# Lecture 32: The Expanding Universe Readings: Sections 26-5 and 28-2

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1 Lecture 32: The Expanding Universe Readings: Sections 26-5 and 28-2 Key Ideas Measuring the Distances to Galaxies and Determining the Scale of the Universe Distance Methods: Trigonometric Parallaxes Spectroscopic Parallaxes Cepheid Period-Luminosity Relation Galaxy Standard Candles Galaxy Luminosities Hubble s Law: Galaxies are receding from us Recession velocity gets larger with distance Hubble Parameter Present-day rate of expansion of the Universe Cosmological Redshifts Due to the expansion of space Redshift distances Redshift maps of the Universe The Distance Problem (again!) Cepheid P-L relation is good but limited: Limit ~30-40 Mpc (and that s with the Hubble Space Telescope) Very laborious to use (100 s of HST orbits) Only works for Spiral or Irregular galaxies Cepheids found in young star clusters Ellipticals have only old stars Only practical out to the Virgo Cluster This is only just next-door in cosmic terms Need other methods to estimate very large cosmic distances. Large distances=many light years away=the Universe at a very young age Mapping the Universe

2 No single distance method is universal. Must work up towards large distances. Bootstrap Process: Build up from near to far Each step calibrates the next step Errors made in first steps affect the accuracy of all following steps The Distance Ladder See Figure Step 1: The Astronomical Unit 1 AU = Mean Earth-Sun Distance Method: Geometric Triangulation Radar bounced off inner planets Orbits of planets give the geometry Works out to ~50 AU Permits measurement of: Trigonometric Parallaxes to nearby stars Step 2: Trigonometric Parallaxes Calibrated by the AU (size of Earth s orbit) Method: Stellar Parallaxes Use Earth as the baseline Ground-based: works out to ~100 pc Hipparcos: works out to ~1000 pc Permits measurement of: Luminosities of nearby stars Distances to nearby star clusters Step 3: Spectroscopic Parallaxes Calibrated by Trigonometric Parallaxes Method: Spectroscopic Parallaxes Relate spectral type to luminosity in calibrated H-R Diagram Works OK for indvidual stars Works best for clusters of stars Permits measurement of Distance to star clusters out to ~50-60 kpc

3 Just reaches out the Large Magellanic Cloud Step 4: Cepheids Calibrated by cluster H-R diagrams Method: Period-Luminosity Relation Cepheids: supergiants in young clusters Calibrate the Cepheid Period-Luminosity relation in the LMC Cepheids give distances to Nearby spiral galaxies out to Mpc Only works for spirals (need Pop I stars) Step 5: Galaxy Standard Candles Now that we can measure the distances to nearby spiral galaxies, we need to find a way to measure distances to distant galaxies. Look for bright standard candles found in both spiral and elliptical galaxies Type Ia Supernova explosions Planetary Nebula luminosity distribution Globular cluster luminosity distribution Calibrated by Cepheid Period-Luminosity distances Nearby similar objects (from other steps) Variety of techniques get used Mix and match to seek consistent results All rely on previous steps, especially Step 4 Argue endlessly about the details Bottom Line Works out to Mpc, depending on method Gives distances out to Virgo and Coma clusters Step 6: Galaxy Luminosities Calibrated by the Virgo Cluster distance Method Assume distant galaxies are like nearby ones Use correlations between luminosity & distance-independent properties of galaxies

4 Compute luminosity distances using the entire galaxy Tully-Fisher Relation for Spirals Galaxy Luminosity-Rotation Speed relation Measure rotation speed from 21-cm radio emission (distance independent) Fundamental Plane Relation for Ellipticals: Galaxy Luminosity Line Width Size relation Measure absorption-line widths from spectra (distance independent) Current Status Current critical areas: Distance to the LMC, which calibrates the extragalactic Cepheid P-L relation Refinement of other standard candles, especially Type I supernovae Search for new geometrical methods The Expanding Universe Discovery of Expansion : Vesto Slipher, working at Lowell Observatory, measured radial velocities from spectra of 25 galaxies Found 21 of the 25 galaxies showed a redshift speeds of some > 2000 km/sec Most of these galaxies appear to be rapidly receding away from us Hubble s Discovery 1929: Edwin Hubble measured the distances to 25 galaxies Used Cepheids in Andromeda & Local Group Used brightest stars in other galaxies Compared distances and recession velocities Discovered Recession velocity gets larger with distance Systematic expansion of the Universe See Figure 26-15

5 Hubble s Law v = H 0 d v=recession velocity in km/sec d=distance in Mpc H 0 = expansion rate today (Hubble Parameter) H 0 = 70 ± 7 km/sec/mpc In words: The more distant a galaxy, the faster its recession velocity Only good for galaxies that are in the Hubble flow, that is, whose motions aren t dominated by random peculiar velocities. This formula does not work for Andromeda, for example. Interpretation Hubble s Law demonstrates that the Universe is expanding in a systematic way: The more distant a galaxy, the faster it appears to be moving away from us. Hubble Parameter: Rate of expansion today Comments: Empirical result based only on data Not an exact law Nature of the Expansion General Expansion of Space All observers in different galaxies see the same expansion around them. No center all observers appear to be at the center What is the recession velocity? NOT motions through space Expansion of space: galaxies carried along Figure 28-3 Hubble Parameter: H 0 Measures the rate of expansion today

6 H 0 = 70 ± 7 km/sec/mpc Based on Hubble Space Telescope observations of Cepheids in nearby galaxies H 0 is hard to measure: Recession speeds are easy to measure from the shifts of spectral lines But distances are very hard to measure Galaxies also have extra motions Cosmological Redshifts All galaxies (with very few exceptions) are receding from us. Recession is quantified in terms of the cosmological redshift of the galaxy, z. z = " observed # " emitted " emitted Not a Doppler shift: measures expansion of spacetime, not motions through space. As the Universe expands, recession velocities gets larger, light waves get stretched and redder Cosmological Redshift of light Figure 28-4 Step 7: Redshift Distances For nearby galaxies, redshift (z) is directly proportional to the distance through the Hubble Law d = v H 0 = cz H 0 z=redshift c=speed of light This formula is only valid for relatively nearby galaxies. Method: Measure the redshift of a galaxy with spectra

7 Use the estimate of the Hubble Parameter Assume pure Hubble Expansion or attempt to statistically correct for random galaxy motions. Allows us to probe the Universe on the largest observable scales. Limitations: Value of H 0 is only known at 10% Need to know the distances from other methods first to measure H 0 Random motions of galaxies affects measurements of z for nearby galaxies At large distances, the conversion between z and distance is much more complicated. Astronomers use cosmological redshift as a surrogate for distance, especially for more distant galaxies. Mapping the Universe Map the distribution of galaxies using their cosmological redshifts. Largest maps include ~250,000 galaxies Reveals sheets and filaments of galaxies surround great voids Depth is ~ Mpc Relative distances are good, but the absolute scale is only known to ~10% See Figure Hubble s Law & its Discontents Ideally, we could just use the Hubble Law: d = v H 0 = cz H 0 At least nearby, all you need to measure is the cosmological redshift, z. Problem: What is H 0?

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