightyears
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----------------------------- Age of the Universe = 1/Ho = 1/72 km/sec/mpc
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----------------------------- Age = 13.56 * 10^9 years
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- The Abell galaxy was sighted just 460 million years after the Universe was born ( or, 200 million years later according to these less rigorous calculations above.)
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- The galaxy is in the constellation Virgo and it is named Abell 1835 IR 1916.
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- The light from Abell has been stretched 11 times its original wavelength because Abell is traveling at a velocity 98% the speed of light. Of course, it is all relative, from Abell’s perspective we are traveling 98% the speed of light away from it.
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- The light from Abell has taken 13 billion years to reach us and the light is extremely faint. Not only is it very far away, 13 billion lightyears away, the radiation is greatly weakened by the redshift. The photon has been enlarged 11 times its original wavelength. This is the same as weakening its energy by a factor of 11.
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- To explain why the energy, the wavelength, and the frequency are all related by a factor of 11 we need to know that they are all mathematically direct relationships.
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----------------------------- Energy is = Planck’s constant * frequency
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----------------------------- Energy is = Planck’s constant * speed of light / wavelength
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----------------------------- Frequency is = speed of light / wavelength.
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- The light from Abell started out at a frequency of 2,465 trillion cycles / second.
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----------------------------- f = c / w = 2.998*10^8 meters/sec / 121.6*10^-9 meters/cycle
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----------------------------- f = 2.237*10^14 cycles/second.
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- Using the same formula Abell’s light arrived shifted to the red end of the spectrum to a lower frequency of 223.7 trillion cycles per second, 11 times lower.
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- The wavelengths went from 121.6 nanometers to 1340 nanometers longer, 11 times longer, respectively.
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- The Energy of the light is l1 times lower, going form 10.195 electron-volts to 0.925 electron-volts.
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----------------------- E = h*f = 4.136*10^-15 ev*sec * 24.65*10^14 cycles/sec
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----------------------- h = Planck’s constant
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----------------------- E = 10.195 electron-volts
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- In any given second we will receive 1/11th as many of the feeble photons as we would if the redshift had not occurred. On top of this we are seeing the galaxy when it first appeared. Galaxies back then were much smaller.
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- Abell is 1/1000th the size that our Milky Way is today. Small galaxies later merged as building blocks to become the large galaxies that populate the universe today.
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- The astronomers found Abell with a brightness magnitude of, M=26 in the near infrared wavelengths. Fortunately there is a large galaxy cluster between us and Abell. The large mass and gravitational curvature created by this cluster created a gravitational lens that amplified the faint light by a factor of 25 to 100 times.
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- The light thought it was going in a straight line to us but in fact the curvature of space caused by the giant mass in between us caused it to curve and focus magnifying the light like a giant magnifying glass. This in effect increased Abell’s brightness by 3.5 to 5 magnitudes. (See review 52 - Sedna - The Tenth Planet for lessons on how brightness magnitudes are calculated.)
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- The formula for the Magnitude of brightness of a star, compared to the star Vega is 2.5^M.
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- Therefore, M = 31 = 2.5 ^ 31 = 2.2*10^12, or 2.2 trillion times fainter than the star Vega.
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- Review 52 on the planet Sedna describes how brightness magnitudes are calculated.
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- For comparison the planet Sedna has a magnitude, M = 21 = 2.5^21 = 2.3*10^8, or 230 million times fainter than the star Vega.
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- The light from Abell started out as a strong Lyman-alpha emission from hydrogen atoms at 121.6 nanometers wavelength in the far ultraviolet. It finally reached us 13 billion years later but it was shifted to 1,340 nanometers in the near-infared wavelengths.
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---------------------------- Observed wavelength = wo = 1,340 nanometers
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---------------------------- Actual Wavelength = wa = 121.6 nanometers.
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---------------------------- Redshift = z = wo - wa / wa
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---------------------------- z = 1340 - 121.6 / 121.6
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---------------------------- z = 10.02
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- The original, actual wavelength of 121.6 nanometers was created by the Lyman-alpha emission from hydrogen atoms. Scientists studying the spectral lines of atomic hydrogen learned that the wavelengths of hydrogen follow the formula:
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--------------------------- 1 / wavelength = R ( 1/n1^2 - 1/n2^2 )
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---------------------------- Where R is the Rydberg Constant.(See footnote)
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For the Lyman series of spectral lines are in the ultraviolet, n1 = 1 and the value of n2 = 1 for the alpha line.
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- The value of the Rydberg constant contains the reduced mass of the electron so its value is slightly different for each type of atom. If we assume the mass of the nucleus is infinite by comparison and the actual rest mass for the electron is:
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------------------------------ R = 1.0973731534 * 10^-7 / meter
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- This represents the binding energy of the electron in a hydrogen atom in the ground state to be 13.6058 electron volts. When the electron transitions between the second Bohr orbit (n=2) to the lowest Bohr orbit, the ground state, (n=1) the energy emitted is 10.2 electron-volts.
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- A 121.6 nanometer wavelength photon has an energy of 10.2 electron volts. The ultraviolet radiation that we see is coming from giant clouds of hydrogen gas cooling down inside the Abell galaxy. It has had quite a journey since then.
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On March 9, 2004 Hubble telescope released its images of the Ultra Deep Field, a very long time exposure of only 3 square minutes of arc containing over 10,000 galaxies. The magnitudes of some are as faint as M = 31, which is 2.2 trillion times fainter than the star Vega. Many of these galaxies have redshifts as great as 7 to 12. There is much to study here but a galaxy even more far, far away than Abell may soon be discovered.
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-------------------------------
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- (Footnote) Johannes Robert Rydberg, a Swedish physicist, was studying spectroscopy in 1897. He worked out a relationship for the various spectral lines produced by different elements. His work was purely empirical, that is he learned by experiment, not by theory.
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- His equations obtained the correct results but he had no explanations for why. The explanations would have to wait for Niels Henrik David Bohr, a Danish physicist, who in 1922 won the Nobel Prize for determining that the electrons outer shell determines the chemical properties of the atoms of each element.
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- May 18, 2019. 53
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--------------------- Saturday, May 18, 2019 -------------------------
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