Streaming motions of galaxy clusters within 12 000 km s−1– II. New photometric data for the Fundamental Plane

We present new R -band photometric data for 447 galaxies, gathered for the 'Streaming Motions of Abell Clusters' (SMAC) project. The data comprise 629 individual measurements of the Fundamental Plane (FP) parameters effective radius ( R _e) and surface brightness (〈 μ 〉_e), derived from r ^1/4-law profile fitting. More than a third of the galaxies were observed more than once. The photometric precision is ∼0.02 mag as judged from comparisons of aperture photometry between repeat observations of galaxies. The combination     which enters into the Fundamental Plane relation, has internal uncertainties of ∼0.008, corresponding to < 2 per cent in estimated distance. Taken individually, the (correlated) internal errors in R _e and 〈 μ 〉_e are ∼8 per cent and ∼0.12 mag respectively. Comparisons with literature data constrain the external random errors to ≲5 per cent in distance (per observation), which is small in comparison to the ∼20 per cent scatter in the FP. The data will form part of a merged catalogue of FP parameters, presented in a companion paper.     

Stellar velocity profiles and line strengths out to four effective radii in the early-type galaxies NGC 3379 and 821

We use the integral-field spectrograph SAURON to measure the stellar line-of-sight velocity distribution and absorption line strengths out to four effective radii ( R _e) in the early-type galaxies NGC 3379 and 821. With our newly developed observing technique, we can now probe these faint regions in galaxies that were previously not accessible with traditional long-slit spectroscopy. We make optimal use of the large field-of-view and high throughput of the spectrograph: by adding the signal of all ∼1400 lenslets into one spectrum, we obtain sufficient signal-to-noise in a few hours of observing time to reliably measure the absorption line kinematics and line strengths out to large radius.
We find that the line strength gradients previously observed within 1 R _e remain constant out to at least 4 R _e, which puts constraints on the merger histories of these galaxies. The stellar halo populations are old and metal poor. By constructing orbit-based Schwarzschild dynamical models, we find that dark matter is necessary to explain the observed kinematics in NGC 3379 and 821, with 30–50 per cent of the total matter being dark within 4 R _e. The radial anisotropy in our best-fitting halo models is less than in our models without halo, due to differences in orbital structure. The halo also has an effect on the  Mg  b – V _esc  relation: its slope is steeper when a dark matter halo is added to the model.     

Stellar indices and kinematics in Seyfert 1 nuclei

We present spectra of six type 1 and two type 2 Seyfert galaxies, a starburst galaxy and a compact narrow-line radio galaxy, taken in two spectral ranges centred around the near-infrared Ca  ii triplet (∼8600 Å), and the Mgb stellar feature at 5180 Å. We measured the equivalent widths (EWs) of these features and the Fe₅₂ and Fe₅₃ spectral indices.
We found that the strength of the infrared Ca  ii triplet (CaT) in type 1 Seyfert galaxies with prominent central point sources is larger than what would be expected from the observed strength of the blue indices. This could be explained by the presence of red supergiants in the nuclei of Seyfert 1 galaxies. On the other hand, the blue indices of these galaxies could also be diluted by the strong Fe  ii multiplets that can be seen in their spectra.
We have also measured the stellar‐ and gas-velocity dispersions of the galaxies in the sample. The stellar velocity dispersions were measured using both the Mgb and CaT stellar features. The velocity dispersion of the gas in the narrow-line region (NLR) was measured using the strong emission lines [O  iii ] λλ 5007, 4959 and [S  iii ] λ 9069. We compare the gas- and star-velocity dispersions and find that the magnitudes of both are correlated in Seyfert galaxies.
Most of the Seyfert 1 galaxies that we observe have stellar‐velocity dispersions somewhat greater than that of the gas in the NLR.     

