Close Pairs Research Articles

Solar sail chaotic pitch dynamics and its control in Earth orbits

The attitude dynamics and control for solar sail orbiting a celestial body (e.g., the Earth) are critical for the space missions. In the paper, the pitch dynamics is addressed by considering the torques by the center-of-mass and center-of-pressure offset, the gravity gradient, the internal damping and the control vane. The chaotic pitch motion is analytically detected for the sailcraft in the circular and elliptical orbits with small eccentricities using the Melnikov’s method. The validity of the Melnikov method is numerically verified by checking the Poincare surface of section and the power spectral density. The stability criterion method with some improvements is utilized to stabilize the chaotic pitch motion onto the reference unstable periodic motion embedded in the chaotic attractor. The reference unstable periodic motion is obtained based on the calculation of the close return pairs. The small control input torques and the stabilization effects are presented, and the advantages of the modified stabilization method are clarified based on the numerical simulations.

The TWA 3 Young Triple System: Orbits, Disks, Evolution

Abstract We have characterized the spectroscopic orbit of the TWA 3A binary and provide preliminary families of probable solutions for the TWA 3A visual orbit, as well as for the wide TWA 3A–B orbit. TWA 3 is a hierarchical triple located at 34 pc in the ∼10 Myr old TW Hya association. The wide component separation is 1.″55; the close pair was first identified as a possible binary almost 20 years ago. We initially identified the 35-day period orbital solution using high-resolution infrared spectroscopy that angularly resolved the A and B components. We then refined the preliminary orbit by combining the infrared data with a reanalysis of our high-resolution optical spectroscopy. The orbital period from the combined spectroscopic solution is ∼35 days, the eccentricity is ∼0.63, and the mass ratio is ∼0.84; although this high mass ratio would suggest that optical spectroscopy alone should be sufficient to identify the orbital solution, the presence of the tertiary B component likely introduced confusion in the blended optical spectra. Using millimeter imaging from the literature, we also estimate the inclinations of the stellar orbital planes with respect to the TWA 3A circumbinary disk inclination and find that all three planes are likely misaligned by at least ∼30°. The TWA 3A spectroscopic binary components have spectral types of M4.0 and M4.5; TWA 3B is an M3. We speculate that the system formed as a triple, is bound, and that its properties were shaped by dynamical interactions between the inclined orbits and disk.

The formation of direct collapse black holes under the influence of streaming velocities

We study the influence of a high baryonic streaming velocity on the formation of direct collapse black holes (DCBHs) with the help of cosmological simulations carried out using the moving mesh code {\sc arepo}. We show that a streaming velocity that is as large as three times the root-mean-squared value is effective at suppressing the formation of H$_{2}$-cooled minihaloes, while still allowing larger atomic cooling haloes (ACHs) to form. We find that enough H$_{2}$ forms in the centre of these ACHs to effectively cool the gas, demonstrating that a high streaming velocity by itself cannot produce the conditions required for DCBH formation. However, we argue that high streaming velocity regions do provide an ideal environment for the formation of DCBHs in close pairs of ACHs (the "synchronised halo" model). Due to the absence of star formation in minihaloes, the gas remains chemically pristine until the ACHs form. If two such haloes form with only a small separation in time and space, then the one forming stars earlier can provide enough ultraviolet radiation to suppress H$_{2}$ cooling in the other, allowing it to collapse to form a DCBH. Baryonic streaming may therefore play a crucial role in the formation of the seeds of the highest redshift quasars.

Fast link prediction for large networks using spectral embedding

Many link prediction algorithms require the computation of a similarity metric on each vertex pair, which is quadratic in the number of vertices and infeasible for large networks. We develop a class of link prediction algorithms based on a spectral embedding and the k closest pairs algorithm that are scalable to very large networks. We compare the prediction accuracy and runtime of these methods to existing algorithms on several large link prediction tasks. Our methods achieve comparable accuracy to standard algorithms but are significantly faster.

