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70 Falmouth Street Portland, Maine 04103
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Founded January 1970
Julian date: 2457683.16
"Never stop."
THE DAILY ASTRONOMER
Thursday, October 20, 2016
The Cepheid Keys
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TONIGHT'S SCIENCE LECTURE:
"Learning from Nature"
"Learning from Nature"
USM neurobiologist Dr. Douglas Currie discusses how scientists
can learn more about human biology by studying animals in their
natural environments.
Where: Southworth Planetarium
When: 7:00 p.m. (Doors open at 6:30 p.m.)
How much; by donation
Call 207-780-4249 or consult the web-page
for more information.
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Astronomical "facts" are all very well, but the most compelling aspect of astronomy in our mind is the means by which astronomers garnered these facts that we take for granted today. Throughout the centuries, most notably the last two of them, humanity has accumulated such a store of astronomical knowledge that we couldn't learn it all even if we had ten full lifetimes to devote to its study. Every piece of that knowledge was made possible through a combination of countless hours of observations, meticulous data analysis and the collaboration of myriad researchers, most of whom receive scant credit for their contributions. Whenever we cite these facts, we often gloss over the efforts of those obscure scientists who acquired them for us.
Today, we provide elaboration on a topic we introduced in yesterday's article: on knowing the Andromeda Galaxy's distance . We mentioned that it was more than 2.2 million light years away. How were astronomers ever able to measure that distance?
A light year, incidentally, is the distance light travels in one year through a vacuum. As this speed slightly exceeds 186,000 miles a second, a light beam propagating through space traverses 5.8 trillion miles during one Earth year! To give one an idea about how much space separates objects, the closest star to our solar system, Proxima Centauri, is 4.2 light years away. The most distant stars we observe with the unaided eye are about 3000 light years away. With that in mind, it seems all the more extraordinary that we know that the Andromeda Galaxy,* the closest major spiral galaxy to our own, is 2.2 million light years away: a measurement made less than one hundred years ago.
We begin with a famous relation in astronomy; something called "The Distance Modulus," which relates a star's apparent magnitude (apparent brightness), absolute magnitude (actual brightness), and distance. (See "From the Catacombs of Infinite Knowledge.") If one knows two of these values, one can determine the other. This modulus is quite intuitive. We measure a star's apparent magnitude directly just by observing it on Earth. This brightness value does not yield information about its actual brightness, however. For all we know, a given bright star could be comparatively faint, but close; conversely, a faint star could be quite intrinsically brilliant, but far away. If we can figure out the star's distance, we would know its true brightness. Or, if we can somehow ascertain a star's absolute magnitude, we can compare it to its apparent magnitude and measure its distance.
The trick is knowing a star's intrinsic brightness. And, with a certain type of variable star, Cepheid variables, we can directly know its brightness by observing its variability period. Cepheid variables are giant stars that pulsate, growing larger and then smaller and then larger again over a period that can last many weeks. Conveniently, the variability period: the between successive minima (least brightness) or maxima (greatest brightness) depends on its intrinsic brightness. The brighter the Cepheid variable, the longer the variability period. As brightness relates directly to a star's luminosity, or energy output, these correlation between the variability period and brightness is called "The Period-Luminosity Relation."
This relationship was first established by a survey of Cepheid variable in the Small Magellanic Cloud, a satellite galaxy to the Milky Way approximately 160,000 light years away. It was noticed that the brighter Cepheid variables in the SMC had longer periods than the dimmer ones. As astronomers assumed that the stars within the SMC were at equal distances from Earth, they determined that the Cepheidvariable's luminosity affected the star's variability period.**
Edwin Hubble, certainly not an obscure astronomer, measured the distances to Cepheid variables within the Andromeda Galaxy and, by extension, to the Andromeda Galaxy itself He knew the absolute magnitude by the amount of time they needed to cycle through one variability period. He then compared it with the star's apparent magnitude, discernible through his powerful telescope. He determined that the Andromeda Galaxy was about 900,000 light years from Earth. Though this measurement was enough to place the Andromeda Nebula, as it was then called, well outside the Milky Way Galaxy's boundaries, it was less than half the currently accepted value. Astronomers later learned that there are two classes of Cepheid variables, each of which has its own period-luminosity relation. Hubble used 'cluster variables,' which yielded an incorrect distance to the Andromeda Galaxy.