The concentration–velocity dispersion relation in galaxy groups

Based on results from cold dark matter N -body simulations, we develop a dynamical model for the evolution of subhaloes within group-sized host haloes. Only subhaloes more massive than 5 × 10⁸ M_⊙ are considered, because they are massive enough to possibly host luminous galaxies. On their orbits within a growing host potential the subhaloes are subject to tidal stripping and dynamical friction. At the present time  ( z = 0)  , all model hosts have equal mass  ( M _vir= 3.9 × 10¹³ M_⊙)  but different concentrations associated with different formation times. We investigate the variation of subhalo (or satellite galaxy) velocity dispersion with host concentration and/or formation time. In agreement with the Jeans equation, the velocity dispersion of subhaloes increases with the host concentration. Between concentrations of ∼5 and ∼20, the subhalo velocity dispersions increase by a factor of ∼1.25. By applying a simplified tidal disruption criterion, that is, rejection of all subhaloes with a tidal truncation radius below 3  kpc at   z = 0  , the central velocity dispersion of the 'surviving' subhalo sample increases substantially for all concentrations. The enhanced central velocity dispersions in the surviving subhalo samples are caused by a lack of slow tangential motions. Additionally, we present a fitting formula for the anisotropy parameter which does not depend on concentration if the group-centric distances are scaled by r _s, the characteristic radius of the Navarro, Frenk & White profile. Since the expected loss of subhaloes and galaxies due to tidal disruption increases the velocity dispersion of surviving galaxies, the observed galaxy velocity dispersion can substantially overestimate the virial mass.     

Dark matter in elliptical galaxies – I. Is the total mass density profile of the NFW form or even steeper?

Elliptical galaxies are modelled as Sérsic luminosity distributions with density profiles (DPs) for the total mass adopted from the DPs of haloes within dissipationless ΛCDM (cold dark matter) N -body simulations. Ellipticals turn out to be inconsistent with cuspy low-concentration NFW models representing the total mass distribution, neither are they consistent with a steeper −1.5 inner slope, nor with the shallower models proposed by Navarro et al., nor with NFW models 10 times more concentrated than predicted, as deduced from several X-ray observations – the mass models, extrapolated inwards, lead to local mass-to-light ratios that are smaller than the stellar value inside an effective radius ( R _e), and to central aperture velocity dispersions that are much smaller than observed. This conclusion remains true as long as there is no sharp steepening (slope < −2) of the dark matter DPs just inside 0.01 virial radii.
The very low total mass and velocity dispersion produced within R _e by an NFW-like total mass profile suggests that the stellar component should dominate the dark matter component out to at least R _e. It should then be difficult to kinematically constrain the inner slope of the DP of ellipticals. The high-concentration parameters deduced from X-ray observations appear to be a consequence of fitting an NFW model to the total mass DP made up of a stellar component that dominates inside and a dark matter component that dominates outwards.
An appendix gives the virial mass dependence of the concentration parameter, central density and total mass of the Navarro et al. model. In a second appendix are given single integral expressions for the velocity dispersions averaged along the line of sight, in circular apertures and in thin slits, for general luminosity density and mass distributions, with isotropic orbits.     

Stellar velocity dispersion in narrow-line Seyfert 1 galaxies

Several authors have recently explored, for narrow-line Seyfert 1 galaxies (NLS1s), the relationship between black hole mass ( M _BH) and stellar velocity dispersion (σ_*). Their results are more or less in agreement and seem to indicate that NLS1s fill the region below the fit obtained by Tremaine et al., showing a range of σ_* similar to that of Seyfert 1 galaxies, and a lower M _BH. Until now, the [O  iii ] width has been used in place of the stellar velocity dispersion, but some indications have begun to arise against the effectiveness of the gaseous kinematics in representing the bulge potential, at least in NLS1s. Bian & Zhao have stressed the urgency of producing true σ_* measurements. Here, we present new stellar velocity dispersions obtained through direct measurements of the Ca  ii absorption triplet (∼8550 Å) in the nuclei of eight NLS1 galaxies. The resulting σ_* values and a comparison with σ_[O III] confirm our suspicion that [O  iii ] typically overestimates the stellar velocity dispersion. We demonstrate that NLS1s follow the   M _BH–σ_*  relation as Seyfert 1, quasars and non-active galaxies.     

