Accretion Disk Theory Research Articles

The solar dynamo begins near the surface

The magnetic dynamo cycle of the Sun features a distinct pattern: a propagating region of sunspot emergence appears around 30° latitude and vanishes near the equator every 11 years (ref. 1). Moreover, longitudinal flows called torsional oscillations closely shadow sunspot migration, undoubtedly sharing a common cause2. Contrary to theories suggesting deep origins of these phenomena, helioseismology pinpoints low-latitude torsional oscillations to the outer 5–10% of the Sun, the near-surface shear layer3,4. Within this zone, inwardly increasing differential rotation coupled with a poloidal magnetic field strongly implicates the magneto-rotational instability5,6, prominent in accretion-disk theory and observed in laboratory experiments7. Together, these two facts prompt the general question: whether the solar dynamo is possibly a near-surface instability. Here we report strong affirmative evidence in stark contrast to traditional models8 focusing on the deeper tachocline. Simple analytic estimates show that the near-surface magneto-rotational instability better explains the spatiotemporal scales of the torsional oscillations and inferred subsurface magnetic field amplitudes9. State-of-the-art numerical simulations corroborate these estimates and reproduce hemispherical magnetic current helicity laws10. The dynamo resulting from a well-understood near-surface phenomenon improves prospects for accurate predictions of full magnetic cycles and space weather, affecting the electromagnetic infrastructure of Earth.

How Long Will the Quasar UV/Optical Flickering Be Damped?

The UV/optical light curves of Active Galactic Nuclei (AGNs) are commonly described by the Damped Random Walk (DRW) model. However, the physical interpretation of the damping timescale, a key parameter in the DRW model, remains unclear. Particularly, recent observations indicate a weak dependence of the damping timescale upon both wavelength and accretion rate, clearly being inconsistent with the accretion-disk theory. In this study, we investigate the damping timescale in the framework of the Corona Heated Accretion disk Reprocessing (CHAR) model, a physical model that describes AGN variability. We find that while the CHAR model can reproduce the observed power spectral densities of the 20 yr light curves for 190 sources from Stone et al., the observed damping timescale, as well as its weak dependence on wavelength, can also be well recovered through fitting the mock light curves with DRW. We further demonstrate that such weak dependence is artificial due to the effect of inadequate durations of light curves, which leads to best-fitting damping timescales lower than the intrinsic ones. After eliminating this effect, the CHAR model indeed yields a strong dependence of the intrinsic damping timescale on the bolometric luminosity and rest-frame wavelength. Our results highlight the demand for sufficiently long light curves in AGN variability studies and important applications of the CHAR model in such studies.

Geometry of massive particle surfaces

We propose a generalization of the photon surfaces of Claudel, Virbhadra and Ellis to the case of massive charged particles, considering a timelike hypersurface such that any worldline of a particle with mass $m$, electric charge $q$ and a fixed total energy $\mathcal{E}$, initially touching it, will forever remain in this hypersurface. Such surfaces can be defined not only with particle motion equations, but instead using the partially umbilic nature of the surface geometry. Such an approach should be especially useful in the case of nonintegrable equations of motion. It can be applied to the theory of nonthin accretion disks, and can also serve as a new tool for some general problems such as uniqueness theorems, Penrose inequalities, and hidden symmetries. A condition for the stability of worldlines is derived, which reduces to differentiation along the flow of surfaces of a certain energy. A number of examples of electrovacuum and dilaton solutions are considered; conditions are found for marginally stable surfaces of massive particles, regions of stable or unstable surfaces of massive particles and photons, as well as solutions that satisfy the no-force condition.

Null geodesics and QNMs in the field of regular black holes

In this paper, we analyze the null geodesics of regular black holes (BHs). A detailed analysis of geodesic structure, both null geodesics and timelike geodesics, has been investigated for the said BH. As an application of null geodesics, we calculate the radius of photon sphere and gravitational bending of light. We also study the shadow of the BH spacetime. Moreover, we determine the relation between radius of photon sphere [Formula: see text] and the shadow observed by a distance observer. Furthermore, we discuss the effect of various parameters on the radius of shadow [Formula: see text]. Also, we compute the angle of deflection for the photons as a physical application of null-circular geodesics. We find the relation between null geodesics and quasinormal mode (QNM) frequency in the eikonal approximation by computing the Lyapunov exponent. It is also shown that (in the eikonal limit) the QNMs of BHs are governed by the parameter of null-circular geodesics. The real part of QNMs frequency determines the angular frequency, whereas the imaginary part determines the instability timescale of the circular orbit. Next, we study the massless scalar perturbations and analyze the effective potential graphically. Massive scalar perturbations are also discussed. As an application of timelike geodesics, we compute the innermost stable circular orbit (ISCO) and marginally bound circular orbit (MBCO) of the regular BHs which are closely related to the BH accretion disk theory. In the appendix, we calculate the relation between angular frequency and Lyapunov exponent for null-circular geodesics.

