Key Concepts: Lecture 21: Measuring the properties of stars (cont.) The Hertzsprung-Russell (HR) Diagram (L versus T) The Hertzprung-Russell Diagram The Stefan-Boltzmann Law: flux emitted by a black body = σt 4 Binary Stars: measurements of stellar mass Hertzprung and Russell found Stars did not occur with all possible combination of temperature and luminosity Stars tended to group together A large number of stars (including the Sun) were found in a band they called the Main Sequence This suggested that the observed properties of stars are interrelated Luminosity Hot Cool The Hertzprung-Russell Diagram In an attempt to understand the physical nature of the stars, astronomers tried to find correlations between their observed properties Temperature or Spectral Class Luminosity The American Henry Norris Russell (1913) and the Danish engineer Ejnar Hertzsprung (1911) independently made a diagram showing these stellar properties. Stars group themselves in various parts of the diagram. Question Why would stars with the same temperature (spectral class and/or color) have very different luminosities?
Luminosity and Sizes of Stars Stefan-Boltzman Law: the energy emitted every second by an object at temperature T is proportional to T 4 and is proportional to the surface area of the object. Therefore total luminosity of stars L = 4 π R 2 σ T 4 Radius of star temperature Stefan-Boltzman constant The Sizes of Stars If you know the luminosity of a star and its temperature you can find its size Stefan-Boltzman law: L = 4 π R 2 σ T 4 So we have: R 2 = L / (4 π σ T 4 ) then take square root for R Luminosity Classes Stars with the same temperatures but different luminosities fall into Luminosity Classes Larger stars are more luminous White dwarfs are smallest Supergiants the largest White dwarfs Supergiants Direct imaging of the size of largest giant stars See C&M Chapter 10.4
The Sizes of Main Sequence Stars Sizes of Stars Rise of Main Sequence (MS) is due to both temperature and size Hot MS stars about 10x the size of Sun Cold MS stars about 1/10x the size of Sun Super giants are about 1000x the size of the Sun White dwarfs are about (1/100)x the size of the Sun Sizes of Planets & Stars Video See also Astronomy Picture of the Day from February 22nd 2011 http://apod.nasa.gov/apod/ap110222.html
Binary Stars Binary stars: Two stars orbiting each other due to mutual gravitational attraction About half of stars we see in the sky are actually binary stars (but they are too close to separate with our eyes). If we can measure the orbit, it allows direct measurement of masses of stars by using Newton s adaptation of Kepler s 3rd Law (just like measuring the mass of Jupiter by measuring the orbit of its moons). Binary stars orbit around their center of mass Actually this is also true of the Sun and the planets of our Solar System, but since the Sun is so massive the center of mass (e.g., of Sun-Jupiter) is inside the Sun, near its actual center. Visual Binaries Binary systems for which both stars can be seen and period of orbit & separation can be directly observed Visual binaries give us the best information about stellar masses Newton s adaptation of Kepler s 3rd Law: (m 1 + m 2 ) P 2 = a 3 Spectroscopic Binaries Some binary stars are too far from us for us to see the separate stars. Using spectra we can detect the presence of two stars Presence of spectral features characteristic of two different types of stars A periodic Doppler shifting of spectral lines (see next slide)
Doppler Effect The Mass-Luminosity Relation Doppler Effect change or shift in wavelength (frequency) of light due to the motion of source with respect to the observer v / c = (Δλ) / λ blue shifted Source at rest Source in motion red shifted For Main Sequence stars the luminosity is related to the mass approximately as L M 4 Eclipsing Binaries Binary systems where one star passes in front of the other The apparent brightness of the system changes periodically due to the eclipses of the stars From light curves we can work out: Details of orbits Shapes and sizes of stars Relative temperatures of stars The Reason for the Main Sequence The main sequence (MS) is a sequence of stellar mass Low mass MS stars appear cool High mass MS stars are hot The relation between radius, temperature and mass is determined by the balance between gravity and the pressure that prevents the star from collapsing or blowing itself apart