V. Stars http://sgoodwin.staff.shef.ac.uk/phy111.html
0. The local HR diagram We saw that locally we can make an HR diagram of absolute luminosity against temperature. We find a main sequence, giants and white dwarfs.
1. Going further We only know the absolute luminosity if we know the distance, but we only know the parallax distances out to about 100 pc (further to some bright stars). The problem is that if we see a star with a surface temperature of 3000K is it a nearby red dwarf, or a distant red giant? Without more information than colour and apparent brightness we just can t tell. And what are their physical properties mass and radius?
1. Spectral types We saw that spectra can be used to classify stars into types from hot to cool: OBAFGKM Simply at low temperatures very little material is ionised and molecules can even exist. The easiest elements to ionise are metals (e.g. Fe), then things like O or C, then H, and finally He.
1. Spectral types So what lines of an element we see vary with surface temperature.
1. Spectral types The Sun is a G-star and we see lots of neutral and ionised metal lines. (The O 2 lines below are due to the Earth s atmosphere.)
1. Spectral types Important to remember: What we see is the surface (photosphere). The lines we see do not directly tell us about abundances. In the Sun s photosphere we see lots of iron lines, but the Sun is 98% H-He as are most stars. Its just that iron has lots of lines in the visible.
1. Spectral types So why are some stars so much more luminous than others? To be more luminous they must be producing more energy, and it turns-out that this depends on their mass. More massive stars produce more energy per unit time and so are more luminous. (Only on the main sequence though as we ll see red giants can be low-mass stars.)
2. Surface gravity Exactly what we see in a spectrum (lines, line shapes, ionisation state) depends on temperature and pressure. Exactly how is a mix of thermodynamics and quantum mechanics, but the upshot is that from the spectra we can measure both. Pressure depends on the gravity which depends on mass and radius (small and massive = high gravity). So spectra give us surface temperature and surface gravity (a mix of radius and mass).
3. Physical properties of stars We need to calibrate our models using some stars for which we know the absolute luminosity, temperature, mass and radius. The Sun is one calibrator we know all of these in detail. We also calibrate using binary stars.
3. Binaries and mass If we can observe a close binary and measure the orbital velocities of the components we can get their masses from Kepler s laws
3. Binaries and mass If we can observe a close binary and measure the orbital velocities of the components we can get their relative masses from Newton s laws. If the system eclipses then we can get absolute masses and also measures of their radii.
3. Binaries and mass But the upshot is we can calibrate our models and so use spectra to get the stellar surface temperatures, pressures, gravity, and so their masses and radii.
4. Metallicity From spectra we can also get the relative abundances of different elements. Almost all stars are about ¾ H and ¼ He. The Sun is about 2% other elements (other stars vary from almost no other elements to around 5%). Confusingly astronomers call ALL elements other than H and He metals. (Fe is a metal, but so are O and N.) We ll come back to this quite a few times later as it turnsout to be really important.
5. Stellar properties We find that stars range in mass from about 10-2 M to about 10 2 M. (Technically stars less than about 0.1M are brown dwarfs not stars as they do not burn H.) About 90% of stars lie on the main sequence (as we ll see this is where they spend most of their lives burning H in their cores). The is for Solar values (M is a Solar mass = 2x10 30 kg).
5. Stellar properties On the main sequence we find fairly good relationships between mass and luminosity (also temperature and radius as they all all related): This is true for roughly Solar-mass stars the power-law varies a bit (you might see it as 3 or 4, it depends on the range). For very high-mass stars its roughly linear but we ll go with this
5. Stellar properties On the main sequence this mass-luminosity relationship means that there is a mass-spectral type relationship. On the HR diagram: O-stars are hot and very luminous (top left): very luminous means very massive (>20 M ). M-stars are cool and very faint (bottom right): so lowmass (<0.5 M ). G-stars are in-between (the Sun sits in the middle): so intermediate-mass (1 M ).
Summary From spectra we can get the surface temperature, pressure, and gravity. Spectra also give the composition (metallicity). Binary stars allow us to calibrate our models by giving the masses and radii of some stars. We find a mass-luminosity relationship on the main sequence more luminous stars are more massive. The main sequence OBAFGKM spectral sequence is a temperature sequence (from high to low temperature), and a mass sequence (from high to low mass).
Key points To know the OBAFGKM sequence is both a temperature and mass sequence on the main sequence. To be able to describe very broadly what elements and their ionisation states that we see in different spectral types and why. To know the mass-luminosity relationship for the main sequence.
Quickies A main sequence star shows lines of ionised He, is it a high- or low-mass star? Briefly justify your answer. Two stars are observed with the same apparent brightness. One shows lines of ionised H, the other lines of TiO. Which star is closer? Briefly justify your answer. Two M-stars are observed: one is a giant, the other a dwarf. Give ONE way of telling the difference. A star has a luminosity of 10 4 L. Give a rough estimate of its mass. Suggest ONE spectral line you might look for to distinguish an G-star from an O-star.
Notes For ease (and space) I will use the symbols for various elements: By far the most common elements: H hydrogen He - helium Other reasonably common elements: C carbon O oxygen N nitrogen Fe iron Si silicon S sulfur K potassium Ca calcium P phosphorus Ar argon Na soldium Mg magnesium Ni nickle Ti titanium
Notes When writing down an element sometimes the atomic number is added so: 12 C (spoken aloud as carbon 12 ). The atomic number is the total number of protons and neutrons in the nucleus, so 12 C is lighter than 14 C. What defines the element is the number of protons in the nucleus carbon always has 6. So 12 C has 6 protons and 6 neutrons, and 14 C has 6 protons and 8 neutrons. Because the nucleus of 14 C is so much larger it is unstable and will decay to 12 C (it is created in the atmosphere by impacts with cosmic rays, 14 C has a half-life of 5730 years and is the carbon in carbon dating ).
Notes When classifying stars the star is given one of the OBAFGKM spectral classifications. Within this a number 0-9 says how hot it is, so an M0 is hotter than an M9 (the coolest type of star). The Sun is a G2 star (at the hot-end of the Gs). Roman numerals are used to distinguish sizes as determined by the surface pressure measured by the lines. V is a main sequence star, and I, II, III types of giant star. So the Sun is formally a G2 V star. (To add an extra layer of confusion main sequence stars are often called dwarfs, so the Sun is a G-dwarf.) For even more complication stars <0.01M are not really stars as they can not burn H. They are brown dwarfs and are very cool and have spectral types LTY (although it is arguable if the Y subtype even exists). So you might see a spectral sequence as OBAFGKMLTY. I won t ever talk about types LTY.