Since there is little to no canonical information about the Vulcan system, other than "Vulcan has no moon" from the TOS Episode, The Man Trap, there is room for speculation.
Stuff we can figure about Vulcan
It can be implied that Vulcan is higher gravity than Earth; in the extended universe, it's routinely listed as 1.4 G's. (As exemplified in Decipher's Worlds for the Star Trek Roleplaying Game.) Likewise, it's extensively assumed in the extended universe that it is indeed orbiting 40 Eridani. (0.86 solar masses, 0.46 sols luminosity.) It needs to be slightly brighter apparent luminosity, call it 1.05. So it needs to appear about 2.3x the brightness of Sol... and that means we need to figure it's about 0.23 AU orbit.
Vulcan is thus about 2.7 earth masses.
The gravity looks Earthlike. So, let's assume it's a fairly earthlike body.
It's cool - I'll examine that later. It's got a lot of water.
There are several possibilities as to what Delta Vega could be.
- Double Planet
- LaGrange Point co-orbital body
- "horseshoe orbit" co-orbital body
- eccentric orbit.
- Vulcan's parent Planet. ("Vulcan has no moon, it is a moon!")
So, let's first see if it's plausible that it is a planet.
For our purposes, it needs to orbit no closer than the sum of the hill spheres.
Assuming similar density, that puts it at about 18,000 km diameter.
Given the appearance on screen, it appears to be about 4x the size of our moon. Our moon is about 1736 km diameter; for simplicity, I'll use 1700. (Earth is about 12742 km.) the moon is roughly 1/7th earth's diameter, or about 1/10 the diameter of Vulcan. So, were it at lunar distance, it should appear about 10x the size of the moon; this implies it's 4x further, or about 1.2 million KM. Normally, this would be a problem...
Simplified greatly, a hill sphere is the radius at which a body captures other bodies in its region.
For reference, Earth's Hill Sphere is about 1.471 million km. Hence the problem. Anything within that radius should end up orbiting Earth, and nothing should orbit within 2x that, because it would be unstable.
Vulcan's Hill Sphere, however, isn't nearly so big; 0.499 million km based upon the above assumptions.
Placing Delta Vega
Assuming the same excentricity as Earth for both worlds, we know that it has to have a perehelion no further than Vulcan's Perehelion plus about 1.2 million km.
But it really doesn't need to be even that far. Because of their relative proximity to the star, their hill spheres are pretty small. Vulcan's is 499,000 km and Delta Vega's around 369,000 km. So... a close approach of 1.2 million km is probably a safe orbit, especially if, at that point, Vulcan is approaching apohelion and Delta Vega is approaching perihelion.
So, using 3.49E+07 km for Vulcan's semi-major, and 3.610E+07 km for Delta Vega's, we get about 0.95 (40 Eridani)s Luminosity from Vulcan. This should be plenty warm for liquid water. Increasing the eccentricity and semi-major axis of Delta Vega would potentially explain the glaciation better.
Bottom Line: Delta Vega could be another body orbiting 40 Eridani from Vulcan.