Astronomical Distances Blendon Middle School April 13 2010

Astronomical Distances Blendon Middle School April 13, 2010 Dr. Uwe Trittmann Otterbein College

Astronomical Distances • Locations in the sky are easy to measure: 2 angles • Distances from observer are hard (one length) Together they give the location of an object in three-dimensional space

The Trouble with Angles • Angular size of an object cannot tell us its actual size – depends on how far away it is • Sun and Moon have very nearly the same angular size (30' = ½ ) when viewed from Earth

Angles and Size

Without Distances … • We do not know the size of an object • This makes it hard to figure out the “inner workings” of an object • We can’t picture the structure of the solar system, galaxy, cosmos

The Universe is structured on different length scales Stars nebulae molecular clouds star clusters THE UNIVERSE clusters and superclusters galaxies like the Milky Way quasars Solar System black holes pulsars Sun planets terrestrial jovian moons comets meteors asteroids dust voids Big --------------- small

Powers of Ten – From Man to Universe - 100 meters =1 meter The Human Scale

Street Size 103 meters =1000 m = 1 km Harbour

City Size 104 meters = 10, 000 m =10 km Chicago

Planet Size: thousands of km • 1000 km = 1, 000 m = 1 million meters

Star Size: 1, 000, 000 m =1 billion meters • The Sun (a typical star): diameter 1. 4 million km.

Solar System Scale Venus, Earth, Mars Orbits 1011 meters =100, 000, 000 m =100, 000 km = about 1 A. U. (Astronomical Unit)

Farther out: Nebulae – Where stars are born. . .

… and die ! • How big ARE these? • They APPEAR tiny!

Black Holes – Dead Stars • How big is a black hole?

Galaxies • How big is a galaxy? • Are all galaxies the same size?

Clusters of Galaxies • What is the distance between galaxies?

The Universe • How big is the Universe? • Does this question make sense? • If yes, can we answer it while living IN the universe?

Different lengths scales Different length units • Human scale: meters (yards) – Human height: 1. 8 m • Geographical scale: kilometers (miles) – Distance to Cincinnati: 100 mi • Solar system scale: Astronomical Unit – Distance Earth-Sun: 1 A. U. • Intragalactic scale: lightyears (parsecs) – Next star: 4 lightyears • Intergalactic scale: millions of lightyears (Megaparsecs) – Andromeda galaxy: 2. 2 million lightyears = 0. 67 Mpc • Cosmological Scale: billions of ly (Gigaparsecs) – Edge of observable universe: about 15 billion ly

Different lengths scales Different length measurements • • Human scale: yardstick Geographical scale: triangulation Solar system scale: Radar ranging Intragalactic scale: – Close stars: stellar parallax – Far: spectroscopic parallax • Intergalactic scale: – Close: Variable stars – Far: Tully-Fisher relation • Cosmological Scale: Hubble’s Law

Astronomical Distance Measurements • Fundamental technique uses triangulation: • Objects appear to move with respect to background if looked at from different vantage points • Try looking at you thumb with only your left, then right eye • The more thumb jumps, the closer it is! • Measure “jump”, get distance • See: Link, Link 2

Distances to the Stars 1. Measurements ½ year apart! 2. Parallax can be used out to about 100 light years • The bigger the parallactic angle, the closer the star! – – • A star with a measured parallax of 1” is 1 parsec away 1 pc is about 3. 3 light years The nearest star (Proxima Centauri) is about 1. 3 pc or 4. 3 lyr away – Solar system is less than 1/1000 lyr

Insight • Some stars are close to us (4 ly), other are far away (1000 ly) • This means that some stars appear dim but are actually very bright • That means that stars have different sizes, temperatures, life expectancy…

Our Stellar Neighborhood

Scale Model • If the Sun = a golf ball, then – – – Earth = a grain of sand The Earth orbits the Sun at a distance of one meter Proxima Centauri lies 270 kilometers (170 miles) away Barnard’s Star lies 370 kilometers (230 miles) away Less than 100 stars lie within 1000 kilometers (600 miles) • The Universe is almost empty! • Hipparcos satellite measured distances to nearly 1 million stars in the range of 330 ly • almost all of the stars in our Galaxy are more distant

Luminosity and Brightness • Luminosity L is the total power (energy per unit time) radiated by the star, actual brightness of star, cf. 100 W lightbulb • Apparent brightness B is how bright it appears from Earth – Determined by the amount of light per unit area reaching Earth – B L / d 2 • Just by looking, we cannot tell if a star is close and dim or far away and bright

Brightness: simplified • 100 W light bulb will look 9 times dimmer from 3 m away than from 1 m away. • A 25 W light bulb will look four times dimmer than a 100 W light bulb if at the same distance! • If they appear equally bright, we can conclude that the 100 W lightbulb is twice as far away!

