<p>Stars typically do form in clusters, because to get the gravitational instability to initiate, you need a very large mass-- much larger than the mass of a single star.  A typical mass for the gravitational instability is about a million solar masses, though it can vary by an order of magnitude depending on the situation.  But you don't get a single star of that mass because after the instability starts (on the scale of a "giant molecular cloud"), it fragments into smaller bits, which are the star clusters, which fragment into further bits, which are the stars.  There are two basic types of clusters, "open" and "globular", where the open clusters are not gravitationally bound so the stars wander away from each other after forming (which is presumably what happened to the Sun).  The globular clusters stay bound for very long times and can even wander away from the plane of the spiral galaxy and still be together as clusters, but obviously the Sun is not in one of those and is not old enough to have completely left the plane of the galaxy (though it does oscillate up and down through the plane).  A typical open cluster might be a thousand stars, so it seems likely the Sun might have about a thousand "sister" stars spread around the plane by now, but we'll never know which ones those are since the age cannot be determined precisely enough.</p>

CC BY-SA 3.0
2016-09-29T17:28:07.023Z
It's not entirely true that stars in open clusters aren't bound. They can survive for timescales on the order of $\sim10^8$ years, which isn't insignificant compared to the lifespan of many massive stars. But their lifespans are certainly much smaller than those of globular clusters.
HDE 226868
CC BY-SA 3.0
2016-09-29T19:16:04.727Z
There is no such thing as a typical cluster, but by chance you may have the answer about right.
ProfRob
CC BY-SA 3.0
2016-09-29T19:17:30.797Z
Also not true that "we'll never know". Efforts are underway - search for "chemical tagging" and "solar twins".
ProfRob
CC BY-SA 3.0
2016-09-29T23:49:13.277Z
"There's no such thing as a typical cluster."  I'm afraid I find that statement rather meaningless.  And I am quite correct, lucky or otherwise, that we'll never know what stars formed with our Sun, because what astronomers mean by a "solar twin" is never going to be proof that it formed with our Sun.  Do some more research, perhaps starting with https://arxiv.org/abs/1608.03788.  There you will find the term "solar twin" is used in the open cluster M67.  By the way, no one is suggesting the Sun formed in M67!
Ken G
CC BY-SA 3.0
2016-09-30T01:31:23.277Z
On the issue of gravitational binding, it's true that when we see an open cluster, the stars are still weakly bound, so that's why it still exists.  But those represent only some of the stars that form in that cluster, so the Sun could have been one that became unbound as the gas in the cluster dispersed.  So it's true that open clusters should not be described as gravitationally unbound, better would be to say they are so weakly bound that stars in them can often become unbound.
Ken G
CC BY-SA 3.0
2016-09-30T06:48:22.950Z
By no such thing as a typical cluster, I mean that the number of stars per cluster has a power law distribution and is not peaked. There are more "clusters" by number that are smaller than 1000 stars.
ProfRob
CC BY-SA 3.0
2016-09-30T12:52:01.570Z
All power laws are peaked, of course.
Ken G
CC BY-SA 3.0
2016-09-30T13:02:38.823Z
By which I mean, power laws always require a cutoff.  But more to the point, what is relevant to the concept of a "typical cluster for a star to form in" is not the distribution over the number of stars in a cluster, it is the distribution you get when you sample stars at random, and ask what is the size of the cluster they formed in.  That distribution will peak at around a thousand stars, which is what I'm talking about, and what sources like that cited article are talking about.
Ken G
CC BY-SA 3.0
2016-09-30T13:39:33.840Z
Well I didn't want to get into that detail, but since you raise it. $dP/dN \propto N^{-1}$ (roughly, according to the Adams review I cite [section 3]), where $P$ is the probability of a particular star being born in a cluster of size $N$. Which means the Sun has far more chance of being born in a cluster much smaller than 1000 stars if you have no other information. So a "typical cluster" in the sense in which you use it in your answer and the comment above would be *much* smaller than 1000 and the distribution is flat in $\log N$.
ProfRob
CC BY-SA 3.0
2016-09-30T14:44:20.153Z
You should have read the rest of section 3, where it says "half of the stellar population would be born within systems with N ≥ 1000, but