Nuclear absorption and emission in the AGN merger NGC 6240 : the hard X-ray view

We present the analysis of four NuSTAR observations of the luminous infrared galaxy merger NGC 6240 , hosting a close pair of highly obscured active galactic nuclei (AGNs). Over a period of about 2 yr, the source exhibits hard X-ray variability of the order of 20 per cent, peaking around 20 keV. When the two AGNs are resolved with Chandra , column densities in the range of NH ∼ 1–2 × 1024 cm−2 are estimated for both of them. The exact values are hard to determine, as they appear to depend on aspects that are sometimes overlooked in Compton-thick objects, such as the covering factor of the absorber, iron abundance and the contamination in the Fe K band from foreground hot-gas emission. Nearly spherical covering and slightly subsolar iron abundance are preferred in this case. While the southern nucleus is suggested to be intrinsically more powerful, as also implied by the mid-IR and 2–10 keV brightness ratios, solutions involving a similar X-ray luminosity of the two AGNs cannot be ruled out. The observed variability is rather limited compared to the one revealed by the Swift /BAT light curve, and it can be fully explained by changes in the continuum flux from the two AGNs, without requiring significant column density variations. NGC 6240 is hereby confirmed to represent a unique opportunity to investigate the X-ray (and broad-band) properties of massive galaxy mergers, which were much more frequent in the early Universe.

Scalable Electron Correlation Methods. 3. Efficient and Accurate Parallel Local Coupled Cluster with Pair Natural Orbitals (PNO-LCCSD).

A well-parallelized local singles and doubles coupled-cluster (LCCSD) method using pair natural virtual orbitals (PNOs) is presented. The PNOs are constructed using large domains of projected atomic orbitals (PAOs) and orbital specific virtual orbitals (OSVs). We introduce a hierarchy of close, weak, and distant pairs, based on pair energies evaluated by local Møller-Plesset perturbation theory (LMP2). In contrast to most previous implementations of LCCSD methods, the close and weak pairs are not approximated by LMP2 but treated by higher-order methods. This leads to greatly improved accuracy for large systems, in particular when long-range dispersion interactions are important. Close pair amplitudes are optimized using approximate LCCSD equations, in which slowly decaying terms that mutually cancel at long-range are neglected. For weak pairs, the same approximations are used, but in addition, the nonlinear terms are neglected (coupled electron pair approximation). Distant pairs are treated by spin-component scaled (SCS)-LMP2 using multipole approximations. For efficiency reasons, various projection approximations are also introduced. The impact of these approximations on absolute and relative energies depends on the PNO domain sizes. The errors are found to be negligible, provided that sufficiently large PNO domains are used for close and weak pairs. For the selection of these domains the usual natural orbital occupation number criterion is found to be insufficient, and an additional energy criterion is used. For extended one-dimensional systems, the computational effort of the method scales nearly linearly with the number of correlated electrons, but the linear scaling regime is usually not reached in real-life applications for three-dimensional systems. Nevertheless, due to the parallelization that is efficient up to about 100-200 CPU cores (dependent on the molecular size), accurate calculations for three-dimensional molecules with about 100 atoms and augmented triple-ζ basis sets (e.g., cc-pVTZ-F12) can be carried out in 1-3 h of elapsed time (depending on the molecular structure and the number of CPU cores, excluding the time for Hartree-Fock). The convergence of the results with respect to the thresholds and options that control the domain, pair, and projection approximations is extensively tested. Benchmark examples for several difficult and large cases are presented, which demonstrate that the errors of relative energies (e.g., reaction energies, barrier heights) caused by the pair and projection approximations can be reduced to below 1 kJ mol-1. The remaining errors are mainly caused by the finite PAO domains. The larger these are made, the more intramolecular or intermolecular basis set superposition errors are introduced, and the canonical results are approached only very slowly. This problem is eliminated in the explicitly correlated variant of our method (PNO-LCCSD-F12), which will be described in a separate paper, along with a larger set of benchmark calculations.

Cross-language transfer of semantic annotation via targeted crowdsourcing: task design and evaluation

Modern data-driven spoken language systems (SLS) require manual semantic annotation for training spoken language understanding parsers. Multilingual porting of SLS demands significant manual effort and language resources, as this manual annotation has to be replicated. Crowdsourcing is an accessible and cost-effective alternative to traditional methods of collecting and annotating data. The application of crowdsourcing to simple tasks has been well investigated. However, complex tasks, like cross-language semantic annotation transfer, may generate low judgment agreement and/or poor performance. The most serious issue in cross-language porting is the absence of reference annotations in the target language; thus, crowd quality control and the evaluation of the collected annotations is difficult. In this paper we investigate targeted crowdsourcing for semantic annotation transfer that delegates to crowds a complex task such as segmenting and labeling of concepts taken from a domain ontology; and evaluation using source language annotation. To test the applicability and effectiveness of the crowdsourced annotation transfer we have considered the case of close and distant language pairs: Italian–Spanish and Italian–Greek. The corpora annotated via crowdsourcing are evaluated against source and target language expert annotations. We demonstrate that the two evaluation references (source and target) highly correlate with each other; thus, drastically reduce the need for the target language reference annotations.

