arXiv subjects

Sven Meyer

Publications and source records attributed to Sven Meyer.

16 recordsLinked to original sources

arXiv2019

Generalised model-independent characterisation of strong gravitational lenses V: reconstructing the lensing distance ratio by supernovae for a general Friedmann universe

We determine the cosmic expansion rate from supernovae of type Ia to set up a data-based distance measure that does not make assumptions about the constituents of the universe, i.e. about a specific parametrisation of a Friedmann cosmological model. The scale, determined by the Hubble constant $H_0$, is the only free cosmological parameter left in the gravitational lensing formalism. We investigate to which accuracy and precision the lensing distance ratio $D$ is determined from the Pantheon sample. Inserting $D$ and its uncertainty into the lensing equations for given $H_0$, esp. the time-delay equation between a pair of multiple images, allows to determine lens properties, esp. differences in the lensing potential ($Δϕ$), without specifying a cosmological model. We expand the luminosity distances into an analytic orthonormal basis, determine the maximum-likelihood weights for the basis functions by a globally optimal $χ^2$-parameter estimation, and derive confidence bounds by Monte-Carlo simulations. For typical strong lensing configurations between $z=0.5$ and $z=1.0$, $Δϕ$ can be determined with a relative imprecision of 1.7%, assuming imprecisions of the time delay and the redshift of the lens on the order of 1%. With only a small, tolerable loss in precision, the model-independent lens characterisation developed in this paper series can be generalised by dropping the specific Friedmann model to determine $D$ in favour of a data-based distance ratio. Moreover, for any astrophysical application, the approach presented here, provides distance measures for $z\le2.3$ that are valid in any homogeneous, isotropic universe with general relativity as theory of gravity.

astro-ph.CO↗

arXiv2018

Long Range Effects in Gravity Theories with Vainshtein Screening

In this paper we study long range modifications of gravity in the consistent framework of bigravity, which introduces a second massive spin-2 field and allows to continuously interpolate between the regime of General Relativity (mediated by a massless spin-2 field) and massive gravity (mediated by a massive spin-2 field). In particular we derive for the first time the equations for light deflection in this framework and study the effect on the lensing potential of galaxy clusters. By comparison of kinematic and lensing mass reconstructions, stringent bounds can be set on the parameter space of the new spin-2 fields. Furthermore, we investigate galactic rotation curves and the effect on the observable dark matter abundance within this framework.

astro-ph.CO↗

arXiv2017

On the implementation of the spherical collapse model for dark energy models

In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by Herrera et al. 2017, we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity $δ_{\rm c}$, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the $Λ$CDM models. We further discuss the evolution of $δ_{\rm c}$ for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.

astro-ph.CO↗

arXiv2017

Shear and vorticity in the spherical collapse of dark matter haloes

Traditionally the spherical collapse of objects is studied with respect to a uniform background density, yielding the critical over-density $δ_\mathrm{c}$ as key ingredient to the mass function of virialized objects. Here we investigate the shear and rotation acting on a peak in a Gaussian random field. By assuming that collapsing objects mainly form at those peaks, we use this shear and rotation as external effects changing the dynamics of the spherical collapse, which is described by the Raychaudhuri equation. We therefore assume that the shear and rotation have no additional dynamics on top of their cosmological evolution and thus only appear as inhomogeneities in the differential equation.

astro-ph.CO↗

arXiv2017

Light propagation in linearly perturbed $Λ$LTB models

We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and perform a suitable spherical harmonic decomposition. This allows to map the abstract gauge-invariant perturbation variables to well-known quantities from weak gravitational lensing like convergence or cosmic shear. The resulting set of differential equations can effectively be solved by a Green's function approach leading to line-of-sight integrals sourced by the perturbation variables on the backward lightcone. The resulting spherical harmonic coefficients of the lensing observables are presented and the shear field is decomposed into its E- and B-modes. Results of this work are an essential tool to add information from linear structure formation to the analysis of spherically symmetric dust models with the purpose of testing the Copernican Principle with multiple cosmological probes.

