Local Eddington Limit Research Articles

Modelling the spectral energy distribution of super-Eddington quasars

ABSTRACT We develop a broad-band spectral model, agnslim, to describe super-Eddington black hole accretion disc spectra. This is based on the slim disc emissivity, where radial advection keeps the surface luminosity at the local Eddington limit, resulting in L(r) ∝ r−2 rather than the r−3 expected from the Novikov-Thorne (standard, sub-Eddington) disc emissivity. Wind losses should also be important but these are expected to produce a similar radiative emissivity. We assume that the flow is radially stratified, with an outer standard disc, an inner hot Comptonizing region and an intermediate warm Comptonizing region to produce the soft X-ray excess. This gives the model enough flexibility to fit the observed data, but with the additional requirement of energy conservation to give physical constraints. We use this to fit the broad-band spectrum of one of the most extreme Active Galactic Nuclei, the Narrow Line Seyfert 1 RX J0439.6−5311, which has a black hole mass of $(6\sim 9)\times 10^6\, \mathrm{M}_\odot$ as derived from the H β line width. This cannot be fit with the standard disc emissivity at this mass, as even zero spin models overproduce the observed luminosity. Instead, we show that the spectrum is well reproduced by the slim disc model, giving mass accretion rates around (5 ∼ 10) × Eddington limit. There is no constraint on black hole spin as the efficiency is reduced by advection. Such extreme accretion rates should be characteristic of the first Quasars, and we demonstrate this by fitting to the spectrum of a recently discovered super-Eddington Quasar, PSO J006 + 39, at z = 6.6.

Super-Eddington accretion discs with advection and outflows around magnetized neutron stars

We present a model for a super-Eddington accretion disc around a magnetized neutron star taking into account advection of heat and the mass loss by the wind. The model is semi-analytical and predicts radial profiles of all the basic physical characteristics of the accretion disc. The magnetospheric radius is found as an eigenvalue of the problem. When the inner disc is in radiation-pressure-dominated regime but does not reach its local Eddington limit, advection is mild, and the radius of the magnetosphere depends weakly on the accretion rate. Once it approaches the local Eddington limit the disc becomes advection-dominated, and the scaling for the magnetospheric radius with the mass accretion rate is similar to the classical Alfvén relation. Allowing for the mass loss in a wind leads to an increase in the magnetospheric radius. Our model can be applied to a wide variety of magnetized neutron stars accreting close to or above their Eddington limits: ultra-luminous X-ray pulsars, Be/X-ray binaries in outbursts, and other systems. In the context of our model we discuss the observational properties of NGC 5907 X-1, the brightest ultra-luminous pulsar currently known, and NGC 300 ULX1, which is apparently a Be/X-ray binary experiencing a very bright super-Eddington outburst.

A global study of type B quasi-periodic oscillation in black hole X-ray binaries

We performed a global study on the timing and spectral properties of type-B quasi-periodic oscillations (QPOs) in the outbursts of black hole X-ray binaries. The sample is built based on the observations of {\it Rossi X-ray Timing Explorer}, via searching in the literature in RXTE era for all the identified type-B QPOs. To enlarge the sample, we also investigated some type-B QPOs that are reported but not yet fully identified. Regarding to the time lag and hard/soft flux ratio, we found that the sources with type-B QPOs behave in two subgroups. In one subgroup, type-B QPO shows a hard time lag that firstly decreases and then reverse into a soft time lag along with softening of the energy spectrum. In the other subgroup, type-B QPOs distribute only in a small region with hard time lag and relatively soft hardness. These findings may be understood with a diversity of the homogeneity showing up for the hot inner flow of different sources. We confirm the universality of a positive relation between the type-B QPO frequency and the hard component luminosity in different sources. We explain the results by considering that the type-B QPO photons are produced in the inner accretion flow around the central black hole, under a local Eddington limit. Using this relationship, we derived an mass estimation of $9.3-27.1$ $\rm{M_{\odot}}$ for the black hole in H 1743-322.

