scholarly journals Evolution of α Centauri b’s protoplanetary disc

2020 ◽  
Vol 496 (2) ◽  
pp. 2436-2447 ◽  
Author(s):  
Rebecca G Martin ◽  
Jack J Lissauer ◽  
Billy Quarles
Keyword(s):  
Steady State ◽  
Aspect Ratio ◽  
Orbital Period ◽  
Circular Orbit ◽  
Planet Formation ◽  
Eccentric Orbit ◽  
Collision Velocity ◽  
Small Disc ◽  
Hydrodynamical Simulations ◽  
Binary Orbit

ABSTRACT With hydrodynamical simulations we examine the evolution of a protoplanetary disc around α Centauri B including the effect of the eccentric orbit binary companion α Centauri A. The initially circular orbit disc undergoes two types of eccentricity growth. First, the eccentricity oscillates on the orbital period of the binary, Porb, due to the eccentricity of the binary orbit. Secondly, for a sufficiently small disc aspect ratio, the disc undergoes global forced eccentricity oscillations on a time-scale of around $20\, P_{\rm orb}$. These oscillations damp out through viscous dissipation leaving a quasi-steady eccentricity profile for the disc that oscillates only on the binary orbital period. The time-averaged global eccentricity is in the range 0.05–0.1, with no precession in the steady state. The periastrons of the gas particles are aligned to one another. The higher the disc viscosity, the higher the disc eccentricity. With N-body simulations we examine the evolution of a disc of planetesimals that forms with the orbital properties of the quasi-steady protoplanetary disc. We find that the average magnitude of the eccentricity of particles increases and their periastrons become misaligned to each other once they decouple from the gas disc. The low planetesimal collision velocity required for planet formation suggests that for planet formation to have occurred in a disc of planetesimals formed from a protoplanetary disc around α Centauri B, said disc’s viscosity must be have been small and planet formation must have occurred at orbital radii smaller than about $2.5\, \rm au$. Planet formation may be easier with the presence of gas.

scholarly journals How much does turbulence change the pebble isolation mass for planet formation?

2018 ◽  
Vol 615 ◽  
pp. A110 ◽  
Author(s):  
S. Ataiee ◽  
C. Baruteau ◽  
Y. Alibert ◽  
W. Benz
Keyword(s):  
Aspect Ratio ◽  
Planet Formation ◽  
Turbulent Viscosity ◽  
Analytical Calculation ◽  
Radial Pressure ◽  
Stokes Number ◽  
High Viscosity ◽  
Necessary Condition ◽  
Pressure Maximum ◽  
Hydrodynamical Simulations

Context. When a planet becomes massive enough, it gradually carves a partial gap around its orbit in the protoplanetary disk. A pressure maximum can be formed outside the gap where solids that are loosely coupled to the gas, typically in the pebble size range, can be trapped. The minimum planet mass for building such a trap, which is called the pebble isolation mass (PIM), is important for two reasons: it marks the end of planetary growth by pebble accretion, and the trapped dust forms a ring that may be observed with millimetre observations. Aims. We study the effect of disk turbulence on the PIM and find its dependence on the gas turbulent viscosity, aspect ratio, and particles Stokes number. Methods. By means of 2D gas hydrodynamical simulations, we found the minimum planet mass to form a radial pressure maximum beyond the orbit of the planet, which is the necessary condition to trap pebbles. We then carried out 2D gas plus dust hydrodynamical simulations to examine how dust turbulent diffusion impacts particles trapping at the pressure maximum. We finally provide a semi-analytical calculation of the PIM based on comparing the radial drift velocity of solids and the root mean square turbulent velocity fluctuations around the pressure maximum. Results. From our results of gas simulations, we provide an expression for the PIM vs. disk aspect ratio and turbulent viscosity. Our gas plus dust simulations show that the effective PIM can be nearly an order of magnitude larger in high-viscosity disks because turbulence diffuse particles out of the pressure maximum. This is quantified by our semi-analytical calculation, which gives an explicit dependence of the PIM with Stokes number of particles. Conclusions. Disk turbulence can significantly alter the PIM, depending on the level of turbulence in regions of planet formation.

scholarly journals Spectroscopic Binaries in the Open Cluster M67

1992 ◽  
Vol 135 ◽  
pp. 155-157 ◽  
Author(s):  
David W. Latham ◽  
Robert D. Mathieu ◽  
Alejandra A.E. Milone ◽  
Robert J. Davis
Keyword(s):  
Circular Orbit ◽  
Main Sequence ◽  
Open Cluster ◽  
Radial Velocities ◽  
Spectroscopic Binaries ◽  
Eccentric Orbit ◽  
Circular Orbits ◽  
Blue Stragglers ◽  
Short Period ◽  
Blue Straggler

