BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9...
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![Page 1: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/1.jpg)
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
![Page 2: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/2.jpg)
Binary Center of MassBalance
point
![Page 3: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/3.jpg)
Binary Separation a = rA + rB
Visual
Binary
Star
![Page 4: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/4.jpg)
SpectroscopicBinary
From Doppler Shift
![Page 5: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/5.jpg)
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
![Page 6: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/6.jpg)
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
![Page 7: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/7.jpg)
Spectroscopic ParametersCenter of Mass
Low Mass Star Velocity Amplitude
High Mass Star Velocity Amplitude
Vel
ocit
y
Time
![Page 8: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/8.jpg)
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
![Page 9: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/9.jpg)
InclinationK velocity = amplitude of radial velocities
v sin(i)
v = velocity
i = 90 degrees, edge on
i = 0 degrees, pole face
![Page 10: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/10.jpg)
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.
![Page 11: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/11.jpg)
Spectroscopic Orbit
Center of Mass Velocity?
![Page 12: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/12.jpg)
Spectroscopic Orbit
Orbital Period?
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Spectroscopic Orbit
![Page 14: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/14.jpg)
Spectroscopic Orbit
K velocities?
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Spectroscopic Orbit
K2 = 115 - 40 = 75
![Page 16: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/16.jpg)
Spectroscopic Orbit
K1 = 65 - 40 = 25
![Page 17: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/17.jpg)
Spectroscopic OrbitK2/K1= M1/M2 = 75/25 = 3
One Star is 3 times more massive than the other.
![Page 18: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/18.jpg)
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)
![Page 19: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/19.jpg)
Algol ( Perseus)Light Curve
Light Intensity
versus
Time
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Eclipsing Binary Light Curve
AB
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Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
![Page 22: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/22.jpg)
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
![Page 23: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/23.jpg)
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
![Page 24: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/24.jpg)
Eclipsing Binary Light Curve
AB
LA + LB
LA + LB
LB + f LA
LA Only
![Page 25: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/25.jpg)
Simple Eclipsing Binary
![Page 26: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/26.jpg)
Unequal Temperature and Size
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Star Spots
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Light Curve Fit
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Light Curve Varieties
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Light Curve Contacts
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Light Curve Contacts
t1
Time interval (t2 - t1) ~ size of “orange” star
t3 t4t2
![Page 32: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/32.jpg)
Light Curve Contacts
t1
Time interval (t3 - t1) ~ size of “yellow” star
t3 t4t2
![Page 33: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/33.jpg)
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.
![Page 34: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/34.jpg)
Determining Radii
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Intrinsic Luminosity L = 4R2T4
Radius obtained from spectroscopic orbit with
eclipse light curve.
Temperature obtained from observations of spectrum.
![Page 36: BINARIES Read Your Textbook: Foundations of Astronomy –Chapter 10 Homework Problems Chapter 9 –Review Questions: 1, 4, 5, 7 –Review Problems: 1-5 –Web.](https://reader036.fdocuments.in/reader036/viewer/2022062804/56649f005503460f94c16319/html5/thumbnails/36.jpg)
Fundamental Stellar Parameters• Spectra
– Distance– Temperature– Chemical Composition– Luminosity (if distance is known)– Velocity
• Binaries– Orbital Velocities– Sizes– Masses– Luminosity
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Fundamental Stellar Parameters