Compton Gamma-Ray Observatory observations of the crab pulsar

We present Crab pulsar light curves and spectra over the ∼50 keV to 10 GeV range from Compton Gamma-Ray Observatory observations made during MJD 48,373-48,406 (1991 April 27-1991 May 30, except for COMPTEL which started observations on April 28). The overall pulse phase-averaged spectrum is not well fitted by a single power law, but a broken power law does fit well, of the form F = A(E/E_B)^(-α1); A(E/E^B)^(-α2) photons cm^-2 s^-1 MeV^-1 fits well (χ²_min = 16, 26 degrees of freedom [dof]), where α₁ is the spectral index for E ≤ E_B and α₂ for E > E_B. For the normalization values to the spectra quoted here, we report phase-averaged intensities, and we applied an estimate to the uncertainty of the absolute calibration of 10%. The best-fit values for the parameters with 68% uncertainties are A = 0.064 ± 0.006, E_B = 0.12 ± 0.03 MeV, α₁ = 1.71^+0.15-0.19, and α₂ = 2.21 ± 0.02. The outer gap model (with gap parameter equal to 0.38, and a normalization factor of 1.08) provided to us by Ho describes the data with an accuracy of better than 20%, but the formal χ²_min is too high with a value of 68 for 28 dof. We derive a statistically equivalent result for the broken power law when we include lower energy data from the OSO 8 satellite. A broken power-law fit to the phase-resolved spectra (peak 1, the bridge, and peak 2) resulted in the following: for peak 1, A = 0.026 ± 0.003, E_B = 0.098 ± 0.02 MeV, α₁ = 1.77^+0.18_-0.25, α₂ = 2.09 ± 0.01, χ²_min = 45, 26 dof; for the bridge, A = 0.001 ± 0.0001, E_B = 0.45^+0.85_-0.15 MeV, α₁ = 1.75 ± 0.12, α₂ = 2.53^+0.10_-0.12, χ²_min, = 16, 23 dof; and for peak 2, A= 0.02 ± 0.002, E_B = 0.13^+0.020_-0.012 MeV, α₁ = 1.71 ± 0.09, α₂ = 2.25 ± 0.02, χ²_min = 21, 26 dof. For peak 1 only, the fit is greatly improved by using an outer gap model. The resultant values are a gap parameter of 0.450 ± 0.003 with a normalization of 0.22 ± 0.02, χ²_min = 32, 28 dof. The separation of the pulse peaks is difficult to quantify objectively because the peaks are not symmetrical. When we use the maximum intensity values of each peak to determine the centroids, we find an energy-independent phase difference of 0.405 ± 0.006 for the CGRO data (50 keV to 10 GeV) and 0.402 ± 0.002 when other data were included covering the range from 0.5 to 300 keV. The energy-independent value of the phase of peak 1 relative to the radio is -0.003 ± 0.012, where the uncertainty includes the absolute timing uncertainty. When the pulse shapes are characterized by asymmetric Lorentzian shapes, within the statistical uncertainty of the fits, the widths of the peaks in the ∼ 100 keV light curve are consistent within a factor of about 1.25 with the widths of the peaks in the ∼ 100 MeV light curve. We discuss these results within the context of a bulk relativistic motion beaming model.