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R. E. Angulo

Publications and source records attributed to R. E. Angulo.

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The miniJPAS survey: a preview of the Universe in 56 colours

The Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS) will soon start to scan thousands of square degrees of the northern extragalactic sky with a unique set of $56$ optical filters from a dedicated $2.55$m telescope, JST, at the Javalambre Astrophysical Observatory. Before the arrival of the final instrument (a 1.2 Gpixels, 4.2deg$^2$ field-of-view camera), the JST was equipped with an interim camera (JPAS-Pathfinder), composed of one CCD with a 0.3deg$^2$ field-of-view and resolution of 0.23 arcsec pixel$^{-1}$. To demonstrate the scientific potential of J-PAS, with the JPAS-Pathfinder camera we carried out a survey on the AEGIS field (along the Extended Groth Strip), dubbed miniJPAS. We observed a total of $\sim 1$ deg$^2$, with the $56$ J-PAS filters, which include $54$ narrow band (NB, $\rm{FWHM} \sim 145$Angstrom) and two broader filters extending to the UV and the near-infrared, complemented by the $u,g,r,i$ SDSS broad band (BB) filters. In this paper we present the miniJPAS data set, the details of the catalogues and data access, and illustrate the scientific potential of our multi-band data. The data surpass the target depths originally planned for J-PAS, reaching $\rm{mag}_{\rm {AB}}$ between $\sim 22$ and $23.5$ for the NB filters and up to $24$ for the BB filters ($5σ$ in a $3$~arcsec aperture). The miniJPAS primary catalogue contains more than $64,000$ sources extracted in the $r$ detection band with forced photometry in all other bands. We estimate the catalogue to be complete up to $r=23.6$ for point-like sources and up to $r=22.7$ for extended sources. Photometric redshifts reach subpercent precision for all sources up to $r=22.5$, and a precision of $\sim 0.3$% for about half of the sample. (Abridged)

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J-PLUS: Tools to identify compact planetary nebulae in the Javalambre and southern photometric local universe surveys

From the approximately $\sim$3,500 planetary nebulae (PNe) discovered in our Galaxy, only 14 are known to be members of the Galactic halo. Nevertheless, a systematic search for halo PNe has never been performed. In this study, we present new photometric diagnostic tools to identify compact PNe in the Galactic halo by making use of the novel 12-filter system projects, J-PLUS (Javalambre Photometric Local Universe Survey) and S-PLUS (Southern-Photometric Local Universe Survey). We reconstructed the IPHAS (Isaac Newton Telescope (INT) Photometric H$α$ Survey of the Northern Galactic Plane) diagnostic diagram and propose four new ones using i) the J-PLUS and S-PLUS synthetic photometry for a grid of photo-ionisation models of halo PNe, ii) several observed halo PNe, as well as iii) a number of other emission-line objects that resemble PNe. All colour-colour diagnostic diagrams are validated using two known halo PNe observed by J-PLUS during the scientific verification phase and the first data release (DR1) of S-PLUS and the DR1 of J-PLUS. By applying our criteria to the DR1s ($\sim$1,190 deg$^2$), we identified one PN candidate. However, optical follow-up spectroscopy proved it to be a H II region belonging to the UGC 5272 galaxy. Here, we also discuss the PN and two H II galaxies recovered by these selection criteria. Finally, the cross-matching with the most updated PNe catalogue (HASH) helped us to highlight the potential of these surveys, since we recover all the known PNe in the observed area. The tools here proposed to identify PNe and separate them from their emission-line contaminants proved to be very efficient thanks to the combination of many colours, even when applied -like in the present work- to an automatic photometric search that is limited to compact PNe.

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J-PLUS: photometric calibration of large area multi-filter surveys with stellar and white dwarf loci

