The conclusions of this paper do not take into account empirical results indicating that most baryonic mass will probably be unable to form stars if trends that have held for the history of the universe so far continue to hold. I’m fairly convinced conclusions made on this basis do not resemble what will actually happen in our universe. I hereby link to a previous time I examined this study on this site and found it wanting:
In short, they don’t take into account that star formation often completely shuts down over time in galaxies despite there still being plenty of gas around, especially as they merge into large galaxies which is a continuing ongoing process, and that if you empirically look at star formation rates over time in the universe we are actually probably in the latter fractions of stars ever formed due to formation constantly declining at a precipitous rate. Their conclusion that we are early (8th percentile) in planet-formation order is based on the fact that something like 8% of baryonic mass in galaxies has become star systems [EDIT: Oops, more than 8% of gas, they have a metallicity cutoff that excludes gas that formed stars early in the history of most galaxies], not a projection of how much WILL eventually form stars, using uniformitarian assumptions rather than what I would consider more realistic models.
When you look at the empirical data, our position in planet-formation order seems likely unremarkable, and probably somewhere not far from the middle.
I don’t see why you think they didn’t take those factors into account; the article clearly says that:
The researchers also used the data to predict that future Earths are more likely to appear inside galaxy clusters and dwarf galaxies, which have yet to use up all their gas for building stars and accompanying planetary systems. Our Milky Way Galaxy, on the other hand, is all tapped out.
In addition, your claim that “Their conclusion that we are early (8th percentile) in planet-formation order is based on the fact that something like 8% of baryonic mass in galaxies has become star systems” doesn’t seem to be true; their conclusion instead seems to be more nuanced and based on taking into account metallicity and empirical rates of habitable planet formation: http://mnras.oxfordjournals.org/content/454/2/1811
What you say after the quote is correct and I will edit my parent comment accordingly, they do include metallicity cutoffs which decreases the contribution from star formation in the early universe, and most of the star formation of old giant ellipticals.
However, they do pretty much explicitly state that their conclusions are based on all potentially star-forming gas within the dark matter halos of galaxies eventually forming stars. This is not a good assumption since galaxy-quenching may be more or less permanent, and if you integrate fits of measured star formation rates over time in the universe into the future they converge towards total final numbers of stars that aren’t THAT much larger than today. Frequent shutdown of star formation after galaxy mergers bring spirals and dwarf galaxies together into large galaxies, other less dramatic quenching events that apparently happen while being poorly understood, and the presence of many galaxies with large amounts of gas that nonetheless have failed to form stars for many gigayears (http://www.dailygalaxy.com/my_weblog/2014/02/giant-elliptical-galaxies-why-are-they-red-and-dead.html , http://mnras.oxfordjournals.org/content/439/3/2291.full.pdf), and empirical studies showing universal rates of star formation are declining very rapidly (I could point to a couple papers, but this one http://arxiv.org/abs/1006.5751 even though it isn’t exactly ABOUT star formation rate has the prettiest graph I’ve seen in figure 1) are not taken into account. See second comment I link to.
EDIT: I’ve gone back into the empirical fits of universal star formation rates found in two recent papers that actually have equations, and after doing some very bothersome math to convert between redshift and universe age, it would appear that the fits not only both converge to a finite number of stars going forward in time but also agree that in terms of TOTAL stars today the universe is between 85 and 95% of the way through the total complement that will ever exist.
The sun then shows up at the ~75th percentile of stars in star-order for both fits (as in 75% show up behind us at the end of time). I am unprepared to rigorously normalize this with metallicities on my own to deal with the fact that the huge early batches of stars 10+ gigayears ago were probably unsuitable for terrestrial planets without putting way more time than I am currently likely to have into the effort, unfortunately.
EDIT 2: I can do a little VERY naive normalization. Read at your own risk:
The study that gives the ~85 percent figure for current existing stars (Yuskel et al 2008) also gives the Sun’s position as about the 85th percentile in currently existing stars and ~75th percentile in total stars ever. The linked study that started this whole conversation (Behroozi & Peeples 2015) gives the Earth’s location as about the 50th percentile amongst currently existing terrestrial planets after their metallicity normalization. If we assume star formation rate since the Earth’s formation is roughly fixed relative to terrestrial planet formation rate (heavy elements having polluted most places) then we get that the Earth formed after 0.5 / (1+0.5*0.15/0.1) = 29% of terrestrial planets.
Examining the paper (Sobral et al 2012) indicating 95% of eventual stars exist, and the sun is currently in the 82nd percentile, and eventual 75th percentile in the same way indicates that the Earth formed after 0.5/(1+0.5*0.05/0.13) = 42% of terrestrial planets. I trust the other number a bit better given it has a better estimation of star formation rates longer ago. I also caution that nobody really understands cutoffs for terrestrial planet formation, and that there could be other important factors, and these numbers only mean so much.
There’s been some rounding here and there as I did all these calculations. May redo them later, in the hopes of making sure I didn’t accidentally tune these numbers or propagate errors.
