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0. Life and Evolution of Stars. Chapter 9. 0. Outline. Masses of Stars: Binary Stars Variable Stars Spectral Types of Stars H-R Diagram The Source of Stellar Energy Life Story of a Star. Video Trailer: Birth of Stars. I. Masses of Stars: Binary Stars. 0. 1. Binary Stars.
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0 Life and Evolution of Stars Chapter 9
0 Outline • Masses of Stars: Binary Stars • Variable Stars • Spectral Types of Stars • H-R Diagram • The Source of Stellar Energy • Life Story of a Star
0 1. Binary Stars More than 50 % of all stars in our Milky Way are not single stars, but belong to binaries: Pairs or multiple systems of stars which orbit their common center of mass. If we can measure and understand their orbital motion, we can estimate the stellarmasses.
0 The Center of Mass (Active_Figure_12) center of mass = balance point of the system Both masses equal => center of mass is in the middle, rA = rB The more unequal the masses are, the more it shifts toward the more massive star.
Types of Binaries: Visual Binaries Spectroscopic Binaries Eclipsing Binaries
0 Visual Binaries (Video_Visual_Binaries) The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly.
0 Spectroscopic Binaries (Video_Spectr_Binaries) Usually, binary separation “a” can not be measured directly because the stars are too close to each other. A limit on the separation and thus the masses can be inferred in the most common case: Spectroscopic Binaries
0 Spectroscopic Binaries (2) The approaching star produces blue shifted lines; the receding star produces red shifted lines in the spectrum. Doppler shift Measurement of radial velocities Estimate of separation “a” Estimate of masses
0 Spectroscopic Binaries (3) Typical sequence of spectra from a spectroscopic binary system Time
0 Eclipsing Binaries (Animation) Usually, the inclination angle of binary systems is unknown uncertainty in mass estimates Special case: Eclipsing Binaries Here, we know that we are looking at the system edge-on!
0 Eclipsing Binaries (2) Peculiar “double-dip” light curve Example: VW Cephei
0 Eclipsing Binaries (3) Example: Algol in the constellation of Perseus From the light curve of Algol, we can infer that the system contains two stars of very different surface temperature, orbiting in a slightly inclined plane.
0 The Light Curve of Algol
II. Variable Stars Video Trailer: Variable Stars Chi Cygni expands and dims, and then contracts and brightens over 408 days
Variable Stars • A variable star is a star that has lost its hydrostatic equilibrium. The brightness and size of a variable star change with time as it evolves. • Two Types of Variable Stars: • Pulsating stars: stars that appear to pulsate and change brightness. Examples are: Cepheid variables – RR Lyrae – Neutron stars (1 to 60 days - About 1 day - A couple of seconds) • Exploding stars: stars that show extreme brightness variability. Examples are: Nova – Supernova – T Tauri
Nova outburst (Active_Figure_27)
0 Spectral Classification of Stars (1) Different types of stars show different characteristic sets of absorption lines. Temperature
0 Spectral Classification of Stars (2) Mnemonics to remember the spectral sequence:
0 Stellar Spectra O B A F Surface temperature G K M
0 The Composition of Stars From the relative strength of absorption lines (carefully accounting for their temperature dependence), one can infer the composition of stars.
0 Organizing the Family of Stars: The Hertzsprung-Russell Diagram We know: Stars have different temperatures, different luminosities, and different sizes. To bring some order into that zoo of different types of stars: organize them in a diagram of Luminosity Temperature (or spectral type) versus Absolute mag. Hertzsprung-Russell Diagram Luminosity or Temperature Spectral type: O B A F G K M
0 The Hertzsprung-Russell Diagram (Simulation) Most stars are found along the Main Sequence
0 The Hertzsprung-Russell Diagram (2) Same temperature, but much brighter than MS stars Stars spend most of their active life time on the Main Sequence (MS).
L α R2 x T4, where, L = Luminosity of star R = Radius of star T = surface temperature of the star.
0 The Brightest Stars The open star cluster M39 The brightest stars are either blue (=> unusually hot) or red (=> unusually cold). (Is this a contradiction?)
0 The Radii of Stars in the Hertzsprung-Russell Diagram Betelgeuse Rigel 10,000 times the sun’s radius Polaris 100 times the sun’s radius Sun As large as the sun
0 The Relative Sizes of Stars in the HR Diagram
Energy of Stars • All stars are considered as huge balls of gases where nuclear fusion in their cores produces most of their energies. • It is possible to calculate an approximate star’s lifetime by determining its mass (tlife ~ 1/M2.5) • Cold (red ones) stars have longer lifetime than hot stars: • O star: ~ 1 million years • G star (Sun): ~ 10 billion years • M star : ~ 5,000 billion years
First stage: all stars start fusing hydrogen (H) to make helium (He) • This stage is considered to be the longest stage in a star’s lifetime ( 90% of its total lifespan) • Second stage: Fusing of helium (He) to make carbon (C) • The life of some stars (like our Sun) stops after this stage, but others will continue processing heavier and heavier elements than carbon in their cores. • For the massive stars (more than 8 solar masses), iron will be the last element that a star can form in its core. • Stars start their lifetime with a light element core (H) and end up with a heavy element core.
Life Story of a Star • Stars are born inside huge interstellar clouds following three stages: • Giant molecular cloud • Dense cores • Protostar T Tauri star • Stars are divided into two main groups: • Stars with masses less than 8 solar mass • Stars with masses larger than 8 solar mass
Stars with mass less than 8 solar mass • Giant molecular cloud • Dense core • T-Tauri star • Main-sequence star: fusing H to make He • Giant star: fusing He to make C • Planetary Nebulae • White Dwarf(with mass less than 1.4 solar mass)
While on the main sequence, a star is in “hydrostatic equilibrium”: inward pressure due to gravity balances the outward pressure due to heat.