We present the photometric calibration of the twelve optical passbands observed by the Javalambre Photometric Local Universe Survey (J-PLUS). The proposed calibration method has four steps: (i) definition of a high-quality set of calibration stars using Gaia information and available 3D dust maps; (ii) anchoring of the J-PLUS gri passbands to the Pan-STARRS photometric solution, accounting for the variation of the calibration with the position of the sources on the CCD; (iii) homogenization of the photometry in the other nine J-PLUS filters using the dust de-reddened instrumental stellar locus in (X - r) versus (g - i) colours, where X is the filter to calibrate. The zero point variation along the CCD in these filters was estimated with the distance to the stellar locus. Finally, (iv) the absolute colour calibration was obtained with the white dwarf locus. We performed a joint Bayesian modelling of eleven J-PLUS colour-colour diagrams using the theoretical white dwarf locus as reference. This provides the needed offsets to transform instrumental magnitudes to calibrated magnitudes outside the atmosphere. The uncertainty of the J-PLUS photometric calibration, estimated from duplicated objects observed in adjacent pointings and accounting for the absolute colour and flux calibration errors, are ~19 mmag in u, J0378 and J0395, ~11 mmag in J0410 and J0430, and ~8 mmag in g, J0515, r, J0660, i, J0861, and z. We present an optimized calibration method for the large area multi-filter J-PLUS project, reaching 1-2% accuracy within an area of 1 022 square degrees without the need for long observing calibration campaigns or constant atmospheric monitoring. The proposed method will be adapted for the photometric calibration of J-PAS, that will observe several thousand square degrees with 56 narrow optical filters.

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J-PLUS: the impact of bars on quenching time-scales in nearby green valley disc galaxies

In a framework where galaxies mostly migrate on the colour-magnitude diagram from star-forming to quiescent, the green valley is considered a transitional galaxy stage. The details of the processes that drive galaxies from star-forming to passive systems still remain unknown. We developed a method that estimates empirically the star formation quenching times-scales of green valley galaxies, assuming an exponential decay model of the SFH and through a combination of narrow and broad bands from J-PLUS and GALEX. We correlate these quenching time-scales with the presence of bars. We find that the J-PLUS colours F0395-g and F0415-g are sensitive to different SFH, showing, a clear correlation with the Dn(4000) and H-delta,A spectral indices. We find that quenching time-scales obtained with our new approach are in agreement with those determined using spectral indices. We also find that galaxies with high bar probability tend to quench their star formation slowly. We conclude that: 1) J-PLUS filters can be used to measure quenching timescales in nearby green valley galaxies; and 2) the resulting star formation quenching time-scales are longer for barred green valley galaxies. Considering that the presence of a bar indicates that more violent processes (e.g., major mergers) are absent in host galaxies, we conclude that the presence of a bar can be used as a morphological signature for slow star formation quenching.

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J-PLUS: Discovery and characterisation of ultracool dwarfs using Virtual Observatory tools

Ultracool dwarfs (UCDs) are objects with spectral types equal or later than M7. Most of them have been discovered using wide-field imaging surveys. The Virtual Observatory (VO) has proven to be of great utility to efficiently exploit these astronomical resources. We aim to validate a VO methodology designed to discover and characterize UCDs in the J-PLUS photometric survey. J-PLUS is a multiband survey carried out with the wide angle T80Cam optical camera mounted on the 0.83-m telescope JAST/T80 in the Observatorio Astrofísico de Javalambre. In this work we make use of the Internal Data Release (IDR) covering 528 deg$^2$. We complement J-PLUS photometry with other catalogues in the optical and IR using VOSA, a VO tool that estimates physical parameters from the spectral energy distribution fitting to collections of theoretical models. Objects identified as UCDs are distinguished from background M giants and highly reddened stars using parallaxes and proper motions from Gaia DR2. We identify 559 UCDs, ranging from i=16.2 to 22.4 mag, of which 187 are candidate UCDs not previously reported in the literature. This represents an increase in the number of known UCDs of about 50% in the studied region of the sky, particularly at the faint end of our sensitivity, which is interesting as reference for future wide and deep surveys such as Euclid. Three candidates constitute interesting targets for exoplanet surveys because of their proximity (<40 pc). We also analyze the kinematics of UCDs in our catalogue and find evidence that it is consistent with a Galactic thin-disk population, except for 6 objects that might be members of the thick disk. The results obtained validate the proposed methodology, which will be used in future J-PLUS and J-PAS releases. Considering the region of the sky covered by the IDR used, we foresee to discover 3,000-3,500 new UCDs at the end of the J-PLUS project.

