Father of Orion Black, grandfather of Sirius and Regulus Black. (BFT)
It is unclear if this is the Grandfather who was awarded the Order of Merlin, First Class for "Services to the Ministry" (OP6). This grandfather could also have been his mother's father, Pollux.One of them gave the Ministry a "load of gold" according to Sirius.
Ancestry: mostly pure-blood; descendants of mixed blood are not recognized by the family.
Family in general: "The Noble and Most Ancient House of Black" (OP6); Sirius' parents were convinced that to be a 'Black' made you "practically royal."
Family crest is mentioned in OP6 but not described; however, Rowling drew it on her Black Family Tree. It shows a shield with greyhounds rampant charged with a chevron, 2 five-pointed stars and a short sword. In the formal language of heraldry, it is: "Sable, a chevron between two mullets in chief and a sword in base, argent." (Thanks to Richard for the terminology).
Family motto: Toujours pur ("always pure" in French) (from tapestry in OP6 and BFT).
Tapestry: a tapestry exists at number twelve Grimmauld Place that has, according to Kreacher, been in the family for seven centuries (OP6). On it the family's births, marriages and deaths are embroidered with gold thread; family members who have been disowned have been "blasted" from the fabric (a small burn like a cigarette burn is where their name is).
Important sources of information on the Black family: OP4 where we meet the portrait of Sirius' mother; OP6 where Sirius explains the Black family tapestry to Harry, and the Black Family Tree, a hand-drawn tree that Rowling donated to Book Aid International in January of 2006. We believe that this tree is meant to represent a portion of the tapestry.
Possible name derivation: Arcturus is the brightest star in the constellation Boötes the Herdsman, and the fourth brightest star in the sky: only Sirius, Canopus and Alpha Centauri outshine it. Loosely translated from Greek as "Guardian of the bear."