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Ewa L. Lokas

Publications and source records attributed to Ewa L. Lokas.

At least 91 records · Page 5Linked to original sources
arXiv2007

Mass modelling of Abell 2634: avoiding the interloper bias

Using an example of the Abell 2634 galaxy cluster we discuss the effect of contamination of kinematic data by interlopers and its impact on mass modelling. The cluster data reveal rich substructure along the line of sight. We demonstrate that it is necessary to apply a few independent methods of interloper removal in order to obtain a reliable sample of cluster members. We present results of three such methods which are commonly used in the literature and have been recently extensively tested on simulated data. Only two of them lead to consistent and reliable samples of cluster galaxies. For both of them we provide parameters of the best-fitting NFW density profile by fitting an isotropic solution of the Jeans equation to the velocity dispersion profiles.

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arXiv2007

Mass modelling of galaxy clusters via velocity moments

We summarize the method of mass modelling of galaxy clusters based on reproducing the dispersion and kurtosis of the projected velocity distribution of galaxies. The models are parametrized within the framework of the NFW density profile, characterized by the virial mass and concentration, together with the constant anisotropy of galaxy orbits. The use of velocity dispersion alone does not allow to constrain all the three parameters from kinematic data due to the mass-anisotropy degeneracy. The degeneracy is broken by introducing the fourth velocity moment, the kurtosis. We tested the method based on fitting both moments on mock data sets drawn from simulated dark matter haloes and showed it to reproduce reliably the properties of the haloes. The method has been applied to estimate the mass, concentration and anisotropy of more than 20 clusters which allowed us to confirm, for the first time using kinematic data, the mass-concentration relation found in N-body simulations.

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arXiv2007

The effect of unbound stars on the mass modelling of the Fornax dwarf

We discuss how different approaches to selecting member stars in kinematic samples of dwarf spheroidal galaxies affect the estimates of their mass and anisotropy of stellar orbits. We demonstrate that the selection of members is an additional source of error compared to the usual uncertainties due to the sampling of velocity moments. As an example we use the kinematic data set for 202 stars in the Fornax dwarf galaxy for which we model the velocity dispersion profile and estimate the mass-to-light ratio and anisotropy assuming that mass follows light. We also show that stronger constraints on these parameters can be obtained if kurtosis of the velocity distribution is included in the analysis. Using the Besancon model of the Milky Way we demonstrate that the majority of contamination in Fornax probably comes from the Milky Way stars.

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arXiv2007

Mass modelling of dwarf spheroidal galaxies: the effect of unbound stars from tidal tails and the Milky Way

We study the origin and properties of the population of unbound stars in the kinematic samples of dwarf spheroidal galaxies. For this purpose we have run a high resolution N-body simulation of a two-component dwarf galaxy orbiting in a Milky Way potential. The dwarf is placed on a highly eccentric orbit, its initial stellar component is in the form of an exponential disk and it has a NFW-like dark matter halo. After 10 Gyrs of evolution the dwarf produces a spheroidal stellar component and is strongly tidally stripped so that mass follows light and the stars are on almost isotropic orbits. From this final state, we create mock kinematic data sets for 200 stars by observing the dwarf in different directions. We find that when the dwarf is observed along the tidal tails the kinematic samples are strongly contaminated by unbound stars from the tails. We also study another source of possible contamination by adding stars from the Milky Way. We demonstrate that most of the unbound stars can be removed by the method of interloper rejection proposed by den Hartog & Katgert. We model the cleaned-up kinematic samples using solutions of the Jeans equation with constant mass-to-light ratio and velocity anisotropy parameter. We show that the Jeans analysis, when applied to cleaned samples, allows us to reproduce the mass and mass-to-light ratio of the dwarf with accuracy typically better than 25 percent. The analysis was applied to the new data for the Fornax dSph galaxy. We show that after careful removal of interlopers the velocity dispersion profile of Fornax can be reproduced by a model in which mass traces light with a mass-to-light ratio of 11 solar units and isotropic orbits. We demonstrate that most of the contamination in the kinematic sample of Fornax probably originates from the Milky Way. (Abridged)

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arXiv2007

The importance of interloper removal in galaxy clusters: saving more objects for the Jeans analysis

We study the effect of contamination by interlopers in kinematic samples of galaxy clusters. We demonstrate that without the proper removal of interlopers the inferred parameters of the mass distribution in the cluster are strongly biased towards higher mass and lower concentration. The interlopers are removed using two procedures previously shown to work most efficiently on simulated data. One is based on using the virial mass estimator and calculating the maximum velocity available to cluster members and the other relies on the ratio of the virial and projected mass estimators. We illustrate the performance of the methods in detail using the example of A576, a cluster with a strong uniform background contamination, and compare the case of A576 to 15 other clusters with different degree of contamination. We model the velocity dispersion and kurtosis profiles obtained for the cleaned data samples of these clusters solving the Jeans equations to estimate the mass, concentration and anisotropy parameter. We present the mass-concentration relation for the total sample of 22 clusters.

