Ejnar Hertzsprung: A Life in Five Chapters

Chapter 1 · A Chemical Engineer Who Trusted a Photographic Plate

Copenhagen, photographic chemistry, and an amateur observatory

1873 – 1905 · Frederiksberg · Copenhagen · St Petersburg · Leipzig

Ejnar Hertzsprung was born at Frederiksberg near Copenhagen in October 1873. His father *Severin* had studied astronomy, could not make a living at it, and became a civil servant in the finance ministry — but kept the interest and taught it to his son.

So Ejnar grew up knowing the sky and knowing that astronomy did not pay.

He trained as a *chemical engineer* at Copenhagen Polytechnic, graduating in 1898, and worked in *St Petersburg* as a chemical engineer for three years. He then studied *photographic chemistry* under Wilhelm Ostwald at Leipzig.

This is the most important fact about him professionally.

Astronomy by 1900 depended almost entirely on the *photographic plate*, and a plate is a chemical device with awkward properties. Its response to light is *non-linear*: doubling the exposure does not double the density. Its sensitivity varies across its surface, and between batches, and with temperature, and with the developer used. It responds differently to different *colours* — early plates were far more sensitive to blue than to red, which systematically distorts the apparent brightness of red stars.

Most astronomers used plates and understood these problems imperfectly. Hertzsprung was a *photographic chemist* who had turned to astronomy, and he understood the errors of his instrument better than almost anybody in the field.

He returned to Denmark in 1902, worked at the small *Urania Observatory* — essentially an amateur institution — with no salary and no professional position.

And it was there, as an unpaid amateur with an unusually good grasp of photographic error, that he did the work.

“The apparent brightness of a star tells us nothing until we know its distance.”

— Attributed to Ejnar Hertzsprung, on stellar photometry

Why this matters

Hertzsprung came to astronomy as a photographic chemist, which meant he understood the errors of the plate — the field's main instrument — better than the astronomers did.

You have the plate, its errors and the amateur observatory. What would you ask?

Ask Hertzsprung

• “What is wrong with a photographic plate as a measuring device?”
• “Why did being a chemist help you as an astronomer?”
• “What did your father show you of the sky?”
• “What is it like doing research with no post?”
• “Why did early plates distort red stars?”

Chapter 2 · Giants and Dwarfs

Same colour, wildly different brightness

1905 – 1907 · Copenhagen

By 1900 the *spectral classes* were established: stars sorted by the appearance of their spectra into the sequence *O B A F G K M*, largely by Annie Jump Cannon at Harvard.

Spectral class is determined by *surface temperature*: O stars are hottest and blue-white, M stars are coolest and red.

Hertzsprung noticed something in the data on stars whose *distances* were known from parallax.

Among stars of *the same* spectral class — say K or M, the cool red ones — some are intrinsically *very faint*, and others are intrinsically *thousands of times brighter than the Sun*.

Same class. Same surface temperature. Enormously different actual output.

And there is only one thing that can be, and the reasoning is simple physics.

A surface at a given temperature radiates a *fixed amount of energy from each square metre*. That is the Stefan–Boltzmann law, and it holds regardless of what the surface belongs to.

So if two stars have the *same* surface temperature and one puts out a thousand times more energy, it must have a thousand times more *surface area*. And a thousand times the area means roughly thirty times the radius.

Some red stars are *enormous* and some are *small*.

Hertzsprung named them *giants* and *dwarfs*. The Sun is a dwarf.

He also noticed that among the hot blue stars, no such split appears — the division exists only at the cool end.

He published in 1905 and 1907, in *Zeitschrift für wissenschaftliche Photographie* — the Journal for Scientific Photography.

It is a perfectly respectable journal, and *astronomers did not read it*.

The most important stellar result of the decade sat in a photographic journal for years, essentially unnoticed.

Why this matters

A surface at a given temperature radiates a fixed amount per square metre, so a star far brighter at the same temperature can only be far larger.

You have the giants, the dwarfs and the wrong journal. What is your question?

