Types of Cepheid Variables and Other Standard
Candles
1. Standard candles and distance measurement
A standard candle is an astronomical object whose intrinsic luminosity, or absolute magnitude, can be
determined from an observable property. Once its absolute magnitude M is known, astronomers compare
it with its apparent magnitude m and calculate the distance using the distance-modulus relation
m − M = 5 log10 (
d
) + A,
10 pc
where d is the distance in parsecs and A is the dimming caused by interstellar extinction. After correcting
for extinction,
d = 10(m−M +5)/5 pc.
Standard candles are therefore not necessarily objects that all have exactly the same luminosity. More
commonly, they are standardizable candles whose luminosity can be predicted from another measurable
quantity, such as pulsation period, colour or light-curve shape.
Cepheid variables are especially useful because their pulsation period is closely related to their intrinsic
luminosity. However, there are two principal Cepheid populations, and they do not obey the same period–
luminosity relation.
2. The two principal types of Cepheid variable
Classical Cepheids: Type I Cepheids
Classical Cepheids, also called Type I Cepheids, Population I Cepheids or Delta Cephei variables, are
relatively young, massive and luminous stars. They are generally several times more massive than the Sun
and are found mainly in the thin disk of the Milky Way, spiral arms, young open clusters and other regions
associated with recent star formation. Their comparatively young ages and concentration near the Galactic
plane identify them as Population I stars.
Classical Cepheids normally have pulsation periods ranging from roughly one or two days to more than 100
days. Their light curves are usually asymmetric: the star brightens rapidly and then fades more gradually.
The exact light-curve shape changes systematically with period, including the appearance and movement of
a secondary “bump” in Cepheids with periods around ten days. This sequence of changing shapes is called
the Hertzsprung progression.
The more slowly a classical Cepheid pulsates, the more luminous it is. This is the classical period–
luminosity relation, or Leavitt law. Classical Cepheids are extremely luminous and can therefore be
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detected individually in nearby galaxies, making them one of the most important calibrators of the
extragalactic distance scale.
Type II Cepheids
Type II Cepheids are older, lower-mass stars associated with Population II. They are commonly found in
globular clusters, the Galactic halo and the Galactic bulge rather than in young spiral arms. They have
periods covering much of the same range as classical Cepheids, but their evolutionary history, mass,
chemical composition and luminosity are different.
At a given pulsation period, a Type II Cepheid is normally about one to two magnitudes fainter than a
classical Cepheid. Consequently, applying the classical Cepheid period–luminosity relation to a Type II
Cepheid would give the wrong absolute magnitude and therefore an incorrect distance.
Type II Cepheids are commonly divided into three subclasses:
Subclass
Approximate
period
General description
BL Herculis
stars
1–4 days
Short-period Type II Cepheids evolving away from the horizontal
branch
W Virginis
stars
4–20 days
Intermediate-period stars in a later, shell-burning evolutionary
phase
RV Tauri
stars
More than about
20 days
Long-period, highly evolved post-asymptotic-giant-branch
objects, often showing alternating deep and shallow minima
The boundaries are approximate, but periods of about 4 and 20 days are normally used to separate the
three groups.
Strictly speaking, modern catalogues recognise more than only two Cepheid classes. They commonly
distinguish classical Cepheids, Type II Cepheids and anomalous Cepheids. Anomalous Cepheids are
usually found in old, metal-poor systems but are brighter and more massive than ordinary RR Lyrae stars
and Type II Cepheids. Nevertheless, the expression “two types of Cepheids” usually refers to the historically
important division between classical Population I Cepheids and Population II, or Type II, Cepheids.
3. Historical discovery of the two populations
The original period–luminosity relation was established from Cepheids in the Magellanic Clouds. Because
the stars within a Magellanic Cloud are approximately at the same distance from Earth, differences in their
apparent brightness mainly reflect differences in their intrinsic luminosity. It was therefore possible to
discover the relation before the absolute distance to every star was known.
Later, Walter Baade recognised that the stars of galaxies could be separated into two broad populations.
Young, relatively metal-rich Population I stars dominate spiral arms, while old Population II stars are
prominent in globular clusters, galactic haloes and bulges. He realised that the pulsating variables
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associated with these populations did not have the same luminosity calibration. The failure to separate the
two populations had caused earlier extragalactic distances to be underestimated. Correcting the calibration
substantially increased the estimated distance to galaxies such as Andromeda and revised the overall
cosmic distance scale.
4. How to determine the type of an observed Cepheid
An astronomer should not classify a Cepheid from its period alone because classical and Type II Cepheids
have overlapping period ranges. A reliable classification normally combines several observations.
4.1 Obtain a complete light curve
The first step is repeated photometry over many nights or months. The measured brightnesses are folded
using a trial period until a repeating phased light curve is obtained. From this curve, the astronomer
measures:
• the pulsation period;
• mean apparent magnitude;
• amplitude;
• colour variation;
• rise and decline times;
• bumps, secondary features or alternating minima.