Same with stars… • Sirius (white) will look 9 times dimmer from 3 lightyears away than from 1 lightyear away. • Vega (also white) is as bright as Sirius, but appears to be 9 times dimmer. • Vega must be three times farther away • (Sirius 9 ly, Vega 27 ly)

Distance Determination Method • Understand how bright an object is (L) • Observe how bright an object appears (B) • Calculate how far the object is away: B L / d 2 So L/B d 2 or d √L/B

Understand Star Brightness: Classify Stars by their Temperature (Color) Class O B A F G K M Temperature 30, 000 K 20, 000 K 10, 000 K 8, 000 K 6, 000 K 4, 000 K 3, 000 K Color blue bluish white yellow orange red Examples Rigel Vega, Sirius Canopus Sun, Centauri Arcturus Betelgeuse The hotter the bluer!

Color. Luminosity Correlation • Hertzprung-Russell Diagram is a plot of absolute brightness (vertical scale) against spectral type or temperature (horizontal scale) • Most stars (90%) lie in a band known as the Main Sequence

Spectroscopic Parallax • From the color of a main sequence star we can determine its absolute brightness • Then, from the apparent brightness compared to absolute luminosity, we can determine the distance d √L/B

Insight • We now know how far away stars are, so we know how big they are, and we can understand how they work. • We understand how big our galaxy is (100, 000 ly) and that some “nebulae” are galaxies like our own

Sizes of Stars • Dwarfs – Comparable in size, or smaller than, the Sun • Giants – Up to 100 times the size of the Sun • Supergiants – Up to 1000 times the size of the Sun • Note: Temperature (Color) changes!

Galaxies are close together – compared to their size The Local Group The Virgo Cluster

Aside: What are stars made out of ? • 90% of the universe is Hydrogen • The rest is mostly Helium • How do we know? By identifying the fingerprints of the elements, aka the light they send out!

Spectral Lines – Fingerprints of the Elements • Can use this to identify elements on distant objects! • Different elements yield different emission spectra

Origin of Spectral Lines: Emission Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”

Origin of Spectral Lines: Absorption Cool gas absorbs light at specific frequencies “the negative fingerprints of the elements”

Use Spectra to measure the Size of the Universe • Measure spectrum of galaxies and compare to laboratory measurement • lines are shifted towards red • This is the Doppler effect: Red-shifted objects are moving away from us

Using Redshift: Hubble’s Law • The final rung on the cosmic distance ladder • Hubble’s observations (1920’s): – Light from distant galaxies is redshifted – The more distant the galaxy, the greater the red-shift • Interpretation: – Galaxies are moving away from us – More distant galaxies are moving faster • The universe is expanding, carrying the galaxies with it!

Hubble’s Law Velocity = H 0 Distance = Velocity /H 0 • H 0 = (65 ± 15) km/sec/Mpc is Hubble’s constant • Compare to distance = velocity time • Appears the universe “exploded” from a single point in the past – the Big Bang • Age of the universe is 1/H 0 or about 14 billion years

The Latest Surprise • Type Ia Supernovae are standard candles • Can calculate distance from brightness • Can measure redshift • General relativity gives us distance as a function of redshift for a given universe Supernovae are further away than expected for any decelerating (“standard”) universe

Supernova Data magnitude • Solid line is best fit to data redshift

Expansion of the Universe • Old lore: – Either it grows forever – Or it comes to a standstill – Or it falls back and collapses (“Big crunch”) – In any case: Expansion slows down! Surprise of the year 1998 (Birthday of Dark Energy): All wrong! It accelerates!