at most 20 percent of that population would end up living in open clusters. In this case,the remaining 80 percent of the stars would be born within “clusters” that dissolve quickly."  What this means is, the dP/dN distribution you cited is contaminated by the selection effect that you only see what remains of the cluster!  You have forgotten all the stars that formed there, and then left-- like the Sun, which we are talking about.
Ken G
CC BY-SA 3.0
2016-09-30T14:46:07.470Z
But I will grant you that all these comments point to an important ambiguity when we talk about "clusters", which is the difference between what was a cluster when the stars formed, and what is a cluster we can still see today.  My comments only refer to the former meaning, as it is the one relevant to the question, but that is different from what an observer would mean by looking at star clusters that still exist.  What is clear is that stars forming "in isolation" is still regarded as reasonably rare, and does not appear to apply to our Sun either.
Ken G
CC BY-SA 3.0
2016-09-30T14:54:35.990Z
Also, we should recognize the possible ambiguities in the meaning of forming "in isolation."  The Bressert paper cited above is all about the density of stars forming in clusters, it is not about stars not forming in clusters, and they are interested in proximity effects during formation.  They are criticizing the view that stars either form with extreme proximity effects, or none, and are saying there is a complete range of proximity effects-- but all of this is within stars clusters containing thousands of stars, as that is their observational sample.
Ken G
CC BY-SA 3.0
2016-09-30T15:18:37.337Z
The Bressert study looks at various definitions of cluster and find that between 10% and 60% of stars are not born in objects that meet those definitions. As far as reading the Adams paper, I read it when it came out and many times since.The $dP/dN \propto N^{-1}$ used in section 3 of Adams is "the probability of being *born* in a cluster of size $N$" (my italics) and fully takes account of infant mortality. Thus *a priori* the Sun has just as much chance of being born in a cluster of size 10-30 as in a cluster of size 1000-3000.
ProfRob
CC BY-SA 3.0
2016-09-30T15:23:37.437Z
Read further on p.11, where you are told that  the observational evidence suggests that half of stars are formed in cluster/groups of size less than 100-300. All this means is that the second clause of your sentence " a typical open cluster might be a thousand stars, so it seems likely the Sun might have about a thousand "sister" stars spread around the plane ", does not follow from the first. The reason that an origin cluster of 1000-10,000 for the Sun is proposed is not because that is a typical cluster.
ProfRob
CC BY-SA 3.0
2016-09-30T20:00:36.050Z
I see that you are right, what Adams is saying is that only about 10 percent of stars form in open clusters of about 1000 stars or so.  The rest form in smaller groups, perhaps even in isolation.  So the Sun does seem to be a bit of a special case.  Of course, this conclusion is also disputed, so it is a matter of current research, but it cannot be claimed that the Sun is typical of all stars.  So my original answer does seem to be correct under somewhat fortuitious circumstances!  I learned something.
Ken G
CC BY-SA 3.0
2016-09-30T21:29:56.413Z
See this Wikipedia listing and it's sources: https://en.wikipedia.org/wiki/HD_162826 .. Pretty cool if correct.
Jack R. Woods
CC BY-SA 3.0
2016-09-30T23:51:13.127Z
It certainly proves there are already authors who are willing to claim they have "almost certainly" identified solar siblings from the same open cluster.  Whether or not others are willing to accept that conclusion remains to be seen-- one has to watch out for the motivations of those who are trying to write grant proposals to seach for solar siblings, and apply a healthy dose of skepticism.  The Sun has made about 18 orbits around the galaxy since its inception, and finding stars that can be traced back to the same place is fraught with sensitivity to the dynamical assumptions.
Ken G
CC BY-SA 3.0
2016-10-01T00:08:02.170Z
So you can count me as doubtful that the trajectories of solar siblings can be known that precisely, but I will admit that I was indeed premature to say it could "never" be shown convincingly.  Perhaps we will indeed someday know so much about our galaxy that we can trace in detail the history of the stars in the solar neighborhood, and see in effect a movie of their star formation histories.
Ken G
CC BY-SA 3.0
2016-09-29T12:52:42.220Z
2016-09-29T12:52:42.220Z
Ken G
<p>Fortunately, there is an extensive and highly respected Annual Reviews of Astronomy and Astrophysics article on this very question - Adams (2010), <a href="https://arxiv.org/abs/1001.5444">https://arxiv.org/abs/1001.5444</a></p>

