Cepheids: Why Does Their Luminosity Vary So Regularly?

What is a Cepheid?

Definition and astronomical role

Cepheids are pulsating variable stars whose luminosity varies periodically due to changes in their size and temperature. These stars are essential in astrophysics because they allow astronomical distances to be measured, both in our galaxy and in nearby galaxies, thanks to the period-luminosity relation. This relation was discovered by the American astronomer Henrietta Swan Leavitt at the beginning of the 20th century. The name of these stars comes from δ Cephei (delta Cephei), in the constellation Cepheus, whose variability was discovered in 1784 by the British astronomer John Goodricke (1764-1786).

Two main families

• Classical Cepheids (population I): young, massive and very luminous stars, located mainly in the spiral arms of galaxies. Their periods range from about 1.5 days to more than 50 days. They follow the period-luminosity relation most used to measure distances.
• Type II Cepheids (population II): much older, less massive and less luminous stars (W Virginis and BL Herculis types, among others). They obey a different period-luminosity relation and are less useful as distance indicators.

Some famous Cepheids

• δ Cephei: the prototype of the class, whose variability has been known since 1784.
• Polaris (the North Star): the closest Cepheid to us, at about 430 light-years. Its period is about four days, and its brightness variations are very small.
• RS Puppis: a massive and very luminous Cepheid, surrounded by a dust nebula, presented below.

Characteristics of Cepheids

Variability and period-luminosity relation

• Variability: Cepheids see their luminosity vary regularly over periods ranging from about one day to more than two months. The known record in the Milky Way, identified in 2024, is 78.1 days. This variation is due to oscillations in the star's internal structure.
• Period-luminosity relation: Henrietta Leavitt (1868-1921) showed that the longer the period of variation of a Cepheid, the higher its intrinsic luminosity. In other words, the absolute magnitude of a Cepheid is directly linked to the period of its oscillations.

What is observed during a cycle

During a cycle, the star changes in size, temperature and therefore color. It goes from a spectral type F (hotter) at maximum brightness to a type G (cooler, like the Sun) at minimum. These stars are yellow giants or supergiants.

Methods for calculating distances in the Universe

The following table compares the main methods of measuring cosmic distances. It shows why Cepheids occupy the first rung of the extragalactic distance ladder: they extend stellar parallax and serve to calibrate more distant indicators.

The discovery of Henrietta Swan Leavitt

Photographic plates of the Magellanic Clouds

Henrietta Swan Leavitt worked at the Harvard Observatory, where she examined photographic plates of the Magellanic Clouds, taken in particular from the Arequipa station in Peru. In 1908, she published a catalog of 1,777 variable stars in the two Clouds, including several dozen Cepheids. In 1912, a short article, signed by Edward Pickering but "prepared by Miss Leavitt", gave the periods of 25 Cepheids in the Small Magellanic Cloud. Her fundamental discovery is the period-luminosity relation: stars whose period of variation is longer are intrinsically brighter.

From relative scale to absolute distances

Since the stars of the Small Cloud are at roughly the same distance from us, their apparent brightness reflected their relative luminosities. Leavitt could not determine the absolute distances of these stars, but she provided an extremely precise relative scale. It remained to fix its zero point. As early as 1913, Ejnar Hertzsprung attempted to calibrate it from Cepheids in the Milky Way, and then Harlow Shapley refined this calibration in 1918. This opened the way to estimating the distances of galaxies and to understanding the scale of the Universe.

Physics of Cepheids

Evolved stars in the instability strip

Classical Cepheids are evolved stars of intermediate to high mass (on the order of 4 to 20 solar masses). They have left the main sequence of the Hertzsprung-Russell diagram (a graph that links the intrinsic luminosity of stars to their surface temperature) and cross the instability strip, a narrow region of the diagram where the envelope becomes capable of sustaining radial pulsations. In this type of pulsation, the star remains spherical and swells and contracts as a whole.

Helium zone instability (κ mechanism)

The variability of Cepheids is due to a process called "helium zone instability". In certain layers of these stars, helium is partially ionized (He⁺ and He²⁺ coexist), which affects the transparency to heat (opacity). This is also called the κ mechanism, from the Greek letter that designates opacity. The idea that these stars pulsate, rather than being binary stars, became established in the 1910s with the work of Shapley and Eddington. The identification of the helium ionization zone as the driving engine of the pulsation dates from the 1950s-1960s.

