ON THE NATURE OF THE PROTOTYPE LUMINOUS BLUE VARIABLE AG CARINAE. II. WITNESSING A MASSIVE STAR EVOLVING CLOSE TO THE EDDINGTON AND BISTABILITY LIMITS

We show that the significantly different effective temperatures (T(eff)) achieved by the luminous blue variable AG Carinae during the consecutive visual minima of 1985-1990 (T(eff) similar or equal to 22,800 K) and 2000-2001 (T(eff) similar or equal to 17,000 K) place the star on different sides of the bistability limit, which occurs in line-driven stellar winds around T(eff) similar to 21,000 K. Decisive evidence is provided by huge changes in the optical depth of the Lyman continuum in the inner wind as T(eff) changes during the S Dor cycle. These changes cause different Fe ionization structures in the inner wind. The bistability mechanism is also related to the different wind parameters during visual minima: the wind terminal velocity was 2-3 times higher and the mass-loss rate roughly two times smaller in 1985-1990 than in 2000-2003. We obtain a projected rotational velocity of 220 +/- 50 km s(-1) during 1985-1990 which, combined with the high luminosity (L(star) = 1.5 x 10(6) L(circle dot)), puts AG Car extremely close to the Eddington limit modified by rotation (Omega Gamma limit): for an inclination angle of 90 degrees, Gamma(Omega) greater than or similar to 1.0 for M(circle dot) less than or similar to 60. Based on evolutionary models and mass budget, we obtain an initial mass of similar to 100 M(circle dot) and a current mass of similar to 60-70 M(circle dot) for AG Car. Therefore, AG Car is close to, if not at, the Omega Gamma limit during visual minimum. Assuming M = 70 M(circle dot), we find that Gamma(Omega) decreases from 0.93 to 0.72 as AG Car expands toward visual maximum, suggesting that the star is not above the Eddington limit during maximum phases.

The battle of Eddington : or, British liberty, a tragedy / by John Penn.

Mode of access: Internet.

Brewer, Orrington, Holden, Eddington : history and families /

Index attached to inside back of volume.

O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.

O problema da matéria escura e o teorema do virial na teoria de gravidade Eddington-Born-Infeld

Dark matter is a fundamental ingredient of the modern Cosmology. It is necessary in order to explain the process of structures formation in the Universe, rotation curves of galaxies and the mass discrepancy in clusters of galaxies. However, although many efforts, in both aspects, theoretical and experimental, have been made, the nature of dark matter is still unknown and the only convincing evidence for its existence is gravitational. This rises doubts about its existence and, in turn, opens the possibility that the Einstein’s gravity needs to be modified at some scale. We study, in this work, the possibility that the Eddington-Born-Infeld (EBI) modified gravity provides en alternative explanation for the mass discrepancy in clusters of galaxies. For this purpose we derive the modified Einstein field equations and find their solutions to a spherical system of identical and collisionless point particles. Then, we took into account the collisionless relativistic Boltzmann equation and using some approximations and assumptions for weak gravitational field, we derived the generalized virial theorem in the framework of EBI gravity. In order to compare the predictions of EBI gravity with astrophysical observations we estimated the order of magnitude of the geometric mass, showing that it is compatible with present observations. Finally, considering a power law for the density of galaxies in the cluster, we derived expressions for the radial velocity dispersion of the galaxies, which can be used for testing some features of the EBI gravity.

Computation of Diffuse Solar Radiation

A technique for computing the spectral and angular (both the zenith and azimuthal) distribution of the solar energy reaching the surface of earth and any other plane in the atmosphere has been developed. Here the computer code LOWTRAN is used for getting the atmospheric transmittances in conjunction with two approximate procedures: one based on the Eddington method and the other on van de Hulst's adding method, for solving the equation of radiative transfer to obtain the diffuse radiation in the cloud-free situation. The aerosol scattering phase functions are approximated by the Hyeney-Greenstein functions. When the equation of radiative transfer is solved using the adding method, the azimuthal and zenith angle dependence of the scattered radiation is evaluated, whereas when the Eddington technique is utilized only the total downward flux of scattered solar radiation is obtained. Results of the diffuse and beam components of solar radiation received on surface of earth compare very well with those computed by other methods such as the more exact calculations using spherical harmonics and when atmospheric conditions corresponding to that prevailing locally in a tropical location (as in India) are used as inputs the computed values agree closely with the measured values.

