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To Infinity and Beyond

A Few of the Ways That astronomers determine distances ______

Dr. Billy Teets, Ph.D. Outreach Astronomer & Acting Director Vanderbilt University Dyer Observatory

Tuesday, October 13, 2020 The

• Parallax

• Fitting

• Cepheid & RR Lyrae Variables

• Type Ia Supernovae Parallax

Determining Distance From Changing Perspectives

Image Credit: Alexandra Angelich (NRAO/AUI/NSF) Parallax

Image Source: Slideplayer.com Parallax

Small Angle Approximation:

Tan(p) = r/d

Thus, p ≈ r/d for small angles d p

r 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

• 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 (1 pc) = 3.26 light-

• Equation becomes d=1/p d • Thus, a parallax angle of 1” p means object is 1 parsec away.

• A parallax angle of 0.1” means the object is 10 away.

r 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 .

1546-1601 Parallax with Hipparcos

 Produced first massive catalog of high-precision stellar positions and proper motions for 118,218 – 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 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 cluster to find the distance to another star cluster

Image Credit: Roth Ritter Background – Magnitudes

(“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 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 () • 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

• m-M=-5+5log(d) Cepheid Variables

Image Credit: Digitized Sky Survey Pulsating Variables – RS

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

Image Credits: Mount Wilson Observatory Historical Archive, (1889-1953) Western Washington University A Cepheid in Andromeda A Cepheid in Andromeda

Images Credits: NASA / ESA / Hubble Heritage Team Type Ia Supernovae

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 . A Couple of Planetary Nebulae

Clown Nebula – NGC 2392 Cat’s Eye Nebula – NGC 6543

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) 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. Supernovae should occur at the same mass

Same mass objects Type Ia exploding – same Supernovae luminosity Know the true as Distance luminosity of one = know the luminosity Markers of others

Can be seen for billions of light- years