Dynamical structure of highly eccentric discs with applications to tidal disruption events

ABSTRACT Whether tidal disruption events circularize or accrete directly as highly eccentric discs is the subject of current research and appears to depend sensitively on the disc thermodynamics. One aspect of this problem that has not received much attention is that a highly eccentric disc must have a strong, non-hydrostatic variation of the disc scale height around each orbit. As a complement to numerical simulations carried out by other groups, we investigate the dynamical structure of TDE discs using the non-linear theory of eccentric accretion discs. In particular, we study the variation of physical quantities around each elliptical orbit, taking into account the dynamical vertical structure, as well as viscous dissipation and radiative cooling. The solutions include a structure similar to the nozzle-like structure seen in simulations. We find evidence for the existence of the thermal instability in highly eccentric discs dominated by radiation pressure. For thermally stable solutions many of our models indicate a failure of the α-prescription for turbulent stresses. We discuss the consequences of our results for the structure of eccentric TDE discs.

Experiments and long-term high-performance computations on amplitude modulations of strato-rotational flows

The present paper describes a combined experimental and high-performance computing study of new specific behaviours of the Strato-Rotational Instability (SRI). The SRI is a purely hydrodynamical instability that consists of a classical Taylor–Couette (TC) system under stable axial density stratification. The density stratification causes a change on the marginal instability transition when compared to classical non-stratified TC systems, making the flow unstable in regions where – without stratification – it would be stable. This characteristic makes the SRI a relevant phenomenon in planetary and astrophysical applications, particularly in accretion disk theory. In spite of many advances in the understanding of strato-rotational flows, the confrontation of experimental data with non-linear numerical simulations remains relevant, since involved linear aspects and non-linear interactions of SRI modes still need to be better understood. These comparisons also reveal new non-linear phenomena and patterns not yet observed in the SRI that can contribute for our understanding of geophysical flows. The experiment designed to investigate these SRI-related phenomena consists of two cylinders that can rotate independently, with the space between these two vertical cylinders filled with a silicon oil. For obtaining a stable density stratification along the cylinder axis, the bottom lid of the setup is cooled, and its top part is heated, with temperature differences varying between , establishing an axial linear gradient, leading to Froude numbers between 1.5<Fr<4.5, where is the inner cylinder rotation and N is the buoyancy frequency. The flow field resulting from the cylinders rotation interacting with the stable density stratification is measured using low frequency Particle Image Velocimetry (PIV). In the present investigation, we focus on cases of moderate Reynolds numbers (, based on the inner cylinder radius and angular velocities), varying between and , and rotation ratio between outer and inner cylinders fixed at , a value slightly smaller than the Keplerian velocity profile, but beyond the Rayleigh limit. The same experimental configuration is also investigated by performing several Direct Numerical Simulations using a parallel high-order compact schemes incompressible code that solves the Boussinesq equations combining a 2d-pencil decomposition and the reduced Parallel Diagonal Dominant for an efficient parallelization. Both simulations and experiments reveal, in agreement with recent linear stability analyses, the occurrence of a return to stable flows with respect to the SRI when the Reynolds numbers increase. Low frequency velocity amplitude modulations related to two competing spiral wave modes, not yet reported, are observed both numerically and experimentally.

