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The Four Basic Parameters of Stars Luminosity Size Mass Surface Temperature Measurements of Star Properties Apparent brightness Direct measurent Parallax Distance Distance + apparent brightness Luminosity ( L=4D2 f) Spectral type (or color) Temperature Luminosity + temperature Radius (L=4R2 T4) Luminosity and temperature are the two independent intrinsic parameters of stars. 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 that are in binary systems (two stars orbiting each other). Fortunately, most stars fall into this category. Most stars in binary systems have a mass that is very similar to its companion … we’ll see why this is soon! 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. -Their orbital period depends on their separation and their masses. 2 4π 3 2 a p = G(M +M ) 1 2 Big p = Small Masses Small p = Big Masses I. Visual Binaries 1 4 2 5 1. 3 2. 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 In Review There are four principal characteristics of a star: Luminosity Surface Temperature Size Mass How may we classify stars? We can take a census of stars and see what’s out there. But first, let’s do some sociology in the classroom. Discussion Question Make a plot that shows the general relationship between height and weight for humans. - now add to your plot the population of basketball players who are very tall and very thin. - now add the population of obese children Classification of Stars 1) Collect information on a large sample of stars. 2) Measure their luminosities (need the distance!) 3) Measure their surface temperatures (need their spectra) The Hertzsprung-Russell Diagram The HR diagram separates The effects of temperature And surface area on stars’ Luminosity and sorts the Stars according to their size The Hertzsprung-Russell Diagram The HR diagram separates The effects of temperature And surface area on stars’ Luminosity and sorts the Stars according to their size The Hertzsprung-Russell Diagram The Main Sequence - all main sequence stars fuse H into He in their cores - this is the defining characteristic of a main sequence star. The Hertzsprung-Russell Diagram Red Giants - Red Giant stars are very large, cool and quite bright. Ex. 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 The Hertzsprung-Russell Diagram White Dwarfs - White Dwarfs are hot but since they are so small, they are not very luminous. The Hertzsprung-Russell Diagram The HR diagram separates The effects of temperature Mass of Star And surface area on stars’ Luminosity and sorts the Stars according to their size Size of Star Mass-Luminosity relation Most stars appear on the Main Sequence, where stars appear to obey a 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! Review Questions 1. 2. 3. What is the Hertzsprung-Russell Diagram? Why are most stars seen along the so-called main sequence? What makes more massive stars hotter and brighter?