A timing view of the heartbeat state of GRS 1915+105

We present a timing analysis of two Rossi X-ray Timing Explorer observations of the microquasar GRS 1915+105 during the heartbeat state. The phase-frequency-power maps show that the intermediate-frequency aperiodic X-ray variability weakens as the source softens in the slow rise phase, and when the quasi-periodic oscillation disappears in the rise phase of the pulse of the double-peaked class its sub-harmonic is still present with a hard phase lag. In the slow rise phase, the energy-frequency-power maps show that most of the aperiodic variability is produced in the corona, and may also induce the aperiodic variability observed at low energies from an accretion disk, which is further supported by the soft phase lag especially in the intermediate-frequency range (with a time delay up to 20 ms). In the rise phase of the pulse, the low-frequency aperiodic variability is enhanced significantly and there is a prominent hard lag (with a time delay up to 50 ms), indicating that the variability is induced by extension of the disk toward small radii as implied by the increase in flux and propagates into the corona. However, during the hard pulse of the double-peaked class, the variability shows no significant lag, which may be attributed to an optically thick corona. These timing results are generally consistent with the spectral results presented by Neilsen et al. (2011, 2012) which indicated that the slow rise phase corresponds to a local Eddington limit and the rise phase of the pulse corresponds to a radiation pressure instability in the disk.

On the Eddington limit for relativistic accretion discs

Standard accretion disc model relies upon several assumptions, the most important of which is geometrical thinness. Whenever this condition is violated, new physical effects become important such as radial energy advection and mass loss from the disc. These effects are important, for instance, for large mass accretion rates when the disc approaches its local Eddington limit. In this work, we study the upper limits for standard accretion disc approximation and find the corrections to the standard model that should be considered in any model aiming on reproducing the transition to super-Eddington accretion regime. First, we find that for thin accretion disc, taking into account relativistic corrections allows to increase the local Eddington limit by about a factor of two due to stronger gravity in General Relativity (GR). However, violation of the local Eddington limit also means large disc thickness. To consider consequently the disc thickness effects, one should make assumptions upon the two-dimensional rotation law of the disc. For rotation frequency constant on cylinders $r\sin\theta=const$, vertical gravity becomes stronger with height on spheres of constant radius. On the other hand, effects of radial flux advection increase the flux density in the inner parts of the disc and lower the Eddington limit. In general, the effects connected to disc thickness tend to increase the local Eddington limit even more. The efficiency of accretion is however decreased by advection effects by about a factor of several.

Massive main-sequence stars evolving at the Eddington limit

The evolution of massive stars even on the main sequence is not yet well understood. Due to the steep mass-luminosity relation, massive main sequence stars become very luminous. This brings their envelopes very close to the Eddington limit. We are analysing stellar evolutionary models in which the Eddington limit is reached and exceeded, and explore the rich diversity of physical phenomena which take place in their envelopes, and investigate their observational consequences. We use the grids of detailed stellar models by Brott et al. (2011) and Koehler et al. (2015), to investigate the envelope properties of core hydrogen burning massive stars. We find that at the stellar surface, the Eddington limit is almost never reached, even for stars up to 500 Msun. When an appropriate Eddington limit is defined locally in the stellar envelope, most stars more massive than 40 Msun actually exceed this limit, in particular in the partial ionization zones of iron, helium or hydrogen. While most models adjust their structure such that the local Eddington limit is exceeded at most by a few per cent, our most extreme models do so by a factor of more than seven. We find that the local violation of the Eddington limit has severe consequences for the envelope structure, as it leads to envelope inflation, convection, density inversions and possibly to pulsations. We find that all models with luminosities higher than 4*10^5 Lsun i.e. stars above 40 Msun show inflation, with a radius increase of up to a factor of about 40. We find that the hot edge of the S Dor variability region coincides with a line beyond which our models are inflated by more than a factor of two, indicating a possible connection between S Dor variability and inflation. Furthermore, our coolest models show highly inflated envelopes with masses of up to several solar masses, and appear to be candidates to produce major LBV eruptions.

On the spreading layer emission in luminous accreting neutron stars

Emission of the neutron star surface potentially contains information about its size and thus of vital importance for high energy astrophysics. In spite of the wealth of data on the emission of luminous accreting neutron stars, the emission of their surfaces is hard to disentangle from their time averaged spectra. A recent X-ray transient source XTE J1701-462 has provided a unique dataset covering the largest ever observed luminosity range for a single source. In this paper, we extract the spectrum of the boundary layer between the inner part of the accretion disc and the neutron star surface with the help of maximally spectral model-independent method. We show compelling evidences that the energy spectrum of the boundary layer stays virtually the same over factor of 20 variations of the source luminosity. It is rather wide and cannot be described by a single temperature blackbody spectrum, probably because of the inhomogeneity of the boundary layer and a spread in the colour temperature. The observed maximum colour temperature of the boundary/spreading layer emission of kT~2.4-2.6 keV is very close to the maximum observed colour temperature in the photospheric radius expansion X-ray bursts, which is set by the limiting Eddington flux at the neutron star surface. Observed stability of the boundary layer spectrum and its maximum colour temperature strongly supports theoretical models of the boundary/spreading layers on surfaces of luminous accreting neutron stars, which assume the presence of a region emitting at the local Eddington limit. Variations in the luminosity in that case lead to changes in the size of this region, but affect less the spectral shape. Elaboration of this model will provide solid theoretical grounds for measurements of the neutron star sizes using the emission of the boundary/spreading layers of luminous accreting neutron stars.