Contraction-expansion cycle

• Contraction phase: when the star contracts, the temperature increases and helium becomes more ionized. The layer becomes more opaque and retains energy instead of letting it pass. This accumulation of energy raises the pressure and makes the star swell.
• Expansion phase: when the star expands, it cools and helium recombines into a less ionized state. The opacity decreases, which allows energy to escape. The pressure drops, gravity takes over again, the star contracts once more and the cycle begins again.

Regularity of pulsations

This pulsation cycle is very regular, which allows the precise relation between period and luminosity. As with the note of a musical instrument, the period depends on the size of the star: it varies as the inverse of the square root of its mean density (P ∝ ρ^−1/2).

Why does the period give the luminosity?

The instability strip covers a narrow temperature interval. The luminosity of a Cepheid therefore depends mainly on its radius, itself linked to its mass by stellar evolution. A more luminous star is larger, therefore less dense on average, therefore slower to pulsate. This is what links the period to the luminosity.

Importance of the discovery

Hubble and external galaxies

At the Mount Wilson Observatory, with the 2.5 m telescope, Edwin Hubble (1889-1953) spotted in October 1923 a Cepheid (named V1) on a photographic plate of the "nebula" of Andromeda. Thanks to the period-luminosity relation, he obtained a distance of about 900,000 light-years, far greater than the dimensions then accepted for the Milky Way. Cepheids observed in M33 and NGC 6822 confirmed the result. His conclusions, presented to the American Astronomical Society on January 1, 1925 and published the same year, demonstrated that certain spiral nebulae are in reality galaxies external to the Milky Way. This discovery changed our understanding of the Universe, showing that it is much vaster than had been thought.

Baade and the doubling of distances

In 1952, the astronomer Walter Baade showed that there are two populations of Cepheids, which obey different period-luminosity relations. This correction multiplied the distances to external galaxies by about two. Andromeda is today at about 2.5 million light-years.

Calibrating Cepheids: from Gaia to the James Webb Space Telescope

Gaia and the zero point

For the period-luminosity relation to give absolute distances, the true luminosity of nearby Cepheids must be known, and therefore their geometric distances. The parallaxes of ESA's Gaia satellite serve this calibration in the Milky Way. The third data release (Gaia DR3, June 2022) contains light curves for 15,006 Cepheids of all types: 5,221 in the field of the Milky Way and its small satellites, 4,663 in the Large Magellanic Cloud, 4,616 in the Small Magellanic Cloud, 321 in the Andromeda galaxy (M31) and 185 in the Triangulum galaxy (M33). Among them, 474 are probably new Cepheids discovered by Gaia.

Three geometric anchors

To fix the zero point, the SH0ES team combines three geometric references: Gaia parallaxes for Milky Way Cepheids, the masers of the galaxy NGC 4258, and the eclipsing binaries of the Large Magellanic Cloud.

Mapping the Milky Way

Classical Cepheids, young and very luminous, also allow the Milky Way to be mapped. The OGLE survey has placed about 2,400 of them on a map of our Galaxy. It also identified in 2024 the known galactic Cepheid with the longest period, OGLE-GD-CEP-1884, with 78.14 days, at about 4.5 kiloparsecs. It exceeds by about ten days the previous record, held by S Vulpeculae.

The James Webb Telescope tests crowding

In distant galaxies, the image of a Cepheid blends with that of neighboring stars. This crowding phenomenon could distort its luminosity, and therefore its distance. In the near infrared, where absorption by dust is low, the resolution of the James Webb Space Telescope is about 2.5 times better than that of Hubble. Over more than 1,000 Cepheids observed in NGC 4258 and five supernova host galaxies, the mean difference between Hubble and Webb measurements is −0.01 ± 0.03 magnitude (Riess et al. 2024). This result rules out crowding as an explanation of the Hubble tension, at about 8 σ. In 2025, the observation of a host galaxy almost devoid of background stars (NGC 3447) confirmed the absence of bias. Webb also reduces the dispersion of the period-luminosity relation.

Cepheids and the tension over the Hubble constant

Two values that do not agree

The Hubble constant, denoted H₀, measures the current expansion rate of the Universe. Calibrated with Cepheids and then type Ia supernovae, the SH0ES team obtains H₀ = 73.04 ± 1.04 km s⁻¹ Mpc⁻¹ (Riess et al. 2022). The cosmic microwave background observed by the Planck satellite, interpreted with the ΛCDM model, gives H₀ = 67.4 ± 0.5. The discrepancy, of about 8%, reaches nearly 5 σ: this is the Hubble tension.