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J-PLUS: Morphological star/galaxy classification by PDF analysis

Our goal is to morphologically classify the sources identified in the images of the J-PLUS early data release (EDR) into compact (stars) or extended (galaxies) using a suited Bayesian classifier. J-PLUS sources exhibit two distinct populations in the r-band magnitude vs. concentration plane, corresponding to compact and extended sources. We modelled the two-population distribution with a skewed Gaussian for compact objects and a log-normal function for the extended ones. The derived model and the number density prior based on J-PLUS EDR data were used to estimate the Bayesian probability of a source to be star or galaxy. This procedure was applied pointing-by-pointing to account for varying observing conditions and sky position. Finally, we combined the morphological information from g, r, and i broad bands in order to improve the classification of low signal-to-noise sources. The derived probabilities are used to compute the pointing-by-pointing number counts of stars and galaxies. The former increases as we approach to the Milky Way disk, and the latter are similar across the probed area. The comparison with SDSS in the common regions is satisfactory up to r ~ 21, with consistent numbers of stars and galaxies, and consistent distributions in concentration and (g - i) colour spaces. We implement a morphological star/galaxy classifier based on PDF analysis, providing meaningful probabilities for J-PLUS sources to one magnitude deeper (r ~ 21) than a classical boolean classification. These probabilities are suited for the statistical study of 150k stars and 101k galaxies with 15 < r < 21 present in the 31.7 deg2 of the J-PLUS EDR. In a future version of the classifier, we will include J-PLUS colour information from twelve photometric bands.

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J-PLUS: The Javalambre Photometric Local Universe Survey

J-PLUS is an ongoing 12-band photometric optical survey, observing thousands of square degrees of the Northern hemisphere from the dedicated JAST/T80 telescope at the Observatorio Astrofísico de Javalambre. T80Cam is a 2 sq.deg field-of-view camera mounted on this 83cm-diameter telescope, and is equipped with a unique system of filters spanning the entire optical range. This filter system is a combination of broad, medium and narrow-band filters, optimally designed to extract the rest-frame spectral features (the 3700-4000Å Balmer break region, H$δ$, Ca H+K, the G-band, the Mgb and Ca triplets) that are key to both characterize stellar types and to deliver a low-resolution photo-spectrum for each pixel of the sky observed. With a typical depth of AB $\sim 21.25$ mag per band, this filter set thus allows for an indiscriminate and accurate characterization of the stellar population in our Galaxy, it provides an unprecedented 2D photo-spectral information for all resolved galaxies in the local universe, as well as accurate photo-z estimates ($Δ\,z\sim 0.01-0.03$) for moderately bright (up to $r\sim 20$ mag) extragalactic sources. While some narrow band filters are designed for the study of particular emission features ([OII]/$λ$3727, H$α$/$λ$6563) up to $z < 0.015$, they also provide well-defined windows for the analysis of other emission lines at higher redshifts. As a result, J-PLUS has the potential to contribute to a wide range of fields in Astrophysics, both in the nearby universe (Milky Way, 2D IFU-like studies, stellar populations of nearby and moderate redshift galaxies, clusters of galaxies) and at high redshifts (ELGs at $z\approx 0.77, 2.2$ and $4.4$, QSOs, etc). With this paper, we release $\sim 36$ sq.deg of J-PLUS data, containing about $1.5\times 10^5$ stars and $10^5$ galaxies at $r<21$ mag.

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Measuring the hydrostatic mass bias in galaxy clusters by combining Sunyaev-Zel'dovich and CMB lensing data

The cosmological parameters prefered by the cosmic microwave background (CMB) primary anisotropies predict many more galaxy clusters than those that have been detected via the thermal Sunyaev-Zeldovich (tSZ) effect. This tension has attracted considerable attention since it could be evidence of physics beyond the simplest $Λ$CDM model. However, an accurate and robust calibration of the mass-observable relation for clusters is necessary for the comparison, which has been proven difficult to obtain so far. Here, we present new contraints on the mass-pressure relation by combining tSZ and CMB lensing measurements about optically-selected clusters. Consequently, our galaxy cluster sample is independent from the data employed to derive cosmological constrains. We estimate an average hydrostatic mass bias of $b = 0.26 \pm 0.07$, with no significant mass nor redshift evolution. This value greatly reduces the tension between the predictions of $Λ$CDM and the observed abundance of tSZ clusters while being in agreement with recent estimations from tSZ clustering. On the other hand, our value for $b$ is higher than the predictions from hydro-dynamical simulations. This suggests the existence of mechanisms driving large departures from hydrostatic equilibrium and that are not included in state-of-the-art simulations, and/or unaccounted systematic errors such as biases in the cluster catalogue due to the optical selection.

