Some of the earliest attempts to measure the distances of the stars was to simply compare their observed brightnesses. By the 1600s it was well established that light obeyed a relation known as the inverse square law, so that closer stars should appear brighter than more distant ones. Specifically, if two stars have the same absolute brightness, but star A is twice as far away as star B, then star A will appear one fourth as bright. Newton and others compared the brightness of the Sun with other stars to estimate stellar distances, but they weren’t very accurate. The problem is that stars can vary significantly in their absolute brightness, and simply comparing stars doesn’t work. Astronomers eventually used other methods such as parallax to measure distances, which eventually led to a range of tools known as the cosmic distance ladder. But now a team has developed a way to determine stellar distances by comparing their brightness, and it’s surprisingly accurate.

What the team did was to analyze at the spectra of stars looking for stars with extremely similar spectra. They refer to such stars as “stellar twins,” but that term implies these stars have a common origin. These stars didn’t necessarily come from the same stellar nursery, but simply have spectra that make them look quite similar. Basically, they are stellar doppelgangers. If two stars have matching spectra, then their chemical composition and temperature should be remarkably similar. Therefore, the team argues, their absolute brightness must also be quite similar. With similar brightnesses, the old inverse square relation should work for measuring their distances.

Spectral twins vs parallax. The blue line would be perfect agreement.

It’s a great idea, but how could we tell if it works? From the Hipparcos survey we have measured the parallax of about 2.5 million stars, and from the HARPS survey we have measured detailed spectra of many of the same stars. So the team looked for spectroscopic twins in the HARPS data that were also in the Hipparcos data. Using the parallax distance of one twin, they then calculated the distance to the other by the inverse square relation. Comparing their calculated distance to the parallax distance they could determine just how accurate their method is. From the Hipparcos distances, there’s an uncertainty of about 3.5%, so if their method was perfect you’d expect a similar variation in their results. What the team found is that their inverse square method agreed within about 7.5%.

So their method isn’t quite as accurate as parallax, but it has the advantage of not being directly limited by distance. If we can measure an accurate spectra of a star, and it has a twin for which we know the distance, we can determine how far away it is fairly accurately. The method could also be used for stars in open clusters, which are notoriously difficult to measure using parallax. It’s an ingenious method, and one more tool that can we can add to the cosmic distance ladder.

Paper: Jofré, P. et. al. Climbing the cosmic ladder with stellar twins. Monthly Notices of the Royal Astronomical Society (2015)

The post Using Doppelganger Stars to Measure Stellar Distances appeared first on One Universe at a Time.

A century ago, we didn’t know the size of the universe. We didn’t even know the size of our galaxy.

In 1838, Friedrich Bessel made a breakthrough in determining stellar distances by measuring the parallax of a star for the first time. While this gave us the distances to many nearby stars, it wasn’t effective beyond a few hundred light years. Even now parallax is only useful to about 1,600 light years. This is a small fraction of our galaxy, much less other galaxies and beyond.

Time lapse of a globular cluster showing variable stars. Credit: J. Hartman and K. Stanek

But in the late 1800s, studies of dense, spherical clusters of stars known as globular clusters found something interesting. Most of the stars in a cluster had a constant brightness, but some (known as RR Lyrae variables) would periodically brighten quickly then slowly fade. They all have a fairly regular period of about half a day, and they all seemed to peak at about the same apparent brightness. Since stars in a globular cluster are all about the same distance away, this meant that RR Lyrae variables must have a uniform maximum brightness. By comparing the brightness of the variables in different clusters, we could then determine just how far away these clusters are.

Shapley’s map of the galaxy with the Sun’s position indicated in red.

In 1918, Harlow Shapley used these variable stars to determine the direction and distance of globular clusters as a way to determine the position of the Sun within the Milky Way. Shapley argued that globular clusters should orbit the gravitational center of the galaxy. By studying the distribution of globular clusters we should be able to determine the size and shape of our galaxy. He found the Milky Way was roughly pancake shaped, with a diameter of perhaps 150,000 light years, and he placed the Sun about 50,000 light years from the center (we now know it is about 27,000 light years). Shapley showed not only that the Sun was not the center of the universe, but that the Milky Way was much larger than anticipated. So large that it might comprise the entirety of creation.

