Thin Disk Model Research Articles

Eccentricity dynamics of wide binaries – I. The effect of Galactic tides

ABSTRACT A major puzzle concerning the wide stellar binaries (semimajor axes a ≳ 103 au) in the Solar neighbourhood is the origin of their observed superthermal eccentricity distribution function (DF), which is well approximated by P(e) ∝ eα with α ≈ 1.3. This DF evolves under the combined influence of (i) tidal torques from the Galactic disc and (ii) scattering by passing stars, molecular clouds, and substructure. Recently, it was demonstrated that Galactic tides alone cannot produce a superthermal eccentricity DF from an initially isotropic, non-superthermal one, under the restrictive assumptions that the eccentricity DF was initially of power-law form and then was rapidly phase-mixed toward a steady state by the tidal perturbation. In this paper, we first prove analytically that this conclusion is valid at all times, regardless of these assumptions. We then adopt a thin Galactic disc model and numerically integrate the equations of motion for several ensembles of tidally perturbed wide binaries to study the time evolution in detail. We find that even non-power-law DFs can be described by an effective power-law index αeff which accurately characterizes both their initial and final states, and that a DF with initial (effective or exact) power-law index αi is transformed by Galactic tides into another power law with index αf ≈ (1 + αi)/2 on a time-scale $\sim 4\, \mathrm{Gyr}\, (a/10^4\mathrm{AU})^{-3/2}$. In a companion paper, we investigate separately the effect of stellar scattering. As the GAIA data continues to improve, these results will place strong constraints on wide binary formation channels.

Magnetically dominated discs in tidal disruption events and quasi-periodic eruptions

ABSTRACT The classical radiation pressure instability has been a persistent theoretical feature of thin, radiatively efficient accretion discs with accretion rates $\sim $ 1 per cent–100 per cent of the Eddington rate. But there is only limited evidence of its occurrence in nature: rapid heartbeat oscillations of a few X-ray binaries and now, perhaps, the new class of hourly X-ray transients called quasi-periodic eruptions (QPEs). The accretion discs formed in tidal disruption events (TDEs) have been observed to peacefully trespass through the range of unstable accretion rates without exhibiting any clear sign of the instability. We try to explain the occurrence or otherwise of this instability in these systems, by constructing steady state 1D models of thin magnetic accretion discs. The local magnetic pressure in the disc is assumed to be dominated by toroidal fields arising from a dynamo sourced by magneto-rotational instability (MRI). We choose a physically motivated criterion of MRI saturation, validated by recent magnetohydrodynamic simulations, to determine the disc magnetic pressure. The resulting magnetic pressure support efficiently shrinks: (1) the parameter space of unstable mass accretion rates, explaining the absence of instability in TDEs and (2) the range of unstable radii in the inner accretion disc, which can shorten the quasi-periods of instability limit-cycles by more than three orders of magnitude, explaining the short periods of QPEs. In addition to examining stability of strongly magnetized discs, we predict other observational signatures such as spectral hardening and jet luminosities to test the compatibility of our disc models with observations of TDE discs.

2.5D magnetohydrodynamic models of circumstellar discs around FS CMa post-mergers – I. Non-stationary accretion stage

ABSTRACT We investigate the dynamic evolution of the gaseous regions around FS CMa post-mergers. Owing to the slow rotation of the central B-type star, the dynamics is driven mainly by the magnetic field of the central star. Recent observations have allowed us to set realistic initial conditions, such as the magnetic field value ($B_\star \approx 6\times 10^{3}\, \mathrm{G}$), the mass of the central star ($M_\star =6\, \mathrm{M}_\odot$), and the initial disc density $\rho _{d0}\in [10^{-13}\, \mathrm{g\, cm^{-3}},10^{-11}\, \mathrm{g \, cm^{-3}}]$. We use the pluto code to perform 2.5D magnetohydrodynamic simulations of thin and thick disc models. Especially relevant for the interpretation of the observed properties of FS CMa post-mergers are the results for low-density discs, in which we find a jet emerging from the inner edge of the disc, as well as the formation of the so-called ‘hot plasmoid’ in the coronal region. Jets are probably detected as discrete absorption components in the resonance lines of FS CMa stars. Moreover, the magnetic field configuration in the low-density plasma region favours the appearance of magnetocentrifugal winds from the disc. The currents towards the star created by the magnetic field may explain accidentally observed material infall. The disc structure is significantly changed owing to the presence of the magnetic field. The magnetic field is also responsible for the formation of a hot corona, as observed in several FS CMa stars through the Raman lines. Our results are valid for all magnetic stars surrounded by a low-density plasma, that is, by some stars showing the B[e] phenomenon.