gr-qc↗

arXiv2017

Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant

We study the dynamical behaviour of gauge-invariant linear perturbations in spherically symmetric dust cosmologies including a cosmological constant. In contrast to spatially homogeneous FLRW models, the reduced degree of spatial symmetry causes a non-trivial dynamical coupling of gauge-invariant quantities already at first order perturbation theory and the strength and influence of this coupling on the spacetime evolution is investigated here. We present results on the underlying dynamical equations augmented by a cosmological constant and integrate them numerically. We also present a method to derive cosmologically relevant initial variables for this setup. Estimates of angular power spectra for each metric variable are computed and evaluated on the central observer's past null cone. By comparing the full evolution to the freely evolved initial profiles, the coupling strength will be determined for a best fit radially inhomogeneous patch obtained in previous works (see Redlich et. al. (2014)). We find that coupling effects are not noticeable within the cosmic variance limit and can therefore safely be neglected for a relevant cosmological scenario. On the contrary, we find very strong coupling effects in a best fit spherical void model matching the distance redshift relation of SNe which is in accordance with previous findings using parametric void models.

astro-ph.CO↗

arXiv2016

Effects of tidal gravitational fields in clustering dark energy models

We extend a previous work by Reischke et al., 2016 by studying the effects of tidal shear on clustering dark energy models within the framework of the extended spherical collapse model and using the Zel'dovich approximation. As in previous works on clustering dark energy, we assumed a vanishing effective sound speed describing the perturbations in dark energy models. To be self-consistent, our treatment is valid only on linear scales since we do not intend to introduce any heuristic models. This approach makes the linear overdensity $δ_{\rm c}$ mass dependent and similarly to the case of smooth dark energy, its effects are predominant at small masses and redshifts. Tidal shear has effects of the order of percent or less, regardless of the model and preserves a well known feature of clustering dark energy: When dark energy perturbations are included, the models resemble better the $Λ$CDM evolution of perturbations. We also showed that effects on the comoving number density of halos are small and qualitatively and quantitatively in agreement with what previously found for smooth dark energy models.

astro-ph.CO↗

arXiv2016

Spherical collapse of dark matter haloes in tidal gravitational fields

We study the spherical collapse model in the presence of external gravitational tidal shear fields for different dark energy scenarios and investigate the impact on the mass function and cluster number counts. While previous studies of the influence of shear and rotation on $δ_\mathrm{c}$ have been performed with heuristically motivated models, we try to avoid this model dependence and sample the external tidal shear values directly from the statistics of the underlying linearly evolved density field based on first order Lagrangian perturbation theory. Within this self-consistent approach, in the sense that we restrict our treatment to scales where linear theory is still applicable, only fluctuations larger than the scale of the considered objects are included into the sampling process which naturally introduces a mass dependence of $δ_\mathrm{c}$. We find that shear effects are predominant for smaller objects and at lower redshifts, i. e. the effect on $δ_\mathrm{c}$ is at or below the percent level for the $Λ$CDM model. For dark energy models we also find small but noticeable differences, similar to $Λ$CDM. The virial overdensity $Δ_\mathrm{V}$ is nearly unaffected by the external shear. The now mass dependent $δ_c$ is used to evaluate the mass function for different dark energy scenarios and afterwards to predict cluster number counts, which indicate that ignoring the shear contribution can lead to biases of the order of $1σ$ in the estimation of cosmological parameters like $Ω_\mathrm{m}$, $σ_8$ or $w$.

astro-ph.CO↗

arXiv2015

The projected gravitational potential of the galaxy cluster MACS~J1206 derived from galaxy kinematics

We reconstruct the radial profile of the projected gravitational potential of the galaxy cluster MACS-J1206 from 592 spectroscopic measurements of velocities of cluster members. For doing so, we use a method we have developed recently based on the Richardson-Lucy deprojection algorithm and an inversion of the spherically-symmetric Jeans equation. We find that, within the uncertainties, our reconstruction agrees very well with a potential reconstruction from weak and strong gravitational lensing as well as with a potential obtained from X-ray measurements. In addition, our reconstruction is in good agreement with several common analytic profiles of the lensing potential. Varying the anisotropy parameter in the Jeans equation, we find that isotropy parameters which are either small, $β\lesssim0.2$, or decrease with radius yield potential profiles which strongly disagree with that obtained from gravitational lensing. We achieve the best agreement between our potential profile and the profile from gravitational lensing if the anisotropy parameter rises quite steeply to $β\approx0. 6$ within $\approx0.5\,\mathrm{Mpc}$ and stays constant further out.

