sub-Keplerian Rotation Research Articles

Density profile of a self-gravitating polytropic turbulent fluid in a rotating disc near to the cloud core

ABSTRACT We obtain two equations (following from two different approaches) for the density profile in a self-gravitating polytropic cylindrically symmetric and rotating turbulent gas disc. The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state of the gas changes from isothermal (in the outer cloud layers) to one of ‘hard polytrope’, and the symmetry changes from spherical to cylindrical. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation describes the balance of the kinetic, thermal, and gravitational energy of a fluid element. We also introduce a method for approximating density profile solutions (in a power-law form), leading to the emergence of three different regimes. We apply, as well, dynamical analysis of the motion of a fluid element. Only one of the regimes is in accordance with the two approaches (energy and force balance). It corresponds to a density profile of a slope −2, polytropic exponent 3/2, and sub-Keplerian rotation of the disc, when the gravity is balanced by the thermal pressure. It also matches with some observations and numerical works and, in particular, leads to a second power-law tail (of a slope ∼−1) of the density distribution function in dense, self-gravitating cloud regions.

High-sensitivity VLBI observations of water masers in the Seyfert galaxy NGC 1068

Abstract We present observational results of water vapor maser emission with our high-sensitivity 22 GHz very long baseline interferometry (VLBI) imaging of the Seyfert galaxy NGC 1068. In this galaxy, there are the following four nuclear radio sources; NE, C, S1, and S2. Among them, the S1 component has been identified as the nucleus while the C component has been considered as attributed to the radio jet. In our VLBI observation, we find the following two types of water maser emission at the S1 component. One is a linearly aligned component that is considered as an edge-on disk with an inner radius of 0.62 pc. The dynamical mass enclosed within the inner radius was estimated to be 1.5 × 107 M⊙ by assuming the circular Keplerian motion. Note, however, that the best-fitting rotation curve shows a sub-Keplerian rotation (v ∝ r−0.24±0.10). The other is water maser emission distributed around the rotating disk component up to 1.5 pc from the S1 component, suggesting a bipolar outflow from the S1 component. Further, we detected water maser emission in the C component for the first time with VLBI, and discovered a ring-like distribution of water maser emission. It is known that a molecular cloud is associated with the C component (both HCN and HCO+ emission lines are detected by ALMA). Therefore, the ring-like maser emission can be explained by the jet collision to the molecular cloud. However, if these ring-like water masing clouds constitute a rotating ring around the C component, it is likely that the C component also has a supermassive black hole with a mass of ∼106 M⊙ that could be supplied from a past minor merger of a nucleated satellite galaxy.

Kinematical Signs of Dust Trapping and Feedback in a Local Pressure Bump in the Protoplanetary Disk around HD 142527 Revealed with ALMA

Abstract We analyzed the archival data of the continuum emission at six wavelengths from 3 to 0.4 mm and 13CO and C18O (1–0, 2–1, and 3–2) lines in the protoplanetary disk around HD 142527 obtained with the Atacama Large Millimeter/submillimeter Array. We performed fitting to the spectral energy distributions obtained at the six wavelengths with the graybody slab models to estimate the distributions of the dust surface density and spectral index of dust absorption coefficient β. We also estimated the distribution of the gas column density by fitting the C18O spectra and measured the disk rotation by fitting the Keplerian disk models to the C18O data. We found super- and sub-Keplerian rotation inside and outside the dust ring in the northwest in the HD 142527 disk, suggestive of the presence of a local pressure bump. In comparison with our estimated dust and gas distributions, the location of the pressure bump is coincident with the region showing a three times higher dust density and a three times lower gas-to-dust mass ratio than the mean values in the disk, suggesting dust trapping in the pressure bump. Nevertheless, there is no correlation between our derived β distribution and the location of the pressure bump. In addition, we found that the width of the dust ring is comparable to or larger than the width of the pressure bump, which could suggest that dust feedback is significant in the pressure bump.