Cepheid Variable Curve. A simplified light curve of a Cepheid variable star.
As its outer layers contract and expand, the star dims and then brightens. Astronomers
know that the variability period is directly related to the star's luminosity, or
intrinsic brightness. (A variability period is the time separating successive minima) The longer the period, the brighter the Cepheid. Therefore, an astronomer can determine a Cepheid variable's true brightness by observing its variability period.
When the two classes were defined, and the measurement to the Andromeda Galaxy refined accordingly, astronomers realized that that splotch of light in the sky we had called the Andromeda Nebula was 2.2 million light years away! The most distant object one can observe with the unaided eye.
Today, we know that the Andromeda Galaxy is just one of billions of galaxies. And, by cosmological standards, Andromeda is so close it is almost the Milky Way Galaxy's Siamese twin. However, calculating Andromeda's distance served as a stepping stone toward the vast cosmic reaches well beyond: reaches that even today we haven't fully fathomed.
*The Andromeda Galaxy, located in the constellation Andromeda, is well positioned for viewing this time of year. Find it high in the evening sky, just north of the Andromeda constellation; or to the northeast of the Great Square of Pegasus. Though approximately four degrees across, the Andromeda Galaxy is somewhat diffuse and therefore observable only in darker regions. Note that the gibbous moon will often obscure it, even when it is in a different part of the sky. So, one might want to wait until the weekend to start trying to find the Andromeda Galaxy.
**We know the stars in the Small Magellanic Cloud are not equidistant from Earth. However, we can assume they are for the purposes of this observation. People in Los Angeles are not all precisely the same distance from us, but Los Angeles is far enough away that we can make a safe assumption that they are.
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FROM THE CATACOMBS OF INFINITE KNOWLEDGE
"The Distance Modulus"
The equation shown above is one of astronomy's most famous mathematical formulae. It relates three variables: M, a star's absolute magnitude; m, a star's apparent magnitude, and d, a star's distance in parsecs. (Yes, of course we'll explain what we just wrote.)
"Magnitude" measures a celestial object's brightness. The small "m" refers to the object's apparent magnitude, or how bright it appears. The large "M" refers to the object's absolute magnitude, or its intrinsic brightness. Technically, the absolute magnitude equals the celestial object's apparent magnitude from a distance of ten parsecs. (A "parsec" is equal to about 3.26 light years.)
The magnitude system is a logarithmic scale that assigns lower numbers to brighter objects. For instance, a star of magnitude 1 is approximately 2.5 times brighter than a star of magnitude 2, but 2.5 times dimmer than a star of magnitude 0. (See "Etched on a dimly lit wall in the catacombs of infinite knowledge")
If we know two of these variables, we can determine the third. As is the case with the Andromeda Galaxy, an astronomer will know the Cepheid variable's apparent magnitude (m) through direct observation. Observation of its variability period yields its luminosity or absolute magnitude (M). Then, the astronomer can utilize her prodigious mathematical skills to calculate the distance.
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ETCHED ON A DIMLY LIT WALL IN THE CATACOMBS OF INFINITE KNOWLEDGE
The 2.5 brightest factor in the magnitude system is actually 2.512. It was so designated because 2.512 is the fifth root of 100. Therefore,a star of magnitude 1.0 is precisely 100 times brighter than a star of magnitude 6.0. 6.0 is generally the naked eye limit for celestial objects. However, some lynx-eyed sky watchers are able to observe slightly dimmer stars than those of the sixth magnitude.
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