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A white dwarf packs about half the Sun's mass into something only slightly bigger than Earth. The first sign that such stars exist came from one woman checking the photographic plates at Harvard. This post tells the story of Williamina Fleming, explains why a faint star with a hot spectrum was a puzzle, and works through the density numbers.
Who was Williamina Fleming?
Her colleague Annie Jump Cannon wrote her obituary in The Astrophysical Journal in 1911. It records that Fleming was born in Dundee, Scotland, on 15 May 1857, and at fourteen was already a pupil-teacher in the Dundee schools. After her marriage she moved to Boston. In 1881, needing to support herself, she entered Harvard College Observatory "as a copyist and computer". A computer then meant a person who did calculations.
The observatory, under Edward C. Pickering, was starting to photograph the spectra of many stars at once by putting a prism in front of the telescope. Fleming was put in charge of examining the plates, storing them and classifying what they showed.
What did she find on the plates?
The first general photographic classification of stellar spectra was assigned to her. Cannon writes that the result, the Draper Catalogue, "gives the spectra of 10,351 stars". From peculiar features in spectra she discovered ten novae, more than three hundred variable stars and fifty-nine gaseous nebulae. Some sceptics blamed such finds on flaws in the film. Cannon notes that she "never doubted the validity of the photographic evidence", and adds: "Her industry was combined with great courage and independence."
In 1899 Harvard made her Curator of Astronomical Photographs. She became an honorary member of the Royal Astronomical Society in 1906. She died of pneumonia on 21 May 1911. Our post on Annie Jump Cannon explains how Cannon later reorganised the classes into O, B, A, F, G, K, M.
How did she spot the first white dwarf?
The story comes from the astronomer Henry Norris Russell, in a 1944 note in The Astronomical Journal. It opens: "The first person who knew of the existence of white dwarfs was Mrs. Fleming; the next two, an hour or two later, Professor E. C. Pickering and I."
Russell had measured distances to a set of stars. Pickering offered to have their spectra looked up on the Harvard plates. The faint ones all turned out to be cool stars of class G or later, as expected. Russell then asked about the companion of 40 Eridani. Pickering telephoned Fleming, who reported within an hour or so that it was of class A, a hot white star.
Russell was puzzled. Pickering smiled and said: "It is just such discrepancies which lead to the increase of our knowledge."
Why does hot and faint mean small?
A star's power output depends on its surface area and temperature: L = 4πR²σT⁴. Compare two stars at the same temperature. Luminosity is proportional to R², so R is proportional to √L.
Worked example, using clearly hypothetical numbers:
Suppose two stars have the same temperature, and one gives out 1/10,000 of the other's power.
The radius ratio is √(1/10,000) = 1/100.
So the faint star is a hundred times smaller across.
A star hotter than its companion yet much fainter is smaller still, because T⁴ works against it. Common mistake: reading "faint" as "far away". Russell already knew the distance, so faintness had to mean small size.
How dense is a white dwarf?
Modern measurements give 40 Eridani B a mass of 0.573 times the Sun's, according to a 2017 study in The Astrophysical Journal. NASA's Imagine the Universe describes a typical white dwarf as about half the Sun's mass and "only slightly bigger than Earth", with a density of about 1 × 10⁹ kg/m³.
Check it yourself, taking Earth's radius as a rough size:
Mass. 0.573 × 1.99 × 10³⁰ kg ≈ 1.14 × 10³⁰ kg.
Volume. (4/3)π(6.37 × 10⁶ m)³ ≈ 1.08 × 10²¹ m³.
Density. 1.14 × 10³⁰ / 1.08 × 10²¹ ≈ 1.05 × 10⁹ kg/m³.
That matches NASA's figure. NASA also notes that Earth's average density is only 5.4 × 10³ kg/m³, so a white dwarf is about 200,000 times denser. Why such a star does not collapse is the subject of our post on the Chandrasekhar limit.
What can a student take from how Fleming worked?
Trust careful evidence. She stood by what the plates showed when others doubted them.
Look closely at the odd case. Her finds came from spectra that did not fit.
Your starting job is not your ceiling. She began as a copyist and ended as a curator who discovered hundreds of objects.
If L = 4πR²σT⁴ still feels like a formula to memorise rather than understand, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing.
Next step: repeat the radius example for a star with twice the temperature of its companion and 1/10,000 of its luminosity.