Magnetic Field Structure of Orion Source I

Abstract We observed polarization of the SiO rotational transitions from Orion Source I (SrcI) to probe the magnetic field in bipolar outflows from this high-mass protostar. Both 43 GHz J = 1–0 and 86 GHz J = 2–1 lines were mapped with ∼20 au resolution, using the Very Large Array (VLA) and Atacama Large Millimeter/Submillimeter Array (ALMA), respectively. The 28SiO transitions in the ground vibrational state are a mixture of thermal and maser emission. Comparison of the polarization position angles in the J = 1–0 and J = 2–1 transitions allows us to set an upper limit on possible Faraday rotation of 104 rad m−2, which would twist the J = 2–1 position angles typically by less than 10°. The smooth, systematic polarization structure in the outflow lobes suggests a well-ordered magnetic field on scales of a few hundred au. The uniformity of the polarization suggests a field strength of ∼30 mG. It is strong enough to shape the bipolar outflow and possibly lead to sub-Keplerian rotation of gas at the base of the outflow. The strikingly high fractional linear polarizations of 80%–90% in the 28SiO v = 0 masers require anisotropic pumping. We measured circular polarizations of 60% toward the strongest maser feature in the v = 0 J = 1–0 peak. Anisotropic resonant scattering is likely to be responsible for this circular polarization. We also present maps of the 29SiO v = 0 J = 2–1 maser and several other SiO transitions at higher vibrational levels and isotopologues.

Magnetohydrodynamics in a cylindrical shearing box

ABSTRACT We develop a framework for magnetohydrodynamical (MHD) simulations in a local cylindrical shearing box by extending the formulation of the Cartesian shearing box. We construct shearing-periodic conditions at the radial boundaries of a simulation box from the conservation relations of the basic MHD equations, taking into account the explicit radial dependence of physical quantities. We demonstrate quasi-steady mass accretion, which cannot be handled by the standard Cartesian shearing box model, with an ideal MHD simulation in a vertically unstratified cylindrical shearing box for up to 200 rotations. In this demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation, whereas the sound velocity and the initial Alfvén velocity have the same radial dependence as that of the Keplerian velocity. Inward mass accretion is induced to balance the outward angular momentum flux of the MHD turbulence triggered by the magnetorotational instability in a self-consistent manner. We discuss detailed physical properties of the saturated magnetic field, in comparison to the results of a Cartesian shearing box simulation.

The FRIED grid of mass-loss rates for externally irradiated protoplanetary discs

We present an open access grid of 3930 calculations of externally evaporating protoplanetary discs. This spans a range of disc sizes (1-400AU), disc masses, UV field strengths (10-10$^4$G$_0$) and stellar masses (0.05-1.9M$_\odot$). The grid is publicly available for download, and offers a means of cheaply including external photoevaporation in disc evolutionary calculations. It can also be queried using an online tool for quick estimates of instantaneous mass loss rates (e.g for convenient evaluation of real observed systems). The `FRIED' grid itself illustrates that for discs around stars $\leq0.3$M$_\odot$ external photoevaporation is effective down to small radii ($<50$AU) down to UV fields at least as weak as 10G$_0$. At the other end of the scale, in a $10^4$G$_0$ environment photoevaporation is effective down to 1AU even for stellar masses at least as high as 1.9M$_\odot$. We also illustrate in which regimes CO survives in the photoevaporative outflow for significant mass loss rates; marking a system a good candidate to detect external photoevaporation in weak-intermediate UV environments through sub-Keplerian rotation. Finally we make illustrative mass loss rate estimates for discs in Taurus based on the Guilloteau et al. (2011) star-disc parameters, finding that around half are expected to have both significant mass loss and retain CO in the photoevaporative outflow.

The linear theory of tidally excited spiral density waves: application to CV and circumplanetary disks

We revisit linear tidal excitation of spiral density waves in the disks of cataclysmic variables (CVs), focusing on scalings with orbital Mach number in order to bridge the gap between numerical simulations and real systems. If an inner Lindblad resonance (ILR) lies within the disk, ingoing waves are robustly excited, and the angular-momentum flux they carry is independent of Mach number. But in most CVs, the ILR lies outside the disk. The wave flux and its scaling with Mach number are then very sensitive to conditions near the disk edge. If the temperature and sound speed vanish there, excitation tends to be exponentially suppressed. If the Mach number remains finite in the outer parts but the radial and vertical density scale lengths become comparable due to subkeplerian rotation, resonance can occur with acoustic-cutoff and stratification frequencies. These previously neglected resonances excite waves, but the Mach-number scaling remains very steep if the radial scale length decreases gradually. The scaling can be less strong - algebraic rather than exponential - if there are sharp changes in surface density at finite sound speed. Shocks excited by streamline-crossing or by the impact of the stream from the companion are unlikely to be important for the angular-momentum budget, at least in quiescence. Our results may also apply to circumplanetary disks, where Mach numbers are likely lower than in CVs.

