Reading and Announcements Read Chapters 8.3, 11.5, 12.1 Quiz #5, Thursday, March 21 Homework #5 due Tuesday, March 19
Measurements of Star Properties Apparent brightness Direct measurement Parallax Distance Distance + apparent brightness Luminosity ( L=4 D2 B) Spectral type (or color) Temperature Luminosity + temperature Radius (L=4 R2 T4)
In Review There are four principal characteristics of a star: Luminosity Surface Temperature Size Mass How can we put all this together so that we can classify stars and understand how they evolve? We can take a census of stars and see what is out there.
How can we study the evolution of stars? Collect a large number of stars (statistical approach). A large sample of stars will contain examples of all stellar life stages and of all stellar types. By looking at some carefully selected observable properties of the stars, we will see trends that will tell us about stellar evolution. But which observables to look at? And how?
Example: a study of cars Plot Horsepower vs. Weight Most cars lie along a sequence. Special cars are off this sequence.
Classification of Stars: Statistical Study 1) Collect information on a large sample of stars: surveys of stars. 2) Measure their luminosities (need the distance!). 3) Measure their surface temperatures (need their spectra or at least their color).
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 Absolute mag. or Luminosity Luminosity versus Temperature (or spectral type) Hertzsprung-Russell Diagram Spectral type: O Temperature B A F G K M
The Hertzsprung-Russell Diagram M os t st ar M sa ai r e n Se fou qu nd en al ce on g th e
The Hertzsprung-Russell Diagram The HR diagram separates the effects of temperature and surface area on a star's luminosity and sorts the stars according to their size.
The Hertzsprung-Russell Diagram Main Sequence Most stars lie along the Main Sequence including the sun.
The Hertzsprung-Russell Diagram Red Giants - Red Giant stars are very large, cool and quite bright. e.g. Betelgeuse is 100,000 times more luminous than the Sun but is only 3,500K on the surface. It s radius is 1,000 times that of the Sun.
The Hertzsprung-Russell Diagram Blue Supergiants
The Hertzsprung-Russell Diagram White Dwarfs - White Dwarfs are hot but since they are so small, they are not very luminous.
L=4πR2 σt4 To calculate a star's radius, you must know its temperature and luminosity. chemical composition and temperature. color and chemical composition. luminosity and surface gravity.
L=4πR2 σt4 If a star is half as hot as our Sun, but has the same luminosity, how large is its radius compared to the Sun? ½ times as large ¼ times as large 4 times larger the same
The Radii of Stars in the Hertzsprung-Russell Diagram Betelgeuse Rigel Polaris Sun 10,00 sun 0 tim s r es t h ad iu s e 10 0 su time n s s rad the ius As lar ge a st he su n
Luminosity Classes Can be determined from the width of spectral absorption lines. I-II: Supergiants III-IV: Giants V: Dwarfs, i.e. main sequence Do not confuse them with white dwarfs The sun is a G2V star.
What is the most common type of star?
Mass: how do you weigh a star? Mass is the single most important property in how a star s life and death will proceed. We can weigh stars using binary stars (two stars orbiting each other). Most stars are in binary systems.
Binary Stars Center of mass (or baricenter) Star A ra rb Star B Ma/Mb = rb/ra -Each star in a binary system moves in its own orbit around the system's center of mass. -Kepler s Third Law: the orbital period depends on the relative separation and the masses of the two stars: au 3 a p2 = (M +M ) 1 2 years Solar Masses Need the distance to get a.
Different types of Binaries Double stars: Not necessarily a binary. Alcor and Mizar Visual binary: can see two stars orbit over time. Spectroscopic binary: can only tell by seeing Doppler shifts of absorption lines. Eclipsing binary: stars pass in front of each other.
I. Visual Binaries
1 4 2 5 1. 3 1. The total spread (size) of the Doppler shift gives velocities about center of mass (gives orbit sizes, ra+rb ). The time to complete one repeating pattern gives period, P. Spectroscopic binaries: Doppler shift tells if it is moving toward or away.
Eclipsing Binaries: Best binaries to measure mass
Mass-Luminosity relation Most stars appear on the Main Sequence, where stars obey a Mass-Luminosity relation: L M3.5
Mass-Luminosity relation L M3.5 For example, if the mass of a star is doubled, its luminosity increases by a factor 23.5 ~ 11. Thus, stars like Sirius that are about twice as massive as the Sun are about 11 times as luminous. The more massive a Main Sequence star is, the hotter (bluer), and more luminous. The Main Sequence is a mass sequence!
The Hertzsprung-Russell Diagram Mass of Star Size of Star
The Hertzsprung-Russell Diagram Heavier Mass of Star Lighter
A main-sequence star can hold its structure for a very long time
Hydrostatic Equilibrium Imagine a star s interior composed of individual shells Within each shell, two forces have to be in equilibrium with eachgravity, i.e. the weight other: Outward pressure from the interior Hydrostatic equilibrium means: Gravity balances pressure. from all layers above
Hydrostatic Equilibrium Outward pressure force must exactly balance the weight of all layers above everywhere in the star. This condition uniquely determines the interior structure of the star. This is why we find stable stars on such a narrow strip (Main Sequence) in the Hertzsprung-Russell diagram.