Lecture 16 Review
Spectra
An early scheme to class stars was by strength of the hydrogen absorption lines, thus, A,B,C,...® weaker lines. A later scheme, called the B-V Index, classed stars according to a logarithmic ratio of the peak amount of radiation in the blue and violet colors. The current scheme is to class stars according to color in a way which is more or less logarithmically proportional to temperature. In this scheme stars are labeled from M (red, cool stars), K, G, F, A, B, O(blue, hot stars) with subclasses running from 1 to 10. In this scheme the Sun is a G2 type yellow star. The mnemonic for this sequence is Oh Be A Fine Girl, Kiss Me.
Principle Spectral Classes of Stars
Type Spectral Temperature (K) Source of Prominent Representative Stars Class Spectral Lines
Bluest-hot O 40,000 Singly Ionized Helium atoms 24.6 eV Alnitak (z Orionis)
Blue B 18,000 Neutral Helium atoms Spica ( a Virginis) Blue-white A 10,000 Neutral Hydrogen atoms Sirius ( a Canis Majoris) White F 7,000 Neutral Hydrogen atoms Procyon ( a Canis Minoris) Yellow-white G 5,500 Neutral Hydrogen, ionized Calcium 6.1 Sun eV
Orange K 4,000 Neutral metal atoms Arcturus ( a Bootes) Coolest-red M 3,000 Molecules and neutral metals Antares ( a Scorpii)
Note: This scale is not linear in temperature. It is close to logarithmic.
The following spectra illustrate the visible spectra for O, B, A, F, G, K, and M stars. The broad white band in each spectrum reflects blackbody radiation characteristic of each class of star. Tracking upward the blackbody radiation is peaking at shorter wavelengths, thus, according to Wien’s Law, higher temperatures. Stefan-Boltzmann Law
L is the bolometric luminosity. Given the surface area of a star is A = 4BR2, then
2 R L æ T ö L = 4BFR2 T4 in Watts or L - R2T4 Þ = ç sun ÷ Rsun Lsun è T ø
This equation shows the radius, luminosity, and temperature of a star in comparison to the Sun.
Example: What is the radius of Sirius, where the temperature, T = 10,000 K, and luminosity, L = 23 Lsun, are determined from spectrum of Sirius.
From the above equation 2 23æ 5700 ö Þ R = R ç ÷ = 1.56 R sirius sun 1 è10,000ø sun Doppler Shift We have discussed Doppler Shift before. Spectra are wavelength shifted according to whether a star is approaching or receding from the Earth. Dl v = - l c From an absorption spectra one can learn about proper motion with respect to the Earth and infer various things about stellar atmospheres.
Mass Most stars form in combinations, many of them are binary systems in which two stars rotate about each other. If one can measure the distance D between the stars, their distances from the center of rotational mass r1 and r2, and the period of rotation T, one can write two equations:
center of mass: m1r1 = m2 r2
4p2 Kepler’s 3rd Law: T2 = D3 G(m1 + m2 ) These are two equations in two unknowns from which the individual masses can be determined.
Important Observation: Stars with identical spectra usually have the same mass.
Zeeman Effect Magnetic fields can split a spectroscopic transition line into two lines. The width of the separation is a measure of the magnetic fields in the stellar atmosphere where the transitions occur. 12 Basic Properties of Stars and How They are Measured
Property Method of Measurement
Distance Trigonometric parallax - 1000 to 2000 nearest stars Luminosity Distance combined with apparent brightness Temperature Color or spectra Diameter Luminosity and temperature - Stefan-Boltzmann Law Mass Measures of binary stars and use of Kepler’s Laws Composition Spectra - absorption lines, widths, strengths Magnetic field Spectra, using Zeeman effect Rotation Spectra, using Doppler effect Atmospheric motions Spectra, using Doppler effect Atmospheric structure Spectra, using opacity effects, limb darkening Circumstellar material Spectra, using absorption lines and Doppler effect Motion Astrometry or spectra, using Doppler effect
Systematics
How do we find relationships between the stars? First, from the stars near enough to determine we obtain distance and relative luminosity. Then, using the procedures outlined above we determine absolute luminosity and radius . From Doppler shift data on double star systems we can determine masses. Finally, from spectra we can determine spectral composition. From this information on a subset of the nearest stars for which these data can be obtained you recognize two important facts:
