scholarly journals Probing the protoplanetary disk gas surface density distribution with 13CO emission

2018 ◽  
Vol 619 ◽  
pp. A113 ◽  
Author(s):  
A. Miotello ◽  
S. Facchini ◽  
E. F. van Dishoeck ◽  
S. Bruderer
Keyword(s):  
Density Distribution ◽  
Power Law ◽  
Surface Density ◽  
Disk Surface ◽  
Input Power ◽  
Disk Radius ◽  
Spatially Resolved ◽  
Radial Profiles ◽  
Power Law Index ◽  
Freeze Out

Context. How protoplanetary disks evolve is still an unsolved problem where different processes may be involved. Depending on the process, the disk gas surface density distribution Σgas may be very different and this could have diverse implications for planet formation. Together with the total disk mass, it is key to constrain Σgas as function of disk radius R from observational measurements. Aims. In this work we investigate whether spatially resolved observations of rarer CO isotopologues, such as 13CO, may be good tracers of the gas surface density distribution in disks. Methods. Physical-chemical disk models with different input Σgas(R) were run, taking into account CO freeze-out and isotope-selective photodissociation. The input disk surface density profiles were compared with the simulated 13CO intensity radial profiles to check whether and where the two follow each other. Results. For each combination of disk parameters, there is always an intermediate region in the disk where the slope of the 13CO radial emission profile and Σgas(R) coincide. In the inner part of the disk, the line radial profile underestimates Σgas, as 13CO emission becomes optically thick. The same happens at large radii where the column densities become too low and 13CO is not able to efficiently self-shield. Moreover, the disk becomes too cold and a considerable fraction of 13CO is frozen out, thus it does not contribute to the line emission. If the gas surface density profile is a simple power-law of the radius, the input power-law index can be retrieved within a ~20% uncertainty if one choses the proper radial range. If instead Σgas(R) follows the self-similar solution for a viscously evolving disk, retrieving the input power-law index becomes challenging, in particular for small disks. Nevertheless, we find that the power-law index γ can be in any case reliably fitted at a given line intensity contour around 6 K km s−1, and this produces a practical method to constrain the slope of Σgas(R). Application of such a method is shown in the case study of the TW Hya disk. Conclusions. Spatially resolved 13CO line radial profiles are promising to probe the disk surface density distribution, as they directly trace Σgas(R) profile at radii well resolvable by ALMA. There, chemical processes like freeze-out and isotope-selective photodissociation do not affect the emission, and, assuming that the volatile carbon does not change with radius, no chemical model is needed when interpreting the observations.

Detect the density profile with LAMOST K giants

2017 ◽  
Vol 13 (S334) ◽  
pp. 387-388
Author(s):  
Yan Xu ◽  
Chao Liu
Keyword(s):  
Density Distribution ◽  
Power Law ◽  
Density Profile ◽  
Milky Way ◽  
Galactic Center ◽  
Fitting Method ◽  
Stellar Halo ◽  
Model Independent ◽  
Power Law Index ◽  
K Giants

AbstractThe density distribution of the Milky Way halo is detected with 5351 LAMOST DR3 metal poor K giants using a nonparametric method. The nonparametric fitting method is a model independent way to estimate the halo density distribution while to a large extent avoiding the influence of the halo substucture. We show that the K giants density profile can be fitted well by single power law. We found no indication of a break in the power law index. The powerlaw index n = 5.0−0.64+0.64. The data show that the stellar halo is flattened at smaller radii, and becomes more spherical farther from the Galactic center. The flattening q(r=15Kpc)is about0.64, q(20Kpc) is about 0.8, q(30Kpc) is about 0.96.

