Variable stars highlight an important fact about the heavens above us: the universe is always changing. The universe is very large, stars and galaxies are very far away, and many changes occur on timescales far longer than we can see. Most things in the sky -- stars, nebulae, and galaxies -- don't appear to change at all during the course of a human lifetime. But variable stars do change on timescales that we can observe. We have now discovered stars that vary on timescales from milliseconds to centuries. Each one can tell us something about itself through its variability, and information that variable stars have provided has given us a better understanding of the larger picture.
One of the key concepts in astronomy is that stars change over time -- they're born from clouds of interstellar gas and dust, they shine by their own light created through nuclear fusion of hydrogen in their cores, and eventually they run out of fuel and die, returning some of their mass back to interstellar space. Their remains can then be taken up into new generations of stars, starting the process over again. The process of change that a star undergoes during its lifetime is called stellar evolution. But this process can take millions or billions of years for a star, much longer than we can hope to observe directly. Since we can't observe stellar evolution over long timescales, how do we know it occurs?
There are many pieces of evidence that point toward our current understanding of stellar evolution. One was the understanding of the nuclear physics responsible for why stars shine, and the subsequent realization that stars have a large but finite source of fuel to create heat. Another piece of evidence was the observational study of star clusters -- groups of stars all born at the same time and place -- and the eventual realization that the properties of star clusters differ depending upon how old they are. Evidence about the physical properties of stars has also come from the study of variable stars. In fact, variable stars often provide the best means of studying the physical properties of individual stars -- their variations turn them into "experimental laboratories" for stellar physics, and have given us many important clues as to what stars are and why they behave the way that they do.
Every time someone observes a variable star, they're collecting evidence of how the star is behaving. We can build hypotheses of why stars vary, and we can then test these hypotheses with all of the data that has been collected. Each piece of evidence provides a different test, and each test allows us to refine our hypotheses, and make a more accurate description of why stars vary. If we can learn enough about individual stars, we can then begin to learn about classes of variable stars. Eventually we can learn about all stars, variable or not, by putting together all of our models and descriptions of different kinds of stars, and then building a better understanding of what stars are and how they evolve in general.
So what do we know about stellar evolution, and how have variable stars contributed to that? Let's explore!
Jump to: Preliminaries: The Hertzsprung-Russell Diagram
Jump to: Star Birth
Jump to: The Main Sequence
Jump to: Leaving The Main Sequence
Jump to: Old Age
Jump to: Binary Stars
Jump to: Star Death
The Hertzsprung-Russell Diagram
When we classify stars, we try to use quantitative measurements of their properties, so that we can better understand how stars differ from one another, and why those differences occur. There are a number of physical characteristics of stars that provide important information on the lives of stars. Two quantities, mass and age, are probably most fundamental. The progress of a star's life is predestined by its mass, because ultimately the mass determines how much energy the star can produce and how quickly it will do so. The age of a star tells you how far along it is in its evolution. However, both of these quantities are hard to measure directly. You can sometimes measure the mass if the star is in a binary system, using the straightforward physics of Newton's laws of motion. But there's no scale that you can rest a star on and measure its mass. Likewise you can't tell a star's age directly just by looking at it. Again, you need some roundabout way of finding this out. Two other parameters are a star's luminosity and temperature, and both of these are related to mass and age in a way that we now understand, but like mass and age, deriving these physical parameters requires some extra work to derive. What would be ideal is to find a way to classify stars based upon a simple observation.
Two astronomers of the early 20th Century, Ejnar Hertzsprung and Henry Norris Russell, discovered an important observational means of comparing different stars with one another. They found that when you plot the brightnesses of individual stars versus their spectral type or color on a graph, the stars lie within well-defined areas within the graph. A star of a given brightness could only lie within a certain range of colors, and a star with a given color could only lie within a certain range of brightnesses. More observational and theoretical research showed that the color-magnitude diagram or Hertzsprung-Russell diagram was a snapshot of the evolutionary states of the stars plotted within the diagram. Stars would be found in different parts of the diagram depending upon their masses and their ages. Furthermore, as a star gets older, it changes in brightness and color in a very predictable way, and that stars of different masses change in very different ways.
Why is this concept important for variable stars? Individual stars have different physical properties and lie at different positions within the H-R diagram, and if a star happens to be variable, the physical information we can gain about the star by studying its variability can tell us about what stars at that position in the H-R diagram are like in general. And because there are different classes of variable stars found throughout the H-R diagram, we've learned a lot about stellar evolution by studying variable stars, even though it may take millions or billions of years for a given star to evolve.
When we talk about stars, we often refer to them based upon their position in the H-R diagram. For example, we call stars that are still burning hydrogen in their cores main sequence stars, and will often refer to stars younger and older than main sequence stars as pre- and post-main sequence stars. Stars that have evolved well beyond the main sequence are often on the red giant branch of the H-R diagram, or might be asymptotic giant branch stars. We might talk about RR Lyrae variables being on the horizontal branch, or beta Cephei stars being on the upper main sequence. All of these are stages of stars' lives, and the classifications help us to put them in context within the broader picture of stellar evolution. In the following sections, we will mention some of these stages of evolution and explain what studying variable stars can tell us about them.
Star Birth
When you look up at the night sky in the early months of the year, you can see two great constellations high in the sky: Taurus and Orion. These constellations are home to what we now know are star forming regions -- concentrations of gas and dust within our Galaxy, collapsing under their own gravity to form new stars. Every star that you see in the sky was once formed inside a star forming region, millions or billions of years ago. These regions in Orion and Taurus are home to some of the youngest stars we can see in the sky, and they're home to some important variable stars as well -- variables that have helped tell the story of how stars are born. You may be very familiar with one of these already: the Great Nebula in Orion, known as the Orion Nebula or Messier 42 (M 42). The Orion Nebula is home to an enormous number of young stars, and it is the light of the most massive of these stars that causes the nebula itself to glow.
