内激波模型中的GRB光度函数与观测值的关系
The GRB luminosity function in the internal shock model confronted to observations
摘要：
我们计算的预期亮度函数的伽玛暴的背景下，内部冲击模型。我们假设GRB中心引擎产生相对论性外流，其特征在于注入动能Edot和对比度的分布在洛伦兹因子Kappa = Gamma_max/Gamma_min中。我们发现，如果对比度的分布向下延伸到接近于1的值（即，如果高度可变和平滑的外流都可以存在），则光度函数有两个分支。在高光度下，它遵循Edot的分布，而在低光度下，它接近斜率为-0.5的幂律。然后，我们检查现有的数据是否可以约束光度函数。使用对数N -对数P曲线，明亮的BATSE爆发的Ep分布和HETE 2获得的XRF/GRB比，我们表明，单一和破碎的幂律可以提供同样好的拟合这些数据。因此，目前的观察无法支持另一种形式。然而，当采用破幂律时，它们清楚地表明低光度斜率~ -0.6 +-0.2，与内部激波模型的预测一致。
英文摘要：
We compute the expected luminosity function of GRBs in the context of the internal shock model. We assume that GRB central engines generate relativistic outflows characterized by the respective distributions of injected kinetic power Edot and contrast in Lorentz factor Kappa = Gamma_max/Gamma_min. We find that if the distribution of contrast extends down to values close to unity (i.e. if both highly variable and smooth outflows can exist) the luminosity function has two branches. At high luminosity it follows the distribution of Edot while at low luminosity it is close to a power law of slope -0.5. We then examine if existing data can constrain the luminosity function. Using the log N - log P curve, the Ep distribution of bright BATSE bursts and the XRF/GRB ratio obtained by HETE2 we show that single and broken power-laws can provide equally good fits of these data. Present observations are therefore unable to favor one form of the other. However when a broken power-law is adopted they clearly indicate a low luminosity slope ~ -0.6 +- 0.2, compatible with the prediction of the internal shock model.
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