It is generally believed that the high energy emissions from isolated pulsars are emitted from relativistic electrons/positrons accelerated in outer magnetospheric accelerators (outergaps) via a curvature radiation mechanism, which has a simple exponential cut-off spectrum. However, many gamma-ray pulsars detected by the Fermi LAT (Large Area Telescope) cannot be fitted by simple exponential cut-off spectrum, and instead a sub-exponential is more appropriate. It is proposed that the realistic outergaps are non-stationary, and that the observed spectrum is a superposition of different stationary states that are controlled by the currents injected from the inner and outer boundaries. The Vela and Geminga pulsars have the largest fluxes among all targets observed, which allows us to carry out very detailed phase-resolved spectral analysis. We have divided the Vela and Geminga pulsars into 19 (the off pulse of Vela was not included) and 33 phase bins, respectively. We find that most phase resolved spectra still cannot be fitted by a simple exponential spectrum: in fact, a sub-exponential spectrum is necessary. We conclude that non-stationary states exist even down to the very fine phase bins.

1. INTRODUCTION
 2. THE PHASE-AVERAGE SPECTRA OF VELA ANDGEMINGA
 3.OUTER GAP MODELS
  3.1 Stationary Outer Gap Models
  3.2 Non-Stationary Outer Gap Model
 4.DATA ANALYSIS
  4.1 Fitting Results for Geminga
  4.2 Fitting Results for Vela
 5. DISCUSSION AND CONCLUSION
 ACKNOWLEDGMENTS
 REFERENCES

• Yating Chai(The University of Hong Kong, Pokfulam, Hong Kong) Corresponding Author
• Kwong-Sang Cheng(The University of Hong Kong, Pokfulam, Hong Kong)
• Jumpei Takata(Huazhong University of Science and Technology, Wuhan 430074, China)