The Peculiar Motions of Early-Type Galaxies in Two Distant Regions VI: The Maximum Likelihood Gaussian Algorithm

The EFAR project is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. Here we describe the maximum likelihood algorithm we developed to investigate the correlations between the parameters of the EFAR database. One-, two-, and three-dimensional gaussian models are constructed to determine the mean value and intrinsic spread of the parameters, and the slopes and intrinsic parallel and orthogonal spread of the Mgb'-Mg2, Mg2-sigma, Mgb'-sigma relations, and the Fundamental Plane. In the latter case, the cluster peculiar velocities are also determined. We show that this method is superior to ``canonical'' approaches of least-squares type, which give biased slopes and biased peculiar velocities. We test the algorithm with Monte Carlo simulations of mock EFAR catalogues and derive the systematic and random errors on the estimated parameters. We find that random errors are always dominant. We estimate the influence of systematic errors due to the way clusters were selected and the hard limits and uncertainties in the selection function parameters for the galaxies. We explore the influence of uniform distributions in the Fundamental Plane parameters and the errors. We conclude that the mean peculiar motions of the EFAR clusters can be determined reliably. In particular, the placement of the two EFAR sample regions relative to the Lauer and Postman dipole allows us to strongly constrain the amplitude of the bulk motion in this direction.Comment: 43 pages, 19 figures, accepted for publication in MNRA

Biological invasions and host–parasite coevolution: different coevolutionary trajectories along separate parasite invasion fronts

Host–parasite coevolution has rarely been observed in natural systems. Its study often relies on microparasitic infections introducing a potential bias in the estimation of the evolutionary change of host and parasite traits. Using biological invasions as a tool to study host–parasite coevolution in nature can overcome these biases. We demonstrate this with a cross-infection experiment in the invasive macroparasite <i>Mytilicola intestinalis</i> and its bivalve host, the blue mussel <i>Mytilus edulis</i>. The invasion history of the parasite is well known for the southeastern North Sea and is characterised by two separate invasion fronts that reached opposite ends of the Wadden Sea (i.e. Texel, The Netherlands and Sylt, Germany) in a similar time frame. The species’ natural history thus makes this invasion an ideal natural experiment to study host–parasite coevolution in nature. We infected hosts from Texel, Sylt and Kiel (Baltic Sea, where the parasite is absent) with parasites from Texel and Sylt, to form sympatric, allopatric and naïve infestation combinations, respectively. We measured infection rate, host condition and parasite growth to show that sympatric host–parasite combinations diverged in terms of pre- and post-infection traits within <100 generations since their introduction. Texel parasites were more infective and more efficient at exploiting the host’s resources. Hosts on Texel, on the other hand, evolved resistance to infection, whereas hosts on Sylt may have evolved tolerance. This illustrates that different coevolutionary trajectories can evolve along separate invasion fronts of the parasite, highlighting the use of biological invasions in studies of host–parasite coevolution in nature

The peculiar motions of early-type galaxies in two distant regions - V. The Mg-sigma relation, age and metallicity

We have examined the Mg-sigma relation for early-type galaxies in the EFAR sample and its dependence on cluster properties. A comprehensive maximum likelihood treatment of the sample selection and measurement errors gives fits to the global Mg-sigma relation of Mg b^'=0.131 log sigma -0.131 and Mg_2=0.257 log sigma -0.305. The slope of these relations is 25 per cent steeper than that obtained by most other authors owing to the reduced bias of our fitting method. The intrinsic scatter in the global Mg- sigma relation is estimated to be 0.016 mag in Mg b^' and 0.023 mag in Mg_2. The Mg- sigma relation for cD galaxies has a higher zero-point than for E and S0 galaxies, implying that cDs are older and/or more metal-rich than other early-type galaxies with the same velocity dispersion. We investigate the variation in the zero-point of the Mg- sigma relation between clusters. We find that it is consistent with the number of galaxies observed per cluster and the intrinsic scatter between galaxies in the global Mg-sigma relation. We find no significant correlation between the Mg-sigma zero-point and the cluster velocity dispersion, X-ray luminosity or X-ray temperature over a wide range in cluster mass. These results provide constraints for models of the formation of elliptical galaxies. However, the Mg-sigma relation on its own does not place strong limits on systematic errors in Fundamental Plane (FP) distance estimates resulting from stellar population differences between clusters. We compare the intrinsic scatter in the Mg-sigma and Fundamental Plane relations with stellar population models in order to constrain the dispersion in ages, metallicities and M/L ratios for early-type galaxies at fixed velocity dispersion. We find that variations in age or metallicity alone cannot explain the measured intrinsic scatter in both Mg- sigma and the FP. We derive the joint constraints on the dispersion in age and metallicity implied by the scatter in the Mg-sigma and FP relations for a simple Gaussian model. We find upper limits on the dispersions in age and metallicity at fixed velocity dispersion of 32 per cent in delta t/t and 38 per cent in delta Z/Z if the variations in age and metallicity are uncorrelated; only strongly anticorrelated variations lead to significantly higher upper limits. The joint distribution of residuals from the Mg- sigma and FP relations is only marginally consistent with a model having no correlation between age and metallicity, and is better matched by a model in which age and metallicity variations are moderately anticorrelated (delta t/t ~ 40 per cent, delta Z/Z ~ 50 per cent and rho ~ -0.5), with younger galaxies being more metal-rich

