There is no canon information on the real-world astronomical identity of the Nebula System. However, several fans have offered proposals based on hints provided within the game. The two primary candidates are the Crab Nebula and the Lupus Nebula, with slightly stronger support for the former.
The main clue upon which most arguments hinge is the briefing for SM1-05, Mystery of the Trinity, which states, "We have entered a nebula, a vast and dense ionized field, and possibly the remnant of a supernova." This clearly foreshadows the ending of the game in which the player personally witnesses a supernova. More importantly, many fans have taken the foreshadowing as sufficient justification to claim that the Shivans caused the Nebula System supernova in addition to the Capella supernova.
Since the Ancients created the Knossos network, the most likely scenario is that the Shivans caused the parent star to go supernova at around the same time they destroyed the Ancients' empire. Calculating from the "about 8,000 years ago" estimate from the perspective of Vasudan scientists in 2335, this places the date at 5,700 B.C., give or take a few hundred years. This hypothesis is, however, challenged by the fact that a second Knossos is located in the nebula, and the supernova would have literally pulverized it had it occurred after the construction of the device. While several theories may explain how the second Knossos eventually survived such a catastrophe and remained fully functional, the challenge to the clue is valid and is rather complicated to address.
Despite this, providing that we accept the main clue as a foundation, the next clue is Bosch's third monologue, which states, "The nebula is the remnant of a supernova thousands if not billions of light years from Earth; and I wonder now if our ancestors witnessed the death of this star erupting over an Egyptian landscape, blazing with the brilliance of four hundred million suns." This gives an approximate estimate for the distance and apparent magnitude of the supernova.
Based on these clues, GalacticEmperor originally suggested the Lupus Nebula in a forum post in 2003.  The available information on SN 1006 (the Lupus supernova) fits the evidence well, as described in this article. Further research led to the suggestion of SN 1054 (the Crab supernova) as a competing candidate.
SN 1006 was about as bright as five billion suns, while SN 1054 was about as bright as 1.25 billion suns. These figures are within approximately one order of magnitude of Bosch's estimate. Furthermore, taking the speed of light into account, SN 1006 erupted in 6,094 B.C., while SN 1054 erupted in 5,246 B.C. These dates are within only 1,000 years (for SN 1054, 500 years) of the Vasudan estimate. Both estimates are surprisingly accurate.
Perhaps the most intriguing connection was discovered by Arcanum in 2006.  According to Wikipedia,
- Theoretical models of supernova explosions suggest that the star that exploded to produce the Crab Nebula must have had a mass of between 8 and 12 solar masses. Stars with masses lower than 8 solar masses are thought to be too small to produce supernova explosions, and end their lives by producing a planetary nebula instead, while a star heavier than 12 solar masses would have produced a nebula with a different chemical composition to that observed in the Crab.
- A significant problem in studies of the Crab Nebula is that the combined mass of the nebula and the pulsar add up to considerably less than the predicted mass of the progenitor star, and the question of where the "missing mass" is remains unresolved.
This suggests that the supernova may have been "artificially triggered" in the same manner as the Capella supernova.