Cosmology and extragalactic astronomy Mat Page Mullard Space Science Lab, UCL 4. Redshift

3. Redshifts This lecture: Redshifts Hubble’s law –the expanding universe Redshift as lookback time Slide 2

Doppler shifts An ambulance moves towards us with velocity v, emitting sound wavelength. For sound, c = f Time between wavecrests t = 1/f = /c In which ambulance travels distance d = vt = v /c ’ = -d = (1-v/c)  = -v/c Slide 3

What if the ambulance was travelling at a substantial fraction of the speed of light? Need to use special relativity to add velocities. (Without derivation)  ’ = Relativistic doppler shift: 1-v 2 /c 2 1-v/c Slide 4

How would redshift work in an expanding universe? Slide 5

Apparent motion in the expansion Slide 6

Redshifts So we just use the velocity and the Doppler shift equation and that tells us what the redshift should be, right? Kind of… In a sense the galaxies behaving according to Hubble’s law aren’t actually moving through space away from us. –The whole Universe in which they are embedded is expanding. The maths is the same though, and the concept of recession velocity is widely used. Slide 7

Cosmological redshift Space expands, so the distance between the wavecrests in radiation expands too. If ‘a’ is a scale factor of the universe, then  rec / em =a rec /a em Slide 8

Hubble’s Law History: –Shapley-Curtis debate, 1920 –Curtis: Most spiral nebulae are redshifted, so they can’t be normal nebulae. –1920’s Slipher and Humason measure many galaxy spectra and redshifts –Hubble measured the distances using Cepheid variables, which he combined with the redshift measurements. Slide 9

Hubble’s law Published in 1929 Relates the redshift (or velocity) of galaxies to their distance Velocity is proportional to distance v = H 0 d Original value out by a factor of several! It took many decades to refine to the currently accepted value –Until early 2000s, known to lie between 50 and 100 km/s/Mpc –HST: H 0 =72+-8 km/s/Mpc –WMAP: H 0 =70+-4 km/s/Mpc Slide 10

Here’s how it looks: Slide 11

Meaning of H 0 Redshift determines the rate of expansion of the universe. H 0 relates the distances of present day galaxies to their velocities. Therefore H 0 is the fractional expansion rate of the universe at the present time. The flow of galaxies away from us as the universe expands is called the ‘Hubble flow’. Slide 12

Note of caution! Galaxies like everything else actually do move around. They have real motions apart from the Hubble flow. So Hubble’s law gives good but still limited precision. For some nearby galaxies, they are so close that H 0 d is tiny, and the observed redshift is dominated by the galaxy’s motion within the Hubble flow - e.g. M31 is blueshifted. This causes the fingers of God in large scale structure pictures that we will meet later! Slide 13

Lookback time Light takes a long time to get to us from distant objects. –We see distant things as they were a long time ago when the light was emitted. –This time difference is called ‘lookback time’. Redshift and the application of Hubble’s law measures the present day distance, but the light wasn’t emitted in the present. –So, its not correct just to divide the distance by the speed of light to get lookback time. –It depends on the history of the Universe, and the way that its expansion has changed with time. Slide 14

Lookback time Lookback time for 5 different cosmological models For constant expansion: T=(1-1/(1+z))/H 0 Slide 15

Redshift - usefulness Lookback time is uncertain. Distance is uncertain. –depend on the cosmological model. –stability rather recent (WMAP 2003)! Years since the start of the Universe even poorer understanding! So extragalactic astronomers often quote the redshift in preference to the quantities that are derived from it - at least redshift doesn’t change as people change their ideas about cosmology. Slide 16

Key points Linear relation between redshift and distance. v=H 0 d The Universe is expanding! H 0 ~ 70 km/s/Mpc Lookback time easily estimated for nearby objects. For very distant objects, lookback time and distance much more uncertain and depend on the cosmological model. Slide 17