I wonder what action did Tenryuu received that scar?
For I know there are two actions.
August 9, 1942: when she was hit by a torpedo from USS Chicago (Tenryuu also caused damage to Chicago). October 2, 1942: when she was hit by a bomb from a B-17.
Oh... this is something interesting about Tenryuu...
3 June 1942: Dry-docked in No. 3 drydock. Two Type 96 25-mm twin mounts are added abaft the after stack. External degaussing coil is fitted. Foremast is reduced in height. Sperry type searchlight from atop the forward bridge is relocated to a new position between the two forward funnels. Sperry type searchlight on aft superstructure is replaced by Type 96 90-cm searchlight. Additional armor is fitted to protect the torpedo warheads.
So the searchlight was somehow replaced and was relocated.
It's kinda starting to annoy me not being able to find a reference to Tenryuu's searchlight damage (Yes, I know, I get obsessed by the dumbest things). Since there are so many images here that mention it, it must've been something that happened. The only thing I've been able to find is this mention of her possibly taking a shell from the Chicago while illuminating Patterson at Guadalcanal.
I suppose it can be chocked up to lack of interest in the tiny details of the Japanese fleet by the English speaking side. Perhaps there are more robust Japanese sources on it.
In the Japanese Wiki at least, it's in battle of Savo Island, when they ganged up on Patterson
Still seems like it only results in recounts of the American side of things that don't really mention hits scored on Japanese ships. Looks like it'd take much more searching than it's worth to cite.