By the 1920s there was a great debate over whether this was actually the case. Shapley felt it was, but others such as Heber Curtis thought otherwise. The debate centered on the distance to certain nebulae. At the time, “nebula” referred to anything (excluding comets) that appeared “fuzzy” rather than distinct like a star or planet. So things like the Orion nebula (a stellar nursery), the Crab nebula (a supernova remnant) were considered nebulae just as they are today, but what we now call galaxies were also known as nebulae. The Andromeda galaxy, for example, was known as the Great Andromeda Nebula. Curtis thought Andromeda was an “island universe” like the Milky Way, likely millions of light years away. Shapley thought Andromeda and other spiral nebula were close to the Milky Way.

Leavitt’s original period-luminosity relation.

The problem was that RR Lyrae couldn’t be used to settle the dispute. While they allowed us to determine the distance to globular clusters thousands of light years away, they were relatively dim and difficult to measure. But in the early 1900s Henrietta Leavitt had found a relation between another type of variable star known as Cepheid variables. Leavitt analyzed more than 1,700 Cepheids to find that their maximum brightness could be determined by the period at which their brightness varied. It became known as the period-luminosity relation. The advantage of Cepheids is that they are much brighter, and could therefore be seen in Andromeda and other spiral nebulae. It was a major breakthrough, but it took more prominent astronomers to make the relation widely known.

Hubble’s original distance-redshift relation.

While Shapley began using Cepheids to better determine the distances of globular clusters, Edwin Hubble measured Cepheids in Andromeda to find that, sure enough, it was a galaxy about 2.5 million light years away. As he measured the distances to other galaxies, he began to notice a pattern. The more distant the galaxy, the greater its observed redshift. This relation became known as Hubble’s law, and it gave us another tool to determine cosmic distances. Since redshift could be measured fairly easily, Hubble’s law had the potential to measure distances across billions of light years. Hubble’s relation was not without its critics. Originally Hubble’s observations only went as far as about 8 million light years. Extrapolating the relation to a billion light years or more seemed a bit presumptuous. We needed another way to determine the distance of the farthest galaxies.

The supernova redshift relation that discovered dark energy.

By the 1970s astronomers began to look toward supernovae as a possible solution. We had observed lots of supernovae in other galaxies by this time, and it was noticed that a particular kind of supernovae known as type Ia seemed to have a consistent maximum brightness. As such they could potentially be used as a standard candle to determine distances. By comparing a supernova’s observed brightness with its actual brightness, we could begin to measure billion light-year distances directly, rather than relying upon Hubble’s law. We found that Hubble’s relation did hold up pretty well over billions of light years, but for the most distant galaxies it didn’t hold up quite so well. In 1998 Saul Perlmutter, Brian Schmidt and Adam Riess had found that supernova distances weren’t consistent with a steadily expanding universe as Hubble’s law implied, but that the universe as a whole must be expanding at an increasing rate. This gave rise to the discovery of dark energy.

Various methods of the cosmic distance ladder.

At the beginning of the 20th century, we were just beginning to map out our galaxy. By the end of the 20th century we had discovered a universe billions of light years across. The methods we now use to determine cosmic distances are known as the cosmic distance ladder. While the overview I’ve given covers the main methods, it’s important to understand that they aren’t the only methods we use. We have several ways to test one method against another, so we have a good understanding of just how accurate these methods are. There are still uncertainties in any distance measurement, and the greater the distance the greater the uncertainty. There are still debates about the strengths and weaknesses of different methods, but not about the overall scale of the cosmos.

In a very real sense we have climbed the ladder from ignorance to knowledge of just how large the universe actually is.

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In the late 1800s Henrietta Leavitt was hired by Edward Pickering of the Harvard College Observatory. “Hired” in this case being a loose term, since Leavitt was not initially paid for her work. She was assigned the task of cataloging the brightness of variable stars from photographic plates. This is a tedious process, which is why it was done by women (known as Pickering’s Harem).

Period vs luminosity for variable stars. Credit: ATNF

As Leavitt cataloged thousands of variable stars in the Magellanic clouds, she noticed a particular trend in a type of variable known as a Cepheid variable, specifically that the rate at which the star varied (its period) correlated with the apparent brightness of the star. By assuming the stars in a particular Magellanic cloud were all essentially the same distance, she was able to demonstrate a linear relationship between absolute brightness (luminosity) and period, seen in the figure here. She published her results in 1912.

