Cosmic Distance Ladder

Akarsh Simha

The cosmic distance ladder refers to the succession of different methods that astronomers use to measure distances to objects in the sky. Some methods, like parallax, work well for only nearby objects. Other methods, like using the cosmological redshift, work only for very distance galaxies. Thus, there are several methods, each with its own limited validity, and hence the name.

Mesures directes

The bottom of the ladder consists of objects whose distances can be directly measured, like the moon (see Lunar Laser Ranging). The same technique, using radio waves, is applied to find distances to planets as well.

For nearby stars, measuring the parallax is possible and yields the distance to the star.

Chandelles standards

"Standard candles" are objects whose intrinsic brightnesses we can know for sure. The apparent magnitude, which is easy to measure, tells us how bright an object appears, not how bright it actually is. Distant objects appear less brighter, because their light gets spread out over a larger area.

In accordance with the inverse square law for light intensities, the amount of light we receive from an object drops with the distance squared. Thus, we may compute the distance to an object if we know both how bright it actually is (absolute magnitude; 'M') and how bright it appears to us on earth (apparent magnitude; 'm'). We may define the distance modulus as follows:

Distance Modulus = M - m = 5 log10 d - 5

Here 'd' is the distance measured in parsecs.

Pour des chandelles standards spéciales, il existe d'autres façons de calculer l'intensité intrinsèque et par conséquent de calculer leurs distances.

Les chandelles standards les plus communes utilisées en astronomie sont :

  • Les céphéides variables : une variété d'étoiles variables périodiques dont la période de variation est liée à son intensité

  • Les variables de type RR de la Lyre : une autre variété d'étoiles variables périodiques avec une relation parfaitement connue entre période et intensité

  • Les supernovas de type Ia : ces supernovas ont une intensité parfaitement connue résultant des lois de physique qui les gouvernent et qui sont utilisées comme des chandelles standards

Autres méthodes

There are many other methods. Some of them rely on the physics of stars, such as the relationship between luminosity and color for various types of stars (this is usually represented on a Hertzsprung-Russel Diagram). Some of them work for star clusters, such as the Moving cluster method and the main-sequence fitting method. The Tully-Fisher relation that relates the brightness of a spiral galaxy to its rotation can be used to find the distance modulus, since the rotation of a galaxy is easy to measure using Doppler shift. Distances to distant galaxies may be found by measuring the Cosmological redshift, which is the redshift of light from distance galaxies that results from the expansion of the universe.

For further information, consult Wikipedia on Cosmic Distance Ladder