Formation and Structure of Magnetized Protoplanetary Disks

AbstractProtoplanetary disks are expected to form through the gravitational collapse of magnetized rotating dense cores. We discuss the structure and emission of models of accretion disks threaded by a poloidal magnetic field and irradiated by the central star, expected to form in this process (Shu et al. 2007; Lizano et al. 2016). The poloidal magnetic field produces sub-keplerian rotation of the gas which can accelerate planet migration (Adams et al. 2009). It can make the disk more stable against gravitational perturbations (Lizano et al. 2010). Also, the magnetic compression can reduce the disk scale height with respect to nonmagnetic disks. We find that the mass-to-flux ratio λ is a critical parameter: disks with a weaker magnetization (high values of λ) are denser and hotter and emit more at millimeter wavelengths than disks with a stronger magnetization (low values of λ). Applying these models to the millimeter observations of the disk around the young star HL Tau indicate the large grains are present at the external radii in order to reproduce the observed 7 mm emission that extends up to 100 AU (Tapia &amp; Lizano 2017). In the near future, observations with ALMA and VLA will be able to determine the level of magnetization of protoplanetary disks, which will be important to understand their formation and evolution.

Radiation-pressure-driven sub-Keplerian rotation of the disc around the AGB star L2Pup

AbstractWe study the sub-Keplerian rotation and dust content of the circumstellar material around the asymptotic giant branch (AGB) star L2 Puppis. We find that the thermal pressure gradient alone cannot explain the observed rotation profile. We find that there is a family of possible dust populations for which radiation pressure can drive the observed sub-Keplerian rotation. This set of solutions is further constrained by the spectral energy distribution (SED) of the system, and we find that a dust-to-gas mass ratio of ∼10−3 and a maximum grain size that decreases radially outwards can satisfy both the rotation curve and SED. These dust populations are dynamically tightly coupled to the gas azimuthally. However, grains larger than ∼ 0.5 μm are driven outwards radially by radiation pressure at velocities ∼5 km s−1, which implies a dust replenishment rate of ∼3 × 10−9 M⊙ yr−1. This replenishment rate is consistent with observational estimates to within uncertainties. Coupling between the radial motion of the dust and gas is weak and hence the gas does not share in this rapid outward motion. Overall, we conclude that radiation pressure is a capable and necessary mechanism to explain the observed rotation profile of L2 Pup, and offers other additional constraints on the dust properties.

On the Magnetic Field of the Ultraluminous X-Ray Pulsar M82 X-2

Abstract The discovery of the ultraluminous X-ray pulsar M82 X-2 has stimulated lively discussion on the nature of the accreting neutron star. In most of the previous studies the magnetic field of the neutron star was derived from the observed spin-up/down rates based on the standard thin, magnetized accretion disk model. However, under super-Eddington accretion the inner part of the accretion disk becomes geometrically thick. In this work we consider both radiation feedback from the neutron star and the sub-Keplerian rotation in a thick disk and calculate the magnetic moment–mass accretion rate relations for the measured rates of spin change. We find that the derived neutron star's dipole magnetic field depends on the maximum accretion rate adopted, but is likely ≲1013 G. The predicted accretion rate change can be used to test the proposed models by comparison with observations.

