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Chapter 10. Stellar Spectra Please read the Wikipedia articles linked on the ”Links” section of the Homepage, as well. They will give you additional important insights into this chapter and the next one on stellar magnitudes and the HR diagram. Most of the light in the Universe at optical wavelengths (i.e. wavelengths that can be seen by the eye) comes from stars. Historically, the optical spectrum was most studied because it is what our eyes detect and because it passes easily through the Earth’s atmosphere. By contrast, ultraviolet and infrared light is largely absorbed in the Earth’s atmosphere and could not be studied until the advent of balloon astronomy and space astronomy. The spectrum of galaxies is largely just the sum of the spectra of the billions of stars that comprise it, although sometimes there are other components such as the interstellar medium and active black holes at the centers of galaxies. Therefore, understanding stellar spectra is key to most areas of astronomy. Our study of the Hydrogen spectrum showed that light passing through Hydrogen gas atoms may excite internal energy levels of the atom causing the absorption of photons of a particular energy (wavelength). This produces ”absorption” lines in the spectrum of stars as the light from their hotter interiors passes through their cooler atmospheres (see lecture slide on Kirchoff’s laws). The lines visible in any star’s spectrum depend on the chemical composition of the atmosphere, but also on the temperature and pressure of the atmosphere. Sometimes elements that are very abundant (e.g. Helium in the solar atmosphere) are not evident in the spectrum because the temperature and/or pressure of the gas is not right for the excitation of the atom to levels needed to absorb optical light. On the other hand, we sometimes see strong lines due to atoms of very low abundance (e.g. Lithium) because the internal energy levels of that atom happen to be conducive to absorbing optical photons of the proper energy given the temperature and pressure of the solar atmosphere. Understanding the differences in the appearance of stellar spectra that arise because of temperature, pressure and composition differences in their atmospheres is decades of fun! 1. Spectral Classification Early studies of stellar spectra, done approximately 100 years ago, immediately revealed a variety of different ”types” of spectra. Note that these observations were, of necessity, done in the optical part of the spectrum. Hence, the dominant feature was the Balmer lines of Hydrogen (since H is the most abundant element and since transitions from the n=2 level to high levels – Balmer transitions – have energies that put them in the optical part of the –2– spectrum). Stars showing the strongest Balmer lines were called ”A” stars. Those with weaker lines were labeled ”B”, ”F”, ”G”, etc. using various letters of the alphabet. Our modern classification scheme retains many of these letter classes, although not all of them, and adds a number, or ”subclass” that divides each spectral class into about 10 subclasses. These are just finer gradations of the classification scheme. It was discovered in the 1920’s that the dominant parameter that made one spectral class different from another was ....... temperature. The classes were then re-organized into a temperature sequence, which is the basis of the modern classification. It runs like this (where I have not shown all the subclasses) O3, O4, ...O9, B0, B1, ...B9, A0....A9, F0...F9, G0...G9, K0....K9, M0...M9, L, T Not all numbers are used and sometimes a decimal is added for even finer division (e.g. a B1.5 star is between a B1 and a B2 star). The L and T stars are extremely cool recent additions to the scheme. These ”stars” are probably actually ”brown dwarfs” since their core temperatures are unlikely to be high enough for the nuclear fusion of Hydrogen to Helium. One pneumonic device for remembering the odd order of the letters (not including L and T) is: Oh Be A Fine Guy (or Girl) Kiss Me. Since stellar spectra depend not only on the temperature of the stellar atmosphere but also on its pressure, there is a second parameter that is needed to classify them. This is called the ”Luminosity Class” and is designated by a Roman Numeral in the modern classification scheme. The names associated with luminosity class are as follows: I – supergiant; II - bright giant; III - giant; IV - subgiant; V - dwarf. A full classification consists of the spectral class, spectral subclass and luminosity class. An example is the Sun, whose classification is G2V. 2. Understanding the Temperature Sequence A basic understanding of the behavior of the Hydrogen lines with stellar temperature (and, note that this is the surface temperature of the star, not its interior temperature, which can be millions of degrees) is as follows. Hydrogen lines in the optical part of the spectrum come from the Balmer lines, which are transitions from the first excited state (n=2) to higher levels. Their strength depends on the abundance of HI (neutral Hydrogen) in the n=2 (first excited state). This is a maximum at a temperature of around 10,000 K, characteristic of A stars. A stars therefore have the strongest H lines (this is, in fact, why they were called A stars). Hotter stars (O and B stars) have weaker H lines because more of the Hydrogen is excited to higher levels and/or ionized (creating HII). Recall that at higher temperatures, all atoms and electrons are moving more rapidly (have higher kinetic energy) so that when –3– they collide with one another they can excite the other atoms to higher energy states and/or ionize them. For stars of lower temperature than A (i.e. the FGK and M stars) the Hydrogen is mostly still in the ground