Testing fundamental physics with distant star clusters: theoretical models for pressure-supported stellar systems

We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in modified Newtonian dynamics (MOND), using the N -body code n-mody , which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo & Nipoti. We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of 10⁴ to  10⁹ M_⊙  and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime  ( a _i, a _e≪ a ₀)  , where the motion of stars is either dominated by internal accelerations  ( a _i≫ a _e)  or constant external accelerations  ( a _e≫ a _i)  . In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime  ( a _i∼ a _e∼ a ₀)  . This allows for a much-improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.     

Optical and infrared diagnostics of SDSS galaxies in the SWIRE survey

We present the rest-frame optical and infrared colours of a complete sample of  1114 z < 0.3  galaxies from the Spitzer Wide-Area Infrared Extragalactic (SWIRE) Legacy Survey and the Sloan Digital Sky Survey (SDSS). We discuss the optical and infrared colours of our sample and analyse in detail the contribution of dusty star-forming galaxies and active galactic nuclei (AGN) to optically selected red sequence galaxies.
We propose that the optical  ( g − r )  colour and infrared  log( L ₂₄/ L _3.6)  colour of galaxies in our sample are determined primarily by a bulge-to-disc ratio. The  ( g − r )  colour is found to be sensitive to the bulge-to-disc ratio for disc-dominated galaxies, whereas the  log( L ₂₄/ L _3.6)  colour is more sensitive for bulge-dominated systems.
We identify ∼18 per cent (195 sources) of our sample as having red optical colours and infrared excess. Typically, the infrared luminosities of these galaxies are found to be at the high end of star-forming galaxies with blue optical colours. Using emission-line diagnostic diagrams, 78 are found to have an AGN contribution and 117 are identified as star-forming systems. The red  ( g − r )  colour of the star-forming galaxies could be explained by extinction. However, their high optical luminosities cannot. We conclude that they have a significant bulge component.
The number densities of optically red star-forming galaxies are found to correspond to ∼13 per cent of the total number density of our sample. In addition, these systems contribute ∼13 per cent of the total optical luminosity density, and 28 per cent of the total infrared luminosity density of our SWIRE/SDSS sample. These objects may reduce the need for 'dry mergers'.     

Origin of disc lopsidedness in the Eridanus group of galaxies

The H  i surface density maps for a sample of 18 galaxies in the Eridanus group are Fourier analysed. This analysis gives the radial variation of the lopsidedness in the H  i spatial distribution. The lopsidedness is quantified by the Fourier amplitude A ₁ of the m = 1 component normalized to the average value. It is also shown that in the radial region where the stellar disc and H  i overlap, their A ₁ coefficients are comparable. All the galaxies studied show significant lopsidedness in H  i . The mean value of A ₁ in the inner regions of the galaxies (1.5–2.5 scalelengths) is ≥ 0.2. This value of A ₁ is twice the average value seen in the field galaxies. Also, the lopsidedness is found to be smaller for late-type galaxies; this is opposite to the trend seen in the field galaxies. These two results indicate a different physical origin for disc lopsidedness in galaxies in a group environment compared to the field galaxies. Further, a large fraction (∼30 per cent) shows a higher degree of lopsidedness ( A ₁≥ 0.3). It is also seen that the disc lopsidedness increases with the radius as demonstrated in earlier studies, but over a radial range that is two times larger than done in the previous studies. The average lopsidedness of the halo potential is estimated to be ∼10 per cent, assuming that the lopsidedness in H  i disc is due to its response to the halo asymmetry.     

