Astronomy Now - January 2021

L

Colin Stuart

Absolute Beginners: The cosmic distance

ladder

ook up at the night sky and you’ll quickly spot that some stars are brighter than others. e most
dazzling, Sirius, is about 1,500 times brighter than the dimmest stars you can see with the
unaided eye. Are the brighter ones really more luminous? Or are they just closer to us? To answer
that, astronomers need a way to measure cosmic distances – no mean feat given that we can’t exactly
extend a ruler all the way across space. e gap between the stars is, instead, bridged using
something called the ‘cosmic distance ladder’. It represents a mixture of different methods, some that
work well for nearby objects and others that are better suited to the farthest reaches of the cosmos.
Each technique relies on the success of the last in the same way that you need to climb one rung of a
ladder to reach the next.

The Earth–Sun distance

e rst rung is the ‘astronomical unit’ (or ‘AU’ for short) – the distance between Earth and the Sun.
Weirdly, we usually calculate this using the planet Venus. From Johannes Kepler’s ird Law of
Planetary Motion, which is a mathematical relationship between the time it takes for a planet to
complete one orbit and its average (mean) distance from the Sun, we know that Venus orbits the
Sun at 72.3 per cent of the distance that Earth does. So, if we can measure the gap between Earth
and Venus, we can scale it up to calculate the full Earth–Sun distance. A few hundred years ago, this
could only be done using a transit of Venus, a rare event that happens about twice a century when
we see Venus’ silhouette pass in front of the Sun. It became so important for measuring cosmic
distances that observatories dispatched astronomers to all corners of the globe to witness transits in
the eighteenth and nineteenth centuries. In modern times, we’ve turned to radar ranging instead,
bouncing radio waves off Venus’ reective surface and timing how long it takes for them to come
back. From this we now know that we orbit 149.6 million kilometres from the Sun, and this is the
size of one AU.

CO-MOVING DISTANCE VS LIGHT-TRAVEL DISTANCE

When we say that galaxies such as GN-z11 are 13.4 billion light years away, that’s actually a bit of a lie. What

we’re really saying is that it was 13.4 billion light years away when the light we’re seeing set off. The ongoing

expansion of the Universe has carried the galaxy even further away in the time it’s taken for the light to reach

us. It is now 31.5 billion light years away, which is called the co-moving distance.

This is why you’ll often read that the observable Universe is 93 billion light years wide, even though it’s only

13.8 billion years old. If you’re thinking that this implies that the Universe has expanded faster than the speed

of light, then you’d be right. The famous restriction that nothing can travel faster than light applies to objects

travelling through space, but not to the rate at which space itself stretches.

Parallax and jumping stars

Knowing the size of the astronomical unit allows us to measure the distances to the nearest stars
using a technique called ‘parallax’. To see how this works, close your left eye and line up one of your
index ngers with the join between the pages of the magazine. Make sure your nger is roughly
halfway between the paper and your face. Keeping your nger in place, switch to your right eye
being closed. You should see your nger jump to the right, relative to the background. Next, repeat
the exercise but with your nger right up to your nose. e jump should be much greater this time.
e size of the jump depends on the distance between your eyes (which we call the ‘baseline’) and
your nger.

To replicate this effect in space, astronomers recreate your eyes by observing a star six months apart,
when Earth is on opposite sides of its orbit around the Sun. is means that the baseline is two
astronomical units. A nearby star (the equivalent of your nger) will appear to jump against the
background stars to a greater extent than a more distant one. Astronomers take the angle through
which the star appears to jump and use trigonometry to translate it into the distance to the star. is
calculation is impossible unless you know the length of the baseline (2AU). If you’ve ever heard the
word ‘parsecs’ be used as a measurement of astronomical distances, instead of light years, it stems
from parallax measurements. An object is said to be one parsec away if its parallax is equal to an
arcsecond (1/3600th of a degree). e word parsec is a portmanteau word from ‘parallax of one
arcsecond’.

e European Space Agency’s Gaia spacecraft has been busy measuring the parallax of stars in our
Milky Way Galaxy since its launch in 2013. By the end of its mission it will have measured the
distance to about 20 million stars with a precision of one per cent or better and to 200 million stars
to better than ten per cent.

Cepheid variable stars

Eventually, however, parallax stops working because the jump becomes imperceptible at distances
beyond a few tens of thousands of light years (~8, 500 parsecs). So astronomers step up to the next
rung of the cosmic distance ladder: ‘standard candles’. Looking at a star is like seeing a light bulb in
the window of a faraway building. e further you are from the bulb, the dimmer it appears. If you
knew the real brightness of the bulb – say 60 watts – you could work backwards and gure out how
far away it is. For us to do the same in space we need a way of knowing how bright an object really is
and that’s where standard candles can help – like light bulbs, they are objects of known brightness.

