In a series of papers, Nikku Madhusudhan and collaborators have explored the possibility that some planets form with more carbon than oxygen in their bulk composition (solar system planets have a C/O ratio of about one half). This is a major change: in the atmosphere the dominant hydrogen-bearing molecule becomes methane instead of water, and in the mantle of rocky planets, carbon compounds replace oxides such as silicates (e.g. silicon carbide instead of silicates). See “diamond planets” in the media coverage.
Öberg and collaborators study the effect of the fact that there are actually several “snow lines” in protoplanetary discs, one for water, one for carbon dioxide and one for carbon monoxide. Inside the snow lines, giant planets can presumably not form, because of the scarcity of condensable material. Now, depending on whether a giant planet forms between the water snow line and the CO snow line, or beyond the CO line, the resulting C/O ratio may be different. With a Sun-like star, the snowlines are at 2, 10 and 40 AU. The paper examines this issue qualitatively to the first order.
The results are that, indeed, gas giants formed behind the CO line could have much larger C/O ratios, potentially above unity. If those planets then migrate close to the star, they could then form carbon-rich hot Jupiters, such as WASP-12 b and HD 189733 b.
One issue with the whole topic is that the evidence for carbon-rich hot Jupiter is not so solid at this point. The inference for WASP-12 b, resulting from the broadband shape of the emission spectrum measured with Spitzer (Madhusudhan et al. 2010), has recently been brought into doubt by new Spitzer observations at the “Extreme Solar Systems II” meeting this September. The evidence for HD 189733b is even shakier (Gibson et al. 2011). Nevertheless the possibility of carbon-rich planets seems well worth exploring as a possibility, even in the absence of confirmed examples at present.