  The photospheric radius is one of the fundamental parameters governing the
radiative equilibrium of a star. We report new observations of the nearest
solar-type stars Alpha Centauri A (G2V) and B (K1V) with the VLTI/PIONIER
optical interferometer. The combination of four configurations of the VLTI
enable us to measure simultaneously the limb darkened angular diameter thetaLD
and the limb darkening parameters of the two solar-type stars in the
near-infrared H band (lambda = 1.65 microns). We obtain photospheric angular
diameters of thetaLD(A) = 8.502 +/- 0.038 mas (0.43%) and thetaLD(B) = 5.999
+/- 0.025 mas (0.42%), through the adjustment of a power law limb darkening
model. We find H band power law exponents of alpha(A) = 0.1404 +/- 0.0050
(3.6%) and alpha(B) = 0.1545 +/- 0.0044 (2.8%), which closely bracket the
observed solar value (alpha_sun = 0.15027). Combined with the parallax pi =
747.17 +/- 0.61 mas recently determined, we derive linear radii of RA = 1.2234
+/- 0.0053 Rsun (0.43%) and RB = 0.8632 +/- 0.0037 Rsun (0.43%). The power law
exponents that we derive for the two stars indicate a significantly weaker limb
darkening than predicted by both 1D and 3D stellar atmosphere models. As this
discrepancy is also observed on near-infrared limb darkening profile of the
Sun, an improvement of the calibration of stellar atmosphere models is clearly
needed. The reported PIONIER visibility measurements of Alpha Cen A and B
provide a robust basis to validate the future evolutions of these models.
