ASTR3 Week 10 Notes

# ASTR3 Week 10 Notes - Week 10-Lecture 26 Hubbles Law The...

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Week 10 11/30/15 ---Lecture 26: Hubble’s Law - The Milky Way Galaxy Hubble’s Law: v = H 0 x d (H 0 = Hubble’s constant) o cz = H 0 x d o Velocity of recession is proportional to distance o z = redshift = change of wavelength / rest wavelength o Implication: the universe is expanding uniformly Implies Big Bang Hubble’s Law o uniform expansion o Velocity proportional to distance is generic feature of global expansion of Universe o Also, every raisin (aka galaxy) sees all the other raisins (galaxies) receding as the raisin bread (universe) expands Quasar redshifts are large o expanding universe → large redshift means large distance o Can use Hubble’s Law to estimate distances from redshifts, for distances up to 100s of Mpc o v = H 0 x d → cz = H 0 x d → d = cz/H 0 The Age of the Universe o In the context of an expanding Universe… H 0 tells us the rate at which galaxies are moving apart from one another

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H 0 has units of km/s/Mpc - tells you redshift (velocity) for an object at a given distance for a galaxy at a given distance in Mpc (millions of pc), H 0 tells you its velocity in km/s H 0 also has units of inverse time: d = v/H 0 ; d = v x t If we run clock backward to when the galaxies were all at one point then 1/H 0 tells us how long it took universe to expand to its current size if the expansion rate was constant; so 1/H 0 roughly estimates age of Universe Our best measurement of the Hubble Constant: H 0 = 72 km/s/Mpc So, the age of the Universe, ~1/H 0 = 13.6 billion years Lookback Time o Since the speed of light is finite… it takes time for light to travel vast distances light reaching us from a galaxy 4 x 10 8 l.y. away took 4 x 10 8 years to arrive we refer to this as lookback time farther out into the Universe we look, farther back in time we see o At vast distances, long lookback times it makes more sense to use lookback time than distance consider the spacetime diagram o What is the distance to this galaxy? distance when the photons were emitted distance when the photons are received o But there is no ambiguity that it took 4 x 10 8 yrs for the photons to get here
Cosmological Redshift Redshift/Doppler Shift o According to the Doppler shift model, the galaxies are moving through space o At some point Hubble’s Law, v = H 0 x d, would have to break down; because v could not be greater than the speed of light o But, in fact, the galaxies are NOT moving through space. Rather, space itself is expanding. At large distances, the Doppler formula is an INCORRECT way of interpreting redshifts of distant galaxies! o If the balloon is space and the coins taped to the surface of the balloon are galaxies, you can see that as space expands, the separations between the coins (galaxies) grow larger Cosmological Redshift o This picture is analogous to the galaxies tracing the expansion of the Universe.

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