<p>At the moment it is debated whether most stars form in clusters. They may do, but there is a lot of evidence for hierarchical structure formation that results in lots of stars forming in relative isolation.</p>

<p>Regardless, there are a number of strands of evidence that can be used to suggest that <strong>the Sun formed in a cluster of somewhere between a thousand and ten thousand siblings</strong> - a bit like the Orion Nebula cluster.</p>

<p>Adams argues for this on the basis of: (1) We have a relatively well-behaved solar system inside the orbit of Neptune. This argues the Sun did not (or rather was not likely to) form in a massive and dense cluster where it suffered lots of very close encounters. On the other hand, the wacky orbits of some more distant objects like Sedna do suggest some early close encounter with another star was required. (2) If the Sun was born in a very massive cluster, it would likely have been born close to some very massive stars. The UV emission from such stars could photoevaporate a circumsolar disk before it formed planets. (3) In tension with this is the probability that the protosolar disk was enriched with radioactive supernova products. This requires the Sun to be born close to moderately massive stars (that would explode on a short timescale), which are only found in moderately massive clusters.</p>

<p>Adams puts these constraints together to estimate a <em>probability</em> that the Sun was born in a cluster of a particular size. Figure 7 of the review shows this to be reasonably sharply peaked between a thousand and ten thousand.</p>

<p>An order of magnitude uncertainty is at least warranted and some of the assumptions and calculations are open to criticism. But it is a starting point for any further research into the matter.</p>

CC BY-SA 3.0
2016-09-30T00:54:55.110Z
i would like to hear more about this idea of stars forming in isolation.  That must be a new idea, because most of the evidence I know about supports the statement in the abstract of that very review article you cited: "Since most stars form within groups and clusters, the question becomes one of determining the nature of the birth aggregate of the Sun."
Ken G
CC BY-SA 3.0
2016-09-30T06:17:12.157Z
@KenG The rival picture is more hierarchical with a continuum of birth environments. This paper has been very influential in the field: https://arxiv.org/abs/1009.1150
ProfRob
CC BY-SA 3.0
2016-09-30T13:09:19.827Z
That is an interesting article, thank you.  I find this particularly interesting: "only a low fraction (< 26%) of stars are formed in dense environments where their formation/evolution (along with their circumstellar disks and/or planets) may be affected by the close proximity of their low-mass neighbours."  So they are not saying most stars don't form in clusters, they are saying they are not affected by proximity effects-- which is not at all the same thing.
Ken G
CC BY-SA 3.0
2016-09-30T13:10:30.420Z
Thanks for yet another superlative answer on this question!  That PDF will keep me reading for awhile. I am wondering, let's say the "Adams picture" is correct the Sun was created in a cluster of 5000 stars.  Regarding the other 4999 stars, for me to understand the general picture is it the case that: (i) we just have utterly no clue where they would be, (ii) they would be randomly distributed *in the whole galaxy*, (iii) we have no clue which they are, but they must all be in our same arm, (iv) we have no clue which they are, but they must all be kicking around quite close to us.
Fattie
CC BY-SA 3.0
2016-09-30T13:14:36.140Z
@KenG - it's a good point that the sentence you quote just there is perfectly ambiguous and can be read either way!
Fattie
CC BY-SA 3.0
2016-09-30T13:47:01.587Z
@JoeBlow How far stars are dispersed and radially migrate is very much an active research topic. Velocity dispersion certainly increases with age. Most likely, the siblings of the Sun are spread in an annulus right around the Milky Way, of uncertain width, but it could be as much as a few kpc. The siblings would have a very close chemical match to the Sun, which allows us to find *candidate* members of the "solar cluster". Most of the siblings would have lower masses than the Sun. Siblings of more than a few solar masses have long since evolved into white dwarfs (or exploded).
ProfRob
CC BY-SA 3.0
2016-09-30T13:50:59.743Z
@RobJeffries - thanks a lot for the follow-up, good one.  Got it.  Perhaps in a couple of centuries, when we have something 10,000x better than GAIA (hard to imagine!) we will have so much data on stars in our galaxy, that, we will indeed be able to pick them all out.
Fattie
CC BY-SA 3.0
2016-09-30T13:52:49.677Z
"Velocity dispersion certainly increases with age" TBC does that sentence mean "the dispersion of sibling stars, caused by the velocity gained when leaving a cluster, increases with age" or "the velocity of a given star, dispersed from a cluster, actually increases with age" {perhaps due to more and more interactions??}
Fattie
CC BY-SA 3.0
2016-09-30T14:50:40.230Z
I'm glad it is now clear that all we will ever see is "candidates" for stars made in the same cluster as the Sun, so we all now agree it is true, rather than false as claimed in other comments, that we cannot know if any given star was born with the Sun.  Progress!
Ken G
CC BY-SA 3.0
2016-09-30T15:26:23.490Z
@KenG My opinion is more nuanced. It is unwise to say "never" in science. It is certainly hard/impossible to do more than give a probability based on what we know now and based on current measurement techniques. But never..? No.
ProfRob
CC BY-SA 3.0
2016-09-30T15:27:26.577Z
@JoeBlow I mean dispersion between siblings, thus they lose both kinematic and spatial coherence with time.
ProfRob
CC BY-SA 3.0
2016-09-30T19:01:13.150Z
@RobJeffries thanks for the clarification.  BTW as always, sorry that (I've observed) many things which are pretty obvious to professionals in this field, are "don't even know the order of magnitude" type issues to armchair readers like myself!  (The things I've been "astounded to learn" on this site, even as a keen popular science reader, amaze me, heh!)
Fattie
CC BY-SA 3.0
2016-09-30T19:50:13.467Z
@RobJeffries On the contrary, that we will "never know" is a clearly scientifically testable prediction.  It may not be one you or I ever get the answer to, but I make the prediction all the same, and it will turn out to be either a true prediction or a false one.  But if you want to parse the statement more carefully, you can interpret it as "a mountain of good evidence tells us it is vastly unlikely we will ever know if any particular other star was born with our Sun."  This is the obvious intention of my remark.
Ken G
CC BY-SA 3.0
2016-09-29T19:47:24.967Z
2016-09-29T19:47:24.967Z
ProfRob
<p>After reading <a href="https://astronomy.stackexchange.com/a/18508/13071">this interesting answer</a>,</p>

