Photoionization modelling of planetary nebulae with realistic density distribution using detailed method for diffuse radiation calculation and Outward Only approximation

2018 ◽  
Vol 8 (1) ◽  
pp. 3-8
Author(s):  
O. Buhajenko ◽  
B. Melekh
Keyword(s):  
Density Distribution ◽  
Outer Part ◽  
Planetary Nebulae ◽  
Diffuse Radiation ◽  
Constant Density ◽  
Approximate Methods ◽  
Detailed Method ◽  
Spatially Extended ◽  
Calculation Algorithms ◽  
Density Radius

The approximate methods to calculate the diffuse ionizing radiation (DIR) during the photoionization modelling (PhM) of the nebular environments are frequently used with purpose to increase the calculation speed of modern photoionization codes as well as for simplification of their calculation algorithms. The most popular Outward Only method in many cases gives the satisfactory calculation precision and speed. However, in our previous studies it was shown that even for nebular environments with constant density the calculation errors, related to usage of approximate method of DIR, are significant for spatially extended or optically thin objects. However, constant density is a bit rough assumption. In present work to compare the detailed method of DIR calculation with Outward Only one we used more realistic density distribution for planetary nebulae proposed by Golovatyy & Mal’kov. Using optimal photoionization models for IC 5117 and NGC 7293, obtained by Melekh et al. and calculated in Outward Only approximation, we recalculated them using detailed method of DIR calculation. While IC 5117 is the most compact (young) and dense planetary nebula from sample used by Golovatyy & Mal’kov, NGC 7293 is the most extended (old) with lowest density one from the same sample. We compared PhM results for these PNe obtained using Outward Only approximation and detailed method of DIR treatment. It was concluded that largest differences in ionization structure of nebula caused by differences in DIR calculation methods are in outer part of PN - at radii larger than maximal density radius. Therefore, [N II], [O II] and [S II] and other emission lines, that achieve the maximal emissivities in outer part of PNe, are the most sensitive to DIR calculation method.

scholarly journals Measuring the local matter density usingGaiaDR2

2019 ◽  
Vol 623 ◽  
pp. A30 ◽  
Author(s):  
A. Widmark
Keyword(s):  
Density Distribution ◽  
Vertical Velocity ◽  
Galactic Plane ◽  
Absolute Magnitude ◽  
Matter Density ◽  
Dark Matter Halo ◽  
Constant Density ◽  
Bayesian Hierarchical ◽  
Error Covariance ◽  
Systematic Effects

Aims.We determine the total dynamical matter density in the solar neighbourhood using the secondGaiadata release (DR2).Methods.The dynamical matter density distribution is inferred in a framework of a Bayesian hierarchical model, which accounts for position and velocity of all individual stars, as well as the full error covariance matrix of astrometric observables, in a joint fit of the vertical velocity distribution and stellar number density distribution. This was done for eight separate data samples, with different cuts in observed absolute magnitude, each containing about 25 000 stars. The model for the total matter density does not rely on any underlying baryonic model, although we assumed that it is symmetrical, smooth, and monotonically decreasing with distance from the mid-plane.Results.We infer a density distribution which is strongly peaked in the region close to the Galactic plane (≲60 pc), for all eight stellar samples. Assuming a baryonic model and a dark matter halo of constant density, this corresponds to a surplus surface density of approximately 5–9M⊙pc−2. For the Sun’s position and vertical velocity with respect to the Galactic plane, we inferZ⊙ = 4.76 ± 2.27 pc andW⊙ = 7.24 ± 0.19 km s−1.Conclusions.These results suggest a surplus of matter close to the Galactic plane, possibly explained by an underestimated density of cold gas. We discuss possible systematic effects that could bias our result, for example unmodelled non-equilibrium effects, and how to account for such effects in future extensions of this work.

scholarly journals Ionic Abundances of S III, O IV and NeV from Infrared Observations of Fine Structure Lines in eight Planetary Nebulae