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arXiv2007

Interloper treatment in dynamical modelling of galaxy clusters

The aim of this paper is to study the efficiency of different approaches to interloper treatment in dynamical modelling of galaxy clusters. Using cosmological N-body simulation of standard LCDM model, we select 10 massive dark matter haloes and use their particles to emulate mock kinematic data in terms of projected galaxy positions and velocities as they would be measured by a distant observer. Taking advantage of the full 3D information available from the simulation, we select samples of interlopers defined with different criteria. The interlopers thus selected provide means to assess the efficiency of different interloper removal schemes found in the literature. We study direct methods of interloper removal based on dynamical or statistical restrictions imposed on ranges of positions and velocities available to cluster members. In determining these ranges, we use either the velocity dispersion criterion or a maximum velocity profile. We also generalize the common approaches taking into account both the position and velocity information. Another criterion is based on the dependence of the commonly used virial mass and projected mass estimators on the presence of interlopers. We find that the direct methods exclude on average 60-70 percent of unbound particles producing a sample with contamination as low as 2-4 percent. Next, we consider indirect methods of interloper treatment which are applied to the data stacked from many objects. In these approaches, interlopers are treated in a statistical way as a uniform background which modifies the distribution of cluster members. Using a Bayesian approach, we reproduce the properties of composite clusters and estimate the probability of finding an interloper as a function of distance from the object centre.

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arXiv2006

Dark Matter in Draco: new considerations of the expected gamma flux in IACTs

A new revision of the gamma flux that we expect to detect in Imaging Atmospheric Cherenkov Telescopes (IACTs) from SUSY dark matter annihilation in the Draco dSph is presented using the dark matter density profiles compatible with the latest observations. This revision takes also into account the important effect of the Point Spread Function (PSF) of the Cherenkov telescope. We show that this effect is crucial in the way we will observe and interpret a possible signal profile in the telescope. Given these new considerations, some light can be shed on the recent signal excess reported by the CACTUS experiment.

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arXiv2005

Mass distribution in nearby Abell clusters

We study the mass distribution in six nearby (z<0.06) relaxed Abell clusters of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of dark matter in galaxy clusters we approximate their total density distribution by the NFW formula characterized by virial mass and concentration. We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density. Using the velocity and position data for 120-420 galaxies per cluster we calculate, after removal of interlopers, the profiles of the lowest-order even velocity moments, dispersion and kurtosis. We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations. Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration. The method is tested in detail on mock data extracted from N-body simulations of dark matter haloes. We find that the best-fitting galactic orbits are remarkably close to isotropic in most clusters. Using the fitted pairs of mass and concentration parameters for the six clusters we conclude that the trend of decreasing concentration for higher masses found in cosmological N-body simulations is consistent with the data. By scaling the individual cluster data by mass we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample. The estimated concentration parameter then lies in the range 1.5 < c < 14 and the anisotropy parameter in the range -1.1 < β< 0.5 at the 95 percent confidence level.

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arXiv2005

The complex velocity distribution of galaxies in Abell 1689: implications for mass modelling

The Abell 1689 galaxy cluster has recently become a subject of intensive study. Thanks to its intermediate redshift (z=0.183) its mass distribution can be reconstructed using numerous methods including gravitational lensing, galaxy kinematics and X-ray imaging. The methods used to yield conflicting mass estimates in the past and recently the cluster mass distribution has been claimed to be in conflict with standard CDM scenarios due to rather large concentration and steep mass profile obtained from detailed studies of Broadhurst et al. using lensing. By studying in detail the kinematics of about 200 galaxies with measured redshifts in the vicinity of the cluster we show that the cluster is probably surrounded by a few structures, quite distant from each other, but aligned along the line of sight. We support our arguments by referring to cosmological N-body simulations and showing explicitly that distant, non-interacting haloes can produce entangled multi-peak line-of-sight velocity distributions similar to that in A1689. We conclude that it is difficult to estimate the cluster mass reliably from galaxy kinematics, but the value we obtain after applying a simple cut-off in velocity agrees roughly with the mass estimated from lensing. The complicated mass distribution around the cluster may however increase the uncertainty in the determination of the density profile shape obtained with weak lensing.