Evidence for variability time-scale-dependent UV/X-ray delay in Seyfert 1 AGN NGC 7469

ABSTRACT Using a month-long X-ray light curve from RXTE/PCA and 1.5 month-long UV continuum light curves from IUE spectra in 1220–1970 Å, we performed a detailed time-lag study of the Seyfert 1 galaxy NGC 7469. Our cross-correlation analysis confirms previous results showing that the X-rays are delayed relative to the UV continuum at 1315 Å by 3.49 ± 0.22 d, which is possibly caused by either propagating fluctuation or variable Comptonization. However, if variations slower than 5 d are removed from the X-ray light curve, the UV variations then lag behind the X-ray variations by 0.37 ± 0.14 d, consistent with reprocessing of the X-rays by a surrounding accretion disc. A very similar reverberation delay is observed between Swift/XRT X-ray and Swift/UVOT UVW2, U light curves. Continuum light curves extracted from the Swift/GRISM spectra show delays with respect to X-rays consistent with reverberation. Separating the UV continuum variations faster and slower than 5 d, the slow variations at 1825 Å lag those at 1315 Å by 0.29 ± 0.06 d, while the fast variations are coincident (0.04 ± 0.12 d). The UV/optical continuum reverberation lag from IUE, Swift, and other optical telescopes at different wavelengths are consistent with the relationship: τ ∝ λ4/3, predicted for the standard accretion disc theory while the best-fitting X-ray delay from RXTE and Swift/XRT shows a negative X-ray offset of ∼0.38 d from the standard disc delay prediction.

Identification of QPO Frequency of GRS 1915+105 as the Relativistic Dynamic Frequency of a Truncated Accretion Disk

Abstract We have analyzed AstroSat observations of the galactic microquasar system GRS 1915+105, when the system exhibited C-type quasi-periodic oscillations (QPOs) in the frequency range of 3.4–5.4 Hz. The broadband spectra (1–50 keV) obtained simultaneously from the Large Area X-ray Proportional Counter and Soft X-ray Telescope can be well described by a dominant relativistic truncated accretion disk along with thermal Comptonization and reflection. We find that while the QPO frequency depends on the inner radii with a large scatter, a much tighter correlation is obtained when both the inner radii and accretion rate of the disk are taken into account. In fact, the frequency varies just as the dynamic frequency (i.e., the inverse of the sound crossing time) does as predicted decades ago by the relativistic standard accretion disk theory for a black hole with a spin parameter of ∼0.9. We show that this identification has been possible due to the simultaneous broadband spectral coverage with temporal information as obtained from AstroSat.

Rapid “Turn-on” of Type-1 AGN in a Quiescent Early-type Galaxy SDSS1115+0544

Abstract We present a detailed study of a transient in the center of SDSS1115+0544 based on the extensive UV, optical, mid-IR light curves (LCs) and spectra over 1200 days. The host galaxy is a quiescent early-type galaxy at z = 0.0899 with a black hole mass of 2 × 107 M ⊙. The transient underwent a 2.5 mag brightening over ∼120 days, reaching a peak V-band luminosity (extinction corrected) of −20.9 mag, then fading 0.5 mag over 200 days, settling into a plateau of &gt;600 days. Following the optical brightening are the significant mid-IR flares at 3.4 and 4.5 μm, with a peak time delay of ∼180 days. The mid-IR LCs are explained as the echo of UV photons by a dust medium with a radius of 5 × 1017 cm, consistent with E(B − V) of 0.58 inferred from the spectra. This event is very energetic with an extinction corrected L bol ∼ 4 × 1044 erg s−1. Optical spectra over 400 days in the plateau phase revealed newly formed broad Hα, β emission with a FWHM of ∼3750 km s−1 and narrow coronal lines such as [Fe vii], [Ne v]. This flare also has a steeply rising UV continuum, detected by multi-epoch Swift data at +700 to +900 days post optical peak. The broad Balmer lines and the UV continuum do not show significant temporal variations. The slow evolving LCs over 1200 days, the constant Balmer lines, and UV continuum at late times rule out tidal disruption event and SN IIn as the physical model for this event. We propose that this event is a “turn-on” AGN, transitioning from a quiescent state to a type-1 AGN with a sub-Eddington accretion rate of 0.017 M ⊙ yr−1. This change occurred on a very short timescale of ∼120–200 days. The discovery of such a rapid “turn-on” AGN poses challenges to accretion disk theories and suggests more future detections of similar events.

What is the real accretion rate on to a black hole for low-angular-momentum accretion?