Young variable stars were first called Orion variables or nebular variables, recognizing the fact that they occur in large numbers within the Orion or other similar gaseous nebulae. These are general names for a broad class of stars known as pre-main sequence or PMS stars. The most famous class of these nebular variables are the T Tauri stars, named for the prototype, T Tauri. These stars appear to be similar to "normal" stars except for a few important differences: they're highly variable, they're less bright than we would expect a star of their size and color to be, they often lie near gaseous nebulae, and they show emission lines -- the light emitted by highly excited atoms of a thin gas. The T Tauri stars were recognized as a distinct group in the 1940s, but it wasn't until the early 1960s that the T Tauri stars were finally understood to be newborn stars, still weakly accreting dust and gas from the nebulae from which they formed. Their variability can be caused by a number of things but much of it is related to accretion. When any mass falls within a gravitational field, some of its gravitational potential energy is converted to kinetic energy. If you hold a ball at eye level and drop it, it will accelerate toward the ground, gaining a kinetic energy equal to the amount of potential energy it lost falling from eye level to the ground. The same thing happens to gas and dust accreting onto a protostar: the gas is falling down the gravitational potential well of the star and accelerating. In this case, the gas gains some kinetic energy but also heats up. The infalling gas has some viscosity (or friction) and as it falls toward the protostar, viscosity within the gas causes it to heat up. As it gets hotter, it gives off more and more light until it impacts the surface, where it gives off even more light.
Some young variables are extreme in their variability. Two variables in the Orion constellation give variable star classes their names: the FU Orionis stars (or FUORs) and UX Orionis stars (UXORs), both closely related in age but different in variability. The FUORs are believed to undergo very large and very long-term brightness variations, sometimes brightening by more than a factor of 100, and then fading again over a course of years or decades. The origins of these outbursts is believed to be rapid accretion of circumstellar material onto the young protostar for a period of a few years. All protostars are now or have recently finished accreting material around them, but FUORs seem to be (temporarily at least) doing it at a more rapid rate. This rapid accretion results in a larger release of energy as light and heat.
The UXORs are almost the opposite. UXORs are stars that vary on very short timescales, getting dimmer rather than brighter. UXORs are believed to be stars with circumstellar disks (as all protostars are at one point) where the disk is clumpy rather than uniform. Some of these clumps are large enough to partially obscure the protostar as they orbit around it, causing the star to dim before our eyes. Essentially, the clumps eclipse their parent star relative to our line of sight.
How do we know all of this? When T Tauri, and FU and UX Ori were discovered, we didn't know they were protostars still in the process of forming. We learned this gradually over time, by making observations, and testing various theories of why they look the way they do. The very first observation astronomers made was simply that "they're variable". That in itself is interesting since most stars are not obviously variable. Astronomers began tracking their brightness over time. Then they discovered other stars whose behavior was similar. The realization that such stars often reside in or near gaseous nebulae, and that nebulae were places where stars were being born eventually led us to conclude that these stars are young, still in the process of forming. More observations in optical light and at other wavelengths showed that their variability originates from some of the same processes by which they form. Stars can brighten when matter accretes onto the star, or when changes occur in the disk of material surrounding them. They can fade as clouds of dust form around the star, or when these clouds orbit around and temporarily obscure them.
We now have a good understanding of how stars form (from collapsing clouds of gas and dust) and how long it takes (a few million years). We know that the process is gradual, and that it continues for a little while even after the protostar begins to shine like star. And we know this accretion process itself leads to variability. New observations still lead to refinements in our understanding, and we continue to study young stars today. These observations extend across the electromagnetic spectrum too, and we observe them with radio telescopes, infrared observatories in space, and even X-ray telescopes in space. Since all stars go through this formation process, the more we know about it the more we can understand the subsequent stages of stellar evolution.
Once a young protostar has accreted all of the gas and dust that it can from the cloud from which it was born, it may be massive enough to burn hydrogen in its core and shine as a star. If and when this happens, it becomes a zero-age main sequence star. The main sequence is defined as the part of a star's lifetime spent burning hydrogen at its core; the start of its main-sequence lifetime is the point at which hydrogen burning first begins, and the end is defined by the point at which it runs out of hydrogen in its core. The amount of time spent on the main sequence can vary from star to star too; the main sequence lifetime is mainly a function of a star's mass. Our Sun will spend between 9 and 10 billion years on the main sequence; a much lower mass star might spend 100 billion years on the main sequence, while a much higher mass star might only spend a few million years.
Stars on the main sequence change very little over this span of their lives, although lots of important changes are happening. The core is slowly converting hydrogen atoms to helium atoms and releasing energy in the process. The changes in composition introduce subtle changes in the structure over time, which also change the temperature of the star and the amount of light it gives off (its "luminosity"). But we have two big problems trying to study and understand these changes: they can take millions or billions of years to become apparent, and they happen deep inside the star where we can't actually see them take place! We understand some of the basic things about stars just by applying the laws of physics as we knew them, and inferring what the inside of the star must be like to explain everything we see on the outside. For example, once physicists in the early 20th century understood that atoms could fuse together to make other atoms and release energy in the process, that knowledge was then applied to stars to explain why they shine and for how long they live.
But there are lots of complex things happening inside stars, and we could learn a lot about them if only we could somehow go inside them and "look around" a little. As it turns out, we can do that, and we do it in exactly the same way that geologists can study the deep interior of the Earth -- by recording its vibrations. We study the conditions deep inside the Earth by watching how sound waves -- especially those created by earthquakes -- propagate around the Earth. If we measure the slight vibrations at the surface of the Earth, we can make a very good measurement of the conditions deep inside the Earth. This is because the sound waves generated at one place on the earth have to travel through the interior to reach other locations. The study of the interior of the Earth using its vibrations is called seismology.
We do something very similar to study the interiors of stars, and we call this asteroseismology. In stars, sound and gravity waves can propagate through the interior in a similar way that the vibrations of an earthquake travel through the Earth. For some stars, we can measure these vibrations by seeing how the brightness of different parts of the star's surface change over time. The vibrations of the star's surface are called pulsations, and we can measure the properties of these pulsations to say something about the conditions inside the star. In many stars -- including our own Sun -- there are many different vibrations happening at the same time; each vibration frequency is called a pulsation mode. (You can think of a "mode" like a note on a piano keyboard. Different notes are different modes.) If we can combine information about each of these different modes into a single model that can explain them all, then this model can tell us a great deal about the inside of the star.