Recent results with James Webb (space telescope)

The SH0ES team published new results in 2025. With Cepheids observed by Webb in 19 host galaxies of 24 type Ia supernovae, it finds H₀ = 73.49 ± 0.93. Adding calibrations by the tip of the red giant branch (TRGB), it obtains 73.18 ± 0.88.

Wendy Freedman's Chicago-Carnegie Hubble Program (CCHP) arrives at other values. With the tip of the red giant branch (TRGB) method alone and 24 calibrating supernovae, it obtains H₀ = 70.39 ± 1.22 (statistical) ± 1.33 (systematic) ± 0.70 (supernovae). With Webb data alone, the TRGB method gives 68.81 ± 1.79 ± 1.32, and that of carbon stars of the asymptotic giant branch (JAGB) gives 67.80 ± 2.17 ± 1.64. Its authors consider these results compatible with the ΛCDM model, without new physics. They also note that the TRGB and JAGB distances agree to better than 1%, and with the Cepheid distances of SH0ES to a little more than 1%.

Sources of uncertainty to watch

• Crowding: tested with Webb, it does not seem to explain the tension.
• Absorption by dust: it reddens and weakens Cepheids, hence the interest of the infrared.
• Metallicity: the content of heavy elements can slightly modify the period-luminosity relation.
• The zero point: it depends on the parallaxes of Gaia, NGC 4258 and the Large Magellanic Cloud.
• The choice of galaxies and supernovae: small samples can shift the final value of H₀.

N.B.:
This field is evolving very quickly. The values above are those published at the date of update of this article and the debate is not settled.

RS Puppis, a Cepheid surrounded by light echoes

A montage from Hubble observations

This video montage was made from observations of the Hubble Space Telescope. It shows the pulsations of the variable star RS Puppis and its environment of thick dark dust clouds. RS Puppis is a Cepheid in the constellation Puppis. The Hubble observations were taken over a period of five weeks in 2010, in order to capture the star at different stages of its 41.4-day cycle. Its brightness varies by a factor of nearly five. The short video is repeated several times to show the light echo mechanism more clearly.

What is a light echo?

The dust surrounding RS Puppis allows a phenomenon known as a light echo to be observed with astonishing clarity. At each maximum of brightness, a wave of light propagates through the nebula. The light reflected by more distant dust layers travels a longer path and arrives later on Earth. This echo creates the illusion of clouds of gas expanding from RS Puppis, whereas no matter is moving in this way. It is somewhat the luminous equivalent of a sound echo.

A distance measured by the echo, then reconsidered

In 2008, Pierre Kervella and his colleagues used light echoes, observed with ESO's NTT telescope, to propose a purely geometric distance of 6,500 ± 90 light-years, presented as the most precise ever obtained for a Cepheid. In 2009, Howard Bond and William Sparks challenged this value. It assumed that the dust zones were located near the plane of the sky, whereas scattering favors light emitted forward and places most of the observed dust in front of the star. Hubble polarimetric images, taken in 2010 and analyzed in 2014, led to a distance of 1,910 ± 80 parsecs, or about 6,200 light-years. This value is compatible with other methods.

N.B.:
The value of 6,500 ± 90 light-years, often cited, should therefore be handled with caution: it claimed a precision of 1.4%, whereas the 2014 polarimetric measurement announces an uncertainty of about 4%.

From brightness to distance: the example of RS Puppis

The distance d (in parsecs) is deduced from the apparent magnitude m, corrected for interstellar absorption A, and the absolute magnitude M: m − A − M = 5 log₁₀(d) − 5. For RS Puppis, the mean apparent magnitude in the visible is 7.12. The interstellar absorption is about 1.4 magnitude and the absolute visual magnitude is about −5.70. We obtain a distance modulus of 11.40, i.e. d ≈ 1,900 parsecs.

N.B.:
Here, the absolute magnitude is itself deduced from the geometric distance measured thanks to light echoes. The exercise illustrates the logic of the calculation. Above all, it shows that RS Puppis falls, to within about 1 σ, on the period-luminosity relation established with other Cepheids.

A massive Cepheid, but ephemeral in its nebula

RS Puppis is one of the most luminous Cepheids in the Milky Way, with a period of 41.5 days. It is the only known galactic Cepheid to be immersed in a large reflection nebula. This dust was not ejected by the star: it is an interstellar cloud that the Cepheid is traversing. Its strong luminosity could, within a few million years, dissipate the neighboring dust and make the light echoes disappear.

Knowing the distance of such a star with accuracy is important, because Cepheids serve as a marker (standard candle) for distances within our galaxy and nearby galaxies.