Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange
3 broken image fixed (click 'rendered output' or 'side-by-side' to see the difference; image retrieved via Wayback Machine); for more info, see https://gist.github.com/Glorfindel83/9d954d34385d2ac2597bbe864466259f
source | link

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram http://sciyag.rubyforge.org/ctioga/gallery/diagramme_HR_temps.pnga 10 solar masses star evolution within the HR diagram
(source: rubyforge.org) !

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).

Addendum

Models are based on stellar physics that should represent quite well what is going on in actual stars (see for example Eggleton paper who wrote the code on which EZ-web is based). You will find some interesting stuff on the BaSTI homepage including bibliographic entries you are looking for. Finally, extensive comparison with experimental data have been done to ensure that stellar models reproduce some real features, for example with the Hipparcos data on the Milky Way (a very simple example on page 30 of this PhD) or with stellar clusters (that are almost isochrones, that is a distribution of stars that all have the same age, see also BaSTI isochrones for more details)

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram http://sciyag.rubyforge.org/ctioga/gallery/diagramme_HR_temps.png!

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).

Addendum

Models are based on stellar physics that should represent quite well what is going on in actual stars (see for example Eggleton paper who wrote the code on which EZ-web is based). You will find some interesting stuff on the BaSTI homepage including bibliographic entries you are looking for. Finally, extensive comparison with experimental data have been done to ensure that stellar models reproduce some real features, for example with the Hipparcos data on the Milky Way (a very simple example on page 30 of this PhD) or with stellar clusters (that are almost isochrones, that is a distribution of stars that all have the same age, see also BaSTI isochrones for more details)

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram
(source: rubyforge.org) !

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).

Addendum

Models are based on stellar physics that should represent quite well what is going on in actual stars (see for example Eggleton paper who wrote the code on which EZ-web is based). You will find some interesting stuff on the BaSTI homepage including bibliographic entries you are looking for. Finally, extensive comparison with experimental data have been done to ensure that stellar models reproduce some real features, for example with the Hipparcos data on the Milky Way (a very simple example on page 30 of this PhD) or with stellar clusters (that are almost isochrones, that is a distribution of stars that all have the same age, see also BaSTI isochrones for more details)

2 More complete answer following a comment
source | link

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram http://sciyag.rubyforge.org/ctioga/gallery/diagramme_HR_temps.png!

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).

Addendum

Models are based on stellar physics that should represent quite well what is going on in actual stars (see for example Eggleton paper who wrote the code on which EZ-web is based). You will find some interesting stuff on the BaSTI homepage including bibliographic entries you are looking for. Finally, extensive comparison with experimental data have been done to ensure that stellar models reproduce some real features, for example with the Hipparcos data on the Milky Way (a very simple example on page 30 of this PhD) or with stellar clusters (that are almost isochrones, that is a distribution of stars that all have the same age, see also BaSTI isochrones for more details)

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram http://sciyag.rubyforge.org/ctioga/gallery/diagramme_HR_temps.png!

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram http://sciyag.rubyforge.org/ctioga/gallery/diagramme_HR_temps.png!

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).

Addendum

Models are based on stellar physics that should represent quite well what is going on in actual stars (see for example Eggleton paper who wrote the code on which EZ-web is based). You will find some interesting stuff on the BaSTI homepage including bibliographic entries you are looking for. Finally, extensive comparison with experimental data have been done to ensure that stellar models reproduce some real features, for example with the Hipparcos data on the Milky Way (a very simple example on page 30 of this PhD) or with stellar clusters (that are almost isochrones, that is a distribution of stars that all have the same age, see also BaSTI isochrones for more details)

1
source | link

You could look at tools like EZ-web or interpolation formulae like those from Hurley, Pols and Tout 2000 to infer how much time a given star (say O-type) spend in a given state compared to the time spend in the Main Sequence. For example an initialy $10M_\odot$ star would spend around 25 Myrs on the main sequence and only 3 Myrs being a red giant as you can see on the next picture that I made during my PhD (in french, sorry). Stage 1 is the main sequence and stage 3 to 5 are various reg giants stages.

a 10 solar masses star evolution within the HR diagram http://sciyag.rubyforge.org/ctioga/gallery/diagramme_HR_temps.png!

Thus you could infer that if you have found 25 $10M_\odot$ stars on the main sequence in your sample, there should be around 3 of them being red giants in the same sample (this reasoning naturally won't hold if your sample has some precise age like a star cluster for example). Knowing the probability to get a given star on the main sequence and converting it to numbers for, say, a million stars, you could know how much red giants you would expect to find in addition to this million stars.

Note that, once again, this reasoning would only hold for stars whose age span is very small compared to the age of the universe (e.g. quite massive stars).