Help finding a sci-fi book with a small space ship

Question

It's a book I read probably sometime between 2003-2007 but it may have been published much earlier, I have a vague feeling it was from the 1990s. I'm in the UK.

Stuff that I remember (sorry it's so vague!):

• I think the cover was dark blue with stars on. It's quite a long book. It's sort of a mystery.
• It's set on a non-Earth colony world and FTL travel is fairly commonplace
• There's a female protagonist
• One of the other characters has (I think) a business which does space exploration
• On his desk he has model space ships, but one of them is an actual alien spaceship with small dead aliens inside
• There are stories about ghosts haunting something, I think it's underwater or on a beach.
• The ghost turns out to be an alien AI which was supposed to protect the little craft but has escaped somehow.
• They went on an exploration mission in the past which went badly and that's how they came back with the tiny ship
• The stars Alnitak and Alnilam are involved - I think that's where they picked it up
• The protagonist steals(?) a spaceship and goes back to where the others originally found the ship to solve the mystery.

I tried searching around for Alnitak and Alnilam but because they're just real star names I haven't had much luck.

Answer 1

I think this is Infinity Beach by Jack McDevitt.

We are alone, because centuries of SETI (Search for Extra-Terrestrial Intelligence) missions found nothing. Until Dr Kimberly Brandywine seeks her clone-sister and the last lost expedition from the Nine Worlds settled from Earth. The ship's log was faked. She loses her career and her lover, steals a starship, and learns too much truth.

The protagonist is Kim Brandywine. The model that turns out to be a real alien starship is called The Valiant (that's the name given by the person who has the model - we never learn what the aliens called it).

I have to confess I don't remember much about the book. It does feature the stars Alnitak and Alnilam. The model originally came from a secret voyage to Alnitak, though it takes a while for Kim to discover this as the ships logs have been altered to conceal the details of that mission. The ship was called The Hunter, and mission was captained by Kile Tripley, but shortly after the return the crew, including Tripley, vanished in a mysterious explosion. At the time of the story the model is owned by Tripley's son.