The Spectral Sharpness Angle of Gamma-ray Bursts

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  • ABSTRACT

    We explain the results of Yu et al. (2015b) of the novel sharpness angle measurement to a large number of spectra obtained from the Fermi gamma-ray burst monitor. The sharpness angle is compared to the values obtained from various representative emission models: blackbody, single-electron synchrotron, synchrotron emission from a Maxwellian or power-law electron distribution. It is found that more than 91% of the high temporally and spectrally resolved spectra are inconsistent with any kind of optically thin synchrotron emission model alone. It is also found that the limiting case, a single temperature Maxwellian synchrotron function, can only contribute up to 58+23−18% of the peak flux. These results show that even the sharpest but non-realistic case, the single-electron synchrotron function, cannot explain a large fraction of the observed spectra. Since any combination of physically possible synchrotron spectra added together will always further broaden the spectrum, emission mechanisms other than optically thin synchrotron radiation are likely required in a full explanation of the spectral peaks or breaks of the GRB prompt emission phase.


  • KEYWORD

    gamma-rays: stars , gamma-ray burst: general , radiation mechanisms: non-thermal , radiation mechanisms: thermal , methods: data analysis

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  • [Fig. 1.] Illustration of how the triangle is constructed and the sharpness angle θ is defined. The vertical and horizontal axis are plotted in logarithmic scale in units of normalized νFν flux and photon energy, respectively.
    Illustration of how the triangle is constructed and the sharpness angle θ is defined. The vertical and horizontal axis are plotted in logarithmic scale in units of normalized νFν flux and photon energy, respectively.
  • [Fig. 2.] Cumulative distribution functions of θ and distributions of σθ. The limits of the normalized blackbody (dotted line), single-electron synchrotron (solid line), and synchrotron with a Maxwellian distribution function (dashed line) are overlaid.
    Cumulative distribution functions of θ and distributions of σθ. The limits of the normalized blackbody (dotted line), single-electron synchrotron (solid line), and synchrotron with a Maxwellian distribution function (dashed line) are overlaid.
  • [Fig. 3.] Distribution of the maximum fraction contributed from the Maxwellian synchrotron function at x = 1. The solid histograms represent the distributions using the best-fit model parameters, while the dashed histogram shows the minimum allowed sharpness by the uncertainties from the best-fit parameters. Spectra with 100% at x = 1 are accumulated in the last bin.
    Distribution of the maximum fraction contributed from the Maxwellian synchrotron function at x = 1. The solid histograms represent the distributions using the best-fit model parameters, while the dashed histogram shows the minimum allowed sharpness by the uncertainties from the best-fit parameters. Spectra with 100% at x = 1 are accumulated in the last bin.
  • [Fig. 4.] Example spectrum taken from GRB 101014.175 (2.560 ? 3.584 sec), showing the maximum contribution to the best-fit model by the Maxwellian synchrotron function, at x = 1. The normalized Maxwellian synchrotron (green curve) and the best-fit model (black curve) overlaid. The black dashed lines show the peak position of the best fit model and the relative normalized flux levels. In this particular spectrum, the Maxwellian fraction is about 65% at x = 1. Deep green data points are from the BGO detector and the others are from the NaI detectors. Triangles represent upper limits. For display purpose, the bin size has been increased by a factor of 5 ? 10 relative to the standard bin size.
    Example spectrum taken from GRB 101014.175 (2.560 ? 3.584 sec), showing the maximum contribution to the best-fit model by the Maxwellian synchrotron function, at x = 1. The normalized Maxwellian synchrotron (green curve) and the best-fit model (black curve) overlaid. The black dashed lines show the peak position of the best fit model and the relative normalized flux levels. In this particular spectrum, the Maxwellian fraction is about 65% at x = 1. Deep green data points are from the BGO detector and the others are from the NaI detectors. Triangles represent upper limits. For display purpose, the bin size has been increased by a factor of 5 ? 10 relative to the standard bin size.
  • [Fig. 5.] Six examples of evolutionary trends of θ. Red, blue, or green color indicates that the best-fit model is exponential cutoff power law (COMP), Band function (BAND), or smoothly broken power law (SBPL), respectively. The light curves are overlaid in arbitrary units. The limits of the normalized blackbody (dotted line), single-electron synchrotron (solid line), and synchrotron emission from a Maxwellian electron distribution (dashed line) are overlaid.
    Six examples of evolutionary trends of θ. Red, blue, or green color indicates that the best-fit model is exponential cutoff power law (COMP), Band function (BAND), or smoothly broken power law (SBPL), respectively. The light curves are overlaid in arbitrary units. The limits of the normalized blackbody (dotted line), single-electron synchrotron (solid line), and synchrotron emission from a Maxwellian electron distribution (dashed line) are overlaid.
  • [Fig. 6.] Sharpness angles plotted against the temporal bin widths per MVT. Red data points show spectra best fit by the exponential cutoff power law (COMP), blue by the Band function (BAND), and green by the smoothly broken power law (SBPL). The vertical dash-dotted line shows where the bin width equals the MVT, only 4.4% of data points are located to the left of the line. The horizontal lines show the limits of the normalized blackbody (dotted), single-electron synchrotron (solid), and synchrotron emission from a Maxwellian electron distribution (dashed).
    Sharpness angles plotted against the temporal bin widths per MVT. Red data points show spectra best fit by the exponential cutoff power law (COMP), blue by the Band function (BAND), and green by the smoothly broken power law (SBPL). The vertical dash-dotted line shows where the bin width equals the MVT, only 4.4% of data points are located to the left of the line. The horizontal lines show the limits of the normalized blackbody (dotted), single-electron synchrotron (solid), and synchrotron emission from a Maxwellian electron distribution (dashed).
  • [Fig. 7.] Comparison between the average sharpness angles, <θ>, to the sharpness angles computed using the time-integrated catalog, θint. The dash-dotted line shows x = y. The solid and dashed lines show the single-electron synchrotron and Maxwellian synchrotron limit, respectively. We note that the error bars of <θ> represent the spread in θ. See main text for the color-coding and details about the plots.
    Comparison between the average sharpness angles, <θ>, to the sharpness angles computed using the time-integrated catalog, θint. The dash-dotted line shows x = y. The solid and dashed lines show the single-electron synchrotron and Maxwellian synchrotron limit, respectively. We note that the error bars of <θ> represent the spread in θ. See main text for the color-coding and details about the plots.