Two-temperature solutions and emergent spectra from relativistic accretion discs around black holes

Aims. We investigate a two-temperature advective transonic accretion disc around a black hole and analyse its spectrum in the presence of radiative processes such as bremsstrahlung, synchrotron, and inverse-Comptonisation. The aim is to link the emergent spectra with constants of motion of the accretion disc fluid, however, the number of unknowns in two-temperature theory exceeds the number of equations for a given set of constants of motion. We intend to remove the degeneracy using a general methodology and obtain a unique solution, along with its spectrum. Methods. We used hydrodynamic equations (continuity, momentum, and energy conservation equation) to obtain sonic points and solutions. To solve these equations of motion we used the 4th order Runge-Kutta method. For the spectral analysis, general and special relativistic effects were taken into consideration. The system is, nonetheless, degenerate and we remove the degeneracy by choosing the solution with maximum entropy, as dictated by the second law of thermodynamics. Results. We obtained a unique transonic solution for a given set of constants of motion. The entropy expression is a tool used to make a selection between the degenerate solutions. We found that Coulomb coupling is a weak energy exchange term, which allows protons and electrons to settle down into two different temperatures, justifying, hence, our study of two-temperature flows. The information of the electron flow allows us to model the spectra. We show that the spectra of accretion solutions depend on the associated constants of motion. At low accretion rates, bremsstrahlung is important. A fraction of the bremsstrahlung photons may be of higher energy than the neighbouring electrons, energising them through the process of Compton scattering. Synchrotron emission, on the other hand, provides soft photons, which can be inverse-Comptonised to produce a hard power law part in the spectrum. Luminosity increases with the increase in the accretion rate of the system, as well as with the increase in BH mass. However, the radiative efficiency of the flow has almost no dependence on the BH mass, but it sharply rises with the increase in the accretion rate. The spectral index, however, hardens with the increase in the accretion rate, while it does not change much with the variation in BH mass. In addition to the constants of motion, the value of the plasma beta parameter and magnitude of magnetic dissipation in the system also helps in shaping the spectrum. A shocked solution exists in two-temperature accretion flows in a limited region of the parameter space. We find that a shocked solution is always brighter than a solution without a shock. Conclusions. An accreting system in two-temperature regime admits multiple solutions for the same set of constants of motion, producing widely different spectra. Comparing the observed spectrum with that derived from a randomly chosen accretion solution would give us a wrong estimation of the accretion parameters of the system. The form of entropy measurement we obtained helped us to remove the degeneracy of the solutions and allowed us to understand the physics of the system, shorn of arbitrary assumptions. In this work, we show how the spectra and luminosities of an accreting system depend on the constants of motion, producing solutions ranging from radiatively inefficient flows to luminous flows. An increase in BH mass quantitatively changes the system, making the system more luminous, while the spectral bandwidth also increases. A higher BH mass system spans the range from radio to gamma-rays. However, increasing the accretion rate around a BH of certain mass has little influence on the frequency range of the spectra.