Mass accretion rate is a key parameter in accretion disk theory. It determines black hole accretion mode. In large scale cosmological simulations studying galaxy formation and evolution, Bondi radius can at most be marginally resolved. In those simulations, Bondi accretion formula is always used to estimate black hole accretion rate. Bondi solution is too simple, which cannot represent the real accretion process. We perform simulations of hot accretion flow at parsec scale irradiated by a low luminosity active galactic nucleus (AGN). We perform 77 simulations with varying density and temperature at outer boundary (10 parsec). Our purpose is to find a formula to calculate real black hole accretion rate based on the gas density and temperature at parsec scale. We define Eddington accretion rate to be $\dot M_{\rm Edd}=10L_{\rm Edd}/c^2$, with $L_{\rm Edd}$ and $c$ been Eddington luminosity and speed of light respectively. We set black hole mass to be $10^8M_{\odot}$, $M_{\odot}$ is solar mass. We find that black hole accretion rate can be expressed as $\frac{\dot M_{\rm BH} }{\dot M_{\rm Edd}}=10^{-3.11} (\rho_0/10^{-22}{\rm g cm}^{-3})^{1.36} (T_0/10^7 {\rm K})^{-1.9}$, with $\rho_0$ and $T_0$ being density and temperature at parsec scale, respectively. We find the formula can accurately predict the luminosity of observed low-luminosity AGNs (with black hole mass $\sim 10^8M_{\odot}$). This formula can be used in the sub-grid models in large scale cosmological simulations with a black hole mass of $\sim 10^8M_{\odot}$.

Constraints on accretion disk size in the massive type 1 quasar PG 2308+098 from optical continuum reverberation lags

Abstract Two years’ worth of u-, g-, r-, i-, and z-band optical light curves were obtained for the massive type 1 quasar PG 2308+098 at z = 0.433 using the 1.05 m Kiso Schmidt telescope/Kiso Wide Field Camera, and inter-band time lags of the light curves were measured. Wavelength-dependent continuum reverberation lag signals of several tens of days relative to the u-band were detected at g, r, i, and z bands, where the longer wavelength bands showed larger lags. From the wavelength-dependent lags, and assuming the standard disk temperature radial profile $T \propto R_{\rm disk}^{-3/4}$ and an X-ray/far-ultraviolet reprocessing picture, a constraint on the radius of the accretion disk responsible for the rest-frame 2500 Å disk continuum emission was derived as $R_{\rm disk} = 9.46^{+0.29}_{-3.12}\:$light-day. The derived disk size is slightly (1.2–1.8 times) larger than the theoretical disk size of Rdisk = 5.46 light-day predicted from the black hole mass (MBH) and Eddington ratio estimates of PG 2308+098. This result is roughly in accordance with previous studies of lower-mass active galactic nuclei (AGNs), where measured disk sizes have been found to be larger than the standard disk model predictions by a factor of ∼3; however, the disk size discrepancy is more modest in PG 2308+098. By compiling literature values of the disk size constraints from continuum reverberation and gravitational microlensing observations for AGNs/quasars, we show that the MBH dependence of Rdisk is weaker than that expected from the standard disk model. These observations suggest that the standard Shakura–Sunyaev accretion disk theory has limitations in describing AGN/quasar accretion disks.

The dynamics of a twisted disc formed after the tidal disruption of a star by a rotating black hole

We consider misaligned accretion discs formed after tidal disruption events occurring when a star encounters a supermassive rotating black hole. We use the linear theory of warped accretion discs to find the disc shape when the stream produced by the disrupted star provides a source of mass and angular momentum that is misaligned with the black hole. The evolution of the surface density and aspect ratio is found from a one dimensional vertically averaged model. We extend previous work which assumed a quasi-stationary disc to allow unrestricted dynamical propagation of disc tilt and twist through time dependent backgrounds. We consider a smaller value of the viscosity parameter, $\alpha =0.01,$ finding the dynamics varies significantly. At early times the disc inclination is found to be nearly uniform at small radii where the aspect ratio is large. However, since torques arise from the Lense-Thirring effect and the stream there is non uniform precession. We propose a simple model for this requiring only the background surface density and aspect ratio. At these times the $\alpha \sim 0.01$ disc exhibits a new feature. An inclined hot inner region joins an outer low inclination cool region via a thin transition front propagating outwards with a speed exceeding that of bending waves in the cool region. These waves accumulate where the propagation speeds match producing an inclination spike separating inner and outer discs. At late times a sequence of quasi-stationary configurations approximates disc shapes at small radii. We discuss observational implications of our results.

