Black Holes: Selected Questions from Minute Papers Will all the material in the Milky Way eventually be sucked into the BH at the center? Does the star that gives up mass to a BH eventually get pulled in to the BH? Star properties: If Betelgeuse is so much more luminous than the sun, why isn t it hotter than the sun? Is it more difficult to measure the distances that are farther away (because the parallax is very small)? Binary Stars: How do you know there are 2 stars (since you can t see 2 stars)? Why are binary stars so very common? Can binary stars have planets around them? Outline - March 2, 2010 Stellar properties recap Spectral Type for stars (pgs. 525-527) Hertzsprung-Russel Diagram (pgs. 530-533) How does the sun shine? (pgs. 495-497, 499-503) Lifetimes of stars: gas guzzlers vs. econoboxes (pgs. 533-534) Where are the oldest known stars? (pgs. 536-538) Stellar Properties Recap Stellar Properties Luminosity (from L = 4π b d 2 ) factor of about 10 billion: 10-4 L sun to 10 6 L sun Just because a star has a radius that is bigger than the sun doesn t necessarily mean that it is more massive than the sun! Temperature (from T = 0.29 / λ max ) factor of about 10: 3,000 K to 30,000 K Radius (from R = {L / 4π σ T 4 } 1/2 ) factor of about 50,000: 0.01 R sun (white dwarf) to 500 R sun (supergiant) Mass (from spectroscopic binary stars) factor of about 1,800: 0.08 M sun (smaller = can t run nuclear fusion) to 150 M sun (larger = pressure overwhelms gravity) Just because a star is more luminous than the sun doesn t necessarily mean that it is more massive than the sun! Just because a star is hotter than the sun, doesn t necessarily mean that it is more massive than the sun! It turns out that this is due to the fact that the radius, temperature and luminosity of stars evolve over time 1
Patterns to the Stars Stellar Spectra Spectral Type (Astronomers like to classify things / put them in bins) The letters O, B, A, F, G, K, M are called the spectral type of the star and describe the appearance of the spectrum (i.e., strong helium lines but weak hydrogen lines, strong hydrogen lines but no helium lines). Depending upon the surface temperature of the star, you see different absorption lines. The hottest stars show strong Helium lines, stars with T = 10,000 K show the strongest Hydrogen lines, and the very coolest stars show strong lines due to molecules (like titanium oxide). This is really is a temperature effect, it is not reflective of different chemical composition for the different stars! Hertzprung-Russel (H-R) Diagram for Stars Take a huge random sample of stars and plot up their luminosity (vertical) and their surface temperature / spectral type (horizontal, with T increasing to the LEFT). Remarkably, you don t get a random plot at all! Roughly 90% of all stars fall on the Main Sequence. These are stars that produce energy by fusion of hydrogen (E = mc2). Any star that is not on the Main Sequence is getting close to the end of its life. The spectral type classifications are historical and come from a time when we didn t know that the different spectra were due to different stellar temperatures. The notation persists today, though! Time-honored mnemonic: Oh Be A Fine Girl/Guy, Kiss Me How do stars shine? Sun as a typical example Ideas that don t work: 1. Flame (like coal or wood) - can t account for sun s observed luminosity and can t produce energy for very long 2. Gravitational contraction ( shrinking sun ) - could only last for 25 million years, plus violates observations of the sun Sun has been generating about 3.84x1026 W of power (more or less) every day for about 4.5 billion years!! 2
Sun cannot be solid Solar Properties Radius = 696,000 km (about 109 times radius of Earth) slower Mass = 2x10 30 kg (about 300,000 times mass of Earth) Luminosity = 3.8x10 26 W Composition (by mass) = 70% hydrogen, 28% helium, 2% heavier elements faster slower Rotation time is 30 days at the poles and 25 days at the equator ( differential rotation ) Surface temperature = 5,800 K Core temperature = 15x10 6 K Core average density = 36 g / cm 3 (about 3 times density of lead) Core pressure = about 200 billion atmospheres (pressure at sea level is 1 atmosphere; pressure deep in the ocean is hundreds of atmospheres) All Main Sequence Stars are Stable (not expanding or contracting by large amounts) E = mc 2 There is a tremendous amount of energy associated with mass! Pressure pushing out exactly balancing gravity pulling in: gravitational equilibrium For about the first 90% of a star s lifetime, it lives on the Main Sequence of the H-R diagram, burning hydrogen. Energy generation takes place in the core only for main sequence stars (e.g., the sun) Properly, the star converts hydrogen into helium through nuclear fusion (but astronomers are notoriously casual about the language). In the sun, the core is about 25% of the diameter and contains about 40% of the total mass. Only in the core is it sufficiently hot and dense for nuclear fusion ( nuclear burning ) to occur!! In the core, it is too hot and too dense for atoms to exist. Instead, you have bare nuclei swimming in a sea of electrons 3