1) Stars have different masses Þ different sizes Þ different temperatures Þ different evolutions Þ different evolutionary rates Þ different endings
2) Stars don’t all form at the same time Þ we see new and old stars. The Sun is about 4.6 billion years old, but the Big Bang happened 15 billion years ago. Stars Within 4 Parsecs
Distance Name Part Apparent Absolute Spectral Mass (MSun) Radius (RSun) (pc) Magnitude Magnitude Type 0.0 Sun A 5 G2 1.0 1.0 Jupiter B -27 0.001 0.1 1.3 Alpha Centauri A 0 4 G2 1.1 1.2 B 1 6 K0 0.9 0.9 C 11 15 M5 0.1 ? 1.8 Bernard’s Star 10 13 M5 ? ? 2.3 Wolf 359 14 17 M8 ? ? 2.5 BD +36o2147 8 10 M2 0.35 ? 2.7 L726-8 A 12 15 M6 0.11 ? B 13 16 M6 0.11 ? 2.9 Sirius A -2 1 A1 2.3 1.8 B 8 11 A5 Wh Df 1.0 0.02 2.9 Ross 154 11 13 M5 ? ? 3.1 Ross 248 12 15 M6 ? ? 3.2 L789-6 12 15 M6 ? ? 3.3 e Eridani 4 6 K2 0.9 ? 3.3 Ross 128 11 14 M5 ? ? 3.3 61 Cygni A 5 8 K5 0.63 ? B 6 8 K7 0.6 ? 3.4 e Indi 5 7 K5 ? ? 3.5 Procyon A 0 3 F5 1.8 1.7 B 11 13 Wh Dwarf 0.6 0.01 3.5 S 2398 A 9 11 M4 0.4 ? B 10 12 M5 0.4 ? 3.5 BD +43o44 A 8 10 M1 ? ? B 11 13 M6 ? ? C ? ? K? ? ? 3.6 t Ceti 4 6 G8 ? 1.0 3.6 CD -36o15693 7 10 M2 ? ? 3.7 BD +5o1668 A 10 12 M4 ? ? B ? ? ? ? ? 3.7 G51-15 15 17 ? ? ? 3.8 L725-32 12 14 M5 ? ? 3.8 CD -39o14192 7 9 M0 ? ? 3.9 Kapteyn’s Star 9 11 M0 ? ? 4.0 Kruger 60 A 10 12 M4 0.27 0.51 B 11 13 M6 0.16 ? C ? ? ? 0.01 ? 4.0 Ross 614 A 11 13 M5 0.14 ? B 15 17 ? 0.08 ? 4.0 BD -12o4523 10 12 M5 ? ? Variations Observed mass 0.1 to 60 Solar masses luminosity 10-6 to 106 Solar luminosities surface temperature a to 10 Solar temperatures radius .01 to 100 Solar radii
In Our Neighborhood 1) Most stars are like our sun, a yellowish white G2 star. 2) Most have similar masses.
Hertzsprung and Russell published luminosity versus spectral class information in 1914. They plotted log(luminosity) versus color index, where color index is roughly proportional to log(temperature). With the exception of a few white dwarfs, they found that the nearby stars were positioned around a single line called the main sequence. Roughly 93% of known stars fall on this same line.
What does this say? It says that differences in stellar spectra arise from a single condition in the stars. This condition is mass. The initial mass of a star says everything about the life of a star.
Hydrogen burning is the most efficient, lowest temperature energy producer. Radiation pressure from the thermonuclear fusion of hydrogen atoms prevents the star from collapsing. Hydrostatic equilibrium occurs when Helmholtz gravitational contraction equals the outward radiation pressure. Example: Consider a star with greater mass than the sun more mass Þ more gravitational pressure Þ more energetic collisions Þ more nuclear interactions Þ more radiation to prevent collapse Þ higher temperatures Þ hotter surface Þ faster rate of burning Þ shorter lifetime
At the same time more mass Þ higher density Þ larger radius Þ greater luminosity What we see in the sky, for the most part, is not the main sequence stars, but the brightest stars. These stars have evolved from the main sequence. These stars may be much further away than nearby, more prevalent, main sequence stars, but their intrinsic luminosity is so great that they are visible over great distances.
17 Brightest Stars in the Sky Star Name Apparent Bolometric Star Type Radius Distance Magnitude Luminosity (LSun) (RSun) (pc) Sun -26.7 1.0 Main sequence 1.0 0.0 Sirius -1.4 23 Main sequence 1.8 2.7 Canopus -0.7 1400? Super giant 30 34 Arcturus -0.1 115 Red giant 25? 11 Rigel Kent 0.0 1.5 Main sequence 1.1 1.33 Vega 0.0 58? Main sequence 3? 8.3 Capella 0.1 90? Red giant 13 14 Rigel 0.1 60,000? Supergiant 40? 280? Procyon 0.4 6 Main sequence 2.2 3.5 Achernar 0.5 650? Main sequence 7? 37 Hadar 0.7 10,000? Giant 10? 150 Betelgeuse 0.7 10,000 Super Giant 800 160 Altair 0.8 9? Main sequence 1.5 5 Aldebaran -.9 125 Red giant 40? 21 Acrux 0.9 2500? Main sequence 3? 110? Antares 0.9 9000? Supergiant 600? 160? Spica 1.0 2300? Main sequence 8 84