Ethan Hawke (inset) and his wife Ryan with their newborn daughter, Indiana, in New York on Aug. 7
Wagner Az/Pacific Coast News (2)
08/07/2011 at 10:10 PM EDT
Ethan Hawke, who has called fatherhood "the greatest pleasure in my life," and his wife, Ryan Hawke, welcomed their second child together two weeks ago, a girl named Indiana, PEOPLE has confirmed.
She's the fourth child for Hawke, who also has two kids with ex-wife Uma Thurman. News of this pregnancy was first reported
On Friday, the family had lunch at La Bottega in the Maritime Hotel, in Manhattan. "He was very happy," an onlooker tells PEOPLE. "Seemed like a proud daddy."
Ethan, 40, and Ryan married in June 2008
. Their daughter
, Clementine Jane, is now 3.
Hawke's children with Thurman are Maya, 13, and Levon, 9.
In 2006, Ethan Hawke said parenting has brought him the greatest joy
and was "the only role that, if I fail, I will consider my life a failure."