Allophone of /ʌ, ʌː/ (which phonetically are central [ɜ, ɜː]) before and after /ŋ, kʰ, k, χ, ʁ/. Exact backness varies; it is most posterior before /χ, ʁ/.
In traditional dialect transcriptions, this vowel is written consequently as ⟨ä⟩, and has existed as a separate vowel in addition to ⟨æ⟩, [æ]. This is because ⟨ä⟩ has evolved from an unrounding of short ⟨o⟩. ⟨ä⟩ has morphed to [æ] with younger speakers.
Before World War II, the /ʌ/ of Received Pronunciation was phonetically close to a back vowel [ʌ], which has since shifted forward towards [ɐ] (a near-open central unrounded vowel). Daniel Jones reported his speech (southern British) as having an advanced back vowel [ʌ̟] between his central /ə/ and back /ɔ/; however, he also reported that other southern speakers had a lower and even more advanced vowel that approached cardinal [a]. In American English varieties, such as in the West, the Midwest, and the urban South, the typical phonetic realization of the phoneme /ʌ/ is an open-mid central [ɜ]. Truly backed variants of /ʌ/ that are phonetically [ʌ] can occur in Inland Northern American English, Newfoundland English, Philadelphia English, some of African-American English, and (old-fashioned) white Southern American English in coastal plain and Piedmont areas. However, the letter ⟨ʌ⟩ is still commonly used to indicate this phoneme, even in the more common varieties with central variants [ɐ] or [ɜ]. That may be because of both tradition and some other dialects retaining the older pronunciation.