A year later Enjar Hertzsprung measured the distance of several Cepheid variables in our a galaxy, and confirmed Leavitt’s period-luminosity relation. This meant Cepheids could be used as “standard candles”. By observing their variable period, one could determine their absolute brightness. Comparing this to their apparent brightness, one can determine their distance. This allowed Edwin Hubble to use observations of Cepheids in the Andromeda galaxy to confirm that it was not simply a nebula, but a galaxy millions of light years away. This confirmed that the Milky Way was also a galaxy, and revolutionized our view of the universe.

Today we know of two main types of Cepheids, defined by their metallicity (which we can determine from their spectra). There is also another type of variable known as RR Lyrae, which are smaller and have shorter periods. Their use as standard candles is critical to our determination of the scale of the universe.

All through the standard behavior of certain variable stars.

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When you look at the night sky it is easy to imagine that the stars are part of a great celestial sphere. Stars appear to be fixed in relation to each other, and they appear to move about the Earth in unison. This is why most ancient cultures imagined that the stars were a part of a sphere or shell of night, and that all the stars were the same distance away from us. This illusion occurs because even the nearest stars are very, very far away. So how is it possible to say with confidence (as I did in an earlier post) that Sirius is 8 light-years away, or that Betelgeuse is 640 light-years away?

There are actually several methods to determine cosmic distances, and these are combined to create what is known as the cosmic distance ladder, but the oldest and most direct method uses the property of parallax. Parallax occurs when you look at an object from two slightly different positions. You probably use it every day, because it is what gives humans depth perception. When you look at an object, each of your eyes has a slightly different point of view. Your brain uses this information to determine which objects are close and which are farther away. This is also why you have to wear special glasses when you go to see a 3D movie. The glasses ensure that your eyes each get a slightly different perspective, which gives the movie the illusion of depth. If you take off the glasses during the movie, it will look slightly blurry. Without the glasses, your eyes see both points of view blurred together.

You can see the effect of parallax with a simple experiment. Hold up your thumb at arm’s length, and look at it with only one eye. Without moving your thumb, switch eyes, and you will see that your thumb appears to move relative to more distant objects. This shift is known as a parallax shift. If you bring your thumb closer and do the experiment again, you’ll see that the parallax shift is larger. If it is farther away, the parallax shift is smaller.

With a little bit of trigonometry, you can calculate the distance to an object by measuring its parallax. This is how astronomers can measure the distances to nearby stars. Astronomers use the motion of the Earth to their advantage. The radius of the Earth’s orbit about the Sun is 93 million miles. By observing the position of a star on a particular night, and then on a night 6 months later, astronomers can measure the parallax shift of the star from two points of view 186 million miles apart. The bigger the parallax shift, the closer the star.  You can see this in the figure below.

The parallax of even the closest stars is very small, on the order of an arcsecond, which is 1/3600 of a degree in angle. The star with the largest stellar parallax is Proxima Centauri, which has a parallax of 1.3 arcseconds. It is the closest star to Earth (except for the Sun), with a distance of 4.2 light-years. Current technology can typically measure parallax down to about a thousandth of an arcsecond, or a maximum distance of about 1,600 light years. For anything more distant, astronomers must use other methods.

Recently astronomers were able to use parallax to measure the distance to a black hole which orbits a star known as V404 Cygni. As the black hole orbits V404 Cygni, it pulls matter from the star into itself. As the material falls into the black hole it produces light. When only a small amount of matter is being drawn in, the region around the black hole doesn’t give off much light, (known as quiescence) but when a large amount of matter falls to the black hole it can give off an intense burst of light. As a result, V404 Cygni will appear to brighten from time to time. The light from the black hole was observed during quiescence over a period of three months using what is known as the High Sensitivity Array (HSA), which consists of five telescopes across the world. By observing the black hole at the same time, and using a technique known as interferometry, astronomers were able to make very precise measurements of the black holes position.

By comparing their measurements with earlier measurements, the authors were able to measure the parallax of a black hole for the first time. They determined that the black hole is about 7,800 light-years away, which is closer than previously thought. It is the farthest distance we’ve measured directly. In the future we hope to measure even greater distances. In October of last year for example, the European Space Agency launched the Gaia Mission, which should be able to measure parallax as small as 20 millionths of an arcsecond, which will measure distances of tens of thousands of light-years.

