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---------------------- 2254 - Cepheids give us the Astronomical Ladder
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- How do we know the distance the stars , or to the galaxies, or to the edge of the Universe? How do we know the Universe is expanding, or how fast it is expanding?
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- To know these things astronomers must create a “distance ladder“, one rung at a time, out to the farthest galaxies.
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- The answer we get when we calculate how fast the Universe is expanding is 74.2 kilometers per second expansion for ever million parsec distance. Translating to other units of measurements we might recognize this is 49,000 miles per hour expansion for every million light years distance.
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- This says the further distance you look the galaxies are receding faster and farther away from us. The reason is the space between us and the galaxies is expanding. The more space you have the faster the separation.
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- This is interesting because if you run this rate of expansion backwards you calculate that the universe was once reduced to a point some 13.86 billion years ago. That point must have been the start of the Big Bang.
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- To get to this conclusion we have to measure the outward velocity of a galaxies that are receding for each distance away. And, we have to know how far away they are.
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- The trick astronomers use is to select a special class of stars called Cepheids to use as milestones of brightness which is then used to calculate distances to galaxies. Cepheid stars are pulsating variables stars. Their brightness and dimness pulsation rates, or periods, correspond directly to their intrinsic brightness.
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- If we know the stars intrinsic brightness we can measure its apparent brightness as seen from Earth and use a simple formula to calculate its distance away.
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-------------- Apparent Brightness = Intrinsic Brightness / 4 *pi * (distance)^2
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--------------- Period of Pulsation = 10 days Then:
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---------------- Intrinsic Brightness = 5,000 * (Luminosity of Sun)
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- Note that 4*pi* r^2 is the circumference of the sphere as the light spreads out from the star. Now using the Apparent Brightness we can calculate radius, or distance to the Cepheid.
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- Astronomer Henrietta Leavitt was the first to make this calculation in1913. To get the first distances she used parallax in basic geometry. As the Earth circles the Sun the view is from a different angle on either side of the orbit. The star shifts its position due to the shift in the observer’s point of view. This tells us the angle at the tip of the triangle. The diameter of Earth’s orbit is the base of the triangle. Simple trigonometry will calculate the distance from Earth to the Cepheid.
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- The Hubble Space Telescope made these measurement on Cepheids that were 6,000 and 12,000 lightyears away. The shift observed in the 6 month intervals was 1/100 of a single pixel on the telescope’s camera. This is like measuring the size of a grain of sand 100 miles away.
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- To get this level of accuracy the telescope used a scanning technique that measured the star’s position a thousand times a minute every six months for 4 years. The telescope slowly slews across the target star capturing the image as a streak of light to gather the data.
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- Cepheid’s are stars that pulsate, varying their brightness in a cyclic manner. Edwin Hubble found a Cepheid star in the Andromeda “Nebula” in 1923. That was the first time astronomers realized that Andromeda was another distant galaxy, (M31) and not a nebula, or gas cloud, in our Milky Way Galaxy. Up until 1923 all astronomy was limited to inside the Milky Way Galaxy.
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- Columbus sailed the Atlantic Ocean in 1492 with uncanny ability to do naked eye fixes on the North Star. The North Star is Polaris at the tip of the handle of the Little Dipper. By keeping the altitude of Polaris fixed in the night sky Columbus kept his expedition on course to within one degree of latitude. Polaris is a Cepheid star that everyone knows as the North Star. Columbus hardly realized he was on the frontier of today’s astronomy.
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- Polaris is only 430 lightyears away. Like all Cepheids Polaris varies in brightness over a given time period, about 4 days for Polaris. Astronomers have learned that they can deduce a Cepheid’s luminosity based on this duration, or period of the cyclic brightness changes. Then by comparing the luminosity of the observed brightness to the actual brightness when it left the star they can determine the distance to the Cepheid. In this case 430 lightyears distance. The dimmer the Cepheid star the further away it is.