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arXiv2005

The Draco dwarf in CDM and MOND

We present interpretations of the line-of-sight velocity distribution of stars in the Draco dwarf spheroidal galaxy in terms of CDM and MOND assuming constant mass-to-light ratio and anisotropy. We estimate the two parameters by fitting the line-of-sight velocity dispersion and kurtosis profiles for stellar samples differing by a number of stars rejected as interlopers. The results of the fitting procedure for CDM, high mass-to-light ratio (131-141 solar units in V-band) and weakly tangential orbits, are similar for different samples, but the quality of the fit is much worse when fewer interlopers are removed. For MOND, the derived mass-to-light ratio (21 solar units) is too large to be explained by the stellar content of the galaxy.

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arXiv2005

Velocity moments of dark matter haloes

Using cosmological N-body simulations we study the line-of-sight velocity distribution of dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis, and their application to estimate the mass profiles of cosmological structures. For each of the ten massive haloes selected from the simulation box we determine the virial mass, concentration and the anisotropy parameter. In order to emulate observations from each halo we choose randomly 300 particles and project their velocities and positions along the line of sight and on the surface of the sky, respectively. After removing interlopers we calculate the profiles of the line-of-sight velocity moments and fit them with the solutions of the Jeans equations. The estimates of virial mass, concentration parameter and velocity anisotropy obtained in this way are in good agreement with the values found from the full 3D analysis.

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arXiv2005

Dark matter distribution in the Draco dwarf from velocity moments

We study the distribution of dark matter in the Draco dwarf spheroidal galaxy by modelling the moments of the line-of-sight velocity distribution of stars obtained from new velocity data of Wilkinson et al. The luminosity distribution is approximated by a Sersic profile fitted to the data by Odenkirchen et al. We assume that the dark matter density profile is given by a formula with an inner cusp and an outer exponential cut-off, as recently proposed by Kazantzidis et al. as a result of simulations of tidal stripping of dwarfs by the potential of the Milky Way. The dark matter distribution is characterized by the total dark mass and the cut-off radius. The models have arbitrary velocity anisotropy parameter assumed to be constant with radius. We estimate the three parameters by fitting both the line-of-sight velocity dispersion and kurtosis profiles, which allows us to break the degeneracy between the mass distribution and velocity anisotropy. The results of the fitting procedure turn out to be very different depending on the stellar sample considered, that is on our choice of stars with discrepant velocities to be discarded as interlopers. For our most reliable sample, the model parameters remain weakly constrained, but the robust result is the preference for weakly tangential stellar orbits and high mass-to-light ratios. The best-fitting total mass is then 7 10^7 M_sun, much lower than recent estimates, while the mass-to-light ratio is M/L_V = 300 and almost constant with radius. If the binary fraction in the stellar population of Draco turns out to be significant, the kurtosis of the global velocity distribution will be smaller and the orbits inferred will be more tangential, while the resulting mass estimate lower.

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arXiv2005

Radial velocity moments of dark matter haloes

Using cosmological N-body simulations we study the radial velocity distribution in dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis. We determine the properties of ten massive haloes in the simulation box approximating their density distribution by the NFW formula characterized by the virial mass and concentration. We also calculate the velocity anisotropy parameter of the haloes and find it mildly radial and increasing with distance from the halo centre. The radial velocity dispersion of the haloes shows a characteristic profile with a maximum, while the radial kurtosis profile decreases with distance starting from a value close to Gaussian near the centre. We therefore confirm that dark matter haloes possess intrinsically non-Gaussian, flat-topped velocity distributions. We find that the radial velocity moments of the simulated haloes are quite well reproduced by the solutions of the Jeans equations obtained for the halo parameters with the anisotropy measured in the simulations. We also study the radial velocity moments for a composite cluster made of ten haloes out to ten virial radii. In this region the velocity dispersion decreases systematically to reach the value of the background, while kurtosis increases from below to above the Gaussian value of 3 signifying a transition from a flat-topped to a strongly peaked velocity distribution with respect to the Gaussian, which can be interpreted as the dominance of ordered flow with a small dispersion. We illustrate the transition by showing explicitly the velocity distribution of the composite cluster in a few radial bins.