Probing quasar viewing angle with the variability structure function

ABSTRACT Given the anisotropic emission from quasar accretion discs, their viewing angle affects estimates of the quasar luminosity, black hole mass, and Eddington ratio. Discs appear overluminous when viewed pole-on and underluminous when viewed at high inclination. In radio-quiet quasars, the viewing angle is usually unknown, although spectroscopic indicators have been proposed. Here, we use a recently discovered universality in the variability structure function (SF) of quasar light curves (LCs), where all quasars show the same SF when clocks run in units of orbital time-scale. As an offset from the mean relation can be caused by incorrect orbital time-scales and thus incorrect luminosities, we correlate these offsets with suggested inclination indicators. We derive SFs from NASA/Asteroid Terrestrial-impact Last Alert System (ATLAS) LCs spanning ∼6 yr of observation, using a sample of 183 luminous quasars with measured H β lines as well as 753 quasars with C iv and Mg ii lines. Starting from the proposed orientation indicators, we expect quasars with narrower H β lines and with more blueshifted C iv lines to be viewed more pole-on and thus appear overluminous. In contrast, our SF analysis finds that presumed pole-on discs appear underluminous, consistently for both line indicators. We discuss possible explanations for the behaviour of quasars with highly blueshifted C iv lines irrespective of inclination angle, including dusty outflows that might render the accretion disc underluminous and flatter disc temperature profiles with longer orbital time-scales than in thin-disc models but reach no satisfying conclusion.

Observational appearances of magnetically charged black holes in Born–Infeld electrodynamics

In this paper, we investigate the observational appearances of magnetically charged black holes in Born–Infeld (BI) electrodynamics. We examine the effects of the magnetic charge and the BI parameter on the geodesics with different impact parameters. Using the backward ray tracing method, we investigate how spherically symmetric accretions interact with black hole shadows and photon spheres. The shadows of infalling accretion are darker than that of static ones. Moreover, the radius of the photon sphere is an intrinsic property of the spacetime independent of accretions. We then study how the thin disk models affect the black hole shadows. After obtaining the transfer functions, we divide photons emitted from the thin disk into three categories: direct emission, lens ring, and photon ring. Applying three emission models, we find that the width of the shadow is dominated by the direct emission, the photon ring and the lens ring can hardly be identified by changing the emission models.

Characterising SMSS J2157–3602, the most luminous known quasar, with accretion disc models

ABSTRACT We develop an accretion disc (AD)-fitting method, utilizing thin and slim disc models and Bayesian inference with the Markov-Chain Monte Carlo approach, testing it on the most luminous known quasar, SMSS J215728.21-360215.1, at redshift z = 4.692. With a spectral energy distribution constructed from near-infrared spectra and broad-band photometry, the AD models find a black hole mass of $\log (M_{\rm {AD}}/{\rm M}_{\odot }) = 10.31^{+0.17}_{-0.14}$ with an anisotropy-corrected bolometric luminosity of $\log {(L_{\rm {bol}}/\rm {erg\, s^{-1}})} = 47.87 \pm 0.10$ and derive an Eddington ratio of $0.29^{+0.11}_{-0.10}$ as well as a radiative efficiency of $0.09^{+0.05}_{-0.03}$. Using the near-infrared spectra, we estimate the single-epoch virial black hole mass estimate to be log (MSE/M⊙) = 10.33 ± 0.08, with a monochromatic luminosity at 3000 Å of $\log {(L(\rm {3000{\AA}})/\rm {erg\, s^{-1}})} = 47.66 \pm 0.01$. As an independent approach, AD fitting has the potential to complement the single-epoch virial mass method in obtaining stronger constraints on properties of massive quasar black holes across a wide range of redshifts.