Simplified models of circumstellar morphologies for interpreting high-resolution data

Equatorial density enhancements (EDEs) are a very common astronomical phenomenon. Studies of the circumstellar environments (CSE) of young stellar objects and of evolved stars have shown that these objects often possess these features. These are believed to originate from different mechanisms, ranging from binary interactions to the gravitational collapse of interstellar material. Quantifying the effect of the presence of this type of EDE on the observables is essential for a correct interpretation of high-resolution data. We seek to investigate the manifestation in the observables of a circumstellar EDE, to assess which properties can be constrained, and to provide an intuitive bedrock on which to compare and interpret upcoming high-resolution data (e.g. \emph{ALMA} data) using 3D models. We develop a simplified analytical parametrised description of a 3D EDE, with a possible substructure such as warps, gaps, and spiral instabilities. In addition, different velocity fields (Keplerian, radial, super-Keplerian, sub-Keplerian and rigid rotation) are considered. The effect of a bipolar outflow is also investigated. The geometrical models are fed into the 3D radiative transfer code {\tt LIME}, that produces 3D intensity maps throughout velocity space. We investigate the spectral signature of the $J$=3$-$2 up to $J$=7$-$6 rotational transitions of CO in the models, as well as the spatial aspect of this emission by means of channel maps, wide-slit position-velocity (PV) diagrams, stereograms, and spectral lines. Additionally, we discuss methods of constraining the geometry of the EDE, the inclination, the mass-contrast between the EDE and the bipolar outflow, and the global velocity field. Finally, we simulated \emph{ALMA} observations...

Kinematics of the inner thousand AU region around the young massive star AFGL 2591–VLA3: a massive disk candidate?

[Context] Recent detections of disks around young high-mass stars support the idea of massive star formation through accretion rather than coalescence, but the detailed kinematics in the equatorial region of the disk candidates is not well known, which limits our understanding of the accretion process. [Aims] This paper explores the kinematics of the gas around a young massive star with millimeter-wave interferometry to improve our understanding of the formation of massive stars though accretion. [Methods] We use Plateau de Bure interferometric images to probe the environment of the nearby (~1 kpc) and luminous (~20000 Lsun) high-mass (10-16 Msun) young star AFGL 2591-VLA3 in continuum and in lines of HDO, H218O and SO2 in the 115 and 230 GHz bands. Radiative transfer calculations are employed to investigate the kinematics of the source. [Results] At ~0.5" (500 AU) resolution, the line images clearly resolve the velocity field of the central compact source (diameter of ~ 800 AU) and show linear velocity gradients in the northeast-southwest direction. Judging from the disk-outflow geometry, the observed velocity gradient results from rotation and radial expansion in the equatorial region of VLA3. Radiative transfer calculations suggest that the velocity field is consistent with sub-Keplerian rotation plus Hubble-law like expansion. The line profiles of the observed molecules suggest a layered structure, with HDO emission arising from the disk mid-plane, H218O from the warm mid-layer, and SO2 from the upper disk. [Conclusions] We propose AFGL 2591-VLA3 as a new massive disk candidate, with peculiar kinematics. The rotation of this disk is sub-Keplerian, probably due to magnetic braking, while the stellar wind may be responsible for the expansion of the disk. The expansion motion [...]

Magnetic fields during the early stages of massive star formation - II. A generalized outflow criterion

Numerical simulations of outflows formed during the collapse of 100-M⊙ cloud cores are presented. We derive a generalized criterion from magnetohydrodynamical wind theory to analyse the launching mechanism of these outflows. The criterion is successfully applied to the whole outflow structure and cases with sub-Keplerian disc rotation. It allows us to decide whether an outflow is driven centrifugally or by the toroidal magnetic pressure. We show that quantities such as the magnetic field line inclination or the ratio of the toroidal to poloidal magnetic field alone are insufficient to determine the driving mechanism of outflows. By performing 12 simulations with variable initial rotational and magnetic energies, we are able to study the influence of the initial conditions on the properties of outflows and jets around massive protostars in detail. Our simulations reveal a strong effect of the magnetic field strength on the morphology of outflows. In runs with weak fields or high rotational energies, well-collimated, fast jets are observed, whereas for strong fields poorly collimated, low-velocity outflows are found. We show that the occurrence of a fast jet is coupled to the existence of a Keplerian protostellar disc. Despite the very different morphologies, all outflows are launched from the discs by centrifugal acceleration with the toroidal magnetic field increasingly contributing to the gas acceleration further away from the discs. The poor collimation of the outflows in runs with strong magnetic fields is a consequence of the weak hoop stresses. This in turn is caused by the slow build-up of a toroidal magnetic field due to strongly sub-Keplerian disc rotation. The mass and momentum outflow rates are of the order of 10−4 M⊙ yr−1 and 10−4 M⊙ km s−1 yr−1, respectively. The mass ejection/accretion ratios scatter around a mean of 0.3 in accordance with observational and analytical results. Based on our results, we suggest an evolutionary scenario for the earliest stage of massive star formation in which initially poorly collimated outflows develop, which successively get better collimated during their evolution due to the generation of fast jets.

