Where was the solar system born? Alternatively, how far back in time can we retrodict the location of the solar system?

Question

I have two related questions:

1. Where in the Milky Way did the solar system form? Is there a particular nebula it can be traced to?

2. How far back in time can we track the location of the solar system within the Milky Way with reasonable certainty?

Notes:

• Obviously, if the answer to (2) is "as far back as the origin of the solar system", then we have an answer to (1), but I suspect that's not the correct answer to (2), so I ask these as separate questions.

• For (2), I would imagine that parallax data from Gaia would be particularly relevant.

• For (1), I wonder if something like relative metal abundances can be measured and give a precise enough "fingerprint" to "match" the solar system to its birthplace.

• For (1), I don't know whether nebulae remain recognizable as nebulae billions of years after their star-forming days -- if not, then the premise of my question may be flawed -- it may be that the birthplace of the solar system has diffused away into the background structure of the Milky Way by now.

Answer 1

Basically no, and not very far back at all.

Star forming regions generally last for at most 10 million years. The "nebula" in which the Sun was born is long gone so cannot be identified.

The motion of the Sun around the Galaxy is not very precisely known. Typical uncertainties in its velocity are about 1 km/s along each axis (towards the Galactic centre, tangential to the Galactic centre and out of the plane of the Galaxy) - see for example Schoenrich, Binney & Dehnen (2010) and How far is the Earth/Sun above/below the galactic plane, and is it heading toward/away from it? .

It just so happens that 1 km/s is about 1 pc per million years. Thus every million years we go back in time, the uncertainty in the Sun's position grows by about 1 pc in each dimension.

A further hazard is that stars do not "orbit" like planets in the Solar System". Their orbits can be perturbed significantly over billions of years by (for example) encounters with giant molecular clouds or passage through spiral arms.

It is therefore impossible to precisely place where the Sun was 4.5 billion years ago. Since its metallicity is slightly higher than the average of stars in the Solar neighbourhood, it is thought it may have originated 1-2 kpc closer to the Galactic centre than it is now (Nieva & Przybilla 2012), though others disagree - Martinez-Barbosa et al. 2015) or claim the Sun may have even originated near the Galactic Bulge (Tsujimoto & Baba 2020).

You raise the issue of a chemical abundance "fingerprint". Unfortunately, although this is a "hot topic" in "Galactic Archaeology", it has borne little fruit so far. There is a great deal of similarity between stars born in different clusters and a great deal of overlap in their chemical abundance signatures. It is doubtful (in my opinion) that true siblings of the Sun will ever be identified in this way.

Answer 2

..and to Cuivienen there is no returning

Nobody knows.

All the stars in the Milky Way Galaxy orbit around the center of mass of the galaxy.

The orbit of the Sun takes about 250 million years. The solar system is believed to be about 4.5 billion years old, and so the Sun has completed about 18 full orbits around the center of the galaxy.

Because no two stars have exactly the same orbits, stars are constantly getting closer to and farther away from their neighboring stars. Over many millions of years, some neighboring stars will pass far ahead of the Sun in their orbits and some will be left far behind in their orbits.

Thus the list of stars which were within ten light years of the Sun a million years ago is somewhat different from the list of stars which are now within ten light years of the Sun, and that list is somewhat different from the list of stars which will be within ten light years of the Sun a million years in the future.

Here is a link to a table of stars which have passed or will pass within 5 light years of the Sun over the past and next few million years according to calculations.

https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brown_dwarfs#Distant_future_and_past_encounters

The closer two stars pass, the stronger their gravitational forces will change both their orbits. The Sun must have had hundreds of close encounters with stars which changed its orbit during its lifetime.

There are an estimated one hunded to four hundred billion stars in our galaxy, and we only have measurements the positons, masses, and motions of about a billion of those stars, about 0.025 to 0.1 of the stars in the galaxy. And many of the measurements of the positions, masses, and motions we have are not very precise.

So at the present time a computer simulation to track the position of the solar system back in time might might have some accuracy for tens of millions of years in the past, but that is a small fraction of the time since since the solar system formed.

2.

A star forming nebula collapses into a cluster of young stars. The new stars include a small fraction of very luminous and short lived stars emitting intense radiation which drives remaining nebular matter outward until it reaches and merges with other nebulae.

So star forming nebulae self destruct. Each leaves behind a void where interstellar interstellar gas and dust have a lower density than average, and a cluster of young stars.

As the open star cluster orbits around the center of the galaxy, it interacts gravitationally with passing stars and the stars in the cluster are gradually pulled out of the cluster and scattered. So open star clusters in the galactic disc last for only hundreds of millions of years before dissipating.

Neither the nebula that formed the solar system nor the open cluster of young stars that formed in that nebula exist any more, having dissipated into the galaxy in general. It is quite possible that some of the stars which formed within ten or twenty light years from the Sun in that nebula are now over fifty thousand light years away from the Sun mixed in with stars which originated in many other now lost nebulae and star clusters.

3.

According to Tolkien's Middle-stories, the first Elves awoke in a place called Cuivienen, the Water of Awakening. And their travels eventually took them far from Cuivienen, to achieve great glory and suffer terrible tragedy. Perhaps some Elves wondered whether it would have been better or worse if they had stayed in Cuivienen.

The narrator of Chapter Three "Of the Coming of the Elves and the Captivity of Melkor" in the Quenta Silmarillion says rather sadly:

In the changes of the world the shapes of lands and of seas have been broken and remade; rivers have not kept their course and neither have mountains remained steadfast; and to Cuivienen there is no returning.

And with the present limits of our knowledge there is no returning, even in calculation, to the birthplace of Earth.