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Luminosity evolution of pulsar outer magnetospheric accelerators as a function of neutron star spin down luminosity. Two extreme chemical compositions of the neutron star envelopes are considered. The red curves correspond to a heavy element envelope, while the blue and black curves correspond to a light element envelope. The solid, dash-dotted, and dash-dot-dot-dot curves represent numerical solutions, while dashed and dotted ones represent analytical solutions. The circles, squares, and triangles designate the pulsars detected by the Fermi satellite: the green filled circles show the radio loud gamma-ray pulsars, while the blue filled squares show the radio quiet ones. From Hirotani 2013, ApJ, 766, 98.