Lecture 6  Spectroscopic and Eclipsing Binaries (1/28/99)
Binaries I   
HR Diagram
Reading:
Chapter 12 (ZG4)
Notes:
pages 20  23
Artists conception of an Xray binary star. The two
stars are so close together that the larger star spills over onto the
white dwarf companion, which gets heated and emits Xrays.
(Courtesy NASA/STSCI)

Key Question: 
How can you measure the radius
of a distant star?


Key Principle: 
Mass Function for Binary Stars


Key Problem: 
Determine densities and radii of
Sirius A & B.

Investigations:
 Spectroscopic Binaries
 What is a Dopper shift?
 How do you find radial velocity from the observed wavelengths of
spectral lines?
 What is the radial velocity corresponding to a 1 Angstrom shift at
5000 Angstroms rest wavelength?
 What is the shift corresponding to a 1 km/s radial velocity at
5000 Angstroms?
 What is the resolving power of a high resolution spectrograph
needed to measure radial velocities with < 1 km/s accuracy?
 What is the orbital velocity of the Earth around the Sun?
 What is the orbital velocity of the Sun induced by Jupiter?
 What is a doubleline spectroscopic binary?
 What role does the inclination of the orbit play in the observed
velocities?
 How do you find the masses from a doubleline binary?
 What is a singleline spectroscopic binary?
 What is the mass function for a binary star?
 How do you find the mass function of a single line binary?
 What is the significance of the mass function, given that the total
mass and the inclination are unknown?
 What effect do orbital eccentricity and inclination have on the
observed velocity curves?
 Eclipsing Binaries
 What is the likely inclination and/or separation of an eclipsing
binary system?
 How do you recognize an eclipsing binary system?
 What are the times of 1st  4th contact?
 How do you find the radii of the stars from the light curves?
 How are the depths of the eclipses related to the temperatures
of the stars? Why?
 If the eclipsing binary is also spectroscopic, what additional
information can be learned?
 Example (see homework 1):
Sirius A & B  Radii and Densities
 System Data II 
Bolometric Magnitude (Sirius A):  +1.33 
Bolometric Magnitude (Sirius B):  +8.57 
Bolometric Magnitude (Sun):  +4.76 
Effective Temperature (Sirius A)  9200 K 
Effective Temperature (Sirius B)  27000 K 
Effective Temperature (Sun)  5770 K 
 What are the luminosities of Sirius A & B in Lsun?
 What are the radii of Sirius A & B?
 What are the mean densities of Sirius A & B?
 Where on the HR diagram do Sirius A & B lie?
 What stellar classifications would you give to Sirius A & B?
The Doppler Effect
The Doppler effect:
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Steven T. Myers