Varunie Vongsvirates has given birth to a baby girl, a source tells PEOPLE

Is Owen Wilson now a father of three?

A source tells PEOPLE that Varunie Vongsvirates welcomed daughter Lyla Aranya Wilson on Tuesday, Oct. 9, and that the little girl — who weighed 6 lbs., 13 oz., and measured 21 inches — is Wilson’s. Vongsvirates gave Lyla her middle name, a Thai moniker, to honor her father’s heritage.

“My sweet little princess 💝 Lyla Aranya Wilson, born on 10-09-18,” Vongsvirates captioned her baby girl’s first photo that she shared to Instagram on Sunday.

The source previously told PEOPLE Wilson was “excited” about the baby — though his rep has not commented.

A Wilson source previously told PEOPLE that “if a paternity test establishes that [Wilson] is the father of another child, he will fulfill all of his obligations to support his child.”

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Premiere Of Disney And Pixar's "Cars 3" - Arrivals
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Owen Wilson

Vongsvirates revealed her pregnancy on Instagram in June, sharing a photograph of their little girl’s ultrasound with the caption, “Say hello to Lyla 👶 3 months to go! 😍”

The new mom gave her Instagram followers tiny glimpses into her pregnancy journey after announcing her bundle of joy on the way, including a peek at her August baby shower venue and a throwback photo from Maui, Hawaii, when she found out she was pregnant.

Alongside a July photograph of herself and friends doing yoga in a park, where she cradled her baby bump, the mom-to-be wrote, “Girl power 💪 #31weekspregnant.”

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Her latest post before the baby photo, from Aug. 7, is a group shot of herself and Wilson, 49, celebrating the premiere of his movie Father Figures in December 2017. She captioned it simply, “#fatherfigure #tb.”

When one follower asked in the latter photo’s comments, “Owen Wilson is papa?” Vongsvirates replied, “Yes” with a kissing-face emoji.

*EXCLUSIVE* Owen Wilson spotted out biking with a friend around Venice Beach
Credit: Backgrid

Owen Wilson

Notoriously private when it comes to his personal life, the actor stopped by The Ellen DeGeneres Show in June 2017 to dish about his work on Cars 3, his famous family as well as how his two boys — Finn, now 4½, and Robert Ford, now 7½ — were developing, personality wise.

“Ford seems like he might even be a little stunt man in training,” said Wilson of his “fearless” older child, sharing a video of the little guy doing a belly flop into a pool off of a diving board.

“He’s a big Jackie Chan fan,” added Wilson, who shares Finn with Caroline Lindqvist and Ford with ex-girlfriend Jade Duel.