Chapter 8: The Family of Stars
Motivation We already know how to determine a star s surface temperature chemical composition surface density In this chapter, we will learn how we can determine its distance luminosity radius mass and how all the different types of stars make up the big family of stars.
Distances to Stars Parallax: A star appears slightly shifted from different positions of the Earth on its orbit. The further away the star is (larger d), the smaller the parallax angle p.
Introduction to Parallax Parallax is the apparent shift in position of a nearby object against a background of more distant objects.
Parallax Angle as a Function of Distance The parallax angle depends on distance.
Apparent Brightness / Apparent Magnitude The more distant a light source is, the fainter it appears. Apparent brightness decreases as the distance to the object increases.
Apparent Brightness / Apparent Magnitude The amount of light received from the star (apparent magnitude) depends to its intrinsic brightness (absolute magnitude) and the distance to it: Star A Star B Earth Both stars may appear equally bright, although star A is intrinsically much brighter than star B.
Distance and Intrinsic Brightness Rigel appears brighter than Betelgeuze. Betelgeuze But, Rigel is 1.6 times further away than Betelgeuze. Thus, Rigel is actually intrinsically brighter than Betelgeuze. Rigel
Absolute Magnitude To characterize a star s intrinsic brightness or luminosity, we define the Absolute Magnitude (M V ): Absolute Magnitude M V = Magnitude that a star would have if it were at a distance of 10 pc.
The Size (Radius) of a Star We already know: flux increases with temperature; hotter stars are brighter But brightness also increases with size: A B Star B will be brighter than star A. Absolute brightness is proportional to the surface area of the star.
Example: Polaris has just about the same spectral type (and thus surface temperature) as our sun, but it is 10,000 times brighter than our sun. Polaris is 100 times larger than the sun. This causes its luminosity to be 10,000 times more than our sun s.
Absolute mag. or Luminosity 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 versus Temperature (or spectral type) Hertzsprung-Russell Diagram Temperature Spectral type: O B A F G K M
The Hertzsprung Russell Diagram Most stars are found along the Main Sequence
The Hertzsprung-Russell Diagram Same temperature, but much brighter than MS stars Must be much larger Giant Stars
Radii of Stars in the Hertzsprung-Russell Diagram Rigel Betelgeuze Polaris Sun 100 times smaller than the sun
Ia Bright Supergiants Ia Ib II III Luminosity Classes Ib: Supergiants II: Bright Giants III: Giants V IV IV: Subgiants V: Main- Sequence Stars
Mass of Stars So far, we know how to find the: -Temperature -Distance -Brightness -Radius of a star. What about the Mass?
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 stellar masses.
The Center of Mass center of mass = balance point of the system Both masses equal => center of mass is in the middle. The more unequal the masses are, the more it shifts toward the more massive star.
Estimating Stellar Masses We can use Kepler s 3 rd Law to estimate the combined mass of the binary stars. The orbital period and orbital speed depend on the distance between the stars and their masses. The more massive the stars, the faster they orbit. We can thus measure the total mass in a binary star system by observing the stars motions. We need to measure how fast they are moving, and the distance they are apart.
Visual Binaries The ideal case: Both stars can be seen directly, and their separation and relative motion can be followed directly.
Spectroscopic Binaries Usually, the binary separation 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
Spectroscopic Binaries 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
Time Spectroscopic Binaries Typical sequence of spectra from a spectroscopic binary system
Eclipsing Binaries 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!
Eclipsing Binaries 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.
The Mass-Luminosity Relation More massive stars are more luminous.
Masses of Stars in the Hertzsprung-Russell Diagram The higher a star s mass, the more luminous (brighter) it is: Masses in units of solar masses L ~ M 3.5 High-mass stars have much shorter lives than low-mass stars: t life ~ M -2.5 Sun: ~ 10 billion yr. 10 M sun : ~ 30 million yr. 0.1 M sun : ~ 3 trillion yr.
Surveys of Stars Ideal situation: Determine properties of all stars within a certain volume Problem: Fainter stars are hard to observe; we might be biased towards the more luminous stars.
Giants and supergiants are extremely rare. Faint, red dwarfs (low mass) are the most common stars. Bright, hot, blue mainsequence stars (highmass) are very rare. A Census of the Stars