Spread of the invasive shell-boring annelid Polydora websteri (Polychaeta, Spionidae) into naturalised oyster reefs in the European Wadden Sea

With globally growing aquaculture activities, the co-introduction of parasites alongside large-scale movements of commercial species poses an increasing risk for marine ecosystems. Here, we present the first record of the shell-boring polychaete Polydora websteri Hartman in Loosanoff and Engle, 1943 in invasive Pacific oysters Crassostrea (Magallana) gigas (Thunberg, 1793) in the European Atlantic Ocean. In October 2014, mud blisters in the shells of wild Pacific oysters and specimens of a spionid polychaete were observed in close proximity to a commercial oyster farm at the island of Sylt (Germany) in the European Wadden Sea. Subsequent investigations indicated that these blisters only occurred near the farm and that no other mollusc species were affected. Morphological and molecular analysis identified the polychaete as Polydora websteri, a species that nowadays widely occurs around the globe, but likely is native to the Asian Pacific. Later sampling activities detected P. websteri also at other locations around Sylt as well as in the Dutch part of the Wadden Sea at the island of Texel. The number of polychaetes in the oysters was, however, relatively low and mostly below 10 individuals per oyster. Together, this evidence suggests that P. websteri is currently extending its range. As the introduction of P. websteri may have severe ecological and economic implications, this study aims to alert others to look for P. websteri at Western European coasts within farmed or wild Pacific oysters to further document its spread

The peculiar motions of early-type galaxies in two distant regions - II. The spectroscopic data

We present the spectroscopic data for the galaxies studied in the EFAR project, which is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. We have obtained 1319 spectra of 714 early-type galaxies over 33 observing runs on 10 different telescopes. We describe the observations and data reductions used to measure redshifts, velocity dispersions and the Mgb and Mg_2 Lick linestrength indices. Detailed simulations and intercomparison of the large number of repeat observations lead to reliable error estimates for all quantities. The measurements from different observing runs are calibrated to a common zero-point or scale before being combined, yielding a total of 706 redshifts, 676 velocity dispersions, 676 Mgb linestrengths and 582 Mg_2 linestrengths. The median estimated errors in the combined measurements are Delta cz=20 km s^-1, Delta sigma sigma =9.1 per cent, Delta Mgb Mgb=7.2 per cent and Delta Mg_2=0.015 mag. Comparison of our measurements with published data sets shows no systematic errors in the redshifts or velocity dispersions, and only small zero-point corrections to bring our linestrengths on to the standard Lick system. We have assigned galaxies to physical clusters by examining the line-of-sight velocity distributions based on EFAR and ZCAT redshifts, together with the projected distributions on the sky. We derive mean redshifts and velocity dispersions for these clusters, which will be used in estimating distances and peculiar velocities and to test for trends in the galaxy population with cluster mass. The spectroscopic parameters presented here for 706 galaxies combine high-quality data, uniform reduction and measurement procedures, and detailed error analysis. They form the largest single set of velocity dispersions and linestrengths for early-type galaxies published to date

The Peculiar Motions of Early-Type Galaxies in Two Distant Regions -- VII. Peculiar Velocities and Bulk Motions

We present peculiar velocities for 85 clusters of galaxies in two large volumes at distances between 6000 and 15 000 km s−1 in the directions of Hercules-Corona Borealis and Perseus-Pisces-Cetus (the EFAR sample). These velocities are based on Fundamental Plane (FP) distance estimates for early-type galaxies in each cluster. We fit the FP using a maximum likelihood algorithm which accounts for both selection effects and measurement errors, and yields FP parameters with smaller bias and variance than other fitting procedures. We obtain a best-fitting FP with coefficients consistent with the best existing determinations. We measure the bulk motions of the sample volumes using the 50 clusters with the best-determined peculiar velocities. We find that the bulk motions in both regions are small, and consistent with zero at about the 5 per cent level. The EFAR results are in agreement with the small bulk motions found by Dale et al. on similar scales, but are inconsistent with pure dipole motions having the large amplitudes found by Lauer & Postman and Hudson et al. The alignment of the EFAR sample with the Lauer & Postman dipole produces a strong rejection of a large-amplitude bulk motion in that direction, but the rejection of the Hudson et al. result is less certain because their dipole lies at a large angle to the main axis of the EFAR sample. We employ a window function covariance analysis to make a detailed comparison of the EFAR peculiar velocities with the predictions of standard cosmological models. We find that the bulk motion of our sample is consistent with most cosmological models that approximately reproduce the shape and normalization of the observed galaxy power spectrum. We conclude that existing measurements of large-scale bulk motions provide no significant evidence against standard models for the formation of structure