AbstractFor almost 400 members of M67 we have accumulated about 5,000 precise radial velocities. Already we have orbital solutions for more than 32 spectroscopic binaries in M67. Many of these orbits were derived by combining the Palomar and CfA observations, thus extending the time coverage to more than 20 years. The distribution of eccentricity versus period shows evidence for tidal circularization on the main sequence. The transition from circular orbits is fairly clean. Excluding the blue stragglers, the first eccentric orbit has a period of 11.0 days, while the last circular orbit has a period of 12.4 days. For longer periods the distribution of eccentricity is the same as for field stars. The blue straggler S1284 has an eccentric orbit despite its short period of 4.2 days.

scholarly journals Steady-State Approach to Low-Aspect-Ratio Reversed-Field Pinch Nuclear Fusion Reactor

2005 ◽  
Vol 81 (11) ◽  
pp. 932-943 ◽  
Author(s):  
Shoichi SHIINA ◽  
Yasuyuki YAGI ◽  
Hisaya SUGIMOTO ◽  
Hisao ASHIDA ◽  
Yoichi HIRANO ◽  
...  
Keyword(s):  
Steady State ◽  
Aspect Ratio ◽  
Fusion Reactor ◽  
Nuclear Fusion ◽  
Reversed Field Pinch ◽  
Nuclear Fusion Reactor ◽  
Low Aspect Ratio ◽  
Reversed Field

Theory of low Mach number compressible flow in a channel

1996 ◽  
Vol 313 ◽  
pp. 131-145 ◽  
Author(s):  
A. Shajii ◽  
J. P. Freidberg
Keyword(s):  
Steady State ◽  
Mach Number ◽  
Aspect Ratio ◽  
Compressible Flow ◽  
Applied Pressure ◽  
Subsonic Flows ◽  
Low Mach Number ◽  
Large Channel ◽  
Channel Aspect Ratio ◽  
Compressibility Effects

The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large channel aspect ratio L/d ∼ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytical results are presented which show, somewhat unexpectedly, that for forced channel flow, steady-state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady-state friction factor and heat transfer coefficient have no validity.

scholarly journals Influences of protoplanet-induced three-dimensional gas flow on pebble accretion

2020 ◽  
Vol 643 ◽  
pp. A21
Author(s):  
Ayumu Kuwahara ◽  
Hiroyuki Kurokawa
Keyword(s):  
Gas Flow ◽  
Planet Formation ◽  
Early Stage ◽  
Three Dimensional ◽  
Stokes Number ◽  
Flow Shear ◽  
Outer Planets ◽  
Symmetric Structure ◽  
Hydrodynamical Simulation ◽  
Hydrodynamical Simulations

Context. Pebble accretion is among the major theories of planet formation. Aerodynamically small particles, called pebbles, are highly affected by the gas flow. A growing planet embedded in a protoplanetary disk induces three-dimensional (3D) gas flow. In our previous work, Paper I, we focused on the shear regime of pebble accretion and investigated the influence of planet-induced gas flow on pebble accretion. In Paper I, we found that pebble accretion is inefficient in the planet-induced gas flow compared to that of the unperturbed flow, particularly when St ≲ 10−3, where St is the Stokes number. Aims. Following on the findings of Paper I, we investigate the influence of planet-induced gas flow on pebble accretion. We did not consider the headwind of the gas in Paper I. Here, we extend our study to the headwind regime of pebble accretion. Methods. Assuming a nonisothermal, inviscid sub-Keplerian gas disk, we performed 3D hydrodynamical simulations on the spherical polar grid hosting a planet with the dimensionless mass, m = RBondi∕H, located at its center, where RBondi and H are the Bondi radius and the disk scale height, respectively. We then numerically integrated the equation of motion for pebbles in 3D using hydrodynamical simulation data. Results. We first divided the planet-induced gas flow into two regimes: flow-shear and flow-headwind. In the flow-shear regime, where the planet-induced gas flow has a vertically rotational symmetric structure, we find that the outcome is identical to what we obtained in Paper I. In the flow-headwind regime, the strong headwind of the gas breaks the symmetric structure of the planet-induced gas flow. In the flow-headwind regime, we find that the trajectories of pebbles with St ≲ 10−3 in the planet-induced gas flow differ significantly from those of the unperturbed flow. The recycling flow, where gas from the disk enters the gravitational sphere at low latitudes and exits at high latitudes, gathers pebbles around the planet. We derive the flow transition mass analytically, mt, flow, which discriminates between the flow-headwind and flow-shear regimes. From the relation between m, mt, flow and mt, peb, where mt, peb is the transition mass of the accretion regime of pebbles, we classify the results obtained in both Paper I and this study into four groups. In particular, only when the Stokes gas drag law is adopted and m < min(mt, peb, mt, flow), where the accretion and flow regime are both in the headwind regime, the accretion probability of pebbles with St ≲ 10−3 is enhanced in the planet-induced gas flow compared to that of the unperturbed flow. Conclusions. Combining our results with the spacial variety of turbulence strength and pebble size in a disk, we conclude that the planet-induced gas flow still allows for pebble accretion in the early stage of planet formation. The suppression of pebble accretion due to the planet-induced gas flow occurs only in the late stage of planet formation, more specifically, in the inner region of the disk. This may be helpful for explaining the distribution of exoplanets and the architecture of the Solar System, both of which have small inner and large outer planets.

