On the Critical Mass Ratio for the 3:1 Resonance in Accretion Disks

Optically thick, geometrically thin accretion disks (ADs) around supermassive black holes are thought to contribute to broad-line emission in type-1 active galactic nuclei (AGN). However, observed emission line profiles most often deviate from those expected from a rotating disk, and the role of ADs in contributing to broad Balmer lines and high-ionization UV lines such as CIVλ1549 in radio-loud (RL or “jetted”) AGN remains unclear. We first quantified the low-ionization broad emission line properties of jetted quasars in the main sequence context. We confirm that broad emission lines show large redward asymmetry both in Hβ and Mg IIλ2800, and an unbiased comparison matching black hole mass and Eddington ratio suggests that the most powerful RL quasars show the highest redward asymmetries in Hβ in the general population of AGN. These shifts can be accounted for gravitational and transverse redshift effects, especially for black hole masses larger than MBH ≈ 108.7 M⊙. The analysis of the extremely jetted quasar 3C 47 added another piece to the puzzle: not only are the low ionization profiles of 3C 47 well-described by a relativistic Keplerian AD model, with disk emission between ≈ 100 and ≈ 1000 gravitational radii, but also the high-ionization line profiles can be understood as a combination of disk plus a failed wind contribution that is in turn hiding the disk emission. Constraints on radio properties and line profile variability suggest that the scenario of 3C 47 might involve the presence of a second black hole with secondary-to-primary mass ratio ∼ 0.5−1. We conjecture that the double peakers — type-1 AGN with Balmer line profiles consistent with AD emission — might have their emission truncated by the sweeping effect of a second black hole, and we analyze the implications for the general AGN population.

We present optical photometry of XTE J2123-058 taken in 1999 and 2000, during its quiescent state. The dominant feature of our R-band light curve is the ellipsoidal modulation of the secondary star; however, in order to fit this satisfactorily, we require additional components that comprise an X-ray-heated Roche lobe-filling secondary star and an accretion disk bulge, i.e., where the gas stream impacts the accretion disk. The observed dip near phase 0.8 is interpreted as the eclipse of inner parts of the accretion disk by the bulge. This scenario is highly plausible given the high binary inclination. Our fits allow us to constrain the size of the quiescent accretion disk to lie in the range (0.26-0.58)RL1 (68% confidence). Using the distance of 9.6 kpc and the X-ray flux inferred from the heated hemisphere of the companion, we obtain an unabsorbed X-ray luminosity of 1.2 × 1033 ergs s-1 for XTE J2123-058 in quiescence. From the observed quiescent optical/IR colors, we find that the power-law index (-1.4) for the spectral distribution of the accretion disk compares well with other quiescent X-ray transients. We also reanalyze the optical light curves of the soft X-ray transient XTE J2123-058 taken during its outburst and decay in 1998. We use a robust method to fit the data using a refined X-ray binary model. The model computes the light arising from a Roche lobe-filling star and flared accretion disk irradiated by X-rays and calculates the effects of shadowing and mutual star/disk eclipses. We obtain relatively accurate values for the binary inclination and mass ratio, which when combined with spectroscopic results obtained in Paper II, gives a neutron star mass in the range 1.04-1.56 M☉ (68% confidence).

This study investigates the interference mechanism between vortex-induced vibration (VIV) and galloping at low mass ratios through numerical simulations of three prismatic sections at a Reynolds number of 200. Three distinct modes of VIV-galloping interference are identified, exhibiting characteristic variations in the vibration amplitude vs reduced velocity relationship across different mass ratios: (i) in the VIV-dominant mode, galloping is suppressed below a critical mass ratio; (ii) the galloping-dominant mode demonstrates increasing galloping amplitude with decreasing mass ratio at a given reduced velocity, with no observable critical mass ratio; (iii) the reattachment-suppressed mode involves boundary layer separation followed by reattachment, which weakly suppresses galloping, consequently, increased damping thereby reinstates galloping vibrations. The three modes exhibit different numbers of inflection points in their respective force coefficient vs angle of attack curves under quasi-steady theory. However, quasi-steady theory is limited in quantifying the influence of mass ratio, necessitating the adoption of the forced motion method incorporating energy transfer for further analysis. Results demonstrate that the single-frequency forced motion method accurately predicts the free vibration response at high mass ratios. However, it fails to adequately represent the pronounced vibration effects induced by significant vortex shedding on the prism at low mass ratios. Incorporating the amplitude component at the vortex shedding frequency enables effective characterization of the distinct VIV-galloping interference behaviors observed under low mass ratio conditions.

