The Stars Recall from Lab 1: Apparent magnitude m = how bright a star looks Star m Sun -– 26.7 Sirius -– 1.42 Rigel, Betelgeuse 0.3, 0.7 (variable) Polaris, Orion's Belt, Big Dipper 2-3 Unaided eye limit 6.5 Binocular limit 10 8-inch telescope limit 13 Hubble Space Telescope limit 30 This is a logarithmic scale: +5 magnitudes = 100 times fainter, +1 magnitude = 2.512 times fainter The limiting magnitude of a telescope (assuming your eye can see m = 6.5) is: m = 7.1 + 5 log A, where A = aperture, in centimeters. Absolute magnitude M is the apparent magnitude a star would look, if it were 10 parsecs (32.6 light-years) away. Therefore, m -– M = 5 log d – 5 or d = 10^([m-M+5]/5] 1 parsec = 3.26 light-years; this unit comes from how we measure stellar distances, by parallax (1 AU covers 1 arcsecond of angle when its distance = 1 parsec.) Absolute magnitude measures how bright a star really is, not just how bright it looks: It therefore measures a star's luminosity = total power output Spectral types: different stars have different lines visible in their spectra. Originally classified by the strength of the hydrogen lines: A, B, C, etc., mainly by Annie Jump Cannon at Harvard, from 1890-1930. From interpreting spectra, Cecelia Payne-Gaposchkin (1925) found: Stars are made of dense gas: the Sun is 1.4 times denser than water. Stars are about 71% hydrogen (H), with about 27% helium, and < 2% all other, heavier elements ("metals"), by mass, or about 90% H, 9% He, and 1% metals, by number of atoms. In 1929, she found: The spectral types change with temperature, which mixed them up: O B A F G K M R N S no longer used, turned out to be just chemically peculiar M types) L T introduced in 1999, for brown dwarfs. Now: O B A F G K M L T Temperatures, in Kelvins: 30,000 10,000 6000 3000 900 K Sub-classes: O3, O4, O5, … , O9, B0, B1, B2, …, B9, A0, A1, A2, … (etc.) (Each sub-class is a few hundred Kelvins.) The Sun is a G2 star, since T = 5800 K. Spectral types and luminosity classes: Stars of the same spectral type (temperature) can have greatly different luminosities, and so therefore must have greatly different radii. e.g. Capella (in Auriga) is a G star, almost the same T as the Sun, but it is 160 times more luminous. This is because Capella has 160 times more area than the Sun, and so must have a radius 12.7 = times greater than the Sun's. So: Capella is a G giant, or G8III; Sun is a G2 dwarf, or G2V. Luminosity classes: Ia, Ib Extreme supergiants II Supergiants (like Betelgeuse or Rigel) III Giants (like Capella or Antares, a K) IV Sub-giants V Dwarfs (like the Sun or Sirius, an A1V) VI Sub-dwarfs (metal-poor) VII White dwarfs (burnt-out stellar remnants) Plot Luminosity (or absolute magnitude) against Spectral type (or temperature): The Herzsprung-Russell (H-R) diagram This shows how the stars change over time, or evolve. The Sun is a G2V star. It has an absolute magnitude M = 4.74. This is not particularly luminous: the brightest supergiants, such as Betelgeuse and Rigel, have M = -–7. But then, the faintest M dwarfs and white dwarfs have M = 15. This puts the Sun in the middle, with respect to luminosity. The Sun is also more luminous than 90% of all stars, about 1/3 of which are M dwarfs, about 1/3 of which are L and T dwarfs (mostly brown dwarfs), and about 1/3 of which are the burned-out remnants of stars, called white dwarfs. Observed number of stars versus spectral type: OBA: 5% (< 1% are O types, but they're visible across the Galaxy.) FGK: 5% (So 5%, or 1 in 20 of the stars could support life!) M: 30% (These have enormous flares and tides, bad for life.) LT: 30% White dwarfs (burned out star cores): 20% Evolved (giant or supergiant) stars of all spectral types: 10% This makes sense, when one considers stellar masses and ages: Main-sequence masses and lifetimes: O 120 solar masses <3 million years (More massive stars come apart, A 3 solar masses 300 million years from radiation pressure.) G 1 solar mass 10 billion years (The Sun is about halfway M 0.1 solar mass >1 trillion years through this.) - Massive stars are more luminous, because they have more nuclear fuel (the hydrogen in their cores), and their cores are hotter since the pressure there is greater, because they're so massive. - More luminous stars expend their nuclear fuel faster; they don't live for very long, so there aren't many of them. Binary stars: Most stars are double, or binary, stars, 30% are single stars with companions orbiting them. 50% are binaries 15% are triples 5% are multiple star systems, with 4 or more stars orbiting each other. Is this telling us something about how stars form? Do the Sun and Jupiter constitute a binary system? Jupiter is over 3 times more massive than all the other planets combined, and nearly all the Solar System's angular momentum. We can measure stellar masses is by observing their orbits, and using Kepler's Third Law and Newton's Law of Gravity. Eclipsing binaries show us stellar radii (sizes).