Description of accretion induced outflows from ultra-luminous sources to under-luminous AGNs

We study the energetics of the accretion-induced outflow and then plausible jet around black holes/compact objects using a newly developed disc-outflow coupled model. Inter-connecting dynamics of outflow and accretion essentially upholds the conservation laws. The energetics depend strongly on the viscosity parameter α and the cooling factor f which exhibit several interesting features. The bolometric luminosities of ultra-luminous X-ray binaries (e.g. SS433) and family of highly luminous AGNs and quasars can be reproduced by the model under the super-Eddington accretion flows. Under appropriate conditions, low-luminous AGNs (e.g. Sagittarius A*) also fit reasonably well with the luminosity corresponding to a sub-Eddington accretion flow with f→1.

Transition from radiatively inefficient to cooling dominated phase in two temperature accretion disks around black holes

We investigate the transition of a radiatively inefficient phase of a viscous two temperature accreting flow to a cooling dominated phase and vice versa around black holes. Based on a global sub-Keplerian accretion disk model in steady state, including explicit cooling processes self-consistently, we show that general advective accretion flow passes through various phases during its infall towards a black hole. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. Hence the flow governs a much lower electron temperature similar to 10(8) - 10(9.5) K compared to the hot protons of temperature similar to 10(10.2) - 10(11.8) K in the range of the accretion rate in Eddington units 0.01 less than or simiar to (M) over dot less than or similar to 100. Therefore, the solutions may potentially explain the hard X-rays and the gamma-rays emitted from AGNs and X-ray binaries. We finally compare the solutions for two different regimes of viscosity and conclude that a weakly viscous flow is expected to be cooling dominated compared to its highly viscous counterpart which is radiatively inefficient. The flow is successfully able to reproduce the observed minosities of the under-fed AGNs and quasars (e.g. Sgr A*), ultra-luminous X-ray sources (e.g. SS433), as well as the highly luminous AGNs and ultra-luminous quasars (e.g. PKS 0743-67) at different combinations of the mass accretion rate and ratio of specific heats.

Two-temperature accretion around rotating black holes: a description of the general advective flow paradigm in the presence of various cooling processes to explain low to high luminous sources

We investigate viscous two-temperature accretion disc flows around rotating black holes. We describe the global solution of accretion flows with a sub-Keplerian angular momentum profile, by solving the underlying conservation equations including explicit cooling processes self-consistently. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. We focus on the set of solutions for sub-Eddington, Eddington and super-Eddington mass accretion rates around Schwarzschild and Kerr black holes with a Kerr parameter of 0.998. It is found that the flow, during its infall from the Keplerian to sub-Kepleria transition region to the black hole event horizon, passes through various phases of advection: the general advective paradigm to the radiatively inefficient phase, and vice versa. Hence, the flow governs a much lower electron temperature similar to 10(8)-10(9.5) K, in the range of accretion rate in Eddington units 0.01 less than or similar to (M) over dot less than or similar to 100, compared to the hot protons of temperature similar to 10(10.2)-10(11.8) K. Therefore, the solution may potentially explain the hard X-rays and gamma-rays emitted from active galactic nuclei (AGNs) and X-ray binaries. We then compare the solutions for two different regimes of viscosity. We conclude that a weakly viscous flow is expected to be cooling dominated, particularly at the inner region of the disc, compared to its highly viscous counterpart, which is radiatively inefficient. With all the solutions in hand, we finally reproduce the observed luminosities of the underfed AGNs and quasars (e. g. Sgr A*) to ultraluminous X-ray sources (e. g. SS433), at different combinations of input parameters, such as the mass accretion rate and the ratio of specific heats. The set of solutions also predicts appropriately the luminosity observed in highly luminous AGNs and ultraluminous quasars (e. g. PKS 0743-67).

