IOP Institute of Physics

# The cosmic distance ladder

Astronomers have identified the most distant quasar yet to be discovered. But how do they know how far away objects are?

Robert Gendler

At the end of June, astronomers identified a quasar that is now believed to be the earliest and most distant known object in the universe. But distances to celestial bodies haven’t always been easily determined – less than a century ago it was thought that our galaxy was the entire extent of the universe.

So how do we measure the distance to stars and galaxies?

Direct measurement
Direct distance measurements are only possible for stars within a distance of a little more than 1000 lightyears even with precision, space-based telescopes.

They use the phenomenon of parallax, which is familiar in everyday life too – objects appear to be in slightly different positions when viewed solely through the left eye compared to when viewed solely through the right eye.

The human brain uses the separation between the two eyes to generate a perception of depth and automatically estimate distance. If vision were only monocular, it would be difficult to determine whether an object is small or far away.

A similar principle can be used to work out the distance to stars, but accurately and mathematically rather than automatically.

Chris Martin

Over the course of a year, as the Earth orbits the Sun, the apparent position of comparatively nearby stars changes relative to much more distant ones, which are so far away that they appear not to move. The angle by which the apparent position changes is inversely proportional to the star’s distance.

This method also defines a unit of distance – the parsec is the distance corresponding to a parallax angle of one arcsecond, or 1/3600th of a degree. The term was coined in 1913 and the unit is equal to about 3.26 ly, so the nearest star to the Sun, Proxima Centauri, is around 1.3 parsecs (4.2 ly) away.

The first successful measurement of the distance to a star using this method was carried out by the German astronomer Friedrich Bassel in 1838, when he determined that 61 Cygni is 10.4 ly away. More accurate recent measurements give a distance of 11.4 ly.

Standard candles
While parallax is used to calibrate the cosmic distance scale by allowing us to work out the distances to nearby stars, other methods must be used for much more distant bodies, since their parallax angle is too small to measure accurately.

One comes from using the inherent brightness of an object – the luminosity of some astronomical bodies is known well enough to be able to calculate their distance.

Since how bright a star appears in the sky (its “apparent magnitude”) is a function of both its actual light output (“absolute magnitude”) and the distance from the observer, knowing the former two allows calculation of the latter.

The bodies of which the intrinsic luminosity is well known are referred to as “standard candles”. One commonly used type of standard candle is the Cepheid variable – a type of star named after Delta Cephei in the constellation Cepheus, in which the luminosity fluctuates over time. Because there is a direct relationship between that luminosity and the period over which it oscillates, the absolute magnitude of any Cepheid variable close enough to see can be worked out.

The identification of this type of star in the Andromeda galaxy, and observations by Edwin Hubble in 1922–3, led astronomers to realise for the first time that Andromeda was much further away than had been thought – outside our own galaxy.

Distances calculated using variable stars as standard candles were recalculated after Walter Baade’s observations in the 1950s revealed that the more distant Cepheids were older and had a lower non-hydrogen content than ones nearby. Their absolute magnitudes had been underestimated, and so they were much further away than had been believed when they were first identified as extragalactic.

At greater distances or areas in which there is no star formation and hence few Cepheids, such as in elliptical galaxies, other astronomical bodies are used to calculate distances in a similar way. These might be RR Lyrae variables (a kind of red giant star) or Type 1a supernovae, for example. For binary systems, the orbital characteristics can be used to calculate mass, and, since there is a direct relationship between mass and luminosity, the absolute magnitude of a star.

Other formulae can also be used to determine absolute magnitude, and therefore distance, such as the Tully-Fisher relation, which links the luminosity of a spiral galaxy with the range of its rotational velocities, and the Faber-Jackson relation, from which the luminosity of an elliptical galaxy can be calculated from the dispersion of velocities of the stars in its centre.

Redshift
As well as realising that the Andromeda Galaxy is separate from our own, Hubble discovered that the redshift of light from other galaxies is proportional to how far away they are – this is now known as Hubble’s law.

The large redshifts of the light from what are now known to be distant galaxies were first noted by the American astronomer Vesto Slipher in 1912, and are a result of the Doppler Effect. Galaxies further from the Earth are moving away from it faster than ones close by.

Hubble massively overestimated the rate at which galaxies’ recession velocities increase with distance because of the error in calibrating those distances that came from confusing the two types of Cepheid variable, as mentioned above.

But increasingly precise measurements of this number, Hubble’s constant, have been made from Allan Sandage’s 1958 estimate onwards. Data from the WMAP satellite in 2010 gave a value of 71.0±2.5 km/s/Mpc.

For the most distant bodies in the universe, corrections have to be made to take general relativity into account.
The quasar discovered in June has a redshift of 7.085, dating it to just 0.77 billion years after the big bang, placing it about 13.35 bn lightyears away.

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