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