The evolution of the size–mass relation at z = 1–3 derived from the complete Hubble Frontier Fields data set

ABSTRACT We measure the size–mass relation and its evolution between redshifts 1 < z < 3, using galaxies lensed by six foreground Hubble Frontier Fields clusters. The power afforded by strong gravitation lensing allows us to observe galaxies with higher angular resolution beyond current facilities. We select a stellar mass limited sample and divide them into star-forming or quiescent classes based on their rest-frame UVJ colours from the ASTRODEEP catalogues. Source reconstruction is carried out with the recently released lenstruction software, which is built on the multipurpose gravitational lensing software lenstronomy. We derive the empirical relation between size and mass for the late-type galaxies with $M_{*}\gt 3\times 10^{9}\, \mathrm{M}_{\odot }$ at 1 < z < 2.5 and $M_{*}\gt 5\times 10^{9}\, \mathrm{M}_{\odot }$ at 2.5 < z < 3, and at a fixed stellar mass, we find galaxy sizes evolve as $R \rm _{eff} \propto (1+z)^{-1.05\pm 0.37}$. The intrinsic scatter is <0.1 dex at z < 1.5 but increases to ∼0.3 dex at higher redshift. The results are in good agreement with those obtained in blank fields. We evaluate the uncertainties associated with the choice of lens model by comparing size measurements using five different and publicly available models, finding the choice of lens model leads to a 3.7 per cent uncertainty of the median value, and ∼25 per cent scatter for individual galaxies. Our work demonstrates the use of strong lensing magnification to boost resolution does not introduce significant uncertainties in this kind of work, and paves the way for wholesale applications of the sophisticated lens reconstruction technique to higher redshifts and larger samples.

Energy, Momentum, Mass and Velocity of a Moving Body

In the weak-field approximation of covariant theory of gravitation the problem of 4/3 is formulated for internal and external gravitational fields of a body in the form of a ball. The dependence of the energy and the mass of the moving substance on the energy of field accompanying the substance, as well as the dependence on the characteristic size of the volume occupied by the substance are described. Additives in the energy and the momentum of the body, defined by energy and momentum of the gravitational and electromagnetic fields associated with the body are explicitly calculated. The conclusion is made that the energy and the mass of the body can be described by the energy of ordinary and strong gravitation, and through the energies of electromagnetic fields of particles that compose the body.

Energy, momentum, mass, and velocity of a moving body in the light of gravitomagnetic theory

In the weak-field approximation of the covariant theory of gravitation the 4/3 problem is formulated for internal and external gravitational fields of a body in the form of a uniform ball. The dependence of the energy and the mass of the moving body on the energy of the field accompanying the body, as well as the dependence on the characteristic size of the body are described. Additions in the energy and the momentum of the system, defined by the energy and momentum of the gravitational and electromagnetic fields, associated with the body, are explicitly calculated. The conclusion is made that the energy and the mass of the system can be described through the energy of ordinary and strong gravitation and through the energies of electromagnetic fields of particles that compose the body.

Atomic data estimation for H and C IV transitions in strong gravitation field

The gravitational field effect on atomic data for H and C IV transitions are considered as a perturbation of initial and final energy levels. We found that this perturbation increases with the principal quantum number. Here we give several expressions for estimation of this effect and its influence on atomic data parameters. Also, the calculations of atomic data for 1s ? 2p (Ly?) and 2s ? 3p transitions of hydrogen atom as well as atomic data for 2s2S1/2?2p2P0 1/2,3/2 transitions of C IV (1UV) as a function of deformation of energy levels due to gravitation field and gravitational redshift are given. The gravitational field effect should be estimated and should be taken into account in calculation of atomic data for emitters in Broad Line Regions (BLRs) of Active Galactic Nuclei (AGN).

8.12. MHD accretion in a black hole magnetosphere

To explain the activity of active galactic nuclei or compact X-ray sources, I consider a black hole magnetosphere in the center of these objects. The considering black hole magnetosphere is composed of a massive black hole with surrounding fluids and magnetic fields, and rotates rapidly. Because of the strong gravitation and the rapid rotation, both an accretion and a wind/jet would be generated from plasma sources (e.g., an accretion disk and its corona). The outgoing flow carries the angular momentum from the plasma source effectively, and then the accretion would go on stationary, releasing its gravitational energy. I assume that the magnetosphere is stationary and axisymmetric, and that the ideal MHD approximation is available for the streaming fluid. I discuss the thermal effects on MHD flows, and then I argue that the trans-fast MHD accretion solution can be broken by highly thermal effects.