Observational predictions of LQG motivated polymerized black holes and constraints from Sgr A* and M87*

Loop quantum gravity inspired partial polymer quantization in four-dimensional spacetime leads to a globally regular black hole with a single horizon. The polymerized black hole metric is characterized by the minimum length parameter k, and mimics the Schwarzschild black hole in the weak-field limit. We present an analytic and numerical investigation of the strong gravitational lensing and shadow morphology to determine the observational impacts of quantum effects. Interestingly, the light deflection angle, the angular separation between the outermost relativistic image, and magnification are significantly larger than those for the Schwarzschild black hole. Using the ray-tracing technique, we simulate the black hole shadows under three distinct optically thin accretion models: static spherical accretion, radially infalling spherical accretion, and the thin accretion disk model. Polymerized black holes' shadow morphology strongly depends on k. We derive constraints on k from the M87* and Sgr A* black hole shadow observations from the Event Horizon Telescope.

The Apparent Absence of Forward Scattering in the HD 53143 Debris Disk

HD 53143 is a mature Sun-like star and host to a broad disk of dusty debris, including a cold outer ring of planetesimals near 90 au. Unlike most other inclined debris disks imaged at visible wavelengths, the cold disk around HD 53143 appears as disconnected “arcs” of material, with no forward-scattering side detected to date. We present new, deeper Hubble Space Telescope Imaging Spectrograph coronagraphic observations of the HD 53143 debris disk and show that the forward-scattering side of the disk remains undetected. By fitting our KLIP-reduced observations via forward modeling with an optically thin disk model, we show that fitting the visible wavelength images with an azimuthally symmetric disk with unconstrained orientation results in an unphysical edge-on orientation that is at odds with recent ALMA observations, while constraining the orientation to that observed by ALMA results in nearly isotropically scattering dust. We show that the HD 53143 host star exhibits significant stellar variations due to spot rotation and revisit age estimates for this system.

Using X-ray continuum-fitting to estimate the spin of MAXI J1305–704

ABSTRACT MAXI J1305–704 is a transient X-ray binary with a black hole primary. It was discovered on 2012 April 9, during its only known outburst. MAXI J1305–704 is also a high inclination low-mass X-ray binary with prominent dip features in its light curves, so we check the full catalogue of 92 Swift/XRT continuous observations of MAXI J1305–704, focusing only on the stable spectra. We select 13 ‘gold’ spectra for which the rms <0.075 and the coronal scattered fraction $f_{\mathrm{sc}} \lesssim 25$ per cent. These ‘gold’ data are optimal thermal-state observations for continuum-fitting modelling, in which the disc extends to the innermost stable circular orbit and is geometrically thin. The black hole spin was unknown for this object before. By utilizing the X-ray continuum fitting method with the relativistic thin disc model kerrbb2 and supplying the known dynamical binary system parameters, we find MAXI J1305–704 has a moderate spin ($a_{*}=0.87_{-0.13}^{+0.07}$) at a 68.3 per cent confidence level. This is the first determination of MAXI J1305–704’s spin.

Universality in the random walk structure function of luminous quasi-stellar objects

Rapidly growing black holes are surrounded by accretion disks that make them the brightest objects in the Universe. Their brightness is known to be variable, but the causes of this are not implied by simple disk models and still debated. Due to the small size of accretion disks and their great distance, there are no resolved images addressing the puzzle. In this work, we study the dependence of their variability on luminosity, wavelength and orbital/thermal timescale. We use over 5,000 of the most luminous such objects with light curves of almost nightly cadence from >5 years of observations by the NASA/ATLAS project, which provides 2 billion magnitude pairs for a structure function analysis. When time is expressed in units of orbital or thermal timescale in thin-disk models, we find a universal structure function, independent of luminosity and wavelength, supporting the model of magneto-rotational instabilities as a main cause. Over a >1 dex range in time, the fractional variability amplitude follows $$\log (A/{A}_{0})\simeq 1/2\times \log (\Delta t/{t}_{{{{\rm{th}}}}})$$ . Deviations from the universality may hold clues as to the structure and orientation of disks. A study of the emission variability of roughly 5,000 of the brightest quasars supports the presence of an optically thick yet geometrically thin accretion disk, and may provide a means of measuring the size and inclination of the disk.