A dynamical mechanism for the origin of nuclear rings

We develop a dynamical theory for the origin of nuclear rings in barred galaxies. In analogy with the standard theory of accretion discs, our theory is based on shear viscous forces among nested annuli of gas. However, the fact that gas follows non circular orbits in an external barred potential has profound consequences: it creates a region of reverse shear in which it is energetically favourable to form a stable ring which does not spread despite dissipation. Our theory allows us to approximately predict the size of the ring given the underlying gravitational potential. The size of the ring is loosely related to the location of the Inner Lindblad Resonance in the epicyclic approximation, but the predicted location is more accurate and is also valid for strongly barred potentials. By comparing analytical predictions with the results of hydrodynamical simulations, we find that our theory provides a viable mechanism for ring formation if the effective sound speed of the gas is low ($\cs\lesssim1\kms$), but that nuclear spirals/shocks created by pressure destroy the ring when the sound speed is high ($\cs\simeq10\kms$). We conclude that whether this mechanism for ring formation is relevant for real galaxies ultimately depends on the effective equation of state of the ISM. Promising confirmation comes from simulations in which the ISM is modelled using state-of-the-art cooling functions coupled to live chemical networks, but more tests are needed regarding the role of turbulence driven by stellar feedback. If the mechanism is relevant in real galaxies, it could provide a powerful tool to constrain the gravitational potential, in particular the bar pattern speed.

Understanding X-ray irradiation in low-mass X-ray binaries directly from their light-curves

The X-ray light-curves of the recurring outbursts observed in low-mass X-ray binaries provide strong test beds for constraining (still) poorly understood disc-accretion processes. These light-curves act as a powerful diagnostic to probe the physics behind the mechanisms driving mass inflow and outflow in these binary systems. We have thus developed an innovative methodology, combining a foundation of Bayesian statistics, observed X-ray light-curves, and accretion disc theory. With this methodology, we characterize the angular-momentum (and mass) transport processes in an accretion disc, as well as the properties of the X-ray irradiation-heating that regulates the decay from outburst maximum in low-mass X-ray transients. We recently applied our methodology to the Galactic black-hole low-mass X-ray binary population, deriving from their lightcurves the first-ever quantitative measurements of the $\alpha$-viscosity parameter in these systems \citep{tetarenko2018}. In this paper, we continue the study of these binaries, using Bayesian methods to investigate the X-ray irradiation of their discs during outbursts of strong accretion. We find that the predictions of the disc-instability model, assuming a source of X-ray irradiation proportional to the central accretion rate throughout outburst, do not adequately describe the later stages of BH-LMXB outburst light-curves. We postulate that the complex and varied light-curve morphology observed across the population is evidence for irradiation that varies in time and space within the disc, throughout individual transient outbursts. Lastly, we demonstrate the robustness of our methodology, by accurately reproducing the synthetic model light-curves computed from numerical codes built to simulate accretion flows in binary systems.

Circular Geodesics, Paczyński-Witta Potential and QNMs in the Eikonal Limit for Ayón-Beato-García Black Hole

We investigate the comprehensive geodesic structure of a spherically symmetric, static charged regular Ayón-Beato and García black hole (BH). We derive the equation of innermost stable circular orbit (ISCO), marginally bound circular orbit (MBCO) and circular photon orbit (CPO) of said BH, which are most relevant to BH accretion disk theory. Using time-like geodesic properties, we derive Paczyński-Witta potential form for this BH which are very relevant to determine the general relativistic effects on the accretion disk. We show that at a certain radius (For example in case of Reissner-Nordstrøm (RN) BH, r ∗ = Q 2 M ), there exists zero angular momentum (ZAM) orbits due to the repulsive gravity. We also show that in the eikonal approximation, the real and imaginary parts of the quasi normal modes (QNM) of the regular BHs can be expressed as in terms of the frequency of the BH and the instability time scale of the unstable null circular geodesics. Moreover, we study the Bañados, Silk and West effect for this BH. We show that the center-of-mass (CM) energy of colliding neutral test particles near the infinite red-shift surface of the regular BHs have the finite energy. In the Appendix section, we have discussed the possibility of a regular ABG BH can act as particle accelerators when two charged test particles of different energies are colliding and approaching to the horizon of the BH provided that one of charged test particle has a critical value of charge.