scholarly journals Alignment of a circumbinary disc around an eccentric binary with application to KH 15D

2019 ◽  
Vol 486 (2) ◽  
pp. 2919-2932 ◽  
Author(s):  
Jeremy L Smallwood ◽  
Stephen H Lubow ◽  
Alessia Franchini ◽  
Rebecca G Martin
Keyword(s):  
Linear Theory ◽  
Smoothed Particle Hydrodynamics ◽  
Circular Orbit ◽  
Local Minimum ◽  
Observational Constraints ◽  
Rapid Rate ◽  
Eccentric Orbit ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Alignment Process

ABSTRACT We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoothed particle hydrodynamics (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a few before it moves towards alignment. The results of the SPH simulations agree well with those of linear theory. We investigate the properties of the circumbinary disc/ring around KH 15D. We determine disc properties based on the observational constraints imposed by the changing binary brightness. We find that the inclination is currently at a local minimum and will increase substantially before settling to coplanarity. In addition, the nodal precession is currently near its most rapid rate. The recent observations that show a reappearance of star B impose constraints on the thickness of the layer of obscuring material. Our results suggest that disc solids have undergone substantial inward drift and settling towards to disc mid-plane. For disc masses ∼0.001 M⊙, our model indicates that the level of disc turbulence is low (α ≪ 0.001). Another possibility is that the disc/ring contains little gas.

scholarly journals The Cluster AgeS Experiment (CASE) – VIII. Age and distance of the Globular Cluster 47 Tuc from the analysis of two detached eclipsing binaries

2020 ◽  
Vol 492 (3) ◽  
pp. 4254-4267 ◽  
Author(s):  
I B Thompson ◽  
A Udalski ◽  
A Dotter ◽  
M Rozyczka ◽  
A Schwarzenberg-Czerny ◽  
...  
Keyword(s):  
Globular Cluster ◽  
Orbital Period ◽  
Surface Brightness ◽  
Eclipsing Binaries ◽  
Helium Abundance ◽  
Eccentric Orbit ◽  
Photometric And Spectroscopic Observations ◽  
Magnitude Diagram ◽  
The Masses ◽  
Gaia Dr2

ABSTRACT We use photometric and spectroscopic observations of the eclipsing binary E32 in the globular cluster 47 Tuc to derive the masses, radii, and luminosities of the component stars. The system has an orbital period of 40.9 d, a markedly eccentric orbit with e = 0.24, and is shown to be a member of or a recent escaper from the cluster. We obtain $M_{\rm p} = 0.862\pm 0.005 \, \mathrm{M}_\odot$, $R_{\rm p} = 1.183\pm 0.003 \, \mathrm{R}_\odot$, $L_{\rm p} = 1.65\pm 0.05 \, \mathrm{L}_\odot$ for the primary and $M_{\rm s} = 0.827\pm 0.005 \, \mathrm{M}_\odot$, $R_{\rm s} = 1.004\pm 0.004 \, \mathrm{R}_\odot$, $L_{\rm s} = 1.14\pm 0.04\, \mathrm{L}_\odot$ for the secondary. Based on these data and on an earlier analysis of the binary V69 in 47 Tuc, we measure the distance to the cluster from the distance moduli of the component stars, and, independently, from a colour – surface brightness calibration. We obtain 4.55 ± 0.03 and 4.50 ± 0.07 kpc, respectively – values compatible within 1$\, \sigma$ with recent estimates based on Gaia DR2 parallaxes. By comparing the M–R diagram of the two binaries and the colour–magnitude diagram of 47 Tuc to Dartmouth model isochrones we estimate the age of the cluster to be 12.0 ± 0.5 Gyr, and the helium abundance of the cluster to be Y ≈ 0.25.