A Clustering-Based Approach to Kinetic Closest Pair

Given a set P of n moving points in fixed dimension d, where the trajectory of each point is a polynomial of degree bounded by some constant, we present a kinetic data structure (KDS) for maintenance of the closest pair on P. Assuming the closest pair distance is between 1 and $$\varDelta $$ over time, our KDS uses $$O(n \log \varDelta )$$ space and processes $$O(n^{2} \beta \log \varDelta \log n + n^{2} \beta \log \varDelta \log \log \varDelta )$$ events, each in worst-case time $$O(\log ^2 n + \log ^2 \log \varDelta )$$ . Here, $$\beta $$ is an extremely slow-growing function. The locality of the KDS is $$O(\log n + \log \log \varDelta )$$ . Our closest pair KDS supports insertions and deletions of points. An insertion or deletion takes worst-case time $$O(\log \varDelta \log ^2 n + \log \varDelta \log ^2 \log \varDelta )$$ . Also, we use a similar approach to provide a KDS for the all $$\varepsilon $$ -nearest neighbors in $$\mathbb {R}^d$$ . The complexities of the previous KDSs, for both closest pair and all $$\varepsilon $$ -nearest neighbors, have polylogarithmic factors, where the number of logs depends on dimension d. Assuming $$\varDelta $$ is polynomial in n, our KDSs obtain improvements on the previous KDSs. Our solutions are based on a kinetic clustering on P. Though we use ideas from the previous clustering KDS by Hershberger, we simplify and improve his work.

PHL 6625: A Minor Merger-associated QSO Behind NGC 247

Abstract PHL 6625 is a luminous quasi-stellar object (QSO) at z = 0.3954 located behind the nearby galaxy NGC 247 (z = 0.0005). Hubble Space Telescope observations revealed an arc structure associated with it. We report on spectroscopic observations with the Very Large Telescope and multiwavelength observations from the radio to the X-ray band for the system, suggesting that PHL 6625 and the arc are a close pair of merging galaxies, instead of a strong gravitational lens system. The QSO host galaxy is estimated to be (4–28) × 1010 M ☉ and the mass of the companion galaxy is estimated to be M * = (6.8 ± 2.4) × 109 M ☉, suggesting that this is a minor merger system. The QSO displays typical broad emission lines, from which a black hole mass of about (2–5) × 108 M ☉ and an Eddington ratio of about 0.01–0.05 can be inferred. The system represents an interesting and rare case where a QSO is associated with an ongoing minor merger, analogous to Arp 142.

Revisiting Connell: competition but not as we know it

Space is one of the primary limiting resources for organisms on the intertidal rocky shore. This paper examined the effect of reduced density on key traits (mortality and growth) on the intertidal barnacles, Chthamalus montagui and Semibalanus balanoides, on the mid-shore in Plymouth, UK. Intra- and interspecific treatments comprising of C. montagui and S. balanoides were manipulated to reduce densities at two similar sites. Changes in mortality and operculum growth were assessed over an 8-week period using digital photography. Covariates of growth included nearest neighbour distance, competition between closest pairs and initial size. Conflicting patterns were observed when comparing growth rates between treatments and sites. At Site 1, interspecific treatments had a lower growth rate than intraspecific treatments, whereas at Site 2, interspecific growth rates were higher. ANCOVA showed that nearest neighbour distance had no significant effect on growth, but when comparing differences in growth of closest neighbouring pairs, C. montagui treatment showed evidence of competition whereas S. balanoides did not. ANCOVA analysis indicated no difference in growth between each outcome of pair competition, suggesting winners are initially bigger than losers. Comparisons of mortality between treatments indicated mortality over time with no significant differences observed between treatments, but response surface methodology (RSM) revealed no effects of competition on mortality of S. balanoides, but negative effects of both intra- and interspecific competition on C. montagui survivorship. Examination of natural populations of barnacles in the mid-shore indicated there was strong spatial variation in growth rates, perhaps driven by small-scale differences within sites.

