to infinity and beyond - vanderbilt university...the cosmic distance ladder • parallax • main...
TRANSCRIPT
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To Infinity and Beyond
Dr. Billy Teets, Ph.D.Outreach Astronomer & Acting DirectorVanderbilt University Dyer Observatory
Tuesday, October 13, 2020
A Few of the Ways That astronomers determine
distances
_________________________
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The Cosmic Distance Ladder
• Parallax
• Main Sequence Fitting
• Cepheid & RR Lyrae Variables
• Type Ia Supernovae
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Parallax
Determining DistanceFrom Changing Perspectives
Image Credit: Alexandra Angelich (NRAO/AUI/NSF)
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Parallax
Image Source: Slideplayer.com
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Parallax
d
r
p
Small Angle Approximation:
Tan(p) = r/d
Thus, p ≈ r/d for small angles
Image Source: Slideplayer.com
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Background – Angles
360 degrees in a complete circle, 180 degrees from one horizon to another
Index finger at arm’s length ~ 1 degree (full moon is one-half degree)
Subdivide degrees into arcminutes, arcseconds, etc.
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds
1 arcsecond = 1000 milli-arcseconds
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Parallax
d
r
p
• Parallax Equation: p ≈ r/d
• Rearranged: d = r/p
• r = 1 Astronomical Unit
• At a distance of 206,265 AU, Earth appears to be 1” from Sun.
• 206,265 AU = 1 parsec (1 pc) = 3.26 light-years
• Equation becomes d=1/p
• Thus, a parallax angle of 1” means object is 1 parsec away.
• A parallax angle of 0.1” means the object is 10 parsecs away.
Image Source: Slideplayer.com
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First Measured Parallax –
61 Cygni
Animation Credits: Wikipedia/IndividusObservantis
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Tycho Brahe and Parallax
Tycho Brahe’s instruments allowed for
much higher precision astrometry.
1546-1601
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Parallax with Hipparcos
Produced first massive catalog of
high-precision stellar positions and
proper motions for 118,218 stars –
released in 1997.
Precision of ~1 milli-arcsecond.
Tycho 1 and 2 catalogs bring final
total up to 2,539,913 stars.
Stars to magnitude 11.
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The Gaia Mission
Successor to
HIPPARCOS
Helping to determine
positions of over 1 billion
stars.
Highest precision
position measurement
accuracy ~ 20 micro-
arcseconds
Image Credit: ESA
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Two Million Stars from Gaia
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Main Sequence
Fitting
Using one star cluster to find the distance to
another star cluster
Image Credit: Roth Ritter
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Background – Magnitudes
Apparent Magnitude (“magnitude”) - Measurement
of how bright an object appears.
Magnitudes follow an inverse logarithmic scale (bigger
number is fainter):
Sun = -26.7
Full Moon = -12.7
Venus (at max) = - 4.2
Mars (tonight) = -2.5
Sirius = -1.46
Faintest naked-eye star ~ +6 to +7 (note positive value)
Faintest object seen by HST ~ +30
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The Hertzsprung-Russell Diagram
• Plot of star luminosity versus temperature
• Hot Stars – Left
• Cool Stars – Right
• Faint Stars – Bottom
• Bright Stars – Top
• Mass increases from bottom-left to top-right along MS
Image Source: Universe Today
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Main Sequence Fitting
• One cluster has a known distance, other cluster has unknown distance.
• Idea: Plot two clusters on HR Diagrams
• Overlay HR Diagrams and Main sequences.
• Corresponding apparent and absolute magnitudes yield distance.
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Main Sequence Fitting
• Analogy: Box of assorted light bulbs
• Bulbs have various wattages (luminosities)
• One illuminated bulb from unknown distance does not tell you bulb wattage.
• Turn on all bulbs – then you can tell which bulb is which.
