scholarly journals How Non-Linear Scaling Relations Unify Dwarf and Giant Elliptical Galaxies

2011 ◽  
Vol 48 ◽  
pp. 231-236 ◽  
Author(s):  
A.W. Graham
Keyword(s):  
Elliptical Galaxies ◽  
Scaling Relations ◽  
Linear Scaling ◽  
Non Linear

scholarly journals Non-linear seismic scaling relations

2018 ◽  
Vol 616 ◽  
pp. A104 ◽  
Author(s):  
T. Kallinger ◽  
P. G. Beck ◽  
D. Stello ◽  
R. A. Garcia
Keyword(s):  
Binary Systems ◽  
Open Clusters ◽  
Eclipsing Binaries ◽  
Probabilistic Methods ◽  
Frequency Separation ◽  
Scaling Relations ◽  
Distance Modulus ◽  
Red Giants ◽  
Eclipsing Binary ◽  
Non Linear

Context. In recent years the global seismic scaling relations for the frequency of maximum power, νmax ∝ g / √Teff, and for the large frequency separation, Δν ∝ √ρ¯, have drawn attention in various fields of astrophysics. This is because these relations can be used to estimate parameters, such as the mass and radius of stars that show solar-like oscillations. With the exquisite photometry of Kepler, the uncertainties in the seismic observables are small enough to estimate masses and radii with a precision of only a few per cent. Even though this seems to work quite well for main-sequence stars, there is empirical evidence, mainly from studies of eclipsing binary systems, that the seismic scaling relations systematically overestimate the mass and radius of red giants by about 15% and 5%, respectively. Various model-based corrections of the Δν-scaling reduce the problem but do not solve it. Aims. Our goal is to define revised seismic scaling relations that account for the known systematic mass and radius discrepancies in a completely model-independent way. Methods. We use probabilistic methods to analyse the seismic data and to derive non-linear scaling relations based on a sample of six red giant branch (RGB) stars that are members of eclipsing binary systems and about 60 red giants on the RGB as well as in the core-helium burning red clump (RC) in the two open clusters NGC 6791 and NGC 6819. Results. We re-examine the global oscillation parameters of the giants in the binary systems in order to determine their seismic fundamental parameters and we find them to agree with the dynamic parameters from the literature if we adopt non-linear scalings. We note that a curvature and glitch corrected Δνcor should be preferred over a local or average value of Δν. We then compare the observed seismic parameters of the cluster giants to those scaled from independent measurements and find the same non-linear behaviour as for the eclipsing binaries. Our final proposed scaling relations are based on both samples and cover a broad range of evolutionary stages from RGB to RC stars: g / √Teff = (νmax / νmax,⊙)1.0075±0.0021 and √ρ¯ = (Δνcor / Δνcor,⊙)[η − (0.0085 ± 0.0025) log2(Δνcor / Δνcor,⊙)]−1, where g, Teff, and ρ¯ are in solar units, νmax,⊙ = 3140 ± 5 μHz and Δνcor,⊙ = 135.08 ± 0.02 μHz, and η is equal to one in the case of RGB stars and 1.04 ± 0.01 for RC stars. Conclusions. A direct consequence of these new scaling relations is that the average mass of stars on the ascending giant branch reduces to 1.10 ± 0.03 M⊙ in NGC 6791 and 1.45 ± 0.06 M⊙ in NGC 6819, allowing us to revise the clusters’ distance modulus to 13.11 ± 0.03 and 11.91 ± 0.03 mag, respectively. We also find strong evidence that both clusters are significantly older than concluded from previous seismic investigations.

Global Scaling Relations for Elliptical Galaxies and Implications for Formation

1987 ◽  
pp. 175-183 ◽  
Author(s):  
S. M. Faber ◽  
A. Dressler ◽  
R. L. Davies ◽  
D. Burstein ◽  
D. Lynden-Bell ◽  
...  
Keyword(s):  
Elliptical Galaxies ◽  
Scaling Relations ◽  
Global Scaling

scholarly journals A Model for the Sequence of Elliptical Galaxies

1987 ◽  
Vol 117 ◽  
pp. 367-367
Author(s):  
Rosemary F. G. Wyse ◽  
Bernard J. T. Jones
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Galaxy Formation ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Elliptical Galaxy ◽  
Elliptical Galaxies ◽  
Density Fluctuations ◽  
Analytic Approximation ◽  
Non Linear

We present a simple model for the formation of elliptical galaxies, based on a binary clustering hierarchy of dark matter, the chemical enrichment of the gas at each level being controlled by supernovae. The initial conditions for the non-linear phases of galaxy formation are set by the post-recombination power spectrum of density fluctuations. We investigate two models for this power spectrum - the first is a straightforward power law, |δk|2 ∝ kn, and the second is Peeble's analytic approximation to the emergent spectrum in a universe dominated by cold dark matter. The normalisation is chosen such that on some scale, say M ∼ 1012M⊙, the objects that condense out have properties - radius and velocity dispersion - resembling ‘typical’ galaxies. There is some ambiguity in this due to the poorly determined mass-to-light ratio of a typical elliptical galaxy — we look at two normalisations, σ1D ∼ 350kms−1 and σ1D ∼ 140kms−1. The choice determines which of Compton cooling or hydrogen cooling is more important during the galaxy formation period. The non-linear behaviour of the perturbations is treated by the homogeneous sphere approximation.

scholarly journals The Challenge of CO Hydrogenation to Methanol: Fundamental Limitations Imposed by Linear Scaling Relations

2020 ◽  
Vol 63 (7-8) ◽  
pp. 635-648
Author(s):  
Ahmed O. Elnabawy ◽  
Julia Schumann ◽  
Pallavi Bothra ◽  
Ang Cao ◽  
Jens K. Nørskov
Keyword(s):  
Co Hydrogenation ◽  
Scaling Relations ◽  
Linear Scaling ◽  
Fundamental Limitations

scholarly journals The Fundamental Scaling Relations of Elliptical Galaxies

2006 ◽  
Vol 641 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Brant Robertson ◽  
Thomas J. Cox ◽  
Lars Hernquist ◽  
Marijn Franx ◽  
Philip F. Hopkins ◽  
...  
Keyword(s):  
Elliptical Galaxies ◽  
Scaling Relations

Linear and non-linear scaling of the Yangtze River flow

2008 ◽  
Vol 22 (10) ◽  
pp. 1532-1536 ◽  
Author(s):  
Guojie Wang ◽  
Buda Su ◽  
Zbigniew W. Kundzewicz ◽  
Tong Jiang
Keyword(s):  
Yangtze River ◽  
River Flow ◽  
Linear Scaling ◽  
The Yangtze River ◽  
Non Linear
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