We suggest a model of the advection-dominated accretion flow (ADAF) with magnetically driven outflows to explain the hysteretic state transition observed in X-ray binaries (XRBs). The transition from a thin disk to an ADAF occurs when the mass accretion rate is below a critical value. The critical mass accretion rate for the ADAF can be estimated by equating the equilibration timescale to the accretion timescale of the ADAF, which is sensitive to its radial velocity. The radial velocity of thin disks is very small, which leads to the advection of the external field in thin disks becoming very inefficient. ADAFs are present in the low/hard states of XRBs, and their radial velocity is large compared with the thin disk. The external field can be dragged inward efficiently by the ADAF, so a strong large-scale magnetic field threading the ADAF can be formed, which may accelerate a fraction of gas in the ADAF into the outflows. Such outflows may carry away a large amount of angular momentum from the ADAF, which significantly increases the radial velocity of the ADAF. This leads to a high critical mass accretion rate, below which an ADAF with magnetic outflows can survive. Our calculations show that the critical luminosity of the ADAF with magnetic outflows can be one order of magnitude higher than that for a conventional ADAF, if the ratio of gas to magnetic pressure in the disk. This can naturally explain the hysteretic state transition observed in XRBs.

Using smoothed particle hydrodynamics, we numerically simulate steady state accretion discs for Cataclysmic Variable Dwarf Novae systems that have a secondary-to-primary mass ratio (0.35 \le q \le 0.55). After these accretion discs have come to quasi-equilibrium, we rotate each disc out of the orbital plane by (\delta = (1, 2, 3, 4, 5,) or (20)^{o}) to induce negative superhumps. For accretion discs tilted $5^{o}$, we generate light curves and associated Fourier transforms for an atlas on negative superhumps and retrograde precession. Our simulation results suggest that accretion discs need to be tilted more than three degrees for negative superhumps to be statistically significant. We also show that if the disc is tilted enough such that the gas stream strikes a disc face, then a dense cooling ring is generated near the radius of impact. In addition to the atlas, we study these artificially tilted accretion discs to find the source to negative superhumps. Our results suggest that the source is additional light from innermost disc annuli, and this additional light waxes and wanes with the amount of gas stream overflow received as the secondary orbits. The nodes, where the gas stream transitions from flowing over to under the disc rim (and vice versa), precess in the retrograde direction.

