By type, how far out do we have good star maps?

Question

First off, these questions asked by others seem related, but each asks a slightly different question and neither have very good answers:

• How well have we mapped our local neighborhood of stars?
• Radius to which all hydrogen-burning stars are known?

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My question is: how does the type of stars relate to the distance at which we are no longer sure we know of all of that type of stars? What about the distances we are reasonably sure we don't know all of them?

While I'm interested in the answer for most star types, the types of primarily interest are the ones that are similar enough to the sun to expect them to be the most likely hosts for earth like planets. (I'm excluding things like giants that would have swallowed any of their original terrestrial planets and red dwarfs where the liquid water range would tidally lock planets.)

For the sake of this question, I will consider a star "known" if we know its location to some reasonably small fraction of its distance (arbitrarily say 10%, though I'd go with something else if there is a compelling reason to). Something that's just a number in the Gaia catalog who's distance is the scientific equivalent of "probably somewhere in our galaxy" is functionally unknown for my use.

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For context, the way this question came up is the question of where to place a fictional story so that authors can get a desired degree of freedom? In order to match reality, it would be necessary to place it close enough that getting (mostly) complete maps of the relevant types of stars is practical. On the other hand, to have no real need to match reality, would require placing it far enough away that the majority of the relevant stars are expected to be unknown for the foreseeable future.

Given that context, how much difference does it make what direction is being considered? do we have much better data looking out of the galactic plane? How about toward or away from the galactic core?

Also, to put some limits on things: if the answer for the "most stars are unknown" distance is well under about 1.5kpc, then that part becomes moot as one of the options has other reasons to place things that far out. If on the other end, we have nearly complete catalogs to greater than 100pc that would also be a "good enough" answer.

Note: based on this Gaia query, there are something like 700k known stars within about 100pc which makes me think there will be a lot of unknown stars in there as well.

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Edit: Using the highly scientific analytic technique of "squint at the graph", this random sample from Gaia (DR2) looks like it has fewer points right on the galactic plane than a little above or below it. As a non-expert, this suggest to me that the quality of that map is degraded there (background noise, extinction, etc.) Does anyone know if this translates to closer "horizons"? If so, how much?

Answer 1

Only rough numbers can be given and I would base them on the Gaia EDR3 catalogue since you are demanding that distances are known and no other big catalogue will have parallaxes (and hence distances, since non-parallax-based distances are usually less accurate than 10%).

There will be no spherical volume that can be given. The sensitivity of Gaia is a complicated function of position on the sky. The average sensitivity depends on stellar brightness, but that in turn does not define an unambiguous distance limit because the brightness depends on both the distance and extinction for a given spectral type.

Sun-like stars that have an absolute G-magnitude of about 4.5. The parallax uncertainties in Gaia EDR3 are about 0.03 mas for G=15 (and this is about the minimum uncertainty, even for brighter stars), 0.07 mas at G=17, then rise rapidly to about 0.5 mas at G=20. Gaia EDR3 is almost photometrically complete to this limit.

At say G=19.5, and ignoring extinction, a solar-type star would be at a distance modulus of 15, or a distance of 10 kpc with a parallax of 0.1 mas. A parallax error of 0.5 mas for a G=19.5 star means its distance is essentially a lower limit. i.e. It is not the photometric limit that defines how complete a sample of solar-type stars with known distances is, it is the parallax uncertainty.

At say G=14.5, the star is at 1 kpc, with a parallax of 1 mas with a 0.03 mas (3%) distance uncertainty.

The sweet spot for a 10% distance error is in between, at about G=16, and at a distance of about 2 kpc.

In the Galactic plane, a solar-type star at 2 kpc would be fainter than G=16 because of extinction, and hence its parallax uncertainty would be bigger. Thus the 2kpc horizon would apply for positions well out of the Galactic plane and will get smaller with decreasing Galactic latitude (on average, because Galactic extinction is patchy).

Note that it isn't possible to conclude that EDR3 is "complete" for solar-type stars out to 2 kpc since the uncertainties in parallax also follow a distribution, they are not homoscedastic. So this is very much a "soft" boundary.

The limit will be closer (larger) for cooler (hotter) main sequence stars because they are fainter (brighter) at the same distance and thus have bigger (smaller) parallax uncertainties.