We should soon have a very accurate map of our cosmic neighborhood.

Paper: J. C. A. Miller-Jones et al.  The First Accurate Parallax Distance to a Black Hole. ApJ 706 L230 (2009)

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The origin of the universe is often portrayed in popular science as a vast sea of darkness.  Centered in this darkness is a bright point of light, which suddenly expands, filling your view with light, fading into a dance of galaxies.  Of course this raises all sorts of questions:  What did the universe expand into? What triggered the initial explosion?  Where did all that matter and energy come from? The problem is, this isn’t how cosmologists see the big bang at all.

Popular science loves to portray cosmology starting with the big bang and ending with our modern universe, but in astrophysics we work the other way around.  We start with what we observe in the universe today, and work back as far as we can to the early moments of the universe.  This is an important distinction, because it means we don’t have to know every detail of the origin of the universe to know quite a bit about its history and early period.  In the same way, biologists don’t have to know exactly how early life appeared on Earth (abiogenesis) to know that the variety of life we see today evolved through natural selection from that early common ancestor.  Understanding that earliest moment is our destination, not our starting hypothesis.

So let’s walk through the process of how what we observe today leads us to conclude that the universe started with a big bang 13.8 billion years ago.  It’s a rather detailed process, but I’ve written about many of the underlying topics before.  Instead of restating all of them here, I’ve just summarized them and added links to earlier posts).  How far you want to delve into the details is up to you, but I think it’s useful to explain just how well we understand the origin and history of the universe.

The first clue was found by observing the relation between a galaxy’s distance and speed. There are various ways we can determine the distance of a particular galaxy.  For example, there are certain variable stars known as Cepheid variables that brighten and darken at a rate correlating to their overall brightness.  There is a type of supernova called type Ia that has a pretty standard brightness.  By observing the apparent brightness of these things in a particular galaxy we can get an accurate measurement of just how far away they actually are.

We can measure the speed of a galaxy by observing the Doppler shift of light coming from the galaxy.  Atoms and molecules emit and absorb light at specific wavelengths.  By observing this spectral pattern we can determine what type of atoms and molecules exist in a particular galaxy.  But if a galaxy is moving away from us, that pattern is shifted a bit toward the red end of the spectrum.  The light waves emitted from the galaxy are stretched a bit due to the galaxy’s motion away from us.  Similarly, if a galaxy is moving toward us, the pattern is shifted a bit toward the blue end of the spectrum, as the light waves bunch up a bit.  You’ve probably experienced this effect with sound, where the sound of a passing car or train sounds higher as it approaches you and lower as it passes you by.

When we observe different galaxies, we find that the light of most galaxies are red shifted.  Not only that, the more distant a galaxy is, the more its light tends to be redshifted.  This was first observed in detail by Edwin Hubble in 1927.  Hubble demonstrated that there was a linear relationship between a galaxies distance and its redshift.  When this was first observed, it was generally thought that the universe was pretty static. If that were the case, then one would expect galactic speeds to be random, with some moving toward us, and some moving away from us.  Since galaxies appear to be receding from us at a rate proportional to their distance, a better model is that of an expanding universe.  Not just fixed region of space where galaxies are flying away from us, because that wouldn’t account for more distant galaxies having greater speeds.  Instead it must be that the universe itself must be expanding, kind of like bread dough rising.

That seems like a rather radical idea (which it was), but it is the model that best fits the data.  It also agrees with Einstein’s theory of relativity, which has been verified extensively.  Einstein had actually had a chance to predict the expansion of the universe, since it’s a consequence of the theory of relativity.  But Einstein assumed the universe must be static, so he introduced a cosmological constant to allow for stationary universe.  More modern observations show that not only is the universe expanding, it is expanding at an ever increasing rate, and one way to account for this is through a cosmological constant.

So if the universe is currently expanding, then in the past the universe must have been smaller.  Extrapolating really, really far back, the universe must have been really, really small.  So it must have had a beginning as a small initial “seed”.  This idea was first proposed by Georges Lemaître, who referred to that initial seed as the primordial atom.  From Hubble’s original data you could get an age for this primordial atom of 10 – 20 billion years, which would be the age of the universe.

Now this is a huge leap.  After all, no one looks at a loaf of rising bread and presumes a week ago it must have begun as ultra dense “primordial dough”.  Many astronomers thought extrapolating cosmic expansion back to a primordial atom was pseudoscientific nonsense.  Among them was astronomer Fred Hoyle, who actually coined the term “big bang”.  (It’s rumored that Hoyle meant the term to mock the idea, but Hoyle denied it.)  Hoyle proposed an alternative interpretation, known as the steady-state model.  In Hoyle’s model, the universe has a process of slow continuous creation of matter, which creates the positive pressure necessary to cause cosmic expansion.  Thus the universe is ever expanding, but is ageless.

Of course both of these models have very clear predictions.  In particular, the big bang model predicts a very specific signature.  If the universe began as a dense primordial fireball, then a remnant of that intensely hot period must still exist.  As the universe expanded its temperature would cool, but it wouldn’t be zero.  So either there is a background temperature to the universe, or the big bang model is wrong.  Given Hubble’s observations of cosmic expansion, that temperature should be a few Kelvin today.  In 1965 just such a background temperature was observed by Penzias and Wilson.  This cosmic microwave background as it now known matched the temperature of a thermal blackbody exactly, with a temperature of 2.7 K.

The cosmic microwave background (CMB) and the evidence of cosmic expansion demonstrated pretty clearly that billions of years ago the universe was a primordial fireball.  But we have to be a bit careful here.  The simple existence of the CMB does not tell us the universe began as a primordial atom.  The CMB is not light from the big bang itself, but light from when the universe had a temperature of about 4000 K.  At higher temperatures hydrogen ionizes into a plasma of electrons and protons.  Light is heavily scattered in a plasma, so it isn’t possible for us to see anything further back than then.

Light travels at a finite speed (about 300,000 km/s), and that means the more distant an object is the longer it takes for the light to reach us.  That means when we view distant objects such as galaxies, we are seeing them as they were in the past.  It also means when we observe something that happened in the past, we observe how it happened light years away from us.  Our best measurement of the age of the CMB is 13.798 billion years ago.  That means the CMB we observe is from a region of space that was 13.798 billion light years from our current position at that time.  Due to the expansion of the universe, that region of space is about 47 billion light years from us today.  In other words, by the time the universe had cooled enough to condense into neutral gas (the time of the CMB), that gas covered a region at least  28 billion light years across, because that was the size of the observable universe at the time.

So now that we know that 13.8 billion years ago the observable universe was a primordial fireball 28 billion light years wide, what’s to say we can extrapolate further back than that?  What if the universe simply began as a fiery expanse of gas?  To go beyond the time of the CMB we need high energy physics.

We know high energy physics pretty well.  We’ve been doing high-energy experiments since the mid 20th century, so we have a good understanding of how matter behaves at high energies.  If we use this knowledge to extrapolate before the CMB, we reach a point where the temperature would be about a billion Kelvin, too hot for atomic nuclei to form.  If the universe began at least that hot, then as it cooled the protons would collide with such energy that a fourth of them would fuse into helium nuclei, a process known as nucleosynthesis.  That means the matter of the post CMB universe would have to consist of about 75% hydrogen and 25% helium by mass (with small traces of elements such as lithium).  This ratio agrees perfectly with the distribution of elements we see today.  We have recently observed the spectra of distant quasars and observed early gas clouds that contain no higher elements (carbon, nitrogen, etc), exactly as we would expect from nucleosynthesis.

Once we’ve reached back to nucleosynthesis, we’ve covered the history of the universe back 13.8 billion years to the time where the initial elements of the universe formed.  At this point the universe is at most about 10 seconds old.  We can extrapolate further back using particle physics, to a time when quarks and gluons form into protons and neutrons, or earlier, where the weak nuclear force and electromagnetism unite into the electroweak force. At this point the universe is no more than a trillionth of a second old, and the observable universe is about the size of a grapefruit.

This is what particle physics, astronomy and astrophysics tells us.  This is what we can demonstrate scientifically.  The early observable universe was once small enough to fit in the palm of your hand.

Of course this is only the observable universe.  Remember that our view is limited by the finite age of the universe.  If that early universe were truly only the size of a grapefruit, then its mass and energy would have curved space over time, and we would see the effects of that curvature on the expansion of the universe.  But to the limits of our measurements the universe has no overall curvature.  That means the universe must be much larger than the region we can observe.  As best we can tell, the universe is infinite in size. So our best understanding of the universe is that it’s infinite in space, finite in time, made of matter, dark matter and dark energy.

