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We present photometric properties of 183 member galaxies in the Abell 426 cluster using the Sloan Digital Sky Survey (SDSS) imaging and spectroscopic observation. Detailed morphology based on visual classification followed by multicomponent image decomposition of 179 galaxies is presented in the SDSS g, r, i bands. More than 80 per cent of the members are early-type galaxies (ETGs), with elliptical, dwarf elliptical (dE), and lenticular morphology and follow the red-sequence in the colour–magnitude diagram (CMD). With a few dEs and spirals in the blue cloud, the cluster CMD is nearly unimodal. The dEs are ∼2-mag fainter and follow a different Sersic index and central velocity dispersion distribution than their bright counterparts. Further, we establish the Kormendy relation (KR) and the fundamental plane relation (FPR) for five different samples of ETGs constructed based on derived physical parameters such as Sersic index, concentration, central velocity dispersion in g, r, i bands. The mean r -band slope and zero-point of the KR are 3.02 ± 0.1 and 18.65 ± 0.03 in close agreement to other cluster ellipticals in the local and higher redshift. Kinematics-based ETG sample produces the least scatter in KR with zero-point getting brighter by ∼1.3 mag from g to i band. The dEs and other low-mass ETGs follow the KR with a similar slope but with ∼1.3 mag fainter zero-point and form a parallel KR. The bright ellipticals follow an FPR with a  = 1.37 ± 0.003, b  = 0.35 ± 0.05, and c  = −9.37 ± 0.02 in the r band; galaxies tend to deviate from this relation at the low-mass end. A catalogue with morphology and 2D structural analysis is available online. [ABSTRACT FROM AUTHOR]

Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to the isothermal (γ=1) Euler-Poisson equations in R2 with possible applications to the formation of plate, spiral galaxies and the evolution of gas-rich, disk-like galaxies. The results complement Yuen's solutions without rotation (Yuen, 2008 [12]). Here, the periodic rotation prevents the blowup phenomena that occur in solutions without rotation. Based on our results, the corresponding 3D rotational results for Goldreich and Weber's solutions are conjectured. [ABSTRACT FROM AUTHOR]

We calculate the mass function evolution in a ΛCDM model by means of the excursion set model and an improved version of the barrier shape obtained in Del Popolo and Gambera [Astron. Astrophys.337, 96 (1998)], which implicitly takes account of total angular momentum acquired by the protostructure during evolution and of a nonzero cosmological constant. We compare the result with Reed et al. [Mon. Not. R. Astron. Soc.346, 565 (2003)], who used a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15. We show that the mass function obtained in the present paper gives similar predictions to the Sheth and Tormen mass function, but it does not show the overprediction of extremely rare objects shown by the Sheth and Tormen mass function. The results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. [ABSTRACT FROM AUTHOR]

We derive the luminosity–temperature relation for clusters of galaxies by means of a modification of the self-similar model to take account of angular momentum acquisition by protostructures and of an external pressure term in the virial theorem. We show that the above effect leads, in X-rays, to a luminosity–temperature relation that scales as L ∝ T5, at scale of groups, flattening to L ∝ T3 for rich clusters and converging to L ∝ T2 at higher temperatures. The fundamental result of the model is that gravitational collapse, which takes account of angular momentum acquisition, can explain the non-self-similarity in the L–T relation, in disagreement with the largely accepted assumption that heating/cooling processes and similar are fundamental in the originating the non-self-similar behavior (shaping) of the L–T relation. [ABSTRACT FROM AUTHOR]

The growth of the density fluctuations is considered to be an important cosmological test. In the standard model, for a matter dominated universe, the growth of the density perturbations evolves with redshift z like (1 1 + z) s with s = 1. This is not fast enough to form galaxies and to account for the observed present-day inhomogeneities. This problem is usually resolved by assuming that at the recombination epoch the baryons settle down in the potential well of the dark matter previously assembled during the radiation era of the universe. This view is challenged in the present paper by using the recently proposed model of a scale-invariant framework for cosmology, the Scale-Invariant Vacuum Theory (Maeder 2017a,2017b,2017c), that enlarges the invariance group subtending the theory of the gravitation. From the continuity equation, the Euler and Poisson equations are written in the scale-invariant framework, the equation governing the growth of density fluctuations δ is obtained. Starting from δ = 1 0 − 5 at a redshift around 1000, numerical solutions for various density background are obtained. The growth of density fluctuations is much faster than in the standard EdS model. The s values are in the range from 2.7 to 3.9 for Ω m between 0.30 and 0.02. This enables the density fluctuations to enter the nonlinear regime with δ > 1 long before the present time, typically at redshifts of about 10, without requiring the presence of dark matter. [ABSTRACT FROM AUTHOR]

We analyse the density profiles of the stellar halo populations in eight Milky Way mass galaxies, simulated within the Λcold dark matter scenario. We find that accreted stars can be well fitted by an Einasto profile, as well as any subsample defined according to metallicity. We detect a clear correlation between the Einasto fitting parameters of the low-metallicity stellar populations and those of the dark matter (DM) haloes. The correlations for stars with [Fe/H] < −3 allow us to predict the shape of the dark matter profiles within residuals of ∼10 per cent, in case the contribution from in situ stars remains small. Using Einasto parameters estimated for the stellar halo of the Milky Way and assuming the later formed with significant contributions from accreted low-mass satellite, our simulations predict α ∼ 0.15 and r2 ∼ 15 kpc for its dark matter profile. These values, combined with observed estimations of the local DM density, yield an enclosed DM mass at ∼8 kpc in the range 3.9–6.7 × 1010 M⊙, in agreement with recent observational results. These findings suggest that low-metallicity stellar haloes could store relevant information on the DM haloes. Forthcoming observations would help us to further constrain our models and predictions. [ABSTRACT FROM PUBLISHER]