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arXiv 1001.0134astro-ph.HE
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相对论激波逃逸的宇宙射线谱

The spectrum of Cosmic Rays escaping from relativistic shocks

Boaz Katz, Peter Meszaros, Eli Waxman

摘要:

我们推导出了在减速相对论激波中加速并在激波之前逃逸的宇宙射线(CR)的时间积分谱的表达式。假设在任何给定时间,CR具有幂律形式,携带恒定比例的冲击等离子体的能量E_tot,并以可达到的最大能量连续逃逸。逃逸粒子的谱对瞬时谱指数高度敏感,这是因为最小能量E_min ~ Γ^2 m_pc^2(其中Γ是激波洛伦兹因子)随时间变化。特别是,逃逸谱可能比正则N(E)\propto E^-2谱要硬得多。对于膨胀到密度为n的等离子体中的激波,在跃迁到非相对论速度时可获得的最大能量处,预计会出现谱裂,E ~ 10 ^19(ε_B/0.1)(n/1 cm^-3)^(1/6)(E_tot/10 ^51 erg)^(1/3)eV,其中ε_B是磁场携带的能通量的分数。如果超高能量的CR是在恒星质量天体爆炸产生的相对论性冲击波减速过程中产生的,那么它们的产生谱可能与正则N(E)\propto E^-2不同。

英文摘要:

We derive expressions for the time integrated spectrum of Cosmic Rays (CRs) that are accelerated in a decelerating relativistic shock wave and escape ahead of the shock. It is assumed that at any given time the CRs have a power law form, carry a constant fraction of the energy E_tot of the shocked plasma, and escape continuously at the maximal energy attainable. The spectrum of escaping particles is highly sensitive to the instantaneous spectral index due to the fact that the minimal energy, E_min ~ Γ^2 m_pc^2 where Γis the shock Lorentz factor, changes with time. In particular, the escaping spectrum may be considerably harder than the canonical N(E)\propto E^-2 spectrum. For a shock expanding into a plasma of density n, a spectral break is expected at the maximal energy attainable at the transition to non relativistic velocities, E ~ 10^19 (ε_B/0.1)(n/1 cm^-3)^(1/6)(E_tot/10^51 erg)^(1/3) eV where ε_B is the fraction of the energy flux carried by the magnetic field. If ultra-high energy CRs are generated in decelerating relativistic blast waves arising from the explosion of stellar mass objects, their generation spectrum may therefore be different than the canonical N(E)\propto E^-2.

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