# Population density of stars within $13$ light-years of us

This item from Fox News refers to "over 600 stars that came within 13 light-years of the sun". Because of the past-tense "came", they could have meant stars that are not now within 13 light-years of us but were at some time in the past. But that is not made explicit in the article.

It is said that the nearest neighboring star is $$4.3$$ light-years from us. And $$13$$ light-years is about $$3$$ times that. So the volume within that distance of use is about $$3^3=27$$ times the volume within $$4.3$$ light-years of us. If there are $$600$$ stars within that larger volume, then the average number of stars within that smaller volume should be $$600/27 \approx 22.$$ But we don't have anywhere near $$22$$ stars within $$4.3$$ light-years of us.

So are we in a neighborhood that is unusually sparsely populated compared with what is typical in that larger volume?

Or is this about stars formerly near us that aren't now?

Or just confused journalists?

The criteria for sample selection are admittedly not made overly clear in the preprint itself (Wysoczańska et al.). It appears that the authors started with a list based on stars that were previously believed to have come close to the Sun at some point in the past or future. That list was then augmented based on data from Gaia's second data release, to get a total of 820 objects, and the motions of those stars were then integrated backwards and forwards in time from the present, based on a model of the galaxy's gravitational field.

Here's where that "over 600 stars" came from. The authors ended their integration for a given star when either (i) the star went more than 3 kpc from the Sun or (ii) the time reached 50 million years in the past or the future. With those cutoffs in place, the astronomers found that during that timespan (50 million years before or after the present), 647 stars were within 4 parsecs of the Sun at some point in time. That's the figure Fox is referring to.

The density of stars in the solar neighbourhood is about 0.003 stars per cubic light year. Therefore at any one time you might expect only around 30 to be within 13 light years of the Sun.

However, stars are moving with respect to each other. These relative motions are of order 10-100 km/s, which translates to about 30-300 light years/million years.

Therefore what we see now is very much a snapshot. Wind the clock forwards or backwards by even 100,000 years, and a completely different set of stars are in our vicinity.

The very precise motions measured by the Gaia astrometry satellite allow you to play that game on a computer. The authors of your paper have done that and identified more than 600 stars that they confidently claim came within 13 light years of the Sun (or will do so in the future).

This is not a complete list. The game can only be played over a limited timescale because uncertainties in velocity become uncertainties in position that grow linearly with time.

Our next close encounter (that we know about) is with Gliese 710, which will approach within 20,000 au in about 1.3 million years time (Bailer Jones et al. 2018).

As to the science in this paper, I am sceptical. The authors look for associations between close approaches of these stars and the integrated orbits of comets back in time. They claim 2 associations out of a proximity search based on these 600 or so stars (although what relevance stars that will make future close approaches is, I don't follow) and 277 comets. These 2 stars came within a thousand au of the relevant comets (though this number is highly uncertain for one of the examples) and would then have perturbed their orbits. It would have been good to see an analysis where they gave all the comets a random phase shift in their orbits to see how many "close approaches" you would expect by chance.

• The very precise motions measured by the Gaia astrometry satellite? Many of the distance measurements have negative parallaxes or error margins that are multiples of the parallax itself. I don't think they'd be that good at measuring proper motion, but maybe I'm missing something? – user21 Dec 7 '19 at 16:38
• @barrycarter yes, you are. The authors only used stars where the astrometry was good and their sample of 600 cannot be considered complete. Secondly you have an odd idea about the reliability of Gaia DR2. There are some faint stars that have a negative parallax and also some very distant stars that (of course) have a negative parallax. The Gaia DR2 data release papers are publicly available for you to read. – Rob Jeffries Dec 7 '19 at 18:17
• Typical levels of uncertainty have a systematic floor level (for stars brighter than about 16th magnitude) of about 0.1 milli-arcsec in parallax and 0.1 mas/yr in proper motion. So star at 10pc has its distance known to 0.1% and a tangential velocity known to 5 m/s (not a typo). The main limitation is precise radial velocities. @BarryCarter – Rob Jeffries Dec 7 '19 at 18:36
• I have worked with the GAIA2 data, and, in general, it's fairly inaccurate in terms of parallax (see github.com/barrycarter/bcapps/tree/master/STACK/bc-gaia.txt for my results + methodology). However, for a specific set of 600 stars, I'm guessing those values might be sufficiently accurate, I'm not sure what you mean by very distant stars that (of course) have a negative parallax-- no stars should have negative parallax (except for errors and proper motion), unless, again, I am missing something. – user21 Dec 8 '19 at 22:08
• @berrycarter distant stars have zero Parallax, and uncertainties, and therefore half should have a negative Parallax. – Rob Jeffries Dec 8 '19 at 22:57