I am a postdoc in the physical sciences. I have recently decided to start applying for some faculty positions. One open position in particular was recently brought to my attention, and I want to apply for it.
If I compare myself to other people I know in my field who are getting offered faculty positions, I'm a little bit on the young/inexperienced side but I do have a comparable publication record, so I would estimate my chances of landing this job are very low, but nonzero.
I discussed this with my former PhD supervisor when asking him for a reference, and he encouraged me to apply and advised me to send an informal enquiry to the head of department before preparing my application. I have seen similar advice elsewhere. My problem is that I don't really understand what kind of thing I should write in such an informal enquiry. Should I directly ask "would you like to me apply for this job"? Is it like a cover letter?
What is the style and content of a "good" informal enquiry for a faculty position?