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BINARIES• Read Your Textbook: Foundations of Astronomy
– Chapter 10
• Homework Problems Chapter 9– Review Questions: 1, 4, 5, 7– Review Problems: 1-5– Web Inquiries: 1
• Homework Problems Chapter 10– Review Questions: 1, 2, 4, 6-8– Review Problems: 1-4, 8– Web Inquiries: 2
Binary Center of MassBalance
point
Binary Separation a = rA + rB
Visual
Binary
Star
SpectroscopicBinary
From Doppler Shift
Spectroscopic OrbitThis represents the orbit of the star that is farthest
from the center of mass. Its velocity amplitude is
higher. It is the lower mass star.
Vel
ocit
y
Time
Spectroscopic OrbitThis represents the orbit of the star that is closest
to the center of mass. Its velocity amplitude is
smaller. It is the higher mass star.
Vel
ocit
y
Time
Spectroscopic ParametersCenter of Mass
Low Mass Star Velocity Amplitude
High Mass Star Velocity Amplitude
Vel
ocit
y
Time
InclinationK velocity = amplitude of radial velocity (m/s)
Doppler effect is maximized for an “edge-on” system;
non-existent for a “pole-on” system.
Inclination ~ 90o
Inclination ~ 0o
InclinationK velocity = amplitude of radial velocities
v sin(i)
v = velocity
i = 90 degrees, edge on
i = 0 degrees, pole face
Spectroscopic Parametersvelocity = velocity of Center of Mass (CoM)
K velocity = amplitude of radial velocity (v sin i)
P = period
Mass ratio M2/M1 = K1/K2
Smaller star orbits farther from the CoM,
Larger star is closer from the CoM.
Smaller star has large K velocity.
Spectroscopic Orbit
Center of Mass Velocity?
Spectroscopic Orbit
Orbital Period?
Spectroscopic Orbit
Spectroscopic Orbit
K velocities?
Spectroscopic Orbit
K2 = 115 - 40 = 75
Spectroscopic Orbit
K1 = 65 - 40 = 25
Spectroscopic OrbitK2/K1= M1/M2 = 75/25 = 3
One Star is 3 times more massive than the other.
Eclipsing Binary
Light Intensity variations are observed
because of blocking of light by each of the
stars in the system if inclination is large enough.
Systems are edge-on or nearly edge-on as seen from
earth. (i.e. inclinations are ~ 90 degrees)
Algol ( Perseus)Light Curve
Light Intensity
versus
Time
Eclipsing Binary Light Curve
AB
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
Simple Eclipsing Binary
Unequal Temperature and Size
Star Spots
Light Curve Fit
Light Curve Varieties
Light Curve Contacts
Light Curve Contacts
t1
Time interval (t2 - t1) ~ size of “orange” star
t3 t4t2
Light Curve Contacts
t1
Time interval (t3 - t1) ~ size of “yellow” star
t3 t4t2
Size Determinations 2 RA = (VA+VB ) ( t2 - t1 )
2 RB = (VA+VB ) ( t3 - t1 )
Velocities obtained from spectroscopic orbit.
Contact times obtained from eclipse light curve.
The radii of the stars are then calculated to yield their
size.
Determining Radii
Intrinsic Luminosity L = 4R2T4
Radius obtained from spectroscopic orbit with
eclipse light curve.
Temperature obtained from observations of spectrum.
Fundamental Stellar Parameters• Spectra
– Distance– Temperature– Chemical Composition– Luminosity (if distance is known)– Velocity
• Binaries– Orbital Velocities– Sizes– Masses– Luminosity
Fundamental Stellar Parameters
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