Identification of members in the central and outer regions of galaxy clusters

The caustic technique measures the mass of galaxy clusters in both their virial and infall regions and, as a byproduct, yields the list of cluster galaxy members. Here we use 100 galaxy clusters with mass M200>=1E14 Msun/h extracted from a cosmological N-body simulation of a LambdaCDM universe to test the ability of the caustic technique to identify the cluster galaxy members. We identify the true three-dimensional members as the gravitationally bound galaxies. The caustic technique uses the caustic location in the redshift diagram to separate the cluster members from the interlopers. We apply the technique to mock catalogues containing 1000 galaxies in the field of view of 12 Mpc/h on a side at the cluster location. On average, this sample size roughly corresponds to 180 real galaxy members within 3r200, similar to recent redshift surveys of cluster regions. The caustic technique yields a completeness, the fraction of identified true members, fc=0.95 (+- 0.03) within 3r200. The contamination increases from fi=0.020 (+0.046;-0.015) at r200 to fi=0.08 (+0.11;-0.05) at 3r200. No other technique for the identification of the members of a galaxy cluster provides such large completeness and small contamination at these large radii. The caustic technique assumes spherical symmetry and the asphericity of the cluster is responsible for most of the spread of the completeness and the contamination. By applying the technique to an approximately spherical system obtained by stacking the individual clusters, the spreads decrease by at least a factor of two. We finally estimate the cluster mass within 3r200 after removing the interlopers: for individual clusters, the mass estimated with the virial theorem is unbiased and within 30 per cent of the actual mass; this spread decreases to less than 10 per cent for the spherically symmetric stacked cluster.Comment: 13 pages, 10 figures, published on Ap

Identification of galaxy cluster substructures with the Caustic method

We investigate the power of the caustic technique for identifying substructures of galaxy clusters from optical redshift data alone. The caustic technique is designed to estimate the mass profile of galaxy clusters to radii well beyond the virial radius, where dynamical equilibrium does not hold. Two by-products of this technique are the identification of the cluster members and the identification of the cluster substructures. We test the caustic technique as a substructure detector on two samples of 150 mock redshift surveys of clusters; the clusters are extracted from a large cosmological $N$-body simulation of a $\Lambda$CDM model and have masses of $M_{200} \sim 10^{14} h^{-1} M_{\odot}$ and $M_{200} \sim 10^{15} h^{-1} M_{\odot}$ in the two samples. We limit our analysis to substructures identified in the simulation with masses larger than $10^{13} h^{-1} M_{\odot}$. With mock redshift surveys with 200 galaxies within $3R_{200}$, (1) the caustic technique recovers $\sim 30-50$\% of the real substructures, and (2) $\sim 15-20$\% of the substructures identified by the caustic technique correspond to real substructures of the central cluster, the remaining fraction being low-mass substructures, groups or substructures of clusters in the surrounding region, or chance alignments of unrelated galaxies. These encouraging results show that the caustic technique is a promising approach for investigating the complex dynamics of galaxy clusters.Comment: 13 pages, 15 figures. Accepted for publication in Ap

The mass accretion rate of galaxy clusters: a measurable quantity

We explore the possibility of measuring the mass accretion rate (MAR) of galaxy clusters from their mass profiles beyond the virial radius $R_{200}$. We derive the accretion rate from the mass of a spherical shell whose inner radius is $2R_{200}$, whose thickness changes with redshift, and whose infall velocity is assumed to be equal to the mean infall velocity of the spherical shells of dark matter halos extracted from $N$-body simulations. This approximation is rather crude in hierarchical clustering scenarios where both smooth accretion and aggregation of smaller dark matter halos contribute to the mass accretion of clusters.Nevertheless, in the redshift range $z=[0,2]$, our prescription returns an average MAR within $20-40 \%$ of the average rate derived from the merger trees of dark matter halos extracted from $N$-body simulations. The MAR of galaxy clusters has been the topic of numerous detailed numerical and theoretical investigations, but so far it has remained inaccessible to measurements in the real universe. Since the measurement of the mass profile of clusters beyond their virial radius can be performed with the caustic technique applied to dense redshift surveys of the cluster outer regions, our result suggests that measuring the mean MAR of a sample of galaxy clusters is actually feasible. We thus provide a new potential observational test of the cosmological and structure formation models.Comment: 11 pages, 7 figures, 5 tables, minor text modifications to match the published version, typos correcte