In the hierarchical galaxy formation model, today's galaxies are the product of frequent galaxy merging, triggering the activity of active galactic nuclei and forming a supermassive black hole binary. A binary may become stalling at the parsec scale and is expected to be detected in nearby normal galaxies, which is inconsistent with observations. In this paper, we investigate the interaction of the supermassive binary black holes (SMBBHs) and an accretion disc and show that the stalling can be avoided due to the interaction and a rapid coalescence of SMMBHs can be reached. A binary formed during galaxy merging within Hubble time is most likely inclined with a random inclination angle and twists the accretion disc, aligning the inner part of the disc with the orbital plane on a time-scale ∼10 3 yr. The twisted inner disc subsequently realigns the rotating central supermassive black hole on a time-scale <∼10 5 yr due to the Bardeen-Petterson effect. It is shown that the detected X-shaped structure in some FR II radio galaxies may be due to the interaction-realignment of the binary and accretion disc occurring within the parsec scale of the galaxy centre. The configuration is very consistent with the observations of X-shaped radio sources. The X-shaped radio feature forms only in FR II radio sources due to the strong interaction between the binary and a standard disc, while the absence of X-shaped FR I radio galaxies is due to the fact that the interaction between the binary and the radiatively inefficient accretion flow in FR I radio sources is negligible. The detection rate, λ X ∼ 7 per cent, of the X-shaped structure in a sample of low-luminous FR II radio galaxies implies that the X-shaped feature forms in nearly all FR II radio sources of an average lifetime t life ∼ 10 8 yr. This is consistent with the estimates of the net lifetime of quasi-stellar objects and radio galaxies and with the picture that the activity of active galactic nuclei is triggered by galaxy merging. As the jet orients vertically to the accretion disc, which is supposed to be aligned with the galactic plane of the host galaxy, the old wings in the X-shaped radio sources are expected to be aligned with the minor axis of the host galaxy while the orientation of the active jet distributes randomly. It is suggested by the model that the binary would remain misaligned with the outer disc for most of the disc viscous time or the lifetime of the FR II radio galaxies and the orientation of the jet in most FR II radio galaxies distributes randomly. As the binary-disc interaction in FR I radio galaxies is negligible or a source evolves from FR II to FR I type after the binary becomes aligned with the outer disc, the jets in most FR I radio galaxies are expected to be vertical to the accretion disc and thus the major axis of the host galaxy. We discuss the relationship of X-shaped and double-double radio galaxies (DDRGs) and suggest that all X-shaped radio sources would evolve into DDRGs after the coalescence of the SMBBHs and that most radio sources evolve from FR II to FR I type after an interruption of jet formation, implying that the average size of FR I radio sources is smaller than that of FR II radio galaxies. The model is applied to two X-shaped radio sources 4C +01.30 and 3C 293 and one DDRG source J0116-473 with a bar-like feature. We show that the SMBBHs in the three objects are minor with mass ratio q ∼ 0.1-0.3.

Critical mass in vortex-induced vibration of a cylinder

Orbital period variations of five W-type overcontact binaries, GW Cep, VY Cet, V700 Cyg, EM Lac and AW Vir, are presented based on the analysis of all available times of light minimum. It is discovered that the period of GW Cep is decreasing at a rate of dP/dt = -6.62 x 10(-8) d yr(-1). For VY Cet and V700 Cyg, a cyclic oscillation is found superimposed on a secular period increase, which can be explained either by the light-time effect of an assumed third body or by magnetic activity cycles. For the other two, EM Lac and AW Vir, the periods show a secular increase. GW Cep is a low mass ratio system with q = 0.37, while the others are high mass ratio systems (q = 0.67, 0.65, 0.63 and 0.76, respectively). The period changes of the five sample stars are in good agreement with Qian's conclusion that low mass ratio overcontact binaries usually show a decreasing period, while the periods of high mass ratio systems are increasing. Based on the period variations of 59 overcontact binaries, a statistical investigation of period change is given. It is confirmed that the period change of a W UMa-type binary star is correlated with the mass ratio (q) and with the mass of the primary component (M-1). Meanwhile, some statistical relations (M-1-P, J(s)-M-1, J(s)-M-2 and J(s)-P) for overcontact binaries are presented using the absolute parameters of 78 systems. From these relations, the following results may be drawn: (i) free mass transfer in both directions exists between the components, which is assumed by thermal relaxation oscillation (TRO) theory; (ii) angular momentum loss (AML) can make a W UMa-type star maintain shallow overcontact and not evolve from overcontact to semidetached configurations as proposed by Rahunen; (iii) the evolution of the W UMa-type systems may be oscillation around a critical mass ratio, while the critical mass ratio varies with the mass of the primary component. These results can be plausibly explained by the combination of the TRO and the variable AML via a change of depth of the overcontact, which is consistent with the X-ray and IUE observations.