RADIATION PRESSURE AND MASS EJECTION IN ρ-LIKE STATES OF GRS 1915+105

We present a unifying scenario to address the physical origin of the diversity of X-ray lightcurves within the rho variability class of the microquasar GRS 1915+105. This 'heartbeat' state is characterized by a bright flare that recurs every ~50-100 seconds, but the profile and duration of the flares varies significantly from observation to observation. Based on a comprehensive, phase-resolved study of heartbeats in the RXTE archive, we demonstrate that very different X-ray lightcurves do not require origins in different accretion processes. Indeed, our detailed comparison of the phase-resolved spectra of a double-peaked oscillation and a single-peaked oscillation shows that different cycles can have basically similar X-ray spectral evolution. We argue that all heartbeat oscillations can be understood as the result of a combination of a thermal-viscous radiation pressure instability, a local Eddington limit in the disk, and a sudden, radiation-pressure-driven evaporation or ejection event in the inner accretion disk. This ejection appears to be a universal, fundamental part of the rho state, and is largely responsible for a hard X-ray pulse seen in the lightcurve of all cycles. We suggest that the detailed shape of oscillations in the mass accretion rate through the disk is responsible for the phenomenological differences between different rho-type lightcurves, and we discuss how future time-dependent simulations of disk instabilities may provide new insights into the role of radiation pressure in the accretion flow.

THE PHYSICS OF THE “HEARTBEAT” STATE OF GRS 1915+105

We present the first detailed phase-resolved spectral analysis of a joint Chandra High Energy Transmission Grating Spectrometer and Rossi X-ray Timing Explorer observation of the rho variability class in the microquasar GRS 1915+105. The rho cycle displays a high-amplitude, double-peaked flare that recurs roughly every 50 s, and is sometimes referred to as the "heartbeat" oscillation. The spectral and timing properties of the oscillation are consistent with the radiation pressure instability and the evolution of a local Eddington limit in the inner disk. We exploit strong variations in the X-ray continuum, iron emission lines, and the accretion disk wind to probe the accretion geometry over nearly six orders of magnitude in distance from the black hole. At small scales (1-10 R_g), we detect a burst of bremsstrahlung emission that appears to occur when a portion of the inner accretion disk evaporates due to radiation pressure. Jet activity, as inferred from the appearance of a short X-ray hard state, seems to be limited to times near minimum luminosity, with a duty cycle of ~10%. On larger scales (1e5-1e6 R_g) we use detailed photoionization arguments to track the relationship between the fast X-ray variability and the accretion disk wind. For the first time, we are able to show that changes in the broadband X-ray spectrum produce changes in the structure and density of the accretion disk wind on timescales as short as 5 seconds. These results clearly establish a causal link between the X-ray oscillations and the disk wind and therefore support the existence of a disk-jet-wind connection. Furthermore, our analysis shows that the mass loss rate in the wind may be sufficient to cause long-term oscillations in the accretion rate, leading to state transitions in GRS 1915+105.