Measuring the dark matter equation of state

The nature of the dominant component of galaxies and clusters remains unknown. While the astrophysics community supports the cold dark matter (CDM) paradigm as a clue factor in the current cosmological model, no direct CDM detections have been performed. Faber and Visser 2006 have suggested a simple method for measuring the dark matter equation of state that combines kinematic and gravitational lensing data to test the widely adopted assumption of pressureless dark matter. Following this formalism, we have measured the dark matter equation of state for first time using improved techniques. We have found that the value of the equation of state parameter is consistent with pressureless dark matter within the errors. Nevertheless, the measured value is lower than expected because typically the masses determined with lensing are larger than those obtained through kinematic methods. We have tested our techniques using simulations and we have also analyzed possible sources of error that could invalidate or mimic our results. In the light of this result, we can now suggest that the understanding of the nature of dark matter requires a complete general relativistic analysis.Comment: 4 pages, 2 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society Letters. Minor revision as suggested by refere

Blooming Trees: Substructures and Surrounding Groups of Galaxy Clusters

We develop the Blooming Tree Algorithm, a new technique that uses spectroscopic redshift data alone to identify the substructures and the surrounding groups of galaxy clusters, along with their member galaxies. Based on the estimated binding energy of galaxy pairs, the algorithm builds a binary tree that hierarchically arranges all the galaxies in the field of view. The algorithm searches for buds, corresponding to gravitational potential minima on the binary tree branches; for each bud, the algorithm combines the number of galaxies, their velocity dispersion and their average pairwise distance into a parameter that discriminates between the buds that do not correspond to any substructure or group, and thus eventually die, and the buds that correspond to substructures and groups, and thus bloom into the identified structures. We test our new algorithm with a sample of 300 mock redshift surveys of clusters in different dynamical states; the clusters are extracted from a large cosmological $N$-body simulation of a $\Lambda$CDM model. We limit our analysis to substructures and surrounding groups identified in the simulation with mass larger than $10^{13} h^{-1} M_{\odot}$. With mock redshift surveys with 200 galaxies within 6 $h^{-1}$~Mpc from the cluster center, the technique recovers $80$\% of the real substructures and $60$\% of the surrounding groups; in $57$\% of the identified structures, at least 60\% of the member galaxies of the substructures and groups belong to the same real structure. These results improve by roughly a factor of two the performance of the best substructure identification algorithm currently available, the $\sigma$ plateau algorithm, and suggest that our Blooming Tree Algorithm can be an invaluable tool for detecting substructures of galaxy clusters and investigating their complex dynamics.Comment: 17 pages, 20 figures, accepted by Ap

Measuring the Mass Distribution in Galaxy Clusters

Cluster mass profiles are tests of models of structure formation. Only two current observational methods of determining the mass profile, gravitational lensing, and the caustic technique are independent of the assumption of dynamical equilibrium. Both techniques enable the determination of the extended mass profile at radii beyond the virial radius. For 19 clusters, we compare the mass profile based on the caustic technique with weak lensing measurements taken from the literature. This comparison offers a test of systematic issues in both techniques. Around the virial radius, the two methods of mass estimation agree to within ~30%, consistent with the expected errors in the individual techniques. At small radii, the caustic technique overestimates the mass as expected from numerical simulations. The ratio between the lensing profile and the caustic mass profile at these radii suggests that the weak lensing profiles are a good representation of the true mass profile. At radii larger than the virial radius, the extrapolated Navarro, Frenk & White fit to the lensing mass profile exceeds the caustic mass profile. Contamination of the lensing profile by unrelated structures within the lensing kernel may be an issue in some cases; we highlight the clusters MS0906+11 and A750, superposed along the line of sight, to illustrate the potential seriousness of contamination of the weak lensing signal by these unrelated structures

