The next obstacle was, trying to figure out exactly what a White Dwarf would look like. I found plenty of references to electron degeneracy, the Chandrasekhar Limit, the types of white dwarfs (DA, DB, DO), their diameter, hydrogen or helium surfaces, even surface convection. What I didn't find was a detailed description of what one might look like up close.
I did find a number of artistic illustrations depicting White Dwarfs. One of the curiosities I noticed was that, in all of the more detailed pictures I came across, the White Dwarf was depicted as having a mottled surface.
For Example:
http://www.rkm.com.au/ASTRONOMY/White-Dwarf.html
http://hubblesite.org/newscenter/newsdesk/archive/releases/2002/10/video/b
http://www2.warwick.ac.uk/fac/sci/physics/research/astro/postgraduate/whitedwarfs/
http://starryskies.com/articles/2004/02/diamond.html
http://www.virtualsciencefair.org/2002/wongj/public_html/whitedwarfs.html
The problem (again) with these images was that, I couldn't find any references explaining the mottled surfaces being depicted. Was it due to the fast moving degenerate electrons coupled with the high temperatures and gravitational fields? I couldn't find an explanation! So, I just went with the flow (so to speak). And here's what I came up with:

And an alternate side view:

I use it in my copy of Celestia in order to depict Sirius-B. Once I finished, I figured I would continue and do an A-Star texture for Sirius-A. This is how it looks thus far:

And a granulation close-up:

I haven't added any Star Spots (Sunspots) since my research is still inconclusive as to whether an A-Star (like Sirius-A) would actually have them. As far as adding the textures to these stars in Celestia, it was easily done by adding a texture parameter under each respective star inside the nearstars.stc file located in the Celestia/Data folder.