Binary Stars Astronomy 315 Professor Lee Carkner Lecture 9

Masses of Stars   How do you find mass?   Weighing means measuring how gravity affects the object   Watch how the star moves under the influence of the gravity of another star

Binary Stars  Many stars are in multiple systems   How do we find binary stars?   Called optical doubles  May just be a projection effect   In orbit around each other

Visual Binaries  The simplest type to observe are visual binaries   The periods of such stars are often very long   Most visual binaries have a relatively stationary bright star and a moving fainter star

Binary Motion of Castor

Problems with Binaries   In order to resolve the stars they have to have a large separation, but his also means a long period   The orbit is not exactly face on to you, so you see its projection onto the plane of the sky

Inclination Effects

Using Binary Stars  Orbital period (P)    Orbital radius (r A and r B )    The center of mass is the common point around which they both orbit  Need the distance to the binary from parallax first

Center of Mass Distances

Ratio of Mass  M A /M B = r B /r A  The more massive star is closer to the center of mass  Examples:   If both stars are equally distant from the center of mass, they have the same mass

Kepler’s 3 rd Law  a = r A + r B  We can relate this to the period via Kepler’s 3 rd Law: M total = M A + M B = a 3 /P 2  where:   a is the semi-major axis of the orbit in astronomical units (AU), 1 Earth-Sun distance  P is the period of the orbit in years (yr)

Orbits Star A Star B Center of Mass a x rBrB rArA

Finding Masses  M A = (M total )(r B ) / (r A + r B )  Where again mass is in solar masses and r is in AU   Newton “discovered” gravity by thinking about Kepler’s laws  He showed that gravitational force depends only on mass and distance

Spectroscopic Binaries   We have to try and find binaries in other ways   We can’t resolve two individual stars (they are too close together)  however, we see two sets of spectral lines

Spectroscopic Binary Motion   Can get the velocity of the orbit from the Doppler shift   Can also get the period of the star from the Doppler shift  Time for Doppler shift to go from zero to max away to zero to max towards to zero

Spectroscopic Binary in Action

Velocities of Binary Components

Spectroscopic Binary Masses   Velocities highest in edge-on system and go to zero in face-on system  We only see component of Doppler shift for motion towards and away from us   Assume a random distribution of inclinations

Masses of Stars  Compare mass to position on HR diagram  Main sequence:   Medium-bright yellow stars have solar masses (M ~ M sun )   White dwarfs   Giants  Large range of masses

Masses on the HR Diagram

Mass Distribution  There is a relationship between mass and luminosity for main sequence stars: L = M 3.5   White dwarfs are very dense   Giants have low density 

Next Time  No homework due Monday  But there is homework due Wednesday  First quiz Monday!  Study guide on web page  Bring (real) calculator and pencil