Reading starlight

Foundations

The thing we could never know

In 1835 the French philosopher Auguste Comte, listing the limits of human knowledge, chose the stars as his example. We might learn their shapes and motions, he wrote, but their chemical composition we would never know by any method. It was a reasonable thing to say. No one would ever hold a piece of a star.

He was wrong within his own lifetime’s reach, and wrong in the most complete way possible. Nearly everything this course has said about stars, their temperatures, their ingredients, their motions, their distances, came from reading their light. This lesson is about how.

The barcode in the rainbow

Pass sunlight through a prism and it spreads into a rainbow, as Newton showed. Look closely, as Joseph von Fraunhofer did in 1814, and the rainbow is crossed by hundreds of thin dark lines, always at the same places. In 1860 Gustav Kirchhoff and Robert Bunsen found out what they were. Heat any element in a flame and it glows at its own exact set of colours; put the same element, cool, in front of a bright light and it swallows exactly those colours. Each element has a barcode. The dark lines in the Sun’s spectrum are the barcodes of the elements in its atmosphere, and by 1864 William Huggins had shown that the stars carry the same barcodes. The stars are made of the same stuff we are.

One line did not match anything known. During the total eclipse of 18 August 1868, observed from Guntur in what is now Andhra Pradesh, a yellow line was recorded in the light of the Sun’s edge that no earthly element produced. It was named helium, for the Sun, and it was not found on Earth for another twenty-seven years. The second most common element in the universe was discovered in starlight first.

The thermometer

Reading which elements are present was the easy part. Reading how much of each was harder, because the strength of a line depends not only on how much of the element there is but on the temperature: a hot enough gas strips electrons off its atoms, and a stripped atom absorbs at different colours or not at all. In 1920 Meghnad Saha, working in Calcutta, wrote down the equation that says exactly what fraction of a gas is ionised at a given temperature and pressure. Suddenly the spectrum was a thermometer, and the line strengths could be turned into amounts.

Five years later Cecilia Payne, using Saha’s equation in her Harvard doctoral thesis, found that stars are made almost entirely of hydrogen and helium, with everything else a trace. The result was so unexpected that the leading astronomer of the day, Henry Norris Russell, persuaded her to call it spurious in print. In 1929 he confirmed it himself. The universe is hydrogen, and the light had been saying so all along.

What else the light says

Colour gives temperature: a star that looks red is cooler than the Sun, a star that looks blue is hotter, because hotter things glow at shorter wavelengths. The Sun, at 5,800 degrees, peaks in the green and looks white; Betelgeuse at 3,500 looks orange-red; Rigel at 12,000 looks blue-white.

Motion shifts the barcode. A star moving away from us has its lines shifted toward the red, one approaching toward the blue, and the size of the shift gives the speed. This is the effect that revealed the expansion of the universe in lesson 1.1, and it also reveals stars swinging around unseen companions, including planets.

The lines have widths and structure too. Fast rotation smears them; high pressure broadens them; a magnetic field splits them. A single spectrum, read carefully, gives a star’s temperature, composition, velocity, rotation, surface gravity and magnetism.

How far

None of this gives distance. For that the light carries no barcode, and astronomers had to build a ladder.

The bottom rung is parallax. Hold a finger at arm’s length and blink from eye to eye; the finger seems to jump against the background. Earth’s orbit is the baseline, and a nearby star shifts against the distant ones by a tiny angle as the year passes. Friedrich Bessel measured the first in 1838, and found the star 61 Cygni about ten light-years away. The angles are minute, and the method reaches only the nearest stars; but the Gaia satellite, since 2013, has measured them for well over a billion stars, to a precision that reaches across much of the Milky Way.

The next rung is the pulsing star Hubble used. In 1912 Henrietta Leavitt, studying photographs at Harvard, found that a class of stars called Cepheids pulse with a rhythm set by their true brightness: the slower the pulse, the brighter the star. Time the pulse and you know how bright the star really is; compare with how bright it looks and you have its distance. Cepheids calibrated by parallax reach neighbouring galaxies. Cepheids in those galaxies calibrate the exploding white dwarfs of lesson 2.3, which are bright enough to be seen across billions of light-years. That is the ladder: each rung standing on the one below.

Looking back

Light takes time to travel, and the distances are so large that the delay matters. Sunlight is eight minutes old when it reaches you. Light from the nearest star, Proxima Centauri, is four years old. Light from Andromeda left it two and a half million years ago, before our species existed. To look far away is to look into the past, and the distance ladder is also a time machine, which is how the rest of this course was written.

Deeper

Wien’s law and colour

The peak wavelength of a blackbody’s emission is 2.9 millimetre-kelvin divided by its temperature. For the Sun at 5,772 kelvin that is about 500 nanometres, in the green; for Betelgeuse at 3,500 kelvin, 830 nanometres, in the near infrared; for Rigel at 12,000 kelvin, 240 nanometres, in the ultraviolet. Colour indices, the difference in brightness between two filters, measure temperature to a few percent for ordinary stars.

