Given Our Date, Is Sun Birth Late?
In our grabby aliens paper, we use a simple model that predicts the appearance of advanced life in terms of when habitable stars are formed, how long they last, and the hard steps power law of when advanced life appears within a planetary habitable lifetime window. We showed that this is well approximated by a power law during grabby alien birthdates, and that humanity looks quite early relative to its predictions.
Using this same model, we can also ask: how early or late is the sun’s birthdate, given our current appearance date? This graph shows the percentage of dates that are after our sun’s birthdate of 9.23Gyr, for stars that give rise to advanced life at 13.77Gyr:
Unless the max planet lifetime is very short, our Sun’s birthdate starts to look substantially late for powers above about five. So either the power is below five, or panspermia happened, in which case Earth’s star had to come later to come after the earlier star of Eden. And in which. case, the power is probably high, as it would be the sum of hard steps on both Earth and Eden.
I am really well aware of all of that. But one can't put everything one knows into a simple calculation. I claims this calculation shows an essential feature of the situation, even if it doesn't model every detail.
You have neglected the fact that stars, and planets, are not homogenous. Small stars predominate and, while long-lived, have narrow orbital zones for habitable planets and often emit dangerous flares. There are also different generations of star systems with different elemental compositions. The first generation of stars consisted of hydrogen and helium, with a small amount of lithium, and were unlikely to have life-bearing planets. The second generation of stars, born from the debris of exploding first-generation stars, have a modicum of heavy elements up to iron; but are deficient in the proportion of such elements as compared to our own solar system, therefore may be less suitable for the evolution of life and technological civilizations. Our sun belongs to the third generation of stars, with a greatly enhanced proportion of heavy elements up to uranium, and is much older than most third-generation stars in our galaxy.