method

cosmic distance measurement

Astronomical techniques using supernovae and standard candles to measure universe expansion.
35 related articles · 5 formulas

Description

Cosmic distance measurement is the set of techniques astronomers use to determine how far away objects are, and by extension, how fast the universe is expanding. The most famous method uses standard candles — objects of known intrinsic brightness, like Type Ia supernovae — whose apparent dimness reveals their distance. This is how the accelerating expansion of the universe was discovered in 1998, leading to the concept of dark energy. Other methods include standard rulers (like the baryon acoustic oscillations imprinted in galaxy clustering) and geometric techniques like parallax and gravitational lensing.

History

The first reliable extragalactic distance measurements were made by Edwin Hubble in the 1920s using Cepheid variable stars. The cosmic distance ladder was refined over the decades, and the use of Type Ia supernovae as standard candles was pioneered in the 1990s by two competing teams, leading to the 2011 Nobel Prize for the discovery of cosmic acceleration.

How it works

The fundamental idea is the inverse-square law: if you know how bright an object really is (its absolute magnitude) and measure how bright it appears (apparent magnitude), the distance follows directly. Type Ia supernovae are ideal because they explode when a white dwarf reaches a critical mass, so their peak luminosity is remarkably uniform — with a small correction for the light-curve shape. For very distant objects, astronomers use the redshift to estimate distance via Hubble's law, but this requires calibrating the Hubble constant, which is where the 'cosmic tension' arises: different methods give slightly different values, as hinted by the title 'Why did cosmology crack?'.

In practice

Distance measurements underpin the determination of the Hubble constant, the age of the universe, and the properties of dark energy. They are also used to map the large-scale structure of the cosmos and to calibrate the luminosity of other astronomical objects.

Fun fact

The title 'How to measure distance to supernova remnants' refers to a clever technique: measuring the apparent expansion rate of the remnant's shell and combining it with the Doppler shift of its spectral lines to get a geometric distance — no standard candle needed.

Concept graph →

Formulas

$$\theta = \nabla_\mu u^\mu$$
Classifies spacetime regions by sign of expansion rates.
What is in the formula
θvariableexpansion scalar — expansion scalar per second
u^μvariablefour-velocity of the fluid or congruence — four velocity
∇_μoperatorcovariant derivative with respect to spacetime coordinate μ — covariant derivative
θ_{\pm}=\frac{2}{r}[\pm1+\dot{r}] · 2605.07848v2
$$P \propto d^2$$
Transmitter power scales with the square of distance.
What is in the formula
PvariableTransmitter power — power watt
dvariableDistance from the transmitter — distance metre
∝operatorIndicates that the left side scales with the square of the right side — proportionality
{эиим}_{{lim}}\approxn_σ(\frac{σ_ν}{100{ян}})(\frac{d}{1{пк}})^21.2*10^{11}{вт} · 2606.04304v1
$$m - M = 5 \log_{10} \left( \frac{d}{10\,{\rm pc}} \right)$$
Relates apparent and absolute magnitudes to distance.
What is in the formula
mvariableapparent magnitude — apparent magnitude
Mvariableabsolute magnitude — absolute magnitude
dvariabledistance to the object — distance parsec
log10operatorbase-10 logarithm — logarithm base 10
m_{\rmbar}-m_{\rmbar}=5\log_{10}(\frac{d}{10{\rmpc}}) · 2606.05144v2
m-m=5\log_{10}(d/10) · 2606.26831
μ=m-m=5\log_{10}(d_l/{пк})-5 · 2607.03569
μ=m-m=5\log_{10}(\frac{d_l}{{мпк}})+25 · 2607.06959
$$\beta = \frac{D_{ds} D_s'}{D_{ds}' D_s}$$
Ratio of angular diameter distances in lensing cosmology.
What is in the formula
βvariableratio of angular diameter distances — distance ratio
D_dsvariableangular diameter distance from lens to source — angular diameter distance metre
D_s'variableangular diameter distance from observer to source in a reference cosmology — angular diameter distance metre
D_ds'variableangular diameter distance from lens to source in a reference cosmology — angular diameter distance metre
D_svariableangular diameter distance from observer to source — angular diameter distance metre
β_{e,{pl}}=(β-(1-λ)(1-β))^{\frac{1}{γ_{{pl}}-1}} · 2607.01005v1
β=\frac{d_{ds1}d_{s2}}{d_{ds2}d_{s1}} · 2607.01005v1
$$r_{\text{snow}} \propto \sqrt{L}$$
Snow line distance scales with square root of luminosity.
What is in the formula
r_snowvariableDistance from star to snow line — distance metre
LvariableStellar luminosity — luminosity watt
∝operatorProportional to — proportionality
r_{{snow}}\approx2.7\sqrt{l/l_☉}{а.е.} · 2607.15144

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