T HE SUN IS 8 LIGHT-MINUTES FROM EARTH, THE NEXT NEAREST STAR IS ABOUT 4 LIGHT-YEARS AWAY, THE CENTER OF OUR MILKY WAY GALAXY —25,000 LIGHT YEARS AWAY.
NOW, for most people; most of us, these distances are unimaginable.
FOR cosmologists , they’re barely a walk around the block.
Our galaxy is but one of tens of millions astronomers have observed, and some of them are well over a billion (YES, with a B) light-years away. But, you ask ----how do astronomers know this?
Features in the spectra of distant galaxies appear at different wavelengths than those in closer galaxies. For these distant galaxies, the shift is always in one direction only–yowards the red----and astronomers call this phenomenon “redshift.”
Objects moving away from us show redshifts, while those moving towards us show blueshifts. It just happens to turn out that redshift is the key to unlocking the distant cosmos’ mysteries.
Slipher and the Sombrero
THE FIRST GALAXY DISCOVERED WITH A LARGE REDSHIFT WAS THE SOMBRERO GALAXY (M104). Some of the light this galaxy emits is absorbed by atoms on its way out.
The Sombrero, like most other galaxies, contains many neutral sodium atoms, which absorb light vibrating with a specific energy. So, when we observe M104’s spectrum, we see a gap at precisely the energy corresponding to sodium’s preferred energy.
In laboratories, scientists measure the wavelength sodium prefers — 589 nanometers (urn). So, astronomers would expect M104’s spectrum to drop off at 589 urn.
In 1912, American astronomer Vesto Slipher at Lowell Observatory in Arizona took M104’s spectrum using about 40 hours of telescope time. His spectrum shows the sodium absorption line not at 589 urn, but at the slightly longer wavelength of 591 urn.
What happened? ‘The light from M104 has been “stretched” in wavelength — redshifted. Astronomers divide the expected wavelength by the new observed wavelength, and then subtract 1 to get the redshift value (denoted as z). For M104, the result is 0.0034. Because z is positive, we know the Sombrero is moving away from us.
Between 1922 and 1929 , Edwin Hubble and Milton Humason at Mount Wilson Observatory collected data showing that more distant galaxies have larger redshifts. THIS DISCOVERY REMAINS THE VERY MOST DIRECT EVIDENCE THAT THE UNIVERSE IS EXPANDING.
For small redshifts like M104’s, the recession speed equals the speed of light multiplied by the redshift. So, the Sombrero Galaxy races away from us at 2.4 million mph (3.9 million km/h).
In 1929, Hubble reported that the redshifts of distant galaxies increase proportionally with their increasing distance. That is, the farther away a galaxy is, the faster it is moving away from us.
Imagine a baseball field that doubles in size every year . After only one year, the pitcher’s mound will be 121 feet (36.9 meters) from home plate. ‘l’he mound, therefore, will be receding from home plate at 60.5 feet (18.4m) per year. A spot in center field that is originally 300 feet (91.4m) from home plate will be 600 feet (1 82.9m) away after. It recedes at 300 feet per year.
So it is in the cosmos. The farthest objects move away from us with the highest speeds, so they show the largest redshifts.
This so-called Hubble’s Law assigns a distance to any cosmic object with a measured redshift. For redshifts much smaller than 0.5, a galaxy’s distance equals 14 billion light-years times its redshift. Applying the Hubble formula to the Sombrero Galaxy with this value for the constant, we find the galaxy is almost 50 million light-years away.
Light doesn’t travel to us instantly — it takes time. So, astronomers talk about “lookback times” the time it takes an object’s light to reach us. We can think of the Sun’s lookback time as 8 minutes; for the center of our galaxy, it’s about 25,000 years; and for M104, it’s 50 million years.
Cosmological redshift tells us how far away an object is and how long ago the light we see was emitted. Redshift also pins down the universe’s “scale factor” at the time a galaxy emitted its light.
Let’s return to the baseball field that doubles in size every year. The scale factor >today, when the pitcher’s mound is 60.5 feet from home plate and the center fielder stands 300 feet away, equals 1. Following a year of expansion, the scale factor is 2. The physical distance between any two points on the baseball field is twice their original distance. That is, the new distance equals the initial distance times the scale factor.
The universe has stretched 1.0034 times since the light we see today from M104 left the galaxy. This means the scale factor when the light left M104 was 1/1.0034, or 99.7 percent. Such a large number means the universe hasn’t expanded much while the light was traveling. Galaxies with larger redshifts are farther away from us, so light left them when the scale factor was smaller than it was for the Sombrero Galaxy.