Active Galactic Nuclei Continuum Reverberation Mapping Based on Zwicky Transient Facility Light Curves

We perform a systematic survey of active galactic nuclei (AGNs) continuum lags using ∼3 days cadence gri-band light curves from the Zwicky Transient Facility. We select a sample of 94 type 1 AGNs at z < 0.8 with significant and consistent inter-band lags based on the interpolated cross-correlation function method and the Bayesian method JAVELIN. Within the framework of the “lamp-post” reprocessing model, our findings are: (1) The continuum emission (CE) sizes inferred from the data are larger than the disk sizes predicted by the standard thin-disk model. (2) For a subset of the sample, the CE size exceeds the theoretical limit of the self-gravity radius (12 lt-days) for geometrically thin disks. (3) The CE size scales with continuum luminosity as R CE ∝ L 0.48±0.04 with a scatter of 0.2 dex, analogous to the well-known radius–luminosity relation of broad Hβ. These findings suggest a significant contribution of diffuse continuum emission from the broad-line region (BLR) to AGN continuum lags. We find that the R CE–L relation can be explained by a photoionization model that assumes ∼23% of the total flux comes from the diffuse BLR emission. In addition, the ratio of the CE size and model-predicted disk size anticorrelates with the continuum luminosity, which is indicative of a potential nondisk BLR lag contribution evolving with the luminosity. Finally, a robust positive correlation between the CE size and black hole mass is detected.

Unveiling the disc structure in ultraluminous X-ray source NGC 55 ULX-1

ABSTRACT Ultraluminous X-ray sources (ULXs) are the most extreme among X-ray binaries in which the compact object, a neutron star or a black hole, accretes matter from the companion star, and exceeds a luminosity of $10^{39} \ \rm erg \, s^{-1}$ in the X-ray energy band alone. Despite two decades of studies, it is still not clear whether ULX spectral transitions are due to stochastic variability in the wind or variations in the accretion rate or in the source geometry. The compact object is also unknown for most ULXs. In order to place constraints on to such scenarios and on the structure of the accretion disc, we studied the temporal evolution of the spectral components of the variable source NGC 55 ULX-1. Using recent and archival data obtained with the XMM-Newton satellite, we modelled the spectra with two blackbody components which we interpret as thermal emission from the inner accretion flow and the regions around or beyond the spherization radius. The luminosity–temperature (L–T) relation of each spectral component agrees with the L ∝ T4 relationship expected from a thin disc model, which suggests that the accretion rate is close to the Eddington limit. However, there are some small deviations at the highest luminosities, possibly due to an expansion of the disc and a contribution from the wind at higher accretion rates. Assuming that such deviations are due to the crossing of the Eddington or supercritical accretion rate, we estimate a compact object mass of 6–14 M⊙, favouring a stellar-mass black hole as the accretor.

Improving black hole accretion treatment in hydrodynamical simulations

ABSTRACT The large-Galactic scales are connected to the many orders of magnitude smaller supermassive black hole (SMBH) scales by an episodic cycle of feeding and feedback. Active Galactic nuclei (AGN) are powered by accretion on to SMBH and the majority of AGN energy in near-Eddington regime is produced in thin subpc accretion discs. Currently, it is very difficult to model processes that occur on vastly different scales, ranging from the circumnuclear gas reservoirs at tens to hundreds of parsecs down to the accretion disc scales at &amp;lt;0.01 pc. While subgrid prescriptions used in large-scale or cosmological simulations are able to reproduce large-scale feedback, we propose using a more realistic model in parsec-scale simulations, where it is important to get accurate time-scales to understand how feedback affects gas dynamics and star formation in the vicinity of the AGN. To test our approach we use a subresolution thin accretion disc model coupled to the SMBH in a set of hydrodynamical simulations of a retrograde collision between a gas ring and a molecular cloud in an environment similar to the Galactic Centre using the SPH code Gadget-3. The disc-mediated feeding of the SMBH is relatively smooth and delayed compared to an instantaneous feeding prescription. While the reduction of accretion due to feedback is present in both accretion disc and instantaneous feeding simulations, a clear central cavity appears only in accretion disc runs – hinting that a less volatile accretion phase could have a greater impact on the surrounding gas.

