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 \theta _ { \mathrm { LD } } and the limb darkening parameters of the two solar-type stars in the near-infrared H band ( \lambda = 1.65 \mu m ) .
We obtain photospheric angular diameters of \theta _ { \mathrm { LD } } ( A ) = 8.502 \pm 0.038 mas ( 0.43 \% ) and \theta _ { \mathrm { LD } } ( B ) = 5.999 \pm 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 \pm 0.0050 ( 3.6 \% ) and \alpha ( B ) = 0.1545 \pm 0.0044 ( 2.8 \% ) , which closely bracket the observed solar value ( \alpha _ { \odot } = 0.15027 ) .
Combined with the parallax \pi = 747.17 \pm 0.61 mas previously determined , we derive linear radii of R _ { A } = 1.2234 \pm 0.0053 R _ { \odot } ( 0.43 \% ) and R _ { B } = 0.8632 \pm 0.0037 R _ { \odot } ( 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 .