Pause to reflect The Strong Force What are the nuclei of atoms made of? What actually holds them together? Gravity is MUCH too weak to overcome mutual repulsion of protons!! The strong force is truly the strongest force in nature, but it is extremely short-range. Strong force is only effective over lengths comparable to the size of atomic nuclei (10-15 m or so); actually limits how big nuclei of atoms can be! If you can get 2 protons within about 10-15 m of each other, the strong force can bind them together ( nuclear fusion ). Key: high temperature (protons moving FAST) and high density (many, many protons all in the same place). Proton-Proton Chain (all stars with M < 8 M sun ) So where does the energy come from???? The mass of 4 protons is greater than the mass of 1 helium nucleus. The mass that is lost is converted into energy (in the form of light). The sun (and all stars that are not white dwarfs or neutron stars ) are very slowly losing mass in order to power themselves. Net result: 4 protons are fused, producing 1 helium nucleus Note: only a tiny amount of mass is actually lost. By the end of its lifetime the sun will have lost about about 10% of its total mass to energy generation. 4
In principle, how long could the sun last by burning hydrogen at its present rate? Mass of 4 protons = 6.690x10-27 kg In principle, how long could the sun last by burning hydrogen at its present rate? The sun must fuse 6.0x10 11 kg of hydrogen every single second. Mass of 1 helium nucleus = 6.643x10-27 kg Mass lost (m lost ) = 0.047x10-27 kg Energy gained = m lost c 2 = (0.047x10-27 )(3.0x10 8 ) 2 = 4.23x10-12 J The sun s mass is 1.99x10 30 kg, and at a current age of 4.5x10 9 years, we know that 70% of that mass is in hydrogen, or 1.39x10 30 kg of hydrogen remains. If the sun converted ALL of it remaining hydrogen into helium (at today s rate of nuclear burning ), how much longer could the sun live? Energy produced by the sun every second = 3.8x10 26 J Remaining lifetime in seconds = remaining H mass / rate of H fusion Sun must run this fusion reaction 8.9x10 37 times every second or it would collapse under gravity!!!! Remaining lifetime in seconds = 1.39x10 30 / 6.0x10 11 = 2.32x10 18 seconds In other words, the sun must fuse 6.0x10 11 kg of hydrogen every single second. That s a lot of hydrogen, but the sun has a lot of mass Remaining lifetime in years = 73.4 billion years!! In principle, how long could the sun last by burning hydrogen at its present rate? What determines a star s Main Sequence lifetime? It s all about MASS. So, if the sun could turn ALL of its hydrogen into helium at its present rate, you would think the sun would live a total of (4.5 + 73.4) = 77.9 billion years. The more massive is a star, the hotter and denser is the star in its core. But, sadly, the sun s lifetime is limited to only about 10 billion years because it can t actually convert all of its hydrogen into helium. The hotter and denser it is in a star s core, the FASTER the conversion of hydrogen to helium happens. HUGE structural changes will happen to the star long before it can burn up all of its hydrogen. High-mass (> 8 M sun ) stars are gas guzzlers Low-mass (< 2 M sun ) are economy cars 5
Main Sequence is a MASS Sequence Estimating the Age of the Universe (What are stars good for?) The highest mass stars live only a few million years. They have a lot of fuel and they re burning it really fast. The lowest mass stars live for 100 s of billions of years. They have very little fuel, but they re burning it extremely efficiently. The Oldest Stars in the Milky Way Globular Star Clusters Spherical groupings of 10,000 to 1 million stars (about 158 known in our Galaxy). All of the stars formed at roughly the same time. Globular clusters have lots of RED stars, but no BLUE stars (because they died long ago and were not replenished ). It stands to reason that you are younger than your mother. It therefore stands to reason that the objects within the universe cannot be older that the universe itself. The ages of the oldest stars puts a limit on the minimum age of the universe!! Globular Cluster H-R Diagram Globular Cluster M55 Globular clusters have short, stubby main sequences that turn off to the red giant region. The turn off point tells you the approximate age. 6
Oldest Stars in the Milky Way Globular cluster M4 is one of the oldest known star clusters (about 13 billion years old), and contains many white dwarfs (the dead cores of low-mass stars that used up all their fuel). 7