Relation between X-ray flux and radio flux from cosmic objects

The relationship between the X-ray flux and the radio flux from cosmic objects is investigated. We consider the emission from energetic electrons on the condition in which a plasma and a magnetic field exist. As energetic electrons under the circumstances emit both X-rays by the bremsstrahlung mechanism and radio waves by the gyrosynchrotron mechanism simultaneously, it is shown that the radio flux density is closely related to the X-ray flux density. Solving an integral equation describing the X-ray flux density at Earth, we obtain the energy spectrum of electrons in the emitting region. Inserting the result into equation of the radio flux density at Earth, we obtain the direct formula between the X-ray flux density and the radio flux density. The relation is independent of the distance between Earth and cosmic sources. Assuming a power-law X-ray spectrum, we evaluate the numerical relation between two flux densities.