Stellar Spectra and the Hertzsprung-Russell Diagram

Transcription

1 Stellar Spectra and the Hertzsprung-Russell Diagram Regions of the HR Diagram The H-R diagram is a graphical representation of the basic attributes of stars. The horizontal axis is a measure of temperature while the vertical axis is a measure of luminosity. Luminosity and temperature are both related to the underlying power source of stars, leading to interesting and informative structure within the HR diagram. In this section, we will learn what this structure tells us about the physics of stars. Here are a few things to notice about the HR diagram: 1) Absolute luminosity increases (or absolute magnitude decreases) from bottom to top. 2) Effective temperature (top axis) increases from right to left. 3) Spectral class (bottom axis) is a function of effective temperature and is therefore also shown on the horizontal axis. 4) Stars are found in specific regions on the HR diagram they are not randomly distributed.

2 5) Most stars are found on the main sequence indicating that stars spend most of their lives there. 6) Main sequence stars increase in luminosity, temperature, and mass from bottom right to top left Luminosity Luminosity (or magnitude) is one of the parameters plotted on the HR diagram. What factors determine a star s luminosity? We know that stars emit a spectrum close to that of a perfect blackbody. Do you remember the formula for blackbody radiation from stars? 2 4 L = 4πR σt σ =. x 5 ( ergs s cm K ) This tells us that the luminosity of a star is given by product of the star s surface area (4πR 2 ) and its surface flux or luminosity per unit area (σt 4 ). The surface flux is determined mainly by the temperature of the star s photosphere. Temperature, however, forms the horizontal axis on the HR diagram, so we can conclude that stars of a given temperature but different luminosity differ mainly by their sizes. For example, take a look at a vertical strip on the diagram above, say at T = 5000K. Since temperature is fixed on this strip, luminosity can only vary if the star s size increases. As we move up in luminosity, we must therefore be moving up in radius. Notice that lower luminosty stars along this strip are labeled Dwarfs while higher luminosity stars are Giants. Temperature and radius are, in principle, independent parameters, but because stars are not randomly distributed on the HR diagram, these parameters must be somehow related. For example, the main sequence forms a fairly narrow band from lower right to upper left. Is there a single underlying parameter that determines both temperature and radius along the main sequence? The answer is yes! The mass of the star varies continuously along the main sequence, increasing from right to left. This is a clue as to the nature of the power source for main sequence stars. Another formula for blackbodies is Wien s Displacement law: λ max T =0. 29 cm K Wien s law tells us that the peak emission wavelength for hotter stars is smaller than for cooler stars. This can easily be seen in the following figure:

3 Notice that hotter blackbodies emit more total power and emit peak power at shorter wavelengths than do cooler blackbodies. Stars do not emit pure blackbody radiation, however. The photosphere, or surface of emission, of the star is covered by an atmosphere of more diffuse gas. There will, in general, be some emission and absorption lines superposed on an approximate blackbody spectral shape due to this gas. These spectral lines can be understood using Kirchoff s laws: 1) A hot dense gas produces a continuous spectrum with no spectral lines. 2) A hot diffuse gas produces emission lines 3) A cool gas in front of a hot continuum source produces absorption lines in the continuous spectrum. Clearly, these laws apply well to stars. The continuum source is the star s dense photosphere. The diffuse atmosphere of the star produces emission and absorption lines. Hot regions of the atmosphere produce emission lines, cooler regions produce absorption lines. Stellar atmospheres are not completely understood at this time. However, temperatures in the atmosphere will clearly depend on the effective temperature of the photosphere. We might expect, therefore, that spectral lines vary in strength regularly on the HR diagram. In other words, we expect to see some correlation between a star s continuum spectrum and its line spectrum. The basis of this correlation is the temperature dependence of the ionization states of the various elements which make up the stellar atmosphere.let s take the hydrogen

4 Balmer series as an example. Balmer spectral lines arise from transitions between hydrogen s second energy level (n=2) and higher levels. For Balmer lines to be strong, a high concentration of hydrogen in the n=2 excited state must exist in the stellar atmosphere. If the atmosphere is too cold, then most of the Hydrogen will be in the ground state (n=1). If the temperature is too high, then most of the hydrogen will be excited to states higher than n=2. In either case, there will be few hydrogen atoms capable of producing Balmer spectral lines. The temperature which maximizes the concentration of hydrogen in the second excited state and therefore maximizes the strengths of Balmer lines, is about 10,000 K. Analogous mechanisms occur for other hydrogen line series (e.g., Paschen, Lyman, etc.) and spectral line series for other elements found in stellar atmospheres. The figure below shows relative spectral line strengths as a function of temperature for various spectral series commonly seen in stellar spectra. Stellar line spectra were originally classified according to the strengths of their hydrogen absorption lines A being the broadest, B slightly narrower, and so on. However, when line spectra were better understood, the classifications were rearranged into a temperature sequence OBAFGKM O being the hottest, B slightly cooler, etc. Several subcategories were also added to each spectral type. The Sun, for example is a G2 star which is slightly cooler than a G1 star like η Cassiopeia. Let s look at some spectra. On the following pages you will see some model spectra for O through M stars. The wavelength range covers 3500 A through 9000 A. Pay special attention to the relative values continuum fluxes, the continuum shapes (e.g., where is the peak of the blackbody?) and absorption line strengths. 1998, David M. Caditz

5

6

7