Main Sequence Dwarf Stars

Okay, Franke, you might be asking right about now. What is Snow White doing in this part of the class, and with the seven dwarfs no less. Well, there seems to be an interesting thing happening here. Astronomers classify all of the stars that are fusing Hydrogen into Helium as dwarf class stars. Furthermore, Annie Jump Canon classified stars into seven spectral groups ... O, B, A, F, G, K, M. Wouldn't you know it, but there are seven dwarves in the Snow White tale. While some of you may by grumpy over my humor, or sneezy due to fall allergies, others may be happy. A few might be sleepy about now, or feel dopey because of lack of computer prowess, or feel like a doc in computers and are not at all bashful about your skills. Whatever, we now enter the realm of the main sequence stars where the plural form of these objects is "dwarfs" unlike the dwarves that were so kind to Snow White.

The luminosities and temperatures of stars are traditionally placed on a graph such as what you see below. The Absolute Visual Magnitude is arrayed against the spectral class. What Hertzsprung and Russell noticed immediately was that 90% of the stars so arrayed demonstrated a direct relation between visual luminosity and temperature. This "curving line" of stars has been called the "Main Sequence," and refers to the fact that all such stars are burning Hydrogen into Helium in their cores. Our Sun is a main sequence star, but there are lots of other stars on the main sequence, and they are the subject of this page.

As the surface temperature of a star increases, so does its absolute visual brightness. Stars that have a cool surface temperature, such as the M class stars to the lower right of the main sequence, produce less light per square meter of surface and thus appear to be less bright. Stars with a hot surface temperature, such as the B and A stars to the left of the main sequence, produce more light per square meter of surface and thus appear to be more bright.

This relationship of brightness per square meter is founded in the Stefan-Boltzmann Law and states that a star that is twice a hot will emit energy at a rate to the 4th power of the temperature. If two stars have the same surface area, the star that is twice as hot will burn 16 times more brightly. A hot star therefore burns MUCH more brightly than a cool star.

As you move through the main sequence from M through G to O, absolute visual magnitudes decline from around +20 (about a million times fainter than the Sun) to about -6 or -7 (over 50,000 times brighter). If you cannot remember what the star magnitude scale is, refer to the webpage.

To get some perspective here, imagine one of the extreme bodies on the main sequence replacing our Sun. To light the day at our presently enjoyed manner (minus the clouds) with a low-end M class star, we would have to be 1000 times closer than we are presently, or a mere 150,000 km away. This distance is less than half the distance to our Moon. At the high end of the O class, we would have to be over 200 times farther away than we are now, or 5 times more distant that Pluto. Once again, keep in mind here that we are not talking about the size of the star, but about its brightness and temperature.

So, a great range of brightness is found among main sequence stars, but what about their sizes. As mentioned above, temperature determines the amount of energy radiated per unit area. But stars are not all uniform in size. The more square meters of surface area, the brighter the star will be. Luminosity therefore depends on temperature and radius. The surface area of a sphere depends on the radius squared. As a result, luminosity varies as T^4 times R^2. If we know the luminosity and temperature, we can find the radius. This is pretty cool, because now we can determine how big a star is by knowing brightness and temperature, and these values we gain from the HR Diagram. There is a catch to this seemingly simple relationship because hot stars produce a great deal of light in the ultraviolet and cool stars produce a lot of infrared. Both of these light waves are not visible and they must be added to the overall luminosity to derive the radius. But, these derivations are problematic for the very large or very small stars and not as much a part of the main sequence. What was surprising to the astronomers was that main sequence stars brighten even faster with increasing temperature than mandated by the Stefan-Boltzmann Law, showing that these stars are also increasing their surface areas. The low end M class stars have diameters roughly twice that of the Earth while the high end O stars have diameters over 10 Sun's.

Hertzsprung's and Russell's greatest discovery, made in the early twentieth century, was that many stars do NOT lie on the main sequence. You will notice two branches above and to the right of the main sequence. These stars are brighter in luminosity, but cooler in temperature ... a seeming contradiction to the Stefan-Boltzmann Law. To behave in such a manner, these stars must be very, VERY big. These stars are called "Giants" and are the subject of future discussion. To the lower left of the HR Diagram is a group of stars whose temperature is very high, but whose luminosity is low. These stars must be very small, and they have been given the name "Dwarfs." They too are the subject of a future chapter in this course.