Dispersion of sausage waves in coronal waveguides with transverse density structuring

2019 ◽  
Vol 488 (1) ◽  
pp. 660-675 ◽  
Author(s):  
I Lopin ◽  
I Nagorny
Keyword(s):  
Density Distribution ◽  
Longitudinal Wave ◽  
Power Law ◽  
Wave Equations ◽  
Wave Dispersion ◽  
Dispersion Properties ◽  
Varying Coefficients ◽  
Uniform Region ◽  
Wave Numbers ◽  
Power Law Index

ABSTRACT We study dispersion properties of fast-sausage waves in a radially structured coronal magnetic tube with continuous radial density distribution. The models, containing either a non-uniform core or inhomogeneous external medium are considered. The dispersion relations are obtained for a power law density distribution in the corresponding non-uniform region, where the power-law index controls the steepness of the tube boundary. The governing wave equations with varying coefficients were solved with the Wentzel–Kramers–Brillouin (WKB) approximation. The model with the non-uniform core supports the existence of trapped and leaky sausage modes. The density non-uniformity in the core modifies the values of cut-off wave numbers kc. The smaller values of cut-offs, normalized to the effective tube radius r0, correspond to the smaller power index p. The wave dispersion (i.e. dVph/dk) decreases for smaller p. This occurs in the range of not too small longitudinal wave numbers k > kc. For the model, containing inhomogeneous environment the basic dispersion properties are generally identical to that for the monolithic tube model, studied in Lopin & Nagorny (2015b). The waves are trapped for all wave numbers, if the power-law index 0 < n < 2. There are both trapped and leaky regimes for n ≥ 2. The wave dispersion decreases for smaller n, in the range of the intermediate values of the longitudinal wave numbers k > kc. The seismological application of the obtained results is discussed.

scholarly journals Proto-planetary disks with CARMA: sub-arsecond observations at millimeter wavelengths

2009 ◽  
Vol 5 (H15) ◽  
pp. 738-738
Author(s):  
Isella Andrea ◽  
John M. Carpenter ◽  
Laura Perez ◽  
Anneila I. Sargent
Keyword(s):  
Surface Density ◽  
Angular Resolution ◽  
Spatial Scales ◽  
Radial Profile ◽  
Continuum Emission ◽  
Disk Radius ◽  
Orbital Radius ◽  
Disk Structure ◽  
Millimeter Wavelengths ◽  
Radial Profiles

Using the Combined Array for Research in Millimeter-wave Astronomy (CARMA) we observed several proto-planetary disks in the dust continuum emission at 1.3 and 2.8 mm (Isella et al. 2009a, 2009b). The observations have angular resolution between 0.15 and 0.7 arcsecond, corresponding to spatial scales spanning from about the orbit of Saturn up to about the orbital radius of Pluto. The observed disks are characterized by a variety of radial profiles for the dust density. We observe inner disk clearing as well as smooth density profiles, suggesting that disks may form, or evolve, in different ways. Despite that, we find that the characteristic disk radius is correlated with the stellar age increasing from 20 AU to 100 AU over about 5 Myr. Interpreting our results in terms of the temporal evolution of a viscous α-disk, we estimate that (i) at the beginning of the disk evolution about 60% of the circumstellar material was located inside radii of 25-40 AU, (ii) that disks formed with masses from 0.05 to 0.4 solar masses and (iii) that the viscous timescale at the disk initial radius is about 0.1-0.3 Myr. Viscous disk models tightly link the surface density Σ(R) with the radial profile of the disk viscosity ν(R)∝ Rγ. We find values of γ ranging from -0.8 to 0.8, suggesting that the viscosity dependence on the orbital radius can be very different in the observed disks. We demonstrate that the similarity solution for the surface density for γ < 0 can explain the properties of some “transitional” disks without requiring discontinuities in the disk surface density. In the case of LkCa 15, a smooth distribution of material from few stellar radii to about 240 AU can produce both the observed SED and the spatially resolved continuum emission at millimeter wavelengths. For two sources, RY Tau and DG Tau, we observed the dust emission with a resolution as high as 0.15 arcsecond, which corresponds to a spatial scale of 20 AU at the distance of the two stars. The achieved angular resolution is a factor 2 higher than any existing observation of circumstellar disks at the same wavelengths and enable us to investigate the disk structure with unprecedent details. In particular, we present a first attempt to derive the radial profile of the slope of the dust opacity β. We find mean values of β of 0.5 and 0.7 for DG Tau and RY Tau respectively and we exclude that β may vary by more than ±0.4 between 20-70 AU. This implies that the circumstellar dust has a maximum grain size between 10 μm and few centimeters.