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The journey of QSO haloes from z=6 to the present

We apply a recently developed scaling technique to the Millennium-XXL, one of the largest cosmological N-body simulations carried out to date 3x10^11 particles within a cube of volume ~70Gpc^3). This allows us to investigate the cosmological parameter dependence of the mass and evolution of haloes in the extreme high-mass tail of the z=6 distribution. We assume these objects to be likely hosts for the population of rare but ultraluminous high-redshift quasars discovered by the Sloan Digital Sky Survey. Haloes with a similar abundance to these quasars have a median mass of 9x10^12 Msun in the currently preferred cosmology, but do not evolve into equally extreme objects at z=0. Rather, their descendants span the full range conventionally assigned to present-day clusters, 6x10^13 to 2.5x10^15 Msun for this same cosmology. The masses both at z=6 and at z=0 shift up or down by factors exceeding two if cosmological parameters are pushed to the boundaries of the range discussed in published interpretations of data from the WMAP satellite. The main factor determining the future growth of a high-mass z=6 halo is the mean overdensity of its environment on scales of 7 to 14 Mpc, and descendant masses can be predicted 6 to 8 times more accurately if this density is known than if it is not. All these features are not unique to extreme high-z haloes, but are generic to hierarchical growth. Finally, we find that extreme haloes at z=6 typically acquired about half of their total mass in the preceding 100 Myr, implying very large recent accretion rates which may be related to the large black hole masses and high luminosities of the SDSS quasars.

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Scaling relations for galaxy clusters in the Millennium-XXL simulation

We present a very large high-resolution cosmological N-body simulation, the Millennium-XXL or MXXL, which uses 303 billion particles to represent the formation of dark matter structures throughout a 4.1Gpc box in a LambdaCDM cosmology. We create sky maps and identify large samples of galaxy clusters using surrogates for four different observables: richness estimated from galaxy surveys, X-ray luminosity, integrated Sunyaev-Zeldovich signal, and lensing mass. The unprecedented combination of volume and resolution allows us to explore in detail how these observables scale with each other and with cluster mass. The scatter correlates between different mass-observable relations because of common sensitivities to the internal structure, orientation and environment of clusters, as well as to line-of-sight superposition of uncorrelated structure. We show that this can account for the apparent discrepancies uncovered recently between the mean thermal SZ signals measured for optically and X-ray selected clusters by stacking data from the Planck satellite. Related systematics can also affect inferences from extreme clusters detected at high redshift. Our results illustrate that cosmological conclusions from galaxy cluster surveys depend critically on proper modelling, not only of the relevant physics, but also of the full distribution of the observables and of the selection biases induced by cluster identification procedures.

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The Millennium Run Observatory: First Light

Simulations of galaxy evolution aim to capture our current understanding as well as to make predictions for testing by future experiments. Simulations and observations are often compared in an indirect fashion: physical quantities are estimated from the data and compared to models. However, many applications can benefit from a more direct approach, where the observing process is also simulated and the models are seen fully from the observer's perspective. To facilitate this, we have developed the Millennium Run Observatory (MRObs), a theoretical virtual observatory which uses virtual telescopes to `observe' semi-analytic galaxy formation models based on the suite of Millennium Run dark matter simulations. The MRObs produces data that can be processed and analyzed using the standard software packages developed for real observations. At present, we produce images in forty filters from the rest-frame UV to IR for two stellar population synthesis models, three different models of IGM absorption, and two cosmologies (WMAP1/7). Galaxy distributions for a large number of mock lightcones can be `observed' using models of major ground- and space-based telescopes. The data include lightcone catalogues linked to structural properties of galaxies, pre-observation model images, mock telescope images, and Source Extractor products that can all be traced back to the higher level dark matter, semi-analytic galaxy, and lightcone catalogues available in the Millennium database. Here, we describe our methods and announce a first public release of simulated surveys (e.g., SDSS, CFHT-LS, GOODS, GOODS/ERS, CANDELS, and HUDF). The MRObs browser, an online tool, further facilitates exploration of the simulated data. We demonstrate the benefits of a direct approach through a number of example applications (galaxy number counts in CANDELS, clusters, morphologies, and dropout selections).