The Sun is perhaps the most important pulsating variable there is, and the study of its pulsations is called helioseismology. The Sun's pulsations are too faint to be seen with the naked eye, but careful study has revealed that there are thousands of pulsation modes present inside the Sun at any given time. Because there are so many modes visible in the Sun, helioseismologists have to fine-tune their models very, very precisely in order to make models match the observed pulsations. Because of that we know to great precision many important things about the inside of the Sun, including: the temperature and density at its center and the way that temperature and density decrease from the center to the surface; the composition of the interior of the Sun, both in its core where hydrogen is being converted to helium, and farther outside the core; and finer details about its structure, such as whether it rotates at a different rate deep inside than it does at the surface.
Much of what we know about the lives of stars has come directly from the study of the variability of the Sun. But it can't tell us everything about all stars because it's just one star, with one mass and one age. If we want to learn about other stars in this way, we have to look for pulsations in other stars. We can do just that for a number of other pulsating stars. One classic example of this is the study of delta Scuti stars. These are stars that can have dozens (rather than thousands) of pulsation modes, but where the modes have large light amplitudes that are easier to detect. Delta Scuti stars on the main sequence are about 1.5 to 3 times as massive as the Sun; we can build models of these stars just as we do for the Sun, and so we can also try to "look inside" these stars as well. In recent years, we've also started to do precise photometry of other "solar-like" stars in hopes of learning more about stars similar to the Sun, but at different stages of their lives. Using small telescopes in space (like WIRE, MOST, and COROT) we can try to detect solar-like oscillations in these other stars, and compare them to what we detect in the Sun. Each star having a different mass, different age, and different chemical composition helps to refine and improve our picture of the structure and evolution of stars.
There's another type of variability that can occur in main-sequence stars, one that we also see on our Sun. If you've ever looked at a picture of the Sun, or looked at it through a solar filter, you might have noticed a number of dark spots on its surface. These spots -- sunspots -- are caused by strong magnetic fields on the Sun that interfere with heat transfer from the Sun's interior to the surface. Magnetic fields can block the movement of gas ("convection") which means that energy inside the Sun can't get out as easily. When this happens, the patch of the Sun's surface above where the gas motion is blocked begins to cool down, and thus appears darker to our eyes -- we see a sunspot.
We now know that this process can happen on any star we see, and on some stars -- particularly very young stars -- the appearance and disappearance of "starspots" results in a large change in brightness. These changes can even be periodic if the star is rotating and the spot survives for several rotation periods of the star. We can see variability due to star spots in RS Canum Venaticorum (or RS CVn) and BY Draconis stars. There's an associated kind of variability that we also see in the Sun: flares. On the Sun, flares are also associated with magnetic fields around sunspots, and are caused by these magnetic fields acting like giant particle accelerators, squeezing the gas in the solar atmosphere and accelerating it to great speed. We see these flares as bright flashes near the surface of the Sun lasting a few minutes. Similar flares probably happen on all stars with magnetic fields but one class of star -- the UV Ceti variables -- have very strong magnetic fields. Their strong magnetic fields, combined with the fact that their surfaces are cooler and dimmer than the Sun, mean that their flares are large and easily measurable. The study of magnetic activity in stars has been an important topic in stellar astrophysics. Our understanding of it is very incomplete, even for our own Sun. We know, for example, that the Sun has a 22-year cycle -- the Solar Cycle -- where sunspot activity waxes and wanes, changing magnetic polarity once per 11 years. But we don't fully understand why this is so. The more we observe this kind of variability in the Sun and other stars, the more we'll know and the better our understanding may become.
Leaving the Main Sequence
The end of the main sequence is defined as the point at which all of the hydrogen in a star's core has been converted into helium, and the nuclear reactions in the core of the star temporarily cease. Since these nuclear reactions provide the heat and pressure that hold up the outer layers of the star against the force of gravity, the star must readjust itself to compensate. The processes that occur during this readjustment cause a number of complex physical changes both inside and outside the star, and the star will change dramatically in appearance during this time. The most notable change is that the star will become a red giant, expanding in diameter, increasing in luminosity, and cooling in temperature. These changes take millions of years, so they're not obvious to our eyes. But as stars undergo these changes they may become true variable stars, or if they are currently variable, that variability may change or even cease altogether. So what are some types of variable star of the post main-sequence?
There are parts of the H-R diagram where we find lots of variable stars. One of these is called the instability strip, which runs from upper right (luminous and cool) to lower left (faint and hot) in the H-R diagram. When a star lies within the instability strip, it may begin to pulsate. In all stars, certain layers within the star can become more opaque to radiation if they become hotter or cooler. When this happens, energy from inside the star can become trapped in that layer, increasing its temperature and pressure. If this layer is located at just the right depth within a star, the layer can act like a piston that drives the outer layers of the star up and down in a periodic fashion, making the star pulsate. We now know that only stars within the instability strip have this layer at just the right depth. We also know based on stellar modeling that stars can lie within this strip at certain parts of their lives depending upon how massive they are. Stars more than a few times the mass of the Sun cross the instability strip after the main sequence. These are the Cepheid variables, named after the class prototype delta Cephei. One of the very important things about Cepheids is that the time it takes them to complete one pulsation cycle (the period) is proportional to the luminosity or absolute brightness of the star. If we can measure the period of the star, then we know its luminosity. This is known as the period-luminosity or P-L relation, and also by the name Leavitt Law, after its discoverer Henrietta Swan Leavitt.
Why is the P-L relation important? There is also a simple relation between the apparent brightness of a star, its distance, and its absolute brightness. If we can measure the apparent brightness of a Cepheid, and then determine its absolute brightness by measuring the period, we will then know the distance to the Cepheid. This is incredibly useful because distances are very hard to measure beyond the solar neighborhood. We've used Cepheid variables to measure distances to star clusters within the Milky Way, and even to measure the distances to other Galaxies. The study of Cepheid variables is a major research effort within astronomy because it provides us one of the best ways to calibrate our measurements of the size of the universe. Other kinds of pulsating stars can be used the same way; both the delta Scuti and RR Lyrae stars pulsate for exactly the same physical reason as the Cepheids, and both have their P-L relations. Delta Scuti stars can be used to measure distances within the Milky Way, and RR Lyrae stars are useful for measuring distances to globular clusters. Of the three, the Cepheids are the most luminous, and so we can see them at greater distances, often in galaxies millions of light years away.
