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Many stories from the golden age of science fiction depicted a far-future Earth in which the sun was reddening and dying. This appeared in both humorous (for example, The Dying Earth series by Jack Vance) and more serious contexts (Earth's Last Citadel by C. L. Moore and Henry Kuttner or City at World's End by Edmond Hamilton; as an aside, the moon in the latter two novels was described as being much closer to Earth in their distant future settings—something that should have been known to be the opposite of what would happen long before the long-term evolution of the sun was understood). Some stories even described a future in which the sun had gone out completely (The Night Land by William Hope Hodgson or Night by John W. Campbell).

City at World's End

However, with the understanding of how stars are powered by nuclear fusion processes, we now know that a gradual dimming and reddening is not what can be expected from the sun as it runs out of hydrogen fuel. When the hydrogen burning is no longer sufficient to support the star against gravitational collapse, helium burning will begin in a hotter, more compressed core, while the outer layers of the star will expand to become a red giant, engulfing the inner planets.

What was the first science fiction work that depicted the transition of our sun (or a similar, sun-like main sequence star) into a red giant? Presumably this would have happened some time after the Second World War. My advisor's advisor Hans Bethe, starting working out the p-p fusion chain that powers the sun in 1939, while by 1965, Louis Henyey and Icko Iben had shown to model stellar evolution between different nuclear burning phases quantitatively. By the 1970s, many science fiction writers seemed to have a grasp of how stellar evolution would work; but what was the first story that described it?

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    The article here (paywalled, but you can bypass it with the site sci-hub.se here) indicates that by 1927, Henry Norris Russell's textbook Astronomy already included speculations about how different star types seen in the Hertzsprung-Russell diagram might be stages in a single star's evolution. Do you only want stories from after the theoretical basis was better worked out by Bethe and others?
    – Hypnosifl
    Commented Jun 8, 2023 at 20:16
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    For a story after stellar evolution was well understood (in this interview, Martin Schwarzschild names this 1952 paper as the one that gave a convincing demo that "red giants were the right configuration toward which evolution would go"), there's "One Face" by Larry Niven from 1965--they find the sun a white dwarf, p. 189 speculates it had first been a red giant & swallowed mercury.
    – Hypnosifl
    Commented Jun 9, 2023 at 0:32
  • Actually, rereading p. 189 of "One Face", a character says the sun "could have left the Main Sequence by going supernova or by suddenly be expanding into a red giant", but then she adds "if it had there wouldn't be any inner planets. So the Sun expanded to a white giant, absorbed Mercury, burnt up the last of its hydrogen and collapsed." So while this story shows Niven was fairly knowledgeable about the science of stellar evolution at the time, it still comes down on the side of a scenario where there was no red giant phase.
    – Hypnosifl
    Commented Jun 9, 2023 at 19:13
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    may be notable. STAR TREK All Our Yesterdays Original Airdate: 14 Mar, 1969 Captain's log, Stardate 5943.7. We have calculated that Beta Niobe will go nova in approximately three and a half hours. youtu.be/poux1cAdVH0 at 2:16 mark Commented Jun 9, 2023 at 20:40
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    HG Wells' The Time Machine has one chapter in which the Traveller goes to a far future time where the sun is large and red. But it only touches on the subject.
    – Chenmunka
    Commented Jun 10, 2023 at 9:13

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Since you said you would count a story depicting the transformation of "a similar, sun-like main sequence star" (a yellow dwarf) into a red giant, one possibility could be Larry Niven's Ringworld (1970), which features this dialogue between the human character Louis Wu and a character named Nessus from an alien species known as "puppeteers", where Nessus explains why humans were never able to locate the home system of the secretive puppeteers:

"In short, we found that a sun was a liability rather than an asset. We moved our world to a tenth of a light year's distance, keeping the primary only as an anchor. We needed the farming worlds, and it would have been dangerous to let our world wander randomly through space. Otherwise we would not have needed a sun at all."

"So," said Louis Wu. "That's why nobody ever found the puppeteer world."

"That was part of the reason."

"We searched every yellow dwarf sun in known space, and a number outside it. Wait a minute, Nessus. Somebody would have found the farming planets. In a Kemplerer rosette."

"Louis, they were searching the wrong suns."

"What? You're obviously from a yellow dwarf."

"We evolved under a yellow dwarf star somewhat like Procyon. You may know that in half a million years Procyon will expand into the red giant stage."

"Finagle's heavy hand! Did your sun blow up into a red giant?"

"Yes. Shortly after we finished moving our world, our sun began the process of expansion. Your fathers were still using the upper thigh bone of an antelope to crack skulls. When you began to wonder where our world was, you were searching the wrong orbits about the wrong suns.