Probing the 2D kinematic structure of early-type galaxies out to three effective radii

We detail an innovative new technique for measuring the two-dimensional (2D) velocity moments (rotation velocity, velocity dispersion and Gauss–Hermite coefficients h ₃ and h ₄) of the stellar populations of galaxy haloes using spectra from Keck DEIMOS (Deep Imaging Multi-Object Spectrograph) multi-object spectroscopic observations. The data are used to reconstruct 2D rotation velocity maps.
Here we present data for five nearby early-type galaxies to ∼three effective radii. We provide significant insights into the global kinematic structure of these galaxies, and challenge the accepted morphological classification in several cases. We show that between one and three effective radii the velocity dispersion declines very slowly, if at all, in all five galaxies. For the two galaxies with velocity dispersion profiles available from planetary nebulae data we find very good agreement with our stellar profiles. We find a variety of rotation profiles beyond one effective radius, i.e. rotation speed remaining constant, decreasing and increasing with radius. These results are of particular importance to studies which attempt to classify galaxies by their kinematic structure within one effective radius, such as the recent definition of fast- and slow-rotator classes by the Spectrographic Areal Unit for Research on Optical Nebulae project. Our data suggest that the rotator class may change when larger galactocentric radii are probed. This has important implications for dynamical modelling of early-type galaxies. The data from this study are available on-line.     

Spatial and kinematical lopsidedness of atomic hydrogen in the Ursa Major group of galaxies

We have carried out the harmonic analysis of the atomic hydrogen (H  i ) surface density maps and the velocity fields for 11 galaxies belonging to the Ursa Major group, over a radial range of 4–6 disc scalelengths in each galaxy. This analysis gives the radial variation of spatial lopsidedness, quantified by the Fourier amplitude A ₁ of the   m = 1  component normalized to the average value. The kinematical analysis gives a value for the elongation of the potential to be ∼10 per cent. The mean amplitude of spatial lopsidedness is found to be ∼0.14 in the inner disc, similar to the field galaxies, and is smaller by a factor of ∼2 compared to the Eridanus group galaxies. It is also shown that the average value of A ₁ does not increase with the Hubble type, contrary to what is seen in field galaxies. We argue that the physical origin of lopsidedness in the Ursa Major group of galaxies is tidal interactions, albeit weaker and less frequent than in Eridanus. Thus systematic studies of lopsidedness in groups of galaxies can provide dynamical clues regarding the interactions and evolution of galaxies in a group environment.     

Precision abundance analysis of bright H ii galaxies

We present high signal-to-noise ratio spectrophotometric observations of seven luminous H  ii galaxies. The observations have been made with the use of a double-arm spectrograph which provides spectra with a wide wavelength coverage, from 3400 to 10 400 Å free of second-order effects, of exactly the same region as that of a given galaxy. These observations are analysed applying a methodology designed to obtain accurate elemental abundances of oxygen, sulphur, nitrogen, neon, argon and iron in the ionized gas. Four electron temperatures and one electron density are derived from the observed forbidden line ratios using the five-level atom approximation. For our best objects, errors of 1 per cent in t _e([O  iii ]), 3 per cent in t _e([O  ii ]) and 5 per cent in t _e([S  iii ]) are achieved with a resulting accuracy of 7 per cent in total oxygen abundances, O/H.
The ionization structure of the nebulae can be mapped by the theoretical oxygen and sulphur ionic ratios, on the one side, and the corresponding observed emission line ratios, on the other – the η and η' plots. The combination of both is shown to provide a means to test photoionization model sequences presently applied to derive elemental abundances in H  ii galaxies.     

Galaxy groups at 0.3 ≤z≤ 0.55 – II. Evolution to z∼ 0

We compare deep Magellan spectroscopy of 26 groups at  0.3 ≤ z ≤ 0.55  , selected from the Canadian Network for Observational Cosmology 2 field survey, with a large sample of nearby groups from the 2PIGG catalogue. We find that the fraction of group galaxies with significant [O  ii ]λ3727 emission (≥5 Å) increases strongly with redshift, from ∼29 per cent in 2dFGRS to ∼58 per cent in CNOC2, for all galaxies brighter than  ∼ M _*+ 1.75  . This trend is parallel to the evolution of field galaxies, where the equivalent fraction of emission-line galaxies increases from ∼53 to ∼75 per cent. The fraction of emission-line galaxies in groups is lower than in the field, across the full redshift range, indicating that the history of star formation in groups is influenced by their environment. We show that the evolution required to explain the data is inconsistent with a quiescent model of galaxy evolution; instead, discrete events in which galaxies cease forming stars (truncation events) are required. We constrain the probability of truncation ( P _trunc) and find that a high value is required in a simple evolutionary scenario neglecting galaxy mergers  ( P _trunc≳ 0.3 Gyr⁻¹)  . However, without assuming significant density evolution, P _trunc is not required to be larger in groups than in the field, suggesting that the environmental dependence of star formation was embedded at redshifts   z ≳ 0.45  .     

