A functional representation of almost isometries

For each quasi-metric space X we consider the convex lattice SLip(1)(X) of all semi-Lipschitz functions on X with semi-Lipschitz constant not greater than 1. If X and Y are two complete quasi-metric spaces, we prove that every convex lattice isomorphism T from SLip(1)(Y) onto SLip(1)(X) can be written in the form Tf = c . (f o tau) + phi, where tau is an isometry, c > 0 and phi is an element of SLip(1)(X). As a consequence, we obtain that two complete quasi-metric spaces are almost isometric if, and only if, there exists an almost-unital convex lattice isomorphism between SLip(1)(X) and SLip(1) (Y).

Pathways to quiescence: SHARDS view on the star formation histories of massive quiescent galaxies at 1.0 < z < 1.5

We present star formation histories (SFHs) for a sample of 104 massive (stellar mass M > 10^10 M_⊙) quiescent galaxies (MQGs) at z = 1.0–1.5 from the analysis of spectrophotometric data from the Survey for High-z Absorption Red and Dead Sources (SHARDS) and HST/WFC3 G102 and G141 surveys of the GOODS-North field, jointly with broad-band observations from ultraviolet (UV) to far-infrared (far-IR). The sample is constructed on the basis of rest-frame UVJ colours and specific star formation rates (sSFRs = SFR/Mass). The spectral energy distributions (SEDs) of each galaxy are compared to models assuming a delayed exponentially declining SFH. A Monte Carlo algorithm characterizes the degeneracies, which we are able to break taking advantage of the SHARDS data resolution, by measuring indices such as MgUV and D4000. The population of MQGs shows a duality in their properties. The sample is dominated (85 per cent) by galaxies with young mass-weighted ages, t_M t_M < 2 Gyr, short star formation time-scales, 〈τ〉 ∼ 60–200 Myr, and masses log(M/M_⊙) ∼ 10.5. There is an older population (15 per cent) with t_M t_M = 2–4 Gyr, longer star formation time-scales, 〈τ〉∼ 400 Myr, and larger masses, log(M/M_⊙) ∼ 10.7. The SFHs of our MQGs are consistent with the slope and the location of the main sequence of star-forming galaxies at z > 1.0, when our galaxies were 0.5–1.0 Gyr old. According to these SFHs, all the MQGs experienced a luminous infrared galaxy phase that lasts for ∼500 Myr, and half of them an ultraluminous infrared galaxy phase for ∼100 Myr. We find that the MQG population is almost assembled at z ∼ 1, and continues evolving passively with few additions to the population.

[C II] and 12^CO(1-0) emission maps in HLSJ091828.6+514223: a strongly lensed interacting system AT z = 5.24

We present Submillimeter Array [C II] 158 μm and Karl G. Jansky Very Large Array 12^CO(1-0) line emission maps for the bright, lensed, submillimeter source at z = 5.2430 behind A 773: HLSJ091828.6+514223 (HLS0918). We combine these measurements with previously reported line profiles, including multiple 12^CO rotational transitions, [C I], water, and [N II], providing some of the best constraints on the properties of the interstellar medium in a galaxy at z > 5. HLS0918 has a total far-infrared (FIR) luminosity L_FIR(8–1000 μm) = (1.6 ± 0.1) × 10^14 L_☉ μ^–1, where the total magnification μ_total = 8.9 ± 1.9, via a new lens model from the [C II] and continuum maps. Despite a HyLIRG luminosity, the FIR continuum shape resembles that of a local LIRG. We simultaneously fit all of the observed spectral line profiles, finding four components that correspond cleanly to discrete spatial structures identified in the maps. The two most redshifted spectral components occupy the nucleus of a massive galaxy, with a source-plane separation <1 kpc. The reddest dominates the continuum map (demagnified L_FIR, component = (1.1 ± 0.2) × 10^13 L_☉) and excites strong water emission in both nuclear components via a powerful FIR radiation field from the intense star formation. A third star-forming component is most likely a region of a merging companion (ΔV ~ 500 km s^–1) exhibiting generally similar gas properties. The bluest component originates from a spatially distinct region and photodissociation region analysis suggests that it is lower density, cooler, and forming stars less vigorously than the other components. Strikingly, it has very strong [N II] emission, which may suggest an ionized, molecular outflow. This comprehensive view of gas properties and morphology in HLS0918 previews the science possible for a large sample of high-redshift galaxies once ALMA attains full sensitivity.

The evolutionary paths among galaxy types on the red sequence at 0.3 < Z < 1.5

We have studied the main evolutionary paths among the galaxy types residing on the massive end of the Red Sequence and nearby locations on the Green Valley during the last ∼9 Gyr. The morphological and star formation properties of a sample of these galaxies at 0 . 3 < z < 1 .5 with stellar masses M_∗ > 5 × 10^10 M_⊙ have been analysed. We present direct observational evidence for the first time of the existence of two main evolutionary paths among the different red galaxy types since z ∼ 1 .5, which provide some clues on the nature of the processes that have governed the assembly of present-day massive quiescent galaxies. The results are in excellent agreement with the hierarchical evolutionary framework proposed in the Eliche-Moral et al. (2010) model. Data from SHARDS (one of the ESO/GTC Large Programmes approved in 2009A) will complement and improve the present findings, shedding some light into many of the still unsettled questions concerning the migration of galaxies from the Blue Cloud to the Red Sequence at z < 1 .5.