Structure of protoplanetary discs with magnetically driven winds

We present a new set of analytical solutions to model the steady state structure of a protoplanetary disc with a magnetically-driven wind. Our model implements a parametrization of the stresses involved and the wind launching mechanism in terms of the plasma parameter at the disc midplane, as suggested by the results of recent, local MHD simulations. When wind mass-loss is accounted for, we find that its rate significantly reduces the disc surface density, particularly in the inner disc region. We also find that models that include wind mass-loss lead to thinner dust layers. As an astrophysical application of our models, we address the case of HL Tau, whose disc exhibits a high accretion rate and efficient dust settling at its midplane. These two observational features are not easy to reconcile with conventional accretion disc theory, where the level of turbulence needed to explain the high accretion rate would prevent a thin dust layer. Our disc model that incorporates both mass-loss and angular momentum removal by a wind is able to account for HL Tau observational constraints concerning its high accretion rate and dust layer thinness.

The general relativistic thin disc evolution equation

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of WKB, local techniques, and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenolgical studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

Accretion in Radiative Equipartition (AiRE) Disks

Abstract Standard accretion disk theory predicts that the total pressure in disks at typical (sub-)Eddington accretion rates becomes radiation pressure dominated. However, radiation pressure dominated disks are thermally unstable. Since these disks are observed in approximate steady state over the instability timescale, our accretion models in the radiation-pressure-dominated regime (i.e., inner disk) need to be modified. Here, we present a modification to the Shakura &amp; Sunyaev model, where the radiation pressure is in equipartition with the gas pressure in the inner region. We call these flows accretion in radiative equipartition (AiRE) disks. We introduce the basic features of AiRE disks and show how they modify disk properties such as the Toomre parameter and the central temperature. We then show that the accretion rate of AiRE disks is limited from above and below, by Toomre and nodal sonic point instabilities, respectively. The former leads to a strict upper limit on the mass of supermassive black holes as a function of cosmic time (and spin), while the latter could explain the transition between hard and soft states of X-ray binaries.

Characterising face-on accretion onto and the subsequent contraction of protoplanetary discs

Observations indicate that stars generally lose their protoplanetary discs on a timescale of about 5 Myr. Which mechanisms are responsible for the disc dissipation is still debated. Here we investigate the movement through an ambient medium as a possible cause of disc dispersal. The ram pressure exerted by the flow can truncate the disc and the accretion of material with no azimuthal angular momentum leads to further disc contraction. We derive a theoretical model from accretion disc theory that describes the evolution of the disc radius, mass, and surface density profile as a function of the density and velocity of the ambient medium. We test our model by performing hydrodynamical simulations of a protoplanetary disc embedded in a flow with different velocities and densities. We find that our model gives an adequate description of the evolution of the disc radius and accretion rate onto the disc. The total disc mass in the simulations follows the theoretically expected trend, except at the lowest density where our simulated discs lose mass owing to continuous stripping. This stripping may be a numerical rather than a physical effect. Some quantitative differences exist between the model predictions and the simulations. These are at least partly caused by numerical viscous effects in the disc and depend on the resolution of the simulation. Our model can be used as a conservative estimate for the process of face-on accretion onto protoplanetary discs, as long as viscous processes in the disc can be neglected. The model predicts that in dense gaseous environments, discs can shrink substantially in size and can, in theory, sweep up an amount of gas of the order of their initial mass. This process could be relevant for planet formation in dense environments.

On the Accretion Rates and Radiative Efficiencies of the Highest-redshift Quasars

Abstract We estimate the accretion rates onto the supermassive black holes that power 20 of the highest-redshift quasars, at , including the quasar with the highest redshift known to date—ULAS J1120 at z = 7.09. The analysis is based on the observed (rest-frame) optical luminosities and reliable “virial” estimates of the BH masses of the quasars, and utilizes scaling relations derived from thin accretion disk theory. The mass accretion rates through the postulated disks cover a wide range, , with most of the objects (80%) having , confirming the Eddington-limited nature of the accretion flows. By combining our estimates of with conservative, lower limits on the bolometric luminosities of the quasars, we investigate which alternative values of best account for all the available data. We find that the vast majority of quasars (∼85%) can be explained with radiative efficiencies in the range , with a median value close to the commonly assumed = 0.1. Within this range, we obtain conservative estimates of for ULAS J1120 and SDSS J0100 (at z = 6.3), and of for SDSS J1148 (at assuming their BH masses are accurate). The implied accretion timescales are generally in the range , suggesting that most quasars could have had mass e-foldings since BH seed formation. Our analysis therefore demonstrates that the available luminosities and masses for the highest-redshift quasars can be explained self-consistently within the thin, radiatively efficient accretion disk paradigm. Episodes of radiatively inefficient, “super-critical” accretion may have occurred at significantly earlier epochs (i.e., ).