cepheid

Cepheids: The Measuring Stick of the Universe

Many stars vary in brightness. Eclipsing binaries, for example, are two stars that periodically obscure each other and rapidly dim. Some stars vary their brightness in an irregular way, such as Mira in Cetus. It has varied with a period from 304 to 355 days.

Cepheid variables are stars that regularly change their brightness over periods between one day and hundreds of days. They are classified as super giants. A light curve of a variable star is a chart that plots its light characteristics in relation to time. Cepheids are usually very regular, often having periods that vary by less than a second. They do not appear to dampen their periods or luminosity. Cepheids show a Doppler shift that follows the brightness cycle of the star. The star gets brighter at the same rate as the frequency decreases. The star is believed to oscillate in size under the tension between its own "gravity" and its internal radiation pressure. Each Cepheid oscillation overshoots its stable radius and so it continues to swing through its equilibrium point like a giant friction less pendulum. The star is cooler and dimmer at its greatest radius, and hotter and brighter at its smallest radius. All engines loose energy, and run down. Why do Cepheids act like a friction less pendulum? Physicists talk about the opaqueness of the star at its maximum compression to "solve" where it gets the energy. Somehow it is consuming mass and energy without damping its period or brightness.

At their peak, Cepheids are brighter and hotter than most stars in the main sequence. This makes them bright enough to be singled out from nearby galaxies. The study of Cepheids suggests two different types of Cepheid stars. Classical Cepheids vary with a period of about a day. Type II Cepheids vary from a few days too about a hundred days.

In 1908, the astronomer Henrietta Leavitt discovered that the brightness of Cepheids is directly related to their periods. She was working in South Africa observing Cepheids in the Small Magellanic Cloud. Cepheids with periods of several months are brighter at their peak than ones whose cycle is only a few days. Humming birds can beat their wings much faster than eagles. Humming birds are hard to see from 50 yards, but eagles can be seen from a mile away.

Imagine that you have a dimmer on your porch light. This dimmer has an electronic feedback system that prevents the light bulb from changing its brightness too fast. Imagine that it takes 20 seconds to turn on a 100-watt bulb to its maximum brightness. If you install a 25-watt bulb in the same porch light, it only takes five seconds to bring it to full brilliance. You decide to test your porch light from a nearby hill with a small spotting scope fitted with a photometer, and a stop watch. You could have an assistant try different sized light bulbs while you record the time to reach full brilliance. Astronomers cannot calibrate the variables of their stellar porch lights without relying on assumptions. They do not have the luxury of traveling to several Cepheids and testing their hypothesis out directly.

You could measure the distances to several porch lights by comparing their apparent brightness. Light dims with the square of the distance. In other words, a 25-watt bulb at 100 meters will have the same apparent brightness as a 100-watt bulb at 200 meters. (Twice distance squared is four times as dim or one fourth brightness). If we use this method to estimate the distance to several porch lights, we must know the wattage of the bulb on the porch. If we thought a 150-watt bulb was 75 watts, our distance estimate would be off by a factor of four.

Astronomers have classified stars by magnitude for two thousand years. The eye responds to brightness in a logarithmic way so the magnitude scale is a logarithmic scale. A star has an apparent magnitude, based on how much light the eye (or an instrument) measures. An equation converts the star's measured brightness to an absolute magnitude. This equation assumes that we know the distance to the star and computes how bright it would be if it were 32.6 light years from earth.

Astronomers use Cepheid stars to measure distance. First the period of a distant Cepheid is measured. The period is the length of time between brightness peaks. Next they measure the peak luminosity. This gives them the apparent brightness. Then they assume that all Cepheids of the same period have the same absolute brightness. The distance is computed by comparing the apparent brightness with the brightness of a closer Cepheid. A Cepheid in a galaxy that is four times as far as a reference Cepheid having the same period should have a sixteenth the apparent brightness. Measuring the period and apparent brightness allows the astronomer to calculate the estimated distance.

