The Neutron Star Collision Signature · AI Generator #GEN-14F4462C

Physics · modern-physics

Problem

Astronomers detect a gamma-ray burst from a neutron star collision located

1.2 \times 10^{26}\;\text{m}

away. The collision converts a small fraction of the neutron star mass into pure electromagnetic energy. The peak gamma-ray flux measured at Earth is

3.4 \times 10^{-4}\;\text{W/m}^2

and lasts for

0.85\;\text{s}

. During the collision, the gamma rays are initially produced with an average energy of

2.1\;\text{MeV}

each. However, due to the extreme gravitational field near the neutron star surface (with gravitational acceleration

g_{ns} = 2.3 \times 10^{11}\;\text{m/s}^2

), the photons experience significant gravitational redshift as they escape. The neutron star has a radius of

12\;\text{km}

and the gamma rays are produced at an altitude of

500\;\text{m}

above its surface. Calculate the mass that was converted to electromagnetic energy during this collision event. *Note: Assume the energy is radiated isotropically and use the weak field approximation for gravitational redshift.*

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