astro-ph.CO↗

arXiv2015

Evolution of linear perturbations in Lemaître-Tolman-Bondi void models

We study the evolution of linear perturbations in a Lemaître-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations to couple at first order. As shown by Clarkson et al. (2009), the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system and generate scalar initial conditions based on Gaussian random fields with an underlying power spectrum for the Bardeen potential. After spherical harmonic decomposition, the initial fluctuations are propagated in time and estimates of angular power spectra of each gauge invariant variable are computed as functions of redshift. This allows to analyse the coupling strength in a statistical way. We find significant couplings up to $25\%$ for large and deep voids of Gpc scale as required to fit the distance redshift relations of SNe.

astro-ph.CO↗

arXiv2015

Reconstructing the projected gravitational potential of Abell 1689 from X-ray measurements

Context. Galaxy clusters can be used as cosmological probes, but to this end, they need to be thoroughly understood. Combining all cluster observables in a consistent way will help us to understand their global properties and their internal structure. Aims. We provide proof of the concept that the projected gravitational potential of galaxy clusters can directly be reconstructed from X-ray observations. We also show that this joint analysis can be used to locally test the validity of the equilibrium assumptions in galaxy clusters. Methods. We used a newly developed reconstruction method, based on Richardson-Lucy deprojection, that allows reconstructing projected gravitational potentials of galaxy clusters directly from X-ray observations. We applied this algorithm to the well-studied cluster Abell 1689 and compared the gravitational potential reconstructed from X-ray observables to the potential obtained from gravitational lensing measurements. [...] Results. Assuming spherical symmetry and hydrostatic equilibrium, the potentials recovered from gravitational lensing and from X-ray emission agree very well beyond 500 kpc. Owing to the fact that the Richardson-Lucy deprojection algorithm allows deprojecting each line of sight independently, this result may indicate that non-gravitational effects and/or asphericity are strong in the central regions of the clusters. Conclusions. We demonstrate the robustness of the potential reconstruction method based on the Richardson-Lucy deprojection algorithm and show that gravitational lensing and X-ray emission lead to consistent gravitational potentials. Our results illustrate the power of combining galaxy-cluster observables in a single, non-parametric, joint reconstruction of consistent cluster potentials that can be used to locally constrain the physical state of the gas.

astro-ph.CO↗

arXiv2014

Probing spatial homogeneity with LTB models: a detailed discussion

Do current observational data confirm the assumptions of the cosmological principle, or is there statistical evidence for deviations from spatial homogeneity on large scales? To address these questions, we developed a flexible framework based on spherically symmetric, but radially inhomogeneous Lemaitre-Tolman-Bondi (LTB) models with synchronous Big Bang. We expanded the (local) matter density profile in terms of flexible interpolation schemes and orthonormal polynomials. A Monte Carlo technique in combination with recent observational data was used to systematically vary the shape of these profiles. In the first part of this article, we reconsider giant LTB voids without dark energy to investigate whether extremely fine-tuned mass profiles can reconcile these models with current data. While the local Hubble rate and supernovae can easily be fitted without dark energy, however, model-independent constraints from the Planck 2013 data require an unrealistically low local Hubble rate, which is strongly inconsistent with the observed value; this result agrees well with previous studies. In the second part, we explain why it seems natural to extend our framework by a non-zero cosmological constant, which then allows us to perform general tests of the cosmological principle. Moreover, these extended models facilitate explorating whether fluctuations in the local matter density profile might potentially alleviate the tension between local and global measurements of the Hubble rate, as derived from Cepheid-calibrated type Ia supernovae and CMB experiments, respectively. We show that current data provide no evidence for deviations from spatial homogeneity on large scales. More accurate constraints are required to ultimately confirm the validity of the cosmological principle, however.

astro-ph.CO↗

arXiv2013

Reconstructing the projected gravitational potential of galaxy clusters from galaxy kinematics

