Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure”...
Transcript of Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure”...
![Page 1: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/1.jpg)
Orbits
![Page 2: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/2.jpg)
Orbits• Angular momentum
mass x velocity x lever arm
Conserved for isolated objects
Change requires torque: force x lever arm
Demo
![Page 3: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/3.jpg)
Orbits• Kepler orbits:
Outer orbits have higher angular momentum
• Angular momentum “barrier”:
Say particle gets kick inward
⇒ smaller lever arm = faster velocity
faster velocity means more centrifugal force
⇒ Particle moves back out
• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/kepler6.htm
![Page 4: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/4.jpg)
Schwarzschild orbits• Angular momentum still conserved
• The only difference is close to BH:
Gravity stronger and stronger
⇒ Gravity can overwhelm angular momentum
• What are the possible orbits?
Circular orbits?
Ellipses?
“Plunging” orbits?
• http://www.fourmilab.ch/gravitation/orbits/
![Page 5: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/5.jpg)
• What are the possible orbits?
Circular orbits: stable only outside 3 x RS
Ellipses: not closed
Hyperbolic orbits: With precession
“Plunging” orbits: orbits inside 3 x RS
Schwarzschild orbits
eventhorizon
“plunging region”
RS unstable stable
![Page 6: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/6.jpg)
• What are the possible orbits?
Circular orbits: stable only outside 3 x RS
Ellipses: not closed
Hyperbolic orbits: With precession
“Plunging” orbits: orbits inside 3 x RS
Schwarzschild orbits
eventhorizon
“plunging region”
RS 3xRS
![Page 7: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/7.jpg)
• Photon (=light) orbits:
Photon can be on unstable circular orbits at 1.5 x RS
Light bending: Green (hyperbolic) orbits
Multiple wraps are possible!
Schwarzschild orbits
eventhorizon
RS 1.5xRS
![Page 8: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/8.jpg)
NOTE: this is not a real image!
Light bendingWhat the sky behind a black hole would look like
![Page 9: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/9.jpg)
How to find black holes
![Page 10: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/10.jpg)
How to find black holes• So far:
Black holes themselves should not emit light
Must be massive and/or really small
Orbits of surrounding objects must be perturbed
![Page 11: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/11.jpg)
How to find black holes• Strategy #1 for finding black holes:
Look for objects whose trajectory is perturbed by a massive dark object
![Page 12: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/12.jpg)
How to find black holes• Strategy #1 for finding black holes:
Look for objects whose trajectory is perturbed by a massive dark object
Measure the mass using Kepler’s laws
“Measure” radius (must be smaller than orbit)
![Page 13: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/13.jpg)
The Galactic center• 17 years of observation:
Stars orbit a dark object
Mass: 3.6 million suns (“supermassive”)
Radius < size of earth orbit
Black hole!
Genzel et al. 2005
![Page 14: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/14.jpg)
The Galactic center• A very dim object
only ~ 100 solar luminosities
“Blackest black hole” known to date!
One of the best cases for existence of black holes
Genzel et al. 2005
![Page 15: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/15.jpg)
hidden inside this bright clump (not from black hole)
NASA / Chandra public image archive
The Galactic center
![Page 16: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/16.jpg)
Other galactic centers...
• ...also host “supermassive black holes”
• More massive galaxies host more massive black holes...
• This method is hard!
• Have to know where to look
• Takes a long time
• Have to resolve stars (only nearby galaxies)
![Page 17: Orbits - UW Madison Astronomy Departmentheinzs/Homepage/PLATO_files/lecture_5.pdf · “Measure” radius (must be smaller than orbit) ... Stars orbit a dark object Mass: 3.6 million](https://reader034.fdocuments.us/reader034/viewer/2022051815/603d94a3892cb677344c54a9/html5/thumbnails/17.jpg)
Black hole formation• Knowing where black holes come from could
help us find them...
• Slight complication:
We don’t know where “supermassive” black holes come from
We do know how to make “small” black holes...