Stability of cloud orbits in the broad-line region of active galactic nuclei

We investigate the global dynamic stability of spherical clouds in the Broad Line Region (BLR) of Active Galactic Nuclei (AGN), exposed to radial radiation pressure, gravity of the central black hole (BH), and centrifugal forces assuming the clouds adapt their size according to the local pressure. We consider both, isotropic and anisotropic light sources. In both cases, stable orbits exist also for very sub-Keplerian rotation for which the radiation pressure contributes substantially to the force budget. We demonstrate that highly eccentric, very sub-Keplerian stable orbits may be found. This gives further support for the model of Marconi et al. 2008, who pointed out that black hole masses might be significantly underestimated if radiation pressure is neglected. That model improved the agreement between black hole masses derived in certain active galaxies based on BLR dynamics, and black hole masses derived by other means in other galaxies by inclusion of a luminosity dependent term. For anisotropic illumination, energy is conserved for averages over long time intervals, only, but not for individual orbits. This leads to Rosetta orbits that are systematically less extended in the direction of maximum radiation force. Initially isotropic relatively low column density systems would therefore turn into a disk when an anisotropic AGN is switched on.

MIGRATION OF EXTRASOLAR PLANETS: EFFECTS FROM X -WIND ACCRETION DISKS

Magnetic fields are dragged in from the interstellar medium during the gravitational collapse that forms star/disk systems. Consideration of mean field magnetohydrodynamics (MHD) in these disks shows that magnetic effects produce subkeplerian rotation curves and truncate the inner disk. This letter explores the ramifications of these predicted disk properties for the migration of extrasolar planets. Subkeplerian flow in gaseous disks drives a new migration mechanism for embedded planets and modifies the gap opening processes for larger planets. This subkeplerian migration mechanism dominates over Type I migration for sufficiently small planets (m_P < 1 M_\earth) and/or close orbits (r < 1 AU). Although the inclusion of subkeplerian torques shortens the total migration time by only a moderate amount, the mass accreted by migrating planetary cores is significantly reduced. Truncation of the inner disk edge (for typical system parameters) naturally explains final planetary orbits with periods P=4 days. Planets with shorter periods P=2 days can be explained by migration during FU-Ori outbursts, when the mass accretion rate is high and the disk edge moves inward. Finally, the midplane density is greatly increased at the inner truncation point of the disk (the X-point); this enhancement, in conjunction with continuing flow of gas and solids through the region, supports the in situ formation of giant planets.

On the large-scale outflows in active galactic nuclei: consequences of coupling the mass supply rate and accretion luminosity

(Abridged) We present two-dimensional hydrodynamical simulations of slowly rotating gas that is under the influence of the gravity of a super massive black hole and is irradiated by a thin UV accretion disc and a spherical X-ray corona. We calculate the accretion luminosity of a system based on the accretion-rate which is assumed to be equal to the mass-supply rate at the radius of ~10^-2 pc. For the models with high temperature gas at large radii (~10 pc) and high luminosities, we find a strong correlation between the mass-outflow rate (Mdot_out) and the luminosity (L). The power law index (q) describing the Mdot_out-L relation is q=2.0(+/-0.1), which is very similar to that for radiation-driven stellar and disc wind models. More surprisingly, for high density at large radii, we find steady state solutions with the accretion luminosity exceeding the Eddington limit. The super-Eddington accretion proceeds in the equatorial region and is possible because the radiation flux from the disc is significantly reduced in the equatorial direction due to the geometrical foreshortening effect. In all models, an outflow is driven from an inflow with sub-Keplerian rotation. For high temperature at large radii, the inflow occurs over a wide range of the polar angles, and the outflow occurs in a relatively narrow polar cone. However, for the super-Eddington cases with low temperature at large radii, the inflow persists only very close to the equatorial plane, resembling a thin accretion disc, while the outflow arises in a wide range of radii and polar angles. The geometry of this extreme inflow-outflow solution is very similar to a radiation-driven wind from a luminous Keplerian accretion disc.