Ask Hertzsprung

• “Why must a brighter star of the same colour be bigger?”
• “How much bigger are we talking about?”
• “Why publish in a photographic journal?”
• “Why does the split appear only among cool stars?”
• “Is the Sun a giant or a dwarf?”

Chapter 3 · Use a Cluster

How to compare stars honestly

1908 – 1911 · Göttingen · Potsdam

There is a fundamental problem in comparing stars, and it is worth stating clearly.

What you *observe* is *apparent* brightness — how bright a star looks. What you want is *intrinsic* brightness — how much light it actually puts out.

The two differ by *distance*. A faint-looking star may be a dim star nearby or a brilliant star far away, and you cannot tell them apart without knowing the distance.

And distances in 1908 were known for only a *few hundred* nearby stars, by parallax, and even those had large uncertainties.

So any plot of brightness against spectral class using apparent brightnesses is *meaningless*. The distances scramble everything.

Hertzsprung's solution is elegant.

Use a *star cluster*.

Every star in a cluster is at *effectively the same distance* from us, because the cluster's diameter is tiny compared with its distance. So while you may not know what that distance *is*, you know it is the *same for every member*.

Which means apparent brightnesses *can* be compared directly. Whatever the unknown distance does, it does the same thing to every star in the group, so the *relative* brightnesses are exactly right.

Plot the members of a cluster — apparent brightness against spectral class — and the distance uncertainty vanishes from the comparison.

Hertzsprung did this for the *Pleiades* and the *Hyades* in 1911.

The stars did *not* scatter randomly. They fell along a *band* running diagonally across the plot, from hot and bright at one end to cool and faint at the other — the *main sequence* — with a separate group of luminous cool stars, the giants, off to one side.

That is the diagram, and it is one of the most useful pictures in science.

*Henry Norris Russell* at Princeton reached the same relation independently, using parallax stars, and published it far more visibly in 1913 with a large audience at the Royal Astronomical Society.

The diagram carries both names.

Why this matters

Every star in a cluster is at effectively the same distance, so their apparent brightnesses can be compared directly even when the distance is unknown.

You have the cluster and the band of stars. What would you ask?

Ask Hertzsprung

• “Why can't you just plot apparent brightness against class?”
• “How does using a cluster solve it?”
• “What is the main sequence?”
• “Why is a band more interesting than a scatter?”
• “Did you mind Russell getting the visibility?”

Chapter 4 · Calibrating the Cepheids

The first real distance to another galaxy

1912 – 1913 · Potsdam

In 1912 *Henrietta Swan Leavitt*, working at Harvard on photographic plates of the Small Magellanic Cloud, published a remarkable relation.

Certain variable stars — *Cepheids* — brighten and dim in a regular cycle. Leavitt found that among the Cepheids in the Small Magellanic Cloud, the ones with *longer periods* are consistently *brighter*.

The crucial point is that these stars are all in the *same cloud*, so at effectively the same distance — the same trick Hertzsprung had used with clusters. So the relation between period and apparent brightness must reflect a real relation between *period and intrinsic brightness*.

So a Cepheid *announces its own true brightness* by how fast it pulses.

That makes it a *standard candle*. Find a Cepheid anywhere, measure its period, and you know how bright it really is. Compare with how bright it looks, and the difference gives the *distance*.

There was one thing missing. Leavitt's relation was *relative*. It gave the ratios but not the absolute scale, because the distance to the Small Magellanic Cloud was unknown.

Somebody had to pin it down by measuring the true brightness of *at least one* Cepheid whose distance was independently known.

*Hertzsprung* did it in 1913. There are no Cepheids close enough for direct parallax, so he used *statistical parallax*: the apparent drift of stars across the sky caused by the Sun's own motion through the galaxy, which over a large sample gives an average distance.

With that calibration the relation became *absolute*.

He immediately applied it and obtained the *first real distance to the Small Magellanic Cloud* — a figure in the tens of thousands of light years, placing it far outside anything then thought to be part of the Milky Way.

