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The HR Diagram Astronomy 315 Professor Lee Carkner Lecture 8 Flux and Luminosity The flux is the amount of energy per second per unit area received from a star Luminosity is the amount of energy per second emitted by the star We measure the flux, but we want to know the luminosity Inverse Square Law What determines how bright a star looks? A star radiates energy in all directions The flux is the luminosity divided by the area of that sphere where d is the distance from the star Flux decreases as the inverse square of the distance Inverse Square Law Distance How do we find distance? Need to use indirect methods Parallax Parallax is the apparent shift in position of an object when viewed from two different point There is a simple geometrical relationship between the shift and the distance to the object Parallax Explained p d ½B View position of star now and then 6 months later If d is the distance to the star and B is the baseline (distance across Earth’s orbit) then: tan p = ½ B / d Using Parallax We normally use a simplified version of this equation: p is in arcseconds (60 arcseconds per arcminute, 60 arcminutes per degree) d is in parsecs (1 pc = 3.26 light years = 3.09 X 1013 km) Can only use parallax to get distances out to 100 pc (1000 pc from space) Parallax in the Classroom p2 Measure the offset from straight ahead for each position Average p1 and p2 to get p Measure B p1 d p2 p1 ½B Absolute Magnitude We can measure the apparent magnitude of a star (m) If we know the distance we can find the absolute magnitude (M) They are related by: m-M = 5 log d - 5 Classifying Stars We can measure: We can now find the temperature and luminosity of near-by stars What results do we get for a large group of stars? The H-R Diagram Make a plot of luminosity versus temperature (or absolute magnitude v. spectral type) What do you see? Stars concentrated in a diagonal band that rums from high L, high T to low L low T HR Diagram Regions on the Diagram The line that the bulk of stars fall on is called the Main Sequence Below the main sequence the stars are hot but dim Above the main sequence we have stars that are bright but cool Size of Stars We can relate the temperature and luminosity to the size with the StefanBoltzmann law L = sAT4 or L = 4pR2sT4 What do we find? Red giants -- large, white dwarfs - small Called red dwarfs Radius of Stars Luminosity Classes Luminosity classes are used to specify where a star falls on the HR Diagram In order of increasing brightness and size: V -IV -III -II -I -- The luminosity class is given after the spectral type: e.g. the sun is G2V Luminosity Classes Census of Stars A quick look at an HR diagram makes it seem as if all regions are equally populated If you take a certain region of space and count all of the stars in it, you find: Reasonable numbers of medium main sequence stars and white dwarfs Relative Numbers of Stars Selection Effect Most stars are faint From a casual look at the sky it would seem like most stars are bright When you select a group of stars to study, the criteria you use to select them affects your answer to your study Spectroscopic Parallax The main sequence is very well defined If you know the luminosity and you measure the flux you can find the distance (F = L/4pd2) Called spectroscopic parallax Determining Star Properties Physics: apparent shift Physics: Spectral lines of object from depend on different vantage temperature points Physics inverse square law Physics: StefanBoltzmann Law Finding Star Properties Next Time OBSERVING TONIGHT 6:30pm, observatory Bring your observing templates Read Chapter 10 Question of the Day: How do we know the masses of stars? List 1 due Friday