The Magnetorotational Instability in Core‐Collapse Supernova Explosions

We investigate the action of the magnetorotational instability (MRI) in the context of iron-core collapse. Exponential growth of the field on the timescale Ω-1 by the MRI will dominate the linear growth process of field-line "wrapping" with the same characteristic time. We examine a variety of initial rotation states, with solid-body rotation or a gradient in rotational velocity, that correspond to models in the literature. A relatively modest value of the initial rotation, a period of ~10 s, will give a very rapidly rotating proto-neutron star and hence strong differential rotation with respect to the infalling matter. We assume conservation of angular momentum on spherical shells. Rotational distortion and the dynamic feedback of the magnetic field are neglected in the subsequent calculation of rotational velocities. In our rotating and collapsing conditions, a seed field is expected to be amplified by the MRI and to grow exponentially to a saturation field. Results are discussed for two examples of saturation fields, a fiducial field that corresponds to vA = rΩ and a field that corresponds to the maximum growing mode of the MRI. We find, as expected, that the shear is strong at the boundary of the newly formed proto-neutron star and, unexpectedly, that the region within the stalled shock can be subject to strong MHD activity. Modest initial rotation velocities of the iron core result in sub-Keplerian rotation and a sub-equipartition magnetic field that nevertheless produce substantial MHD luminosity and hoop stresses: saturation fields of order 1015-1016 G can develop ~300 ms after bounce with an associated MHD luminosity of ~1052 ergs s-1. Bipolar flows driven by this MHD power can affect or even cause the explosions associated with core-collapse supernovae.

Instability of an accretion disk with a magnetically driven wind

We present a linear analysis of the stability of accretion disks in which angular momentum is removed by the magnetic torque exerted by a centrifugally driven wind. The effects of the dependence of the wind torque on field strength and inclination, the sub-Keplerian rotation due to magnetic forces, and the compression of the disk by the field are included. A WKB dispersion relation is derived for the stability problem. We find that the disk is always unstable if the wind torque is strong. The growth time scale of the instability can be as short as the orbital time scale. The instability is mainly the result of the sensitivity of the mass flux to changes in the inclination of the field at the disk surface. Magnetic diffusion in the disk stabilizes if the wind torque is small.

X‐Ray Lines from Hot Flows around White Dwarfs: Application to SS Cygni

Rather than accreting via a disk, some White Dwarfs (WDs) in quiescent Dwarf Novae (DN) could accrete via an Advection-Dominated Accretion Flow (ADAF) possibly responsible for the X-ray Bremsstrahlung emission observed. Such a hot accretion flow is also expected to produce characteristic thermal line emission. Using SS Cyg as a specific example, we show that knowing a priori the inclination and the WD mass in quiescent DN makes X-ray line diagnostics powerful probes of the flow structure in these systems. Current X-ray instruments can discriminate, from their width, between lines emitted from a flow with a Keplerian rotation rate and those emitted at a substantially sub-Keplerian rate. This could be used to observationally test the property of energy advection, which is at the origin of the partial radial pressure support by the hot gas and the sub-Keplerian rotation rate in an ADAF.

Emergent Spectra from Slim Accretion Disks in Active Galactic Nuclei

Recently the vertical structure of accretion disks has received much attention because of the available comparison with observations of the big blue bump, but all the calculations are based on the standard accretion disk model. In this paper we calculate the vertical structure and the emergent spectrum based on the radial structure of slim disks from the height-averaged equations. With the α-prescription of energy generation, we obtain the density profile as a Gaussian distribution, then solve the energy transfer problem in the z-direction. We find that the sub-Keplerian rotation affects the density profile in the z-direction. The advection process plays significant roles in the emergent spectrum, especially for high accretion rates. We show that there are two prominent characteristics of the spectrum: the presence of a maximum frequency in the emergent spectrum, which is very weakly dependent on the accretion rate, and a flattened component. These results are beyond the scope of explanation of the standard model of accretion disks even for the model with the modified blackbody spectrum. The present model is suitable for a wide range of disk parameters.