<p>I was wondering, do we in fact know <strong>if our Sun</strong> in particular was created as part of a star-forming-cluster, or, was it more of a solo creation?</p>

<p>(Or, are all stars created as part of star-forming-clusters, is that the norm and how all stars come to be?)</p>

<p>If yes, indeed are we aware of <strong>which stars around us</strong>, are our sibling star?  (So, there's a list somewhere "stars known to likely be sibling to our Sun from a certain star-forming-cluster".)  Or have they dispersed over the 4 billion years and it's impossible to know, or is it just the case that "all the stars anywhere nearby" are/were indeed siblings from "our" star-forming-cluster?</p>

<p>Further, I'm having trouble grasping the order of magnitude of star-forming-clusters. Consider say "all the stars in our arm of the galaxy": Consider the question "in how many star-forming-clusters did all those stars originate?"  Is the answer like "3", "a few hundred" or "100 million" ??</p>

<p>Perhaps most simply: if sol formed as part of a star-forming-cluster, what's the order of magnitude of <strong>how many stars</strong> formed with it?</p>

<star-formation>
Sun's formation as "part of a star-forming-cluster..."?
Fattie
# Sun's formation as "part of a star-forming-cluster..."?

(Asked by: username_0 on 2016-09-29)

After reading [this interesting answer](https://astronomy.stackexchange.com/a/18508/13071),

I was wondering, do we in fact know **if our Sun** in particular was created as part of a star-forming-cluster, or, was it more of a solo creation?

(Or, are all stars created as part of star-forming-clusters, is that the norm and how all stars come to be?)

If yes, indeed are we aware of **which stars around us**, are our sibling star? (So, there's a list somewhere "stars known to likely be sibling to our Sun from a certain star-forming-cluster".) Or have they dispersed over the 4 billion years and it's impossible to know, or is it just the case that "all the stars anywhere nearby" are/were indeed siblings from "our" star-forming-cluster?

Further, I'm having trouble grasping the order of magnitude of star-forming-clusters. Consider say "all the stars in our arm of the galaxy": Consider the question "in how many star-forming-clusters did all those stars originate?" Is the answer like "3", "a few hundred" or "100 million" ??

