How to measure distances in the Universe?

Comparison of methods for calculating distances in the Universe

Each method covers a different range of distances and serves to calibrate the next, thus forming the cosmic distance ladder.

The parallax method

The principle of parallax

The measurement of distances in our vast observable Universe is fundamental in astrophysics because it then becomes possible to estimate the intrinsic properties of the observed object. Unfortunately, it is very difficult to obtain great precision. To measure the great cosmic distances of the Universe, astronomers chain together several calculation methods on increasingly distant objects. The measurement of a nearby object must be made with full confidence because the methods are linked to one another and each measurement method makes it possible to calibrate the next.

The image of the world around us is reconstructed in real time by our brain from two sets of information. Our two eyes are spaced a few centimetres apart, so the image received by each of these receptors is slightly different. Indeed, for the observed object, each eye gives a position relative to a more distant and immobile background. An object that does not have the same position relative to the background produces an optical effect called the parallax effect. It is this effect that allows our brain to reconstruct a three-dimensional image in order to apprehend the distance of the object.

In astronomy, parallax is the angle under which the observed object is seen from two points distant from one another (the farther apart the observation points, the larger the parallax angle, and therefore the easier it is to measure).

Equatorial parallax

For bodies in the solar system, the Earth's equatorial radius (6,378 km) was chosen. Equatorial parallax is the angle under which an observer located at the centre of the observed object sees the Earth's radius.

This angle directly gives the distance of the object by a simple trigonometric calculation. For example, for an average distance of the Moon of 384,400 km, the lunar equatorial parallax is ≈57' and the apparent diameter of the Moon is ≈31', or ≈½ degree.

Annual parallax

To measure the distance of stars in our Galaxy, the reference is the semi-major axis of Earth's orbit (149,597,870,700 metres, or 1 Astronomical Unit). To measure this annual parallax, it is enough to observe the star twice, at six-month intervals. In other words, astronomers measure the annual parallax angle by measuring the position of a star once, then measuring again 6 months later, when the Earth is on the opposite side of its orbit. However, this is not so easy to measure because the farther the star is from Earth, the weaker the parallax.

For example, for the star closest to the Sun, Proxima Centauri (Alpha Centauri C), located 4.244 light-years away, the parallax is only 0.7 arcseconds, which is tiny; there are 360 degrees in a circle, in each degree there are 60 arcminutes, and in each minute there are 60 arcseconds. But the precision of measurement from Earth only allows a few stars located a few tens of light-years away to be measured.

Astrometric satellites Hipparcos and Gaia

From space, thanks to the Hipparcos satellite (HIgh Precision PARallax COllecting Satellite), we can measure the parallaxes of 120,000 stars with a precision of 2 to 4 milliarcseconds. In 2013, the Gaia satellite succeeded Hipparcos.

Gaia (Global Astrometric Interferometer for Astrophysics) established a catalogue of one billion stars with a precision of up to 10 microarcseconds.

The standard candle method

Henrietta Leavitt's discovery

To measure the distance of very distant stars, the parallax method is no longer possible because it is imprecise. Astronomers use another method, that of "standard candles".
In the 1910s at Harvard University, Henrietta Leavitt (1868-1921) classified the Cepheids of the Magellanic Clouds (two dwarf galaxies neighbouring the Milky Way, located between 150 and 200 light-years away). A Cepheid is a star whose brightness varies according to a well-defined period (between 1 and 135 days). It was in 1908 that the first standard candle was discovered unexpectedly, thanks to Henrietta Leavitt's intuition. She noticed that the periods of Cepheids are greater when they are brighter. The intrinsic luminosity of classical Cepheids thus increases with their period. In other words, the larger and brighter a Cepheid is, the slower its pulsation frequency. She found a relation linking the period of variation (time between two maxima or minima) to the apparent luminosity of these stars.

From Cepheids to distant galaxies

Thus, it is enough to measure the precise distance of one of these Cepheids with the parallax method to obtain a general relation linking the periods and absolute luminosities of Cepheids.
This measurement was carried out for the first time in 1916 at Harvard University by Harlow Shapley (1885-1972), who completed Henrietta Leavitt's discovery. From that date, Cepheids whose intrinsic luminosity is known became "standard candles" for measuring the distance of distant stars and nearby galaxies.
The apparent luminosity of an object therefore depends on its absolute luminosity and its distance. It was by observing variable stars of the Cepheid type that astronomer Edwin Hubble (1889-1953) measured in 1923 the distance of the spiral galaxy M31 (Andromeda, the closest to the Milky Way), using the telescope of the Mount Wilson Observatory, near Pasadena in California.

The type 1a supernova method

The explosion of a white dwarf

For distant galaxies, telescopes can no longer distinguish their stars individually. Astronomers must rely on extremely bright objects as bright as a galaxy. The object used is the type 1a supernova.
Supernovae are rare events in our Milky Way, one to three per century, but on the scale of the Universe, we observe them every day.
A type 1a supernova corresponds to the total explosion of a white dwarf that has crossed the Chandrasekhar mass limit (when the star's radius decreases, the mass tends toward a limit of 1.44 solar masses). Because of their physical properties, white dwarfs fed by matter from a nearby companion cannot exceed this limit.
The type 1a supernova SN 2014J is located in the Cigar Galaxy (Messier 82) at 11.5 ± 0.8 million light-years.

A standard candle of cosmology

This standard candle of cosmology will make it possible to determine extragalactic distances.
Because they always explode at the same point (mass limit), type 1a supernovae always have roughly the same intrinsic luminosity after reaching their maximum luminosity. Type 1a supernovae, very bright and visible at very great distances, therefore serve as standard candles.
To calibrate the method, it is necessary to use type 1a supernovae close enough to be measured by the Cepheid method. Scientists know a few dozen type 1a supernovae sufficiently close.
Type 1a supernovae will make it possible to measure the distance of distant galaxies up to several billion light-years.

The redshift method

Redshift

For even more distant galaxies, astronomers use the method of the redshift of absorption lines in the electromagnetic spectrum.
This redshift is used to measure the duration of light's journey. The "older" the light, the greater the redshift.
Each chemical element or molecule leaves different traces on this spectrum. These traces appear at very specific wavelengths (absorption lines). But if a galaxy moves away from us, its light stretches and the wavelengths of these chemical fingerprints shift toward the red. This shift is linked to the galaxy's distance by Hubble's law. This law states that the farther a galaxy is, the faster it moves away from us as the Universe expands. By measuring redshift, astronomers have been able to identify the first galaxies close to the Big Bang.

Hubble's law and the expansion of the Universe

Thus light reveals the distance of nearby and distant cosmic objects, and astronomers today know how to calculate distances to the very depths of the observable Universe (about 13 billion light-years).
Hubble's law relates the apparent recession velocity of a galaxy to its distance, and today constitutes one of the pillars of the expansion of the Universe. It makes it possible to convert a simple spectral shift into a distance expressed in megaparsecs.

N.B.:
Redshift is a shift toward longer wavelengths of spectral lines and of the entire visible spectrum. There is a correlation between distance and the redshift of optical spectra of galaxies. Redshift is the most widely used method for measuring the distance of extragalactic objects. This phenomenon observed in the light of distant astronomical objects is proof of the expansion of the Universe (dilation of space) and of the Big Bang.