Possible Systematic Rotation in the Mature Stellar Population of a z = 9.1 Galaxy

We present new observations with the Atacama Large Millimeter/submillimeter Array for a gravitationally lensed galaxy at z = 9.1, MACS1149-JD1. [O iii] 88 μm emission is detected at 10σ with a spatial resolution of ∼0.3 kpc in the source plane, enabling the most distant morphokinematic study of a galaxy. The [O iii] emission is distributed smoothly without any resolved clumps and shows a clear velocity gradient with ΔV obs/2σ tot = 0.84 ± 0.23, where ΔV obs is the observed maximum velocity difference and σ tot is the velocity dispersion measured in the spatially integrated line profile, suggesting a rotating system. Assuming a geometrically thin self-gravitating rotation disk model, we obtain , where V rot and σ V are the rotation velocity and velocity dispersion, respectively, still consistent with rotation. The resulting disk mass of M ⊙ is consistent with being associated with the stellar mass identified with a 300 Myr old stellar population independently indicated by a Balmer break in the spectral energy distribution. We conclude that the most of the dynamical mass is associated with the previously identified mature stellar population that formed at z ∼ 15.

Black hole spin measurements based on a thin disc model with finite thickness – I. An example study of MCG−06-30-15

ABSTRACT We present a re-analysis of the XMM–Newton and NuSTAR observing campaigns for the well-studied, X-ray-bright AGN MCG−06-30-15. In particular, we consider a disc model with finite thickness. By fitting the disc reflection spectra in the data, we obtain a black hole spin of 0.87–0.99 (90 per cent confidence range) after taking the thickness of the disc into consideration. Spectral models with a grid of mass accretion rate from 0 to $30{{\,\rm per\,cent}}\,\dot{M}_{\rm Edd}$ are calculated for MCG−06-30-15. This result is obtained by considering a free disc reflection fraction parameter frefl and is consistent with previous measurements based on razor-thin disc models. Besides, an isotropic, point-like geometry, i.e. the ‘lamppost’ geometry, is assumed for the corona in our model. We find that such a geometry overestimates frefl in the data. Therefore, thin disc models with consistent ‘lamppost’ values of frefl provide a worse fit than ones with a free frefl parameter. We discuss possible reasons for the discrepancy between the observed and theoretical values of frefl at the end of the paper. Modifications for the over-simplified lamppost model might be needed when the thickness of the thin disc is considered in future work.

Constraining quasar structure using high-frequency microlensing variations and continuum reverberation

Gravitational microlensing is a powerful tool for probing the inner structure of strongly lensed quasars and for constraining parameters of the stellar mass function of lens galaxies. This is achieved by analysing microlensing light curves between the multiple images of strongly lensed quasars and accounting for the effects of three main variable components: (1) the continuum flux of the source, (2) microlensing by stars in the lens galaxy, and (3) reverberation of the continuum by the broad line region (BLR). The latter, ignored by state-of-the-art microlensing techniques, can introduce high-frequency variations which we show carry information on the BLR size. We present a new method that includes all these components simultaneously and fits the power spectrum of the data in the Fourier space rather than the observed light curve itself. In this new framework, we analyse COSMOGRAIL light curves of the two-image system QJ 0158-4325 known to display high-frequency variations. Using exclusively the low-frequency part of the power spectrum, our constraint on the accretion disk radius agrees with the thin-disk model estimate and the results of previous work where the microlensing light curves were fit in real space. However, if we also take into account the high-frequency variations, the data favour significantly smaller disk sizes than previous microlensing measurements. In this case, our results are only in agreement with the thin-disk model prediction only if we assume very low mean masses for the microlens population, i.e. ⟨M⟩ = 0.01 M⊙. At the same time, including the differentially microlensed continuum reverberation by the BLR successfully explains the high frequencies without requiring such low-mass microlenses. This allows us to measure, for the first time, the size of the BLR using single-band photometric monitoring; we obtain RBLR = 1.6−0.8+1.5 × 1017 cm, in good agreement with estimates using the BLR size–luminosity relation.