So , you are now asking, what is the difference between a "main sequence dwarf," and a "dwarf?" Those stars in the lower left corner of the HR Diagram are all so hot that they are "white hot" and thus called "white dwarf" stars. The second differentiation is that the giant stars are so much bigger than all the main sequence stars that the former "dwarfs" the latter. Even the larger main sequence stars are significantly smaller than any of the giants. Giant stars could easily occupy the inner Solar System.

MAIN SEQUENCE STARS OF NOTE

Since we will leave a more detailed discussion of the M class stars for the next unit, let's ascend the main sequence by leaving our G2V Sun behind and climbing the main sequence to the left. The F class dwarf stars are not well known, though just before we move to the A stars we will find third magnitude Porrima (Gamma Virginis). Through a telescope, this star appears as two F0 stars in orbit around each other.

When we arrive at the A class, we find some very familiar stars. Altair, the A7 star in Aquila, is the southernmost star in the Summer Triangle. Not far away on the main sequence is Sirius (A1), in Canis Major. This is the brightest star in the sky in terms of apparent magnitude, shining at -1. Another bright star in this family is the A0 star Vega, in Lyra. Vega defines the western point of the Summer Triangle and is directly overhead in summer months. Vega shines with an absolute luminosity 50 times greater than our Sun. While Sirius is brighter in the night sky to our eyes, it is farther down the HR Diagram, and this serves to illustrate the role that star distance plays in how bright a star appears to be. Sirius is less that 9 light years distant yet appears brighter to us than Vega, which is actually much more luminous but farther away at a distance of 25 light years. Finally, when we look at the Big Dipper, we will find that the middle 5 stars are all A dwarfs, in order from the bowl through the handle (Merek-A1, Phecda-A0, Megrez-A3, Alioth-A0, and Mizar-A2). The similarity in night sky appearance and main sequence location tells us that these 5 stars are all at nearly the same distance (about 80 light years).

The B stars are typified by B7 Regulus in Leo, at the lion's head, and B3 Alkaid at the Big Dipper handle tip. What is so fascinating to me is that by this place on the main sequence, we start running out of stars that we can see with our naked eye. Second magnitude Zeta Orionis, the left-hand star of Orion's belt (also called Alnitak). This O9.5 star barely makes it into the O class. To go farther, just to O9, we drop to third magnitude Zeta Ophiuchi, and then to Xi Persei (O7). We need a telescope to see the end of the main sequence, pinned down by O6 Theta-1 Orionis C, the brightest star of the "Trapezium," the group of stars that light up the great Orion Nebula. The main sequence actually goes up all the way to O3, near 50,000 K surface temperature, but these stars are too distant for us to see. I guess you are noticing that really bright stars are pretty rare, and indeed they are, but we will reserve the space to learn about why bright, hot stars are rare for a later unit.

STAR NAMES

If you did not learn about this earlier, then here is a brief reminder. Most of the stars have names that were given to them by the earliest astronomers, the Babylonian people, or modern-day Arabs, and are used to describe a place in the constellation. "Sirius" comes from the Greek word meaning "scorching," and it fits its place as the brightest; "Altair" is Arabic for "the eagle" which fits its title in Aquila, the Eagle. "Deneb" is Arabic for "tail," a term befitting of its place at the tail of Cygnus the Swan. Later, Johannes Bayer gave Greek letters to the stars within a constellation in the order of brightness: Alpha, Beta, Gamma, Delta, and so forth, from brightest to dimmest. Therefore, we derive names like Alpha Aquilae (Altair), Alpha Canis Majoris (Sirius), and Alpha Lyrae (Vega). There are other additional formats to delineate one star from another, but this is unnecessary work for you, and I both.

