Probing Gamma-ray Emission of Geminga and Vela with Non-stationary Models

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  • ABSTRACT

    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.


  • KEYWORD

    Vela , Geminga , superposition model

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  • [Fig. 1.] On the left, phase-averaged spectrum of Geminga. On the right, phase-averaged spectrum of Vela.
    On the left, phase-averaged spectrum of Geminga. On the right, phase-averaged spectrum of Vela.
  • [Fig. 2.] The left panel is a sketch of the magnetosphere of a pulsar and possible acceleration sites. The right two panels show the particle acceleration mechanisms of the polar cap model and the outer gap model.
    The left panel is a sketch of the magnetosphere of a pulsar and possible acceleration sites. The right two panels show the particle acceleration mechanisms of the polar cap model and the outer gap model.
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  • [Table 1.] Parameters of Equation (5) for Geminga and six arbitrary cut-offs
    Parameters of Equation (5) for Geminga and six arbitrary cut-offs
  • [Fig. 3.] The left panel is a sketch of the magnetosphere of a pulsar and possible acceleration sites. The right panel shows the mechanisms of the polar cap and the outer gap (De Ona Wilhelmi 2011).
    The left panel is a sketch of the magnetosphere of a pulsar and possible acceleration sites. The right panel shows the mechanisms of the polar cap and the outer gap (De Ona Wilhelmi 2011).
  • [Fig. 4.] Fitting results for phase-averaged spectrum, Peak 1 spectrum, Bridge Emission spectrum, Peak 2 spectrum, and Off Pulse spectrum of Geminga: red solid line is the best-fit sub-exponential spectrum and blue line is the result of no-stationary superposition model.
    Fitting results for phase-averaged spectrum, Peak 1 spectrum, Bridge Emission spectrum, Peak 2 spectrum, and Off Pulse spectrum of Geminga: red solid line is the best-fit sub-exponential spectrum and blue line is the result of no-stationary superposition model.
  • [Fig. 5.] Ten part spectra of bridge emission of Geminga; each part was fitted by simple-exponential spectrum. Part 1, part 6, part 7, part 8, and part 10 can be fitted by simple-exponential spectrum.
    Ten part spectra of bridge emission of Geminga; each part was fitted by simple-exponential spectrum. Part 1, part 6, part 7, part 8, and part 10 can be fitted by simple-exponential spectrum.
  • [Fig. 6.] Seven part spectra of peak 2 of Geminga; each part was fitted by simple-exponential spectrum. Only part 1 and part 6 can be fitted by simple-exponential spectrum.
    Seven part spectra of peak 2 of Geminga; each part was fitted by simple-exponential spectrum. Only part 1 and part 6 can be fitted by simple-exponential spectrum.
  • [Fig. 7.] Ten part spectra of off pulse of Geminga; each part was fitted by simple-exponential spectrum. Only part 2, part 5, and part 6 can be fitted by simple-exponential spectrum.
    Ten part spectra of off pulse of Geminga; each part was fitted by simple-exponential spectrum. Only part 2, part 5, and part 6 can be fitted by simple-exponential spectrum.
  • [Table 2.] Parameters of Equation (5) for Vela and six arbitrary cut-offs
    Parameters of Equation (5) for Vela and six arbitrary cut-offs
  • [Fig. 8.] Fitting results for phase-averaged spectrum, Peak 1 spectrum, Bridge Emission spectrum, Peak 2 spectrum, and Off Pulse spectrum of Vela: red solid line is the best-fit sub-exponential spectrum and blue line is the result of no-stationary superposition model.
    Fitting results for phase-averaged spectrum, Peak 1 spectrum, Bridge Emission spectrum, Peak 2 spectrum, and Off Pulse spectrum of Vela: red solid line is the best-fit sub-exponential spectrum and blue line is the result of no-stationary superposition model.
  • [Fig. 9.] Four part spectra of peak 1 of Vela; each part was fitted by simple-exponential spectrum. Only part 4 can be fitted by simple-exponential spectrum.
    Four part spectra of peak 1 of Vela; each part was fitted by simple-exponential spectrum. Only part 4 can be fitted by simple-exponential spectrum.
  • [Fig. 10.] Six part spectra of bridge emission 1 of Vela; each part was fitted by simple-exponential spectrum. Part 1 and part 4 can be fitted by simple-exponential spectrum.
    Six part spectra of bridge emission 1 of Vela; each part was fitted by simple-exponential spectrum. Part 1 and part 4 can be fitted by simple-exponential spectrum.
  • [Fig. 11.] Four part spectra of bridge emission 2 of Vela; each part was fitted by simple-exponential spectrum. Part 1, part 2, and part 4 can be fitted by simple-exponential spectrum.
    Four part spectra of bridge emission 2 of Vela; each part was fitted by simple-exponential spectrum. Part 1, part 2, and part 4 can be fitted by simple-exponential spectrum.
  • [Fig. 12.] Five part spectra of peak 2 of Vela; each part was fitted by simple-exponential spectrum. None of these can be fitted by simple-exponential spectrum.
    Five part spectra of peak 2 of Vela; each part was fitted by simple-exponential spectrum. None of these can be fitted by simple-exponential spectrum.
  • [Fig. 13.] Bar charts of cut-off energies of small phase bins for Geminga (left) and Vela (right).
    Bar charts of cut-off energies of small phase bins for Geminga (left) and Vela (right).