Density Profile of the Ambient Circumnuclear Medium in Seyfert 1 Galaxies

Abstract The shape of the ambient circumnuclear medium (ACM) density profile can probe the history of accretion onto the central supermassive black holes in galaxies and the circumnuclear environment. However, due to the limitations of instrument resolution, the density profiles of the ACM for most galaxies remain largely unknown. In this work, we propose a novel method to measure the ACM density profile of active galactic nuclei (AGNs) by the equilibrium between the radiation pressure on the warm absorbers (WAs, a type of AGN outflow) and the drag pressure from the ACM. We study the correlation between the outflow velocity and ionization parameter of WAs in each of the five Seyfert 1 galaxies (NGC 3227, NGC 3783, NGC 4051, NGC 4593, and NGC 5548), inferring that the density profile of the ACM is between n ∝ r −1.7 and n ∝ r −2.15 (n is number density and r is distance) from 0.01 pc to parsec scales in these five AGNs. Our results indicate that the ACM density profile in Seyfert 1 galaxies is steeper than the prediction by the spherically symmetric Bondi accretion model and the simulated results of the hot accretion flow, but more in line with the prediction by the standard thin-disk model.

Accretion disc sizes from continuum reverberation mapping of AGN selected from the ZTF survey

ABSTRACT We present the accretion disc-size estimates for a sample of 19 active galactic nuclei (AGNs) using the optical g-, r-, and i-band light curves obtained from the Zwicky Transient Facility survey. All the AGNs have reliable supermassive black hole (SMBH) mass estimates based on previous reverberation mapping measurements. The multiband light curves are cross-correlated, and the reverberation lag is estimated using the Interpolated Cross-Correlation Function method and the Bayesian method using the javelin code. As expected from the disc-reprocessing arguments, the g − r band lags are shorter than the g − i band lags for this sample. The interband lags for all, but five sources, are larger than the sizes predicted from the standard Shakura Sunyaev (SS) analytical model. We fit the light curves directly using a thin disc model implemented through the javelin code to get the accretion disc sizes. The disc sizes obtained using this model are on an average 3.9 times larger than the prediction based on the SS disc model. We find a weak correlation between the disc sizes and the known physical parameters, namely the luminosity and the SMBH mass. In the near future, a large sample of AGNs covering broader ranges of luminosity and SMBH mass from large photometric surveys would be helpful in a better understanding of the structure and physics of the accretion disc.

The Nature of Black Hole Shadows

Abstract A distinct visual signature occurs in black holes that are surrounded by optically thin and geometrically thick emission regions. This signature is a sharp-edged dip in brightness that is coincident with the black hole’s shadow, which is the projection of the black hole’s unstable-photon region on the observer’s sky. We highlight two key mechanisms that are responsible for producing the sharp-edged dip: (i) the reduction of intensity observed in rays that intersect the unstable-photon region, and thus the perfectly absorbing event horizon, versus rays that do not (blocking); and (ii) the increase of intensity observed in rays that travel along extended, horizon-circling paths near the boundary of the unstable-photon region (path-lengthening). We demonstrate that the black hole shadow is a distinct phenomenon from the photon ring, and that models exist in which the former may be observed but not the latter. Additionally, we show that the black hole shadow and its associated visual signature differ from the more model-dependent brightness depressions associated with thin-disk models because the blocking and path-lengthening effects are quite general for geometrically thick and optically thin emission regions. Consequentially, the black hole shadow is a robust and fairly model-independent observable for accreting black holes that are in the deep sub-Eddington regime, such as low-luminosity active galactic nuclei.

Estimating the Black Hole Spin for the X-Ray Binary MAXI J1820+070

Abstract MAXI J1820+070 is a newly discovered black hole X-ray binary, whose dynamical parameters, namely the black hole mass, the inclination angle, and the source distance, have recently been estimated. Insight-HXMT have observed its entire outburst from 2018 March 14. In this work, we attempted to estimate the spin parameter a *, using the continuum-fitting method and applying a fully relativistic thin disk model to the soft-state spectra obtained by Insight-HXMT. It is well known that a * is strongly dependent on three dynamical parameters in this method, and we have examined two sets of parameters. Adopting our preferred parameters: M = 8.48 − 0.72 + 0.79 M ⊙ , i = 63° ± 3°, and D = 2.96 ± 0.33 kpc, we found a slowly spinning black hole of a * = 0.14 ± 0.09 (1σ), which gives a prograde spin parameter as the majority of other systems show. It is also possible for the black hole to have a retrograde spin (less than 0) if different dynamical parameters are taken.