When a chart of mine has a hole in it, my first suspect is always the pipeline. A filter that dropped rows or a batch that never arrived. Gaia DR3 came out in June with positions for 1.8 billion sources. If you count them per square degree, the map has black spots all along the Milky Way. I know the textbook answer. These are clouds of dust in front of the stars. But I had never seen it in numbers and I did not know that the same catalog can tell how far away the dust is. I wanted to check both with the public archive only.
All of it is ADQL queries to the ESA Gaia archive and about 230 lines of Python with numpy and scipy. The archive also has the 2MASS point source catalog.
One small cloud
Barnard 68 is a dark cloud in Ophiuchus, a few arcminutes across. I took all Gaia stars within 15 arcminutes of its center and counted them in rings. Between 6 and 15 arcminutes there are 223 stars per square arcminute. At that density the central half arcminute should have 175 stars. It has 0. Within 1 arcminute there are 9 out of 700 expected, which is 1.3%. All 9 are fainter than G = 19.
A real gap between the stars would look the same in Gaia. Color separates them. Dust absorbs blue light much more than infrared, so a survey in the near infrared should see through it better. 2MASS works at 1.2 to 2.2 microns. In the same central half arcminute it has 7 stars out of 17 expected, which is 41%. Within 1 arcminute it has 33 out of 68.
The stars 2MASS still sees are also red. The H−Ks color in the center has median 0.91 against 0.21 in the field around. With the extinction law of Rieke and Lebofsky from 1985 this is about 11 magnitudes in V. A star behind the cloud is about 25,000 times fainter in visible light. The reddest star gives about 26 magnitudes. These are only the stars that made it through, the middle is darker and 2MASS does not see through it. Alves and colleagues mapped this cloud properly in 2001 with much deeper infrared images.
Where is it
My plan was to take the stars around Barnard 68 with good parallaxes and find the nearest reddened one. It did not work. Within 1.2 arcminutes Gaia has 23 stars and 13 of them have a parallax. The stars I need are the ones in front of the cloud. None of the 13 can be shown to be closer than 1 kpc. With a strict cut I should expect only 0.18 foreground stars within 1.5 arcminutes, so for a cloud this small the plan was wrong from the start.
So I zoomed out. Barnard 68 is one of the small dark cores at the edge of a much bigger cloud, the Pipe nebula. I counted all Gaia stars in a box of 9 by 8 degrees around it, 47 million stars in 7200 cells of 0.1 degree. A cell is dark if it has less than 40% of the median of the 2 by 2 degree square around it. It is clear if it has more than 90%. That gave 5108 clear cells and 145 dark ones, the biggest groups of them on Barnard 59 and on the wide part of the Pipe. Then I compared dark and clear cells by distance. I kept stars with a parallax above 1.5 mas and an error below 10%, so closer than about 670 pc.
The first result was nonsense. Closer than 100 pc the clear cells had 130 stars per square degree and the dark ones 9, which is 14 times fewer. Dust cannot hide a star that is in front of it. And 130 is too many anyway. The whole sky has about 8 stars per square degree closer than 100 pc. I spent some time on the cell selection before I looked at the stars. The box had 7526 “stars closer than 100 pc”. 6678 of them were fainter than G = 19 and 4513 had a bad astrometric fit (RUWE above 1.4). The field toward the Galactic center is very crowded, faint stars there get wrong parallaxes and the dense clear cells have more of them. I removed stars fainter than 19 and with RUWE above 1.4. The missing quality cut was mine.
With the cut, every distance bin up to 200 pc has 0.77 to 1.09 times the density of the clear cells. The dark cells have only 61 stars there, so it is noisy. Beyond 200 pc it is 0.56 to 0.70. The counts say the dust is somewhere in front of 200 pc and not much more.
The step
Gaia also estimates the extinction A_G for most stars brighter than G = 19. The GSP-Phot pipeline gets it from the low resolution BP/RP spectrum together with the parallax. I don’t trust the absolute values much. In front of the cloud they are around 0.5 magnitudes, which looks too high for stars at 100 pc. But the change is clear. In dark cells the median A_G is between 0.44 and 0.65 in every bin closer than 160 pc, with 4 to 9 stars per bin. Further than 160 pc it is between 1.62 and 2.28. In clear cells it grows slowly, from about 0.5 to 0.7 between 100 and 300 pc.
I fitted one step to 220 stars of the dark cells between 80 and 400 pc. It lands at 157 pc, between 2 stars at 156.9 and 158.4 pc. A_G goes from 0.52 to 1.95. In 2000 bootstrap resamples 95% of the steps are between 149 and 185 pc. On the clear cells the same fit finds no real step, the best one is 0.58 to 0.78 at 255 pc.
Lombardi and colleagues in 2006 got about 130 pc for the Pipe from Hipparcos and Tycho parallaxes, with a wide error. Alves and Franco in 2007 got 145 ± 16 pc. Dzib and others in 2018 measured the young stars inside Barnard 59 with Gaia DR2 and got 163 ± 5 pc. The closest to my method is Zucker and others in 2020, Gaia DR2 parallaxes plus photometry. They got 180 pc for the same part of the Pipe. So my 157 is near Dzib and 23 pc short of Zucker, though 180 is still inside my interval. None of this is new. Counting stars against a dark cloud goes back to Max Wolf in 1923 and the distances above are better work than mine. But I did not expect a few archive queries and a step fit to land in the same range.
What I did not check
The dark cells are chosen by Gaia star counts, not by an independent dust map. Stars in front of the cloud are a small share of all stars, so they should not move the selection much. But it is an assumption. A_G from GSP-Phot is a model estimate with its own systematics and I use it only as a relative measure. Before 157 pc the dark cells have only 19 stars with A_G, so the “before” level stands on very few points. I did not fit separate parts of the Pipe. For Barnard 68 I have no distance at all, only the proof that it is dust. And the 2MASS extinction for its center is a lower bound, because no stars are detected in its darkest part.