It is the darkest time of year. The earliest sunset for the Adirondacks occurred on Saturday, Dec. 10 at 4:19 p.m. (on a flat horizon). Those of you who prefer light in the evening can now start watching the time of sunset slowly creep toward later times, getting to 4:24 p.m. by Christmas!
In spite of this, the longest night won't occur until Dec. 21-22, when the winter solstice takes place at 12:30 a.m. That night will last for 15 hours and nine minutes, giving Dec. 23 a mere eight hours and 51 minutes of daylight. Though the days will then begin to lengthen, mornings will continue to get darker until the latest sunrises occur on Jan. 2 and 3 at 7:34 a.m. The simplest explanation for why the latest sunrise, shortest day and earliest sunset don't occur on the same date is that solar noon (the middle of the hours of daylight) doesn't occur at clock noon. For a more detailed explanation, read my column of Dec. 14, 2010.
In this darkest time of the year, it makes sense to talk about a class of dark objects that have been in the news lately and that are deliciously weird: black holes. Surprisingly, the first person to write about the idea that gravity could be so strong that it could prevent light from leaving a star was John Mitchell, a geologist, in 1784.
Since Isaac Newton had published his laws of dynamics in 1687, the idea and calculation of escape velocity, the speed at which a ball must be thrown to escape a planet or star, was well known. John Mitchell wrote in a letter to Henry Cavendish, discoverer of hydrogen, of the possibility of a "dark star" so massive that light could not escape.
He proposed that such a star could be detected by its gravitational effects on its companion if it were one of a binary star.
For a star the size of the sun to become a dark star, it would have to be 250,000 times more massive than the sun. Such a star would collapse under its own weight. And in fact, the term "black hole" was coined in 1967 by Princeton Professor John Wheeler, exploring the gravitational collapse of stars under Einstein's theory of general relativity.
In a black hole, matter contracts under gravity to essentially zero radius, resulting in infinite density. Black holes are not extraordinary for their mass, but for the fact that it's all concentrated at the very center. If the sun became black hole tomorrow, there would be no change in its gravitational pull on the Earth so Earth's orbit would not change, nor would Venus' or Mercury's. It would just get dark. Then it would get cold ... and keep getting colder! The fact that it was a black hole would matter a lot to us, but wouldn't matter to solar system orbits until an object got very close to its center.
The strength of the gravitational force on an object is proportional to one over the distance squared (F = GMm/r2 for those who remember high school physics). Since black holes have no surface, objects can get very close to the center and experience an extremely strong gravitational force. At the surface of our sun, the force on a one-liter bottle of water (1 kg), its weight, is 27 times larger than its weight on Earth. If we squeezed all the mass of the sun to fit within Earth's size, the bottle's weight would be 325,000 times larger than on Earth. If we squeezed it into the size of the moon, the weight would be 4.4 million times larger and if we squeezed it into 10 km, it would be 135 billion times larger! Thus it's the possibility of getting close to the center that makes the gravitational pull of black holes huge.
Since the force increases, the speed necessary to escape the gravitational pull also increases. At Earth's surface, a ball has to be thrown at a speed of 25,000 mph to escape the planet. On the sun's surface, the throw would have to be at 1.4 million mph.
Shrink the sun down to Earth's size, and the throw would have to be at 14 million mph. Shrink it down to 10 km, and the throw has to be at 365 billion mph! Shrink the sun down to smaller than 3 km, and even the speed of light is too slow for an object to escape.
That's the size where our star would become a black hole. Strange as they sound, there is a preponderance of evidence that black holes do exist. Even though light can't escape them, they do give away their presence. First, as Mitchell realized, they can be unseen orbital partners in binary systems. Also, as material that comes close does fall in, it accelerates to very high speeds. Charged particles radiate when they accelerate so they emit light as they fall, shining in high-energy X-rays just before they disappear from sight.
In 1962, an Aerobee rocket carrying Geiger counters to sample celestial X-rays detected bright sources in the direction of Cygnus. In 1964, another observation confirmed the source and it was officially named Cygnus X-1. The early X-ray telescopes could not pin-point the position, but in 1971 Cyg X-1 was also observed in radio and the position determined. There turned out to be a giant blue star, HDE 226868, at this position. Spectral observations revealed motion indicating that it was orbiting a companion. The companion was at a distance 20 percent of Earth's distance from the sun, but no companion other than the X-ray and radio source could be seen. It was thus suggested that the X-ray source was a black hole.
The latest X-ray telescope, Chandra (chandra.harvard.edu), has pegged its mass as being 14.8 times the mass of the sun and spinning more than 800 times each second. It is thought to have formed from the gravitational collapse of a star originally 40 times the mass of the sun. Why did it collapse? Stars are nuclear explosions contained by gravity. As long as nuclear fusion continues in the core of the star, the heat and pressure it generates hold the star up against gravity. When a star uses up its fuel and the core cools, however, gravity gets the upper hand. Initially the core contracts, causing inner layers of the star to fall toward the center, crushing the core with their weight. By the time the outer layers fall in, the center is so dense that the outer layers can bounce off to explode in a supernova. This bounce is what can compress the core so strongly that even the nuclei of atoms can't withstand the force and it collapses into a black hole. When the star is massive enough, it is thought that the collapsing inner layers crush the core into a black hole so that there is no bounce, no supernova explosion and the black hole forms "in the dark." This is what is thought to have happened to the star that created Cyg X-1.
As shown in the diagram, Cyg X-1 is very near the ? (Eta) Cygni, half-way between Sadr (SAD-der, the "belly" of the swan) and Albireo (Al-BEER-ee-oh, "the beak" of the swan). It is about 6,000 light years from Earth, so even the giant companion star is invisible without a large telescope. But if you had X-ray eyes it would be far brighter than just about every other object in the sky. As the swan, winging its way south along the Milky Way, slowly dives toward the horizon to disappear for the winter, take some time to gaze in the direction of this weirdest of celestial objects. It's not as impressive as the 10-billion solar mass black holes discovered recently and announced earlier this month, but it was the first one we were confident in identifying. It's pretty amazing how much this invisible object has taught astronomers in the past 50 years!
For more information, X-ray images and an artist's impression of what Cyg X-1 may look like, go to the Chandra site at chandra.harvard.edu or just Google "Cyg X-1 Chandra."
If you have any questions about black holes or any other astronomy, please visit the Adirondack Public Observatory web site at apobservatory.org or email Aileen at email@example.com.