Henrietta Leavitt's Law: How a Blinking Star Measures the Universe

Some stars breathe. They swell and shrink on a regular cycle, and their brightness rises and falls with it, like a lighthouse with a fixed rhythm. In 1912 Henrietta Swan Leavitt noticed that, for one class of these stars, the rhythm tells you how bright the star really is. Once you know that, comparing it with how bright the star looks tells you how far away it is. That relation, the period–luminosity law, is now usually called Leavitt's law, and it is the idea behind our Henrietta Swan Leavitt sticker and the Leavitt's Law poster.

Who was Henrietta Leavitt?

Leavitt (1868–1921) graduated from what became Radcliffe College and worked at the Harvard College Observatory as one of its “computers”, the staff who measured and catalogued stars on photographic plates Henrietta Swan Leavitt, Wikipedia^[1]. The observatory's director, Edward Charles Pickering, assigned her the variable stars of the Small and Large Magellanic Clouds, photographed with the Bruce telescope at Harvard's southern station in Arequipa, Peru Henrietta Swan Leavitt, Wikipedia^[1]. She identified 1,777 variable stars and, in a 1908 paper in the Annals of Harvard College Observatory, noted that the brighter ones had the longer periods Henrietta Swan Leavitt, Wikipedia^[1]. She gradually lost her hearing during her life, and she died of cancer in December 1921 Henrietta Swan Leavitt, Wikipedia^[1].

What exactly did Leavitt discover in 1912?

The key text is a short Harvard circular dated 3 March 1912, issued under Pickering's name, which states that it “has been prepared by Miss Leavitt” Leavitt & Pickering 1912, Harvard Circular 173^[2]. It lists the periods of 25 variable stars in the Small Magellanic Cloud, arranged in order of length, and notes that the brighter variables have the longer periods, a pattern first remarked on in the 1908 catalogue Leavitt & Pickering 1912, Harvard Circular 173^[2]. When she plotted their magnitudes against the logarithm of the period, she wrote:

“A straight line can readily be drawn among each of the two series of points corresponding to maxima and minima, thus showing that there is a simple relation between the brightness of the variables and their periods. The logarithm of the period increases by about 0.48 for each increase of one magnitude in brightness.” Leavitt & Pickering 1912, Harvard Circular 173^[2]

The crucial step is in the next sentences. All these stars sit in the same distant cloud, so their differences in apparent brightness must be differences in real brightness: “Since the variables are probably at nearly the same distance from the Earth, their periods are apparently associated with their actual emission of light” Leavitt & Pickering 1912, Harvard Circular 173^[2]. She also hoped that “the parallaxes of some variables of this type may be measured” Leavitt & Pickering 1912, Harvard Circular 173^[2], which is exactly what was needed to turn her relation into a ruler.

How does the period tell you the distance?

Astronomers measure brightness in magnitudes, a logarithmic scale on which a bigger number means fainter. Leavitt's law says that a Cepheid's absolute magnitude M, its brightness as seen from a standard distance, is a straight-line function of the logarithm of its period:

M = a·log₁₀(P / 1 d) + b

Here P is the pulsation period in days, and a and b are constants that must be calibrated for the wavelength band being used. Leavitt's 1912 figure, about 0.48 in log P per magnitude Leavitt & Pickering 1912, Harvard Circular 173^[2], corresponds to a slope of roughly −2.1 magnitudes per factor of ten in period: a star that pulses ten times more slowly is about two magnitudes, or about seven times, brighter.

Next, measure the star's apparent magnitude m. The difference m − M, the distance modulus, depends only on the distance d Distance modulus, Wikipedia^[3]:

m − M = 5·log₁₀(d / 10 pc)

with d in parsecs (1 pc ≈ 3.086 × 10¹⁶ m) and dust absorption ignored. For example, Benedict and colleagues used Hubble Space Telescope parallaxes of ten Milky Way Cepheids to calibrate the relation and found a distance modulus for the Large Magellanic Cloud of 18.50 ± 0.03, falling to 18.40 ± 0.05 after a metallicity correction Benedict et al. 2007^[4]. Our own arithmetic turns 18.50 into d = 10^{18.50/5 + 1} pc ≈ 50 kpc, roughly 160,000 light-years.

Why do Cepheids pulse at all?

Leavitt did not know, and it took decades to work out. The accepted explanation is the κ-mechanism, sometimes called the Eddington valve, where κ is the symbol for gas opacity Cepheid variable, Wikipedia^[5]. In a layer of the star where helium is partly ionized, compression heats the gas and ionizes helium further, and doubly ionized helium is more opaque than singly ionized helium Cepheid variable, Wikipedia^[5]. The layer traps heat, is pushed outward, expands and cools, becomes more transparent, lets the heat out and falls back. The star behaves like a heat engine with a valve. Larger, more luminous Cepheids have lower mean densities and therefore pulse more slowly, which is the physical root of Leavitt's correlation.

