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  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 p d ½ B

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 km)   Can only use parallax to get distances out to 100 pc (1000 pc from space)

Parallax in the Classroom  Measure the offset from straight ahead for each position  Average p 1 and p 2 to get p  Measure B p1p1 d ½ B p1p1 p2p2 p2p2

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 Stefan- Boltzmann law L =  AT 4 or L = 4  R 2  T 4   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/4  d 2 )  Called spectroscopic parallax 

Determining Star Properties  Physics: apparent shift of object from different vantage points   Physics inverse square law   Physics: Spectral lines depend on temperature   Physics: Stefan- Boltzmann 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