And we are a part of it all.

The post Primeval Atom appeared first on One Universe at a Time.

This post was originally written as a guest post for Ethan Siegel’s Starts With A Bang!

A recent Pew survey has found that one third of Americans believe that humans and other living things have existed in their present form since the dawn of time. That’s one third of the adult population who reject evolution, which is the bedrock theory of biology. Indirectly, they also reject the foundations of geology, physics and astronomy. Much of the commentary about this survey has focused on the religious and political correlations, but let’s look at the science behind the ideas. If evolution is correct (and it is) then it must have occurred over billions of years, not a mere 10,000 or so. So how do we know — really, really know — that the Universe is billions of years old? It all comes down to a bit of astronomy.

It’s taken 10,000 years just for the light in the yellow circle to reach us. Credit: NASA

One way we determine the age of the Universe is through cosmic distances. Since light travels at a finite speed, the light from distant objects takes time to reach us. The more distant the objects we can see, the older the Universe must be. So how far does 10,000 years get you? Not very far, as you can see in the figure above. For anything outside the yellow circle, the light has taken longer than 10,000 years to reach us. If the Universe was only 10,000 years old, we wouldn’t yet see anything beyond that circle. The faint glow of the Milky Way in a dark sky? Most of it would be missing. The Large Magellanic Cloud? Totally gone. The Andromeda galaxy? Not a chance. The night sky of a young Universe would be darker, and not nearly as interesting.

So how do we know our distances are correct? There are actually several methods to determine cosmic distances, and these are combined to create what is known as the cosmic distance ladder. The most direct method uses the property of parallax. Parallax occurs when you look at an object from two slightly different positions. You probably use it every day, because it is what gives humans depth perception. When you look at an object, each of your eyes has a slightly different point of view. Your brain uses this information to determine which objects are close and which are farther away. This is also why you have to wear special glasses when you go to see a 3D movie. The glasses ensure that your eyes each get a slightly different perspective, which gives the movie the illusion of depth. If you take off the glasses during the movie, it will look slightly blurry. Without the glasses, your eyes see both points of view blurred together.

Determining the parallax of a star. Credit: : NASA, ESA, and A. Feild.

You can see the effect of parallax with a simple experiment. Hold up your thumb at arm’s length, and look at it with only one eye. Without moving your thumb, switch eyes, and you will see that your thumb appears to move relative to more distant objects. This shift is known as a parallax shift. If you bring your thumb closer and do the experiment again, you’ll see that the parallax shift is larger. If it is farther away, the parallax shift is smaller.

With a little bit of trigonometry, you can calculate the distance to an object by measuring its parallax. This is how astronomers can measure the distances to nearby stars, using the motion of the Earth to their advantage. The radius of the Earth’s orbit about the Sun is 150 million kilometers. By observing the position of a star on a particular night, and then on a night months later, astronomers can measure the parallax shift of the star from two points of view. The bigger the parallax shift, the closer the star. The recently launched Gaia spacecraft can measure parallax with a precision of a few microarcseconds, which gives us the ability to measure stellar distances up to 30,000 light years away with an accuracy of 10%.

Beyond that distance parallax is too small to be of use, so we can use another method looking at a type of star known as a cepheid variable. Cepheid variables are stars that vary in brightness over a period of days. The first such star to be observed was Delta Cephei in 1784 (the fourth brightest star in the constellation of Cepheus), hence the name. For nearby Cepheids, we can determine their distance via parallax. We can also determine their apparent magnitude (how bright they appear), and given their distance we can determine their absolute magnitude (how bright they actually are) using the fact that the brightness of an object decreases with distance following what is known as an inverse square law.

The period brightness relation for Cepheids. Credit: NASA / JPL-Caltech / Carnegie

In the early 1900s astronomer Henrietta Leavitt analyzed more than 1700 variable stars to discover the luminosity-period relation for Cepheid variables. By looking at Cepheids in a particular Magellanic cloud she was able to demonstrate a linear relationship between absolute brightness (luminosity) and period, such as seen in the figure above. This meant Cepheids could be used as “standard candles”. By observing their variable period, we can determine their absolute brightness. Comparing this to their apparent brightness, we can determine their distance. From the Hubble telescope we have observations of Cepheid variables in lots of nearby galaxies, for which we can measure galactic distances out to about 100 million light years.

