XII. The distance scale h"p://sgoodwin.staff.shef.ac.uk/phy111.html
0. How far away are galaxies? We discussed galaxies without thinking about how we know the distances to these galaxies. Only in the past 20 years have astronomers really started agreeing about the distances to other galaxies (when I did a similar course in about 1990 estimates varied by factors of two).
1. Standard candles Determining distances relies on what are known as standard candles if you know how bright a particular object is, then if you observe its apparent brightness in a distant galaxy you can calculate the distance to that galaxy. We use a variety of standard candles to work out from nearby parallax distances in the MW from local stars, to stars in clusters, to more distant stars and clusters. But all of our very local standard candles are faint and impossible to see in other galaxies.
1. The instability strip Some stars are unstable Particular zones in their interiors can have high opacities, this means energy cannot escape, and so they heat-up then they expand and cool, as they cool their opacities drop and so even more energy escapes, so they cool more which causes their opacities to rise This causes them to pulsate.
1. Cepheids The most important variables in the instability strip are Cepheid variables as they have luminosities of 10 2-10 4 L sun, very distinctive lightcurves, and a (now) well-known periodluminosity relationship.
1. Cepheids One of the main reasons for building the HST (and why it is Hubble ) was to observe Cepheids out to about 20Mpc. This is the distance of the Virgo cluster of galaxies and knowing the distance to that allowed us to calibrate other distance indicators.
2. The Hubble Constant In the 1910s it was know that other galaxies were (almost) all receding from us: they all showed a redshift. Spectral lines will shift to the blue (shorter wavelength) if an object is approaching, or to the red (longer wavelength) if it is receding.
2. The Hubble Constant In 1929 Hubble showed what was anticipated by theory that recession velocity, v r, was proportional to distance, D: v r = H 0 D Where H 0 is the Hubble Constant. We now know H 0 ~70 km s -1 Mpc -1.
2. The Hubble Constant This tells us that the Universe is expanding and we can get an age estimate for the Universe, but for now we can just use it as a distance estimator. If a galaxy is receding at 7000 km/s, its redshift distance is ~100 Mpc. This works if the Hubble velocity is high enough to washout peculiar local motions due to the gravity of other galaxies (typically these are 100-500 km/s). But recession velocity is a good proxy for distance.
2. Redshift, z Recession velocities are usually quoted as redshift (z) which is related to what fraction of the age of the Universe that distance corresponds to (as light takes time to reach us). The fraction of the age of the Universe is 1/(1+z) so we live at z=0 (fraction=1), z=1 is at half the current age (fraction=1/2).
2. Redshift, z In astronomy we are always looking at things as they were in the past. The light from a star 30pc away left it about 100 yrs ago (30pc~100 lyr). The light from the Andromeda galaxy left it about 1.5Myr ago, and the light from something in the Virgo Cluster about 65 Myr ago (about when the dinosaurs were killed). We ll see we think the Universe is ~14Gyr old, so light from an object >14Glyr (5000Mpc) away will not have had enough time to reach us yet. (It s rather more complex than this as the Universe is expanding and this adds all sorts of extra fiddly general relativity to the problem.)
3. SNIa Type Ia supernovae are used as a standard candle for extremely large distances (as they are very bright). They all have different peak brightnesses, but the speed at which they decay depends on that peak brightness, so they can each be scaled afterwards to determine their distance.
4. Secondary indicators There are various other distance indicators you might come-across (Tully-Fisher, surface brightness, globular cluster luminosity function, D n -Σ, etc.). These are calibrated from the Cepheid distances to the Virgo cluster and then can be used for more distant galaxies (and the vast majority of galaxies in which we haven t had a SNIa). But we really needn t bother with them here the astronomers will get to do them all later
5. Large scale structure Surveys of galaxies now get >10 5 galaxy redshifts and can map the distribution of galaxies in a huge fraction of the local Universe. They find many galaxies in clusters and super-clusters, with small groups (like our own local group) fairly common, and galaxies strung between clusters and super-clusters along filaments.
5. Large scale structure Surveys of galaxies now get >10 5 galaxy redshifts and can map the distribution of galaxies in a huge fraction of the local Universe. They find many galaxies in clusters and superclusters, with small groups (like our own local group) fairly common, and galaxies strung between clusters and superclusters along filaments.
5. Galaxy mergers Ellipticals are more common in clusters and superclusters, with spirals typically found in low-density regions. Ellipticals are more common in clusters because galaxies collide the denser the environment, the more often they collide. A collision causes a burst of star formation and exhausts the gas, destroys discs and leaves an elliptical galaxy.
Summary Distances are measured using standard candles the most important are Cepheid variables and SNIa. Combined with recession velocities this leads to Hubble s Law H 0 =v r D. The recession velocity is often quoted in terms of redshift how far back as a fraction of the age of the Universe we are observing. Galaxies are most often found in groups (like ours), clusters, and super-clusters, connected by filaments in a cosmic web.
Key points To understand what a standard candle is and why they are important. To understand how Hubble s Law can be used to get a distance from a recession velocity. And that redshift is a measure of both distance and lookback time.
Quickies At what redshift was the Sun born? At what Hubble recession velocity would a galaxy at 700 Mpc have? From observations of Cepheids we know a galaxy is at 10 Mpc. We measure its recession velocity as 30 km s -1. Why would this velocity surprise you, and what is the probable explanation?
Notes The relationship between redshift and distance is linear for low values of z, but becomes rather complex when we look at very distant objects (very far back in time). As the Universe expands the value of H 0 changes as the geometry of the Universe changes. Partly this is a standard result from applying general relativity, but recently it has become clear that something odd is happening. We ll talk about dark matter in the next lecture, and dark energy very briefly later. Really understanding this will have to wait until general relativity and cosmology courses in 3 rd year.