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- Cepheids pulsate due to a very defined process causing them to shrink and expand varying their surface temperature and brightness ( See footnote 1 for the detailed physics involved in pulsating stars). Cepheid pulsations can have cyclical durations from 1 o 100 days. Cepheid stars live for only 60 million years but they shine 500 to 30,000 times brighter than our Sun. This extreme brightness allows astronomers to see them over great distances.
- Supernovae Type 1A are exploding stars that have a standard light curve of luminosity. Supernovae are much, much brighter than Cepheids. Astronomers can see supernovae at billions of lightyears distance. Astronomers find a nearby galaxy that has both supernovae and Cepheids. They calculate the distance to the pulsating Cepheids and since they are in the same galaxy as the supernova they know the distance that corresponds to the supernova brightness light curve.
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- Astronomers can then use the brightness / distance ratio to calculate the distance to those far off supernova having the same light curve.
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- Cepheid luminosity varies through a cycle, where the color ( temperature) and radius change:
--------------------- pale yellow ---------- maximum luminosity
--------------------- yellow ----------------
-------------------- orange -----------------minimum luminosity
------------------- yellow -----------------
-------------------- pale yellow ------------ maximum luminosity
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The duration of this cycle can be used to determine the luminosity:
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------------------ Period -------------------------- Brightness ( times our Sun )
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------------------ 2 days -------------------------- 500
------------------ 3 days -------------------------- 1,000
------------------ 5 days -------------------------- 1,200
------------------ 10 days -------------------------- 5,000
------------------ 30 days -------------------------- 10,000
------------------ 50 days -------------------------- 30,000
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- Using this data astronomers have calculated that the galaxies are moving away from each other in an expanding Universe at 74.2 kilometers per second per mega parsec. A mega parsec is 3.26 million lightyears. 74.2 km / sec is 161,000 miles per hour, or:
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----------------- 47,000 miles per hour per million lightyears
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---------------- For every million lightyears distance you look the galaxy is receding at a velocity of 47,000 miles per hour.
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---------------- If a Cepheid is in a galaxy 1 billion lightyears away, it is traveling away from us at 47,000,000 miles per hour. Light travels at 670,000,000 miles per hour, so that is 7% the speed of light.
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- When astronomers look far enough away the galaxy is moving at 100% the speed of light and the light will never reach us. The galaxy goes beyond the Observable Universe. Remember the galaxy is not speeding away, the space between us and the galaxy is expanding. That is why receding galaxies can exceed the light speed barrier. The light speed barrier applies to mass not to the vacuum of space.
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- Do you want to learn the physics causing Cepheids to pulsate? Cepheids are special stars that contain a layer of helium at just the right temperature and pressure to undergo this cyclic pulsation:
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------------ Helium atoms in the pulsating layer are singly ionized, losing one electron and having a net He+1 charge. Singly ionized helium atoms are transparent to light radiation so light energy passes through this layer.
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--------------- Helium atoms absorb some of the energy and get hotter. The atoms lose their second electron and become doubly ionized, He+2 charge. Doubly ionized helium is opaque to light , blocking the light, acting as a dam, lifting the layer, expanding the star’s radius.
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------------- The expansion reduces the pressure and temperature allowing helium atoms to gradually capture electrons and revert back to singly ionized atoms, He+1. The layer is transparent again releasing the energy stored below the pulsation layer.
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---------------- With the pressure released the pulsation layer contracts. The He+1 begins to absorb energy again and the cycle starts all over again.
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- The cycle is vary repeatable. It is the same or every Cepheid. Once you know the period of pulsation you know how far away it is.
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- Other Reviews on astronomy:
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- 2235 - Astronomical distances. Astronomers are historians, everything they see happened in the past. This review lists 14 other reviews available about astronomy, available upon request.
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- February 2, 2019 --- 1055
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-------------------------- Sunday, February 3, 2019 --------------------------
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