Review of Chapters 14, 15, 16 Galaxies and the expansion of the Universe 5/4/2009 Habbal Astro 110-01 Review Lecture 36 1
Recap: Learning from Light How does light tell us what things are made of? Every kind of atom, ion, and molecule produces a unique set of spectral lines, seen in emission or absorption spectra. How does light tell us the temperatures of dense objects? We can determine temperature from the (continuous) spectrum of thermal radiation. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 2
Relationship between luminosity and apparent brightness The inverse-square law for light: Brightness = Luminosity 4π (distance) 2 We can determine a starʼs distance if we know its luminosity and can measure its apparent brightness: Distance = Luminosity 4π x Brightness 5/4/2009 Habbal Astro 110-01 Review Lecture 36 3
Getting the Mass from the Orbital velocity M r = r v 2 / G Take v = 220 km/s: orbital velocity of Sun around center of galaxy r = 28,000 ly: orbital radius M r = 1.9 10 41 kg M r /M S = 10 11 5/4/2009 Habbal Astro 110-01 Review Lecture 36 4
Doppler Shift and Rotation 5/4/2009 Habbal Astro 110-01 Review Lecture 36 5
Size of the Milky Way (side view) Diameter ~ 100,000 light years Thickness ~ 1,000 light years (flatter than a CD!) Distance from Sun to center ~ 30,000 light years About 100 billion stars in total. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 6
Stellar components of the Milky Way 1. Disk: rotating, thin collection of stars, gas & dust. 2. Halo: tenuous outer sphere of stars & globular clusters, and very little gas. 3. Bulge: spherical concentration of stars near the center 5/4/2009 Habbal Astro 110-01 Review Lecture 36 7
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How do we measure the mass of the Galaxy? Sunʼs orbital motion (radius & velocity) tell us the mass inside Sunʼs orbit: ~1.0 x 10 11 M sun. Cannot measure the mass outside of the Sunʼs orbit in this fashion. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 9
Orbital velocity law M r = r v 2 / G Take v = 220 km/s: orbital velocity of Sun around center of galaxy r = 28,000 ly: orbital radius M r = 1.9 10 41 kg M r /M S = 10 11 Similar calculations of orbits of distant stars most of galaxyʼs mass is far from center and distributed throughout halo. But since donʼt see emission dark matter (otherwise stars far away would have v decreasing with distance like planets) 5/4/2009 Habbal Astro 110-01 Review Lecture 36 10
Star-gas-star cycle Recycles gas from old stars into new stars. With each cycle, more heavy elements are made by nuclear fusion in stars. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 11
Summary of Galactic Recycling Gas Cools Stars make new heavy elements by fusion. Dying stars expel gas and new elements, producing hot bubbles of gas (~10 6 K). These emit X-rays. This hot gas cools, allowing atomic hydrogen clouds to form (~100-10,000 K). This hydrogen emits at 21-cm wavelength emission line. Further cooling permits molecules (CO, etc) to form, making molecular clouds (~30 K). CO emits an emission line spectrum at 3 mm. Gravity forms new stars (and planets) in molecular clouds. Process starts over. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 12
We observe star-gas-star cycle operating in the Milky Wayʼs disk using many different wavelengths of light. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 13
Much of the star formation in disk galaxies happens in the spiral arms. Ionization Nebulae Blue (massive) stars Dusty Gas Clouds Whirlpool Galaxy 5/4/2009 Habbal Astro 110-01 Review Lecture 36 14
Stellar Orbits Use Newtonʼs version of Keplerʼs 3 rd law: mass = 3-4 10 6 M S In size of solar system black hole in center of Milky Way Recent evidence from bright X-ray flare emission 5/4/2009 Habbal Astro 110-01 Review Lecture 36 15
Distances to Galaxies and the Age of the Universe 5/4/2009 Habbal Astro 110-01 Review Lecture 36 16
The Cosmological Distance Ladder No single method or tool can measure distance to all types of objects (planets, stars, galaxies, etc.) Use a variety of methods and tools, each one moving farther out and depending on the preceeding method distance ladder 5/4/2009 Habbal Astro 110-01 Review Lecture 36 17
The Cosmological Distance Ladder: Tools for measuring distances Direct methods for relatively close objects: Radar/Ranging Parallax/Geometry Indirect methods: (Brightness Luminosity) relation: B = L/(4π d 2 ) Standard candles Main sequence stars and clusters (use of H-R diagram) Cepheid variables White dwarf supernovae Doppler shifts Hubbleʼs Law v = H d 5/4/2009 Habbal Astro 110-01 Review Lecture 36 18
The cosmological distance ladder from planets in our Solar System out to ~10 billion light-years away. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 19
Step 1: Radar ranging Determine size of solar system using radar ranging 5/4/2009 Habbal Astro 110-01 Review Lecture 36 20
Step 2: Parallax Determine distances of stars out to a few hundred light-years using parallax Parallax angle p = 1/2 total parallax shift each year. Distance d = 1/p in parsec (= 3.26 light years) with p in arcseconds 5/4/2009 Habbal Astro 110-01 Review Lecture 36 21
Relationship between luminosity and apparent brightness The inverse-square law for light: Brightness = Luminosity 4π (distance) 2 We can determine a starʼs distance if we know its luminosity and can measure its apparent brightness: Distance = Luminosity 4π x Brightness NEED: A standard candle: an object whose luminosity we can determine without measuring its distance. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 22
Standard candles A light source of a known, standard luminosity. Compare luminosity with observed brightness get the distance 5/4/2009 Habbal Astro 110-01 Review Lecture 36 23
Distant Standard candles: white dwarf supernovae They are the most luminous standard candles and tell us the distances to the most distant galaxies. White dwarf supernovae are exploding white dwarf stars that have reached the 1.4 M S limit They all should have nearly the same luminosity (10 10 L S ) because originate from stars of same mass Because very bright can be detected in distant galaxies Measure their brightness, + luminosity distance 5/4/2009 Habbal Astro 110-01 Review Lecture 36 24
