Binary Stars PHYS390 (Astrophysics) Professor Lee Carkner Lecture 6

Questions 1)If m 1 is much larger than m 2, what are  and M approximately equal to?  Since  = m 1 m 2 /(m 1 +m 2 ) and M = m 1 +m 2, M ~ m 1,  ~ m 2 2)If m 1 is much larger than m 2, what is the total kinetic energy of the system and which mass has all the kinetic energy?  Since K = ½  v 2 and  ~ m 2, K = ½m 2 v 2 and the smaller mass has all the kinetic energy (it is the only thing moving)

Spectroscopic Binaries  For spectroscopic binaries we cannot find a or    The radial velocity v r is related to the actual orbital velocity v by v r = v sin i    For circular, edge-on orbits, v max is the true orbital velocity

Mass and Velocity  m 1 /m 2 = v 2r /v 1r  m 1 +m 2 = (P/2  G)[(v 1r +v 2r ) 3 /sin 3 i]   Where we can measure both v 1r and v 2r

Inclination and Statistics  Often we can’t find i   We can’t find mass for one star, but we can find an average mass for a class of stars   Gives mass-luminosity relationship  How does mass produce luminosity?

Eclipsing Binaries   Light will dim when hotter star goes behind cooler   From Doppler shift we can get the velocity of each star  Smaller = v s   Relative velocity v = v s + v l

Eclipsing Binaries and Radius  r s = (v/2)(t b -t a )  Time for smaller to emerge from behind larger is just t c -t a, so radius is r l = (v/2)(t c -t a )

Eclipse Flux Variations  Maximum light = B 0   Primary minimum = B p   Secondary minimum = B s  Larger star completely behind smaller B0B0 BpBp BsBs

Temperature  B 0 -B p =  B 0 -B s =  Since flux is proportional to temperature to the 4 th power, (B 0 -B p )/(B 0 -B s ) = [1-(B p /B 0 )]/[1-(B s /B 0 )]= (T s /T l ) 4 

Next Time  Test #1  For Friday:  Read: 8.1  Homework: 8.1, 8.6a