Pion production in accretion disks around rotating BH

Unlike keplerian flows the accretion models with a significant advection are extremely hot. Hence the production of $\pi^{0}$ meson through hadronic interactions (proton proton collission) and subsequent emission of $\gamma$ rays becomes a possibility. We have used the pion production cross-section from \cite{kxi} to calculate the the rate of $\pi^0$ and hence $\gamma$ ray production. Matter accreting on to a black hole may be heated to very high temperatures and radiate $\gamma$ rays. The accretion of matter onto a black hole can be considered as a hydrodynamic flow, and hence governed by the fluid equations, which is basically the conservation of energy momentum tensor and fluid current for a relativistic flow.} We have considered steady state inviscid general relativistic hydrodynamic fluid equations in cylindrical Boyer -Lindquist coordinates. The accreting material is considered to be forming a rotating disk in the equatorial plane. The disk is assumed to be in vertical equilibrium other than the near horizon region. The geometrical units ($G=c=M_{BH}=1$) have been used to represent hydrodynamic equations and the flow variables. The background geometry is the Kerr geometry in axisymmetric coordinates. Emissivity due to gamma ray production in the accretion disc through the reaction $$p+p\rightarrow p+p+\pi^{0}(2\gamma),$$ computed using the velocity weighted cross-section average of $pp$ interaction \cite{col86, kxi}, has been incorporated in the dimensionless temperature and bulk velocity gradient through the first law of thermodynamics. We have investigated the effect of the interaction on the flow profile.