Answer 2

There is a question on a related topic:

Why aren't new stars in Earth's relative proximity constantly discovered?

I quote from my answer:

The 1991 third Gleise catalog of stars within 25 parsecs (84.64 light years) of the Sun includes 3,803 stars. A sphere with a radius of 25 parsecs has a volume of 65,449.8469 cubic parsecs. So the stars in the catalog have a density of about 0.0581055 stars per cupic parsec.

Wikipedia's List of nearest stars and brown dwarfs lists stars and brown dwarfs within 5 parsecs of the Sun. That list has a volume of 523.598776 cubic parsecs. Omitting 11 brown dwarfs, and including the Sun, there are 65 stars in that radius. So the stars in that list have a density of 0.1241408 stars per cubic parsec.

However, the individual stars in the list are grouped in star sysems containing 1, 2, or 3 stars each. There are 50 star systems in the list, so the star systems have a density of 0.0954946 star systems per cubic parsec.

I am not certain whether the Gleise catalog lists individual stars or star systems. So I don't know if the stellar density of listed stars in the Gleise catalog is 0.4680612 or 0.6084689 the density of stars in the list of nearby stars.

Either way, it indicates that the percentage of stars whose distances have been measured decreeses with distances of just tens of parsecs.

Of course a bunch more stars within 75 parsecs of Earth may have been discovered in the 30 years since the third Gleise catalog in 1991.

Apparently the Gaia observatory studies stars down to apparent magiitude 20. Stars of higher magnitudes are less bright than stars of lower magnitudes. Absolute magnitudes ae defined as equal to the apparent magnitudes that stars would have at a distance of 10 parsecs.

A magnitude difference of 5 magnitudes is equal to a difference of 100 times in brightness. A star which is time times as far away as a star of equal brightness will have only 0.001 the apparent brightness.

A star of absolute magnitude 0 will have an apparent magnitude of 0 at a distance of 10 parsecs, an apparent magnitude of 5 at a distance of 100 parsecs, an apparent magnitude of 10 at a distance of 1,000 parsecs, an apparent magnitude of 15 at adistance of 10,000 parsecs, and an apparent magnitude of 20 at a distance of 100,000 parsecs.

The faintest known star at the moment is 2MASS J0523-1403, 12.7 parsecs or 41.6 light years from Earth, with an absolute magnitude of 20.6 and an apparent magnitude of 21.05. So even if it was only 10 parsecs away it would be too dim to be studied by *Gaia.

Wolf 424 A has an absolute magnitude of 14.97, very close to 15. It is callsed as an M5.5Ve star. At a distance of 10 parsecs it would have an apparent magitude of 14.97, and at a distance of 100 parsecs it would have an apparent magnitude of 19.97.

Groombridge 34 A has an absolute magnitude of 10.32 and is a M1.5V star. It would have an apparent magnitude of 10.32 at a distance of 10 parsecs, 15.32 at a distance of 100 parsecs, and 20.32 at a distance of 1,000 parsecs.

Alpha Centauri A has an absolute magnitude of 4.38. It is a G2V class star. It would have an apparent magnitude of 4.38 at a distance of 10 parsecs, an apparent magnitude of 9.38 at a distance of 100 parsecs, an apparent magnitude of 14.38 at a distance of 1,000 parsecs, and an apparent magnitude of 19.38 at a distance of 10,000 parsecs.

So if someone wants to set a science fiction story in a volume of space where almost all the stars, even dim red dwarfs, are already known and their distances from Earth, and thus their positions relaive to each other, are known with fairly high accuracy, so that an interestalalr voyage could be plotted in three dimensional space and not be proven to be inaccurate soon, they would want to select a volume of space within maybe 100 parsecs of Earth, possibly much closer.

On the other hand, a science fiction writer might want to set a story in a volume of space where they can put stars of any assortment of types they want, and in any random spatial distribution they want, without worrying about the star positions being discovered to be inaccurate any time soon. Suppose they want a volume of space about 10 light years on a side. If they select such a volume far enough from Earth that the errors in stellar position are hundreds of light years, it should be a while before new advances in astrometry enable distance mesaurements accurate enough to tell which stars are within that cupbe of space.