Classical Eddington Limit Research Articles

Unveiling the Nature of SN 2011fh: A Young and Massive Star Gives Rise to a Luminous SN 2009ip−like Event

Abstract In recent years, many Type IIn supernovae have been found to share striking similarities with the peculiar SN 2009ip, whose true nature is still under debate. Here, we present 10 yr of observations of SN 2011fh, an interacting transient with spectroscopic and photometric similarities to SN 2009ip. SN 2011fh had an M r ∼ −16 mag brightening event, followed by a brighter M r ∼ −18 mag luminous outburst in 2011 August. The spectra of SN 2011fh are dominated by narrow to intermediate Balmer emission lines throughout its evolution, with P Cygni profiles indicating fast-moving material at ∼6400 km s−1. HST/WFC3 observations from 2016 October revealed a bright source with M F814W ≈ −13.3 mag, indicating that we are seeing the ongoing interaction of the ejecta with the circumstellar material or that the star might be going through an eruptive phase five years after the luminous outburst of 2011. Using HST photometry of the stellar cluster around SN 2011fh, we estimated an age of ∼4.5 Myr for the progenitor, which implies a stellar mass of ∼60 M ⊙, using single-star evolution models, or a mass range of 35–80 M ⊙, considering a binary system. We also show that the progenitor of SN 2011fh exceeded the classical Eddington limit by a large factor in the months preceding the luminous outburst of 2011, suggesting strong super-Eddington winds as a possible mechanism for the observed mass loss. These findings favor an energetic outburst in a young and massive star, possibly a luminous blue variable.

Resolved atomic lines reveal outflows in two ultraluminous X-ray sources.

Ultraluminous X-ray sources are extragalactic, off-nucleus, point sources in galaxies, and have X-ray luminosities in excess of 3 × 10(39) ergs per second. They are thought to be powered by accretion onto a compact object. Possible explanations include accretion onto neutron stars with strong magnetic fields, onto stellar-mass black holes (of up to 20 solar masses) at or in excess of the classical Eddington limit, or onto intermediate-mass black holes (10(3)-10(5) solar masses). The lack of sufficient energy resolution in previous analyses has prevented an unambiguous identification of any emission or absorption lines in the X-ray band, thereby precluding a detailed analysis of the accretion flow. Here we report the presence of X-ray emission lines arising from highly ionized iron, oxygen and neon with a cumulative significance in excess of five standard deviations, together with blueshifted (about 0.2 times light velocity) absorption lines of similar significance, in the high-resolution X-ray spectra of the ultraluminous X-ray sources NGC 1313 X-1 and NGC 5408 X-1. The blueshifted absorption lines must occur in a fast-outflowing gas, whereas the emission lines originate in slow-moving gas around the source. We conclude that the compact object in each source is surrounded by powerful winds with an outflow velocity of about 0.2 times that of light, as predicted by models of accreting supermassive black holes and hyper-accreting stellar-mass black holes.

NATURE OF THE EXTREME ULTRALUMINOUS X-RAY SOURCES

In this proof-of-concept study we demonstrate that in a binary system mass can be transferred toward an accreting compact object at extremely high rate. If the transferred mass is efficiently converted to X-ray luminosity (with disregard of the classical Eddington limit) or if the X-rays are focused into a narrow beam then binaries can form extreme ULX sources with the X-ray luminosity of Lx>10^42 erg/s. For example, Lasota & King argued that the brightest known ULX (HLX-1) is a regular binary system with a rather low-mass compact object (a stellar-origin black hole or a neutron star). The predicted formation efficiencies and lifetimes of binaries with the very high mass transfer rates are large enough to explain all observed systems with extreme X-ray luminosities. These systems are not only limited to binaries with stellar-origin black hole accretors. Noteworthy, we have also identified such objects with neutron stars. Typically, a 10 Msun black hole is fed by a massive (10 Msun) Hertzsprung gap donor with Roche lobe overflow rate of 10^-3 Msun/yr (2600 MEdd). For neutron star systems the typical donors are evolved low-mass (2 Msun) helium stars with Roche lobe overflow rate of 10^-2 Msun/yr. Our study does not prove that any particular extreme ULX is a regular binary system, but it demonstrates that any ULX, including the most luminous ones, may potentially be a short-lived phase in the life of a binary star.

Eddington limit for a gaseous stratus with finite optical depth

Abstract The Eddington luminosity of a spherical source is usually defined for a uniformly extending normal plasma. We usually suppose that the gas can accrete to the central object at the sub-Eddington luminosity, while it would be blown off from the central luminous source in the super-Eddington case. We reconsider this central dogma of the Eddington limit under the radiative transfer effect for the purely scattering case, using analytical and numerical methods. For the translucent isolated gas cloud (stratus) with finite optical depth, the concept of the Eddington luminosity is drastically changed. In an heuristic way, we find that the critical condition is approximately expressed as Γ = (1 + μ* + τc)/2, where Γ (=L/LE) is the central luminosity L normalized by the Eddington luminosity LE, τc is the optical depth of the stratus, and μ* ($=\sqrt{1-R_*^2/R^2}$) is the direction cosine of the central object, R* being the radius of the central object, and R the distance from the central object. When the optical depth of the stratus is around unity, the classical Eddington limit roughly holds for the stratus; Γ ∼ 1. However, when the optical depth is greater than unity, the critical condition becomes roughly Γ ∼ τc/2, and the stratus would infall on to the central source even at the highly super-Eddington luminosity. When the optical depth is less than unity, on the other hand, the critical condition reduces to Γ ≳ (1 + μ*)/2, and the stratus could be blown off in some limited ranges, depending on μ*. This new concept of the Eddington limit for the isolated stratus could drastically change the accretion and outflow physics of highly inhomegeneous plasmas, with relevance for astrophysical jets and winds and supermassive black hole formation.