The apparent brightness of Cepheids and their periods are used by astronomers to estimate the distances to nearby galaxies. Distant galaxies are too dim to allow individual Cepheids to be resolved. The apparent brightness of the brightest galaxy in a cluster is compared with the brightness of a similar closer galaxy where the Cepheid process has been used. Cepheids are also used to calibrate the distance versus red shift relationship of even more distant objects. In this way, the Cepheids become the first division on a tape measure used to measure the size and age of the entire universe.

For three years a small European satellite, Hipparcos, took photographs 1 degree wide in swaths around the earth. The mirror on Hipparcos could look in two directions at once. These photos give a three-dimensional picture of different parts of the sky. They can be used to calculate the parallax to nearby stars in our galaxy. None of our galaxy's Cepheids are close to the earth, so measuring their parallax is not easy with ground-based telescopes. The photos from Hipparcos resulted in a 10% increase in the distance estimates to the reference Cepheids in our galaxy. This in turn resulted in a 10% increase in the estimated distance to neighboring galaxies. This resulted in a 10% increase in the estimated size and age of the universe. In other words, Cepheids are critical to the measurement of the universe. If our assumptions are in error, the measurements of the size and age of the universe could be in gross error. It is of interest that the parallax measurements from Hipparcos are not necessarily supported by other techniques. Astronomers used interferometer measurements from Mount Wilson to measure the Pleiads cluster and arrived at distances 10% farther than Hipparcos.

Astronomers use assumptions when they use Cepheids to measure the universe. They actually use many different methods to measure distances. They compare the results from different methods. All distance measuring, with the exception of those to very close objects, rely entirely on the fundamental assumption. If the assumption were false, the various techniques could agree with each other within some margin of error, and still have gross errors in reality. The primary assumption, which the Greek philosophers invented, is critical to the whole system, not just the Cepheid yardstick. The fundamental assumption is so important that no one ever talks about it directly. Questions relating to the fundamental assumption are not allowed in the world of scientific reasoning. Scientists accept the assumption by faith. Most of them are not even aware of its existence, since they have never thought of material things apart from the assumption. It is a very dangerous process to test the fundamental assumption. If the results are bewildering, you could end up questioning everything you already "know". Questioning the fundamental assumption involves debates that the Greeks "settled" long ago. Those kinds of questions are never asked today. Fortunately we have the written records of the Greek philosophers. We can read the arguments they used to invent the assumption that is so sacred today.

Are you brave enough to test the assumption? You can test it using astronomical measurements. The measurements, however, were recorded by ancient astronomers. What they recorded is very interesting. Some kinds of measurements agree closely with our measurements. Other kinds of measurements do not agree. The disagreements and agreements are just the ones you would expect if the fundamental assumption were false. Is it possible their measurements were accurate and the fundamental assumption is the problem? It is very clear that the archaic astronomers did not imagine the starry universe the way we do.

Remember that you cannot examine your fundamental principle while you are assuming it. You cannot examine the foundation of your house from inside the house. You have to leave the house and dig around to test the strength of the foundation. To test the foundational assumption, you must first move to an alternate assumption. Then from the perspective of the other assumption you can see to test the first assumption.

Truth is a wonderful thing. Sometimes people say, "Truth is in the eye of the beholder." Throughout history people believed things that eventually proved false. That does not mean we are so much smarter than they were. It means it is often hard to recognize truth about the physical universe. One of the best tests for truth is to look for falsity. If something is provably false, then it cannot be true. Remember that positive proofs often rely entirely on assumptions. Negative proofs can test the assumptions themselves. A test of the fundamental assumption is not a test to see if we can find agreement. It is always easy to find agreement with something you believe. Instead one should test for discrepancies that may suggest something is wrong. If we deny the fundamental assumption, can we still account for the observational data of the universe AND at the same time explain the discrepancies? Truth is always worth the risk involved in asking the most important questions.

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