We develop a method for reconstructing the two-dimensional, projected gravitational potential of galaxy clusters from observed line-of-sight velocity dispersions of cluster galaxies. It is the third of an intended series of papers aiming at a unique reconstruction method for cluster potentials combining lensing, X-ray, Sunyaev-Zel'dovich and kinematic data. The observed galaxy velocity dispersions are deprojected using the Richardson-Lucy algorithm. The obtained radial velocity dispersions are then related to the gravitational potential by using the tested assumption of a polytropic relation between the effective galaxy pressure and the density. Once the gravitational potential is obtained in three dimensions, projection along the line-of-sight yields the two-dimensional potential. For simplicity we adopt spherical symmetry and a known profile for the anisotropy parameter of the galaxy velocity dispersions. We test the method with a numerically simulated galaxy cluster and galaxies identified therein. We extract a projected velocity-dispersion profile from the simulated cluster and pass it through our algorithm, showing that the deviation between the true and the reconstructed gravitational potential is less then 10% within approximately 1.2 Mpc/h from the cluster centre.

astro-ph.CO↗

arXiv2013

Joint reconstruction of galaxy clusters from gravitational lensing and thermal gas. II. Inversion of the thermal Sunyaev-Zel'dovich effect

This paper continues a series in which we intend to show how all observables of galaxy clusters can be combined to recover the two-dimensional, projected gravitational potential of individual clusters. Our goal is to develop a non-parametric algorithm for joint cluster reconstruction taking all cluster observables into account. In this paper, we begin with the relation between the Compton-y parameter and the Newtonian gravitational potential, assuming hydrostatic equilibrium and a polytropic stratification of the intracluster gas. We show how Richardson-Lucy deconvolution can be used to convert the intensity change of the CMB due to the thermal Sunyaev-Zel'dovich effect into an estimate for the two-dimensional gravitational potential. Synthetic data simulated with characteristics of the ALMA telescope show that the two-dimensional potential of a cluster with mass 5*10^14 M_sun/h at redshift 0.2 is possible with an error of < 5% between the cluster centre and a radius r < 0.9 Mpc/h.

astro-ph.CO↗

arXiv2013

Joint reconstruction of galaxy clusters from gravitational lensing and thermal gas I. Outline of a non-parametric method

We present a method to estimate the lensing potential from massive galaxy clusters for given observational X-ray data. The concepts developed and applied in this work can easily be combined with other techniques to infer the lensing potential, e.g. weak gravitational lensing or galaxy kinematics, to obtain an overall best fit model for the lensing potential. After elaborating on the physical details and assumptions the method is based on, we explain how the numerical algorithm itself is implemented with a Richardson-Lucy algorithm as a central part. Our reconstruction method is tested on simulated galaxy clusters with a spherically symmetric NFW density profile filled with gas in hydrostatic equilibrium. We describe in detail how these simulated observational data sets are created and how they need to be fed into our algorithm. We test the robustness of the algorithm against small parameter changes and estimate the quality of the reconstructed lensing potentials. As it turns out we achieve a very high degree of accuracy in reconstructing the lensing potential. The statistical errors remain below 2.0% whereas the systematical error does not exceed 1.0%.

astro-ph.CO↗

arXiv2012

Relativistic virialization in the Spherical Collapse model for Einstein-de Sitter and ΛCDM cosmologies

Spherical collapse has turned out to be a successful semi-analytic model to study structure formation in different DE models and theories of gravity. Nevertheless, the process of virialization is commonly studied on the basis of the virial theorem of classical mechanics. In the present paper, a fully generally-relativistic virial theorem based on the Tolman-Oppenheimer-Volkoff (TOV) solution for homogeneous, perfect-fluid spheres is constructed for the Einstein-de Sitter and ΛCDM cosmologies. We investigate the accuracy of classical virialization studies on cosmological scales and consider virialization from a more fundamental point of view. Throughout, we remain within general relativity and the class of FLRW models. The virialization equation is set up and solved numerically for the virial radius, y_{vir}, from which the virial overdensity Δ_{V} is directly obtained. Leading order corrections in the post-Newtonian framework are derived and quantified. In addition, problems in the application of this formalism to dynamical DE models are pointed out and discussed explicitly. We show that, in the weak field limit, the relative contribution of the leading order terms of the post-Newtonian expansion are of the order of 10^{-3}% and the solution of Wang & Steinhardt (1998) is precisely reproduced. Apart from the small corrections, the method could provide insight into the process of virialization from a more fundamental point of view.

astro-ph.CO↗