Wide Binaries in TGAS: Search Method and First Results

AbstractHalf of all stars reside in binary systems, many of which have orbital separations in excess of 1000 AU. Such binaries are typically identified in astrometric catalogs by matching the proper motions vectors of close stellar pairs. We present a fully Bayesian method that properly takes into account positions, proper motions, parallaxes, and their correlated uncertainties to identify widely separated stellar binaries. After applying our method to the >2 × 106stars in the Tycho-Gaia astrometric solution from Gaia DR1, we identify over 6000 candidate wide binaries. For those pairs with separations less than 40,000 AU, we determine the contamination rate to be ≈5%. This sample has an orbital separation (a) distribution that is roughly flat in log space for separations less than ~5000 AU and follows a power law ofa−1.6at larger separations.

Search and study of objects of the early universe

The “Big Trio” program is conducted at the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) aiming to investigate a sample of sources with steep and ultra-steep spectra fromthe RCcatalog obtained on the basis of observational data of the “Cold” survey. The population of distant FRII type radio galaxies with steep spectra is of particular interest, since new data indicate the presence of black holes with masses of more than 109 M ⊙ which already formed in these giant stellar systems in the first billion years of life of the Universe, as well as their connection with emerging clusters. There are three sources with z sp > 3 in the sample. According to the observations of the 6-m SAO RAS telescope, the archival data of Subaru and Spitzer, an increased density of objects and several Lyα-emitters have been detected near one of the most powerful radio galaxies, RCJ0311+0507 (4C+04.11) with z = 4.51, which is the second most distant of the known FRII-type galaxies. Another object— RCJ1740+0502 with z = 3.57, is a possible dual AGN candidate. The third source, RCJ0105+0501, is an FRII-type galaxy (z = 3.138) with a host galaxy of a complex structure, possibly generated by interaction in a close pair of galaxies. These radio sources have high radio luminosity (L 500MHz ≈ 1028–1029WHz−1), which requires the presence of a giant black hole with a sufficient accretion rate, and also with a rapid rotation, which in turn can be provided by major merging.

Instance-Optimal Geometric Algorithms

We prove the existence of an algorithm A for computing 2D or 3D convex hulls that is optimal for every point set in the following sense: for every sequence σ of n points and for every algorithm A ′ in a certain class A , the running time of A on input σ is at most a constant factor times the running time of A ′ on the worst possible permutation of σ for A ′. In fact, we can establish a stronger property: for every sequence σ of points and every algorithm A ′, the running time of A on σ is at most a constant factor times the average running time of A ′ over all permutations of σ. We call algorithms satisfying these properties instance optimal in the order-oblivious and random-order setting. Such instance-optimal algorithms simultaneously subsume output-sensitive algorithms and distribution-dependent average-case algorithms, and all algorithms that do not take advantage of the order of the input or that assume the input are given in a random order. The class A under consideration consists of all algorithms in a decision tree model where the tests involve only multilinear functions with a constant number of arguments. To establish an instance-specific lower bound, we deviate from traditional Ben-Or-style proofs and adopt a new adversary argument. For 2D convex hulls, we prove that a version of the well-known algorithm by Kirkpatrick and Seidel [1986] or Chan, Snoeyink, and Yap [1995] already attains this lower bound. For 3D convex hulls, we propose a new algorithm. We further obtain instance-optimal results for a few other standard problems in computational geometry, such as maxima in 2D and 3D, orthogonal line segment intersection in 2D, finding bichromatic L ∞ -close pairs in 2D, offline orthogonal range searching in 2D, offline dominance reporting in 2D and 3D, offline half-space range reporting in 2D and 3D, and offline point location in 2D. Our framework also reveals a connection to distribution-sensitive data structures and yields new results as a byproduct, for example, on online orthogonal range searching in 2D and online half-space range reporting in 2D and 3D.

Galaxy and Mass Assembly (GAMA): probing the merger histories of massive galaxies via stellar populations

The merging history of galaxies can be traced with studies of dynamically close pairs. These consist of a massive primary galaxy and a less massive secondary (or satellite) galaxy. The study of the stellar populations of secondary (lower mass) galaxies in close pairs provides a way to understand galaxy growth by mergers. Here we focus on systems involving at least one massive galaxy - with stellar mass above $10^{11}M_\odot$ in the highly complete GAMA survey. Our working sample comprises 2,692 satellite galaxy spectra (0.1<z<0.3). These spectra are combined into high S/N stacks, and binned according to both an "internal" parameter, the stellar mass of the satellite galaxy (i.e. the secondary), and an "external" parameter, selecting either the mass of the primary in the pair, or the mass of the corresponding dark matter halo. We find significant variations in the age of the populations with respect to environment. At fixed mass, satellites around the most massive galaxies are older and possibly more metal rich, with age differences ~1-2Gyr within the subset of lower mass satellites ($\sim 10^{10}M_\odot$). These variations are similar when stacking with respect to the halo mass of the group where the pair is embedded. The population trends in the lower-mass satellites are consistent with the old stellar ages found in the outer regions of massive galaxies.

Massive close pairs measure rapid galaxy assembly in mergers at high redshift

We compare mass-selected close pairs at z > 1 with the intrinsic galaxy merger rate in the Illustris Simulations. To do so, we construct three 140 arcmin^2 lightcone catalogs and measure pair fractions, finding that they change little or decrease with increasing redshift at z > 1. Consistent with current surveys, this trend requires a decrease in the merger-pair observability time, roughly as (1 + z)^-2, in order to measure the merger rates of the same galaxies. This implies that major mergers are more common at high redshift than implied by the simplest arguments assuming a constant observability time. Several effects contribute to this trend: (1) The fraction of massive, major (4:1) pairs which merge by today increases weakly from ~0.5 at z=1 to ~0.8 at z=3. (2) The median time elapsed between an observed pair and final remnant decreases by a factor of two from z~1 to z~3. (3) An increasing specific star formation rate (sSFR) decreases the time during which common stellar-mass based pair selection criteria could identify the mergers. The average orbit of the pairs at observation time varies only weakly, suggesting that the dynamical time is not varying enough to account by itself for the pair fraction trends. Merging pairs reside in dense regions, having overdensity ~10 to ~100 times greater than the average massive galaxy. We forward model the pairs to reconstruct the merger remnant production rate, showing that it is consistent with a rapid increase in galaxy merger rates at z > 1.

The close pair fraction of BCGs since z = 0.5: major mergers dominate recent BCG stellar mass growth

Using the redMaPPer (red-sequence Matched-filter Probabilistic Percolation) cluster catalogue based on the Sloan Digital Sky Survey (SDSS) photometry, we investigate the importance of major mergers in the stellar mass build-up of brightest cluster galaxies (BCGs) between 0.08 ≤ z ≤ 0.50. We use the SDSS spectroscopy, supplemented with spectroscopic observations from the Southern African Large Telescope at higher redshifts, to identify which BCGs and nearby companions are potential major merger candidates. We use the pair fraction as a proxy for the merger fraction in order to determine how much stellar mass growth the BCGs have experienced due to major mergers. We observe a weak trend of the BCG pair fraction increasing with decreasing redshift, suggesting that major mergers may become more important towards the present day. Major mergers are found to contribute, on average, 24 ± 14 (29 ± 17) per cent towards the stellar mass of a present-day BCG since z = 0.32 (0.45), assuming that half of the companion's stellar mass is accreted on to the BCG. Furthermore, using our merger results in conjunction with predictions from two recent semi-analytical models along with observational measurements from the literature, we find that major mergers have sufficient stellar material to account for the stellar mass growth of the intracluster light between z = 0.3 and 0.

Interaction effects on galaxy pairs with Gemini/GMOS- III: stellar population synthesis

We present an observational study of the impacts of the interactions on the stellar population in a sample of galaxy pairs. Long-slit spectra in the wavelength range 3440-7300 {\AA} obtained with the Gemini Multi-Object Spectrograph (GMOS) at Gemini South for fifteen galaxies in nine close pairs were used. The spatial distributions of the stellar population contributions were obtained using the stellar population synthesis code STARLIGHT. Taking into account the different contributions to the emitted light, we found that most of the galaxies in our sample are dominated by the young/intermediate stellar populations. This result differs from the one derived for isolated galaxies where the old stellar population dominates the disc surface brightness. We interpreted such different behavior as being due to the effect of gas inflows along the disk of interacting galaxies on the star formation in a time scale of the order of about 2Gyr. We also found that, in general, the secondary galaxy of the pairs has a higher contribution of the young stellar population than the primary one. We compared the estimated values of the stellar and nebular extinctions derived from the synthesis method and the H{\alpha}/H\b{eta} emission-line ratio finding that the nebular extinctions are systematically higher than stellar ones by about a factor of 2. We did not find any correlation between nebular and stellar metallicities. We neither found a correlation between stellar metallicities and ages while a positive correlation between nebular metallicities and stellar ages was obtained, with the older regions being the most metal-rich.

