Difficult and incomplete as it is, there is even more to observing stars than cataloging their brightness and distance. Ever since Newton split Sun's white light into light of different colors using a glass prism and Fraunhoffer studied the dark features in the resulting colors, it has been realized that there is a wealth of information in the spectra of stars. In the spectra what we measure is essentially the amount of energy emitted (or absorbed) by a star at a certain color of light. This information used judiciously can tell us a lot about the composition and state of the star.
Following Frauhoffer's work on the Sun's spectra, studies were made into the spectra of other stars as well as the Sun. Peitro Angelo Secchi, a Jesuit priest and astrophysicist, was interested in stellar spectra as a lecturer in Rome. When Jesuits were thrown out of Rome he left for Lancashire, England and then worked for some time in Georgetown University in Washington, D.C., before being allowed to return to Rome. His observations of the stellar spectra led him to conclude that while the spectra of stars were very different from one another, he could designate most into a few groups that shared some basic characteristics. Sir Joseph Norman Lockyer, a clerk in the War Office, got interested in astronomy and the spectrum of the Sun. He established the magazine Nature and edited it until very nearly his death. The difference in the stellar spectra found by Secchi led Lockyer to investigate the nature of these differences. He believed that the atmospheres of the stars were hot enough for atoms to undergo changes. He compared stellar spectra to spectra he observed in the lab under known circumstances. He studied the spectra of gas heated by a flame, an electric arc and an electric spark and found similarities to the stellar spectra. This is because as we go to hotter temperatures, from the flame to the spark, increasing numbers of electrons are torn from the parent atom, leaving it in a different state of excitation. This shows itself in the different spectra of the gas. The same sort of phenomenon is going on in the atmosphere of the Sun.
Following all this excitement many people got interested in the study of stellar spectra. Henry Draper, a doctor from New York City, was one of the first astrophotographers. The Congress struck a gold medal struck in his honor for his photography of the transit of Venus. He and Sir William Huggins, an astronomer from England, were the first to photograph the spectra of a comet. On his death, Henry Draper's widow established the Henry Draper memorial fund in Harvard that allowed the completion of the still used Henry Draper catalogue of stellar spectra. This was a very significant event in American Astronomy. It really heralded in a new phase in the study of astronomy in the United States. And right from the beginning the driving force were female astronomers. Working in the facility at Harvard instituted by E. C. Pickering, A. Maury discovered that she could arrange the spectra of the stars in a continuous series rather than the rough groupings of Secchi. Annie Cannon, who returned to studies after ten years of tending her family, was the secretary to Sarah Whiting in Radcliff, under whom she learnt spectroscopy. Partially deaf, she had incredible reserves of patience and concentration. She catalogued 225,000 stars building up the Henry Draper Catalogue, developing the classification system of spectra to the state it is today. She was the first woman to ever be granted an honorary Ph.D. by Oxford University and was made an honorary member of the Royal Astronomical Society in 1931 (because a woman wasn't allowed to be a full member then). American Astronomical Society still grants a prize to female astronomers that bears her name, and is paid out of a grant from her to the Society.
The classification scheme devised by Annie Cannon is known as the Henry Draper classification system. In this system the spectra are classified into groups named by alphabets, O, B, A, F, G, K and M. The reason for this bizarre naming is that some original classes were dropped and the order of the classes switched around. These broad alphabetical classes are further subdivided into numerical subclasses from 0 to 9. Starting from O0 through to M9 there are 70 classes. Due to historical reasons the stars in the classes O, B and A are called ``early'' types and those in the K and M classes are called the ``late'' types.
The spectral sequence can be understood as a sequence in temperature, the earlier stars being hotter than the later types. Recall the Bohr atom with the nucleus in the middle and the electrons distributed around it. Each electron is in a particular energy state that can absorb a photon of a certain frequency (i.e., energy) and change its energy. If the energy of the photon exceeds a certain value then the electron is raised to such a high energy state that it escapes the clutches of the nucleus altogether. This energy of the photon is called the ionization energy. For a hydrogen atom with one electron there is only one ionization energy at which the one electron can escape the influence of the nucleus. For atoms (viz., carbon, oxygen, nitrogen, etc.) with more than one electron there are many ionization energies. The first ionization energy is the one at which the first electron is released. The second is the one at which the next electron escapes, and so on. Note that after the first electron escapes, the nucleus has fewer electrons to hold onto than before, so the second electron has to overcome a larger tug from the nucleus than the first, even if they were at the same energy state before escape.
In the spectral sequence, the earlier spectral types like the classes O, B and A are dominated by emission from ionized atoms. The intermediate classes, F and G are dominated by neutral atoms and finally the later classes, K and M are dominated by molecules rather than by atoms. The degree of ionization of atoms in a star's atmosphere is governed not just by the temperature of the star but also by density of electrons and other factors. The equation governing the degree of ionization is called the Saha equation, after Meghnad Saha, who established an Institute of Nuclear Physics now named after him in Calcutta, ironically after he had been forced to leave Calcutta University following acrimonious differences with C.V. Raman, the Nobel Laureate discoverer of the Raman Effect. Raman was from the old school of doing Physics where as Saha was deeply interested in the social impact of science which led to irreconcilable differences between the two.
