Review Article:The de thematibus (“on the themes”) of Constantine VII Porphyrogenitus. Translated with introductory chapters and notes by John HALDON [Τranslated Texts for Byzantinists, v. 11], Liverpool University Press 2021

Review Article: The de thematibus (''on the themes") of Constantine VII Porphyrogenitus. Translated with introductory chapters and notes by John Haldon, L[Τranslated Texts for Byzantinists, v. 11],Liverpool University Press 2021Review Article: The de thematibus (“on the themes”) of Constantine VII Porphyrogenitus. Translated with introductory chapters and notes by John Haldon [Τranslated Texts for Byzantinists, v. 11], Liverpool University Press 202

An Integral formula on submanifolds of domains of Cn

A Bochner-Martinelli-Koppelman type integral formula on submanifolds of pseudoconvex domains in Cn is derived; the result gives, in particular, integral formulas on Stein manifolds

A formula for the derivatives of holomorphic functions in C2 in terms of certain integrals taken on boundaries of analytic varieties

AbstractWe derive a Cauchy–Fantappiè type formula which expresses the derivatives of holomorphic functions at a point on a given analytic variety, in terms of the values of the function in an arbitrarily small neighborhood of the curve which bounds the variety. The formula involves derivatives of functions defined by integrals taken on boundaries of nearby analytic varieties. We also apply these formulas to questions related to analytic functionals

Magnetically Controlled Spasmodic Accretion During Star Formation. II. Results

The problem of the late accretion phase of the evolution of an axisymmetric, isothermal magnetic disk surrounding a forming star has been formulated in a companion paper. The "central sink approximation" is used to circumvent the problem of describing the evolution inside the opaque central region for densities greater than 10^11 cm^-3 and radii smaller than a few AUs. Only the electrons are assumed to be attached to the magnetic field lines, and the effects of both negatively and positively charged grains are accounted for. After a mass of 0.1 solar mass accumulates in the central cell (forming star), a series of magnetically driven outflows and associated outward propagating shocks form in a quasi-periodic fashion. As a result, mass accretion onto the protostar occurs in magnetically controlled bursts. We refer to this process as spasmodic accretion. The shocks propagate outward with supermagnetosonic speeds. The period of dissipation and revival of the outflow decreases in time, as the mass accumulated in the central sink increases. We evaluate the contribution of ambipolar diffusion to the resolution of the magnetic flux problem of star formation during the accretion phase, and we find it to be very significant although not sufficient to resolve the entire problem yet. Ohmic dissipation is completely negligible in the disk during this phase of the evolution. The protostellar disk is found to be stable against interchange-like instabilities, despite the fact that the mass-to-flux ratio has temporary local maxima.Comment: Astrophysical Journal, in press. 29 pages, 13 figure

Self-Consistent Analysis of OH-Zeeman Observations: Too Much Noise about Noise

We had recently re-analyzed in a self-consistent way OH-Zeeman observations in four molecular-cloud envelopes and we had shown that, contrary to claims by Crutcher et al., there is no evidence that the mass-to-flux ratio decreases from the envelopes to the cores of these clouds. The key difference between our data analysis and the earlier one by Crutcher et al. is the relaxation of the overly restrictive assumption made by Crutcher et al, that the magnetic field strength is independent of position in each of the four envelopes. In a more recent paper, Crutcher et al. (1) claim that our analysis is not self-consistent, in that it misses a cosine factor, and (2) present new arguments to support their contention that the magnetic-field strength is indeed independent of position in each of the four envelopes. We show that the claim of the missing cosine factor is false, that the new arguments contain even more serious problems than the Crutcher et al. original data analysis, and we present new observational evidence, independent of the OH-Zeeman data, that suggests significant variations in the magnetic-field strength in the four cloud envelopes.Comment: 8 pages, 3 figures, MNRAS in pres

Ambipolar-Diffusion Timescale, Star-Formation Timescale, and the Ages of Molecular Clouds: Is There a Discrepancy?

We re-examine critically the estimates of the duration of different phases of star formation and the lifetimes of molecular clouds, based on the ages of T-Tauri stars, age spreads of stars in clusters, and statistics of pre-stellar cores. We show that all available observational data are consistent with lifetimes of molecular clouds comparable to 10 Myr, as well as with the predictions of the theory of self-initiated, ambipolar-diffusion--controlled star formation. We conclude that there exists no observational support for either "young" molecular clouds or "rapid" star formation.Comment: Accepted for publication in the Astrophysical Journal. 5 pages, 4 figures, uses emulateapj.cl

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment: I. Formulation of the Problem and Method of Solution

We formulate the problem of the formation of magnetically supercritical cores in magnetically subcritical parent molecular clouds, and the subsequent collapse of the cores to high densities, past the detachment of ions from magnetic field lines and into the opaque regime. We employ the six-fluid MHD equations, accounting for the effects of grains (negative, positive and neutral) including their inelastic collisions with other species. We do not assume that the magnetic flux is frozen in any of the charged species. We derive a generalized Ohm's law that explicitly distinguishes between flux advection (and the associated process of ambipolar diffusion) and Ohmic dissipation, in order to assess the contribution of each mechanism to the increase of the mass-to-flux ratio of the central parts of a collapsing core and possibly to the resolution of the magnetic flux problem of star formation. We show how our formulation is related to and can be transformed into the traditional, directional formulation of the generalized Ohm's law, and we derive formulae for the perpendicular, parallel and Hall conductivities entering the latter, which include, for the first time, the effect of inelastic collisions between grains. In addition, we present a general (valid in any geometry) solution for the velocities of charged species as functions of the velocity of the neutrals and of the effective flux velocity (which can in turn be calculated from the dynamics of the system and Faraday's law). The last two sets of formulae can be adapted for use in any general non-ideal MHD code to study phenomena beyond star formation in magnetic clouds. The results, including a detailed parameter study, are presented in two accompanying papers.Comment: 17 pages, emulateapj; accepted for publication in the Astrophysical Journa

Protostar Formation in Magnetic Molecular Clouds beyond Ion Detachment: III. A Parameter Study

In two previous papers we formulated and solved, for a fiducial set of free parameters, the problem of the formation and evolution of a magnetically supercritical core inside a magnetically subcritical parent cloud. In this paper we present a parameter study to assess the sensitivity of the results (1) to the density at which the equation of state becomes adiabatic; (2) to the initial mass-to-flux ratio of the parent cloud; and (3) to ionization by radioactive decay of different nuclei (40K and 26Al) at high densities (number density > 10^12 particles per cubic cm). We find that (1) the results depend only slightly on the density at which the onset of adiabaticity occurs; (2) memory of the initial mass-to-flux ratio is completely lost at late times, which emphasizes the relevance of this work, idependently of the adopted theory of core formation; and (3) the precise source of radioactive ionization alters the degree of attachment of the electrons to the field lines (at high densities), and the relative importance of ambipolar diffusion and Ohmic dissipation in reducing the magnetic flux of the protostar. The value of the magnetic field at the end of the runs is insensitive to the values of the free parameters and in excellent agreement with meteoritic measurements of the protosolar nebula magnetic field. The magnetic flux problem of star formation is resolved for at least strongly magnetic newborn stars. A complete detachment of the magnetic field from the matter is unlikely. The formation of a "magnetic wall" (with an associated magnetic shock) is independent of the assumed equation of state, although the process is enhanced and accelerated by the formation of a central hydrostatic core.Comment: 17 pages, 14 figures, emulateapj; accepted for publication in the Astrophysical Journa