view Abstract Citations (49) References (24) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Vertically driven resonances in accretion disks Lubow, S. H. Abstract The three-dimensional response of an accretion disk in a close binary system to tidal forcing is investigated. It is noted that both horizontal and vertical motions are generated in the disk and that resonances occur at radii where the tidal forcing frequency matches a natural frequency in the disk. It is found that for every value of the azimuthal wavenumber m, resonances involving vertical motions lie closer to the disk center than the corresponding horizontal resonances. For a wide range of mass ratios of the binary, the m = 2 vertical resonance is found to lie inside the maximum disk radius suggested by Paczynski (1971) where the simple periodic orbits begin to intersect. This resonance in most cases lies outside the inviscid disk radius determined by a no-slip condition between the stream and disk edge. It is noted that if this resonance lies inside the disk, horizontally propagating waves are generated which travel toward the disk center. The process of wave generation transfers disk angular momentum to the orbital angular momentum of the stars and therefore has important consequences on the dynamics of disk accretion. Publication: The Astrophysical Journal Pub Date: April 1981 DOI: 10.1086/158808 Bibcode: 1981ApJ...245..274L Keywords: Astronomical Models; Binary Stars; Dynamic Stability; Resonant Frequencies; Stellar Mass Accretion; Tidal Waves; Fourier Analysis; Fourier Series; Three Dimensional Motion; Wave Propagation; Astrophysics full text sources ADS |

The development of eccentric-mode resonances in accretion discs within binary systems is simulated. The measured rotational rates of the resulting eccentric discs are found to agree with the observed superhump periods of SU UMa stars. This lends support to the eccentric-disc model of superhump formation. In addition, the decline of the superhump period is found to be explained by the inwards propagation of the eccentric mode. Measurements of superhump periods therefore constrain both the mass ratio of a system and the structure of its accretion disc

The accretion disks that power active galactic nuclei (AGN) are thought to house populations of stars and compact objects; after forming binaries these compact objects may merge, begetting gravitational waves (GWs) such as those detected by LIGO and VIRGO. We present a comprehensive study of the early evolution of binaries within AGN disks as their orbits are influenced by the surrounding gas, focusing on eccentric and unequal-mass binaries. Nearly equal-mass binaries behave similarly to their equal-mass counterparts: Prograde binaries inspiral, albeit somewhat slowly, and have their eccentricities damped; retrograde binaries inspiral ∼2–3 times faster than their prograde counterparts, and those with near-equal masses are driven quickly toward near-unity eccentricities. However, the primaries in retrograde binaries with mass ratios of m 2/m 1 ≲ 0.4 experience significantly weaker headwinds and retain substantial accretion disks that help damp binary eccentricities, slowing binary inspirals. Additionally, we find that while accretion drives prograde binaries toward equal masses thanks to the exchange of material between the primary and secondary accretion disks, retrograde binaries are driven slowly toward more extreme mass ratios. Prograde binaries, and generally those with low mass ratios, likely accrete for multiple e-folding timescales before merger. On the other hand, high-mass-ratio retrograde binaries may merge before accreting substantially, potentially approaching merger with detectable eccentricity. Future ground-based GW observatories, with their broader frequency coverage, should be particularly useful for studying these populations.