BINARY STARS TELL US ABOUT THE MASS OF THE INDIVIDUALS

Ah, yes ... nothing quite as beautiful as sunset from Luke Skywalker's home planet Tatooine. Here we see a memorable image of such an evening as the double star system of Tatooine sets. William Herschel was the first astronomer to confirm the existence of double stars in the late 1700s. Since his first report, astronomers have found that double stars, or binary systems, are anything but unusual. A prime example is our closest stellar neighbor, Alpha Centauri. Perhaps 80% of the stars in our galaxy are some kind of double system, where two stars are revolving around a common center of mass ... much like Pluto and Charon. Two other examples are seen in the images below. To the left is the star Alberio. This is the tail star in the constellation Cygnus and is one of the most beautiful sights for an astronomy star party. One star is blue and the other orange. To the right is Mizar, the middle star in the handle of the Big Dipper. Mizar is the larger of the two, while Alcor is to the left. However, Mizar and Alcor are not a binary sytem, but only appear that way. Closer examination of Mizar will reveal that it is two stars orbiting very close to each other. This is always a nice object in my telescope. Mizar and Alcor are a visible "pair," but it takes a telescope to see the binary nature of Mizar itself. Castor in Gemini is a double-double system of 4 stars acting as two pairs that orbit each other.

Once the radius of a binary star's mutual orbit is measured, we can find the sum of the component's masses. Once we have the sum and also the ratio of their masses (apparently easy to determine but not part of this course), astronomers can then calculate the mass of the individual stars. From hundreds of studies, astronomers have found that main sequence stars is really a MASS sequence, beginning at the bottom right of the HR Diagram where stars are 8% of the Sun's mass (the minimum mass required for hydrogen-helium fusion), continuing upward through one solar mass in the G stars, to about 20 times that of the Sun among the B stars, and then theoretically to over 100 solar masses among the O stars. The larger the mass, the more gravitational energy available, the greater the compression, and the higher the temperature in the core. As a result, high-mass main sequence stars are much more luminous than low-mass stars.

MAIN SEQUENCE AGES

Stars are amazingly self-regulating. As the nuclear fuel is consumed, the core shrinks a little in response, which drives the temperature up somewhat and causes the remaining fuel to burn faster and the core to eat slowly into the surrounding hydrogen. The result is a slow shrinking of the core, and an increased rate of fusion such that the star's life proceeds toward its death more quickly. While this poses a threat to the Earth with the increased energy output from the aging Sun well BEFORE the Sun goes to the Red Giant stage, it is more important here to realize the implication on the HR Diagram. The star will remain on the main sequence for most of its life, only very slowly brightening and/or cooling at its surface as the fuel supply diminish. This slow change is noticed in the star's motion on the main sequence during its life. Young stars are near the left edge of the main sequence and older stars are near the right edge. The main sequence is therefore not a "line" but a "band," with star positions telling us about their relative age!

Nuclear burning rates are so sensitive to temperature that high-mass stars live much shorter periods of time (in the tens of millions of years), while low mass stars live incredibly long lives (tens of billions to even theoretical trillions of years). The lives of low-mass stars are so lengthy that no K or M dwarf star has had time to evolve off the main sequence in the entire 13 billion year history of the Universe! Due to the short lifespan of O stars, they live and die quickly and are rare in the visible Universe. On the converse, the long lifespans of M stars make them quite numerous. In fact, M class stars are the most common star such that half of our galaxy's mass is tied up in dim red M dwarfs.

MASS IS SUPREME

The final result is that even though two quantities --- mass and age --- are needed to describe the HR Diagram, the second, age, also depends on mass, making mass supreme in the life of a star. The whole story of a star is wrapped up in a continual attempt of gravity to collapse the star and nuclear fusion to convert hydrogen into helium and heavier elements. The main sequence is just one of many pauses and transitions along the way that give life and sparkle to the HR Diagram. Our Sun is halfway through its life on the main sequence.

WHAT NEXT?

With this background established for the main sequence, it is time to look at stars that are at the extremes of the main sequence; stars at the edge; at the faintest, coolest, hottest, brightest, biggest, and smallest. Then we will look at the outer limits of age, at the youngest and oldest, and finally at some of the stranger stars not already encountered.

Let's first look at the faintest and coolest of the stars, or you can return to Star Introduction, or to the Syllabus.


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