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Lecture 19 Stellar Luminosity; Surface Temperature Luminosity from brightness and distance Temperature from color Temperature from lines: spectral type The H-R classification diagram: Main Sequence, Giants, and Dwarfs Mar 3, 2006 Astro 100 Lecture 19 1 Brightness Units • Magnitude: a measurement of relative intensity where a ratio of 10 gives a difference in magnitude of 2.5 (called a "logarithmic" scale). Greek origin, based on human eye. m(star 1) - m(star 2) = -2.5 log10 (brt(star 1) / brt(star 2)) or brt(star 1) / brt(star 2) = 10 -(m(star 1) - m(star 2))/2.5 • Apparent magnitude: magnitudes "relative to the brightness of Vega" (α Lyrae, one of the stars in the Summer Triangle). – So for apparent magnitude, star 2 in the formula is Vega. – This means Vega’s apparent magnitude is 0 – Apparent magnitude is usually written (lower case) "m". • Some Examples Mar 3, 2006 Astro 100 Lecture 19 2 1 Luminosity • Luminosity measured in solar units: "Lsun" Lsun = 3.9x1026 W • Recall relation between Brightness and Luminosity Lum = 4π distance2 Brightness • By combining brightnesses and distances from parallax of nearby stars, find stellar luminosities • L(Vega)/Lsun = b(Vega)/bsun × (d(Vega)/dsun)2 = 10-11 × (7.8/5.5x10-6 )2 = 24 • Bottom Line: By combining brightnesses and distances from parallax of nearby stars, find stellar luminosities have huge range: L(star) = 10-5 - 106 Lsun • This means a star can have a large brightness (low magnitude) if it is close, or if it is intrinsically luminous Mar 3, 2006 Astro 100 Lecture 19 3 Stellar Surface Temperature • One of the easier things to measure is a star’s surface temperature • Like the Sun, stars show absorption line spectra: continuum plus absorption lines. Each depend mainly on the surface temperature. Mar 3, 2006 Astro 100 Lecture 19 4 2 Stellar Continuum Color • The continuous spectrum is approximately a blackbody radiator from opaque gas. • Color => approximate surface Temperature from Wien’s law: Surface Temp = constant/wavelength(maximum) • Range of surface temperatures seen: 3500 - 30,000. The Sun is in the middle. Star Wavelength (maximum) (color) Sun 520 nm (yellow) Rigel (β Ori) 250 nm (ultraviolet-blue) Betelgeuse (α Ori) 800 nm (red-infrared) Mar 3, 2006 Surface Temperature 5800 K 12,000 K 3750 K Astro 100 Lecture 19 5 Stellar Absorption lines - Spectral "Type" • The absorption lines are due to absorption by atoms in its transparent, slightly cooler, overlying atmosphere. Different stars show different absorption lines. Why? – Which spectral lines appear depends mainly on the temperature of the atmosphere. – The elemental composition of stars does not (usually) vary enough to make a big effect. • Example, the hydrogen Balmer Lines. – (Recall these are from photons absorbed by Hydrogen atoms in their second energy state). Mar 3, 2006 Astro 100 Lecture 19 6 3 Balmer Lines • most prominent in stars between 8000 and 15000 K • > 15,000K: – It is so hot that collisions between H atoms knock the electrons off the atoms, leaving them ionized (bare protons). – A bare proton has no lines at all. Balmer lines are weak. • < 8000 K: – The H Balmer absorption lines at visible wavelengths are all due to absorption by atoms starting from the second energy state. – The only way an atom gets into this state is by being hit by a neighbor, and the neighbors at these temperatures are not moving fast enough. Balmer lines are weak. Mar 3, 2006 Astro 100 Lecture 19 7 Spectral Type • Similar (more complex) story for other elements, at other temperatures. Which lines are prominent is quantified by (in order of decreasing temperature) • spectral type letters: O B A F G K M, and • subtype numbers G0,G1...G9. • This turns out to be the easiest way to get the surface temperature of even very faint stars- this has been done for almost a million stars! • Try this applet! It combines the continuum color and lines. http://www.jb.man.ac.uk/distance/life/sample/java/spectype/specplot.htm Star Rigel Surface Temp Spectral Type Lines 12,000 B8 H Balmer lines Sun 5800 G2 Ca+, Fe+ Betelgeuse 3750 M2 TiO molecule Mar 3, 2006 Astro 100 Lecture 19 8 4 Classification Diagram • We now have all the data we need to make a famous diagram which shows what kind of stars there are: • "H-R (Hertzsprung-Russell) Diagram" Luminosity vs Temperature • For historical reasons, luminosity is plotted up and temperature towards left. • Each star is one point on the diagram Mar 3, 2006 Astro 100 Lecture 19 9 Stellar Classes • • • • Find there are only certain kinds of stars Supergiants Very rare. eg Betelgeuse (alpha Ori) Giants Pretty rare. eg Aldebaran (alpha Tau) Main Sequence 90% of stars. eg the Sun . The least luminous (coolest) main sequence stars are by far the most common (albeit the most inconspicuous) • White Dwarfs (a different typing scheme). Probably very common, but so faint that not many are known. eg Sirius B (faint companion to Sirius) Next time: how size comes into it.. Mar 3, 2006 Astro 100 Lecture 19 10 5 Brightness & Luminosity of Some Stars m brtness parallax dist Lum (mag) b(Vega)) (arcsec) (pc) (Lsun) Sun Vega (α Lyr) “Proxima” Cen α Cen Betelgeuse (α Ori) Mar 3, 2006 -27.5 1027.5/2.5 =1011 0.0 1.00 10.7 5.3×10-5 0.1 0.91 0.5 0.63 5x10-6 1 0.128 0.775 0.775 0.011 7.8 1.3 1.3 95 24 6x10-5 1 20,000 Astro 100 Lecture 19 11 Orion Star Colors Betelgeuse 3750 K Rigel 12,000 K Mar 3, 2006 Astro 100 Lecture 19 12 6 Spectral Types Hγ He Hβ Hα Temperature >25,000 11 -25,000 8 -11,000 Ca+ 6 -8,000 5 -6,000 4 -5,000 3 -4,000 CH Mar 3, 2006 TiO Astro 100 Lecture 19 13 H-R Diagram Mar 3, 2006 Astro 100 Lecture 19 14 7