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Linearisation with Cosmological Perturbation Theory

We propose a new method to linearise cosmological mass density fields using higher order Lagrangian perturbation theory (LPT). We demonstrate that a given density field can be expressed as the sum of a linear and a nonlinear component which are tightly coupled to each other by the tidal field tensor within the LPT framework. The linear component corresponds to the initial density field in Eulerian coordinates, and its mean relation with the total field can be approximated by a logarithm (giving theoretical support to recent attempts to find such component). We also propose to use a combination of the linearisation method and the continuity equation to find the mapping between Eulerian and Lagrangian coordinates. In addition, we note that this method opens the possibility of use directly higher order LPT on nonlinear fields. We test our linearization scheme by applying it to the z~0.5 density field from an N-body simulation. We find that the linearised version of the full density field can be successfully recovered on >~5 h^{-1}Mpc, reducing the skewness and kurtosis of the distribution by about one and two orders of magnitude, respectively. This component can also be successfully traced back in time, converging towards the initial unevolved density field at z~100. We anticipate a number of applications of our results, from predicting velocity fields to estimates of the initial conditions of the universe, passing by improved constraints on cosmological parameters derived from galaxy clustering via reconstruction methods.

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Are the 2dFGRS superstructures a problem for hierarchical models?

We introduce an objective method to assess the probability of finding extreme events in the distribution of cold dark matter such as voids, overdensities or very high mass haloes. Our approach uses an ensemble of N-body simulations of the hierar- chical clustering of dark matter to find extreme structures. The frequency of extreme events, in our case the cell or smoothing volume with the highest count of cluster-mass dark matter haloes, is well described by a Gumbel distribution. This distribution can then be used to forecast the probability of finding even more extreme events, which would otherwise require a much larger ensemble of simulations to quantify. We use our technique to assess the chance of finding concentrations of massive clusters or super- clusters, like the two found in the two-degree field galaxy redshift survey (2dFGRS), using a counts-in-cells analysis. The Gumbel distribution gives an excellent descrip- tion of the distribution of extreme cell counts across two large ensembles of simulations covering different cosmologies, and also when measuring the clustering in both real and redshift space. We find examples of structures like those found in the 2dFGRS in the simulations. The chance of finding such structures in a volume equal to that of the 2dFGRS is around 2%.

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How BAO measurements can fail to detect quintessence

We model the nonlinear growth of cosmic structure in different dark energy models, using large volume N-body simulations. We consider a range of quintessence models which feature both rapidly and slowly varying dark energy equations of state, and compare the growth of structure to that in a universe with a cosmological constant. The adoption of a quintessence model changes the expansion history of the universe, the form of the linear theory power spectrum and can alter key observables, such as the horizon scale and the distance to last scattering. The difference in structure formation can be explained to first order by the difference in growth factor at a given epoch; this scaling also accounts for the nonlinear growth at the 15% level. We find that quintessence models which feature late $(z<2)$, rapid transitions towards $w=-1$ in the equation of state, can have identical baryonic acoustic oscillation (BAO) peak positions to those in $Λ$CDM, despite being very different from $Λ$CDM both today and at high redshifts $(z \sim 1000)$. We find that a second class of models which feature non-negligible amounts of dark energy at early times cannot be distinguished from $Λ$CDM using measurements of the mass function or the BAO. These results highlight the need to accurately model quintessence dark energy in N-body simulations when testing cosmological probes of dynamical dark energy.

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The Globular Cluster NGC 5286. II. Variable Stars

We present the results of a search for variable stars in the globular cluster NGC 5286, which has recently been suggested to be associated with the Canis Major dwarf spheroidal galaxy. 57 variable stars were detected, only 19 of which had previously been known. Among our detections one finds 52 RR Lyrae (22 RRc and 30 RRab), 4 LPV's, and 1 type II Cepheid of the BL Herculis type. Periods are derived for all of the RR Lyrae as well as the Cepheid, and BV light curves are provided for all the variables. The mean period of the RRab variables is = 0.656 days, and the number fraction of RRc stars is N(c)/N(RR) = 0.42, both consistent with an Oosterhoff II (OoII) type -- thus making NGC 5286 one of the most metal-rich ([Fe/H] = -1.67; Harris 1996) OoII globulars known to date. The minimum period of the \RRab's, namely Pab,min = 0.513 d, while still consistent with an OoII classification, falls towards the short end of the observed Pab,min distribution for OoII globular clusters. As was recently found in the case of the prototypical OoII globular cluster M15 (NGC 7078), the distribution of stars in the Bailey diagram does not strictly conform to the previously reported locus for OoII stars. We provide Fourier decomposition parameters for all of the RR Lyrae stars detected in our survey, and discuss the physical parameters derived therefrom. The values derived for the RRc's are not consistent with those typically found for OoII clusters, which may be due to the cluster's relatively high metallicity -- the latter being confirmed by our Fourier analysis of the ab-type RR Lyrae light curves. We derive for the cluster a revised distance modulus of (m-M)V = 16.04 mag. (ABRIDGED)

