A New Perspective to the Relation Between Accretion Luminosity and Mass Accretion Rate

In this paper I show that, opposite to what is generally assumed, when a source accretes matter at the so-called Eddington mass accretion rate M˙ed, the generated accretion luminosity Lacc is smaller than Led, the Eddington accretion luminosity that can stop accretion. I demonstrate my thesis using pieces of informations that, one by one, are well known in the accretion theory but that, for some reason, they are not considered altogether. Namely, I use the following facts: i) Lacc, in the ideal case, is equal to the rate at which kinetic energy is deposited into the accreting source; ii) radiation pressure decreases the velocity of the infalling matter; iii) the generally accepted formula Lacc=GMM˙/R is valid only if the matter is in free fall. To give a quantitative demonstration of my thesis I use two accretion models: the first is the very simple spherical accretion of zero-temperature, fully ionized hydrogen; then I use a model developed some years ago where the energy transfer between matter and radiation is taken into account. The fact that M˙ed generates a Lacc<Led can have consequences in all the cases in which one would need to model accretion with M˙>M˙ed to reproduce the observations.