B fields in OB stars (BOB): The magnetic triple stellar system HD 164492C in the Trifid nebula.

HD 164492C is a spectroscopic triple stellar system that has been recently detected to possess a strong magnetic field. We have obtained high-resolution spectroscopic and spectropolarimetric observations over a timespan of two years and derived physical, chemical, and magnetic properties for this object. The system is formed by an eccentric close spectroscopic binary (Ca1-Ca2) with a period of 12.5 days, and a massive tertiary Cb. We calculated the orbital parameters of the close pair, reconstructed the spectra of the three components, and determined atmospheric parameters and chemical abundances by spectral synthesis. From spectropolarimetric observations, multi-epoch measurements of the longitudinal magnetic fields were obtained. The magnetic field is strongly variable on timescales of a few days, with a most probable period in the range of 1.4-1.6 days. Star Cb with Teff~25000 K is the apparently fastest rotator and the most massive star of this triple system and has anomalous chemical abundances with a marked overabundance of helium, 0.35+/-0.04 by number. We identified this star as being responsible for the observed magnetic field, although the presence of magnetic fields in the components of the Ca pair cannot be excluded. Star Ca1 with a temperature of about 24000 K presents a normal chemical pattern, while the least massive star Ca2 is a mid-B type star (Teff~15000 K) with an overabundance of silicon. The obtained stellar parameters of the system components suggest a distance of 1.5 kpc and an age of 10-15 Myr.

Microfield dynamics in dense hydrogen plasmas with high-Z impurities.

We use large-scale classical molecular dynamics to determine microfield properties for several dense plasma mixtures. By employing quantum statistical potentials (QSPs) to regularize the Coulomb interaction, our simulations follow motions of electrons as well as ions for times long enough to track relaxation phenomena involving both types of particles. Coulomb coupling, relative to temperature, of different pairs of species in the hot, dense matter being simulated ranges from weak to strong. We first study the effect of such coupling differences, along with composition and QSP differences, on the roles of electrons and various mixture components in determining probability distributions of instantaneous, total microfields experienced by the ions. Then, we address two important dynamical questions: (1) How is the quasistatic part of the total field to be extracted from the time-dependent simulation data? (2) Under what conditions does the commonly used approximation of ions with fixed Yukawa-like screening by free electrons accurately describe quasistatic fields? We identify a running, short-time average of the total field at each ion as its slowly evolving, quasistatic part. We consider several ways to specify the averaging interval, and note the influence of ion dynamics in this issue. When all species are weakly coupled, the quasistatic fields have probability distributions agreeing well with those we obtain from simulations of Yukawa-screened ions. However, agreement deteriorates as the coupling between high-Z ions increases well beyond unity, principally because the Yukawa model tends to underestimate the true screening of close high-Z pairs. Examples of this fact are given, and some consequences for the high-field portions of probability distributions are discussed.

The cosmic assembly of stellar haloes in massive Early-Type Galaxies

Using the exquisite depth of the Hubble Ultra Deep Field (HUDF12 programme) dataset, we explore the ongoing assembly of the outermost regions of the most massive galaxies ($\rm M_{\rm stellar}\geq$ 5$\times$10$^{10}$ M$_{\odot}$) at $z \leq$ 1. The outskirts of massive objects, particularly Early-Types Galaxies (ETGs), are expected to suffer a dramatic transformation across cosmic time due to continuous accretion of small galaxies. HUDF imaging allows us to study this process at intermediate redshifts in 6 massive galaxies, exploring the individual surface brightness profiles out to $\sim$25 effective radii. We find that 5-20\% of the total stellar mass for the galaxies in our sample is contained within 10 $< R <$ 50 kpc. These values are in close agreement with numerical simulations, and higher than those reported for local late-type galaxies ($\lesssim$5\%). The fraction of stellar mass stored in the outer envelopes/haloes of Massive Early-Type Galaxies increases with decreasing redshift, being 28.7\% at $< z > =$ 0.1, 15.1\% at $< z > =$ 0.65 and 3.5\% at $< z > =$ 2. The fraction of mass in diffuse features linked with ongoing minor merger events is $>$ 1-2\%, very similar to predictions based on observed close pair counts. Therefore, the results for our small albeit meaningful sample suggest that the size and mass growth of the most massive galaxies have been solely driven by minor and major merging from $z =$ 1 to today.