The Saha equation

For a gas in thermal equilibrium, the ratio of ionised to neutral atoms depends on temperature through a Boltzmann factor in the ionisation energy, on the electron density, and on the statistical weights of the states. Saha applied it to the Sun’s chromosphere in 1920 and to stellar spectra generally in 1921, explaining why the lines of neutral hydrogen are strongest not in the hottest stars, where hydrogen is ionised, but in stars around ten thousand kelvin. The Harvard spectral sequence, until then an empirical ordering, became a temperature sequence, and abundance analysis became possible.

Parallax geometry

A star at one parsec shows a parallax of one second of arc, one 3,600th of a degree; a star at ten parsecs, a tenth of that. Bessel’s 61 Cygni gave 0.31 arcseconds, about 3.2 parsecs; the modern value is 3.5. Gaia’s third data release contains positions, parallaxes and proper motions for about 1.5 billion sources, with parallax errors of a few tens of microarcseconds for bright stars, which corresponds to percent-level distances out to a kiloparsec or more.

Cepheids and supernovae

The period–luminosity relation arises because a Cepheid’s pulsation period depends on its mean density, and its luminosity on its mass and radius, which are linked. Leavitt’s original sample was twenty-five stars in the Small Magellanic Cloud, all at about the same distance, so their apparent brightnesses could be compared directly. Calibrating the zero point of the relation, that is, finding the absolute brightness of a Cepheid of given period, requires parallaxes of nearby Cepheids, and that calibration has been a dominant source of error in the distance ladder for a century. Type Ia supernovae have a scatter of about 40 percent in peak brightness before correction, reduced to about 10 percent by Phillips’s 1993 observation that brighter events decline more slowly, and to a few percent with colour corrections.

The ladder’s rungs and the tension

Parallax to Cepheids in the Milky Way and the Magellanic Clouds; Cepheids to the host galaxies of type Ia supernovae within about 40 megaparsecs; supernovae to the smooth expansion flow beyond. The 2022 analysis of this chain gives 73.0 ± 1.0 kilometres per second per megaparsec. The afterglow, extrapolated with the standard model, gives 67.4 ± 0.5. Each rung has been re-examined for systematic errors, most recently with Webb re-observing the Cepheids, without closing the gap.

The new senses

Starlight is no longer only light. Radio telescopes read the 21-centimetre line of hydrogen and the emission of molecules; infrared telescopes see through dust; X-ray and gamma-ray telescopes see the hottest and most violent processes. Neutrinos from the Sun and from SN 1987A, and gravitational waves from merging black holes and neutron stars, are messengers that carry no light at all. Comte was wrong not once but in every band of the spectrum and beyond it.

Frontier

One percent

The goal of the distance ladder is a one-percent measurement of the expansion rate, at which point either the tension with the afterglow becomes undeniable or a systematic error is found. Gaia’s fourth data release, Webb’s observations of Cepheids and of the tip of the red-giant branch, and independent routes through gravitational-wave sirens and masers are all aimed at this. Active research.

Reading the atmospheres of planets

The same technique that read the Sun in 1860 now reads the atmospheres of planets around other stars: as a planet passes in front of its star, the star’s light filters through the planet’s air and picks up its barcode. Water, carbon dioxide and methane have been read this way. The question of whether any of those barcodes will ever show the signature of life belongs to a later chapter.

Transcript and shot list

Target runtime about 6 minutes. Built as one prohibition and everything that broke it, in the order the methods arrived, finishing back at the sentence that started it. Shot types: ANIM is rendered from code with Manim, AI is a generated shot from Higgsfield with the shared style reference, REAL is agency imagery with credit, CAM is the narrator.

[00:00] S01 · ANIM · Typographic: 1835, Comte; the sentence “their chemical composition we shall never know” fades in and is crossed through.

In 1835 the philosopher Auguste Comte, listing the limits of human knowledge, chose the stars as his example. We might learn their shapes and motions, he wrote, but their chemical composition we would never know, by any method. A reasonable thing to say. No one would ever hold a piece of a star. He was wrong within a generation, and wrong in the most complete way possible. Nearly everything we know about stars came from reading their light.

[00:36] S02 · ANIM · Cosmic calendar; the last quarter-second of the year, labelled “every measurement in this lesson”.

Everything in this lesson was learned in the last two centuries. On the cosmic calendar, the final half-second.

[00:44] S03 · ANIM · Sunlight through a prism into a rainbow; dark lines appear across it; an element in a flame glows at the same colours; the lines become a barcode.