On the Eddington limit and Wolf-Rayet stars

We examine some properties of stars evolving close to the classical Eddington limit for electron-scattering opacity, when these stars maintain a chemically homogeneous structure as a result of mixing and/or mass loss. We consider analytical relations and models computed with the Geneva code. Homologous, chemically homogeneous stars evolving with a constant Eddington factor obey a relation of the form mu^2 M = const. This applies, for example, to Wolf-Rayet (WR) stars in stages without hydrogen. The value of the constant may depend on the metallicity, initial mass, evolutionary stage, and physical processes included in the considered homologous evolutionary sequence. An average value of the constant between 20 and 40 in solar units is consistent with the masses of Galactic WR stars.

On the Eddington limit in accretion discs

Although the Eddington limit has originally been derived for stars, recently its relevance for the evolution of accretion discs has been realized. We discuss the question whether the classical Eddington limit - which has been applied globally for almost all calculations on accretion discs - is a good approximation if applied locally in the disc. For this purpose, a critical accretion rate corresponding to this type of modified classical Eddington limit is calculated from thin alpha-disc models and slim disc models. We account for the non-spherical symmetry of the disc models by computing the local upper limits on the accretion rate from vertical and radial force equilibria separately. It is shown that the results can differ considerably from the classical (global) value: The vertical radiation force limits the maximum accretion rate in the inner disc region to much less than the classical Eddington value in thin alpha-discs, while it allows for significantly higher accretion rates in slim discs. We discuss the implications of these results for the evolution of accretion discs and their central objects.

Black hole accretion: theoretical limits and observational implications

AbstractRecently, the issue of the role of the Eddington limit in accretion discs became a matter of debate. While the classical (spherical) Eddington limit is certainly an over-simplification, it is not really clear how to treat it in a flattened structure like an accretion disc. We calculate the critical accretion rates and resulting disc luminosities for various disc models corresponding to the classical Eddington limit by equating the attractive and repulsive forces locally. We also discuss the observational appearance of such highly accreting systems by analyzing their spectral energy distributions. Our calculations indicate that the allowed mass accretion rates differ considerably from what one expects by applying the Eddington limit in its classical form, while the luminosities only weakly exceed their classical equivalent. Depending on the orientation of the disc relative to the observer, mild relativistic beaming turns out to have an important influence on the disc spectra. Thus, possible super-Eddington accretion, combined with mild relativistic beaming, supports the idea that ultraluminous X-ray sources host stellar mass black holes and accounts partially for the observed high temperatures of these objects.

The Eddington Luminosity Limit for Multiphased Media

We consider the effective Eddington luminosity in a locally inhomogeneous medium by averaging out the coarse, small-scale behavior. We show that the ratio between the emitted flux and the average radiation force changes. The mean luminosity therefore can theoretically exceed the classical Eddington limit. It is further shown that acoustic modes are unstable under most relevant conditions, and they unavoidably grow in such a way that they change the effective limiting Eddington luminosity. The instability and the increased limiting luminosity can explain the observed super-Eddington luminosity phenomenon in novae.

Boundary instability of the magnetized photosphere of a neutron star

The cyclotron resonance of electron scattering cross-section is shown to decrease the value of critical luminosity of neutron star below the classical Eddington limit corresponding to Thomson scattering. If the radiative flux prevails over critical one, instability of photospheric boundary in forms of ejection or MHD-pulsations might be evolved, giving rise to generation of hard gamma-photons and relativistic particles.

Effects of electron-positron pair opacity for spherical accretion onto black holes

The paper considers e(+)e(-) pair production by nonthermal processes in spherically symmetric accretion onto a black hole and solves for local pair densities by balancing pair production against pair annihilation and spatial inflow. Assuming that the pairs are coupled to the ions, it is found that the increased opacity due to pairs can substantially increase the radius within which radiation is trapped by the infalling matter and carried into the hole and can substantially decrease the effective Eddington limit. The principal new results are that: (1) the escaping luminosity L varies with the mass accretion rate M according to L varies inversely as M exp 2/3 for an intermediate range of M; and (2) the luminosity can reach about one-half of the pair-reduced Eddington limit while only about 1/20 of the classical Eddington limit. 13 references.

Radiatively accelerated nova envelopes

Photoionization calculations are presented to describe the thermal structure, ionization, and radiative acceleration of the dense envelope surrounding an active nova. It is shown that the envelope will be strongly accelerated outward when the nova has a luminosity at or below the classical Eddington limit, which is effectively super-Eddington in the outer layers due to the increased opacity of the gas from photoelectric and line absorption. The opacity is increased by factors of about 100 to 10,000 over electron scattering alone, and calculations suggest that the envelope will be driven off much faster than was previously thought, while terminal velocities and mass loss rates are close to those observed.

Radiation force on a relativistic plasma and the Eddington limit

Calculations of the radiation force due to Thomson scattering on a relativistic plasma are presented and discussed in relation to certain astronomical objects which operate within a few orders of magnitude of their Eddington luminosity. The radiation force on a hot isotropic plasma is shown to exceed that on a cold plasma by a factor depending on the electron Lorentz factor, which can be substantial in a relativistic plasma. In such a plasma, radiative bulk acceleration is found to occur through the anisotropic loss of internal energy during the Thomson scattering, resulting in an effect termed a Compton rocket. The Compton rocket is shown to be a relevant acceleration mechanism in situations where a relativistic electron plasma lies in the vicinity of a luminous source operating near the classical Eddington limit, including compact galactic X-ray sources and objects associated with active galactic nuclei (quasars, blazars, and Seyfert nuclei).