His published figure contained an arithmetical slip which put it out by a factor of ten, and it was corrected.

Ten years later *Edwin Hubble* found a Cepheid in the Andromeda nebula and used exactly this calibrated relation to show that Andromeda is a separate galaxy.

Why this matters

A Cepheid announces its true brightness by its pulsation period, which turns it into a standard candle — but only once somebody calibrates the scale.

You have Leavitt's relation and the missing scale. What is your question?

Ask Hertzsprung

• “What did Leavitt find, and why does it work?”
• “Why is a relative relation not enough?”
• “What is statistical parallax?”
• “How does a standard candle give you a distance?”
• “What happened to the factor of ten?”

Chapter 5 · Leiden, and Ninety-Four Years

A self-effacing man and a diagram that outlasted everything

1919 – 1967 · Leiden · Denmark

Hertzsprung was brought out of obscurity by *Karl Schwarzschild*, who read the photographic-journal papers, recognised what they were, and invited him to Göttingen in 1909 and then to Potsdam.

In 1919 he moved to *Leiden* in the Netherlands, and became *director* of the observatory there in 1935.

He was, by every account, extremely *self-effacing*. He did not promote his work, did not press priority claims, and did not object when the diagram became known primarily by Russell's name in the English-speaking world. Colleagues described him as modest to a degree that damaged his reputation.

He was also an exceptionally *careful* observer, and much of his working life went into unglamorous, essential things: photographic photometry, the measurement and correction of *systematic errors*, double-star measurements, proper motions, and the properties of variable stars.

He worked into his *eighties*, and produced papers after retiring to Denmark.

He died at Roskilde in October 1967, aged *ninety-four*.

The *Hertzsprung–Russell diagram* has turned out to be the most useful picture in stellar astronomy, and the reason is that it is not merely a classification — it is a *history*.

A star spends most of its life on the *main sequence*, fusing hydrogen into helium, sitting at a position fixed by its mass. When the hydrogen in the core runs out, it *leaves* the main sequence, expands and cools at the surface, and moves up and to the right into the *giant* region. Later still it may shed its outer layers and become a hot faint *white dwarf*, in the bottom left.

So the diagram is a map of *stellar evolution*, and the position of a star on it tells you its mass, its age and its future.

Hertzsprung had no idea of any of this. The physics — what powers a star, why it leaves the main sequence — is Eddington's and Bethe's, decades later. He found the *pattern* and could not explain it, and the pattern turned out to be the shape of every star's life.

Why this matters

The Hertzsprung-Russell diagram is not a classification but a history: a star's position on it gives its mass, its age and its future.

You have the pattern you could not explain and ninety-four years. What would you ask?

Ask Hertzsprung

• “Why is the diagram a map of stellar lives?”
• “Did it bother you to find a pattern you could not explain?”
• “Why did Schwarzschild go looking in a photographic journal?”
• “Did being self-effacing cost you?”
• “What is a white dwarf doing at the bottom of the diagram?”

What Hertzsprung changed

The Hertzsprung–Russell diagram is the single most useful picture in stellar astronomy, and the giant–dwarf division it displays is Hertzsprung's. His calibration of Leavitt's Cepheid period–luminosity relation gave the first real distance to the Small Magellanic Cloud and opened the way to measuring the distances of galaxies.

A debate that continues

Hertzsprung published the giant-and-dwarf discovery in a photographic journal astronomers did not read, and Henry Norris Russell's independent and far more visible publication in 1913 meant the result was long credited chiefly to Russell.

Keep exploring — ask Hertzsprung

• “Where should a result be published?”
• “What else can be learned from a cluster?”
• “What would you have made of stellar fusion?”

Related lives

• Cecilia Payne — Who Read What The Stars Are Made Of
• Arthur Eddington — Who Told Them To Find A Hotter Place
• Edwin Hubble — Who Made the Universe Much Larger
• Gustav Kirchhoff — Who Read The Sun's Chemistry

Related themes

Stars and stellar classification · Distance measurement · Stellar evolution