scholarly journals The Resolved Kennicutt-Schmidt Law in Nearby Galaxies

2012 ◽  
Vol 8 (S292) ◽  
pp. 335-335
Author(s):  
R. Momose ◽  
J. Koda ◽  
R. C. Kennicutt ◽  
F. Egusa ◽  
S. K. Okumura ◽  
...  
Keyword(s):  
Star Formation ◽  
Power Law ◽  
Surface Density ◽  
Star Formation Rate ◽  
Formation Rate ◽  
Line Emission ◽  
Molecular Gas ◽  
Disk Galaxies ◽  
Nearby Galaxies ◽  
Power Law Index

AbstractThe Kennicutt-Schmidt law (Schmidt 1959; Kennicutt 1998, hereafter K-S law) is a power law correlation between area averaged star formation rate (ΣSFR) and gas surface density (Σgas). Despite its importance, the physics that underlie this correlation has remained unclear. The power law index, N, is a prime discriminator of the mechanisms that regulate star formation and form the K-S law (e.g. Leroy et al. 2008; Tan 2010). We present a study of the resolved K-S law for 10 nearby disk galaxies using our new CO(1-0) data at 750 and 500 pc resolutions. The CO(1-0) line emission is established as a tracer of the molecular gas column density, and results in a super-linear correlation (N = 1.3 and 1.8). We discuss the cause of the discrepancy between previous studies, and the mechanism of star formation indicated from our new results.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Jet Impingement Heat Transfer of Confined Single and Double Jets with Non-Newtonian Power Law Nanofluid under the Inclined Magnetic Field Effects for a Partly Curved Heated Wall

2021 ◽  
Vol 13 (9) ◽  
pp. 5086
Author(s):  
Fatih Selimefendigil ◽  
Hakan F. Oztop ◽  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Particle Size ◽  
Aspect Ratio ◽  
Power Law ◽  
Volume Fraction ◽  
Inclined Magnetic Field ◽  
Magnetic Field Effects ◽  
Power Law Nanofluid ◽  
Power Law Index

Single and double impinging jets heat transfer of non-Newtonian power law nanofluid on a partly curved surface under the inclined magnetic field effects is analyzed with finite element method. The numerical work is performed for various values of Reynolds number (Re, between 100 and 300), Hartmann number (Ha, between 0 and 10), magnetic field inclination (γ, between 0 and 90), curved wall aspect ratio (AR, between 01. and 1.2), power law index (n, between 0.8 and 1.2), nanoparticle volume fraction (ϕ, between 0 and 0.04) and particle size in nm (dp, between 20 and 80). The amount of rise in average Nusselt (Nu) number with Re number depends upon the power law index while the discrepancy between the Newtonian fluid case becomes higher with higher values of power law indices. As compared to case with n = 1, discrepancy in the average Nu number are obtained as −38% and 71.5% for cases with n = 0.8 and n = 1.2. The magnetic field strength and inclination can be used to control the size and number or vortices. As magnetic field is imposed at the higher strength, the average Nu reduces by about 26.6% and 7.5% for single and double jets with n greater than 1 while it increases by about 4.78% and 12.58% with n less than 1. The inclination of magnetic field also plays an important role on the amount of enhancement in the average Nu number for different n values. The aspect ratio of the curved wall affects the flow field slightly while the average Nu variation becomes 5%. Average Nu number increases with higher solid particle volume fraction and with smaller particle size. At the highest particle size, it is increased by about 14%. There is 7% variation in the average Nu number when cases with lowest and highest particle size are compared. Finally, convective heat transfer performance modeling with four inputs and one output is successfully obtained by using Adaptive Neuro-Fuzzy Interface System (ANFIS) which provides fast and accurate prediction results.