Additional Material

Powers of Ten – From Man to Universe - 100 meters =1 meter The Human Scale

Powers of Ten – From Man to Universe - 101 meters =10 meters Lawn and Blanket

Powers of Ten – From Man to Universe - 102 meters =100 meters Highway and Boats

Powers of Ten – From Man to Universe - 103 meters =1000 m Harbour

Powers of Ten – From Man to Universe - 104 meters =10 km Chicago Lakeshore

Powers of Ten – From Man to Universe - 105 meters =100 km Chicago & L. Michigan

Powers of Ten – From Man to Universe - 106 meters =1000 km Lake Michigan

Powers of Ten – From Man to Universe - 107 meters =10000 km The Earth

Powers of Ten – From Man to Universe - 108 meters =100000 km Earth in Space

Powers of Ten – From Man to Universe - 109 meters =1000000 km Moon Orbit

Powers of Ten – From Man to Universe 1010 meters Part of Earth’s Orbit around the Sun

Powers of Ten – From Man to Universe - 1011 meters = ca. 1 A. U. (Astronomical Unit) Earth’s Orbit

Powers of Ten – From Man to Universe - 1012 meters Inner Planets’ Orbits

Powers of Ten – From Man to Universe - 1013 meters Outer Planet’s Orbits

Powers of Ten – From Man to Universe - 1014 meters Solar System in Space

Powers of Ten – From Man to Universe - 1015 meters The Sun “a bright star”

Powers of Ten – From Man to Universe - 1016 meters = ca. 1 ly (light year) The Sun “just another star”

Powers of Ten – From Man to Universe - 1017 m = ca. 10 ly Distinct Stars

Powers of Ten – From Man to Universe - 1018 m = 100 ly Sun in center; Arcturus (α Tauri)

Powers of Ten – From Man to Universe - 1019 m = 1000 ly A cloud of Stars - making up constellations

Powers of Ten – From Man to Universe - 1020 m = ca. 10000 ly Clouds - made out of Stars

Powers of Ten – From Man to Universe 1021 m =100000 ly The Milky Way – Our Galaxy

Powers of Ten – From Man to Universe - 1022 m =1, 000 ly The Milky Way in Space

Powers of Ten – From Man to Universe - 1023 m 6 = 10 x 10 ly The Local Group of Galaxies

Powers of Ten – From Man to Universe - 1024 m 8 = 10 ly The Virgo Cluster of Galaxies (incl. the local Group)

Powers of Ten – From Man to Universe 1025 m = 109 ly The Universe: Many clusters of galaxies – and even more empty space

The “old” Planets Mercury Venus Mars Jupiter Saturn

The “new” Planets Uranus (1781) Neptune (1846) Pluto (1930) (“dwarf planet” since 2006)

Kepler’s Third Law: Relating Orbits The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis: P 2 a 3 a Planet Semi-Major Axis Mercury 0. 387 Venus 0. 723 Earth 1. 000 Mars 1. 524 Jupiter 5. 203 Saturn 9. 539 Uranus 19. 19 Neptune 30. 06 Pluto 39. 53 (A. U. ) Jupiter: 53 / 122 = 125/144 ~ 1 P Orbital Period 0. 241 0. 615 1. 000 1. 881 11. 86 29. 46 84. 01 164. 8 248. 6 (Earth years) Eccentricity ____ 0. 206 0. 007 0. 017 0. 093 0. 048 0. 056 0. 046 0. 010 0. 248 P 2/a 3 1. 002 1. 001 1. 000 0. 999 1. 000 1. 001

The Problem with Kepler’s Third Law • The square of a planet’s orbital period is proportional to the cube of its orbital semi-major axis: P 2 a 3 • But: everything is expressed in “Earth units”, i. e. one Earth year, and one Earth-Sun distance. • Problem: How big are these units?

Practical Problem: Determine the Sun’s Diameter? • Trickier than you might think • We know only how big it appears – It appears as big as the Moon • Need to measure how far it is away – Kepler’s laws don’t help (only relative distances) • Without knowing its size, we don’t know how much energy it can produce, so we can’t figure out how the Sun “works”

Solution: relate to distances on Earth or fundamental constants • Use two observations of Venus transit in front of Sun – Captain Cook in the 1700 s – Hard and not very precise (100, 000 km) • Modern way: bounce radio signal off of Venus (measure traveling time of light) – In the 1960 s, very precise (few centimeters)

Insight • Sun is 109 times bigger than Earth • Up to the 1930 s no mechanism was known to produce so much energy • Know that the Sun fuses hydrogen to helium

More Insight: Understanding Variable Stars yields another Method • Two useful types: – Cepheids – RR Lyrae • Again, method uses insight to get absolute brightness, then concludes distance from apparent brightness

Cepheids • • • Named after δ Cephei Period-Luminosity Relations Used as “standard candles” “yard-sticks” for distance measurement Cepeids in Andromeda Galaxies established the “extragalacticity” of this “nebula”

Cepheids • Henrietta Leavitt (1908) discovers the period-luminosity relationship for Cepheid variables • Period thus tells us luminosity, which then tells us the distance • Since Cepheids are brighter than RR Lyrae, they can be used to measure out to further distances