High-mode stationary waves in stratified flow over large obstacles

2010 ◽  
Vol 644 ◽  
pp. 321-336 ◽  
Author(s):  
JODY M. KLYMAK ◽  
SONYA M. LEGG ◽  
ROBERT PINKEL
Keyword(s):  
Steady State ◽  
Aspect Ratio ◽  
Vertical Component ◽  
Phase Speed ◽  
Stratified Flow ◽  
Buoyancy Frequency ◽  
Stationary Waves ◽  
Vertical Wavelength ◽  
Mean Velocity ◽  
Lee Wave

Simulations of steady two-dimensional stratified flow over an isolated obstacle are presented where the obstacle is tall enough so that the topographic Froude number, Nhm/Uo ≫ 1. N is the buoyancy frequency, hm the height of the topography from the channel floor and Uo the flow speed infinitely far from the obstacle. As for moderate Nhm/Uo (~1), a columnar response propagates far up- and downstream, and an arrested lee wave forms at the topography. Upstream, most of the water beneath the crest is blocked, while the moving layer above the crest has a mean velocity Um = UoH/(H−hm). The vertical wavelength implied by this velocity scale, λo = 2πUm/N, predicts dominant vertical scales in the flow. Upstream of the crest there is an accelerated region of fluid approximately λo thick, above which there is a weakly oscillatory flow. Downstream the accelerated region is thicker and has less intense velocities. Similarly, the upstream lift of isopycnals is greatest in the first wavelength near the crest, and weaker above and below. Form drag on the obstacle is dominated by the blocked response, and not on the details of the lee wave, unlike flows with moderate Nhm/Uo.Directly downstream, the lee wave that forms has a vertical wavelength given by λo, except for the deepest lobe which tends to be thicker. This wavelength is small relative to the fluid depth and topographic height, and has a horizontal phase speed cpx = −Um, corresponding to an arrested lee wave. When considering the spin-up to steady state, the speed of vertical propagation scales with the vertical component of group velocity cgz = αUm, where α is the aspect ratio of the topography. This implies a time scale = tNα/2π for the growth of the lee waves, and that steady state is attained more rapidly with steep topography than shallow, in contrast with linear theory, which does not depend on the aspect ratio.

Experimental Determination of Oscillatory Lift and Moment Distributions on Fully Submerged Flexible Hydrofoils

1963 ◽  
Vol 7 (04) ◽  
pp. 24-41
Author(s):  
Guido E. Ransleben ◽  
H. Norman Abramson
Keyword(s):  
Steady State ◽  
Wind Tunnel ◽  
Aspect Ratio ◽  
Experimental Determination ◽  
Theoretical Predictions ◽  
Wind Tunnel Data

Measured span wise distributions of steady state and oscillatory lift and moment on fully submerged cantilever hydrofoils are presented. The hydrofoils were of aspect ratio 5 rectangular platform, and were towed at speeds sufficiently low to avoid cavitation. The data are compared with theoretical predictions and wind-tunnel data previously obtained at higher values of reduced velocity.

scholarly journals Measurements and laser-wavelength dependence of mass-ablation rate and ablation pressure in planar layered targets

1991 ◽  
Vol 9 (3) ◽  
pp. 769-778 ◽  
Author(s):  
F. Dahmani ◽  
T. Kerdja
Keyword(s):  
Steady State ◽  
Energy Transport ◽  
Laser Light ◽  
Plasma Heating ◽  
Wavelength Dependence ◽  
Ablation Rate ◽  
Laser Wavelength ◽  
Ablation Pressure ◽  
Hydrodynamical Simulations ◽  
Laser Flux

Layered-targets experiments at 1.06-μm laser light have been performed in order to measure mass-ablation rate ṁ and ablation pressure Pa as a function of absorbed laser flux Ia and laser wavelength λL at irradiances of 1011-4.5 × 1012 W/cm2. The results can be put in the forms ṁ(g/cm2-s) ≈ 4.25 × 105[Ia(W/cm2)/1014]5/9(1 μm/λL)4/9 and Pa(Mbar) ≈ 20[Ia(W/cm2)/1014]7/9(1 μm/λL)2/9, which are consistent with the estimates obtained from a steady-state self-regulated model for plasma heating and with hydrodynamical simulations. Results show also a small lateral energy transport.

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