US Open champion Jon Rahm warned his rivals he still has room for improvement after setting the clubhouse target on day two of the abrdn Scottish Open.

Rahm shrugged off a bizarre incident on his opening hole at the Renaissance Club, when a spectator nonchalantly walked on to the 10th tee and took a club out of playing partner Rory McIlroy's bag, to race to the turn in just 29 shots.

And although the 26-year-old could only cover the front nine in level par, a second round of 65 gave him a halfway total of 11 under par and a one-shot lead over South Africa's George Coetzee, who carded a second successive 66.

"Those first 10 holes I played incredible," Rahm said. "I was seven under through 10 and the three pars I had were short putts that could have been made. They were clearly birdie chances. That's not always going to happen.

"There were moments of luck too. If my second shot on 16 went two yards further than it did I would have had no shot to the pin. There were a couple of others like that. It was good golf combined with good luck.

"After that the elements changed and I was playing some holes in a wind I had never played before. I got a little hesitant.

"I made some aggressive swings without thinking about it as much as I could have because I was playing so well and maybe could have taken a step back. Swing-wise it's good. If I just clean up some little mistakes it could be better."

World number three Justin Thomas and England's Ian Poulter were three shots off the pace on eight under, with American Scottie Scheffler another stroke back after a brilliant 63.

In contrast, McIlroy was set to miss the cut after adding a 71 to his opening 70 to finish one under par.

The 32-year-old was seventh in the US Open last month but laboured to a tie for 59th in the Irish Open last week and on current form faces an uphill battle to end his winless streak in majors in the Open Championship at Royal St George's.