state. There is not enough kinetic energy around, in general, or photons of high enough energy to excite the atoms to n - 2. Hence, although there is a lot of HI, there is not a very strong set of Balmer lines, because there are not a lot of HI atoms in the n=2 state to absorb photons of the right energy. Similar things apply to the other atoms but they have much different energy level diagrams. For example, the optically visible lines in Helium also arise from excited states, but the energy needed to excite those states is much higher than the energy needed to get HI to the n=2 level. Hence, Helium is often hard to see in stars. Only the hottest stars (O and B stars) show lines of Helium, even though it is the second most abundant atom in the atmospheres of almost all stars. Note that Helium also has two ionization states. In its neutral state (HeI) it has 2 electrons. It can lose one of those, in which case it becomes HeII, or singly ionized Helium. We see lines of HeI in B stars, which are hotter than A stars, but not as hot as O stars. We see lines of HeII in O stars. These are the distinguishing characteristics of these classes of stars and, once the lines can be identified, this helps us understand how to sort the spectral classes in terms of temperature. Some lines of some “metals” (for astronomers, the term metals is used for everything other than Hydrogen or Helium – no one ever said we were good chemists!), such as Sodium (Na) there are lines visible in the optical region of the spectrum that arise from the ground state of the neutral atom (NaI). Hence, it turns out that the NaI line (or lines) can be extremely strong in stars of the right temperature (e.g. the Sun), even though sodium is way less abundant that, say, helium. Similarly, some metals, such as calcium have optical transitions from the ground state of one of the ionized stages of the atom, in this case CaII (the singly ionized Ca atom). Hence, we see strong lines in the Sun due to singly ionized Ca, although, again, it is not nearly as abundant as helium or many other atoms. In this way, the interpretation of stellar spectral types (the term “spectral type” is used to indicate spectral class plus luminosity class) in terms of surface temperature and surface pressure (or radius, as we shall see) has been developed. It turns out that most stars have about the same chemical composition in the stellar atmospheres (surfaces). By mass, they are about 73% Hydrogen and 25% Helium and 2% metals. Some stars tend to be more metal poor – i.e. down to only a fraction of a percent of metals, but none are much richer in metals and all have about the same proportion of H and He. What makes one star’s spectrum different from another star’s spectrum is primarily temperature and pressure (radius). Of course, these remarks apply to “normal” stars – the vast majority. Naturally, there are –4– some odd balls that go against the trend, but these are covered later (or not at all in this introductory course!) 3. Relationship between Spectral Type and Luminosity of a Star One of the great advantages of the two-dimensional (spectral class plus luminosity class) aspect of the spectral classification scheme is that it is sufficient to specify the luminosity of a star. To understand the reason, we recall that the spectrum of a star is approximately the same as the spectrum of a black body (i.e. the Planck law) at the same temperature. The Stefan-Boltzmann law for black bodies comes from integrating the flux at all wavelengths and tells how the total flux (represented here by F) varies with temperature (T), namely F = σT 4 . Recall that σ is the Stefan-Boltzmann constant. The flux is the energy per unit time per unit area (e.g. joules/sec/m2 or watts/m2 ). The luminosity of a star is its total power output (i.e. its wattage if it were a light bulb) and is measured in Watts (in the mks system). To go from flux (F) to luminosity (L) we need to multiply by the area of the star, which for a sphere of radius R is 4πR2 . Combining with the Stefan-Boltzmann equation, we have the fundamental equation for the luminosity of a star, that depends on its surface temperature and size, namely L = 4πR2 σTe4 Note that we have written the temperature here as “effective temperature” (Te ). This recognizes that it is not really appropriate to assign a single temperature to the atmosphere of a star – many different layers, at different temperatures, contribute to the visible light that we see. Therefore, we refer to the effective temperature of the atmosphere as the temperature of a Black Body that would have the equivalent flux (watts per square meter) as the star does. Note also that we assume when we write the equation above that the star is spherically symmetric and radiates exactly the same amount of flux in all directions. This is generally true for most normal stars. We see then, that the spectral type of a star should be well correlated with its luminosity, since the spectral type has two parameters, T and pressure, and L depends on two parameters, T and R. Since pressure depends on R (a large star has a lower surface gravity and therefore a lower pressure), there is essentially a one-to-one correspondence between L and spectral type. Astronomers slip back and forth between radius and luminosity all the time, even in the way we name the luminosity classes: –5– I - supergiant II - bright giant (mixed terminology!) III - giant IV - sub-giant V - dwarf As an example, the Sun is a G2V star and has a certain luminosity (wattage). All other G2V stars have the same luminosity (to within our ability to determine it!) All B2V stars, also have the same luminosity and that is much larger than the luminosity of a G2V star. All BI stars (i.e. B supergiants) have much larger luminosity than all B2V stars, etc. etc.