binary stars how they help us to determine the mass of stars and the size of our galaxy
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BINARY STARS
How they help us to determine
the mass of stars and the size of our galaxy.
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How do they form?
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Mizar A and B are visual binaries.
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The very bright star, Sirius, is actually a visual binary, too.
• Sirius is the main star in the constellation Canis Major, so it is called Alpha Canis Majoris.
• It is actually a blue-white giant (A) with a white dwarf companion (B).
• The elliptical orbit has been well-plotted out.
ORION
SIRIUS
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The orbit of Sirius B:
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Revolution around the center of mass
• In reality both objects revolve around a common point, known as the center of mass.
• The center of mass is closer to the more massive object and farther from the less massive one.
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Binary star orbits are usually double ellipses:
• The center of mass (•) is close to the massive blue star. It revolves around in a small elliptical orbit.
• The less massive yellowyellow star revolves in a much larger orbit.
• Notice the pattern of a binary system in motion. Visual Binary Animation
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20 = 4
5 1
4:1 ratio in mass
Ratio of the masses
Star AStar B
5 AU 20 AU
DB = MA
DA MB
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Kepler’s Law….Modified
• In the Solar System, we ignore the mass of the sun and the planets (since M1 = 1 and M2 is very small).
• With binary stars, the masses must be taken in account.
• If we know D and P, we can determine the masses of both stars.
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Finding the masses of binary stars with Kepler’s Law
M1 + M2 = D3
P2
MA + MB = 103
52
MA + MB =
1000 ÷25 = 40 suns
Star A
Star B
D = 10 AU
P = 5 yrs
MA = 32 suns
MB = 8 suns
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Eclipsing Binary Stars
The stars have different luminosities, and they eclipse each other as they revolve around the center of mass.
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The stars are too close to be seen separately.
• When an eclipse occurs, you can tell which star is brighter.
• The flat bottoms (2,4) indicate that one star is smaller than the other.
• When the cycle repeats, you can tell the period of revolution.
Eclipsing Binary Animation
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Spectroscopic Binaries
• We can’t see their orbits or see eclipses, but we can observe Doppler shifts in the spectrum.
• These shifts occur when stars move toward us (blue shift) or away from us
(red shift).
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Revolving Stars cause Doppler shifts only when moving away or toward the observer. The larger the shift the higher the velocity.
Spectroscopic Binary Animation
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How does this help us with non-binary stars?
It can help to determine their masses, luminosities, and their distances from Earth.
K3 star
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Find luminosity from the H-R Diagram
The K5 (orange star) has a luminosity of 0.1 (10-1) suns.
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Mass-Luminosity Graph
• Since the luminosity of this K5 star is 10-1 (0.1) its mass is around 0.6 sun.
• This is a red-orange dwarf (on the main sequence).
• This method works only for main sequence stars.
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Distance is found from the difference between the apparent and the absolute magnitudes by the formula:
D = 10(Mapp - Mabs + 5)/5
D = 10(2 - 7 + 5)/5 = 100 =
1 parsec
L = 0.1
Mabs = 7
Mapp = 3
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Try this yourself!
You find an A0 star. Use the H-R diagram to find its luminosity.
Then find its mass from this graph.
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Now find the distance…
What is its absolute magnitude?
Suppose we see this star as a
fifth magnitude star.
Substitute into this formula:
D = 10(Mapp - Mabs + 5)/5
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Hate Math? Try this method…
• Determine the difference between the apparent and absolute magnitude of this A0 star.
• Then read the result off of this graph.
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CONCLUSIONS!• From the study of binary stars we can
determine the masses of stars.• If we know the mass of a main-sequence star,
we can determine its luminosity from a graph or by formula.
• The H-R diagram can be used to find absolute magnitude, temperature, and spectral class.
• We can estimate the distance of the star from the magnitude difference graph, or by using the second formula.