Classical and Type II Cepheids often have distinguishable light-curve shapes. Large surveys such as OGLE
and Gaia classify Cepheids partly through light-curve morphology and the Fourier parameters obtained by
decomposing the light curve into sinusoidal components.
Light-curve shape by itself, however, is not always decisive. Pulsation in the first overtone, unusual Type II
stars, binary companions and incomplete sampling can make one category resemble another.
4.2 Place the star on a period–luminosity diagram
The strongest test is to compare the star’s absolute magnitude with the luminosity predicted by the two
period–luminosity relations.
If its distance is known independently—for example, from a reliable parallax—the absolute magnitude can
be calculated. The star is then placed on a plot of absolute magnitude against log P .
• A star lying on the brighter classical-Cepheid relation is probably Type I.
• A star approximately one to two magnitudes below it at the same period is probably Type II.
For Cepheids in another galaxy, all the stars can be assumed to have approximately the same distance. They
form separate sequences in an apparent-magnitude-versus-period diagram, with Type II Cepheids forming
the fainter sequence. Observations of the Magellanic Clouds clearly show the classical and Type II Cepheids
occupying different period–luminosity sequences.
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A reddening-free or nearly reddening-free quantity called a Wesenheit magnitude is often used instead of
an ordinary magnitude. It combines brightness and colour so that interstellar extinction has much less
effect. Gaia studies use period–Wesenheit relations together with photometry and parallax information
when classifying Cepheids.
An important practical point is that an isolated Cepheid cannot be classified reliably from its apparent
magnitude and period alone. A faint star could either be an intrinsically faint Type II Cepheid or a more
distant classical Cepheid. Some independent distance, population information or detailed light-curve and
spectral evidence is required.
4.3 Examine the star’s location and surrounding population
The star’s environment gives another strong clue:
• A Cepheid in a young open cluster, spiral arm, star-forming region or thin Galactic disk is likely a
classical Cepheid.
• A Cepheid in a globular cluster, the Galactic halo or an old bulge population is likely a Type II
Cepheid.
Classical Cepheids trace the young disk and spiral structure, whereas Type II Cepheids trace older bulge and
halo populations.
This is supporting evidence rather than absolute proof because stars can move from their birthplaces, and
some unusual binary systems can have unexpected properties.
4.4 Obtain a spectrum
Spectroscopy can provide:
• metallicity, particularly [Fe/H];
• effective temperature;
• surface gravity;
• radial-velocity variation;
• chemical abundance peculiarities.
A relatively metal-rich star is more consistent with a classical Cepheid, while an old, metal-poor star is more
consistent with a Type II Cepheid. Spectroscopic peculiarities and differences in radial-velocity behaviour
can also help separate the two groups.
Metallicity is not a perfect one-step classifier because the metallicity ranges overlap, particularly among
stars in different galaxies. It should therefore be combined with luminosity and population information.
4.5 Use kinematics and astrometry
Gaia parallax and proper-motion measurements can help determine the star’s luminosity and Galactic orbit.
• A low-velocity orbit close to the Galactic disk supports a young classical-Cepheid classification.
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• A high-velocity, eccentric or halo-like orbit supports an old Type II classification.
Modern classification pipelines therefore combine astrometry, multiband photometry, period–luminosity or
period–Wesenheit position, light-curve structure and information from previous catalogues rather than
relying on a single property.
Practical classification procedure
For an unknown Cepheid, a sensible procedure would be:
1. Observe it repeatedly and determine a precise period.
2. Construct phased light curves in two or more filters.
3. Correct the mean brightness for interstellar extinction, or calculate a Wesenheit magnitude.
4. Use parallax or its host system’s known distance to calculate its absolute magnitude.
5. Compare its position with classical and Type II period–luminosity relations.
6. Examine the light-curve shape and Fourier parameters.
7. Obtain a spectrum to estimate metallicity and radial velocity.
8. Check whether its location and motion correspond to a young disk population or an old halo, bulge
or globular-cluster population.
The period–luminosity position would normally carry the greatest weight, while the light curve, spectrum
and environment would confirm the result.
5. Other important standard candles
RR Lyrae variables
RR Lyrae stars are old, low-mass horizontal-branch stars with much shorter periods than Cepheids,
normally less than one day. Their optical luminosities are relatively similar, with a correction for metallicity,
while in infrared wavelengths they follow useful period–luminosity–metallicity relations.
They are common in globular clusters and old stellar populations, so they are excellent for measuring
distances within the Milky Way and the Local Group. They are much less luminous than Cepheids and
therefore cannot generally be observed across equally large distances.
Tip of the red-giant branch
Low-mass red giants eventually reach a maximum luminosity before helium ignites in their cores. This
produces a sharp cutoff called the tip of the red-giant branch, or TRGB, in a galaxy’s colour–magnitude
diagram.