A galaxy with a measured redshift gives astronomers a distance, a scale factor, and a lookback time. Now, when you hear an astronomer refer to “a galaxy at redshift 17 you can translate: The galaxy emitted its light at redshift 1, at a lookback time of 7.6 billion years ago, when the universe was half its present size at a scale factor of 0.5.
For objects with large redshifts, the simple distance formula explained above doesn’t apply. In fact, the very notion of distance becomes ambiguous. Imagine putting down an infinitely long ruler at a fixed time and reading off the distance between us and a quasar at redshift 5.8. Place the ruler down today, and the distance is 27 billion light-years. (Astronomers call this the “co-moving distance.”) Back when the quasar emitted this light, all distances were smaller by a factor of 6.8, so , at that time, the ruler would have shown 4 billion light-years.
Yet another way to measure distance is to sit on top of a photon and click off the miles as it travels toward us . The distance out to redshift 5.8 measured this way is 12.5 billion light-years.
Two very important features of cosmic distances are changing the face of modern cosmology. First, they can be measured, which is remarkable in itself. And distances can teach us about how cosmic expansion has changed over time.
The distance to a given redshift depends on the universe’s expansion speed. For nearby objects, the distance is inversely proportional to the Hubble constant, which measures how fast the universe is expanding today. This low-redshift formula (distance equals 14 billion light-years times z) assumes a particular value of the Hubble constant . If the Hubble constant were larger, then the Sombrero’s distance would be smaller. (Got it?)
For objects at larger redshifts, the formula is more complicated, but the principle is the same. If the universe expanded rapidly in the past, then the scale factor increased rapidly, and light had a relatively small time to travel to us. So the very distance to a given redshift is smaller if the universe expanded rapidly.
If we had some independent way of measuring distances, then, a table of distances vs. redshifts would tell us how fast the universe has expanded throughout history.
So, distances would matter if we could find a way to measure them without redshift. But what do astronomers do if they can’t build a billion-light-year ruler?
Astronomers use the fact that objects far away from us appear dimmer than those that are closer. More quantitatively, the flux from an object is inversely proportional to the square of the distance between us. If we know the intrinsic luminosity of the object in question — say, because it is a “standard candle:’ a class of objects all with similar 2 brightnesses — we can use the observed brightness to infer distance.
This standard astronomical gimmick works in cosmology only if astronomers define yet another distance — the “luminosity distance This equals redshift plus 1 times the co-moving distance, and astronomers can compute it from the universes expansion history. So, astronomers can use the observed brightness of a standard candie to infer a history of cosmic expansion.
The most celebrated objects for which astronomers have obtained luminosity distances are type Ia supernovae. This class of exploding stars is useful for two reasons. First, supernovae are among the brightest objects in the sky and can be detected at great distances . Second, type Ia supernovae - serve as standard candles. Although they aren’t equally bright, characteristics of these explosions — especially how rapidly they fade out — let astronomers infer how bright a given supernova actually is. Starting in the mid 1990s, astronomers accumulated such information about a handful of distant supernovae.
During the past decade, this number has ballooned to hundreds . The results are surprising: High-redshift type Ta supernovae are much fainter than scientists expected them to be . So, the luminosity distances are larger than expected, which corresponds to the fact that the young universe expanded more slowly than it does now. As the headlines proclaimed in 1998: THE UNIVERSE’S EXPANSION IS ACCELERATING.
Ordinary matter — protons, neutrons, and even exotic dark matter — cant produce an accelerating universe. Imagine an expanding sphere enclosing 100 particles of matter. It becomes less dense as time goes on, and gravitational forces between the particles only slow the expansion.
Whatever causes this cosmic acceleration, it’s truly an exotic form of energy that isn’t diluted as the volume enclosing it expands. Physicists have dubbed this “dark
energy” A major challenge of contemporary physics is to understand what dark energy is and how it fits into our theories of subatomic particles.
By probing the universe on the largest scales imaginable and measuring cosmic distances, astronomers have stumbled on the biggest mystery in fundamental physics. AND IT ALL BEGAN WITH REDSHIFT.
Scott Dodelson, director of the Center for Particle Astrophysics at the Fermi National Accelerator Laboratory in Batavia Illinois, wrote Modern Cosmology (Academic Press, 2003).
May 2007. (Pgs. 40-43)
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