Many types of stars can pulsate, but not all are regular pulsators with a well-defined period, and most stars outside the instability strip are not strong and regular pulsators. Some red giant stars are pulsating variables, but don't have very strict periods, and don't have large amplitudes. In fact, you can hardly detect variability in red giants at all with the eye, and you often need more sensitive equipment to measure their pulsations. Other stars pulsate because they give off so much light that they're close to blowing themselves apart. The most massive stars, those with more than 20-30 times the mass of our Sun, race through their supplies of nuclear fuel so quickly that they'll only live for a few million years. Because they burn their nuclear fuel so quickly, sometimes it has a difficult time escaping from the inside of the star, and this too can make a star "pulsate" in a way. The massive S Doradus stars sometimes have enormous outbursts capable of blowing off their own outer layers into space. The stars Eta Carinae in the southern hemisphere and P Cygni in the northern hemisphere are examples of two of these. Both of these stars show evidence for low-amplitude pulsations, and can occasionally undergo enormous eruptions, once every few centuries. It is likely that one day (perhaps soon) that eta Carinae and P Cygni will both end their lives as the ultimate variable stars -- supernovae. (More on those later!)
Old Age
All stars will eventually run out of fuel given enough time. The great majority of stars in the universe will pass through a phase of their lives where they swell up to enormous size -- larger than the orbits of Earth and Mars -- and become the most luminous stars in their neighborhood. These stars -- the asymptotic giant branch (or AGB) stars -- can be considered the last stage of stellar evolution when a star is truly a "star", an object that shines due to energy created by thermonuclear reactions deep inside. After a star has passed through the red giant branch and landed on the red clump (Population I stars) or the horizontal branch (Population II), it has a core made mostly of carbon or oxygen surrounded by layers of helium and hydrogen. These layers of helium and hydrogen are themselves layered according to whether the material is undergoing nuclear fusion or not; burning helium slowly settles onto the carbon core, while burning hydrogen slowly settles onto the helium shell. These burning shells are the main reason why AGB stars are so luminous; because the shell is closer to the surface, the outer layers become much hotter and so the star puffs up to enormous size. But because the star has such a large surface area, the amount of energy escaping from any one part of the surface is much lower than for a main sequence star, and so is much, much cooler. That's why AGB stars are red -- most have temperatures no more than 3000 to 3500 K.
What's most interesting is the short length of time stars spend on the AGB. A star may spend less than a million years evolving from the end of the red giant branch to the end of the AGB. That is a long time on human timescales, but very, very short in the life of a star! Further, some changes that occur on the AGB happen not on million-year timescales, but over a few centuries or a few decades! AGB stars undergo occasional events called thermal pulses, where the layer of helium surrounding the core suddenly undergoes thermonuclear burning, causing large changes to the star's structure, its luminosity, and its temperature. These events are called thermal pulses, and they're predicted to occur in all AGB stars by theoretical models of stellar evolution. If they occur, they happen very fast compared to other timescales in stellar evolution, and it's possible (though not proven) that we've seen some of these changes happen in a very few stars while we've watched over the past few hundred years.
The AGB is the locus of one of the most famous and earliest-known classes of variable star, and one near and dear to variable star observers: the Mira variables. Miras, named for the class prototype Mira (aka Mira Ceti, omicron Ceti, or omi Cet) are giant, pulsating variable stars so large that it takes them a hundred days or more to complete one pulsation cycle. They have large light amplitudes of at least 2.5 magnitudes, and some stars vary by ten magnitudes -- a factor of 10,000 in brightness! And they're huge, sometimes larger than the orbit of Mars.
Everything about the Mira variables is large, including and especially their importance in astrophysics. Like the Cepheids and other pulsators, the Mira variables have a Period-Luminosity relationship, and so can be used as distance indicators under some circumstances. Mira variables also have very high mass loss rates, and so they are the origin of a large fraction of processed interstellar material in galaxies; most (if not all) of the matter that makes up the world around us -- including ourselves -- came from inside an AGB star. And some Mira variables have observational records longer than a century, some much, much longer; these long observational records allow researchers to study evolutionary changes in Mira stars, one of the few instances where this is possible. The period of a Mira is dependent upon its size, and so if the average diameter of the star expands or contracts over time, its period will increase or decrease by a proportional amount. A very small number of known Mira variables have shown large changes in period that suggest long-term changes are occurring inside the star, and although it isn't proven that these changes are caused by thermal pulses, the possibility exists. Mira itself was first discovered in the year 1596, and a few other Mira variables were discovered in the 17th century. By the end of the 19th century, many more Mira variables were known, and today there are many dozens of Mira variables with light curves spanning a century or more. Such light curves are an incredible resource for stellar astrophysicists, and are one of the main reasons why organizations like the AAVSO encourage observations of variable stars. It may be that an astrophysicist in the future may use your observations of a Mira variable today to make an important discovery about the lives of AGB stars!
After the AGB, a star's lifetime is nearly over. The last stage of a star's life as a self-contained star may be the RV Tauri stage, characterized by pulsations with periods between 30 and 150 days. Some RV Tauri stars are known to have dust shells around them, and it's possible they've already passed through the AGB and Mira phases and are headed toward becoming planetary nebulae and white dwarfs. Their pulsations aren't regular, but instead seem to be weakly chaotic: while they may have cycles of maxima and minima that are fairly regular, their lightcurves often don't repeat from one cycle to the next, and often get out of sync over many cycles. While their behavior is sometimes similar to the Cepheid-like W Virginis stars, the RV Tauri stars seem to have gone slightly "over the edge" -- they're so luminous relative to their masses that they can no longer maintain regular pulsations. These stars are subdivided further into types "RVa" and "RVb", with the former maintaining a nearly constant mean magnitude and the latter having long secondary periods on the order of 1000 days or more where the star gets substantially fainter before returning to its former brightness. The reasons why there are two types isn't yet proven, but it may be due to the lack or presence of circumstellar material that periodically obscures the central star.
It's important to note one thing about the structure of stars at this point. Interiors of all stars become hotter and denser as you go deeper and deeper inside, for the same reason that the pressure in the ocean gets larger and larger the deeper you go. The weight of the mass above you increases the deeper you go in the star, until the pressures become very, very great. When a star is on the main sequence, these pressures are high by human standards, but atoms still behave like (mostly) normal matter, and the gas inside a star obeys physical rules -- called an equation of state -- similar to what we might observe here on earth. (The ideal gas law you might have learned in chemistry of physical science classes is an example of an equation of state.) But as stars age and more of the core is converted to heavier and heavier elements like helium, carbon, and oxygen, something happens. The gas becomes so dense and the atoms so highly compressed that they stop acting like normal matter -- the material becomes degenerate, meaning that the electronic fields of individual atoms can no longer keep them separated as they normally do. When this happens, the behavior of the gas fundamentally changes, and follows a degenerate equation of state. The gas no longer responds as quickly to heating by expanding or increasing in pressure as an ideal gas might, and so one of the key things that allows a star to keep its thermonuclear fires burning stops working.
A star whose core is in such a state is destined to die very, very soon in cosmic terms, and this core -- which is very dense, very small, and very hot -- is called a white dwarf. If a star has a core in this state, it will very soon begin blowing away material from its outer layers, until eventually the white dwarf core is exposed, and is all that remains of the star that was. The process by which this happens is very spectacular for anyone who happens to catch a star in the middle of this process. As the material flows away from the star into space, it becomes more diffuse and nebular in nature, while remaining lit by the hot stellar remnant within, forming what we see as a planetary nebula.
One of the key things that we learn from variable stars near the ends of their lives is how stars begin to return some of their mass back to space around them, and it is this cast-off stellar material that will later compose the clouds of gas and dust within galaxies that make up new generations of stars. Some of the material that is shed by older stars will be recycled into new generations of stars, and so learning about the evolution of stars also tells us how galaxies themselves evolve over time.
Binary Systems
Before we discuss the last stage of a star's life, let's take a moment to discuss another class of stars that can span all stages of stellar evolution -- the binary stars. Many stars are members of binary or multiple systems, and understanding how these systems form and evolve over time is an important part of stellar astronomy. Binary stars are particularly interesting because they give us more opportunities to determine the physical characteristics of these systems.
How? The light that stars give off contains a lot of information about them, and by applying all of the different measurement tools that we have at our disposal, astronomers can learn a lot about stars. First, the stars are moving relative to one another, and their motions cause their light to be doppler shifted back and forth in wavelength every time the stars complete an orbit. Measurement of these shifts can tell us how fast the stars are moving relative to their center of motion, and we can then make inferences about their masses and the sizes of their orbits. Second, eclipses mean that one star periodically obscures the other. Since one star obscures the other, we can try to map the shape and size of the stars based upon the eclipse light curves. Individual stars within the system might be distorted in shape if the stars are close to one another in their orbits. Stars also don't appear uniformly bright, but instead are dimmer toward their edges relative to our line of sight. (You can see this in photographs of the Sun -- it looks brighter at the center than toward the edges.) If you can measure this during eclipses, you can learn something about the temperature structure of the star's atmosphere. Third, when we follow binary stars over long periods of time, we may find that the orbital period changes in ways that can only be caused by specific things, such as precession or the presence of a third body in the system.
So assuming we can measure the properties of binary stars so that we know what they look like right now, what does that mean for our understanding of stellar evolution? Pairs of widely separated stars can evolve normally, as single stars do. However, if the stars are in close proximity to each other, or evolve to become closer to each other, they may dramatically influence the other star, forever changing its evolutionary course. The most dramatic way in which one star can influence the evolution of the other is through mass transfer. Each star has its own gravitational field, and during most of a star's life, the majority of a star's mass will reside well within the confines of its own gravitational well. But when two stars are close together, the shape of the gravitational field gets complicated. If you envision the strength of a gravitational field around a star like a topographic map, then there is a contour line separating the two stars, where the gravitational pull of each star balances out the other. Any mass that rests on that equipotential surface -- called the Roche limit -- is pulled equally by the two stars; if it crosses that line, then it will be pulled toward the other star. This is how mass transfer works. If a star grows in size -- which stars do as they get older -- then it may grow to the point where it is larger than the Roche limit. When it does, matter will start to spill over from one star and fall onto the other. When this happens, things can get very interesting! This mass transfer, also called accretion, is responsible for a number of different kinds of stellar variability, many of them being very dramatic indeed. In fact, mass accretion is responsible for some of the most energetic events in the universe. (More on those in a moment.)
The Algol variables are examples of mass-transferring main-sequence stars. Algols are binary star systems made of two relatively normal stars where one is transferring matter onto its companion. The variability we see is caused primarily by eclipses, but we also see variability due to this mass transfer. The most prominent of these stars is Algol itself, also known as beta Persei, the second brightest star in the constellation Perseus. Algol is known to be bright in X-rays and has strong stellar flares like solar flares on the Sun. This high energy variability originates from the interactions of magnetic fields on the individual stars with the mass transfer stream from one star to the other.
In the long term, mass transfer fundamentally changes the way stars evolve. As we mentioned earlier, the evolutionary path of a star is defined almost entirely by one parameter: its mass. If you know a star's mass, then you can predict a star's evolutionary path with great precision. However, what happens if you change the star's mass mid-way through its lifetime? Changing a star's mass fundamentally changes how the star evolves over time. If you increase a star's mass, you will increase the speed at which it burns its nuclear fuel and shorten its lifetime. You might substantially change the interior structure of the star. You might even change a star's ultimate fate; the way stars end their lives is also very strongly dependent upon its initial mass, and so adding to a star's mass might make the difference between it ending its life as a non-descript white dwarf or catastrophically as a supernova.
Stellar Death: white dwarfs and supernovae
Once a star passes through the asymptotic giant branch, what's left for it to do? The answer to that question varies widely depending upon a star's past history and present circumstances. There are two very important parameters for a star that determine its eventual fate: how massive is the star at the end of its life, and is it a single star or a binary? We'll first discuss what part the star's mass plays in how it ends its life.
White dwarfs
First, if a star reaches the end of the AGB with less than about 1.4 times the mass of the Sun, it will end its life as a white dwarf; if more than that, it will collapse into a neutron star ending its life as a supernova explosion. This mass limit, known as the Chandrasekhar limit, is the limit above which white dwarfs will collapse under their own weight -- the inward force of gravity becomes stronger than the outward force of electron degeneracy pressure, and the white dwarf implodes. The differences between those two fates could not be more different. Most stars will end their lives as white dwarfs, since most stars are relatively low mass. A star born with less than about eight times the mass of the Sun can probably lose enough mass during its lifetime to wind up below the Chandrasekhar limit by the time it dies, and well over 99 percent of all stars in the universe today are below that mass.
Stars that die as white dwarfs typically pass through one last phase of substantial mass loss, called the post-asymptotic giant branch (pAGB), and are often variable during this phase since they're in such an unstable state. The great temperature and pressure of the core serves to blow off most of the outer layers of the star, and in the process, stars can undergo any number of changes. One of these is pulsation (similar to RV Tauri pulsation), and pulsations are observed in many pAGB stars. Three other changes are directly related to the evolutionary changes happening deep inside the star: end-of-life evolutionary changes, very brief outbursts known as thermal pulses, and dust obscuration. The nuclear reactions that power stars run faster at higher temperatures and pressures, and so late in a star's life, it is racing through its supply of fuel very quickly. Evolutionary changes happen on timescales of decades and centuries, and to some extent, these subtle changes in luminosity and temperature may be visible if we look long and carefully enough. Sometimes the changes are much faster than that, and more drastic too. Thermal pulses are rapid thermonuclear burning events deep within the star where a thin layer of accumulated material becomes hot and dense enough to undergo nuclear fusion. When this happens it happens very quickly, generating even more heat and pressure that change the surface temperature, size, and luminosity of the star. Finally, the evolutionary changes and thermal pulses will drive mass loss from the surface of the star, and the mass loss rate at this stage of evolution is very large. Stars can lose nearly a tenth of a percent of their mass in just one year, which sounds like a small amount except that it adds up quickly in the space of a thousand years! This lost mass can generate dust around the star, which can obscure the star itself over time.
There are two types of variables that exemplify these behaviors. One are the R Coronae Borealis stars, named for the class prototype R CrB. At most times, R CrB hovers near naked-eye visibility at 6th magnitude, but seemingly at random it undergoes dramatic fades of several magnitudes in as little as two weeks. These events are almost certainly caused by dust obscuration, but whether each dip is a separate dust-forming event around the entire star, or simply an obscuration of the star on our line of sight by an orbiting dust cloud isn't entirely clear. There are about two dozen R CrB stars known today. This is a very small number, due to the fact that this is a very short stage of a star's life. In the several billion years that a star might live, it might spend only a few thousand years in the R CrB stage, so we'll only see a handful at a given time.
Another, still rarer class of variables doesn't even have a definitive name yet, although its properties are exemplified by the strange variable FG Sagittae. Like the R CrB stars, FG Sge is a pAGB star nearing the end of its life, but is likely to be very far along in this process. Tellingly, FG Sge is surrounded by a spherical shell, clearly reminiscent of planetary nebulae, and it has likely been shedding mass at a prodigious rate for thousands of years. FG Sge was discovered in the 1940s as a variable with irregular variability on timescales of a few days, and by the early 1960s it was clear that it was also slowly brightening by a few percent per year since the late 19th century. By the late 1960s it leveled of at around 9th magnitude, but in the early 1990's it underwent a precipitous decline, and it has varied irregularly by several magnitudes since then. It isn't known exactly what's happening, but the suspicion is that the long-term brightening was a rapid evolutionary change or the end of a thermal pulse, the result of which was greatly enhanced mass loss. This lost mass is now starting to condense into dust which obscures the star. The proto-planetary nebula that we see today is probably the result of previous episodes just like this one in which the star episodically lost mass in the recent past, and at some point, FG Sge will undergo one last event like this before shedding the last of its outer layers and leaving behind a planetary nebula and a white dwarf. Two other stars, V605 Aquilae and V4334 Sagittarius (Sakurai's Object), may have already reached this point and are well on their way to becoming white dwarfs.
After all the envelope has been lost and all of the nuclear burning and evolutionary changes have ceased, we're left with the final remains of a star's innermost core: a white dwarf. White dwarfs are the white hot remains of stars, mostly made of carbon and oxygen, and just a few thousand kilometers in size. They no longer shine by burning nuclear fuel, but by shedding the leftover heat from their past lives. Even though they're no longer living stars as we consider them, white dwarfs can still be variables! In particular, white dwarfs can pulsate, and the physics behind these pulsations is similar to those in normal stars. The only difference is the pulsation period; instead of taking months, weeks, days, or hours to undergo one pulsation cycle, it may only take them just a few minutes! White dwarfs are small, dense stars -- no more than a few thousand kilometers across -- and since the pulsation period is related to how long it takes a perturbation to travel through the star the variability make take just a few hundred seconds. We study pulsations in white dwarfs just as we do for the Sun and delta Scuti stars, for the purpose of asteroseismology. Just as in those main sequence stars, the pulsations of white dwarfs can tell us a great deal about their interiors, and we've learned a great deal about the properties of matter at very high densities and temperatures by studying them. We can even study how white dwarf pulsations change slowly over time as the star cools; the hottest white dwarfs cool fastest, and so it's possible to track their changes over many years and decades and deduce how quickly the star is cooling. This measurement is an important one for cosmology, since the coolest white dwarfs in the sky put a lower limit on the age of the universe.
Neutron stars, black holes, and supernovae
So what if a star is above the Chandrasekhar limit when it reaches the end of it's life? Lower mass stars typically stop their nuclear burning when the core is converted entirely to carbon and oxygen. It takes a great deal of temperature and pressure to reach the energy levels required to begin the thermonuclear burning of these elements. You can reach these levels in more massive stars, and in principle you can extract energy from all thermonuclear reactions up to a hard limit, that of thermonuclear burning of iron. All thermonuclear burning reactions are exothermic to that point, and so nuclear reactions will help to increase the temperature and pressure inside a star. If there's enough energy and pressure to star the reaction, you can start burning oxygen, neon, magnesium, silicon, and so on, all the way up to iron. If the core of the star is converted entirely to iron and then reaches the limit where it can start to burn, it will start to draw energy from its surroundings -- the reaction is endothermic. This is a catastrophe, because it is this very same energy that holds up the outer layers of the star against collapse, and so the star implodes violently. The result of this implosion is a supernova, one of the most energetic events in the universe. In a flash, the pent up gravitational potential energy is released, unleashing runaway nuclear reactions that create every element in the periodic table along with a storm of subatomic particles that blast away the outer layers of the star at close to the speed of light. For a few months, the amount of energy released by a supernova can equal the combined light of every other star in a galaxy -- the light of a hundred billion stars or more.
What's left over from this titanic explosion is again dependent upon the mass of the star. If the collapsed core is less than about three solar masses, the result will be an ultradense object called a neutron star -- an object ten kilometers across with three times the mass of the Sun, where all of its matter has been crushed so tightly that it composed of little more than atomic nuclei. Such objects are the most extreme form of visible matter in the universe and bear little resemblance to anything else in human experience. Their behavior can be just as bizarre, making them one of the most extreme kinds of variables known. The first variable neutron star was discovered in 1967, before it was even known such objects could even exist. A graduate student studying the universe at radio wavelengths discovered a repeating signal so regular that it was first assumed to originate from an alien intelligence. It was later found to be an ultradense object spinning on its axis many times per second, and the variability came from radiation from it's magnetic poles rotating in and out of view. These objects are now known as pulsars, and some pulsars have been found that spin as quickly as a thousand times a second. An even more extreme variable neutron star is a magnetar -- a neutron star with a powerful magnetic field that undergoes enormous outbursts at high energies. Magnetars can emit huge amounts of high energy radiation detectable from across the entire Milky Way. These outbursts can be so strong that the radiation can affect the Earth's atmosphere, increasing its temperature and causing it to expand, endangering satellites in low Earth orbit.
Even these aren't the most extreme fate of massive stars. If a star is above the three solar mass limit, not even the atomic forces that keep nuclei apart can keep the star from collapsing under the force of its own gravity. This creates one of the strangest objects in the universe: a black hole. These objects have such strong gravitational fields that their escape velocites are larger than the speed of light; anything that comes within a few kilometers -- a point called the event horizon -- is trapped forever, since there's no way it can travel faster than light to escape. What happens then? No one knows -- our understanding of the laws of physics breaks down at such extreme limits. Theorists predict that black holes might emit a kind of radiation, but nothing like that has ever been observed, and it is impossible to study a black hole directly. But black holes themselves have been observed indirectly, and this is a good point to begin our final discussion of variables: how they behave as members of binary stars.
White dwarf, neutron star, and black hole binary stars
Earlier, we mentioned binaries in which one star transferred matter to the other star, in a process called accretion. In systems where one member of the binary pair is a compact object, the accretion process can release an enormous amount of energy. The energy generated by accretion comes from gravitational potential energy, and material falling onto a compact object like a white dwarf, neutron star, or back hole falls into a very deep potential well. Depending upon how the accretion process occurs, it can release hundreds or thousands of times the luminous output of the Sun. Such objects are given a universal name of cataclysmic variables, although their properties vary wildly from one star to another, and are broken down into a number of different subclassifications.
White dwarf binaries are the most common form of accreting binary system, and they share a number of similar properties. The dwarf novae are binaries composed of a white dwarf primary and a Sun-like, main-sequence star in orbit around one another. Material is pulled off of the main-sequence star, and spirals around and down onto the white dwarf through an accretion disk. Depending upon the rate of mass transfer (how much mass flows off of the donor star onto the white dwarf), these stars can exhibit a number of different kinds of variability. All of them will show some low-amplitude, irregular variability caused by the material impacting the surface of the white dwarf. But in many of these stars the accretion rate is high enough that the accretion disk itself can go into outburst, brightening by a factor of 100 or more.
The stars SS Cygni and U Geminorum, both discovered in the mid-19th century, are prime examples of this. SS Cygni goes into outburst roughly once every 80 days, and U Geminorum about once every 200 days. The outbursts of dwarf novae become more frequent as the mass accretion rate increases, so stars with higher mass accretion rates outburst more often. Z Camelopardalis is an example of such a star. It rarely goes out of its outburst state for more than a few days. The Z Cam stars also exhibit another peculiarity in that the accretion disk can sometimes get stuck in a bright or "high" state, in an event known as a standstill. Such stars may show vigorous outbursts once every few days for months or years, and then suddenly enter this bright standstill for months or years more. At the highest mass accretion rates, the accretion disk never goes out of its outburst state since matter keeps piling onto the disk so quickly. Such stars are called novalike variables for reasons that will be made clear in a moment. A good example of such a star is V Sagittae, whose wildly irregular light curve shows little coherence over time. Another example is TT Arietis, a star discovered in the late 1960s, that for most of its life remains locked in a permanently bright, flat state around magnitude 10, with very rare extended dips of several magnitudes or more when the mass accretion inexplicably turns off for weeks or months at a time.
What happens to all the matter that piles up on the white dwarf? Over time, the white dwarf's mass will grow. Since the accreted material is coming from the outer layers of a normal star, it is mostly hydrogen and helium. Sometimes, if enough mass builds up on the white dwarf's surface, the temperature and pressure of the accreted material can rise high enough that it undergoes thermonuclear fusion, just as it would in the star's core. When this happens, the system becomes a classical nova, brightening not by a factor of 100, but a factor of 10000 or more for a short time. The word "nova" is the latin word for "new", and that's exactly what novae appear to be: new stars. They suddenly appear in familiar constellations, where they remain for a few days or weeks, until fading from view again. There have been a great many famous novae throughout the past century. Perhaps one of the most famous was Nova Persei 1901, a star now known as GK Persei. Nova Per 1901 brightened from an obscure magnitude around 10 or so all the way to magnitude 1, clearly visible among the bright stars of the sky. Over days and weeks if faded from easy view until dropping from naked eye visibility entirely, becoming a target for the larger telescopes of that era. More recent famous novae include Nova Delphinium 1967 (HR Del) and Nova Cygni 1992 (V1974 Cyg).
