There are lots of different ways to hold the state of the circuit. In general though, the technique is called "latching." Wikipedia has a decent article on digital logic latches:
http://en.wikipedia.org/wiki/Latch_(electronics)
One easy way is to do it with relays, as described in this thread:
https://www.physicsforums.com/showthread.php?t=123692
Here's a page on how to do it with pictures:
http://www.eleinmec.com/article.asp?24 (scroll down till you get to the part on Latching Relays)
The term "Latching Relay" can either mean the technique described in the post, or a special kind of relay that holds state mechanically even with the power off (you don't want that one). See Wikipedia's relay page if you're interested though.
If you want to do it with solid-state digital logic latches, see second half of this PDF:
http://www.discovercircuits.com/PDF-FILES/4013oneshots.PDF
It doesn't do exactly what you want (i.e. if it gets bright, then dark, then bright again, the buzzer will go off (and you'll have to reverse the polarity on the inputs to your op amp comparator), but it's a good starting point.
Here's something more like what you want, though, using a 555 timer:
http://www.eleinmec.com/article.asp?5
Leave the reset button out of the circuit, and replace the trigger button and the 10k resistor above it with the output of the op amp (i.e. hook up the op amp's output to pin 2, and don't include the pullup resistor or the switch). That ought to do what you want, you can leave your current circuit pretty much the same, but you might need to unity-gain buffer the output of the 555 if you don't get enough current (I haven't looked at a 555 datasheet as of late so I don't know what kind of current sourcing you can expect). It's good practice anyway.
Hope this helps.