The luminosity of the tip, particularly in red and near-infrared bands, can be calibrated and used as a
standard candle. TRGB stars belong to old populations and can therefore be found in the haloes of many
different types of galaxies, where dust and crowding may be lower than in star-forming disks. RR Lyrae
stars, Type II Cepheids and the TRGB are the three major Population II stellar distance indicators.
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Mira variables
Mira variables are pulsating asymptotic-giant-branch stars with long periods, commonly hundreds of days,
and very large changes in brightness. In infrared bands, suitable oxygen-rich Miras follow a period–
luminosity relation.
Miras are very bright in the infrared and can be found in old and intermediate-age populations. This makes
them useful where classical Cepheids are rare or where dust obscuration makes optical observations
difficult. Their disadvantages include long observing campaigns, circumstellar dust and differences between
chemical and pulsation subclasses. Miras are now being developed as an independent first-rung calibrator
of the distance ladder.
Red-clump and J-region asymptotic-giant-branch stars
Red-clump stars are core-helium-burning stars that occupy a compact region of a colour–magnitude
diagram. Their average luminosity can be calibrated, although it depends on population age and metallicity.
A newer related method uses carbon-rich asymptotic-giant-branch stars located in the J region of nearinfrared colour–magnitude diagrams. These JAGB stars have a relatively narrow luminosity distribution in
the near-infrared and are being investigated as an alternative calibration method for nearby galaxies.
Type Ia supernovae
Type Ia supernovae are among the most important extragalactic distance indicators. They are
thermonuclear explosions involving white dwarfs and are bright enough to be detected across cosmological
distances.
They are not perfectly identical explosions. Astronomers correct their peak luminosities using the shape and
colour of their light curves: slowly declining Type Ia supernovae are generally more luminous than rapidly
declining ones. After these corrections, they function as standardizable candles.
Their absolute luminosity must first be calibrated using a nearby host galaxy whose distance has been
measured using Cepheids, the TRGB or another primary indicator. Once calibrated, Type Ia supernovae
extend the distance ladder far beyond the range of individual Cepheids and are used to measure cosmic
expansion.
Planetary-nebula luminosity function
Planetary nebulae emit strongly in the doubly ionised oxygen line at 500.7 nm. Within a galaxy, the
brightest planetary nebulae have an empirically calibrated upper luminosity cutoff. Astronomers compare
the observed cutoff of the planetary-nebula luminosity function with its calibrated absolute value to
estimate the galaxy’s distance.
Unlike Cepheids, this is a population method rather than a standard candle based on one specific object. It
is especially useful in galaxies that do not contain recent star formation.
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Globular-cluster luminosity function
The distribution of globular-cluster luminosities in many galaxies has a characteristic turnover. Once the
absolute magnitude of this turnover is calibrated, its observed magnitude can provide a distance.
The method can be applied to elliptical galaxies and other systems without Cepheids, but it is affected by
the age, metallicity, evolution and completeness of the globular-cluster population. It is therefore generally
less precise than the best Cepheid, TRGB or Type Ia supernova measurements.
Novae
A nova occurs when accumulated matter undergoes a thermonuclear runaway on the surface of a white
dwarf. Relations between peak luminosity and the rate at which the nova fades have historically allowed
novae to be used as approximate standard candles.
Novae are relatively bright, but their luminosities and light curves show considerable diversity. They are
therefore less precise and less widely used than Cepheids or Type Ia supernovae.
6. The cosmic distance ladder
No single standard candle covers every astronomical distance. Instead, astronomers construct a cosmic
distance ladder:
1. Geometrical methods such as parallax and maser distances calibrate nearby stars.
2. These distances calibrate Cepheids, RR Lyrae stars, the TRGB, Miras and other stellar candles.
3. Cepheids or the TRGB are observed in nearby galaxies that have also hosted Type Ia supernovae.
4. These galaxies establish the absolute luminosity of Type Ia supernovae.
5. Type Ia supernovae are then used to measure distances across a large part of the observable
Universe.
Each rung overlaps with the next, allowing one method to calibrate another. This overlap is important
because every standard candle has possible systematic errors involving extinction, metallicity, stellar
population, crowding, calibration and selection effects.
Conclusion
The two principal Cepheid types are physically different stellar populations. Classical or Type I Cepheids are
young, massive and highly luminous Population I stars, while Type II Cepheids are older, lower-mass
Population II stars. Although their periods overlap, Type II Cepheids are substantially fainter at a given
period and follow a different period–luminosity relation.
The most reliable way to classify an observed Cepheid is to determine its period and extinction-corrected
mean magnitude, establish its distance, and compare its absolute magnitude with the separate classical
and Type II period–luminosity relations. Light-curve morphology, metallicity, Galactic motion and
surrounding stellar population provide additional confirmation.
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Cepheids are only one component of the distance ladder. RR Lyrae variables, the tip of the red-giant branch,
Miras, JAGB stars, Type Ia supernovae and population-based methods such as the planetary-nebula
luminosity function extend reliable distance measurements from the Milky Way to cosmological scales.
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