Actually, Stein 2051B is a white dwarf of class 'DA' which is the most common type. The primary star, Stein 2051A is an M4 dwarf star located 17 light years away; it also goes by the name Gleise 169.1A. So far as I know, Stein 2051A is not a carbon star; it's just an ordinary star with typical solar element composition. The term 'Carbon Star' is usually reserved for certain cool giant or supergiant stars that are cool enough that compounds of carbon are abundant in their atmospheres. Generally, if the outer layers have been enriched with carbon by convection from the deep core where advanced stages of nuclear burning have taken place, the surface layers will have abundant molecules of compounds in carbon such as carbon monoxide ... CO and carbon sulfide...CS. These can be detected spectroscopically. Other old stars in which oxygen is abundant are rich in compounds such as silicon monoxide....SiO and titanium oxide... TiO.