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The Birth and Growth of Neutralino Haloes

We use the Extended-Press-Schechter (EPS) formalism to study halo assembly histories in a standard $Λ$CDM cosmology. A large ensemble of Monte Carlo random walks provides the {\it entire} halo membership histories of a representative set of dark matter particles, which we assume to be neutralinos. The first generation halos of most particles do not have a mass similar to the free-streaming cut-off $M_{f.s.}$ of the neutralino power spectrum, nor do they form at high redshift. Median values are $M_1 = 10^5$ to $10^7M_{f.s.}$ and $z_1 = 13$ to 8 depending on the form of the collapse barrier assumed in the EPS model. For almost a third of all particles the first generation halo has $M_1>10^9M_{f.s.}$. At redshifts beyond 20, most neutralinos are not yet part of any halo but are still diffuse. These numbers apply with little modification to the neutralinos which are today part of halos similar to that of the Milky Way. Up to 10% of the particles in such halos were never part of a smaller object; the typical particle has undergone $\sim 5$ "accretion events' where the halo it was part of falls into a more massive object. Available N-body simulations agree well with the EPS predictions for an "ellipsoidal" collapse barrier, so these may provide a reliable extension of simulation results to smaller scales. The late formation times and large masses of the first generation halos of most neutralinos imply that they will be disrupted with high efficiency during halo assembly.

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The Fate of Substructures in Cold Dark Matter Haloes

We use the Millennium Simulation, a large, high resolution N-body simulation of the evolution of structure in a LambdaCDM cosmology, to study the properties and fate of substructures within a large sample of dark matter haloes. We find that the subhalo mass function departs significantly from a power law at the high mass end. We also find that the radial and angular distributions of substructures depend on subhalo mass. In particular, high mass subhaloes tend to be less radially concentrated and to have angular distributions closer to the direction perpendicular to the spin of the host halo than their less massive counterparts. We find that mergers between subhaloes occur. These tend to be between substructures that were already dynamically associated before accretion into the main halo. For subhaloes larger than 0.001 times the mass of the host halo, it is more likely that the subhalo will merge with the central or main subhalo than with another subhalo larger than itself. For lower masses, subhalo-subhalo mergers become equally likely to mergers with the main subhalo. Our results have implications for the variation of galaxy properties with environment and for the treatment of mergers in galaxy formation models.

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The assembly bias of dark matter haloes to higher orders

We use an extremely large volume ($2.4h^{-3}{\rm Gpc}^{3}$), high resolution N-body simulation to measure the higher order clustering of dark matter haloes as a function of mass and internal structure. As a result of the large simulation volume and the use of a novel ``cross-moment'' counts-in-cells technique which suppresses discreteness noise, we are able to measure the clustering of haloes corresponding to rarer peaks than was possible in previous studies; the rarest haloes for which we measure the variance are 100 times more clustered than the dark matter. We are able to extract, for the first time, halo bias parameters from linear up to fourth order. For all orders measured, we find that the bias parameters are a strong function of mass for haloes more massive than the characteristic mass $M_{*}$. Currently, no theoretical model is able to reproduce this mass dependence closely. We find that the bias parameters also depend on the internal structure of the halo up to fourth order. For haloes more massive than $M_{*}$, we find that the more concentrated haloes are more weakly clustered than the less concentrated ones. We see no dependence of clustering on concentration for haloes with masses $M<M_{*}$; this is contrary to the trend reported in the literature when segregating haloes by their formation time. Our results are insensitive to whether haloes are labelled by the total mass returned by the friends-of-friends group finder or by the mass of the most massive substructure. This implies that our conclusions are not an artefact of the particular choice of group finding algorithm. Our results will provide important input to theoretical models of galaxy clustering.

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