Stars are luminous balls of gas (like the Sun) that are so distant that even the nearest appear as points of light to all but the largest telescopes. Stars gave early astronomers constellations to name and to track across the seasons. They are also markers that outline the shapes of galaxies. They gave us a first guess at the distribution of matter in the universe.
Although stars seem simple next to complex structures like galaxies, stellar astronomers still have to combine concepts from all across modern physics to understand how (and where) they form, glow, and evolve. To determine their distances (and hence the distances to clusters, galaxies, and the visible depths of the universe), we need to understand general relativity and how radiation is affected by matter and space. To determine their ages and compositions, we need to understand quantum mechanics and nuclear fusion. To understand how they are formed and evolve we need to understand how all four fundamental forces of nature interact. Stars tell us that the laws of physics are applicable and constant throughout the universe. These distant points of light in the night sky and our Sun share the same physical laws — the same law of gravity, the same type of energy source (the fusion of atomic nuclei), the same principles of quantum mechanics. In addition, our knowledge of stars supports the Copernican world-view: our Sun is a typical star, of middle age and medium size.
But stars are not just useful in the pursuit of astronomy – their importance to us is fundamental. Stars provide the universe with light, energy and chemical enrichment. Without stars there would be no radiation to supply heat and light to planets. Without stars there would be no elements heavier than hydrogen and helium and life is not possible without elements like carbon, nitrogen, or oxygen. Stars also tell us that the chemistry we see around us is not unusual. The elements that make up planets and people were generated in generations of stares that lived and died before the Solar System formed. The same process is going on all over our galaxy, and in all of the 100 billion galaxies in the universe. Chemistry is universal.
Stars also mark the transition between our local neighborhood (the Solar System) and the universe at large. The star closest to Earth is the Sun. The next nearest star is 260,000 times as far from us as we are from the Sun. It is 6800 times as far away from us as we are from Pluto. If we make a model of the Solar System the size of a poker chip, our neighbor stars would be dots smaller than the period at the end of this sentence, scattered about 100 meters apart.
This extreme distance makes the study of other stars a challenge. We can get at the details of other stellar surfaces only in a few rare cases. Using the largest optical interferometers, we can take very low resolution images of the nearest and largest stars. To date, less than a dozen stars have been resolved, including Altair, Betelgeuse, Regulus, and three members of the Algot triple system. The observations of Betelgeuse in particular are interesting because they reveal through the presence of starspots the existence of convection on other stars. Starspots are inferred on the surface of other stars based on gradual, observed changes in brightness that correspond to the rotation rate of the star being observed. When part of a star with more starspots is seen, it's overall light appears dimmer, and as a side with fewer spots is seen, it appears brighter. Since the amount by which a star is covered in star spots changes with time, the overall brightness fluctuations aren't constant. By creating models for how much of the star must be covered with spots to produce the observed fluctuations, it is possible to infer, in combination with information on stellar flares, many details about distant star's magnetic activity.
While surface details are hard to resolve, many other characteristics of other stars are easy to observe. For instance, telescopes focus faint radiation coming from distant stars, and spread it into a spectrum. Some stellar properties, like temperature, surface gravity and rotation, and the chemical composition, are measured directly through interpreting spectra. Other properties, like size and mass, can only be inferred using a physical model for the structure of the star, which is constructed using the foundational principles of modern physics.
We have found giant stars bigger than 9 A.U. in radius — this is nearly the size of Saturn's orbit! At the other extreme, we've also found stellar remnants the size of the Earth, and even as small as an asteroid! There are red stars and blue stars. There are stars with such low density atmospheres that you could see your hand before your face if you were within their envelope, and stars of such high density that their properties are similar to diamonds. There are stars that are isolated, and stars that are locked in orbit with one or many companions. Some stars are blowing off shells of gas and dust and others are consuming mass from their neighbors. As we look across the sky it quickly becomes apparent that stars come in a vast cornucopia of sizes, densities, compositions, and environments. This makes it a challenge to come up with a physical model that can explain all that is observed, but this is a challenge that theoretical astronomers relish.
By studying large samples of stars it is possible to uncover patterns in stellar properties. The study and classification of populations is a vital part of science. Although classification alone does not guarantee understanding, it can point the way forward. For example, paleontology starts with the collection and classification of fossils. This process gives no information about which fossils are older than others. By connecting our classification to which geological layers the fossils came from, we start to get a sense of how species evolve on Earth under the guiding hand of natural selection. In a similar way, as soon as astronomers could begin to measure different properties of stars, they began to categorize the stars and speculate about their life cycles.
One of the keys to decoding stars was the realization that all the stars in globular clusters and open clusters of stars have formed at roughly the same time and from the same material. Stars within these groups thus only differ in their mass. Once the effect of mass is understood, it becomes possible to use different clusters to understand the effects of age and composition. With the realization that stars produce light via nuclear fusion, it was possible to start building models of stars and try and match simulations to reality.
While it isn't possible to observe even the shortest lived stars going through more then the smallest fraction of their evolution, it is possible to observe stars of a given mass at a variety of ages by looking around the sky and infer how that mass stars ages. This is much like trying to understand how humans grow up by observing people in a crowded mall during a single day. While it may be possible to see one particular toddler learning to walk, in general, the development of a single person can't be seen. But, it may be possible, by correlating observed characteristics with age, to determine how men and women age.
The details of the lives of stars of different masses are discussed in other articles. In general, we now understand that stars are gravity engines, using fusion to forge heavy elements from lighter elementss. The light we see is a by-product of the fusion reactions. We understand that high mass stars create the heaviest elements and live the shortest lives, while small dwarf stars may only convert hydrogen to helium at a slow rate for an extremely long time. We know that the heaviest stars have lifetimes shorter than the age of the humans species, while the lightest stars live far longer than the age of the universe to this point. We know that stars leave behind collapses corpes that include some of the most exoctic states of matter imaginable. As much we learn about stars, they continue to fire our imaginations.