1983 ◽  
Vol 103 ◽  
pp. 512-512
Author(s):  
M.A. Shure ◽  
T.L. Herter ◽  
J.R. Houck ◽  
D.A. Briotta ◽  
W.J. Forrest ◽  
...  
Keyword(s):  
Fine Structure ◽  
Electron Temperature ◽  
Planetary Nebulae ◽  
Optical Observations ◽  
Constant Density ◽  
Line Flux ◽  
Infrared Observations ◽  
Infrared Measurements ◽  
Fine Structure Lines

The Kuiper Airborne Observatory has been used to make measurements of the infrared forbidden lines of (SIII) 18.72μm, (NeV) 24.28μm and (OIV) 25.87μm in eight planetary nebulae. In all cases the beam was larger than the emitting region. The observed line fluxes are used to determine ionic abundances under the assumption of constant density throughout the relevant volume as determined by optical observations. In some cases the NeV near UV lines are used in conjunction with the infrared measurements to determine the electron temperature in the NeV emission regions. The (SIII) 33.47μm line can be used with the (SIII) 18.72μm line flux to characterize the clumping within the nebulae.

Frontogenesis in a fluid with horizontal density gradients

1989 ◽  
Vol 202 ◽  
pp. 1-16 ◽  
Author(s):  
J. E. Simpson ◽  
P. F. Linden
Keyword(s):  
Density Distribution ◽  
Density Gradient ◽  
Initial Density ◽  
Vertical Shear ◽  
Horizontal Gradient ◽  
Constant Density ◽  
Piecewise Constant ◽  
Vertical Density ◽  
Step Density ◽  
Horizontal Density Gradient

The adjustment under gravity of a fluid containing a horizontal density gradient is described.’ The fluid is initially at rest and the resulting motion is calculated as the flow accelerates, driven by the baroclinic density field. Two forms of the initial density distribution are considered. In the first the initial horizontal gradient is constant. A purely horizontal motion develops as the isopycnals rotate towards the horizontal. The vertical density gradient increases continually with time but the horizontal density gradient remains unchanged. The horizontal velocity has a uniform vertical shear, and the gradient Richardson number is constant in space and decreases monotonically with time to ½. The second density distribution consists of a piecewise constant gradient with a jump in the gradient along a vertical isopycnal. The density is continuous. In this case frontogenesis is predicted to occur on the isopycnal between the two constant-density-gradient regions, and the timescale for the formation of a front is determined. Laboratory experiments are reported which confirm the results of these calculations. In addition, lock exchange experiments have been carried out in which the horizontal mean gradient is represented by a series of step density differences separated by vertical gates.

scholarly journals Evolution of Planetary Nebulae Envelopes: An Empirical Approach

1993 ◽  
Vol 155 ◽  
pp. 370-370
Author(s):  
V.V. Golovaty ◽  
Yu. F. Malkov
Keyword(s):  
Integral Equation ◽  
Density Distribution ◽  
Radial Distribution ◽  
Empirical Investigation ◽  
Planetary Nebulae ◽  
Symmetric Case ◽  
Radio Continuum ◽  
Spherically Symmetric ◽  
Gas Density ◽  
Approximative Expression

We carried out the empirical investigation of the evolution of gas density distribution in the envelopes of planetary nebulae (PN). For this purpose we analysed the isophotal maps of 10 PN in the lines H alpha, H beta or in the optically thin radio continuum. To obtain the spatial radial distribution of gas density n(r) (where n = n(H)+n(He)) we used Abell's integral equation in the simplest, spherically-symmetric case. We found that n(r) for all PN envelopes in our sample can be described by an approximative expression:

scholarly journals Density Distribution and Chemical Abundances in NGC 7027

1978 ◽  
Vol 76 ◽  
pp. 357-358
Author(s):  
Andrea Preite-Martinez ◽  
Nino Panagiat
Keyword(s):  
Density Distribution ◽  
Planetary Nebula ◽  
Constant Density ◽  
Chemical Abundances ◽  
Line Intensities ◽  
Ngc 7027

The data available on permitted and forbidden line intensities of the planetary nebula NGC 7027 have been analyzed in terms of non-constant density models. The significance of the derived density distribution is discussed. Some implications to the determination of the chemical abundances are also discussed.

