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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
_________________________
The Cosmic Distance Ladder
• Parallax
• Main Sequence Fitting
• Cepheid & RR Lyrae Variables
• Type Ia Supernovae
Parallax
Determining DistanceFrom Changing Perspectives
Image Credit: Alexandra Angelich (NRAO/AUI/NSF)
Parallax
Image Source: Slideplayer.com
Parallax
d
r
p
Small Angle Approximation:
Tan(p) = r/d
Thus, p ≈ r/d for small angles
Image Source: Slideplayer.com
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
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
First Measured Parallax –
61 Cygni
Animation Credits: Wikipedia/IndividusObservantis
Tycho Brahe and Parallax
Tycho Brahe’s instruments allowed for
much higher precision astrometry.
1546-1601
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.
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
Two Million Stars from Gaia
Main Sequence
Fitting
Using one star cluster to find the distance to
another star cluster
Image Credit: Roth Ritter
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
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
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.
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.
Main Sequence Fitting
• First, find nearby cluster distance (e.g., Hyades)
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
Main Sequence Fitting
• Next, locate a “Mystery Cluster” (e.g., Pleiades) of unknown distance
Image Credit: NASA/ESA/AURA/Caltech
Main Sequence Fitting
• Plot Mystery Cluster’s stars on HR Diagram
• Locate MS
Note: Just have apparent brightness, not true luminosity
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
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)
Cepheid Variables
Image Credit: Digitized Sky Survey
Pulsating Variables
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)
Light Echoes from RS Puppis
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.
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
Period-Luminosity Relationship
Edwin Hubble Resizes Universe
(1889-1953)Image Credits: Mount Wilson Observatory Historical Archive,
Western Washington University
A Cepheid in Andromeda
A Cepheid in Andromeda
Images Credits: NASA / ESA / Hubble Heritage Team
Type IaSupernovae
Image credit: NASA, ESA, A. Riess and the SH0ES team
Acknowledgement: Mahdi Zaman
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.
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
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)
Type Ia Supernovae
Image Credit: NASA, ESA, M. Kornmesser and M. Zamani (ESA/Hubble), and A. Riess (STScI/JHU) and the SH0ES team
Type Ia Supernovae
Credit: ESO
Roche Lobe Overflow
Images Credit: A. Somily
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.
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