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the disk is essentially collisionless. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell plasma simulations. We focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field, B, until the Alfven velocity, v(A), is comparable to the speed of light, c (independent of the initial value of v(A)/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the pressure perpendicular to B being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume-averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission-from the radio to the gamma-rays-of systems such as Sgr A*.

关于相对论热力学中的温度变换

本文在评述了半个世纪以来关于温度相对论变换关系式的各种不同结果和争议后;论证了可逆过程中元功的表示式,给出了与Einstein类似的正确推导。文中指出了Eddington-Ott-Mφller观点和Landsberg观点的错误,并对Mφller模型进行了具体的修正,其结果仍与Planck-Einstein一致。

Temperature transformation in relativistic thermodynamics

This paper reviews conflicting results on relativistic transformation formula for tem-perature obtained by different authors in the last half century, discusses the proper expres-sion for elementary work done under reversible processes, and presents a correct derivationof the transformation formula, rather similar in spirit to that of Einstein. It is pointed outthat the point of view adopted by Eddington, Ott, Mφller and Landsberg are erroneous,and that by correctly carrying out detailed analysis for Mφller's working model, which wasoriginally proposed to disprove Planck-Einstein result, we have arrived instead at a result incomplete agreement with that of Planck-Einstein. Thercupon this long standing controversyover the temperature transformation dilemma for relativistic thermodynamics is clarified.

Evidence for relativistic features in the X-ray spectrum of Mrk 335

We present an analysis of hard X-ray features in the spectrum of the bright Sy 1 galaxy Mrk 335 observed by the XMM-Newton satellite. Our analysis confirms the presence of a broad, ionized Fe Ka emission line in the spectrum, first found by Gondoin et al. The broad line can be modelled successfully by relativistic accretion disc reflection models. This interpretation is unusually robust in the case of Mrk 335 because of the lack of any ionized ('warm') absorber and the absence a clear narrow core to the line. Partial covering by neutral gas cannot, however, be ruled out statistically as the origin of the broad residuals. Regardless of the underlying continuum we report, for the first time in this source, the detection of a narrow absorption feature at the rest frame energy of ~5.9 keV. If the feature is identified with a resonance absorption line of iron in a highly ionized medium, the redshift of the line corresponds to an inflow velocity of ~0.11-0.15c. We present a simple model for the inflow, accounting approximately for relativistic and radiation pressure effects, and use Monte Carlo methods to compute synthetic spectra for qualitative comparison with the data. This modelling shows that the absorption feature can plausibly be reproduced by infalling gas providing that the feature is identified with Fe xxvi. We require the inflowing gas to extend over a limited range of radii at a few tens of r to match the observed feature. The mass accretion rate in the flow corresponds to 60 per cent of the Eddington limit, in remarkable agreement with the observed rate. The narrowness of the absorption line tends to argue against a purely gravitational origin for the redshift of the line, but given the current data quality we stress that such an interpretation cannot be ruled out. © 2006 The Authors.

Energy expenditure during activity in the American lobster Homarus americanus:Correlations with body acceleration

How animals manage time and expend energy has implications for survivorship. Being able to measure key metabolic costs of animals under natural conditions is therefore an important tool in behavioral ecology. One method for estimating activity-specific metabolic rate is via derived measures of acceleration, often 'overall dynamic body acceleration' (ODBA), recorded by an instrumented acceleration logger. ODBA has been shown to correlate well with rate of oxygen consumption (V ?o) in a range of species during activity in the laboratory. This study devised a method for attaching acceleration loggers to decapod crustaceans and then correlated ODBA against concurrent respirometry readings to assess accelerometry as a proxy for activity-specific energy expenditure in a model species, the American lobster Homarus americanus. Where the instrumented animals exhibited a sufficient range of activity levels, positive linear relationships were found between V ?o and ODBA over 20min periods at a range of ambient temperatures (6, 13 and 20°C). Mixed effect linear models based on these data and morphometrics provided reasonably strong predictive power for estimating activity-specific V ?o from ODBA. These V ?o-ODBA calibrations demonstrate the potential of accelerometry as an effective predictor of behavior-specific metabolic rate of crustaceans in the wild during periods of activity. © 2013 Elsevier Inc.