The peculiar motions of early-type galaxies in two distant regions - II. The spectroscopic data

We present the spectroscopic data for the galaxies studied in the EFAR project, which is designed to measure the properties and peculiar motions of early-type galaxies in two distant regions. We have obtained 1319 spectra of 714 early-type galaxies over 33 observing runs on 10 different telescopes. We describe the observations and data reductions used to measure redshifts, velocity dispersions and the Mgb and Mg2 Lick linestrength indices. Detailed simulations and intercomparison of the large number of repeat observations lead to reliable error estimates for all quantities. The measurements from different observing runs are calibrated to a common zeropoint or scale before being combined, yielding a total of 706 redshifts, 676 velocity dispersions, 676 Mgb linestrengths and 582 Mg2 linestrengths. The median estimated errors in the combined measurements are dcz=20 km/s, dsigma/sigma=9.1%, dMgb/Mgb=7.2% and dMg2=0.015 mag. Comparison of our measurements with published datasets shows no systematic errors in the redshifts or velocity dispersions and only small zeropoint corrections to bring our linestrengths onto the standard Lick system. We have assigned galaxies to physical clusters by examining the line-of-sight velocity distributions based on EFAR and ZCAT redshifts, together with the projected distributions on the sky. We derive mean redshifts and velocity dispersions for these clusters, which will be used in estimating distances and peculiar velocities and to test for trends in the galaxy population with cluster mass. The spectroscopic parameters presented here for 706 galaxies combine high quality data, uniform reduction and measurement procedures, and detailed error analysis. They form the largest single set of velocity dispersions and linestrengths for early-type galaxies published to date.Comment: 27 pages, 18 figures, accepted by MNRA

The peculiar motions of early-type galaxies in two distant regions. IV. The photometric fitting procedure

The EFAR project is a study of 736 candidate early-type galaxies in 84 clusters lying in two regions toward Hercules-Corona Borealis and Perseus-Cetus at distances cz ~ 6000--15,000 km s-1. In this paper we describe a new method of galaxy photometry adopted to derive the photometric parameters of the EFAR galaxies. The algorithm fits the circularized surface brightness profiles as the sum of two seeing-convolved components, an R1/4 and an exponential law. This approach allows us to fit the large variety of luminosity profiles displayed by the EFAR galaxies homogeneously and to derive (for at least a subset of these) bulge and disk parameters. Multiple exposures of the same objects are optimally combined and an optional sky-fitting procedure has been developed to correct for sky-subtraction errors. Extensive Monte Carlo simulations are analyzed to test the performance of the algorithm and estimate the size of random and systematic errors. Random errors are small, provided that the global signal-to-noise ratio of the fitted profiles is larger than ~300. Systematic errors can result from (1) errors in the sky subtraction, (2) the limited radial extent of the fitted profiles, (3) the lack of resolution due to seeing convolution and pixel sampling, (4) the use of circularized profiles for very flattened objects seen edge-on, and (5) a poor match of the fitting functions to the object profiles. Large systematic errors are generated by the widely used simple R1/4 law to fit luminosity profiles when a disk component, as small as 20% of the total light, is present. The size of the systematic errors cannot be determined from the shape of the chi 2 function near its minimum because extrapolation is involved. Rather, we must estimate them by a set of quality parameters, calibrated against our simulations, which take into account the amount of extrapolation involved to derive the total magnitudes, the size of the sky correction, the average surface brightness of the galaxy relative to the sky, the radial extent of the profile, its signal-to-noise ratio, the seeing value, and the reduced chi 2 of the fit. We formulate a combined quality parameter Q, which indicates the expected precision of the fits. Errors in total magnitudes MTOT less than 0.05 mag and in half-luminosity radii Re less than 10% are expected if Q = 1, and less than 0.15 mag and 25% if Q = 2; 89% of the EFAR galaxies have fits with Q = 1 or Q = 2. The errors on the combined fundamental plane quantity FP = log Re-0.3, where is the average effective surface brightness, are smaller than 0.03 even if Q = 3. Thus, systematic errors on MTOT and Re only have a marginal effect on the distance estimates that involve FP. We show that the sequence of R1/n profiles, recently used to fit the luminosity profiles of elliptical galaxies, is equivalent (for n <= 8) to a subsample of R1/4 and exponential profiles, with appropriate scale lengths and disk-to-bulge ratios. This suggests that the variety of luminosity profiles shown by early-type galaxies may be due to the presence of a disk component

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde