Definitions

# Standard candle

A standard candle is an astronomical object that has a known luminosity. Standard candles are the basis for several important methods of deriving distances in extragalactic astronomy and cosmology in the cosmic distance ladder.

## Theory

Comparing its known luminosity (or its derived logarithmic quantity, the absolute magnitude) and its observed brightness (apparent magnitude) the distance to the object can be calculated as:

$5 log_\left\{10\right\} frac\left\{D\right\}\left\{mathrm\left\{kpc\right\}\right\} = m -M -5,$

where D is the distance, kpc is kiloparsec (103 parsec), m the apparent magnitude and M the absolute magnitude (both in the same band at rest). (Note that this is closely related to the distance modulus of an object.)

## Examples

Standard candles include:

• RR Lyrae variables — red giants typically used for measuring distances within the galaxy and in nearby globular clusters.
• Eclipsing binaries — In the last decade, measurement of eclipsing binaries' fundamental parameters has become possible with 8 meter class telescopes. This makes it feasible to use them as indicators of distance. Recently, they have been used to give direct distance estimates to the LMC, SMC, Andromeda Galaxy and Triangulum Galaxy. Eclipsing binaries offer a direct method to gauge the distance to galaxies to a new improved 5% level of accuracy which is feasible with current technology up to a distance of around 3 Mpc.
• Cepheid variables — the preferred choice in extragalactic astronomy, out to the range of a few tens of Mpc.
• Type Ia Supernovae — that have a very well-determined maximum absolute magnitude as a function of the shape of their light curve and are useful in determining extragalactic distances up to a few hundred Mpc. A notable exception is SN 2003fg, the "Champagne Supernova," a type Ia supernova of unusual nature.

In galactic astronomy, X-ray bursts (thermonuclear flashes on the surface of a neutron star) are used as standard candles. Observations of X-ray burst sometimes show X-ray spectra indicating radius expansion. Therefore, the X-ray flux at the peak of the burst should correspond to Eddington luminosity, which can be calculated once the mass of the neutron star is known (1.5 solar masses is a commonly used assumption). This method allows distance determination of some low-mass X-ray binaries. Low-mass X-ray binaries are very faint in the optical, making measuring their distances extremely difficult.

## Problems with standard candles

The primary issue with standard candles is the recurring question of how standard they are. For example, all observations seem to indicate that type Ia supernovae that are of known distance have the same brightness (corrected by the shape of the light curve). However, it is not known why they should have the same brightness, and the possibility that the distant type Ia supernovae have different properties than nearby type Ia supernovae exists.

That this is not merely a philosophical issue can be seen from the history of distance measurements using Cepheid variables. In the 1950s, Walter Baade discovered that the nearby Cepheid variables used to calibrate the standard candle were of a different type than the ones used to measure distances to nearby galaxies. The nearby cepheid variables were population I stars with much higher metal content than the distant population II stars. As a result, the population II stars were actually much brighter than believed, and this had the effect of doubling the distances to the globular clusters, the nearby galaxies, and the diameter of the Milky Way.