Beyond this distance, Cepheid variables are too faint to use accurately, so we need another method. This is often done with another class of standard candle known as a Type Ia Supernova. This type of supernova can often occur when two white dwarfs are in close orbit with each other. A white dwarf is formed when a Sun-sized star begins to run out of hydrogen to fuse in its core. The star fuses helium for a while, causing it to swell into a red giant. Depending on its mass, a star will fuse some higher elements in its core, and the resulting heat and light drives off much of the outer material of the star, but there comes a point where the star simply can’t keep fusing higher elements. After this, what remains of the star compresses down to a white dwarf. In a white dwarf it isn’t the heat and pressure of fusion that balances against the weight of gravity, but the pressure of the electrons pushing against each other. Type Ia Supernova are typically caused by a collision or merger of two white dwarfs. If the two stars are in a close binary orbit, particularly with a third star orbiting at as part of a trinary system, the orbits of the white dwarfs can degrade to the point where they collide, resulting in a supernova explosion.

What makes these type of supernovae particularly interesting is that they always have about the same brightness. We’ve observed Type Ia Supernovae in galaxies whose distance was already known from the Cepheid variables. We can observe how bright the supernovae appear, and knowing their distance we can determine how bright they actually are. What we find is that Type Ia Supernovae always have the same luminosity.

This property means we can use them as a standard candle as well. If we observe a Type Ia Supernova in a distant galaxy, we can observe how bright it appears. Since we know how bright it actually is, we can calculate the distance to the galaxy, since the more distant a light source is, the dimmer it appears. We can therefore use this type of supernova to measure the distance to its galaxy. This allows us to measure cosmic distances of billions of light years.

Now, as a skeptic you might point out that all I’ve done is shown that the Universe is large, not that it is old. Sure, the light of distant galaxies might take billions of years to reach us now, but what if the speed of light were much faster in the past? How do we know that the speed of light hasn’t changed over time?

A bright line spectrum. Credit: Chris Heilman

One of the things we can do is look at the emission and absorption spectra of atoms and molecules in distant stars, nebulae and galaxies. The patterns of these spectra allow us to identify these atoms and molecules, like a kind of fingerprint. But they also allow us to test whether physical constants have changed over time. Not just the speed of light, but the charge of the electron, Planck’s constant and others. If any of these constants had changed over time, the lines in a spectrum would shift relative to each other. The pattern would spread apart in some areas and scrunch together in others. When we look at distant objects, we find no such shift in any of them. Given the limits of our equipment, this means the speed of light can have changed no more than one part in a billion over the past 7 billion years. As far as we can observe, the speed of light has always been the same.

So this gives us confidence in a wonderful aspect of observational astronomy. When you look at more and more distant objects, you are also looking further back into time. But we can take that idea one step further, because not only do we know the Universe is old, we know just how old it is using the Doppler effect. The observed color of light can be affected by the relative motion of its source. If a light source is moving toward us, the light we see is more bluish than we would expect (blueshifted). If a light source is moving away from us, the light is more reddish (redshifted). The faster the source is moving, the greater the shift.

The Hubble relation for galaxies. Credit: Right, Robert P. Kirshner; Left, Edwin Hubble

We’ve measured this color shift for lots of stars, galaxies and clusters, and when we plot a graph of the distance of galaxies versus their redshift we find an interesting relation, seen above. The greater a galaxy’s distance, the greater its redshift. This means galaxies are not simply moving at random, as you would expect in a stable, uniform Universe. Instead, the more distant the galaxy the faster it is moving away from us. This relation between distance and speed is the same in all directions, which means the Universe seems to be expanding in all directions. Of course if the Universe is expanding, then it must have been smaller in the past. In other words, the Universe has a finite age, and it began very small, very dense (and therefore very hot). We call that starting point the Big Bang. If you do the math, you get an age of about 13.8 billion years.

Of course the story I’ve told here is just one path to the age of the Universe. We have lots of other observational evidence such as the cosmic microwave background, stellar evolution, baryon acoustic oscillations, and the hydrogen/helium ratio, to say nothing of planetary science, geology, and biology. This confluence of evidence points to a Universe that is not thousands, but billions of years old.

There was a time when the idea of a small, young Universe seemed reasonable. We now know that it is far older and far more wondrous than we ever expected.

