  We study open topological gravity in two dimensions, or, the intersection
theory on the moduli space of open Riemann surfaces initiated by Pandharipande,
Solomon and Tessler. The open free energy, the generating function for the open
intersection numbers, obeys the open KdV equations and Buryak's differential
equation and is related by a formal Fourier transformation to the
Baker-Akhiezer wave function of the KdV hierarchy. Using these properties we
study the genus expansion of the free energy in detail. We construct explicitly
the genus zero part of the free energy. We then formulate a method of computing
higher genus corrections by solving Buryak's equation and obtain them up to
high order. This method is much more efficient than our previous approach based
on the saddle point calculation. Along the way we show that the higher genus
corrections are polynomials in variables that are expressed in terms of genus
zero quantities only, generalizing the constitutive relation of closed
topological gravity.