SPECTRAL STATES OF XTE J1701 – 462: LINK BETWEEN Z AND ATOLL SOURCES

We have analyzed 866 RXTE observations of the 2006-2007 outburst of the accreting neutron star XTE J1701-462, during which the source evolves from super-Eddington luminosities to quiescence. The X-ray color evolution first resembles the Cyg X-2 subgroup of Z sources, with frequent excursions on the horizontal and normal branches (HB/NB). The source then decays and evolves to the Sco X-1 subgroup, with increasing focus on the flaring branch (FB) and the lower vertex of the "Z". Finally, the FB subsides, and the source transforms into an atoll source, with the lower vertex evolving to the atoll soft state. Spectral analyses suggest that the atoll stage is characterized by a constant inner disk radius, while the Z stages exhibit a luminosity-dependent expansion of the inner disk, which we interpret as effects related to the local Eddington limit. Contrary to the view that the mass accretion rate ($\dot{m}$) changes along the Z, we find that changes in $\dot{m}$ are instead responsible for the secular evolution of the Z and the subclasses. Motion along the Z branches appears to be caused by three different mechanisms that may operate at roughly constant $\dot{m}$. For the Sco X-1-like Z stage, we find that the FB is an instability track that proceeds off the lower vertex when the inner disk radius shrinks from the value set by the X-ray luminosity toward the value measured for the atoll soft state. Excursions up the NB occur when the apparent size of the boundary layer increases while the disk exhibits little change. The HB is associated with Comptonization of the disk emission. The Z branches for the Cyg X-2-like stage are more complicated, and their origin is unclear. Finally, our spectral results lead us to hypothesize that the lower and upper Z vertices correspond to a standard thin disk and a slim disk, respectively.

Eddington‐limited X‐Ray Bursts as Distance Indicators. I. Systematic Trends and Spherical Symmetry in Bursts from 4U 1728−34

We investigate the limitations of thermonuclear X-ray bursts as a distance indicator for the weakly magnetized accreting neutron star 4U 1728-34. We measured the unabsorbed peak flux of 81 bursts in public data from the Rossi X-Ray Timing Explorer (RXTE). The distribution of peak fluxes was bimodal: 66 bursts exhibited photospheric radius expansion (presumably reaching the local Eddington limit) and were distributed about a mean bolometric flux of 9.2 × 10-8 ergs cm-2 s-1, while the remaining (non-radius expansion) bursts reached 4.5 × 10-8 ergs cm-2 s-1, on average. The peak fluxes of the radius expansion bursts were not constant, exhibiting a standard deviation of 9.4% and a total variation of 46%. These bursts showed significant correlations between their peak flux and the X-ray colors of the persistent emission immediately prior to the burst. We also found evidence for quasi-periodic variation of the peak fluxes of radius expansion bursts, with a timescale of 40 days. The persistent flux observed with RXTE/ASM over 5.8 yr exhibited quasi-periodic variability on a similar timescale. We suggest that these variations may have a common origin in reflection from a warped accretion disk. Once the systematic variation of the peak burst fluxes is subtracted, the residual scatter is only 3%, roughly consistent with the measurement uncertainties. The narrowness of this distribution strongly suggests that (1) the radiation from the neutron star atmosphere during radius expansion episodes is nearly spherically symmetric and (2) the radius expansion bursts reach a common peak flux that may be interpreted as a standard candle intensity. Adopting the minimum peak flux for the radius expansion bursts as the Eddington flux limit, we derive a distance for the source of 4.4-4.8 kpc (assuming RNS = 10 km), with the uncertainty arising from the probable range of the neutron star mass MNS = 1.4-2 M☉.

The Ocean and Crust of a Rapidly Accreting Neutron Star: Implications for Magnetic Field Evolution and Thermonuclear Flashes

We investigate the atmospheres, oceans, and crusts of neutron stars accreting at rates sufficiently high (typically in excess of the local Eddington limit) to stabilize the burning of accreted hydrogen and helium. For hydrogen-rich accretion at global rates in excess of 10-8 M☉ yr-1 (typical of a few neutron stars), we discuss the thermal state of the deep ocean and crust and their coupling to the neutron star core, which is heated by conduction (from the crust) and cooled by neutrino emission. We estimate the Ohmic diffusion time in the hot, deep crust and find that it is noticeably shortened (to less than 108 yr) from the values characteristic of the colder crusts in slowly accreting neutron stars. As suggested by Konar & Bhattacharya, at high accretion rates the flow timescale competes with the Ohmic diffusion time in determining the evolution of the crust magnetic field. At a global accretion rate of ≈ 3 × 10−9 M☉ yr-1, the Ohmic diffusion time across a scale height equals the flow time over a large range of densities in the outer crust. In the inner crust (below the neutron drip), the diffusion time is always longer than the flow time for sub-Eddington accretion rates. We speculate on the implications of these calculations for magnetic field evolution in the bright accreting X-ray sources.

X-ray bursts associated with envelope expansion

The precursor associated with a long X-ray burst is interpreted in terms of the stellar envelope expansion. The mass flow driven by the radiation pressure in excess of the local Eddington limit and the grey atmosphere model correctly describe the burst profiles in different energy ranges.