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
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.
"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"
If we only quantify over stars that give rise to advanced life at 13.77Gyr, then the maximum planet lifetime shouldn't matter as long as it's >13.77Gyr. For example, a planet that will live for 14Gyr will be neither more nor less likely to yield intelligent life 13Gyr into its existence than a planet that will live 20Gry. And yet, the graph keeps sloping downwards after 13.77Gyrs.
Why is this?
(My best hypothesis: planet-lifetimes implicitly also varies what kind of stars/planets you're considering, and contingently, it seems like planets with long maximum lifespans have appeared earlier than planets with short maximum lifespans in the past; making our planet relatively later.)
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.
"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"
If we only quantify over stars that give rise to advanced life at 13.77Gyr, then the maximum planet lifetime shouldn't matter as long as it's >13.77Gyr. For example, a planet that will live for 14Gyr will be neither more nor less likely to yield intelligent life 13Gyr into its existence than a planet that will live 20Gry. And yet, the graph keeps sloping downwards after 13.77Gyrs.
Why is this?
(My best hypothesis: planet-lifetimes implicitly also varies what kind of stars/planets you're considering, and contingently, it seems like planets with long maximum lifespans have appeared earlier than planets with short maximum lifespans in the past; making our planet relatively later.)
Not sure what you mean by "governing". More literally, we calculated % error averaged over those birthdates.
“... well approximated by a power law during grabby alien birthdates...”
I understand this better with “during” replaced by “governing”. Does that still convey your intended meaning?