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  • Another candidate from 1969 could be Lester del Rey's "Rescue Team", a short 2-page piece available on google books here, the second page says their mission was "to explore a star that had just turned red giant and to test our theories that such a star is one that has used up its hydrogen fuel"--the story doesn't directly confirm that the star had previously been a sunlike yellow dwarf though.
    – Hypnosifl
    Commented Jun 10, 2023 at 21:35
  • An earlier ambiguous possibility is Ossian's Ride by Fred Hoyle from 1959--main story concerns mysterious developments of new advanced technology but ending (SPOILERS) reveals that the tech is being introduced by aliens, one says they were being "cooked alive as our star became brighter and brighter". Hoyle presumably was thinking of a star becoming a red giant, p. 256 of this paper on the history of red giant models (sci-hub link) says a Hoyle/Schwarzschild 1955 paper "solved the giants issue".
    – Hypnosifl
    Commented Jun 12, 2023 at 16:12
  • Another possibility: "Brink of Creation" by Dean McLaughlin, from the October 1958 issue of "Worlds of IF". Doesn't show a specific example of a sun-like star that later becomes a red giant, but does state that red giants are the end of certain star's lives, see p. 101 which says "the stars themselves were old now, their hydrogen nearing exhaustion. Fever-hued red giants, most of them, they were swollen things slowly guttering down to extinction." P. 95 also talks about how new stars form from "thick clouds of black dust".
    – Hypnosifl
    Commented Jun 24, 2023 at 2:15
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Astrophysicists were beginning to calculate the future evolution of stars at least as early as the early 1960s.

Stephen H. Dole, in Habitable Planets for Man, 1964, discussed the qualities necessary for a world to be habitable for humans.

https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf

For example, a world has to have an atmosphere with a partial pressure of between 60 and 400 mmHg of oxygen to be breathable for humans. On pages 61 to 63 Dole discusses how long it co took Earth from its initial formation to acquire an atmosphere with enough free oxygen, produced by photosynthetic lifeforms. The present day answer is about 4 billion years, meaning that Earth has been habitable for humans for only about 600 million years.

Dole concludes that: "In general, it is probably safe to conclude that a planet must have existed for 2 or 3 billion years, under fairly steady conditions of solar radiation, before it has matured enough to be habitable."

On pages 67 to 72 Dole discusses the properties of the primary. Dole says that stars shine fairly steady on the main sequence until their available hydrogen is mostly used up, then swell into red giants, destroying life on any previously habitable planets, and then shrink to white dwarfs, perhaps having become novas during the process. More massive stars use up their hydrogen quicker and remain on the main sequence for shorter times.

Stars potentially capable of having habitable planets belong to spectral classes F, G, and K, in order of decreasing mass and luminosity. Spectral classes are further subdivided with numbers from 0 to 9 in order of decreasing mass and luminosity. Roman numerals are used to describe whether the stars are main sequence stars - V means main sequence.

According to the information available to Dole at the time of writing, stars with mass equal to or less than 1.4 solar masses and spectral types of F2V or colder, would remain on the main sequence for at least the minimum time of 3 billion years Dole considered necessary for a planet to become habitable.

Low mass dim stars have their circumstellar habitable zones (which Dole called "ecospheres"), where planets are expected to have the right temperatures for liquid water using life forms, so close to them that planets in them would become tidally locked, which Dole considered incompatible with habitability. Dole calculated that the inner part of the "ecosphere" of a star would be too close starting with a mass of 0.88 Sun and the whole ecosphere would be to close to the star starting with a mass of 0.72 Sun, a K1V class star.

So any science fiction writer who read Habitable Planets for Man in 1964 or later would realize that stars of type F2V to K1V were the only classes of stars likely to have planets with atmospheres breathable for humans. And if they wanted their stories to seem scientifically plausible to their more scientifically educated readers they would restrict depicting human habitable planets to those orbiting stars of spectral types F2V to K1V.

Jack Vance's five "Demon Princes" novels were published from 1964 to 1981.

https://en.wikipedia.org/wiki/Demon_Princes

In the first two, the protagonist makes his base on a human colony on a planet of the star Rigel, Beta Orionis, a B8 I supergiant. In the later books the protagonist makes his base of operations on a human colony planet orbiting the star Vega, Alpha Lyrae, an A0V class star. Neither Rigel nor Vega can last on the main sequence long enough for a planet to naturally become habitable for humans, though the problem is many times worse for Rigel than for Vega.

And I think I remember a quote in one of the "Demon Princes" books where it is stated that it is a scientific mystery how Rigel can have habitable planets, and terraforming by an ancient advanced civilization is suggested.

In this story identification question,

"Demon Flute" Story in Analog

I asked about a story which was identified in an answer as "Music Hath Charms", by Timothy Zahn, in Analog, April, 1985. In that story there are at least four stars known to have habitable planets; the star of the human colony planet that is the setting, Earth's star The Sun, Vega, and Algol, the "Demon Star".

And I wrote a letter to Stanley Schmidt, editor of Analog, pointing out that two of the four stars in the story with habitable planets, Vega and Algol, should not have habitable planets. As I remember, Schmidt wrote back, and didn't seem to consider stories with stars of the wrong spectral class to have habitable planets to be a problem.

And sometime later, I read an article by Schmidt with advice for science writers, including not to use stars of the wrong spectral classes to have habitable planets, and using Vega as an example of a class of star not to use.

So I guess than in the years since 1964 the more scientifically literate science fiction writers have gradually come to abandon putting habitable planets in orbit around stars of the wrong spectral classes to have habitable planets.

And avoiding stars more massive and luminous than main sequence class F stars is due to knowing that those more massive stars will become red giants too soon to have habitable planets.

And the earliest examples I can think of putting habitable worlds around only stars of the correct spectral classes may date to the 1950s in juvenile science fiction novels. Robert A. Heinlein's Starman Jones (1954) and Time for the Stars both have statements that spectral class G stars are the most likely to have habitable planets. So possibly the future evolution of various types of stars had already been calculated by astrophysicists by the time Heinlein wrote those novels.

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