Ardha Chandra is the sixth mudra of the 28 Single Hand Mudras (Asamyutta Hasta) as described in the Abhinaya Darpana.
From Pataaka, extand your thumb out away from your palm.
It is used to denote the following:-
It denotes the eight phase of the wanning fortnight of the moon. (Half Moon)
A hand seizing the throat
Consecrating and bathing an image
Source or beginning
Touching of ones limbs
Accosting ordinary people