Perhaps most simply: if sol formed as part of a star-forming-cluster, what's the order of magnitude of **how many stars** formed with it?

**Tags:** star-formation

---

## 2 answers

### Answer by username_3 on 2016-09-29. Score: 5 | Accepted answer

Fortunately, there is an extensive and highly respected Annual Reviews of Astronomy and Astrophysics article on this very question - Adams (2010), <https://arxiv.org/abs/1001.5444>

At the moment it is debated whether most stars form in clusters. They may do, but there is a lot of evidence for hierarchical structure formation that results in lots of stars forming in relative isolation.

Regardless, there are a number of strands of evidence that can be used to suggest that **the Sun formed in a cluster of somewhere between a thousand and ten thousand siblings** - a bit like the Orion Nebula cluster.

Adams argues for this on the basis of: (1) We have a relatively well-behaved solar system inside the orbit of Neptune. This argues the Sun did not (or rather was not likely to) form in a massive and dense cluster where it suffered lots of very close encounters. On the other hand, the wacky orbits of some more distant objects like Sedna do suggest some early close encounter with another star was required. (2) If the Sun was born in a very massive cluster, it would likely have been born close to some very massive stars. The UV emission from such stars could photoevaporate a circumsolar disk before it formed planets. (3) In tension with this is the probability that the protosolar disk was enriched with radioactive supernova products. This requires the Sun to be born close to moderately massive stars (that would explode on a short timescale), which are only found in moderately massive clusters.

Adams puts these constraints together to estimate a *probability* that the Sun was born in a cluster of a particular size. Figure 7 of the review shows this to be reasonably sharply peaked between a thousand and ten thousand.

An order of magnitude uncertainty is at least warranted and some of the assumptions and calculations are open to criticism. But it is a starting point for any further research into the matter.

> **Comments:**
> **username_1**: i would like to hear more about this idea of stars forming in isolation.  That must be a new idea, because most of the evidence I know about supports the statement in the abstract of that very review article you cited: "Since most stars form within groups and clusters, the question becomes one of determining the nature of the birth aggregate of the Sun."  
> **username_3**: @KenG The rival picture is more hierarchical with a continuum of birth environments. This paper has been very influential in the field: https://arxiv.org/abs/1009.1150  
> **username_1**: That is an interesting article, thank you.  I find this particularly interesting: "only a low fraction (< 26%) of stars are formed in dense environments where their formation/evolution (along with their circumstellar disks and/or planets) may be affected by the close proximity of their low-mass neighbours."  So they are not saying most stars don't form in clusters, they are saying they are not affected by proximity effects-- which is not at all the same thing.  
> **username_0**: Thanks for yet another superlative answer on this question!  That PDF will keep me reading for awhile. I am wondering, let's say the "Adams picture" is correct the Sun was created in a cluster of 5000 stars.  Regarding the other 4999 stars, for me to understand the general picture is it the case that: (i) we just have utterly no clue where they would be, (ii) they would be randomly distributed *in the whole galaxy*, (iii) we have no clue which they are, but they must all be in our same arm, (iv) we have no clue which they are, but they must all be kicking around quite close to us.  
> **username_0**: @KenG - it's a good point that the sentence you quote just there is perfectly ambiguous and can be read either way!  
> **username_3**: @JoeBlow How far stars are dispersed and radially migrate is very much an active research topic. Velocity dispersion certainly increases with age. Most likely, the siblings of the Sun are spread in an annulus right around the Milky Way, of uncertain width, but it could be as much as a few kpc. The siblings would have a very close chemical match to the Sun, which allows us to find *candidate* members of the "solar cluster". Most of the siblings would have lower masses than the Sun. Siblings of more than a few solar masses have long since evolved into white dwarfs (or exploded).  
> **username_0**: @RobJeffries - thanks a lot for the follow-up, good one.  Got it.  Perhaps in a couple of centuries, when we have something 10,000x better than GAIA (hard to imagine!) we will have so much data on stars in our galaxy, that, we will indeed be able to pick them all out.  
> **username_0**: "Velocity dispersion certainly increases with age" TBC does that sentence mean "the dispersion of sibling stars, caused by the velocity gained when leaving a cluster, increases with age" or "the velocity of a given star, dispersed from a cluster, actually increases with age" {perhaps due to more and more interactions??}  
> **username_1**: I'm glad it is now clear that all we will ever see is "candidates" for stars made in the same cluster as the Sun, so we all now agree it is true, rather than false as claimed in other comments, that we cannot know if any given star was born with the Sun.  Progress!  
> **username_3**: @KenG My opinion is more nuanced. It is unwise to say "never" in science. It is certainly hard/impossible to do more than give a probability based on what we know now and based on current measurement techniques. But never..? No.  
> **username_3**: @JoeBlow I mean dispersion between siblings, thus they lose both kinematic and spatial coherence with time.  
> **username_0**: @RobJeffries thanks for the clarification.  BTW as always, sorry that (I've observed) many things which are pretty obvious to professionals in this field, are "don't even know the order of magnitude" type issues to armchair readers like myself!  (The things I've been "astounded to learn" on this site, even as a keen popular science reader, amaze me, heh!)  
> **username_1**: @RobJeffries On the contrary, that we will "never know" is a clearly scientifically testable prediction.  It may not be one you or I ever get the answer to, but I make the prediction all the same, and it will turn out to be either a true prediction or a false one.  But if you want to parse the statement more carefully, you can interpret it as "a mountain of good evidence tells us it is vastly unlikely we will ever know if any particular other star was born with our Sun."  This is the obvious intention of my remark.  