Cepheid variable stars are great standard candles. As their name suggests, they vary their brightness,
but in a very regular way because they pulsate in and out. Polaris, the Pole Star, is perhaps the most
famous Cepheid variable, which is somewhat ironic given its reputation for constancy. Henrietta
Swan Leavitt (1868– 1921), an astronomer at Harvard College Observatory, pioneered the use of
Cepheids as celestial yardsticks back at the start of the twentieth century. She used parallax to
measure the distances to nearby Cepheid variables and worked backwards to calculate their true
brightness. In doing so, she discovered that inherently brighter Cepheid variables take longer to vary
their brightness. So now, if we see a Cepheid too far away for parallax to work, we can still gure out
its true brightness from the time it takes to brighten and dim. en, like the light bulb, we can work
out how far away we are from it based on how dim it appears to us. A separate class of variable star,
called RR Lyrae stars and often found in globular clusters, can be used a similar fashion, particularly
in and around our own Galaxy.

Standardised supernovae

Unfortunately, while telescopes like Hubble can pick out individual Cepheids in nearby galaxies, they
aren’t bright enough to be seen half away across the Universe. Luckily, exploding stars called
supernovae are. ey can briey outshine the entire galaxy in which they reside because they emit
more energy in a short burst than the Sun will during its entire 10-billion-year existence.

One particular kind of supernova – a Type Ia (pronounced ‘one a’) – is another form of standard
candle. ey are so bright that they can be seen from a distance of up to about 10 billion light years,
which is about three-quarters of the way across the observable Universe. Type Ia supernovae
detonate when a star called a white dwarf reaches a critical size, usually by stealing gas from a
neighbour. e threshold is called the Chandrasekhar limit and it is equivalent to 1.44 Suns worth
of stuff. Reach this mass and a white dwarf ’s interior will be so hot that it will blow itself to
smithereens in a thermonuclear explosion. If these white dwarfs always explode with the same
amount of mass, then the resulting supernovae will all have the same inherent brightness
characteristics, just as all 60-watt light bulbs do. Once again, the dimmer ones must be further away.

Type Ia supernovae were famously used in the 1990s to chart the expansion history of the Universe.
Astronomers reached the unexpected conclusion that the Universe’s growth has been speeding up of
late, something put down to the actions of a mysterious force called dark energy.

Redshift and the expanding Universe

What about the very furthest galaxies visible in space? At that lofty distance even a supernova isn’t
visible. So astronomers use ‘redshift’ instead. Leavitt used Cepheid variables to measure the distances
to local galaxies. en in the 1920s, astronomer Edwin Hubble measured the speed at which the
galaxies appear to be moving away from us as the Universe expands. As space stretches, so does the
light from the receding galaxies. e light appears shifted towards the red end of the spectrum,
which is where the term ‘redshift’ comes from. Hubble discovered that more distant galaxies are
moving away faster, and so they have a greater redshift. e relationship between distance and speed
of recession is called the Hubble–Lemaître Law (named also for the Belgian physicist Georges
Lemaître, who independently developed the theory behind it). If you want to know the distance to a
faraway galaxy, all you need to do is measure how much its light is redshifted and use the Hubble–
Lemaître Law to work it out.

e galaxy known as GN-z11 has one of the highest redshifts ever measured. It translates to a
distance of 13.4 billion light years. Distances this big always make me think of the children’s book
Guess How Much I Love You by Sam McBratney (who sadly died in September 2020). e book is
supposed to illustrate the huge love between parent and child, ending with the seemingly impressive
token of loving them “to the Moon and back”. e cosmic distance ladder tells us, though, that this
is an insignicant amount of love. e Moon is the closest thing to us in space, at a mean distance
of just 384, 400 kilometres away. What you should really say is that I love you to GN-z11 and back –
a distance that’s a staggering 300, 000 trillion times greater. at’s undeniable love!

Colin Stuart (@skyponderer) is an astronomy author and speaker. Get a free e-book at colinstuart.net/newsletter.

The cosmic distance ladder allows astronomers to measure the distance to galaxies across the Universe, thanks to several different
methods that build upon one another, like one climbs a ladder one rung at a time.

Astronomers utilise a number of ingenious methods for measuring distance in space, whether

it be to the Sun, to nearby stars, or to the farthest galaxies, writes Colin Stuart.

Transits of Venus were used to measure the astronomical unit – the Earth–Sun distance – which is the rst rung on the cosmic
distance ladder. Image: Jamie Cooper.

How astronomers are able to measure the distance to stars using the parallax method. A star’s position will be seen to jump slightly
relative to the background stars from opposite points in Eartth’s orbit around the Sun.

The timing of the pulsations of Cepheid variable stars, such as RS Puppis pictured here, is directly related to their intrinsic
luminosity, so astronomers can calculate how far away they are based on how quickly they pulsate and how faint they appear to us.

Type Ia supernovae have standardisable brightnesses that allows astronomers to deduce how far away they are.

The different scales at which three different rungs on the cosmic distance ladder - Cepheid variables, type Ia supernovae and
cosmological redshift - operate, extending from millions of light years (Mly) to billions of light years (Bly).

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Absolute Beginners: The cosmic ...

January 2021

Astronomy Now