Properties of Cepheids • Period of pulsation: a few days • Luminosity: 200 -20000 suns • Radius: 10 -100 solar radii

Properties of RR Lyrae Stars • Period of pulsation: less than a day • Luminosity: 100 suns • Radius: 5 solar radii

• Extends the cosmic distance ladder out as far as we can see Cepheids – about 50 million ly • In 1920 Hubble used this technique to measure the distance to Andromeda (about 2 million ly) • Works best for periodic variables Distance Measurements with variable stars

Cepheids and RR Lyrae: Yard-Sticks • Normal stars undergoing a phase of instability • Cepheids are more massive and brighter than RR Lyrae • Note: all RR Lyrae have the same luminosity • Apparent brightness thus tells us the distance to them! – Recall: B L/d 2

Insight: How does our Galaxy look like?

Other Galaxies • Edwin Hubble identified single stars in the Andromeda nebula (“turning” it into a galaxy) • Measured the distance to Andromeda to be 1 million Ly (modern value: 2. 2 mill. Ly) • Conclusion: it is 20 times more distant than the milky way’s radius Extragalacticity! Old theory (Milky Way is the universe) falsified!

The Tully-Fisher Relation • A relation between the rotation speed of a spiral galaxy and its luminosity • The more mass a galaxy has the brighter it is the faster it rotates the wider the spectral lines are • Measuring rotation speed allows us to estimate luminosity; comparing to observed (apparent) brightness then tells us the distance

Electromagnetic Spectrum Energy: low medium high

Electromagnetic Radiation: Quick Facts • There are different types of EM radiation, visible light is just one of them • EM waves can travel in vacuum, no medium needed • The speed of EM radiation “c” is the same for all types and very high ( light travels to the moon in 1 sec. ) • The higher the frequency, the smaller the wavelength ( f = c) • The higher the frequency, the higher the energy of EM radiation (E= h f, where h is a constant)

Visible Light • Color of light determined by its wavelength • White light is a mixture of all colors • Can separate individual colors with a prism

Three Things Light Tells Us • Temperature – from black body spectrum • Chemical composition – from spectral lines • Radial velocity – from Doppler shift

Temperature Scales Fahrenheit Centigrade Kelvin 459 ºF 273 ºC 0 K 32 ºF 0 ºC 273 K Human body temperature 98. 6 ºF 37 ºC 310 K Water boils 212 ºF 100 ºC 373 K Absolute zero Ice melts

Black Body Spectrum • Objects emit radiation of all frequencies, but with different intensities Ipeak Higher Temp. Ipeak Lower Temp. fpeak<fpeak

Cool, invisible galactic gas (60 K, fpeak in low radio frequencies) Dim, young star (600 K, fpeak in infrared) The Sun’s surface (6000 K, fpeak in visible) Hot stars in Omega Centauri (60, 000 K, fpeak in ultraviolet) The higher the temperature of an object, the higher its Ipeak and fpeak

Activity: Black Body Radiation • • • Pick up a worksheet Form a group of 3 -4 people Work on the questions on the sheet Fill out the sheet and put your name on top Hold on to the sheet until we’ve talked about the correct answers • Hand them in at the end of the lecture or during the break • I’ll come around to help out !

Kirchhoff’s Laws: Bright lines Heated Gas emits light at specific frequencies “the positive fingerprints of the elements”

Kirchhoff’s Laws: Dark Lines Cool gas absorbs light at specific frequencies “the negative fingerprints of the elements”

Kirchhoff’s Laws 1. A luminous solid or liquid (or a sufficiently dense gas) emits light of all wavelengths: the black body spectrum 2. Light of a low density hot gas consists of a series of discrete bright emission lines: the positive “fingerprints” of its chemical elements! 3. A cool, thin gas absorbs certain wavelengths from a continuous spectrum dark absorption ( “Fraunhofer”) lines in continuous spectrum: negative “fingerprints” of its chemical elements, precisely at the same wavelengths as emission lines.

Spectral Lines • Origin of discrete spectral lines: atomic structure of matter • Atoms are made up of electrons and nuclei – Nuclei themselves are made up of protons and neutrons • Electrons orbit the nuclei, as planets orbit the sun • Only certain orbits allowed Quantum jumps!

• The energy of the electron depends on orbit • When an electron jumps from one orbital to another, it emits (emission line) or absorbs (absorption line) a photon of a certain energy • The frequency of emitted or absorbed photon is related to its energy E=hf (h is called Planck’s constant, f is frequency)