---

### Answer by username_1 on 2016-09-29. Score: 2

Stars typically do form in clusters, because to get the gravitational instability to initiate, you need a very large mass-- much larger than the mass of a single star. A typical mass for the gravitational instability is about a million solar masses, though it can vary by an order of magnitude depending on the situation. But you don't get a single star of that mass because after the instability starts (on the scale of a "giant molecular cloud"), it fragments into smaller bits, which are the star clusters, which fragment into further bits, which are the stars. There are two basic types of clusters, "open" and "globular", where the open clusters are not gravitationally bound so the stars wander away from each other after forming (which is presumably what happened to the Sun). The globular clusters stay bound for very long times and can even wander away from the plane of the spiral galaxy and still be together as clusters, but obviously the Sun is not in one of those and is not old enough to have completely left the plane of the galaxy (though it does oscillate up and down through the plane). A typical open cluster might be a thousand stars, so it seems likely the Sun might have about a thousand "sister" stars spread around the plane by now, but we'll never know which ones those are since the age cannot be determined precisely enough.

> **Comments:**
> **username_2**: It's not entirely true that stars in open clusters aren't bound. They can survive for timescales on the order of $\sim10^8$ years, which isn't insignificant compared to the lifespan of many massive stars. But their lifespans are certainly much smaller than those of globular clusters.  
> **username_3**: There is no such thing as a typical cluster, but by chance you may have the answer about right.  
> **username_3**: Also not true that "we'll never know". Efforts are underway - search for "chemical tagging" and "solar twins".  
> **username_1**: "There's no such thing as a typical cluster."  I'm afraid I find that statement rather meaningless.  And I am quite correct, lucky or otherwise, that we'll never know what stars formed with our Sun, because what astronomers mean by a "solar twin" is never going to be proof that it formed with our Sun.  Do some more research, perhaps starting with https://arxiv.org/abs/1608.03788.  There you will find the term "solar twin" is used in the open cluster M67.  By the way, no one is suggesting the Sun formed in M67!  
> **username_1**: On the issue of gravitational binding, it's true that when we see an open cluster, the stars are still weakly bound, so that's why it still exists.  But those represent only some of the stars that form in that cluster, so the Sun could have been one that became unbound as the gas in the cluster dispersed.  So it's true that open clusters should not be described as gravitationally unbound, better would be to say they are so weakly bound that stars in them can often become unbound.  
> **username_3**: By no such thing as a typical cluster, I mean that the number of stars per cluster has a power law distribution and is not peaked. There are more "clusters" by number that are smaller than 1000 stars.  
> **username_1**: All power laws are peaked, of course.  
> **username_1**: By which I mean, power laws always require a cutoff.  But more to the point, what is relevant to the concept of a "typical cluster for a star to form in" is not the distribution over the number of stars in a cluster, it is the distribution you get when you sample stars at random, and ask what is the size of the cluster they formed in.  That distribution will peak at around a thousand stars, which is what I'm talking about, and what sources like that cited article are talking about.  
> **username_3**: Well I didn't want to get into that detail, but since you raise it. $dP/dN \propto N^{-1}$ (roughly, according to the Adams review I cite [section 3]), where $P$ is the probability of a particular star being born in a cluster of size $N$. Which means the Sun has far more chance of being born in a cluster much smaller than 1000 stars if you have no other information. So a "typical cluster" in the sense in which you use it in your answer and the comment above would be *much* smaller than 1000 and the distribution is flat in $\log N$.  