Air Quality Trend of PM10. Statistical Models for Assessing the Air Quality Impact of Environmental Policies

A statistical modelling of PM10 concentration (2006–2015) is applied to understand the behaviour, to know the influence of the variables to exposure risk, to treat the missing data to evaluate air quality, and to estimate data for those sites where they are not available. The study area, Castellón region (Spain), is a strategic area in the framework of EU pollution control. A decrease of PM10 is observed for industrial and urban stations. In the case of rural stations, the levels remain constant throughout the study period. The contribution of anthropogenic sources has been estimated through the PM10 background of the study area. The behaviour of PM10 annual trend is tri-modal for industrial and urban stations and bi-modal in the case of rural stations. The EU Normative suggests that 90% of the data per year are necessary to control air quality. Thus, interpolation statistical methods are presented to fill missing data: Linear Interpolation, Exponential Interpolation, and Kalman Smoothing. This study also focuses on testing the goodness of these methods in order to find the ones that better approach the gaps. After analyzing graphically and using the RMSE the last method is confirmed to be the best option

Variability of PM10 in industrialized-urban areas. New coefficients to establish significant differences between sampling points

One of the main problems that arise in the assessment of air quality in an area is to estimate the number of representative sampling points of each microenvironment within it. We present a new model that reduces the variability and increases the quality of the comparison of the sampling points. The study is based on the comparison between a city in eastern Spain, Vila-real, a macro city in México, Monterrey and the Piemonte region regarding the assessment of PM10 in microenvironments. Vila-real is located in the province of Castellón. This province is a strategic area in the framework of European Union (EU) pollution control. On the other hand, Monterrey in México, located in the northern state of Nuevo León, has several problems with particulate material in the atmosphere produced by the extraction of building materials in the hill that surround the city. Finally, the Piemonte region, which is located in the north of Italy, has to be in consideration due to higher concentrations of PM10 in the Po river basin. In the case of Vila-real the PM10 samples were collected by a medium volume sampler according to European regulations. Particle concentration levels were determined gravimetrically (EN 12341:1999). In the case of Monterrey the PM10 concentrations were determined by Beta Ray Attenuation according to US-EPA regulations. In the Piemonte region, the average concentration of PM10 was also obtained by means of the Beta Ray Attenuation as well as using gravimetric instruments. The methodology carried out in this paper is a useful tool for developing future Air Quality Plans in other industrialised areas

Reliability Validation of a Low-Cost Particulate Matter IoT Sensor in Indoor and Outdoor Environments Using a Reference Sampler

A suitable and quick determination of air quality allows the population to be alerted with respect to high concentrations of pollutants. Recent advances in computer science have led to the development of a high number of low-cost sensors, improving the spatial and temporal resolution of air quality data while increasing the effectiveness of risk assessment. The main objective of this work is to perform a validation of a particulate matter (PM) sensor (HM-3301) in indoor and outdoor environments to study PM2.5 and PM10 concentrations. To date, this sensor has not been evaluated in real-world situations, and its data quality has not been documented. Here, the HM-3301 sensor is integrated into an Internet of things (IoT) platform to establish a permanent Internet connection. The validation is carried out using a reference sampler (LVS3 of Derenda) according to EN12341:2014. It is focused on statistical insight, and environmental conditions are not considered in this study. The ordinary Linear Model, the Generalized Linear Model, Locally Estimated Scatterplot Smoothing, and the Generalized Additive Model have been proposed to compare and contrast the outcomes. The low-cost sensor is highly correlated with the reference measure ( R2 greater than 0.70), especially for PM2.5, with a very high accuracy value. In addition, there is a positive relationship between the two measurements, which can be appropriately fitted through the Locally Estimated Scatterplot Smoothing model