Bayesian joint inversion of muographic and gravimetric data for the 3D imaging of volcanoes, case study of the Puy de Dôme

2020 ◽  
Author(s):  
Anne Barnoud ◽  
Valérie Cayol ◽  
Peter Lelièvre ◽  
Valentin Niess ◽  
Cristina Cârloganu ◽  
...  
Keyword(s):  
Density Distribution ◽  
Joint Inversion ◽  
A Priori ◽  
High Energy ◽  
Quality Data ◽  
Constant Density ◽  
Density Structure ◽  
Spatial Covariance ◽  
Massif Central ◽  
Gravimetric Data

<p>We present a method to jointly invert muographic and gravimetric data to infer the 3D density structure of volcanoes.</p><p>Muography and gravimetry are two independent methods that are sensitive to the density distribution. The gravimetric inversion allows to reconstruct the 3D density variations but the process is well-known to be ill-posed leading to non unique solutions. Muography provides 2D images of mean densities from the detection of high energy atmospheric muons crossing the volcanic edifice. Several muographic images can be used to reconstruct the 3D density distribution but the number of imagdes is generally limited by instrumentation and field contstraints.</p><p>The joint inversion of muographic and gravimetric data aims at reconstructing the 3D density structure of an edifice, benefiting from the advantages of both methods. We developed a robust inversion scheme based on a Bayesian formalism. This approach takes into account the data errors and a priori information on the density distribution with a spatial covariance so that smooth models are obtained. The a priori density standard deviation and the spatial correlation length are the two hyperparameters that tune the regularization, hence that control the inversion result. The optimal set of hyperparameters is determined in a systematic way using Leave One Out (LOO) and Cross Validation Sum of Squares (CVSS) criteria (Barnoud et al., GJI 2019). The method also allows to automatically determine a constant density offset between gravimetry and muography to overcome a potential bias in the measurements (Lelièvre et al., GJI 2019).</p><p>The case of the Puy de Dôme volcano (French Massif Central) is studied as proof of principle as high quality data are available for both muography (Le Ménédeu et al., EGU 2016; Cârloganu et al., EGU 2018) and gravimetry (Portal et al., JVGR 2016). We develop and validate the method using synthetic data computed from a model based on the Puy de Dôme topography and acquisition geometry, as well as on real data.</p>

scholarly journals A Comparison of Nebular Distance Scales

1993 ◽  
Vol 155 ◽  
pp. 174-174
Author(s):  
M. Samland ◽  
J. Köppen ◽  
A. Acker ◽  
B. Stenholm
Keyword(s):  
Planetary Nebulae ◽  
Distance Scale ◽  
Constant Density ◽  
Image Position ◽  
Almost All ◽  
Central Stars ◽  
Angular Radius ◽  
Hr Diagram

Determination of the positions of central stars of planetary nebulae in the HR-diagram requires the knowledge of nebular distances. For almost all nebulae, these can only be given in terms of statistical scales. These scales have in common that they assume all nebulae to have the same structure (e.g. constant density) and that a unique ionized mass-radius relation exists. If the mass-radius relation is given by Mion = M0 · (R/R0)η, the distance d(pc) of planetary nebulae can be expressed as a function the de-reddened Hβ-flux (erg cm−2s−1) and the angular radius θ(arcsec): M0 and R0 are in solar masses and pc (Te = 10000 K, He/H = 0.1). The parameter η characterizes the distance scale: e.g. Shklovsky (1956) η = 0, Maciel L. Pottasch (1980) η = 1, Pottasch (1984) η = 3/2, Daub (1982) η = 5/3, and Kwok (1985) η = 9/4.

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