Download Lecture 12

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 102-104Lsun,
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, vr, was proportional to distance, D:
vr = H 0 D
Where H0 is the Hubble Constant.
We now know H0~70 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, Dn-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 >105 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 >105 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 H0=vrD. 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 H0 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 3rd year.