Ch 07-04 Binary Stars

• "Double stars"
  Apparent double stars (e.g. Mizar and Alcor, 12 arcmin separation)
  Binary stars
  Binaries are actually very common. (Mizar itself consists of two stars 14'' apart; Mizar A and Mizar B, as well as Alcor, are also found to be binaries.)
  
  
   
• Classification of binary stars
  • visual binaries
  • astrometric binaries
  • spectrum binaries
  • spectroscopic binaries
  • eclipsing binaries
  
   
• Mass determination of binary stars
  • For visual binaries
    
    P² = 4π²a³ / G(m₁+m₂)
    m₁+m₂ = a³ / P²       (in M_⊙, AU, yr)
    
    * some problems: distance, inclination, mass ratio
     
  • One example for astrometric binaries: Sirius
    In 1844, the wavy path of its proper motion found
    In 1862, Sirius B discovered, m=7.5; so it became a visual binary
    M_A~ 2.35 M_⊙
    M_B~ 0.98 M_⊙, size ~ R_⊕, a white dwarf!
     
  • From many determinations of stellar mass in binaries, mainly from spectroscopic binaries (see below), a mass-luminosity relation was found for main-sequence stars:
    L is roughly proportional to M^3.5.
    
    
     
  • The mass function of a spectroscopic binary