Large-scale galactic turbulence: can self-gravity drive the observed H i velocity dispersions?

Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s⁻¹  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10⁻³ M_⊙ yr⁻¹ kpc⁻²  .     

A search for the third lensed image in JVAS B1030+074

Central gravitational image detection is very important for the study of the mass distribution of the inner parts (∼100 pc) of lens galaxies. However, the detection of such images is extremely rare and difficult. We present a 1.7-GHz High Sensitivity Array (HSA) observation of the double-image radio lens system B1030+074. The data are combined with archive Very Long Baseline Array and global very long baseline interferometry (VLBI) observations, and careful consideration is given to the effects of noise, clean ing and self-calibration. An upper limit is derived for the strength of the central image of 180 μJy (90 per cent confidence level), considerably greater than would have been expected on the basis of a simple analysis. This gives a lower limit of ∼10³ for the ratio of the brightest image to the central image. For cusped models of lens mass distributions, we have made use of this non-detection to constrain the relation between inner power-law slope β of the lensing galaxy mass profile, and its break radius r _b. For   r _b > 130 pc  the power-law slope is required to be close to isothermal  (β > 1.8)  . A flatter inner slope is allowed if a massive black hole is present at the centre of the lensing galaxy, but the effect of the black hole is small unless it is ∼10 times more massive than that implied by the relation between black hole mass and stellar velocity dispersion. By comparing four epochs of VLBI observations, we also detected possible superluminal motion in the jet in the brighter image A. The B jet remains unresolved, as expected from a simple lens model of the system.     

Further constraints on the evolution of Ks-selected galaxies in the GOODS/CDFS field

We have selected and analysed the properties of a sample of  2905 K_s < 21.5  galaxies in  ∼131 arcmin²  of the Great Observatories Origins Deep Survey (GOODS) Chandra Deep Field South (CDFS), to obtain further constraints on the evolution of K_s -selected galaxies with respect to the results already obtained in previous studies. We made use of the public deep multiwavelength imaging from the optical B through the infrared (IR) 4.5-μm bands, in conjunction with available spectroscopic and COMBO17 data in the CDFS, to construct an optimized redshift catalogue for our galaxy sample. We computed the K_s -band luminosity function and determined that its characteristic magnitude has a substantial brightening and a decreasing total density from   z = 0  to  〈 z 〉= 2.5  . We also analysed the colours and number density evolution of galaxies with different stellar masses. Within our sample, and in contrast to what is observed for less massive systems, the vast majority (∼85–90 per cent) of the most massive  ( M > 2.5 × 10¹¹ M_⊙)  local galaxies appear to be in place before redshift   z ∼ 1  . Around 65–70 per cent of the total assemble between redshifts   z = 1  and 3 and most of them display extremely red colours, suggesting that plausible star formation in these very massive systems should mainly proceed in obscured, short-time-scale bursts. The remaining fraction (up to ∼20 per cent) could be in place at even higher redshifts   z = 3–4  , pushing the first epoch of formation of massive galaxies beyond the limits of current near-IR surveys.     

Black hole demographics from the relation

We analyse a sample of 32 galaxies for which a dynamical estimate of the mass of the hot stellar component, M _bulge, is available. For each of these galaxies, we calculate the mass of the central black hole, M _•, using the tight empirical correlation between M _• and bulge stellar velocity dispersion. The frequency function     is reasonably well described as a Gaussian with     and standard deviation ∼0.45; the implied mean ratio of black hole mass to bulge mass is a factor of ∼5 smaller than generally quoted in the literature. We present marginal evidence for a lower, average black hole mass fraction in more massive galaxies. The total mass density in black holes in the local Universe is estimated to be ∼     consistent with that inferred from high-redshift     active galactic nuclei.     