The conclusions of this paper do not take into account empirical results indicating that most baryonic mass will probably be unable to form stars if trends that have held for the history of the universe so far continue to hold. I’m fairly convinced conclusions made on this basis do not resemble what will actually happen in our universe. I hereby link to a previous time I examined this study on this site and found it wanting:
http://lesswrong.com/lw/mpa/september_2015_media_thread/cpz6
http://lesswrong.com/lw/mpa/september_2015_media_thread/crhi
In short, they don’t take into account that star formation often completely shuts down over time in galaxies despite there still being plenty of gas around, especially as they merge into large galaxies which is a continuing ongoing process, and that if you empirically look at star formation rates over time in the universe we are actually probably in the latter fractions of stars ever formed due to formation constantly declining at a precipitous rate. Their conclusion that we are early (8th percentile) in planet-formation order is based on the fact that something like 8% of baryonic mass in galaxies has become star systems [EDIT: Oops, more than 8% of gas, they have a metallicity cutoff that excludes gas that formed stars early in the history of most galaxies], not a projection of how much WILL eventually form stars, using uniformitarian assumptions rather than what I would consider more realistic models.
When you look at the empirical data, our position in planet-formation order seems likely unremarkable, and probably somewhere not far from the middle.
I don’t see why you think they didn’t take those factors into account; the article clearly says that:
In addition, your claim that “Their conclusion that we are early (8th percentile) in planet-formation order is based on the fact that something like 8% of baryonic mass in galaxies has become star systems” doesn’t seem to be true; their conclusion instead seems to be more nuanced and based on taking into account metallicity and empirical rates of habitable planet formation: http://mnras.oxfordjournals.org/content/454/2/1811
What you say after the quote is correct and I will edit my parent comment accordingly, they do include metallicity cutoffs which decreases the contribution from star formation in the early universe, and most of the star formation of old giant ellipticals.
However, they do pretty much explicitly state that their conclusions are based on all potentially star-forming gas within the dark matter halos of galaxies eventually forming stars. This is not a good assumption since galaxy-quenching may be more or less permanent, and if you integrate fits of measured star formation rates over time in the universe into the future they converge towards total final numbers of stars that aren’t THAT much larger than today. Frequent shutdown of star formation after galaxy mergers bring spirals and dwarf galaxies together into large galaxies, other less dramatic quenching events that apparently happen while being poorly understood, and the presence of many galaxies with large amounts of gas that nonetheless have failed to form stars for many gigayears (http://www.dailygalaxy.com/my_weblog/2014/02/giant-elliptical-galaxies-why-are-they-red-and-dead.html , http://mnras.oxfordjournals.org/content/439/3/2291.full.pdf), and empirical studies showing universal rates of star formation are declining very rapidly (I could point to a couple papers, but this one http://arxiv.org/abs/1006.5751 even though it isn’t exactly ABOUT star formation rate has the prettiest graph I’ve seen in figure 1) are not taken into account. See second comment I link to.
EDIT: I’ve gone back into the empirical fits of universal star formation rates found in two recent papers that actually have equations, and after doing some very bothersome math to convert between redshift and universe age, it would appear that the fits not only both converge to a finite number of stars going forward in time but also agree that in terms of TOTAL stars today the universe is between 85 and 95% of the way through the total complement that will ever exist.
The sun then shows up at the ~75th percentile of stars in star-order for both fits (as in 75% show up behind us at the end of time). I am unprepared to rigorously normalize this with metallicities on my own to deal with the fact that the huge early batches of stars 10+ gigayears ago were probably unsuitable for terrestrial planets without putting way more time than I am currently likely to have into the effort, unfortunately.
EDIT 2: I can do a little VERY naive normalization. Read at your own risk:
The study that gives the ~85 percent figure for current existing stars (Yuskel et al 2008) also gives the Sun’s position as about the 85th percentile in currently existing stars and ~75th percentile in total stars ever. The linked study that started this whole conversation (Behroozi & Peeples 2015) gives the Earth’s location as about the 50th percentile amongst currently existing terrestrial planets after their metallicity normalization. If we assume star formation rate since the Earth’s formation is roughly fixed relative to terrestrial planet formation rate (heavy elements having polluted most places) then we get that the Earth formed after 0.5 / (1+0.5*0.15/0.1) = 29% of terrestrial planets.
Examining the paper (Sobral et al 2012) indicating 95% of eventual stars exist, and the sun is currently in the 82nd percentile, and eventual 75th percentile in the same way indicates that the Earth formed after 0.5/(1+0.5*0.05/0.13) = 42% of terrestrial planets. I trust the other number a bit better given it has a better estimation of star formation rates longer ago. I also caution that nobody really understands cutoffs for terrestrial planet formation, and that there could be other important factors, and these numbers only mean so much.
There’s been some rounding here and there as I did all these calculations. May redo them later, in the hopes of making sure I didn’t accidentally tune these numbers or propagate errors.