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arXiv2004

Breaking the mass / anisotropy degeneracy in the Coma cluster

We provide the first direct lifting of the mass/anisotropy degeneracy for a cluster of galaxies, by jointly fitting the line of sight velocity dispersion and kurtosis profiles of the Coma cluster, assuming an NFW tracer density profile, a generalized-NFW dark matter profile and a constant anisotropy profile. We find that the orbits in Coma must be quasi-isotropic, and find a mass consistent with previous analyses, but a concentration parameter 50% higher than expected in cosmological N-body simulations. We then test the accuracy of our method on realistic non-spherical systems with substructure and streaming motions, by applying it to the ten most massive structures in a cosmological N-body simulation. We find that our method yields fairly accurate results on average (within 20%), although with a wide variation (factor 1.7 at 1 sigma) for the concentration parameter, with decreased accuracy and efficiency when the projected mean velocity is not constant with radius.

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arXiv2003

Cluster mass functions in the quintessential Universe

We use $N$-body simulations to measure mass functions in flat cosmological models with quintessence characterized by constant $w$ with $w=-1$, -2/3 and -1/2. The results are compared to the predictions of the formula proposed by Jenkins et al. at different redshifts, in terms of FOF masses as well as Abell masses appropriate for direct comparison to observations. The formula reproduces quite well the mass functions of simulated haloes in models with quintessence. We use the cluster mass function data at a number of redshifts from Carlberg et al. to constrain $Ω_0$, $σ_8$ and $w$. The best fit is obtained in the limit $w \to 0$, but none of the values of $w$ in the considered range $-1 \le w < 0$ can actually be excluded. However, the adopted value of $w$ affects significantly the constraints in the $Ω_0-σ_8$ plane. Taking into account the dependence on $w$ we find $Ω_0=0.32 \pm 0.15$ and $σ_8=0.85_{-0.12}^{+0.38}$ (68% c.l.). Since less negative $w$ push the confidence regions toward higher $Ω_0$ and lower $σ_8$ we conclude that relaxing the assumption of $w=-1$ typically made in such comparisons may resolve the discrepancy between recent cluster mass function results (yielding rather low $Ω_0$ and high $σ_8$) and most other estimates. The fact that high $w$ values are preferred may however also point towards some unknown systematics in the data or the model with constant $w$ being inadequate.

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arXiv2003

How reliable is the kinematical evidence for dark matter: the effects of non-sphericity, substructure and streaming motions

Using cosmological $N$-body simulations of dark matter haloes, we study the effects of non-sphericity, substructure and streaming motions in reproducing the structure and internal kinematics of clusters of galaxies from kinematical measurements. Fitting an NFW model to the 3D density profile, we determine the virial mass, concentration parameter and velocity anisotropy of the haloes, and then calculate the profiles of projected velocity moments, as they would be measured by a distant observer. Using these mock data, we apply a Jeans analysis for spherical objects to reproduce the line-of-sight velocity dispersion and kurtosis and fit the three parameters. We find that the line-of-sight velocity dispersion and kurtosis profiles of a given halo can vary considerably with the angle of view of the observer. We show that the virial mass, concentration parameter and velocity anisotropy of the haloes can be reproduced satisfactorily independently of the halo shape, although the virial mass tends to be underestimated, the concentration parameter overestimated, while the recovered anisotropy is typically more tangential than the true one. The mass, concentration and velocity anisotropy of haloes are recovered with better precision when their mean velocity profiles are near zero.

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arXiv2003

Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy

We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalised formula based upon the results of cosmological N-body simulations. Its inner slope (cuspy or flat), concentration, and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line-of-sight velocity dispersion alone does not allow to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3% of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope $α$ and concentration $c$: the best-fitting profiles have the two parameters related with $c=19 - 9.6 α$. Our best-fitting NFW profile has concentration $c=9$, which is 50% higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of $2.9 h_{70}^{-1}$ Mpc is $1.4 \times 10^{15} h_{70}^{-1} M_{\sun}$ (with 30% accuracy), 85% of which is dark. At this distance from the cluster centre, the mass-to-light ratio in the blue band is $351 h_{70}$ solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass-to-light ratio and baryonic fraction of the Universe, with $Ω_0=0.29 \pm 0.1$.

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