Celtic "a"

The Celtic languages are intriguing and full of a lot of complicated history.  One simple mystery to me about the Celtic languages, however, is the origin of their short /a/.  If IE did not have /a/, and the laryngeals were not common in main syllables between consonants, what then is the origin of Celtic /a/, which on the surface seems to be quite common in Welsh and Irish?  One item that piqued my interest in reading Cowgill's (I believe it is he) Welsh Grammar was his positing of schwa secundum, the reduced vowel, to explain some noun such as hadl or similar meaning "seat" or similar, from the *sed- root.  What is the explanation of this noun (I don't remember its exact form but I know for sure it had a and was from the *sed- root), i.e. its /a/ vowel?  Could there actually have been some sort of reduced vowel, a schwa secundum?  Or is it perhaps a development of unstressed *e or *o, or some other conditioned change?  As well, are there any scholarly works which explain the origin of /a/ in Celtic?

 

Andrew