Pass sunlight through a prism and it spreads into a rainbow. Look closely, as Fraunhofer did in 1814, and the rainbow is crossed by hundreds of thin dark lines, always in the same places. In 1860 Kirchhoff and Bunsen found out what they were. Heat any element in a flame and it glows at its own exact colours. Put it, cool, in front of a bright light, and it swallows exactly those colours. Every element has a barcode. The dark lines in sunlight are the barcodes of the Sun’s ingredients, and by 1864 the stars had been read too. They’re made of the same stuff we are.

[01:34] S04 · ANIM · A map: Guntur, Andhra Pradesh, 18 August 1868; an eclipse; a yellow line in the spectrum that matches nothing; the word helium; a clock runs 27 years to 1895.

One line matched nothing known. During the total eclipse of the 18th of August 1868, observed from Guntur in what is now Andhra Pradesh, a yellow line was recorded in the light of the Sun’s edge that no earthly element produced. It was named helium, for the Sun. It wasn’t found on Earth for another twenty-seven years. The second most common element in the universe was discovered in starlight first.

[02:06] S05 · ANIM · Typographic: Calcutta, 1920, Meghnad Saha; an equation; a spectrum becomes a thermometer; then Harvard, 1925, Cecilia Payne; a pie of hydrogen and helium.

Reading which elements are present was the easy part. How much of each was harder, because a hot enough gas strips the electrons off its atoms, and a stripped atom absorbs different colours or none. In 1920 Meghnad Saha, working in Calcutta, wrote down the equation that says exactly what fraction of a gas is ionised at a given temperature. Suddenly the spectrum was a thermometer. Five years later Cecilia Payne used it to show that stars are almost entirely hydrogen and helium. The result was so unexpected that the leading astronomer of the day persuaded her to call it spurious in print. Four years after that, he confirmed it himself.

[02:57] S06 · ANIM · Three stars: red, white, blue, with temperatures; then a barcode sliding red and blue as a star recedes and approaches; then lines widening and splitting.

What else does the light say? Colour gives temperature. Red is cooler than the Sun, blue is hotter, because hotter things glow at shorter wavelengths. Motion shifts the barcode: away from us, toward the red; toward us, the blue. That’s the effect that revealed the expansion of the universe, and it also reveals stars wobbling around unseen planets. Fast rotation smears the lines. Pressure broadens them. A magnetic field splits them. One spectrum, read carefully, gives temperature, composition, speed, spin, gravity and magnetism.

[03:36] S07 · ANIM · A finger at arm’s length jumps between eyes; the Earth’s orbit as a baseline; a nearby star shifts against the background; Bessel, 1838, 61 Cygni; then Gaia and a counter past a billion stars.

None of that gives distance. For that, astronomers built a ladder. The bottom rung is parallax. Hold a finger at arm’s length and blink from eye to eye: it jumps against the background. Earth’s orbit is the baseline, and a nearby star shifts against the far ones as the year passes. Bessel measured the first in 1838 and found 61 Cygni about ten light-years away. The angles are tiny and the method reaches only the nearest stars. But the Gaia satellite has now measured them for well over a billion.

[04:17] S08 · ANIM · Harvard, 1912, Henrietta Leavitt; a Cepheid pulsing; period against brightness on a straight line; Hubble in 1923 finds one in Andromeda; then supernovae extend the ladder off the top of the frame.

The next rung is the pulsing star Hubble used. In 1912 Henrietta Leavitt found that Cepheid variables pulse with a rhythm set by their true brightness: the slower the beat, the brighter the star. Time the beat, and you know how bright it really is. Compare with how bright it looks, and you have the distance. Cepheids, calibrated by parallax, reach the nearby galaxies. Cepheids in those galaxies calibrate the exploding white dwarfs of lesson 2.3, bright enough to be seen across billions of light-years. Each rung stands on the one below.

[04:00] S09 · ANIM · Light-travel clocks: Sun 8 minutes; Proxima 4 years; Andromeda 2.5 million years, with a hominin silhouette; the ladder becomes a timeline.

And light takes time. Sunlight is eight minutes old when it reaches you. Light from the nearest star is four years old. Light from Andromeda left it two and a half million years ago, before our species existed. To look far away is to look into the past. The distance ladder is also a time machine, and it’s how the rest of this course was written.

[05:30] S10 · ANIM · Labels: ESTABLISHED for composition, temperature, motion and the lower rungs; ACTIVE RESEARCH for the top of the ladder and the tension.

The scorecard. That we can read a star’s ingredients, temperature and motion from its light, and measure distances out to the nearby galaxies: established, for over a century. The top of the ladder, and the disagreement it produces with the afterglow about how fast the universe expands: active research.

[05:53] S11 · AI into ANIM · A night sky; every star briefly shows its barcode; the calendar returns.

So, Comte. The composition of the stars, forever unknowable by any method. It took one prism, a yellow line seen from Guntur, an equation from Calcutta, and a thesis from Harvard. Next lesson: the star we know best of all.

Shot list

One AI shot, ten code-rendered shots. Estimated Higgsfield use: 2 to 4 generations including retries.