Transcript Visual Binary - Purdue Physics

Binary Star Systems
• Orbit of each star is an ellipse, with focus (F) located at the
center of mass.
• The stars are always located directly opposite the center of
mass.
Kepler’s 3rd law:
(orbital period)2 =
const. x (semimajor
axis)3
Center of mass
equation:
m1 d1 = m2 d2
Kepler’s third law for near-circular orbits
( m1 + m2 ) P2 = 4 π2 G-1 ( d1 + d2 )3
where P = orbital period of each star around the center of
mass
If the orbits are non-circular, use semi-major axes instead of d
What quantities would you need to measure in order to
determine the mass of each star?
Binary system simulator
http://astro.unl.edu/naap/ebs/animations/ebs.html
Visual Binary
• Can resolve the two stars individually with a telescope.
Not a chance superposition since one star moves on an
elliptical orbit relative to the other
Astrometric Binaries
• Only one star can be resolved by telescopes
• Companion star causes the main one to wobble
• Technique also used to find exoplanets
Sirius astrometric binary system
• Orbits are to scale, but the star sizes are not
Center of
mass
Spectroscopic Binaries
• A star in a binary
system will move
toward and away
from us as it orbits
the center of mass
• We can detect these motions via Doppler
shifts of lines in the star’s spectrum
𝑟𝑎𝑑𝑖𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
𝑟𝑒𝑠𝑡 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
If only the two radial velocities are known, then we can get:
𝑃 v1,r + v2,r
𝑚1 + 𝑚2 =
2𝜋𝐺
sin 𝑖
3
Where v1,r is the component of the star’s velocity along
your line of sight, and i is the inclination angle of the orbit.
i = 0° means the binary is in the plane of the sky
• If only one radial velocity is known, a useful
quantity is the mass function:
P v1,r 3
( 𝑚2 sin 𝑖)3
𝑓(𝑚1 , 𝑚2 ) =
=
2𝜋G
(𝑚1 + 𝑚2 )2
• If the inclination angle i of the orbit is known,
then we can derive the mass ratio 𝑚1 /𝑚2
Eclipsing Binaries
• The ‘gold standard’ of binary systems. Since
inclination ≈ 90°, you can determine the
orbits, masses, & radii of both stars.
II Persei