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Main Sequence Fitting
• First, find nearby cluster distance (e.g., Hyades)
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Main Sequence Fitting
• Plot all of the stars on HR Diagram
• With known distance, we can convert apparent brightness to true luminosity as well
• Locate MS
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Main Sequence Fitting
• Next, locate a “Mystery Cluster” (e.g., Pleiades) of unknown distance
Image Credit: NASA/ESA/AURA/Caltech
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Main Sequence Fitting
• Plot Mystery Cluster’s stars on HR Diagram
• Locate MS
Note: Just have apparent brightness, not true luminosity
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Main Sequence Fitting
• Invoke Cosmological Principle
• Star clusters are made mostly of hydrogen and helium. Very small differences in “metals”
• Star formation mechanisms should be the same for all clusters
• Overlay our HR diagrams
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Main Sequence Fitting
• Overlay clusters and align MS
• Mystery Cluster’s apparent magnitude coincides with calibration cluster’s absolute magnitude
• m-M=-5+5log(d)
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Cepheid Variables
Image Credit: Digitized Sky Survey
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Pulsating Variables
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Cepheid Variable – RS Puppis
Image Credit: NASA, ESA, G. Bacon (STScI), the Hubble Heritage Team (STScI/AURA)-Hubble/Europe Collaboration, and H. Bond (STScI and Pennsylvania State University)
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Light Echoes from RS Puppis
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Pulsating Variable Stars
• Helium acts as a temperature regulator – Helium Ionization Zone.
• Rising temperature doubly ionizes helium – energy is absorbed, which ionizes the helium.
• Gas opacity increases as temperature rises due to the freed electrons of the ionized gas.
• Trapped energy causes star to expand to cool.• Cooling helium recombines with electrons, gas
becomes more transparent to light, energy flows out• Star shrinks and heats up.• Cycle repeats.
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Pulsating Variables
• Henrietta Leavitt recognizes Period-Luminosity Relationship.
• Longer period = greater max luminosity.
• Know true and apparent luminosities.
• Can determine distances.• Cepheids are giants – seen
great distances. Henrietta Leavitt(1868-1921)
Image Credit: Harvard-Smithsonian Center for Astrophysics
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Period-Luminosity Relationship
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Edwin Hubble Resizes Universe
(1889-1953)Image Credits: Mount Wilson Observatory Historical Archive,
Western Washington University
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A Cepheid in Andromeda
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A Cepheid in Andromeda
Images Credits: NASA / ESA / Hubble Heritage Team
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Type IaSupernovae
Image credit: NASA, ESA, A. Riess and the SH0ES team
Acknowledgement: Mahdi Zaman
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Low-Mass Stars Die Gently
• Stars below 8M
do not have enough mass to go supernova.
• As star becomes distended, gently sloughs off outer layers over thousands of years.
• Core collapses to become a white dwarf, a planet-size body of degenerate matter.
• Forms a planetary nebula.
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A Couple of Planetary Nebulae
Left Image credit: NASA/Andrew Fruchter (STScI) Right Image Credit: NASA, ESA, HEIC, and The Hubble Heritage Team (STScI/AURA); Ack.: R. Corradi (INGoT, Spain) and Z. Tsvetanov (NASA)
Clown Nebula – NGC 2392 Cat’s Eye Nebula – NGC 6543
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A Nearby White Dwarf
• Sirius, a binary star system.
• Only about 9 light-years away.
• Brightest star in night sky.
• Companion is a white dwarf of approximately 1 solar mass.
Image Credit: NASA, ESA, H. Bond (STScI), and M. Barstow (University of Leicester)
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Type Ia Supernovae
Image Credit: NASA, ESA, M. Kornmesser and M. Zamani (ESA/Hubble), and A. Riess (STScI/JHU) and the SH0ES team
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Type Ia Supernovae
Credit: ESO
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Roche Lobe Overflow
Images Credit: A. Somily
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Type Ia Supernovae as Distance Markers
• White dwarfs come in various sizes
• Mass of white dwarf builds up over time through numerous novae.
• As mass is added, temperature increases.
• Mass may eventually reach 1.4 solar masses.
• Temperature is hot enough to fuse carbon.
• Degenerate star tries to fuse all at once.
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Type Ia Supernovae as Distance
Markers
Supernovae should occur at the same mass
Same mass objects exploding – same luminosity
Know the true luminosity of one = know the luminosity of others
Can be seen for billions of light-years