Most novae probably recur on very long timescales, perhaps many centuries or millenia, since it takes them that long to build up enough mass to trigger a thermonuclear explosion. But in a very few cases, the rate of mass transfer is high enough and the mass of the white dwarf is high enough that they recur on observable timescales of years or decades. These are known as recurrent novae. One such nova, U Scorpii, was recently in the news as its early 2010 outburst was predicted in advance and widely followed by astronomers around the world. RS Ophiuchi and T Coronae Borealis are two more examples of such novae. These stars are particularly interesting because it is believed that their white dwarf stars are near the maximum masses for white dwarf stars, around 1.4 solar masses. Because of this, any mass that accretes onto them will slowly push the star closer to the Chandrasekhar limit. When this happens, the gravitational collapse of the white dwarf results not in a classical novae, but in something far larger -- a type Ia supernovae, briefly becoming not 10000 times brighter but billions of times brighter. No one has yet seen a classical or recurrent nova become a supernova, but it's likely that in the not too distant future, some of the recurrent novae we know today will end their lives as supernovae.
There are other kinds of accreting white dwarf systems that don't fall into these neat categories. A very similar type of system involves a normal star and a white dwarf, but the white dwarf has a strong magnetic field, and its magnetism interferes with the mass accretion and inhibits the formation of an accretion disk. In these systems, called polars, matter flows onto the white dwarf's magnetic poles along the field lines, releasing a huge amount of energy as it impacts. The most famous of these stars is AM Herculis, and the polars are also designated as the "AM Her" objects.
A much different type of system involves a white dwarf in a wide orbit around a giant star, where the white dwarf isn't accreting from the secondary itself, but instead accretes from a strong wind from these giant stars. These systems, known as symbiotic stars, often remain quiescent or undergo slow, rolling changes in brightness for years at a time. Only occasionally will they undergo large outbursts of several magnitudes caused either by changes in the accretion flow onto the primary, or by the onset of steady thermonuclear burning on the surface. The star Z Andromedae is the classic example of such a star, and is the class prototype; discovered in 1901, it has been varying irregularly since its discovery, sometimes weakly oscillating around 10th magnitude, at other times undergoing decades-long periods of outbursts of two magnitudes or more.
Rarer cases of accreting binaries with compact primaries involve not white dwarfs but neutron stars and black holes. Neutron stars and black holes originate from more massive stars; since massive stars are rarer, so too are the binaries that involve these stars. But when they do occur, they tend to be spectacular. Close binaries involving a neutron star or black hole rather than a white dwarf are most prominent in X-ray rather than optical light, and are known as X-ray binaries. Such systems can release an enormous amount of energy in X-rays, and are often detected first in X-rays and later in the optical. One of the most famous of these was the very first non-solar X-ray source observed by early satellites in the 1960s. A source called "Scorpius X-1" was first detected by an Aerobee rocket in 1964, brighter than any other cosmic source barring the Sun and the Moon (which reflects the X-ray light of the Sun). In 1966 it was identified with an optical source, and given the variable star designation of V818 Scorpii. It consists of a neutron star and a normal star in a close binary system, and the X-rays are generated close to the neutron star's surface, where the inner edge of the accretion disk reaches the star. Material at the surface is traveling so fast -- a significant fraction of the speed of light -- that it emits X-rays rather than optical light on impact. A few dozen of these systems are now known to exist in our Galaxy.
Another more extreme type of system involves a black hole rather than a neutron star. X-ray source was found in Cygnus in 1970, and dubbed "Cygnus X-1". Within a few years, the optical counterpart of the X-ray source was found to be a bright blue star, HD 226868, and was given the name V1357 Cygni. Since the visible component is a luminous blue star, it had to be massive, several times the mass of the Sun. But the system was found to be a binary rather than a single star, and the spectroscopic evidence showed that the companion to the blue star had to be even more massive, perhaps 10 solar masses or more. Importantly, the companion was optically faint -- nearly all of the light was coming from the blue star and not the massive companion. This pointed toward the primary being a new type of object, a black hole. It is likely that both stars formed at about the same time less than 100 million years ago, and both were very massive. The more massive star of the pair evolved very quickly, ran out of fuel, and collapsed into a black hole. Its companion, the still visible bright blue star, is living on borrowed time. If it does not shed several solar masses of material, then it too will run out of fuel and collapse, either into a neutron star, or into a black hole just like its companion. They will then be a pair of dead stars, orbiting silently about one another, sensed only by their mutual gravitation. This is perhaps the most extreme fate for a star's lifetime, and makes a fitting end to this story as well.
Summary
Astronomy is one of the grandest of sciences, having as its subject the entire cosmos in which we live. Variable stars are just one piece of the scientific puzzle of astronomical research, and there's a great deal more to learn about stars, Galaxies, and the universe as a whole. With advances in technology have come equal advances in our understanding of the visible (and invisible) universe, and growth in our knowledge of the universe will continue for a long time to come.
The study of variable stars remains one of the best ways of learning about stars, and they will remain an important topic of interest for as long as we need to learn more about stars and the universe in which we live. There are many more classes of variable star than were discussed here, and each of those can tell us about the stars that make them up. We encourage you to learn more about them, both on our website, and on your own.
All of these stars and more are open to new scientific study and new insights, and important discoveries can come from anyone willing to make careful observations and rigorous and honest analysis. You can participate in the scientific study of variable stars and variable star research. It is the hard and careful work of observers just like you who have generated the many millions of variable star observations found in the AAVSO International Database, providing a rich resource for the astronomical community to learn from. We hope you can join with the thousands of variable star observers who have contributed to the AAVSO over the past century and become a part of this great endeavor.