This bit is known as the warm sector. Before the depression begins to form the air flows of the tropical air and polar air, which are separated by the polar front, are parallel to each other but in opposite directions. The warm sector is sometimes called the depression's own "captured portion of the polar front" and the isobars which represent the air flows remain straight and parallel.
There are several books which describe this, and the one I use is Ray Sanderson's Meteorology at Sea and you will see from his excellent description with diagrams of the formation of a depression what I have just tried to describe.