The fundamental plane of elliptical galaxies with modified Newtonian dynamics

The modified Newtonian dynamics (MOND), suggested by Milgrom as an alternative to dark matter, implies that isothermal spheres with a fixed anisotropy parameter should exhibit a near-perfect relation between the mass and velocity dispersion of the form M ∝ σ  ⁴. This is consistent with the observed Faber–Jackson relation for elliptical galaxies: a luminosity–velocity dispersion relation with large scatter. However, the observable global properties of elliptical galaxies comprise a three-parameter family; they lie on a 'fundamental plane' in a logarithmic space consisting of central velocity dispersion, effective radius ( r _e) and luminosity. The scatter perpendicular to this plane is significantly less than that about the Faber–Jackson relation. I show here that, in order to match the observed properties of elliptical galaxies with MOND, models must deviate from being strictly isothermal and isotropic; such objects can be approximated by high-order polytropic spheres with a radial orbit anisotropy in the outer regions. MOND imposes boundary conditions on the inner Newtonian regions which restrict these models to a dynamical fundamental plane of the form where the exponents may differ from the Newtonian expectations ( α =2, γ =1). Scatter about this plane is relatively insensitive to the necessary deviations from homology.     

Compact groups in theory and practice – III. Compact groups of galaxies in the Sixth Data Release of the Sloan Digital Sky Survey

We present the largest publicly available catalogue of compact groups (CGs) of galaxies identified using the original selection criteria of Hickson, selected from the Sixth Data Release of the Sloan Digital Sky Survey (SDSS DR6). We identify 2297 CGs down to a limiting magnitude of   r = 18 (∼0.24 groups  deg⁻²), and 74 791 CGs down to a limiting magnitude of   r = 21 (∼6.7 groups  deg⁻²). This represents 0.9 per cent of all galaxies in the SDSS DR6 at these magnitude levels. Contamination due to gross photometric errors has been removed from the bright sample of groups, and we estimate it is present in the large sample at the 14 per cent level. Spectroscopic information is available for 4131 galaxies in the bright catalogue (43 per cent completeness), and we find that the median redshift of these groups is   z _med= 0.09  . The median line-of-sight (LOS) velocity dispersion within the CGs from the bright catalogue is  σ_LOS≃ 230 km s⁻¹  , and their typical intergalactic separations are of the order of 50–100 kpc. We show that the fraction of groups with interloping galaxies identified as members is in good agreement with the predictions from our previous study of a mock galaxy catalogue, and we demonstrate how to select CGs such that the interloper fraction is well defined and minimized. This observational data set is ideal for large statistical studies of CGs, the role of environment on galaxy evolution and the effect of galaxy interactions in determining galaxy morphology.     

Near-infrared properties of i-drop galaxies in the Hubble Ultra Deep Field

We analyse near-infrared Hubble Space Telescope ( HST )/Near-Infrared Camera and Multi-Object Spectrometer F 110 W ( J ) and F 160 W ( H ) band photometry of a sample of 27 i '-drop candidate   z ≃ 6  galaxies in the central region of the HST /Advanced Camera for Surveys Ultra Deep Field . The infrared colours of the 20 objects not affected by near neighbours are consistent with a high-redshift interpretation. This suggests that the low-redshift contamination of this i '-drop sample is smaller than that observed at brighter magnitudes, where values of 10–40 per cent have been reported. The J – H colours are consistent with a slope flat in   f_ν ( f_λ ∝λ⁻²)  , as would be expected for an unreddened starburst. However, there is evidence for a marginally bluer spectral slope  ( f_λ ∝λ^−2.2)  , which is perhaps indicative of an extremely young starburst (∼10 Myr old) or a top heavy initial mass function and little dust. The low levels of contamination, median photometric redshift of   z ∼ 6.0  and blue spectral slope, inferred using the near-infrared data, support the validity of the assumptions in our earlier work in estimating the star formation rates, and that the majority of the i -drop candidates galaxies lie at   z ∼ 6  .