Finding the Expansion Rate and the Age of the Universe Learning Goals 1. Determine a value for the Hubble constant through analysis of measurements of the angular sizes and redshifts of galaxies. 2. Estimate the corresponding age of the universe and compare it with the age of the Sun and the Milky Way. 3. Explain why Hubble’s law implies that the universe is expanding. 4. Summarize how our view of the universe has changed as the value of the Hubble constant has improved. Galaxy Types: Sizes – Dwarf and Giant • An elliptical or irregular galaxy can be a dwarf galaxy or a giant galaxy. All spirals are giant; that is, all are approximately the same actual size. Standard Ruler • Standard Candle: An object where we are quite confident we know its actual luminosity. • Standard Ruler: An object where we are quite confident we know its actual size. • Assume all spiral galaxies that look similar are very close in actual physical size, no matter where located. • Must first KNOW actual size by using the KNOWN distance to a nearby spiral galaxy - Andromeda galaxy. Variable Stars: Cepheid Variables Vs. RR Lyrae Variables These pulsating variable stars are extremely important for determining distances. Specifically, they have a relationship between their pulsation period and luminosity. Cepheid variables: High-mass stars becoming supergiants. • Periods from 1 to 100 days. More luminous stars have longer periods. RR Lyrae variables: Low-mass stars on the horizontal branch. Less luminous than Cepheid variables. Standard Candles 7 Andromeda Galaxy: Measure �, know D from period- luminosity measurements of Cepheid variable stars, solve for s. Distant Galaxy: Measure �, know s from standard ruler assumption, get D from small angle formula. Standard Ruler - Why is assumption important? � How would we know if the difference in � angular sizes was due to distances or to the galaxies actually being different actual size? 120 ACTIVITY 26 ● Finding the Expansion Rate and the Age of the Universe TABLE 26.1 ConfirmationContinued. for galaxies being spiral VELOCITY DISTANCE GALAXY IMAGE GALAXY SPECTRUM GALAXY ID REDSHIFT (km/s) (Mpc) NGC 1832 0.00646 1,937 32 NGC 2276 0.00806 2,417 26 NGC 2775 0.00451 1,353 20 NGC 2903 0.00186 556 10 NGC 3034 0.00073 219 12 NGC 3147 0.00935 2,804 22 ACTIVITY 26 ● Finding the Expansion Rate and the Age of the Universe 121 TABLE 26.1 ConfirmationContinued. for galaxies being spiral VELOCITY DISTANCE GALAXY IMAGE GALAXY SPECTRUM GALAXY ID REDSHIFT (km/s) (Mpc) NGC 3227 0.00365 1,093 17 NGC 3368 0.00301 903 15 NGC 3623 0.00254 762 8 NGC 3627 0.00234 703 9 NGC 4775 0.00624 1,572 24 NGC 5248 0.00384 1,152 13 (continued) Standard ruler gives estimate of distances ➔ x-axis Examination of the redshifts of the spectra gives us the recessional velocities ➔ y-axis Expanding Universe: Doppler Shift Measurements • Recall: Redshifted spectral lines = movement away; blue shifted spectral lines = movement toward. Doppler shift measurements demonstrate that all galaxies, except the nearest the Milky Way, show redshifts in their spectra. The closest galaxies show blueshifts due to local gravitational effects. All galaxies show redshifts on large scales in the universe. Expanding Universe: Hubble’s Law • If we measure distances and velocities, we find Hubble’s law. => The recession velocity of a galaxy is proportional to the distance of that galaxy. Hubble constant (H0): constant of proportionality. y = mx + b Hubble’s Law: v = Hod v = Ho d + 0 1. find distances to “nearby” galaxies using standard candles 2. use spectra to find recessional velocities 3. fit slope to data 4. find recessional velocities of far galaxies 5. d = v/Ho 400 Mpc =1.3x109 light years 16 .