It is obvious from common experience that color and temperature of a
source of light are connected. Hence the adjectives red-hot,
white-hot, etc. In the case of black-body radiation there is a
mathematical way of describing this connection. This is called the
Wien's law after Wilhelm (Carl Werner Otto Fritz Franz!) Wien, the
Nobel laureate in Physics, its discoverer. This law says that the
maximum energy radiated by a blackbody at a temperature T, is at the
wavelength (i.e., color),
We don't actually have to measure the full spectrum to be able to
measure the temperature of the star. Which is fortunate as this is a
very slow and difficult process, particularly for faint stars. Recall
that the magnitude of a star is connected to the total flux from
it. Suppose now we look at not all the emission from a star but
emission only in some fixed ranges of color, say in the red range, or
the blue range. The magnitude of the star will be different in
different ranges of color, because the emission from the star (like a
blackbody) is different in different colors depending on its
temperature. The difference between the magnitudes (which is the
ratio of the fluxes) in the two color ranges is called the color
index of the star. This is directly connected to the temperature of
the star through the Plank's curve giving the distribution of energy
in wavelengths for a source of given temperature.
Along with her pioneering work on spectral classification A. Maury also noticed that stars having the same spectral type also happened to have difference in features like the strength and definition of each line. It was later seen that this depended on the brightness of the star. So stars of same spectral type could have different luminosities. W.W. Morgan and P.C. Keenan devised a classification scheme for stars according to their luminosity. In this ``M-K system'' the luminosity classes are; Ia, Ib, II, III, IV and V in decreasing order of brightness.
In 1905 Ejnar Hertzsprung a Danish amateur astronomer, who was a chemical engineer, with an interest in astronomical photography noticed a relationship between the brightness of a star and its color. Henry Norris Russell was a Ph.D. from Princeton, and a professor there. Based on Hertzsprung's conclusions and his own studies on the distances of stars, Russell plotted the absolute brightness of stars against their colors. This diagram is called the Hertzsprung-Russell diagram and is of fundamental importance to astronomy.
What the Hertzsprung-Russell diagram shows is that the stars do not have random values of absolute magnitudes or colors. If you plot all stars in the plane with absolute magnitude along the Y axis and color along the X axis they appear to fall on localized bands. Since color is connected to temperature and magnitude to luminosity, this means that temperature and luminosity of stars are not disconnected. Most of the stars fall on the band Main Sequence, hence the name. These are mostly stars of the luminosity class V. These are the ordinary stars, like the Sun that are in their prime. Brighter than these stars, starting at colors around the Sun are stars belonging to the luminosity class III. These are called the giants. Scattered above these are the Supergiants. Below the main-sequence are a set of stars that are called the white dwarfs.
Most of modern astronomy has been and continues to be an effort to understand the Hertzsprung-Russell diagram. As a consequence we will spend the next chapter trying to understand the basic phenomenon that shape the basic features of this diagram.
From the beginning of telescopic observations, there has been an interest in binary stars. Two father and son teams were at the forefront on this. One was the Herschels, William and John, and the other the Struves, Wilhelm and Otto. Later Hertzsprung's introduction of photography to the study of binary stars greatly improved the detection rate of binaries. Curiously both Hertzsprung and Russell's primary interest were binary stars. The technique is to first find two stars that are close together. Then they must be observed, over and over again over the years, to see if they move together. If they do, then they are designated to be a visual binary. These are binary stars that can actually be observed to be moving around each other visually.
Another kind of binary star is the spectroscopic binary. To understand this we need to understand the Doppler-Fizeau effect. In 1842 the Austrian physicist, C. Doppler found that if the source of a sound moves towards or away from the listener the pitch of the sound changes. As the whistle of a train approaching or leaving a station. He suggested that the same may be true of light, with its color changing according to whether the source of light is moving towards or away from us. So if a star is moving towards us it should have a different color from its color if it were stationary. This was further clarified by the French physicist H. Fizeau who showed that the effect would be apparent from shifts in the color atomic spectra rather than gross color changes. This was confirmed by the British astronomer W. Huggins for Sirius.
Spectroscopic binaries are binary stars that appear to be single even in large telescopes but whose atomic spectra reveal their duplicity. The spectral lines shared by the two stars are duplicated as each star is at a different velocity. Moreover the color of these lines change with time as the stars rotate in their orbits.
Another type of binary stars are the eclipsing binaries. These also appear single whose light changes periodically. The first known of such stars is called Algol, a name that mean a demon in Arabic. These are binary stars whose members periodically eclipse the other and hence cause a change in brightness. If we also detect shifts in color due to Doppler-Fizeau effect then we can map the orbit of the two stars. From this we can use Newtonian gravity to measure the mass of the two stars.
A final method to find binary stars is to locate stars with trajectories that wobble. These have companions that are too faint to see but can affect the orbit of the brighter star. This is a very important method in the detection of planets and solar systems.
As we said before, the brightness of a star depends on its
temperature and its surface area.
If we know the distance to the star
we can find out its brightness. We can use its colors to measure its
temperature. Then we can extract its radius from the above
relationship. This is how radii are ``measured'' for most stars.
In the case of large stars there is a more direct way. A.A. Michelson, the American physicist and Nobel Laureate devised an instrument to measure the radius of stars directly. But this method requires very bright and large stars. It does show however that there are stars many times as large as the Sun. Betelgeuse for example has a radius 400-500 times that of the Sun!
Now if we can measure the mass of the star (
) and its radius
(
) we can calculate its density as simply,
When we do this we can find the stars fall into three categories. One
group of stars with roughly solar mass and radii. Another group of
stars that are very bright and have much larger radii than the sun but
are not very much more massive. Consequently they have very low
density. And a third group of stars that have again similar masses as
the Sun, but are much fainter with much smaller radii. These therefore
have much higher densities than Sun. The first type of stars, like the
Sun are the Main sequence, the second type the giants and the last
types are the white dwarfs. Understanding the relationship and
connections between these different types of stars has been and in
some ways remain one of the main goals of Astronomy.