Some details about the APOD of 2010 December 7

This picture is a computer generated image of the distortions caused by a spherically symmetric, uncharged (Schwarzschild) black hole. (Note: all the images of this page are under CC-BY-SA 3.0 licence. In case you intend yo reuse them, please credit my name and institution, i.e., Alain Riazuelo, IAP/UPMC/CNRS.)

Click on the image to see full resolution picture

This is to be compared with the picture without black hole:

Click on the image to see full resolution picture

This picture is familiar to many amateur or professional astronomers. It is almost centered of the Large Magellanic Cloud. Above it one easily notices the southernmost part of the Milky Way with, from left to right, Alpha and Beta Centauri, the Southern Cross, and then the huge Argo Navis, now splitted into three constellations (from left to right, Carina, Vela and Puppis). At the right of the picture, the brightest spot is Sirius, from Canis Major. The second brightest star, close to the LMC is Canopus. The brightest star of the lower part of the picture is Achernar, at the edge of Eridanus.

If one zooms at the exact center of this picture, one sees an anonymous, undocumented 7.5 magnitude star, which happens to be HD 49359 (or HIP 32073, or SAO 249630):

When one puts a black hole (almost) exactly between a star and the observer, then the star apparent luminosity enormously increases and the star itself seems to split into two separate images which are found at two opposite points of a circle surrounding the balck hole shadow. This circle shows fewer but brighter stars than the rest of the image is called the Einstein ring. This ring shows a highly distorted and magnified view of what is exactly behind the black hole:

Approximate position of the Einstein ring. The faint star HD 49359 appears as a set of two very bright stars on two opposite points of the ring.

In fact, the celestial sphere we saw in the absence of the black hole is pushed away the Einstein ring. Between
the Einstein ring and the edge of the black hole shadow, one has a copy of the whole celestial sphere. It is actually possible to connect any star seen within the Einstein ring to its primary image outside the ring. The segment that joins these two images always intersect the geometrical center of the black hole, and the closer is the primary image to the Einstein ring, the closer is its secondary image. The picture below shows some associations of two star images:

Some primary/secondary image association of bright astronomical objects. Cyan rings show the two images of the Small Magellanic Cloud. Magenta rings shows the two images of Alpha and Beta Centauri. The yellow rings show the two images of Gamma Crucis (the redder, uppermost star of the Southern Cross). The two images of Canopus are shown within the white rings. Primary image of Sirius is nolonger visible as it is now pushed beyond the right edge of the picture, but Sirius secondary image is visible at the left of the black hole.

Actually, the region within the Einstein ring does not show a single copy of the celestial sphere, but an infinity of such copies. However, all of these except the first one are shrunk to a very  thin line very close to the edge of the black hole shadow. When looking carefully, it is possibly to have a hint of their existence. In this picture, it becomes obvious from the fact that one sees two faint spots which are perfectly aligned with the two very bright images of HD 49359. They are indeed the second and third ghost image of this star:

In the last images, we also see the first ghost image of the Milky Way, together with the Southern Cross ghost image. The faint glow that is a few pixels away the ghost image of HD 49359 is in fact the second ghost image of the Milky Way. Also, the even more faint glow that seems to touch the black hole shadow is a third, now completely unrecognizable, ghost image of the Milky Way. Should one zoom this image by a tremendous factor, we would see other ghost images of the Milky Way.

A few technicalities

For those who might be interested in technical details:
  • The image was done using a starless background image, coming from the 2MASS survey.
  • A realistic star catalogue (the Henry Draper Catalogue)  was added once the distortion of the image was computed.
  • This means that we have implicitely replaced our Sun by a black hole, even though it is somehow astrophysically inconsistent.
  • The black hole size or mass does not matter here. What matter is the ratio between the observer distance of the black hole and the black hole radius. Using the incorrect but common claim that distance are accurately expressed in term of the usual Schwarzschild coordinate, this ratio is here equal to 9, i.e., we are at R = 20 M in the usual Schwarschild coordinate system.
  • Image opening angle is fairly large: 116 degrees. It was produced on a flat screen using stereographic projection.
  • Because of tidal effects, physiological constraints impose that the black hole must be fairly massive in order an observer so close to a black hole does not quickly become ripped apart by the black hole enormous gravitational field. Putting such a massive black hole in the visinity of our Solar System is, again, not 100% realistic.
  • The 2560×2048 image was initially computed at a twice larger resolution (5k×4k) and then shrunk to its current size so a to allow smoother details.