Magnetic Fields and Afterglows of BdHNe: Inferences from GRB 130427A, GRB 160509A, GRB 160625B, GRB 180728A and GRB 190114C

GRB 190114C is the first binary-driven hypernova (BdHN) fully observed from the initial supernova appearance to the final emergence of the optical SN signal. It offers an unprecedented testing ground for the BdHN theory and it is here determined and further extended to additional gamma-ray bursts (GRBs). BdHNe comprise two subclasses of long GRBs with progenitors a binary system composed of a carbon-oxygen star (CO$_\textrm{core}$) and a neutron star (NS) companion. The CO$_\textrm{core}$ explodes as a SN leaving at its center a newborn NS ($\nu$NS). The SN ejecta hypercritically accretes both on the $\nu$NS and the NS companion. BdHNe I are the tightest binaries where the accretion leads the companion NS to gravitational collapse into a black hole (BH). In BdHN II the accretion onto the NS is lower, so there is no BH formation. We observe the same structure of the afterglow for GRB 190114C and other selected examples of BdHNe I (GRB 130427A, GRB 160509A, GRB 160625B) and for BdHN II (GRB 180728A). In all the cases the explanation of the afterglow is reached via the synchrotron emission powered by the $\nu$NS: their magnetic fields structures and their spin are determined. For BdHNe I, we discuss the properties of the magnetic field embedding the newborn BH, inherited from the collapsed NS and amplified during the gravitational collapse process, and surrounded by the SN ejecta.Comment: 7 figures, 3 tables, submitted to Ap

Exponential inequalities for positive linear mappings

In this article, we present exponential-type inequalities for positive linear mappings and Hilbert space operators, by means of convexity and the Mond-Pe\v cari\'c method. The obtained results refine and generalize some known results. As an application, we present extensions for operator-like geometric and harmonic means