The scales of Ahir Bhairav (also called Ahir Bhairavi in Carnatic music) as used in Carnatic music are as follows :
Aarohanam (Ascending) : S R1 G3 M1 P N2 D2 M1 P D2 S
Avarohanam (Descending) : S N2 D2 P M1 P G3 R1 S
In the Hindustani system, the scale is :
Aarohan : S r G m P G m D n S’
Avarohan : S’ n D P m G r S
It is considered a combination of Bhairav and Kafi.
This is basically a Hindustani Raga but in the Carnatic system can be seen as a Janya raga, derived from Chakravaham (below), 16th on the Melakarta Scale. Though it has exactly the same scale as Chakravaham, it is quite unmistakable due to the emphasis placed on different notes.
In the Hindustani system, it is considered to be a morning Raga. Its moods are varied and include devotion, love, separation, longing and dejection. In Carnatic music, some well-known compositions are Pibare Ramarasam, Sadasiva Brahmendra’s song set to music by Balamuralikrishna and Ethanai Koti Inbam by Subrahmanya Bharati. However, my reference for raga recognition is the Hindi film song ‘Poocho Na Kaise’ by Manna Dey from the film Meri Surat Teri Ankhen and the Hindustani bandish ‘Albela Saajan Ayo Re’ (used in the film Hum Dil De Chuke Sanam) and is sung par-excellence by Rashid Khan. If you have the time, do listen to this; it is simply wonderful music.
Note : The 12 notes in the octave are named as below. Please note that C is used as Sa for the sake of simplicity as the scale is relative in Carnatic Music. Also note that the scales paint only a superficial picture of the raga as the gamakas(ornamentations) are a very important part of a raga.