From the Magellanic Clouds to an expanding universe

Leavitt's law gave relative distances; it needed one absolute calibration. About a year later Ejnar Hertzsprung estimated distances to several Milky Way Cepheids, setting the zero point Henrietta Swan Leavitt, Wikipedia^[1]. In 1923–24 Edwin Hubble found Cepheids in the Andromeda Nebula and used Leavitt's law to show that it lay far outside the Milky Way, a galaxy in its own right Henrietta Swan Leavitt, Wikipedia^[1]. Hubble then combined such distances with galaxy velocities, finding the linear velocity–distance relation that became evidence for cosmic expansion Hubble 1929^[6] Henrietta Swan Leavitt, Wikipedia^[1].

There was one big surprise along the way. In the 1940s Walter Baade recognized two separate populations of Cepheids, with type II Cepheids about 1.5 magnitudes fainter than classical ones at the same period, and correcting the mix-up roughly doubled the distance to Andromeda and to the galaxies beyond Cepheid variable, Wikipedia^[5]. The same story of hidden assumptions in the cosmic distance scale runs through Vera Rubin's rotation curves and Cecilia Payne's discovery of what stars are made of, two more results that came out of careful measurement by women astronomers.

Leavitt's law and the Hubble tension (open)

Cepheids are still the backbone of the local measurement of the Hubble constant H₀, the present expansion rate. The Hubble Space Telescope Key Project found H₀ = 72 ± 8 km/s/Mpc in 2001 Freedman et al. 2001^[7]. In 2022 the SH0ES team, calibrating Cepheids with Gaia parallaxes, water masers in the galaxy NGC 4258 and eclipsing binaries in the Large Magellanic Cloud, and then using them to calibrate type Ia supernovae, reported H₀ = 73.04 ± 1.04 km/s/Mpc Riess et al. 2022^[8]. The Planck satellite's analysis of the cosmic microwave background, which assumes the standard ΛCDM model, gives H₀ = 67.4 ± 0.5 km/s/Mpc Planck Collaboration 2020^[9]. The two disagree at about the 5σ level, and whether the cause is an unrecognized measurement error or new physics is an open question Hubble's law, Wikipedia^[10].

Quick FAQ

Is it called Leavitt's law or the period–luminosity relation?

Both. Period–luminosity relation describes it; Leavitt's law credits the person who found it Henrietta Swan Leavitt, Wikipedia^[1].

Did Leavitt win a Nobel Prize?

No. Gösta Mittag-Leffler tried to nominate her in 1924 and then learned she had died three years earlier; the prize is not awarded posthumously Henrietta Swan Leavitt, Wikipedia^[1].

Was Leavitt the first to find Cepheids?

No. Edward Pigott found the variability of Eta Aquilae in 1784, and John Goodricke found that of Delta Cephei a few months later Cepheid variable, Wikipedia^[5]. Leavitt's contribution was the relation between period and luminosity.

Where can I find more?

Browse the Astrophysics collection or read about who really discovered famous physics results.

References

1. Wikipedia, “Henrietta Swan Leavitt”. https://en.wikipedia.org/wiki/Henrietta_Swan_Leavitt
2. H. S. Leavitt and E. C. Pickering (1912), “Periods of 25 Variable Stars in the Small Magellanic Cloud,” Harvard College Observatory Circular 173 (full text as reproduced in the UCLA online archive). http://cwp.library.ucla.edu/articles/leavitt/leavitt.note.html
3. Wikipedia, “Distance modulus”. https://en.wikipedia.org/wiki/Distance_modulus
4. G. Fritz Benedict et al. (2007), “Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations,” The Astronomical Journal 133, 1810–1827 (DOI 10.1086/511980; metadata verified via Crossref). https://doi.org/10.1086/511980
5. Wikipedia, “Cepheid variable”. https://en.wikipedia.org/wiki/Cepheid_variable
6. Edwin Hubble (1929), “A relation between distance and radial velocity among extra-galactic nebulae,” Proceedings of the National Academy of Sciences 15, 168–173 (DOI 10.1073/pnas.15.3.168; metadata verified via Crossref). https://doi.org/10.1073/pnas.15.3.168
7. Wendy L. Freedman et al. (2001), “Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant,” The Astrophysical Journal 553, 47–72 (DOI 10.1086/320638; metadata verified via Crossref). https://doi.org/10.1086/320638
8. Adam G. Riess et al. (2022), “A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s −1 Mpc −1 Uncertainty from the Hubble Space Telescope and the SH0ES Team,” The Astrophysical Journal Letters 934, L7 (DOI 10.3847/2041-8213/ac5c5b; metadata verified via Crossref). https://doi.org/10.3847/2041-8213/ac5c5b
9. Planck Collaboration (N. Aghanim et al.) (2020), “Planck 2018 results. VI. Cosmological parameters,” Astronomy & Astrophysics 641, A6 (DOI 10.1051/0004-6361/201833910; metadata verified via Crossref). https://doi.org/10.1051/0004-6361/201833910
10. Wikipedia, “Hubble's law”. https://en.wikipedia.org/wiki/Hubble%27s_law

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.