scholarly journals Blocks Size Frequency Distribution in the Enceladus Tiger Stripes Area: Implications on Their Formative Processes

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 82
Author(s):  
Maurizio Pajola ◽  
Alice Lucchetti ◽  
Lara Senter ◽  
Gabriele Cremonese
Keyword(s):  
Frequency Distribution ◽  
Power Law ◽  
Size Frequency Distribution ◽  
Surface Stresses ◽  
Size Frequency ◽  
The One ◽  
Power Law Index ◽  
Comet 67P ◽  
South Polar ◽  
Degree Of Fragmentation

We study the size frequency distribution of the blocks located in the deeply fractured, geologically active Enceladus South Polar Terrain with the aim to suggest their formative mechanisms. Through the Cassini ISS images, we identify ~17,000 blocks with sizes ranging from ~25 m to 366 m, and located at different distances from the Damascus, Baghdad and Cairo Sulci. On all counts and for both Damascus and Baghdad cases, the power-law fitting curve has an index that is similar to the one obtained on the deeply fractured, actively sublimating Hathor cliff on comet 67P/Churyumov-Gerasimenko, where several non-dislodged blocks are observed. This suggests that as for 67P, sublimation and surface stresses favor similar fractures development in the Enceladus icy matrix, hence resulting in comparable block disaggregation. A steeper power-law index for Cairo counts may suggest a higher degree of fragmentation, which could be the result of localized, stronger tectonic disruption of lithospheric ice. Eventually, we show that the smallest blocks identified are located from tens of m to 20–25 km from the Sulci fissures, while the largest blocks are found closer to the tiger stripes. This result supports the ejection hypothesis mechanism as the possible source of blocks.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

Thermorheological Characterization of Elastoviscoplastic Carbopol Ultrez 20 Gel

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
M. A. Hassan ◽  
Manabendra Pathak ◽  
Mohd. Kaleem Khan
Keyword(s):  
Experimental Investigation ◽  
Yield Stress ◽  
Elastic Properties ◽  
Viscous Dissipation ◽  
Power Law ◽  
Effect Of Temperature ◽  
Rheological Parameters ◽  
Frequency Range ◽  
Power Law Index

The temperature and concentration play an important role on rheological parameters of the gel. In this work, an experimental investigation of thermorheological properties of aqueous gel Carbopol Ultrez 20 for various concentrations and temperatures has been presented. Both controlled stress ramps and controlled stress oscillatory sweeps were performed for obtaining the rheological data to find out the effect of temperature and concentration. The hysteresis or thixotropic seemed to have negligible effect. Yield stress, consistency factor, and power law index were found to vary with temperature as well as concentration. With gel concentration, the elastic effect was found to increase whereas viscous dissipation effect was found to decrease. Further, the change in elastic properties was insignificant with temperature in higher frequency range of oscillatory stress sweeps.

scholarly journals Predicting observational signatures of coronal heating by Alfvén waves and nanoflares

2007 ◽  
Vol 3 (S247) ◽  
pp. 279-287
Author(s):  
Patrick Antolin ◽  
Kazunari Shibata ◽  
Takahiro Kudoh ◽  
Daiko Shiota ◽  
David Brooks
Keyword(s):  
Power Law ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Power Law Distribution ◽  
Longitudinal Modes ◽  
Heating Mechanism ◽  
Set Up ◽  
Power Law Index ◽  
Power Law Distributions ◽  
Release Processes

AbstractAlfvén waves can dissipate their energy by means of nonlinear mechanisms, and constitute good candidates to heat and maintain the solar corona to the observed few million degrees. Another appealing candidate is the nanoflare-reconnection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power law distribution in frequency whose index may tell us whether small heating events contribute substantially to the heating or not. In this work we show a link between the power law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfvén waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy through shocks; in the second model numerous heating events with nanoflare-like energies are input randomly along the loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-D MHD code. The obtained coronae differ in many aspects, for instance, in the simulated intensity profile that Hinode/XRT would observe. The intensity histograms display power law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.

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