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A new supernova was discovered in a nearby galaxy in October of 2012, and it’s recently been identified as a type Ia supernova. Astronomers and astrophysicists are interested in the type of supernova because there are several ways a supernova can occur, and they are categorized by type.

The first categorization of supernova is into type I or II.  This depends on whether we detect hydrogen in the explosion, as measured by the emission lines.  If we don’t detect hydrogen, it is type I, and if we detect hydrogen, it’s type II.  These are then categorized into smaller subgroups.  For type I, if we detect silicon then it is type Ia.  Otherwise we look for a helium line, and if we detect one, it’s type Ib, and if not, type Ic.  The type II supernova are categorized based upon the overall spectrum of light as well as how the brightness of the supernova decays over time.

You’ll often see a lot of discussion about type Ia supernovae like this recent one. The reason for this is that this particular type of supernova has a standard maximum brightness, and its brightness dies off in a distinctive way.  You can see this in the figure below.  Because of this distinct brightness and pattern, we can use type Ia supernova as “standard candles.”  That is, we can observe their apparent brightness and compare it to the absolute brightness of type Ia supernova.  By comparing the two, we know how far away the supernova is.  This lets us determine the distance of galaxies.  It is the measurement of type Ia supernova that lets us compare galactic distance to redshift, which tells us the universe is not only expanding but accelerating.

Relatively close supernovae like this latest one are useful because they allow us to take precise measurements of both the light spectrum and the brightness over time, which helps us better calibrate the measurements of more distant galaxies.

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Last time I wrote about how a special type of variable star known as a Cepheid variable could be used to determine galactic distances out to about a hundred million light years. To determine greater distances we need another useful tool. This turns out to be a special type of supernova known as Type Ia.

Supernova light curve. Source: Berkeley Lab

A Type Ia supernova has a unique light curve. In other words if you measure its luminosity as a function of time, its brightness decays in a very particular way. This is because the energy it gives off is dominated by the radioactive decay of Nikel-56 to Cobalt-56 to Iron-56. As a result all Type Ia supernova have the same decay of brightness over time. This light curve is in fact how we identify them as Type Ia rather than some other type of supernova.

The other interesting aspect of these supernova is that they all have an absolute magnitude of about -19.3. This means we can measure their apparent magnitude and use their absolute magnitude to determine their distance. Observations from the Hubble telescope have measured Type Ia supernova more than 10 billion light years away. As a result we can measure the expansion very precisely. So precisely that we now know the universe is accelerating.

The light curves of these supernova also allow us to prove that the red shift we observe in distant galaxies is really due to their motion away from us, and not due to some unknown physics. When we observe the curves distant supernova, we find that they have the same shape, but decay more slowly. The supernova appears slowed down because of its rapid motion away from us. This time dilation effect is exactly what we would expect for a supernova that’s racing away from us.

Now we just have to figure out why it’s accelerating.

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A while ago I wrote about how you can use depth perception (in astronomy we call it parallax) to measure the distance of nearby stars. While this works well, it only works if the stars are closer than about 1500 light years. So how do we measure more distant objects, such as nearby galaxies which are millions of light years away? For that we use an interesting type of star known as a Cepheid variable.

Cepheid variables are stars that vary in brightness over a period of days. The first such star to be observed was Delta Cephei in 1784, hence the name. For nearby Cepheids, we can determine their distance via parallax. We can also determine their apparent magnitude, and given their distance we can determine their absolute magnitude. I’ve written about the relation between apparent brightness and distance earlier.

It turns out there is a linear relationship between the average brightness of a Cepheid variable star (its luminosity) and the period at which its brightness varies. In the figure below I’ve plotted the luminosity of some Cepheid stars vs their period. You can see there is a nice linear relation between them.

Brightness vs period for Cepheid stars.

What this means is that if you determine the period of a Cepheid variable you can calculate its absolute magnitude. By measuring its apparent magnitude you can calculate its distance. From the Hubble telescope we have observations of Cepheid variables in nearby galaxies. From this we can measure galactic distances up to about 100 million light years.

So by using parallax we can determine the distance of nearby stars. We can also prove the Cepheid variable relationship. From the Cepheid relationship we can determine distance to nearby galaxies. For more distant galaxies we have to use a different trick involving supernovas, but that is a story for another time.

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