The activity of active galaxy may be triggered by the merge of galaxies and present-day galaxies are probably the product of successive minor mergers. The frequent galactic merges at high redshift imply that active galaxy harbors supermassive unequal-mass binary black holes in its center at least once during its life time. In this paper, we showed that the recently discovered double-lobed FR II radio galaxies are the remnants of such supermassive binary black holes. The inspiraling secondary black hole opens a gap in the accretion disk and removes the inner accretion disk when it merges into the primary black hole, leaving a big hole of about several hundreds of Schwarzschild radius in the vicinity of the post-merged supermassive black hole and leading to an interruption of jet formation. When the outer accretion disk slowly refills the big hole on a viscous time scale, the jet formation restarts and the interaction of the recurrent jets and the inter-galactic medium forms a secondary pair of lobes. We applied the model to a particular double-lobed radio source B1834+620 and showed that the orbit of the secondary is elliptical with a typical eccentricity $e \simeq 0.68$ and the mass ratio $q$ of the secondary and the primary is $0.01 \la q \la 0.4$. The accretion disk is a standard $\alpha$-disk with $0.01 \la \alpha \la 0.04$ and the ratio of disk half height $H$ and radius $r$ is $\delta \simeq 0.01$. The model predicates that double-lobed radio structure forms only in FR II radio galaxies.

The role of physical turbulent viscosity is to hamper flow dynamics. Such effect, in an accretion disc involves an enhanced radial mass and angular momentum transport in high compressibility conditions. A sticking effect throughout the disc also affects low compressibility disc’s dynamics. Pairs of compressibility-viscosity values, together with initial kinematic conditions at the inner Lagrangian point, can define a well-bound accretion disc, whilst other pairs cannot produce such well-bound structures. In this work, the role of the stellar mass ratio M1/M2 between the compact primary and the companion in a close binary (CB) is also taken into account. Results show that such role is essential in modifying domains where parameters compressibility-viscosity-injection velocity in L1 allow a well defined disc consistency. The hygher the M1/M2 mass ratio, the wider is the domain where the accretion disc shows a well-bound consistent structure.

The merger of supermassive black holes produces millihertz gravitational waves (GWs), which are potentially detectable by the future Laser Interferometer Space Antenna (LISA). Such binary systems are usually embedded in an accretion disk environment at the center of an active galactic nucleus (AGN). Recent studies suggest the plasma environment imposes measurable imprints on the GW signal if the mass ratio of the binary is around q ∼ 10−4 − 10−3. The effect of the gaseous environment on the GW signal is strongly dependent on the disk’s parameters; therefore, it is believed that future low-frequency GW detections will provide us with precious information about the physics of AGN accretion disks. We investigated this effect by measuring the viscous torque via modeling of the evolution of magnetized tori around the primary massive black hole. Using the general relativistic magnetohydrodynamic HARM-COOL code, we performed 2D and 3D simulations of weakly magnetized, thin accretion disks, with a possible truncation and transition to advection-dominated accretion flow. We studied the angular momentum transport and turbulence generated by the magnetorotational instability. We quantified the disk’s effective alpha viscosity and its evolution over time. We applied our numerical results to quantify the relativistic viscous torque on a hypothetical low-mass secondary black hole via a 1D analytical approach, and we estimated the GW phase shift due to the gas environment.

An analysis is presented of a numerical investigation of the dynamics and geometry of accretion discs in binary systems with mass ratios q < 0.1, applicable to ultra-compact X-ray binaries, AM CVn stars and very short period cataclysmic variables. The steady-state geometry of the disc in the binary reference frame is found to be quite different from that expected at higher mass ratios. For q ~ 0.1, the disc takes on the usual elliptical shape, with the major axis aligned perpendicular to the line of centres of the two stars. However, at smaller mass ratios the elliptical gaseous orbits in the outer regions of the disc are rotated in the binary plane. The angle of rotation increases with gas temperature, but is found to vary inversely with q. At q = 0.01, the major axis of these orbits is aligned almost parallel to the line of centres of the two stars. These effects may be responsible for the similar disc structure inferred from Doppler tomography of the AM CVn star GP Com (Morales-Rueda et al. 2003), which has q = 0.02. The steady-state geometry at low mass ratios is not predicted by an inviscid, restricted three-body model of gaseous orbits; it is related to the effects of tidal-viscous truncation of the disc near the Roche lobe boundary. Since the disc geometry can be inferred observationally for some systems, it is proposed that this may offer a useful diagnostic for the determination of mass ratios in ultra-compact binaries.