> **username_1**: You should have read the rest of section 3, where it says "half of the stellar population would be born within systems with N ≥ 1000, but at most 20 percent of that population would end up living in open clusters. In this case,the remaining 80 percent of the stars would be born within “clusters” that dissolve quickly."  What this means is, the dP/dN distribution you cited is contaminated by the selection effect that you only see what remains of the cluster!  You have forgotten all the stars that formed there, and then left-- like the Sun, which we are talking about.  
> **username_1**: But I will grant you that all these comments point to an important ambiguity when we talk about "clusters", which is the difference between what was a cluster when the stars formed, and what is a cluster we can still see today.  My comments only refer to the former meaning, as it is the one relevant to the question, but that is different from what an observer would mean by looking at star clusters that still exist.  What is clear is that stars forming "in isolation" is still regarded as reasonably rare, and does not appear to apply to our Sun either.  
> **username_1**: Also, we should recognize the possible ambiguities in the meaning of forming "in isolation."  The Bressert paper cited above is all about the density of stars forming in clusters, it is not about stars not forming in clusters, and they are interested in proximity effects during formation.  They are criticizing the view that stars either form with extreme proximity effects, or none, and are saying there is a complete range of proximity effects-- but all of this is within stars clusters containing thousands of stars, as that is their observational sample.  
> **username_3**: The Bressert study looks at various definitions of cluster and find that between 10% and 60% of stars are not born in objects that meet those definitions. As far as reading the Adams paper, I read it when it came out and many times since.The $dP/dN \propto N^{-1}$ used in section 3 of Adams is "the probability of being *born* in a cluster of size $N$" (my italics) and fully takes account of infant mortality. Thus *a priori* the Sun has just as much chance of being born in a cluster of size 10-30 as in a cluster of size 1000-3000.  
> **username_3**: Read further on p.11, where you are told that  the observational evidence suggests that half of stars are formed in cluster/groups of size less than 100-300. All this means is that the second clause of your sentence " a typical open cluster might be a thousand stars, so it seems likely the Sun might have about a thousand "sister" stars spread around the plane ", does not follow from the first. The reason that an origin cluster of 1000-10,000 for the Sun is proposed is not because that is a typical cluster.  
> **username_1**: I see that you are right, what Adams is saying is that only about 10 percent of stars form in open clusters of about 1000 stars or so.  The rest form in smaller groups, perhaps even in isolation.  So the Sun does seem to be a bit of a special case.  Of course, this conclusion is also disputed, so it is a matter of current research, but it cannot be claimed that the Sun is typical of all stars.  So my original answer does seem to be correct under somewhat fortuitious circumstances!  I learned something.  
> **username_4**: See this Wikipedia listing and it's sources: https://en.wikipedia.org/wiki/HD_162826 .. Pretty cool if correct.  
> **username_1**: It certainly proves there are already authors who are willing to claim they have "almost certainly" identified solar siblings from the same open cluster.  Whether or not others are willing to accept that conclusion remains to be seen-- one has to watch out for the motivations of those who are trying to write grant proposals to seach for solar siblings, and apply a healthy dose of skepticism.  The Sun has made about 18 orbits around the galaxy since its inception, and finding stars that can be traced back to the same place is fraught with sensitivity to the dynamical assumptions.  
> **username_1**: So you can count me as doubtful that the trajectories of solar siblings can be known that precisely, but I will admit that I was indeed premature to say it could "never" be shown convincingly.  Perhaps we will indeed someday know so much about our galaxy that we can trace in detail the history of the stars in the solar neighborhood, and see in effect a movie of their star formation histories.  

---