Main Sequence fitting For main sequence stars, use their spectral type/color to determine their luminosity Luminosity Brightness + Luminosity Temperature (spectral type) distance 5/4/2009 Habbal Astro 110-01 Review Lecture 36 25
Main-Sequence Fitting All main-sequence stars of a particular spectral type have about the same luminosity Identify a star cluster that is close enough to determine its distance by parallax and plot on H-R diagram: [Brightness + distance] luminosity Standard: Hydes Cluster Look at far away clusters, measure their brightness, assume same luminosity as counterparts in nearby clusters [Luminosity + brightness] distance 5/4/2009 Habbal Astro 110-01 Review Lecture 36 26
Step 3 Apparent brightness of star clusterʼs main sequence tells us its distance. Example: Hyades are 7.5 times as bright as that of Pleiades So, Pleiades must be apple7.5 = 2.75 times as far away 5/4/2009 Habbal Astro 110-01 Review Lecture 36 27
Discovery of Luminosity-Distance relation in Cepheid variables Henrietta Levitt 1912: Discovered that the periods of Cepheids are very closely related to their luminosities 1. period-luminosity relation allows the determination of a Cepheidʼs luminosity 2. by measuring its brightness distance Hubble then used Cepheids in galaxies to measure their distances 5/4/2009 Habbal Astro 110-01 Review Lecture 36 28
Step 4 Because the period of a Cepheid variable star tells us its luminosity, we can use these stars as standard candles. Example of measuring the change in brightness of a Cepheid variable, with a period of ~50 days. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 29
Measured variability period Cepheidʼs luminosity. [Luminosity + apparent brightness] distance. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 30
Recall: Standard candles A light source of a known, standard luminosity White dwarf supernovae are the most luminous standard candles They tell us the distances to the most distant galaxies. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 31
Step 5 Apparent brightness of white-dwarf supernova tells us the distance to its galaxy. Very distant supernova Can be observed to much greater distance than any other type of star. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 32
Hubbleʼs law derived from Doppler Redshift of distant galaxies Redshift of a galaxy tells us its distance through Hubbleʼs Law: distance = velocity H 0 The Hubble Constant 5/4/2009 Habbal Astro 110-01 Review Lecture 36 33
Hubbleʼs Law: (galaxy velocity) = H 0 x (galaxy distance) 5/4/2009 Habbal Astro 110-01 Review Lecture 36 34
We can measure the speed of a galaxy from its redshift Hubbleʼs Law then gives its distance 5/4/2009 Habbal Astro 110-01 Review Lecture 36 35
The Universe had a beginning time = distance / speed = 1/H 0 They all started in the same place The Big Bang! 5/4/2009 Habbal Astro 110-01 Review Lecture 36 36
Distances between faraway galaxies change while light travels lookback time Lookback time: difference between current age of Universe and age of Universe when light left the object distance? The more distant a galaxy, the greater its redshift, and the faster it moves away from us 5/4/2009 Habbal Astro 110-01 Review Lecture 36 37
Measuring H0 (Hubbleʼs constant) gives the age of the Universe 13.6 billion years We canʼt see anything older than this: this is the cosmological horizon 5/4/2009 Habbal Astro 110-01 Review Lecture 36 38
Cosmological Horizon = the limit of the observable Universe. The Universe has a finite age of ~14 billion years. Hence, this is the maximum lookback time and defines how far back in time we can see. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 39
Do supermassive black holes really exist? Measuring the orbits of stars at the center of the Milky Way indicate a black hole of mass of ~4 million M Sun 5/4/2009 Habbal Astro 110-01 Review Lecture 36 40
Measuring masses of spiral galaxies Use the 21-cm emission line of hydrogen gas clouds to trace orbital motions. (Can also use stellar motions, but gas clouds are found to larger distances.) Measure the galaxyʼs rotation curve to determine the total mass as a function of separation from the center. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 41
Rotation curve = a plot of velocity versus orbital radius. Solar systemʼs rotation curve declines because the Sun has almost all the mass. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 42
Rotation curves measure the mass distribution Solar System Milky Way Rotation curve declines with distance because the Sun has nearly all the mass. Rotation curve stays flat with distance, meaning the mass is more spread out. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 43
Rotation curves measure the mass distribution The stars in the Milky Way go out to ~50,000 light-yrs. Milky Way If the stars represented all the mass in the galaxy, then the rotation curve would decline at large separations. But it doesnʼt! Most of the Milky Wayʼs mass seems to be dark matter!! Rotation curve stays flat with distance, meaning the mass is more spread out. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 44
The true mass distribution of galaxies The visible portion of a galaxy lies deep in the heart of a large halo of dark matter. Dark matter halo cannot be detected at any wavelength. Only detectable through its gravitational influence. The total mass in dark matter is about 10x more than in stars!! 5/4/2009 Habbal Astro 110-01 Review Lecture 36 45
Spiral galaxies all tend to have flat rotation curves indicating large amounts of dark matter. 5/4/2009 Habbal Astro 110-01 Review Lecture 36 46
old older oldest Estimated age of the Universe depends on the assumed amount of dark matter and dark energy 5/4/2009 Habbal Astro 110-01 Review Lecture 36 47
End of Review 5/4/2009 Habbal Astro 110-01 Review Lecture 36 48
Your feedback What did you like most about this course What did you find the most difficult What did you not like Suggestions? 5/4/2009 Habbal Astro 110-01 Review Lecture 36 49